Dark_jet_GRS1915+105_github.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1fcc5b0c",
   "metadata": {},
   "source": [
    "# A bow shocks near GRS 1915+105\n",
    "\n",
    "This notebook is partly based off the calculations presented by Gallo et al. 2004 to interpret the bow shock observed in the vicinity of Cyg X-1. Calculations have been adapted to the case of GRS 1915+105, near which we identified a bow shock similar to (albeit much larger than) that seen close to Cyg X-1. \n",
    "Significant additions have been made based on (i) Kaiser et al. 2004, who already modeled a structure near GRS 1915+105 observed in radio, but did not see any large-scale bow shock due to the limited sensitivity of the VLA images they used; and (ii) the python ThunderBooks by R. Fender (https://github.com/robfender/ThunderBooks), which have been used to clarify some of the calculations below. \n",
    "\n",
    "A significant difference with respect to Gallo et al. 2004 is that we make the (reasonable) assumption that the hydrogen emitting the bow shock radiation is fully ionized for the densities we are dealing with. This is supported by Saha's equation that predicts that with densities of the order 0.1-1000 particles per unit volume, all hydrogen should be ionized at a temperature of ~10000K. In order to have an ionization fraction different from 1, the density has to be at least 1E+06 particles/cm$^3$, which is way higher than the average ISM density.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0599dd66",
   "metadata": {},
   "source": [
    "For interpreting the interactions of the large-scale jet structure of GRS 1915+105 with its environment we use the\n",
    "model developed by Kaiser & Alexander (1997, KA97) for the jets of radio galaxies, and adapted for galactic sources in and Kaiser et al. (2004). We assume that the supersonic jets end in strong shock fronts at the location where they impact on the ambient gas. The gas coming up the jets inflates two lobes that are overpressured with respect to the environment. The lobes therefore expand sideways and thus a bow shock is driven into the surrounding ISM. We identify three regions: \n",
    "\n",
    "a) **IRAS 19132+1035** corresponds to the compressed and shock-heated ISM in front of the jet.\n",
    "\n",
    "b) **a non thermal cylindrical feature** near IRAS 19132+1035 and to its north-east edge, pointing towards GRS 1915+105, which corresponds to the strong shock that originates at the end of the postulated large-scale jet, which in AGN is identified with a hot spot.\n",
    "\n",
    "c) **A radio lobe**, clearly detected in the MeerKAT image at an average flux density of 0.2 mJy, which corresponds to the edge-brightened radio lobe inflated by the jet material. In the old VLA data, such a bow shock was not detected due to limited sensitivity (interestingly, it was predicted by Kaiser et al. 2004, at approximately the currently observed flux density).\n",
    "\n",
    "- - - - - \n",
    "\n",
    "In order to determine the properties of the jet, we will do as follows.\n",
    "\n",
    "(1) We **derive the density of the shocked material** in IRAS 19132, assuming that the gas is fully ionised and that the radiation is Bremsstrahlung for a minimum temperature of T ~ 10$^4$K, and modeling the IRAS region as a solid sphere. Then we **infer the pre-shock ISM density** knowing that it should be about a factor of 4 smaller than in the shocked region. \n",
    "\n",
    "(2) We model the non-thermal cylindrical feature at the north edge of IRAS and we **derive the minimum energy magnetic field and pressure** assuming synchrotron emission (based on results in the literature that indicate a steep spectrum).\n",
    "\n",
    "(3) We **estimate the jet advancing velocity** assuming that it equals the velocity of the bow shock in the ISM. From here we can **estimate the jet age**. \n",
    "\n",
    "(4) We **estimate the jet energy transport rate** using the density derived above, and the lobe aspect ratio measured from the MeerKAT image. \n",
    "\n",
    "(5) Finally, we study the emission properties of the jets, and we **infer the magnetic field and pressure from the radio lobes**, and the **pressure within the non-thermal region** at the north side of IRAS, and compare the values to check the self-consistency of the model.\n",
    "\n",
    "(6) As a check, we estimate the jet transfer rate also via two simplified methods, based on (i) the estimate of the hentalphy on the jet-ISM system; (ii) a different use of the minimum energy argument previously applied to AGN. \n",
    "\n",
    "\n",
    "Note that the treatment below is based on a minimum Bremstrahlung temperature of 1.2e+4 K, which affects the electron density and the jet velocity, as well as the jet power transfer rate. This is done to obtain a strict lower limit to the transferred jet power Q$_{jet}$. At the end of the notebook we will repeat the calculation using a reasonable temperature range in a MC simulation.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121094ef",
   "metadata": {},
   "source": [
    "### Some units:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9bef778a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib_inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ipympl\n",
    "\n",
    "#%matplotlib widget\n",
    "%matplotlib notebook\n",
    "# Some Constats and Units\n",
    "\n",
    "pc = 3.086E+18       # 1 pc, cm \n",
    "mh = 1.6735575E-24   # Hydrogen mass, g \n",
    "me = 9.1093837E-28   # Electron mass, g \n",
    "eV = 1.602176634E-12 # ElectronVolt, erg\n",
    "Jy = 1.0E-23         # 1 Jansky (erg/s/cm2/Hz), cgs\n",
    "kb = 1.380649E-16;   # K boltzman, cgs\n",
    "h =  6.6261E-27;     # Plank constant, cgs \n",
    "c = 3.0e10           # Speed of light, cgs \n",
    "Na = 6.022E+23       # Avogadro's number\n",
    "Z=1                  # Hydrogen atomic number\n",
    "e = 4.8e-10          # Electric charge cm3/2 g1/2 s-1\n",
    "\n",
    "# Some useful functions\n",
    "\n",
    "# Gaunt factor \n",
    "def gaunt(nu, T, z):\n",
    "    # The Gaunt factor\n",
    "    gammaeu = 0.57721\n",
    "    F1 = 128.*(1**2)*(kb**3)*(T**3)    \n",
    "    F2 = me * (e**4)*(nu**2)*(z**2)\n",
    "    \n",
    "    G = (3**0.5 / (2.*np.pi)) * (np.log(F1/F2) - gammaeu**2)\n",
    "    \n",
    "    return G\n",
    "\n",
    "# Electron density (cylinder unit volume - bow shock)\n",
    "def ne(d,F,DR,T_axis,nu,Z):\n",
    "    L14 = F*Jy*4*np.pi*(d*1e3*pc)**2               # Monochormatic ring luminosity in erg/sec/Hz\n",
    "    Vol = ((np.pi)*(bmaj/2)*(bmin/2))*(DR)*(d*1e3*4.8*1e-6*pc)**3 #Unit volume of the bowshock in cm3 - beam area X DR \n",
    "    kappa_nu = L14 / Vol\n",
    "    C_radio = 6.8*1e-38\n",
    "    ne_squared = kappa_nu/(C_radio*(T_axis**-0.5) * gaunt(nu, T_axis, Z))\n",
    "    n_e = (ne_squared**0.5) # units: cm^-3\n",
    "    return n_e\n",
    "\n",
    "# Electron density (sphere - IRAS)\n",
    "def nesph(d,Firas,Riras,Temp,nu,Z):\n",
    "    Rirascm = Riras*0.048*d/10*pc                   # IRAS source size (diameter), cm\n",
    "    Liras14 = Firas*Jy*(4*np.pi*(d*1000*pc)**2);    # Monochormatic ring luminosity in erg/sec/Hz \n",
    "                                                    # (d needs to be divided by 10!)\n",
    "    fill = 0.5                                      # Volume filling factor\n",
    "    Volsph = fill*4/3*np.pi*(Rirascm/2)**3;         # Volume = 4/3 pi (D/2)^3, with D = diameter\n",
    "    C_radio = 6.8*1e-38\n",
    "    nesph = np.sqrt( (Liras14/Volsph*(np.sqrt(Temp)))/(C_radio*gaunt(nu, Temp, Z)*np.exp(h*nu/(kb*Temp ))) )  \n",
    "    return nesph                                    # Electron density from Bremmsstralung emissivity \n",
    "\n",
    "# Electron density (unit volume - IRAS) - NOT using this, not appropriate\n",
    "def neuv(d,F,DR,T_axis,nu,Z):\n",
    "    bmaj = 6.6           # Beam major axis, arcsec\n",
    "    bmin = 6.6           # Beam minor axis, arcsec\n",
    "    L14 = F*Jy*4*np.pi*(d*1e3*pc)**2 # Average Monochormatic ring luminosity in erg/sec/Hz\n",
    "    Vol = ((np.pi)*(bmaj/2)*(bmin/2))*(DR)*(0.048*d10*pc)**3; \n",
    "    kappa_nu = L14 / Vol\n",
    "    C_radio = 6.8*1e-38\n",
    "    ne_squared = kappa_nu/(C_radio*(T_axis**-0.5) * gaunt(nu, T_axis, Z))\n",
    "    n_e_uv = (ne_squared**0.5) # units: cm^-3\n",
    "    return n_e_uv\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cb4a6785",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lobe diameter [pc] (lobesizepc) = 2.707e+01\n",
      "Lobe diameter [cm] (lobesizecm) = 8.354e+19\n",
      "Source-ring separation (projected) [pc] (dispcP) ~ 4.602e+01\n",
      "Source-ring separation (projected) [cm] (discmP) ~ 1.420e+20\n",
      "Source-ring separation (de-projected) [pc] (dispc) ~ 5.314e+01\n",
      "Source-ring separation (de-projected) [cm] (discm = Lj)~ 1.640e+20\n",
      "Tmin ~ 10000.0\n",
      "Tmax ~ 3000000\n",
      "Gaunt_min ~ 7.922358562065102\n"
     ]
    }
   ],
   "source": [
    "# Some Constats and Units\n",
    "\n",
    "pc = 3.086E+18       # 1 pc, cm \n",
    "mh = 1.6735575E-24   # Hydrogen mass, g \n",
    "me = 9.1093837E-28   # Electron mass, g \n",
    "eV = 1.602176634E-12 # ElectronVolt, erg\n",
    "Jy = 1.0E-23         # 1 Jansky (erg/s/cm2/Hz), cgs\n",
    "kb = 1.380649E-16;   # K boltzman, cgs\n",
    "h =  6.6261E-27;     # Plank constant, cgs \n",
    "c = 3.0e10           # Speed of light, cgs \n",
    "Na = 6.022E+23       # Avogadro's number\n",
    "Z=1                  # Hydrogen atomic number\n",
    "e = 4.8e-10          # Electric charge cm3/2 g1/2 s-1\n",
    "\n",
    "# Observation-specific quantities\n",
    "\n",
    "nu = 1.2839E+9;      # Observing frequency, in Hz (L-band, MeerKAT, slightly lower than for Cyg X-1, Westerbork)\n",
    "bmaj = 6.6           # Beam major axis, arcsec\n",
    "bmin = 6.6           # Beam minor axis, arcsec\n",
    "\n",
    "# Source specific quantities\n",
    "\n",
    "d10 = 0.94;          # distance in units of 10 kpc, GRS 1915+105 --- KNOWN (Reid & Miller-Jones 2023)  \n",
    "incl = 60;           # Source inclination to line of sight, deg --- KNOWN (Reid et al. 2014)\n",
    "incl_err = 5         # Error on inclination angle\n",
    "o_a = 10             # Upper limit to jet opening angle\n",
    "o_a_err = 0          # Jet opening angle error\n",
    "Flobe = 0.00015;     # Bow shock/lobe flux density, Jy/beam -- MEASURED\n",
    "Flobe_err = Flobe/10; \n",
    "Firas = 0.057;       # IRAS source INTEGRATED flux density, Jy -- MEASURED \n",
    "Firas_err = Firas/10\n",
    "Firasmean = 0.0033;       # IRAS source MEAN flux density, Jy -- MEASURED \n",
    "Firasmean_err = Firas/10\n",
    "\n",
    "Fcyl = 0.0052;       # Northern feature flux density, Jy -- MEASURED\n",
    "DR = 60              # Ring thickness, arcsec (on average) -- MEASURED\n",
    "DR_err = 0.3\n",
    "DRcm = (DR)*(0.048*d10*pc) # Ring thickness, in cm (on average)\n",
    "Riras = 36           # IRAS source angular size (diameter), arcsec -- MEASURED \n",
    "Riras_err = bmaj/2\n",
    "Rirascm = Riras*0.048*d10*pc # IRAS source size (diameter), cm\n",
    "\n",
    "theam = 10;                                   # Lobe angular size (diameter ortogonal to jet direction) in arcmin (projected) GRS 1915 --- MEASURED\n",
    "lobesizepc = (theam*60)*0.048*d10             # Lobe diameter in pc GRS 1915+105 --- MEASURED\n",
    "lobesizecm = lobesizepc*pc                    # Lobe diameter (does NOT need to be de-projected 'cause this is measured as ortoigonal to the jet direction) in cm GRS 1915+105\n",
    "\n",
    "disamin = 17;                                 # Lobe-source angular distance in arcmin (projected) GRS 1915+105 --- MEASURED\n",
    "disamin_err = 0.2\n",
    "dispcP = (disamin*60)*0.048*d10;              # source-ring separation (projected), in pc (= Lj, pc)\n",
    "discmP = dispcP*pc;                           # source-ring separation, (projected) in cm\n",
    "dispc = (disamin*60)*0.048*d10/np.sin(incl*np.pi/180);  # source-ring separation (DE-PROJECTED), in pc (= Lj, pc)\n",
    "discm = dispc*pc;                             # source-ring separation, DE-PROJECTED in cm (= Lj, cm)\n",
    "\n",
    "print('Lobe diameter [pc] (lobesizepc) =', '{:.3e}'.format(lobesizepc)) #Lj\n",
    "print('Lobe diameter [cm] (lobesizecm) =', '{:.3e}'.format(lobesizecm)) #Lj\n",
    "print('Source-ring separation (projected) [pc] (dispcP) ~','{:.3e}'.format(dispcP))\n",
    "print('Source-ring separation (projected) [cm] (discmP) ~','{:.3e}'.format(discmP))\n",
    "print('Source-ring separation (de-projected) [pc] (dispc) ~','{:.3e}'.format(dispc))\n",
    "print('Source-ring separation (de-projected) [cm] (discm = Lj)~','{:.3e}'.format(discm))\n",
    "\n",
    "# Assumptions\n",
    "x = 1;               # Ionization fraction at T ~ 10^4\n",
    "n_iter = 5000\n",
    "\n",
    "\n",
    "Tmax = np.max(3*(10**6));\n",
    "Tmin = np.min(1e+4);                         # Lower-limit to post-shock temperature -- ASSUMED \n",
    "                                             # (from arguments based on Bremsstrahlung nature of the emission)\n",
    "                                             # Also see Saha's equation below\n",
    "\n",
    "T_axis = np.linspace(Tmin,Tmax, n_iter, endpoint=True)\n",
    "\n",
    "g = gaunt(nu, Tmin, Z)\n",
    "\n",
    "\n",
    "print('Tmin ~' ,Tmin)\n",
    "print('Tmax ~' ,Tmax)\n",
    "print('Gaunt_min ~' ,g)\n",
    "\n",
    "#print('Rirascm', Rirascm)\n",
    "#Liras14 = Firas*Jy*(4*np.pi*(d10*10*1000*pc)**2);\n",
    "#print('Liras', Liras14)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26f398f1",
   "metadata": {},
   "source": [
    "## Large scale structure of the jet"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87c458a2",
   "metadata": {},
   "source": [
    "### 1)  IRAS 19132 - Bremsstrahlung\n",
    "\n",
    "The emission from IRAS 19132 is characterised by a flat radio spectrum, which suggests a bremsstrahlung origin from a gas emitting at a temperature of T $\\sim 10^4K$. This is supported by the detection of a H92$\\alpha$ recombination line with width 25 km/s (Rodriguez & Mirabel 1998), which suggests a temperature of at least T $\\sim$1.2$\\times$ 10$^4K$.\n",
    "\n",
    "\n",
    "\n",
    "The **monochromatic emissitivty $\\epsilon_\\nu$ of ionised hydrogen due to thermal bremsstrahlung** is given by (Longair 1994). \n",
    "\n",
    " $$\\epsilon_\\nu = \\frac{L_\\nu}{V} = C_{radio} g(\\nu, T) \\frac{n_e^2}{\\sqrt{T}} \\exp{(\\frac{h\\nu}{k_b T})} ~~ erg~s^{-1}~cm^{-3}~Hz^{-1}$$\n",
    "\n",
    "where \n",
    "\n",
    "$$ C_{radio} = 6.8\\times 10^{-38} erg~s^{-1}~cm^{-3}~Hz^{-1} $$\n",
    "\n",
    "Note that in Kaiser+2004 the constant is ~$10^{50}$ because the number densities are expressed in particles per meter cube: $(m^3)^2 = 10^{12} (cm^3)^2$.\n",
    "\n",
    "The above assumes that **the number of electrons $n_e$ equals the number of protons $n$** (pure hydrogen gas), and that the density and temperature are uniform within the volume considered. $\\epsilon_\\nu$ is the expression of the Bremsstrahlung emissivity for a pure hydrogen gas emitting at a temperature T, and $V$ is the source unit volume. Since we have no information regarding the extent of the emission regions along our line of sight or their exact three-dimensional geometrical structure, **we assume a spherical shape with diameter 36 arcsec, multiplied by a filling factor f$\\sim$0.5** to take into account the fact that the region is probably multi-phase (hot gas and cold gas may co-exist), and only the hot gas is responsible for the Bremsstrahlung emission. \n",
    "\n",
    "From the Bremsstrahlung emissivity we can derive the electron density. \n",
    "\n",
    "$$n_e = \\sqrt\\frac{\\epsilon_\\nu}{g(\\nu, T) \\sqrt{T} C_{radio} \\exp{(\\frac{h\\nu}{k_b T})}}$$\n",
    "\n",
    "where the Gaunt factor g($\\nu$) is given by \n",
    "\n",
    "$$g(\\nu, T) \\approx \\frac{\\sqrt{3}}{2 \\pi}\\left[\\ln \\left(\\frac{128 \\epsilon_0^2 k^3 T^3}{m_e e^4 \\nu^2 Z^2}\\right)-\\gamma^2\\right]$$\n",
    "\n",
    "As stated above, since we assume that the hydrogen in the region is fully ionized, the electron number density also corresponds to the total particle number density (under the assumption that the ISM is almost all hydrogen). \n",
    "**The electron density _in the shock_ is about 140 particles per cm$^3$**, and thus, assuming that the shock is approximately 4 times denser than the surrounding medium, **the unshocked ISM electron density is about 35 particles per cm$^3$**. This is consistent with the typical density of an HII region, a factor ~10 or larger than the typical ISM density (1/cm$^3$). Since the bow shock seems to be connected with an HII region (CHIMPS 4894, based on SIMBAD, see http://simbad.cds.unistra.fr/simbad/sim-id?Ident=CHIMPS+4894&), the density we find seems appropriate. "
   ]
  },
  {
   "cell_type": "code",
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   "id": "641b477b-5199-48f9-b208-4ead3e2dd890",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">> Particle number density of shocked gas in the lobe [1/cm3] (ntmin = ne/x) = 2.305e+01\n",
      ">> Particle number density of shocked gas in the lobe [1/cm3] (ntmax = ne/x) = 7.692e+01\n",
      ">> Min Particle number density of shocked gas in IRAS (using unit volume) [1/cm3] (ntmin = ne/x) = 1.081e+02\n",
      ">> Max Particle number density of shocked gas in IRAS (using unit volume) [1/cm3] (ntmax = ne/x) = 3.608e+02\n",
      "!!! IRAS estimates probably underestimated because the volume is smaller (not cylinders)\n"
     ]
    }
   ],
   "source": [
    "neuvmin = neuv(d10*10,Flobe,DR,Tmin,nu,Z)\n",
    "neuvmax = neuv(d10*10,Flobe,DR,Tmax,nu,Z)\n",
    "ntuvmin = neuvmin/x;                                    # Total particle density, which equals the electron \n",
    "ntuvmax = neuvmax/x;                                    # Total particle density, which equals the electron \n",
    "print('>> Particle number density of shocked gas in the lobe [1/cm3] (ntmin = ne/x) =','{:.3e}'.format(ntuvmin))\n",
    "print('>> Particle number density of shocked gas in the lobe [1/cm3] (ntmax = ne/x) =','{:.3e}'.format(ntuvmax))\n",
    "\n",
    "neuvminiras = neuv(d10*10,Firasmean,DR,Tmin,nu,Z)\n",
    "neuvmaxiras = neuv(d10*10,Firasmean,DR,Tmax,nu,Z)\n",
    "ntuvminiras = neuvminiras/x;                                    # Total particle density, which equals the electron \n",
    "ntuvmaxiras = neuvmaxiras/x;                                    # Total particle density, which equals the electron \n",
    "print('>> Min Particle number density of shocked gas in IRAS (using unit volume) [1/cm3] (ntmin = ne/x) =','{:.3e}'.format(ntuvminiras))\n",
    "print('>> Max Particle number density of shocked gas in IRAS (using unit volume) [1/cm3] (ntmax = ne/x) =','{:.3e}'.format(ntuvmaxiras))\n",
    "print('!!! IRAS estimates probably underestimated because the volume is smaller (not cylinders)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "903267f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ring unit volume [cm^3] (ringuv) = 5.541e+54\n",
      "Ring average monochromatic Luminosity [erg/s/Hz] (Liras14) = 1.586e+19\n",
      "IRAS volume [cm^3] (Volsph) = 6.595e+55\n",
      "IRAS INTEGRATED monochromatic Luminosity [erg/s/Hz] (Liras14) = 6.027e+21\n",
      ">> Particle number density of shocked gas [1/cm3] (ntmin = ne/x) = 1.842e+02\n",
      ">> Particle number density of shocked gas [1/cm3] (ntmax = ne/x) = 6.147e+02\n",
      ">> Particle number density of un-shocked gas [1/cm3] (nt0min = ntmin/4) = 4.605e+01\n",
      "Density of shocked gas [g/cm3] (rhomin) = 4.223e-22\n",
      "Density of un-shocked gas [g/cm3] rho0min = 1.056e-22\n",
      "2.8623624950617084e-36\n",
      "9.139682466870654e-35\n",
      ">> Pressure inside IRAS (ideal gas conditions) [erg/cm3] (Pideal) =  2.543e-10\n",
      ">> Pressure in the ISM (ideal gas conditions) [erg/cm3] (pidealunsh) = 1.272e-12\n"
     ]
    }
   ],
   "source": [
    "# Section 1: Calculating the gas density downstream with respect to the shock front, assuming \n",
    "# bremsstralung emission\n",
    "\n",
    "fill = 1\n",
    "Volsph = fill*4/3*np.pi*(Rirascm/2)**3;             # Volume = 4/3 pi (D/2)^3, with D = diameter\n",
    "Liras14 = Firas*Jy*(4*np.pi*(d10*10*1000*pc)**2);   # Monochormatic luminosity in erg/sec/Hz \n",
    "                                                    # for a pure hydrogen gas emitting at Temp\n",
    "nemin = nesph(d10*10,Firas,Riras,Tmin,nu,Z)\n",
    "nemax = nesph(d10*10,Firas,Riras,Tmax,nu,Z)\n",
    "ntmin = nemin/x;                                    # Total particle density, which equals the electron \n",
    "ntmax = nemax/x;                                    # Total particle density, which equals the electron \n",
    "                                            ## density divided by ionization fraction, which in \n",
    "                                                    ## this case is 1 (for fully ionized hydrogen)\n",
    "rhomin = ntmin*1.370*mh                             ## Density of the gas post-shock, i.e. down-stream of \n",
    "                                                    ## the shock, g/cm3\n",
    "rho0min = rhomin/4;                                 ## Density of the pre-shock gas, i.e. up-stream of the \n",
    "                                                    ## shock, g/cm3\n",
    "   \n",
    "ringuv = ((np.pi)*(bmaj/2)*(bmin/2))*(DR)*(0.048*d10*pc)**3; \n",
    "Llobe = Flobe*Jy*(4*np.pi*(d10*10*1000*pc)**2);    # Monochormatic luminosity in erg/sec/Hz \n",
    "\n",
    "\n",
    "#print('Ring thickness [cm] (DRcm) =','{:.3e}'.format(DRcm))\n",
    "print('Ring unit volume [cm^3] (ringuv) =','{:.3e}'.format(ringuv))\n",
    "print('Ring average monochromatic Luminosity [erg/s/Hz] (Liras14) =', '{:.3e}'.format(Llobe))\n",
    "\n",
    "print('IRAS volume [cm^3] (Volsph) =', '{:.3e}'.format(Volsph))\n",
    "print('IRAS INTEGRATED monochromatic Luminosity [erg/s/Hz] (Liras14) =', '{:.3e}'.format(Liras14))\n",
    "print('>> Particle number density of shocked gas [1/cm3] (ntmin = ne/x) =','{:.3e}'.format(ntmin))\n",
    "print('>> Particle number density of shocked gas [1/cm3] (ntmax = ne/x) =','{:.3e}'.format(ntmax))\n",
    "print('>> Particle number density of un-shocked gas [1/cm3] (nt0min = ntmin/4) =','{:.3e}'.format(ntmin/4))\n",
    "print('Density of shocked gas [g/cm3] (rhomin) =','{:.3e}'.format(rhomin))\n",
    "print('Density of un-shocked gas [g/cm3] rho0min =','{:.3e}'.format(rho0min))\n",
    "\n",
    "print(Llobe/ringuv)\n",
    "print(Liras14/Volsph)\n",
    "\n",
    "R = Na*kb # gas constant\n",
    "# Cross check the pressure of gas in ideal conditions. \n",
    "# pressure of gas inside IRAS source assuming ideal conditions\n",
    "pidealmin = ntmin*kb*Tmin\n",
    "pidealmax = ntmin*kb*Tmax\n",
    "\n",
    "print('>> Pressure inside IRAS (ideal gas conditions) [erg/cm3] (Pideal) = ', '{:.3e}'.format(pidealmin))\n",
    "\n",
    "# pressure of gas of unshocked material assuming ideal conditions, and T = 50K\n",
    "pidealunsh = ntmin*kb*50\n",
    "print('>> Pressure in the ISM (ideal gas conditions) [erg/cm3] (pidealunsh) =', '{:.3e}'.format(pidealunsh))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c92a5d1",
   "metadata": {},
   "source": [
    "### 2) Northern feature in IRAS 19132 - Synchrotron emission from gas (hot spot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b36e7bc7",
   "metadata": {},
   "source": [
    "The radio maps of IRAS 19132+1035 show an elongated feature pointing in the direction of GRS 1915+105, with lengths of 17.4 arcsec, and width of 7.9 arcsec, and with a steep radio spectrum, located to the northwest of the main flat spectrum region. In the old VLA images this spectrum is consistent with a power law F $\\propto$ $\\nu^\\alpha$ with $\\alpha$ = -0.8.  This spectral index is typical for synchrotron emission and hence it implies the presence of a relativistic plasma consisting of magnetic field and a population of relativistic electrons. \n",
    "\n",
    "We will assume that we observe(or infer) a radio spectrum with some spectral index $\\alpha$ between upper and lower frequencies $\\nu_1, \\nu_2$. We will need the integrated radio luminosity between these limits, and not just the specific radio luminosity at a certain frequency.\n",
    "\n",
    "$$L=4 \\pi D^2 \\int_{\\nu_1}^{\\nu_2} F_{\\nu} d\\nu = 4 \\pi D^2 F_{\\nu_2} \\nu_2^{-\\alpha} \\left( \\frac{\\nu_2^{\\alpha+1} - \\nu_1^{\\alpha+1}}{\\alpha+1} \\right) $$\n",
    "\n",
    "(an equivalent formula can of course be constructed using $\\nu_1$ as the reference frequency). \n",
    "Here we use $\\alpha = (1-p)/2$.**\n",
    "\n",
    "Note, in comparing the analysis here with the simplified (but relatively accurate) formula of Longair et al. 1994, that the $L_{\\nu}$ used in that formula is the 'specific' luminosity in units erg s$^{-1}$ Hz$^{-1}$ whereas the *integrated* luminosity used here and defined above is in erg s$^{-1}$, and is therefore a larger quantity).\n",
    "\n",
    "The energy density in magnetic fields is $B^2 / 8\\pi$ (in cgs units), therefore for a volume $V$ the total energy in B fields is:\n",
    "\n",
    "$$E_B = \\frac{B^2}{8 \\pi} f V $$\n",
    "\n",
    "where $f$ is a *filling factor* which represents the fraction of the physical source's volume which is actually occupied by the magnetic field and relativistic particles.\n",
    "\n",
    "Given a population of electrons with a power law distribution $-p$ between energy limits $E_1$ and $E_2$, the total energy in these electrons is given by:\n",
    "\n",
    "$$E_e = c_2^{-1} L B^{-2} \\frac{(p-3)}{(p-2)} \\frac{(E_1^{2-p}-E_2^{2-p})}{(E_1^{3-p}-E_2^{3-p})}$$\n",
    "\n",
    "For a given electron energy and magnetic field, we can characterise the synchrotron emission as coming from a single frequency $\\nu = c_1 B E^2$, i.e. $E = \\nu^{1/2} c_1^{-1/2} B^{-1/2}$. So, we can write:\n",
    "\n",
    "$$E_e = c_2^{-1} c_1^{1/2} \\tilde{c}(p, \\nu_1, \\nu_2) B^{-3/2} L = c_{12}(p,\\nu_1,\\nu_2) B^{-3/2} L$$\n",
    "\n",
    "where\n",
    "\n",
    "$$c_{12} = c_2^{-1} c_1^{1/2} \\tilde{c}(p, \\nu_1, \\nu_2)$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\tilde{c}(p, \\nu_1, \\nu_2) = \\frac{(p-3)}{(p-2)} \\frac{\\nu_1^{(2-p)/2}-\\nu_2^{(2-p)/2}}{\\nu_1^{(3-p)/2}-\\nu_2^{(3-p)/2}}$$\n",
    "\n",
    "The pseudo-constant $c_{12}$ encapsulates all the information about the observed (or interpolated, extrapolated, assumed) frequency range of the observations and the slope of the energy spectrum between those limits. \n",
    "\n",
    "Since $E_B \\propto B^2$, the total energy is given by\n",
    "\n",
    "$$E_{e+B} = E_e + E_B =  const. B^{-3/2} + const. B^2$$\n",
    "\n",
    "and therefore *there must be a minimum of the total energy as a function of $B$* (assuming there are no other contributions to the energy budget which have a different dependence on $B$). This minimum occurs at *equipartition* of the energy, when $E_e$ and $E_B$ are almost equal (which can be calculate by differenting $E_{e+B}$ with respect to $B$):\n",
    "\n",
    "$$E_B = \\frac34 \\eta E_e$$\n",
    "\n",
    "where $\\eta$ indicates how much energy is stored in the protons which accompany the electrons (in the case of a normal baryonic plasma); $\\eta = 1$ is generally considered for the minimum energy condition.\n",
    "Substituting the above expressions, the equipartition magnetic field is given by:\n",
    "\n",
    "$$B_{eq} = (6 \\pi \\frac{\\eta}{f} c_{12} \\frac{L}{V})^{2/7} $$\n",
    "\n",
    "\n",
    "\n",
    "For minimum energy conditions the total pressure in this feature is then given by:\n",
    "\n",
    "$$ p = \\frac{7}{9} \\frac{B^2_{min}}{8\\pi}(k+1)$$\n",
    "\n",
    "with k equal the ratio of the internal energy stored in any particles that do not contribute to the synchrotron emission to the sum of the energy in the magnetic field and in the relativistic electrons.\n",
    "Here we assume a cylindrical geometry for the northern feature, with a radius equivalent to 3.9 arcsec and a length of 17.4 $\\times$ sin$\\theta^{-1}$ arcsec, where $\\theta$ is the angle of the long axis of the cylinder to our line of sight.\n",
    "\n",
    "The volume of the feature is **Vcyl ~ 2e+54 cm$^3$**, and its total luminosity is **Lcyl ~ 1.7e+29 erg/s**. The predicted minimum energy **magnetic field is Bmin ~ 2.2e-05 G**, and the minimum energy **pressure is 1.6e-11 erg/cm$^3$**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "063eefd6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cylinder Integrated Luminosity [erg/s] (Lcy) = 1.998e+29\n",
      "Cylinder Volume [cm3] (VolCyl) = 2.592e+54\n",
      ">> Cylinder magnetic field density [G] (Bmin) =  2.182e-05\n",
      ">> Cylinder pressure [erg/cm3] (pmincyl) ~ 1.488e-11\n"
     ]
    }
   ],
   "source": [
    "# This is adapted from the ThunderBook \"Equipartition analysis\" (https://github.com/robfender/ThunderBooks)\n",
    "D = d10*10\n",
    "k = 0.01          \n",
    "nu1=1.0e7\n",
    "nu2=1.0e11\n",
    "p=2.5\n",
    "alpha=(1.0-p)/2.0\n",
    "eta = 1\n",
    "f = 1\n",
    "\n",
    "# Pseudoconstant\n",
    "c1=6.27e18\n",
    "c2=2.37e-3\n",
    "# speed of light \n",
    "c=3.0e10\n",
    "# relativistic sound speed of c/sqrt[3]\n",
    "cs=c/(3.0**0.5)\n",
    "\n",
    "ctildetop=(nu1**((2.0-p)/2.0))-(nu2**((2.0-p)/2.0))\n",
    "ctildebottom=(nu1**((3.0-p)/2.0))-(nu2**((3.0-p)/2.0))\n",
    "ctilde=((p-3.0)/(p-2.0))*(ctildetop/ctildebottom)\n",
    "c12=(c2**-1.0)*(c1**0.5)*ctilde\n",
    "\n",
    "def LumTot(snu2,D,nu1,nu2,alpha): \n",
    "# here s is the flux density at the upper frequency nu2\n",
    "    L2 = 4 * np.pi * ((D * 3.1e21)**2.0) * (snu2 * 1e-26) * (nu2**(-alpha)) * ((nu2**(1+alpha))-(nu1**(1+alpha))) / (1+alpha)\n",
    "    #print (('Calculated total radiative luminosity'),('L ='),('%.2e' % L2),(' erg / sec '))\n",
    "    return L2\n",
    "\n",
    "Lcy = LumTot(Fcyl,(d10*10),nu1,nu2,alpha)    #  Note that this is the INTEGRATED luminosity, not the monochromatic one\n",
    "\n",
    "\n",
    "rcyl = 3.9\n",
    "lencyl = 17.4\n",
    "\n",
    "rcylcm = rcyl*(0.048*d10*pc)                         # Radius of cylindric feature, cm\n",
    "lencylcm = lencyl*(0.048*d10*pc)/np.sin(incl*np.pi/180)  # Lenght of cylindric feature, cm\n",
    "VolCyl = np.pi*rcylcm**2*lencylcm                   # Volume of cylindric feature, cm3\n",
    "\n",
    "Bmin = (6*np.pi*(eta/f)*c12*Lcy/VolCyl)**(2/7)  # Equipartition magnetic field, Gauss\n",
    "# Total pressure in this feature for minimum energy conditions\n",
    "\n",
    "pmincyl = 7/9*Bmin**(2)/(8*np.pi)*(k+1)       # Equipartition pressure, erg/cm3\n",
    "\n",
    "\n",
    "print('Cylinder Integrated Luminosity [erg/s] (Lcy) =','{:.3e}'.format(Lcy))\n",
    "print('Cylinder Volume [cm3] (VolCyl) =','{:.3e}'.format(VolCyl))\n",
    "print('>> Cylinder magnetic field density [G] (Bmin) = ','{:.3e}'.format(Bmin))\n",
    "print('>> Cylinder pressure [erg/cm3] (pmincyl) ~','{:.3e}'.format(pmincyl))\n",
    "\n",
    "# From Kaiser+2004, for a reality check\n",
    "\n",
    "#LcylK = 6e+18*D**2\n",
    "#VolK = 9.9E-05*(D)**3/math.sin(incl*np.pi/180)*pc**3\n",
    "#BminK = 1.0E-6*120*(math.sin(incl*np.pi/180)/(D))**(2/7)\n",
    "#pminK = 1.0E-10*(4.3*(math.sin(incl*np.pi/180)/(D))**(4/7))*(k+1)\n",
    "\n",
    "#print('LcylK ~',LcylK)\n",
    "#print('VolK ~',VolK)\n",
    "#print('BminK ~',BminK)\n",
    "#print('pminK ~',pminK)\n",
    "\n",
    "#print(lencyl*2./pc)\n",
    "#print(lencyl/pc)\n",
    "#print(alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8584269",
   "metadata": {},
   "source": [
    "## The jet model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "680fea13",
   "metadata": {},
   "source": [
    "For interpreting the interactions of the large-scale jet structure of GRS 1915+105 with its environment we use the\n",
    "model developed in Kaiser & Alexander (1997, KA97) for the jets of radio galaxies, and adapted for galactic sources in and Kaiser et al. (2004). The supersonic jets end in strong shock fronts at the location where they impact on the ambient gas. The gas coming up the jets inflate two lobes that are overpressured with respect to the environment. The lobes therefore expand sideways and thus a bow shock is driven into the surrounding ISM. We identify three regions: \n",
    "\n",
    "a) **IRAS 19132** corresponds to the compressed and shock-heated ISM in front of the jet.\n",
    "\n",
    "b) **the norther cylindrical feature** near IRAS 19132+1035, pointing towards GRS 1915+105, corresponds to the strong shock that originates at the end of the postulated large-scale jet.\n",
    "\n",
    "c) **the radio lobe clearly seen in the MeerKAT image at an average flux density of 0.2 mJy** corresponds to the edge-brightened radio lobe inflated by the jet material. In the old VLA data such a bow shock was not detected due to limited sensitivity (but it was predicted by Kaiser et al. 2004, at approximately the currently observed flux density).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ace502af",
   "metadata": {},
   "source": [
    "### 1) Applicability (characteristic jet lenght)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ab65f3b",
   "metadata": {},
   "source": [
    "The model assumes a constant energy transport rate, Q0, for each side of the jet. This transport rate is averaged over the lifetime of the jets. We assume that the ambient medium has a constant density. Under these circumstances the evolution of the large-scale structure created by the jet (lobe and bow shock), is self-similar once the jet extends beyond its characteristic length scale, given by (KA97): \n",
    "\n",
    "$$ L_0 = (\\frac{\\rho_0^2 Q_0}{\\dot{M}_0^3})^{-1/4} = [\\frac{Q_0^2}{\\rho_0^2 c^6(\\gamma_j -1)}]^{1/4}$$\n",
    "\n",
    "where $\\dot{M_0}$ is the mass transport rate of the jet, and $\\gamma_j$ is the Lorentz factor of the jet material.\n",
    "\n",
    "The density of the gas that has been shock-heated by the impact of the jets, which we calculated based on the Bremsstrahlung luminosity of IRAS 19132, is approximately 4 times that of the pre-shock value $\\rho_0$. \n",
    "\n",
    "Estimating the Lorentz factor of jet flows is notoriously difficult (e.g., Fender 2003). Furthermore, the observed motion of radio ‘‘knots’’ in the jets may simply reflect the motion of shocks along the jets rather\n",
    "than the bulk motion of the jet material. Any estimate of $\\gamma_j$ will also depend on the distance to the source and the orientation of the jet to our line of sight. Here we use the conservative lower limit  $\\gamma_j$ = 1.1, which maximizes L$_0$.\n",
    "\n",
    "For reasonable values of Q$_0$ (~ 10$^{36}$ erg/s, see below), L$_0$ is of the order  10$^{-05}$ pc, i.e.,  orders of magnitude smaller than the jet lenght L$_j$ (> 40 pc), and therefore the model by KA97 is valid for GRS 1915+105. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dabeb9f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Characteristic jet length scale [pc] (L0) =  1.614e-05\n",
      "Jet length [pc] (Lj) =  5.314e+01\n"
     ]
    }
   ],
   "source": [
    "# Calculation of L0\n",
    "\n",
    "gammaj = 1.02\n",
    "Q0 = 1.0E+36\n",
    "\n",
    "L0 = ( (Q0**2) / (rho0min**2*c**6*(gammaj-1)) )**(1/4)\n",
    "\n",
    "print('Characteristic jet length scale [pc] (L0) = ', '{:.3e}'.format(L0/pc))\n",
    "print('Jet length [pc] (Lj) = ', '{:.3e}'.format(discm/pc))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00a4991c",
   "metadata": {},
   "source": [
    "### 2) Shock front velocity and age of the jet\n",
    "\n",
    "KA97 showed that the velocity of the bow shock is roughly equal to the advance speed of the end of the jet driving this shock, which is given by:\n",
    "\n",
    "$$ \\dot{L} = \\sqrt{\\frac{16 k_b}{3 m_p}T}$$\n",
    "\n",
    "where $m_p$ is the mass of the proton. \n",
    "For a strong shock in a mono-atomic gas, the expansion velocity is set by the temperature of the shocked gas. If the shock is radiative, then the initial post-shock temperature can be higher than that of the thermalized, bremsstrahlung-emitting gas. A stringent constraint on the temperature could come from X-ray observations, which we will have soon via Chandra. \n",
    "\n",
    "We estimate a minimum **shock velocity of 23 Km/s**, which implies that the bow shock will be highly supersonic with respect to the unshocked ISM. Note that the kinematic of the gas in the region is complex,  and hence T$_{min}$ could be overestimated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f3eb4f4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">> Shock front velocity [Km/s] (vd1 = Ldotmin) ~ 2.098e+01\n",
      ">> Min Shock front velocity [cm/s] (vd1 = Ldotmin) ~ 2.098e+06\n",
      ">> Max Shock front velocity [cm/s] (vd1 = Ldotmin) ~ 3.633e+07\n"
     ]
    }
   ],
   "source": [
    "vdmin = ( (16*Tmin*kb)/(3*mh) )**(1/2)/1.0E+5;# Lower-limit to Ljdot, i.e., post-shock velocity, in Km/s\n",
    "\n",
    "vdmaxcm = ( (16*Tmin*kb)/(3*mh) )**(1/2);     # Lower-limit to Ljdot, i.e., post-shock velocity, in cm/s\n",
    "vdmaxcm = ( (16*Tmax*kb)/(3*mh) )**(1/2);     # Upper-limit to Ljdot, i.e., post-shock velocity, in cm/s\n",
    "\n",
    "vdmincm = vdmin*1.0E+5;  #Ldot                # Lower limit to ring velocity, in cm/s \n",
    "\n",
    "print('>> Shock front velocity [Km/s] (vd1 = Ldotmin) ~','{:.3e}'.format(vdmin))\n",
    "print('>> Min Shock front velocity [cm/s] (vd1 = Ldotmin) ~','{:.3e}'.format(vdmincm))\n",
    "print('>> Max Shock front velocity [cm/s] (vd1 = Ldotmin) ~','{:.3e}'.format(vdmaxcm))\n",
    "\n",
    "#TminP = 20\n",
    "#print(( (16*TminP*kb)/(3*mh) )**(1/2)/1.0E+5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49ef3a6b",
   "metadata": {},
   "source": [
    "For a constant density medium Kaiser+2004 showed that the jet length within the lobe grows with the time $t$ in such a way that\n",
    "\n",
    "$$ L_j = C_1 ~(\\frac{Q_0}{\\rho_0})^{1/5}~ t^{3/5}$$ \n",
    "\n",
    "Taking the time derivartive of this equation we obtain:\n",
    "\n",
    "$$ \\dot{L_j} = \\frac{3 Lj}{5 t}$$\n",
    "\n",
    ", which implies:\n",
    "\n",
    "$$ t = \\frac{3 L_j}{5 \\dot{L_j}} $$\n",
    "\n",
    "This expression can be used to estimate the upper limit to the age of the jet, which is approximately 1 Myr.\n",
    "C1 is a dimensionless constant that depends on the thermodynamical properties of the jet material, and on the aspect ratio, R, of the lobe inflated by the jet (R is the length of the lobe divided by its width). The esplicit form of C1 is the following:\n",
    "\n",
    "$$ C_1=\\left(\\frac{C_2}{C_3\\theta^2}\\frac{(\\Gamma_x+1)(\\Gamma_c-1)(5-\\beta)^3}{18\\left[9\\{\\Gamma_c+(\\Gamma_c-1)\\frac{C_2}{4\\theta^2}\\}-4-\\beta\\right]}\\right)^{\\frac{1}{(5-\\beta)}}$$\n",
    "\n",
    "with\n",
    "\n",
    "$$C_2=\\left(\\frac{(\\Gamma_c-1)(\\Gamma_j-1)}{4\\Gamma_c}+1\\right)^{\\frac{\\Gamma_c}{(\\Gamma_c-1)}}\\frac{(\\Gamma_j+1)}{(\\Gamma_j-1)}$$\n",
    "\n",
    "and \n",
    "\n",
    "$$C_3=\\frac{\\pi}{4R_{\\rm ax}^2}$$\n",
    "\n",
    "\n",
    "(Tetarenko et al. 2018, Appendix C), and the value of the constant is calculated below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4ad4cc65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con1 ~ 1.9932080579528801\n"
     ]
    }
   ],
   "source": [
    "# The constant C1 is given in the following (see Appendix C in Tetarenko et al. 2018): \n",
    "\n",
    "# The constant C1 can ba calculated making assumptions on the jet properties and on the environment, \n",
    "# which we will treat as uniform in density. We also make assumptions on the adiabatic index of the \n",
    "# material in the cavity, in the external medium, and in the jet. \n",
    "# Keeping the adiabatic indices = 5/3, in order to recover a constant of about 2, we need to assume \n",
    "# jet opening angle of 30 degrees, which might be a bit high. \n",
    "\n",
    "Gammac = 5/3                            # Adiabatic index of the material in the cavity, -- ASSUMED \n",
    "Gammax = 5/3                            # Adiabatic index of the material in the external medium, -- ASSUMED \n",
    "Gammaj = 5/3                            # Adiabatic index of the material in the jet, -- ASSUMED \n",
    "\n",
    "def C_cons(g_c,g_j,g_x,ope):\n",
    "    beta = 0                                # density profile index (beta = 0 for a uniform density medium), -- ASSUMED \n",
    "    theta_ra = ope*np.pi/180                # Jet opening angle, in radiants\n",
    "    C2_0 = (((g_c-1)*(g_j-1))/(4*g_c) + 1 )**(g_c/(g_c-1)) * ((g_j+1)/(g_j-1))\n",
    "    Rax_0 = np.sqrt((1/4*(C2_0/theta_ra**2))) # axial ratio of the jet-blown cavity                         \n",
    "    C3_0 = np.pi/(4*Rax_0**2)\n",
    "    C1_0 = ((C2_0)/(C3_0*theta_ra**2)*((g_x+1)*(g_c-1)*(5-beta)**3)/(18*(9*(g_c + (g_c -1)*(C2_0/(4*theta_ra**2))) - 4 - beta)) )**(1/(5-beta))\n",
    "    return C1_0\n",
    "\n",
    "Con1 = C_cons(Gammac, Gammaj,Gammax, 30)\n",
    "\n",
    "print('Con1 ~', Con1)\n",
    "\n",
    "#print(dispc)\n",
    "#print(lobesizepc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5b28b959",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jet age [Myr] (tmaxMyr) = 1.488e+00\n",
      "Jet age [Myr] (tmaxMyr) = 8.588e-02\n"
     ]
    }
   ],
   "source": [
    "# Section 3: the jet age\n",
    "\n",
    "def age(disamin,d,incl,v):\n",
    "    disasec = disamin*60 #lobe target seperation in arcsec (projected)\n",
    "    dispc = disasec*d*1e3*4.8*1e-6  #lobe target separation in pc (projected)\n",
    "    discmP = dispc*pc #lobe target sepeartion in cm (projected)\n",
    "    discm = discmP/np.sin(incl*np.pi/180) #lobe target de-projected seperation to account for the inclination angle\n",
    "    t = 3/5*(discm/v) #time in seconds\n",
    "    t_age_Myr = t/(365.*24.*60*60)/1.0E+6 #age of shock in Myr\n",
    "    return t_age_Myr\n",
    "    \n",
    "tmaxMyr = age(disamin,(d10*10),incl,vdmincm)\n",
    "tminMyr = age(disamin,(d10*10),incl,vdmaxcm)\n",
    "\n",
    "tsmax = tmaxMyr*(365.*24.*60*60)*1.0E+6          # Upper limit to lobe age in s\n",
    "tsmin = tminMyr*(365.*24.*60*60)*1.0E+6          # Upper limit to lobe age in s\n",
    "\n",
    "#print(disamin,(d10*10),incl,vdmincm)\n",
    "print('Jet age [Myr] (tmaxMyr) =', '{:.3e}'.format(tmaxMyr))\n",
    "print('Jet age [Myr] (tmaxMyr) =', '{:.3e}'.format(tminMyr))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d56b25d",
   "metadata": {},
   "source": [
    "We note that based on the results of the sub-mm observations reported by Tetarenko et al. 2018 \n",
    "(https://ui.adsabs.harvard.edu/abs/2018MNRAS.475..448T/) the shock velocity estimated from the SiO detection would be ~ 1Km/s, which implies a jet of approximately 25 Myr, i.e. significantly older than what we predict."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5789b2f5",
   "metadata": {},
   "source": [
    "### 3) Energetics\n",
    "\n",
    "Assuming that the jet direction remains constant over time,  and that the jet is colliding with a medium of densit $\\rho_0$, the power Q$_{jet}$ being transported by the jets averaged over its lifetime, **is solely dependent on the properties of the ISM** at the interaction site. Combining the equations for $L_j$ and $\\dot{L_j}$ given above we obtain: \n",
    "\n",
    "$$ Q_{jet} = (\\frac{5}{3})^3~\\frac{\\rho_0}{C_1^5}L_j^2 ~\\dot{L_j}^3$$\n",
    "\n",
    "The constant C$_1$ can be calculated and it depends on the aspect ratio R of the lobe inflated by the jet, the lobe lenght divided by its width. For extragalactic jet sources, R ~ 2. In the case of the lobe in GRS 1915+105, R is appriximately R ~ 11.16/sin(theta)/8 = 1.5, hence we will assume C$_1$ = 1.5. Below we calculate the constant explicitly (note that a value of 1.5 implies a jet opening angle of 50 degrees).\n",
    "We obtain that the **minimum energy transferred to the environment is Q$_{jet}$ ~ 1.4e+37 erg/s**. \n",
    "\n",
    "The pressure inside the lobe is given by: \n",
    "\n",
    "$$ p = 0.0675 \\frac{C_1^{10/3}}{R^2}(\\frac{\\rho_0 Q_0^2}{L_j^4})^{1/3}$$\n",
    "\n",
    "Which is $p_{lobe}$ ~ 3.6e-11 erg/cm$3$, i.e. significantly overpressured with respect to the unshocked ISM (for a temperature of 50K, a typical ISM pressure would be of the order 10$^{-12}$ erg/cm$3$ assuming that ideal gas conditions, see Section 1), but similar to the pressure we obtain for the cylindrical feature stemming from IRAS 19132+1035."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "10d71586",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">> Minimum transferred jet power [erg/s] (Qjetmin) ~  3.144e+35\n",
      ">> Jet pressure [erg/cm3] (pminlobes) ~  2.258e-12\n"
     ]
    }
   ],
   "source": [
    "# Section 4: the jet energy transport rate\n",
    "\n",
    "# Con1arb = 2\n",
    "# Rarb = 2\n",
    "\n",
    "# Min and max depend on the temperature, which gives both the jet velocity and material density. \n",
    "\n",
    "# Qjetminarb = (5/3)**3 * rho0min/(Con1arb**5)*(discm**2)*(vdmincm**3)   # Lower limit to time averaged jet power \n",
    "\n",
    "# pminjetarb = 0.0675*(Con1arb**(10/3)/Rarb**2)*(rho0min*Qjetmin**2/(discm**4))**(1/3)\n",
    "# print(Con1arb,Rarb,rho0min,Qjetmin,discm)\n",
    "\n",
    "# print(Qjetminarb,pminjetarb)\n",
    "\n",
    "\n",
    "def power(theta,d,nee,disamin,vcm):\n",
    "    beta = 0\n",
    "                                           # Theta is the jet opening angle in degrees\n",
    "                                           # d is the distance in kpc\n",
    "                                           # nee is the number of electrons\n",
    "                                           # disamin lobe target seperation in arcsec (projected)\n",
    "                                           # vcm velocity\n",
    "    theta_rad = theta*np.pi/180            # Jet opening angle, in radiants\n",
    "    Con2 = (((Gammac-1)*(Gammaj-1))/(4*Gammac) + 1 )**(Gammac/(Gammac-1)) * ((Gammaj+1)/(Gammaj-1))\n",
    "    Rax = np.sqrt((1/4*(Con2/theta_rad**2))) # axial ratio of the jet-blown cavity                         \n",
    "    Con3 = np.pi/(4*Rax**2)\n",
    "    Con1 = ((Con2)/(Con3*theta_rad**2)*((Gammax+1)*(Gammac-1)*(5-beta)**3)/(18*(9*(Gammac + (Gammac -1)*(Con2/(4*theta_rad**2))) - 4 - beta)) )**(1/(5-beta))\n",
    "    #nt=ne/x #where x is the ionisation fraction and is 1, use ne and nt interchangeably in the next equation  \n",
    "    rho = nee*1.370*mh;                    # Density of the gas up-stream of the shock, in cm-3 (calculated above with the calorimetry method above)\n",
    "    rho0 = rho/4;                          # Density of the gas, down-stream of the shock, in cm-3\n",
    "    disasec = disamin*60                   # lobe target seperation in arcsec (projected)\n",
    "    dispc = disasec*d*1e3*4.8*1e-6         # lobe target separation in pc (projected)\n",
    "    discmP = dispc*pc                      # lobe target sepeartion in cm (projected)\n",
    "    discm = discmP/np.sin(incl*np.pi/180)  # lobe target de-projected seperation to account for the inclination angle\n",
    "    Pjet = (5/3)**3 * rho0/(Con1**5)*(discm**2)*vcm**3   # Upper limit to time averaged jet power \n",
    "    return Pjet\n",
    "\n",
    "Qjetmin  = power(o_a,d10*10,nemin,disamin,vdmincm)\n",
    "\n",
    "#print(Rax,Con1)\n",
    "\n",
    "def press(theta,d,nee,disamin,vcm):\n",
    "    beta = 0\n",
    "                                           # Theta is the jet opening angle in degrees\n",
    "                                           # d is the distance in kpc\n",
    "                                           # nee is the number of electrons\n",
    "                                           # disamin lobe target seperation in arcsec (projected)\n",
    "                                           # vcm velocity\n",
    "    theta_rad = theta*np.pi/180            # Jet opening angle, in radiants\n",
    "    Con2 = (((Gammac-1)*(Gammaj-1))/(4*Gammac) + 1 )**(Gammac/(Gammac-1)) * ((Gammaj+1)/(Gammaj-1))\n",
    "    Rax = np.sqrt((1/4*(Con2/theta_rad**2))) # axial ratio of the jet-blown cavity                         \n",
    "    Con3 = np.pi/(4*Rax**2)\n",
    "    Con1 = ((Con2)/(Con3*theta_rad**2)*((Gammax+1)*(Gammac-1)*(5-beta)**3)/(18*(9*(Gammac + (Gammac -1)*(Con2/(4*theta_rad**2))) - 4 - beta)) )**(1/(5-beta))\n",
    "    #nt=ne/x #where x is the ionisation fraction and is 1, use ne and nt interchangeably in the next equation  \n",
    "    rho = nee*1.370*mh;                    # Density of the gas down-stream of the shock, in cm-3 (calculated above with the calorimetry method above)\n",
    "    rho0 = rho/4;                          # Density of the gas, up-stream of the shock, in cm-3\n",
    "    disasec = disamin*60                   # lobe target seperation in arcsec (projected)\n",
    "    dispc = disasec*d*1e3*4.8*1e-6         # lobe target separation in pc (projected)\n",
    "    discmP = dispc*pc                      # lobe target sepeartion in cm (projected)\n",
    "    discm = discmP/np.sin(incl*np.pi/180)  # lobe target de-projected seperation to account for the inclination angle\n",
    "    Pjet = (5/3)**3 * rho0/(Con1**5)*(discm**2)*vcm**3   # Upper limit to time averaged jet power \n",
    "    pminjet = 0.0675*(Con1**(10/3)/Rax**2)*(rho0*Pjet**2/(discm**4))**(1/3)\n",
    "    return pminjet\n",
    "\n",
    "pminjet = press(o_a,d10*10,nemin,disamin,vdmincm)\n",
    "\n",
    "print('>> Minimum transferred jet power [erg/s] (Qjetmin) ~ ','{:.3e}'.format(Qjetmin))\n",
    "print('>> Jet pressure [erg/cm3] (pminlobes) ~ ','{:.3e}'.format(pminjet))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e1f44081",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum transferred jet power based on Tetarenko+2018 [erg/s] (QjetminT) ~ 4.045e+34\n",
      "1.0219225980102382e-20\n"
     ]
    }
   ],
   "source": [
    "# Based on electron density from Tetarenko et al. 2018\n",
    "vdminT = 1 #; Km/s\n",
    "vdmincmT = vdminT*1.0E+5;\n",
    "\n",
    "Con1T = 6\n",
    "fT = 0.1\n",
    "DT = 8.6\n",
    "rho0T  = 2.6E-18/DT**3/fT /4 #---- Assuming bremsstrahlung emission, so dividing by 4 to accound for \n",
    "                             #     the pre-shock vs post-shock difference. \n",
    "n0T  = rho0T/(1.37*mh)\n",
    "\n",
    "QjetminT = (5/3)**3 * rho0T/(Con1**5)*(discm**2)*(vdmincmT**3)   # Lower limit to time averaged jet power \n",
    "print('Minimum transferred jet power based on Tetarenko+2018 [erg/s] (QjetminT) ~','{:.3e}'.format(QjetminT))\n",
    "print(rho0T)      \n",
    "      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d1f51de0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temperature from molecular gas density [K] (TT) = 1.371e+10\n"
     ]
    }
   ],
   "source": [
    "C_radio = 6.8*1e-38\n",
    "TT = (C_radio*g*n0T**2/(Liras14/Volsph)*np.exp(h*nu/(kb*2000 )) )**2 #--- this ignores the T in the exponential, which doesn't count for high T values.\n",
    "\n",
    "print('Temperature from molecular gas density [K] (TT) =', '{:.3e}'.format(TT))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52744d73",
   "metadata": {},
   "source": [
    "### 4) Emission Properties of the Model\n",
    "\n",
    "#### Radio emission form the lobes\n",
    "\n",
    "In the case of AGN a substantial fraction of the energy transported by the jet gives rise to a population of relativistic electrons and a magnetic field in the lobes. The emission from the lobes is easily detected in radio, and similar emission should emerge around the jets in microquasars. \n",
    "\n",
    "We assume that the conditions of minimum energy hold in the lobe, and so the maximum synchrotron luminosity is obtained from a given amount of energy (e.g., Longair 1994). We neglect any energy losses of the relativistic electrons due to radiation processes. We can infer the minimum energy magnetic field B$_{min}$ using the equation given in section 1 (minimum energy condition), and compare it with the magnetic field density we obtained for the cylindrical feature near the IRAS source (see Section 2). \n",
    "\n",
    "We obtain a minimum energy magnetic field of **Bmin ~ 6.5e-6 G**, and a minimum energy **pressure is p$_{}$ = 1.3e-12 erg/cm$^3$**, which are close enough to the values we obtained for the cylindrical feature. \n",
    "Curiously, the flux density we measure from the MeerKAT image of the bow shock is consistent with the flux density \n",
    "predicted by Kaiser et al. 2004, who argued that a (at the time invisible) synchrotron lobe would have had a flux density of approximately 0.1 mJy/beam at a resolution of 4 arcsec (i.e., comparable with the MeerKAT resolution), which was below the 1-$\\sigma$ rms noise of the VLA data taken in the '90s.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c19b24aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equipartition lobe magnetic field [G] (Bminlobe) = 6.377e-06\n",
      "Equipartition lobe pressure [erg/cm3] (pminlobe) = 1.271e-12\n"
     ]
    }
   ],
   "source": [
    "VlobeU = ((np.pi)*(bmaj/2)*(bmin/2))*(DR)*(0.048*d10*pc)**3 #unit volume of in the lobe structure, assuming a cylindrical geometry\n",
    "\n",
    "Llobe = LumTot(Flobe,(d10*10),nu1,nu2,alpha)\n",
    "\n",
    "Bminlobe = (6*np.pi*(eta/f)*c12*Llobe/VlobeU)**(2/7)  # Equipartition magnetic field, Gauss\n",
    "\n",
    "# Total pressure in this feature for minimum energy conditions\n",
    "\n",
    "pminlobe = 7/9*Bminlobe**(2)/(8*np.pi)*(k+1)       # Equipartition pressure, erg/cm3\n",
    "\n",
    "print('Equipartition lobe magnetic field [G] (Bminlobe) =','{:.3e}'.format(Bminlobe))\n",
    "print('Equipartition lobe pressure [erg/cm3] (pminlobe) =','{:.3e}'.format(pminlobe))\n",
    "\n",
    "#Slobe = 0.08*(D/f**(-7))**(1/8)*(math.sin(incl*np.pi/180))**(-2)*(k+1)**(-7/4)\n",
    "#print('Slobe ~',Slobe)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ca161f8",
   "metadata": {},
   "source": [
    "# MC-based parameters estimates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "012a5b3c",
   "metadata": {},
   "source": [
    "### 1) Electron density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "97d2868e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.94\n"
     ]
    }
   ],
   "source": [
    "# Redefine distance for simplicity\n",
    "d = d10*10          #distance to GRS 1915 in kpc, Reid et al. 2014\n",
    "d_err = 0.7        #error in distance measured \n",
    "print(d10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "85c53701",
   "metadata": {},
   "outputs": [],
   "source": [
    "from joblib import Parallel, delayed\n",
    "import multiprocessing\n",
    "from scipy.stats import gaussian_kde,rv_continuous\n",
    "from scipy import stats\n",
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2ee3c6b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iter = 5000\n",
    "n_cores = 16         # Number of parallel threads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cdc7b22c",
   "metadata": {},
   "outputs": [],
   "source": [
    "class custom_dist_analytical(rv_continuous):\n",
    "    def _pdf(self, xx):\n",
    "        return testf(xx)\n",
    "\n",
    "np.random.seed(124)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ee20504a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Source parameters:\n",
    "dist = np.random.normal(d,d_err, n_iter)\n",
    "Flux = np.random.normal(Firas,Firas_err,n_iter)\n",
    "Ring_thic = np.random.normal(Riras,Riras_err,n_iter) #ring thickness in arcsec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2d0159f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  40 tasks      | elapsed:    0.4s\n",
      "[Parallel(n_jobs=16)]: Done 384 tasks      | elapsed:    0.5s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 510.0802408152434 ; Lower limit =  391.5532116476201 ; Upper limit =  625.0226479870133\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4160 tasks      | elapsed:    0.6s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.7s finished\n"
     ]
    }
   ],
   "source": [
    "elec_density = Parallel(n_jobs=n_cores,verbose=5)(delayed(nesph)(dist[i],Flux[i],Ring_thic[i],T_axis[i],nu,Z) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(elec_density,50)\n",
    "low_lim = np.percentile(elec_density,16)\n",
    "high_lim = np.percentile(elec_density,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a22c9f74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "%matplotlib inline\n",
    "histplot = plt.hist(elec_density,bins=70,color='royalblue',edgecolor='blue',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel(r'$n_e(T)$ [cm$^{-3}$]', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "#plt.title(str(name))\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a3a7cd4-744f-4185-a359-4f65cf8578e4",
   "metadata": {},
   "source": [
    "### Assuming that the bow shock is from Bremsstrahlung emission instead of Synchrotron\n",
    "\n",
    "We use a cylindrical unit volume in the bow shock (beam time thickness) and the average flux density (0.15 mJy/beam). The resulting particle density should be compared with that from the IRAS modelling. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0dca8fee-46ff-48e2-9c60-e518883d3461",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 83.60746521759373 ; Lower limit =  65.45764629002511 ; Upper limit =  96.07244004641895\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.3s\n",
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.4s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.4s finished\n"
     ]
    }
   ],
   "source": [
    "Fluxuv = np.random.normal(Flobe,Flobe_err,n_iter)\n",
    "elec_densityuv = Parallel(n_jobs=n_cores,verbose=5)(delayed(ne)(dist[i],Fluxuv[i],Ring_thic[i],T_axis[i],nu,Z) for i in range(n_iter))\n",
    "median = np.percentile(elec_densityuv,50)\n",
    "low_lim = np.percentile(elec_densityuv,16)\n",
    "high_lim = np.percentile(elec_densityuv,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0343b48-b4b0-485a-ab18-34b1b466c350",
   "metadata": {},
   "source": [
    "Unshocked version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f198f54d-53c7-40a7-af2a-2168d3aa4a1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 20.901866304398432 ; Lower limit =  16.364411572506278 ; Upper limit =  24.018110011604737\n"
     ]
    }
   ],
   "source": [
    "print('Median =',median/4,'; Lower limit = ',low_lim/4,'; Upper limit = ',high_lim/4)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10737ef3",
   "metadata": {},
   "source": [
    "### 2) Shock velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "bba46f8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.098e+06 3.633e+07\n"
     ]
    }
   ],
   "source": [
    "v_range =    ((16*T_axis*kb)/(3*mh))**(1/2)/1e5\n",
    "v_range_cm = ((16*T_axis*kb)/(3*mh))**(1/2)\n",
    "print('{:.3e}'.format(min(v_range_cm)),'{:.3e}'.format(max(v_range_cm)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d75f97b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "ax.yaxis.set_ticks_position('both')\n",
    "ax.xaxis.set_ticks_position('both')\n",
    "ax.get_yaxis().set_tick_params(direction='in', which='both')\n",
    "ax.get_xaxis().set_tick_params(direction='in', which='both')\n",
    "\n",
    "ax.plot(v_range, T_axis, 'r-', lw=3)\n",
    "\n",
    "ax.set_ylim(1e4, 1.1e6)\n",
    "#ax.set_ylim(3., 5e2)\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "\n",
    "ax.set_xlabel(r'Velocity [km s$ˆ{-1}$]')\n",
    "ax.set_ylabel(r'Temperature [K]')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d099e9f5",
   "metadata": {},
   "source": [
    "### 3) Jet age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "625f2391",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 0.12234532613196332 Lower limit =  0.09352310247000262 Upper limit =  0.2162871677167302 Absolute upper limit: 1.2562973519834066\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "# Generating distribution arrays for measurements\n",
    "len_min = np.random.normal(disamin,disamin_err, n_iter) #distance between bowshock and target in arcmin\n",
    "i_angle = np.random.normal(incl,incl_err,n_iter)        #inclination angle\n",
    "#Obtaining distribution of age for different input parameters\n",
    "t_age = Parallel(n_jobs=n_cores,verbose=5)(delayed(age)(len_min[i],dist[i],i_angle[i],v_range_cm[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(t_age,50)\n",
    "low_lim = np.percentile(t_age,16)\n",
    "high_lim = np.percentile(t_age,84)\n",
    "tsmax_sim = np.percentile(t_age,95)\n",
    "tsabs_sim = np.percentile(t_age,99.9)\n",
    "print('Median =',median,'Lower limit = ',low_lim,'Upper limit = ',high_lim, 'Absolute upper limit:',tsabs_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e745269b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 0.12234532613196332 Lower limit =  0.09352310247000262 Upper limit =  0.2162871677167302\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "print('Median =',median,'Lower limit = ',low_lim,'Upper limit = ',high_lim)\n",
    "histplot = plt.hist(t_age,bins=70,color='royalblue',edgecolor='blue',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('Age [Myr]', fontsize=12)\n",
    "plt.xlim(0,1.3)\n",
    "#plt.title(str(name))\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2f74833",
   "metadata": {},
   "source": [
    "### 4) Jet power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c2ecb96a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "open_angle =  5.472794821496475\n",
      "d =  9.399999999999999\n",
      "elec_density =  510.7095639352123\n",
      "len_min =  16.99751246889851\n",
      "v_range_cm =  24296199.482018065\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 3.0682803696709095e+38 Lower limit =  3.260577845163175e+37 Upper limit =  1.4972040589807843e+39\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "# Generating distribution arrays for measurements\n",
    "open_angle = np.random.uniform(1, o_a, n_iter) #opening angle distribution\n",
    "#Obtaining distribution for different input parameters\n",
    "\n",
    "print('open_angle = ',np.mean(open_angle))\n",
    "print('d = ', d)\n",
    "print('elec_density = ',np.mean(elec_density))\n",
    "print('len_min = ',np.mean(len_min))\n",
    "print('v_range_cm = ',np.mean(v_range_cm))\n",
    "\n",
    "\n",
    "power_j = Parallel(n_jobs=n_cores,verbose=5)(delayed(power)(open_angle[i],d,elec_density[i],len_min[i],v_range_cm[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(power_j,50)\n",
    "low_lim = np.percentile(power_j,16)\n",
    "high_lim = np.percentile(power_j,84)\n",
    "print('Median =',median,'Lower limit = ',low_lim,'Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4501295f-7ca7-430c-bb78-32d736da3a63",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 5.0214642256473265e+37 Lower limit =  5.279678971109995e+36 Upper limit =  2.385576977923226e+38\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "power_juv = Parallel(n_jobs=n_cores,verbose=5)(delayed(power)(open_angle[i],d,elec_densityuv[i],len_min[i],v_range_cm[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(power_juv,50)\n",
    "low_lim = np.percentile(power_juv,16)\n",
    "high_lim = np.percentile(power_juv,84)\n",
    "print('Median =',median,'Lower limit = ',low_lim,'Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "ea525113",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "histplot = plt.hist(power_j,bins=70,color='royalblue',edgecolor='blue',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('Power', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "#plt.title(str(name))\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e1320ae-010e-452c-ab58-ddb96d4c545e",
   "metadata": {},
   "source": [
    "##### 4A) Total injected power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "0a93b23d-e3a8-40ef-ae81-bbc7f9e28bdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.515187397324081e+47\n"
     ]
    }
   ],
   "source": [
    "def totalpower(Pjet,jet_age):\n",
    "    Ptot = Pjet*jet_age \n",
    "    return Ptot\n",
    "\n",
    "powtot = totalpower(Qjetmin,tsmin)\n",
    "print(powtot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8b226c34-6729-4e72-9407-9fc9ded587ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 1.26901174626673e+45 Lower limit =  1.806535849000671e+44 Upper limit =  4.9788155600668986e+45\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.1s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.1s finished\n"
     ]
    }
   ],
   "source": [
    "totpower_j = Parallel(n_jobs=n_cores,verbose=5)(delayed(totalpower)(power_j[i], t_age[i]) for i in range(n_iter))\n",
    "median = np.percentile(totpower_j,50)\n",
    "low_lim = np.percentile(totpower_j,16)\n",
    "high_lim = np.percentile(totpower_j,84)\n",
    "print('Median =',median*(365.0*24.0*60.0*60.0),'Lower limit = ',low_lim*(365.0*24.0*60.0*60.0),'Upper limit = ',high_lim*(365.0*24.0*60.0*60.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4702b786-4495-4730-84d0-15b476cf3301",
   "metadata": {},
   "source": [
    "##### 4B) Jet pressure\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4bcfc08b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.2s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 2.0161527766525957e-10 Lower limit =  2.8220484815652916e-11 Upper limit =  7.762809643842584e-10\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "press_j = Parallel(n_jobs=n_cores,verbose=5)(delayed(press)(open_angle[i],d,elec_density[i],len_min[i],v_range_cm[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(press_j,50)\n",
    "low_lim = np.percentile(press_j,16)\n",
    "high_lim = np.percentile(press_j,84)\n",
    "print('Median =',median,'Lower limit = ',low_lim,'Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cb1a4389",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "#print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)\n",
    "histplot = plt.hist(press_j,bins=70,color='royalblue',edgecolor='blue',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('Pressure', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "#plt.title(str(name))\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cb8fa50",
   "metadata": {},
   "source": [
    "### 5) Pseudo constant\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1d35803a",
   "metadata": {},
   "outputs": [],
   "source": [
    "open_a = np.random.uniform(1,o_a, n_iter) #opening angle\n",
    "g_c = np.random.uniform(4/3,5/3, n_iter) \n",
    "g_j = np.random.uniform(4/3,5/3, n_iter) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3ef3ed5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.396947195498367 ; Lower limit =  3.673687969405048 ; Upper limit =  6.106664684788413\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "ce_1 = Parallel(n_jobs=n_cores,verbose=5)(delayed(C_cons)(g_c[i],g_j[i],(5.0/3),open_a[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(ce_1,50)\n",
    "low_lim = np.percentile(ce_1,16)\n",
    "high_lim = np.percentile(ce_1,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4a4fd0db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.396947195498367 ; Lower limit =  3.673687969405048 ; Upper limit =  6.106664684788413\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)\n",
    "histplot = plt.hist(ce_1,bins=70,color='royalblue',edgecolor='blue',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('C1 constant', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "plt.title('Varying all three')\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "85380a56",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.228298243302703 ; Lower limit =  3.5246880761027373 ; Upper limit =  5.879026958634341\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "ce_1 = Parallel(n_jobs=n_cores,verbose=5)(delayed(C_cons)(g_c[i],(5.0/3),(5.0/3),open_a[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(ce_1,50)\n",
    "low_lim = np.percentile(ce_1,16)\n",
    "high_lim = np.percentile(ce_1,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "474d0cbd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.228298243302703 ; Lower limit =  3.5246880761027373 ; Upper limit =  5.879026958634341\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#PLOT\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)\n",
    "histplot = plt.hist(ce_1,bins=70,color='Purple',edgecolor='black',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('C1 constant', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "plt.title('Without varying g_j')\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "eb459401",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.2s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.39711184147335 ; Lower limit =  3.67731407934992 ; Upper limit =  6.106505571194216\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.3s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.3s finished\n"
     ]
    }
   ],
   "source": [
    "ce_1 = Parallel(n_jobs=n_cores,verbose=5)(delayed(C_cons)((5.0/3),g_j[i],(5.0/3),open_a[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(ce_1,50)\n",
    "low_lim = np.percentile(ce_1,16)\n",
    "high_lim = np.percentile(ce_1,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "cd3ec772",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 4.39711184147335 ; Lower limit =  3.67731407934992 ; Upper limit =  6.106505571194216\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#PLOT\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)\n",
    "histplot = plt.hist(ce_1,bins=70,color='pink',edgecolor='magenta',density=True,alpha=0.7)\n",
    "plt.vlines([low_lim,high_lim],0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.vlines(median,0,max(histplot[0])*1.1,linestyles=':',colors='midnightblue')\n",
    "plt.ylim(0,max(histplot[0])*1.1)\n",
    "plt.ylabel('Probability density', fontsize=12)\n",
    "plt.xlabel('C1 constant', fontsize=12)\n",
    "#plt.xlim(0,400)\n",
    "plt.title('Without varying g_c')\n",
    "plt.minorticks_on()\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.tick_params(axis='both', which='major', length=9)\n",
    "plt.tick_params(axis='both', which='minor', length=4.5)\n",
    "plt.tick_params(axis='both', which='both',direction='in',right=True,top=True)\n",
    "#plt.savefig(str(name)+'_peculiar_velocity.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf539f33",
   "metadata": {},
   "source": [
    "# Other simple jet estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf14c1b2",
   "metadata": {},
   "source": [
    "### 1) Enthalpy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18da7e40",
   "metadata": {},
   "source": [
    "Often in the AGN community the jet power is estimated by calculating the enthalpy and dividing by an appropriate timescale. Enthalpy is defined as  $dH = dU + pdV$ (from thermodynamics). It includes the energy stored in a volume and the work done in excavating it, so it measures the total energy/heat input by the jet. \n",
    "\n",
    "Enthalpy of an ideal gas with adiabatic index $\\gamma$ is given by \n",
    "$$\n",
    "H = U + P V = \\frac{PV}{(\\gamma -1)} + PV \n",
    "$$\n",
    "which for non-relavistic ideal gas comes out as $H= 4 PV$. The jet power is thus\n",
    "\n",
    "$$\n",
    "Q = \\frac{4PV}{\\tau}\n",
    "$$\n",
    "\n",
    "where: \n",
    "* $P$ is the the pressure from the minimum energy condition applied to synchrotron emission from the lobes\n",
    "* $V$ is the the volume from assuming a spherical bubble with radius equal to the approximate radius of the bubble near GRS 1915\n",
    "* $\\tau$ is the the jet age from the jet length divided by the bow shock velocity \n",
    "\n",
    "From above we have that the minimum energy pressure in the lobe is $P \\sim 1.3\\times 10^{-12}~{\\rm erg~s^{-1}}$. \n",
    "\n",
    "We assume that the lobe is a cylinder with length equal to the source-to-bow shock distance, and width equal to the lobe width. \n",
    "\n",
    "This implies a volume of the order $10^{60}$ cm$^3$. \n",
    "The (upper limit to the) jet age $\\tau$ is around $1.1$ Myr from the self-similar estimate (but this is the same order  as just lengh/shock velocity $L/\\dot{L}$. \n",
    "\n",
    "Putting this all together we get:\n",
    "$$\n",
    "Q  \\sim 1.2\\times 10^{35}~{\\rm erg~s}^{-1} \n",
    "$$\n",
    "which is not too far our estimate from the self-similar model. Note that this is a lower limit because we used an upper limit for $\\tau$. Additioanlly, it's easy for this to be higher, as a the presence of a non radiating pressure component (and/or a non volume filling synchrotron plasma) would increase the value. \n",
    "\n",
    "If we take the pressure from the self-similar model (but on this case the estimate is not indipendent any more), then the pressure inside the lobe is $P \\sim 3.6\\times 10^{-11}~{\\rm erg~s^{-1}}$, and the enthaly becomes: \n",
    "$$\n",
    "Q  \\sim 3.6\\times 10^{36}~{\\rm erg~s}^{-1} \n",
    "$$\n",
    "\n",
    "In the simulation below we see that if we calculate properly the limits, this estimate is perfectly consistent with the jet energy estimated in the self similar model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fab5cfe5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lobe Volume ellipsoidal [cm**3] ~  5.993e+59\n",
      "Lobe Volume cylinder [cm**3] ~  8.990e+59\n",
      "Average jet power (ellipsoidal) [erg/s] (H) ~  2.558e+35\n",
      "Average jet power (cylinder) [erg/s] (H) ~  3.837e+35\n"
     ]
    }
   ],
   "source": [
    "def enthalpy(P,Vlobe,tau):\n",
    "    QH = 4*P*Vlobe/tau\n",
    "    return QH\n",
    "\n",
    "\n",
    "P = pminlobe\n",
    "Llobe = discm\n",
    "tau = tsmax_sim*(365.*24.*60*60)*1.0E+6\n",
    "Blobe = lobesizecm\n",
    "VlobeCyl = np.pi*(Llobe)*(Blobe/2)**2     # Assuming that the volume here is cylinder\n",
    "                                       # with length equal to the source-to-bow shock\n",
    "                                       # distance, and the width is the lobe width.  \n",
    "\n",
    "Vlobe = 4/3*np.pi*(Llobe/2)*(Blobe/2)**2 # Assuming that the volume here is an ellipsoidal shape\n",
    "                                        # with length equal to the source-to-bow shock\n",
    "                                        # distance, and the width is the lobe width.  \n",
    "\n",
    "QH  = enthalpy(P,Vlobe,tau)\n",
    "QHcyl  = enthalpy(P,VlobeCyl,tau)\n",
    "\n",
    "print('Lobe Volume ellipsoidal [cm**3] ~ ', '{:.3e}'.format(Vlobe))\n",
    "print('Lobe Volume cylinder [cm**3] ~ ', '{:.3e}'.format(VlobeCyl))\n",
    "\n",
    "print('Average jet power (ellipsoidal) [erg/s] (H) ~ ', '{:.3e}'.format(QH))\n",
    "print('Average jet power (cylinder) [erg/s] (H) ~ ', '{:.3e}'.format(QHcyl))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d6b1c9aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Using backend LokyBackend with 16 concurrent workers.\n",
      "[Parallel(n_jobs=16)]: Done  48 tasks      | elapsed:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 512 tasks      | elapsed:    0.1s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median = 1.1571428609442019e+38 ; Lower limit =  1.2259114908620877e+37 ; Upper limit =  5.6758417655665575e+38\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=16)]: Done 4224 tasks      | elapsed:    0.1s\n",
      "[Parallel(n_jobs=16)]: Done 4969 out of 5000 | elapsed:    0.2s remaining:    0.0s\n",
      "[Parallel(n_jobs=16)]: Done 5000 out of 5000 | elapsed:    0.2s finished\n"
     ]
    }
   ],
   "source": [
    "tau = np.multiply(t_age,(365.0*24.0*60.0*60.0)*1.0E+6)\n",
    "\n",
    "QHdis = Parallel(n_jobs=n_cores,verbose=5)(delayed(enthalpy)(press_j[i],Vlobe,tau[i]) for i in range(n_iter))\n",
    "\n",
    "median = np.percentile(QHdis,50)\n",
    "low_lim = np.percentile(QHdis,16)\n",
    "high_lim = np.percentile(QHdis,84)\n",
    "print('Median =',median,'; Lower limit = ',low_lim,'; Upper limit = ',high_lim)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68896132",
   "metadata": {},
   "source": [
    "### 2) The \"Hotspot Method\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e98976",
   "metadata": {},
   "source": [
    "Under the assumption of equipartition, Godfrey and Shabala (https://arxiv.org/abs/1301.3499) give the hotspot power as \n",
    "\n",
    "$$\n",
    "Q_{\\rm GS} = A c \\frac{B_{\\rm eq}^2}{8\\pi} g\n",
    "$$\n",
    "\n",
    "where $g$ is a complicated expression which we could evaluate, but for the simplicity's sake we will take their estimate of $g \\approx 2$ from the AGN case. $A$ is the area of the hotspot surface, which we will assume is a circular surface with radius $R \\approx 7.6 \\times 10^{18}~{\\rm cm}$ based on the are of the elongated feature north-west from the IRAS region. The minimum energy magnetic field as estimated above is as $22~{\\rm \\mu G}$. \n",
    "We thus have: \n",
    "\n",
    "$$\n",
    "Q_{\\rm GS} = A c \\frac{B_{\\rm eq}^2}{8\\pi} = 2 \\pi R^2 c \\frac{B_{\\rm eq}^2}{8\\pi} \\sim 1.7 \\times 10^{36}~{\\rm erg~s}^{-1}\n",
    "$$\n",
    "\n",
    "We note that this is once more a lover limit, and, again, departures from equipartition will increase this estimate, which is already remarkably consistent with the \"average\" power estimate above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "640e9c7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hotspotpower(rcyl,lencyl,Bmin):\n",
    "    A = 2*rcyl*lencyl\n",
    "    QHS =  A*c*Bmin**2/(8*np.pi)\n",
    "    return QHS\n",
    "\n",
    "QHS = hotspotpower(rcylcm,lencylcm,Bmin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "1c61c490",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average jet power (GS) ~ 1.727e+36\n"
     ]
    }
   ],
   "source": [
    "print('Average jet power (GS) ~', '{:.3e}'.format(QHS))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d0ef941",
   "metadata": {},
   "source": [
    "(No simulation here 'cause there's no distribution to build)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9703a3c0-4ad1-4fdd-96f3-604a955d5ead",
   "metadata": {},
   "source": [
    "## Jet power constraint from proper motion time "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "34f636d3-7454-4c0c-ac24-737d2d165a74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">> Lower limit on Temperature as set by the proper motion (0.17 My to slice through IRAS) ~ 7.656e+05\n"
     ]
    }
   ],
   "source": [
    "disasec =disamin*60 #lobe target seperation in arcsec (projected)\n",
    "dispc = disasec*d10*10*1e3*4.8*1e-6  #lobe target separation in pc (projected)\n",
    "discmP = dispc*pc #lobe target sepeartion in cm (projected)\n",
    "discm = discmP/np.sin(incl*np.pi/180) #lobe target de-projected seperation to account for the inclination angle\n",
    "\n",
    "L = discm\n",
    "tauup = 0.17*(365.*24.*60*60)*1.0E+6           #upper limit to jet age\n",
    "Tlow = ((3*L/(5*tauup))**2)*((3*mh)/(16*kb))  #lower limit to temperature\n",
    "neup = nesph(d10*10,Firas,Riras,Tlow,nu,Z)\n",
    "\n",
    "print('>> Lower limit on Temperature as set by the proper motion (0.17 My to slice through IRAS) ~','{:.3e}'.format(Tlow))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f486d5f9",
   "metadata": {},
   "source": [
    "### All the important quantities in one place"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d93fa8f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---- IRAS ---- \n",
      "IRAS diameter [arcsec and pc] = 3.600e+01  and  1.624e+00\n",
      "IRAS volume [cm] = 6.595e+55\n",
      "IRAS flux density [mJy] = 5.700e+01\n",
      "Electron temperature [K] = 1.000e+04 - 3.000e+06\n",
      "Shock-compressed Electron density [particles/cm3] = 3.916e+02 - 6.250e+02\n",
      "Pre-Shock Electron density [particles/cm3] = 9.789e+01 - 1.563e+02\n",
      "Shock velocity [Km/s] = 2.098e+01 - 3.633e+02\n",
      "Pressure inside IRAS (ideal gas conditions) [erg/cm3] (Pideal) =  2.543e-10  and  7.630e-08\n",
      "Pressure in ISM (ideal gas conditions) [erg/cm3] = 1.272e-12\n",
      "\n",
      " ---- Hot spot (Cylinder)----\n",
      "Cylinder flux density [mJy] = 5.200e+00\n",
      "Cylinder Integrated Luminosity [erg/s] (Lcy) = 1.998e+29\n",
      "Cylinder radius [arcsec and pc] = 3.900e+00  and  1.760e-01\n",
      "Cylinder length [arcsec and pc] = 1.740e+01  and  9.065e-01\n",
      "Cylinder Volume [cm3] =  and  2.592e+54\n",
      "Cylinder pressure [erg/cm3]  ~ 1.488e-11\n",
      "Cylinder magnetic field density [G] =  2.182e-05\n",
      "\n",
      " ---- Lobe ----\n",
      "Lobe flux density [mJy] = 1.500e-01\n",
      "Source-ring separation (projected) [arcsec and pc] ~  and  1.700e+01 4.602e+01\n",
      "Lobe diameter [arcmin and pc]  = 1.000e+01  and  2.707e+01\n",
      "Ring thickness [arcsec and pc] = 6.000e+01  and 2.707e+00\n",
      "Lobe Volume [cm**3] ~  5.993e+59\n",
      "Equipartition lobe pressure [erg/cm3] = 1.271e-12\n",
      "Jet pressure [erg/cm3] ~  2.258e-12\n",
      "Equipartition lobe magnetic field [G] = 6.377e-06\n",
      "\n",
      " ---- Energetics -----\n",
      "Jet age [Myr] = 9.352e-02  and  2.163e-01\n",
      "Jet power [erg/s]  ~  3.261e+37  and  1.497e+39\n",
      "Jet power Enthalpy [erg/s]  ~  1.226e+37  and  5.676e+38\n",
      "Jet power Hot Spot [erg/s]  ~  1.727e+36\n",
      "Jet pressure (inside IRAS) [erg/cm3] =  2.822e-11 - 7.763e-10\n",
      "Pseudo constant C  ~  3.302e+00  and  9.028e+00\n"
     ]
    }
   ],
   "source": [
    "print('---- IRAS ---- ')\n",
    "\n",
    "print('IRAS diameter [arcsec and pc] =', '{:.3e}'.format(Riras),' and ','{:.3e}'.format(Rirascm/pc))\n",
    "print('IRAS volume [cm] =', '{:.3e}'.format(Volsph))\n",
    "print('IRAS flux density [mJy] =','{:.3e}'.format(Firas*1000))\n",
    "print('Electron temperature [K] =','{:.3e}'.format(min(T_axis)),'-','{:.3e}'.format(max(T_axis)))\n",
    "print('Shock-compressed Electron density [particles/cm3] =','{:.3e}'.format(np.percentile(elec_density,16)),'-','{:.3e}'.format(np.percentile(elec_density,84)))\n",
    "print('Pre-Shock Electron density [particles/cm3] =','{:.3e}'.format(np.percentile(elec_density,16)/4),'-','{:.3e}'.format(np.percentile(elec_density,84)/4))\n",
    "\n",
    "print('Shock velocity [Km/s] =','{:.3e}'.format(min(v_range)),'-','{:.3e}'.format(max(v_range)))\n",
    "print('Pressure inside IRAS (ideal gas conditions) [erg/cm3] (Pideal) = ', '{:.3e}'.format(pidealmin),' and ', '{:.3e}'.format(pidealmax))\n",
    "\n",
    "print('Pressure in ISM (ideal gas conditions) [erg/cm3] =', '{:.3e}'.format(pidealunsh))\n",
    "\n",
    "\n",
    "print('\\n','---- Hot spot (Cylinder)----')\n",
    "\n",
    "print('Cylinder flux density [mJy] =','{:.3e}'.format(Fcyl*1000))\n",
    "print('Cylinder Integrated Luminosity [erg/s] (Lcy) =','{:.3e}'.format(Lcy))\n",
    "print('Cylinder radius [arcsec and pc] =','{:.3e}'.format(rcyl),' and ', '{:.3e}'.format(rcylcm/pc))\n",
    "print('Cylinder length [arcsec and pc] =','{:.3e}'.format(lencyl),' and ','{:.3e}'.format(lencylcm/pc))\n",
    "print('Cylinder Volume [cm3] =',' and ','{:.3e}'.format(VolCyl))\n",
    "print('Cylinder pressure [erg/cm3]  ~','{:.3e}'.format(pmincyl))\n",
    "print('Cylinder magnetic field density [G] = ','{:.3e}'.format(Bmin))\n",
    "\n",
    "\n",
    "print('\\n','---- Lobe ----')\n",
    "\n",
    "print('Lobe flux density [mJy] =','{:.3e}'.format(Flobe*1000))\n",
    "print('Source-ring separation (projected) [arcsec and pc] ~',' and ','{:.3e}'.format(disamin),'{:.3e}'.format(dispc))\n",
    "print('Lobe diameter [arcmin and pc]  =', '{:.3e}'.format(theam),' and ','{:.3e}'.format(lobesizecm/pc))\n",
    "print('Ring thickness [arcsec and pc] =','{:.3e}'.format(DR),' and','{:.3e}'.format(DRcm/pc))\n",
    "print('Lobe Volume [cm**3] ~ ', '{:.3e}'.format(Vlobe))\n",
    "print('Equipartition lobe pressure [erg/cm3] =','{:.3e}'.format(pminlobe))\n",
    "print('Jet pressure [erg/cm3] ~ ','{:.3e}'.format(pminjet))\n",
    "print('Equipartition lobe magnetic field [G] =','{:.3e}'.format(Bminlobe))\n",
    "\n",
    "print('\\n','---- Energetics -----')\n",
    "\n",
    "print('Jet age [Myr] =','{:.3e}'.format(np.percentile(t_age,16)),' and ','{:.3e}'.format(np.percentile(t_age,84)))\n",
    "print('Jet power [erg/s]  ~ ','{:.3e}'.format(np.percentile(power_j,16)),' and ','{:.3e}'.format(np.percentile(power_j,84)))\n",
    "print('Jet power Enthalpy [erg/s]  ~ ','{:.3e}'.format(np.percentile(QHdis,16)),' and ','{:.3e}'.format(np.percentile(QHdis,84)))\n",
    "print('Jet power Hot Spot [erg/s]  ~ ', '{:.3e}'.format(QHS))\n",
    "print('Jet pressure (inside IRAS) [erg/cm3] = ', '{:.3e}'.format(np.percentile(press_j,16)),'-','{:.3e}'.format(np.percentile(press_j,84)))\n",
    "print('Pseudo constant C  ~ ','{:.3e}'.format(min(ce_1)),' and ','{:.3e}'.format(max(ce_1)))\n",
    "\n"
   ]
  }
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