AAA_Final_Kapahi_NED.ipynb

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  {
   "cell_type": "raw",
   "id": "82649843-98ae-4e78-9e66-51652970b59d",
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   "source": [
    "Go to CasJobs and query the database for galaxy redshifts and angular size (Petrosian Radii)\n",
    "https://skyserver.sdss.org/CasJobs/SubmitJob.aspx\n",
    "SELECT\n",
    "    s.z AS Redshift,\n",
    "    p.petroRad_r as petroRad_r\n",
    "FROM\n",
    "    PhotoObj p\n",
    "JOIN\n",
    "    SpecObj s ON p.objID = s.bestObjID\n",
    "WHERE\n",
    "    s.class = 'GALAXY'\n",
    "    AND s.zWarning = 0\n",
    "    AND p.petroRad_r IS NOT NULL\n",
    "\n",
    "    \n",
    "Redshift\tpetroRad_r\n",
    "0.4906398\t2.997337\n",
    "0.5672536\t2.447188\n",
    "0.08190863\t5.863024\n",
    "0.2527134\t3.93891\n",
    "0.5479502\t3.284203\n",
    "0.1405521\t2.872508    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9e30169-6afb-48f5-bf81-6a4b65137f81",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Re-import necessary libraries due to code reset\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# Load the data\n",
    "file_path = \"./KapahiData/MyResult_20241226.csv\"\n",
    "data = pd.read_csv(file_path, delimiter=\",\")  # Assuming tab-separated values; adjust if different\n",
    "print(\"Number of Galaxies =\", len(data))\n",
    "# Bin the data by redshift\n",
    "bins = pd.interval_range(start=0, end=1, freq=0.1)  # Adjust the range and bin size as needed\n",
    "data['Redshift_bin'] = pd.cut(data['Redshift'], bins=bins)\n",
    "\n",
    "# Calculate the median PetroRad_r for each bin\n",
    "binned_data = data.groupby('Redshift_bin')['petroRad_r'].median().reset_index()\n",
    "binned_data.columns = ['Redshift_bin', 'Median_petroRad_r']\n",
    "\n",
    "# Define the model function A + Bz\n",
    "def size_model(z, A, B):\n",
    "    return A + B*z\n",
    "\n",
    "# Extract the midpoint of the redshift bins as numeric values\n",
    "x_data = binned_data['Redshift_bin'].apply(lambda x: x.mid).astype(float)\n",
    "y_data = np.log(binned_data['Median_petroRad_r'].values)\n",
    "\n",
    "# Perform the curve fitting\n",
    "params, covariance = curve_fit(size_model, x_data, y_data)\n",
    "A_fit, B_fit = params\n",
    "\n",
    "# Generate a smooth curve for the fit\n",
    "z_fit = np.linspace(min(x_data), max(x_data), 100)\n",
    "petroRad_fit = size_model(z_fit, A_fit, B_fit)\n",
    "\n",
    "# Plot the original data and the fit\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(x_data, y_data, 'o', label=\"Binned Data (Log of Median PetroRad_r)\", markersize=8)\n",
    "plt.plot(z_fit, petroRad_fit, '-', label=f\"Fit: $A + Bz$ (A = {A_fit:.2f}, B = {B_fit:.2f})\", linewidth=2)\n",
    "plt.xlabel(\"Redshift (z)\", fontsize=14)\n",
    "plt.ylabel(\"Log of Median PetroRad_r (arcseconds)\", fontsize=14)\n",
    "plt.title(\"Fit: Galaxy Size vs. Redshift (Log Space)\", fontsize=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.grid()\n",
    "plt.savefig(\"./Drawing_For_Publications/Kapahi_SDSSMedian.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "954e459a-d22a-4b2a-a791-0ac442dd5d30",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "\n",
    "# Constants for Lambda-CDM cosmology\n",
    "c = 3e5  # Speed of light in km/s\n",
    "H0 = 70  # Hubble constant in km/s/Mpc\n",
    "Omega_m = 0.3  # Matter density parameter\n",
    "Omega_Lambda = 1 - Omega_m  # Dark energy density parameter\n",
    "\n",
    "# Angular diameter distance function\n",
    "def angular_diameter_distance(z):\n",
    "    # Integrand for the comoving distance\n",
    "    def integrand(z_prime):\n",
    "        return 1.0 / np.sqrt(Omega_m * (1 + z_prime)**3 + Omega_Lambda)\n",
    "    \n",
    "    # Perform the integral from 0 to z\n",
    "    comoving_distance, _ = quad(integrand, 0, z)\n",
    "    # Convert to angular diameter distance\n",
    "    return (c / H0) * comoving_distance / (1 + z)\n",
    "\n",
    "# Define the redshift range\n",
    "z_values = np.linspace(0.01, 2, 100)\n",
    "\n",
    "# Calculate angular diameter distances for the redshift range\n",
    "d_A_values = np.array([angular_diameter_distance(z) for z in z_values])\n",
    "\n",
    "# Assume a proper size of the galaxies (in kpc)\n",
    "L = 10  # Proper size in kpc\n",
    "\n",
    "# Convert proper size to angular size (arcseconds)\n",
    "theta_values = (L / d_A_values) * 206265  # Convert radians to arcseconds\n",
    "\n",
    "# Plot the angular size as a function of redshift\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(z_values, theta_values, label=\"L-CDM Prediction\", color='orange', linewidth=2)\n",
    "plt.plot(x_data, y_data, 'o', label=\"Binned Data (Log of Mean PetroRad_r)\", markersize=8)\n",
    "plt.plot(z_fit, petroRad_fit, '-', label=f\"Fit: $A + Bz$ (A = {A_fit:.2f}, B = {B_fit:.2f})\", linewidth=2)\n",
    "plt.xlabel(\"Redshift (z)\", fontsize=14)\n",
    "plt.ylabel(\"Angular Size (arcseconds)\", fontsize=14)\n",
    "plt.title(\"Angular Size vs. Redshift in L-CDM Cosmology\", fontsize=16)\n",
    "plt.grid(True)\n",
    "# plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend(fontsize=12)\n",
    "plt.savefig(\"./Drawing_For_Publications/Kapahi_SDSSMedianVS_LCDM.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d66cdef7-d8af-44c9-b46e-ab4ac67c7fad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Re-import necessary libraries due to code reset\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# Load the data\n",
    "file_path = \"./KapahiData/MyResult_20241226.csv\"\n",
    "data = pd.read_csv(file_path, delimiter=\",\")  # Assuming tab-separated values; adjust if different\n",
    "print(\"Number of Galaxies =\", len(data))\n",
    "# Bin the data by redshift\n",
    "bins = pd.interval_range(start=0, end=1, freq=0.1)  # Adjust the range and bin size as needed\n",
    "data['Redshift_bin'] = pd.cut(data['Redshift'], bins=bins)\n",
    "\n",
    "# Calculate the mean PetroRad_r for each bin\n",
    "binned_data = data.groupby('Redshift_bin')['petroRad_r'].mean().reset_index()\n",
    "binned_data.columns = ['Redshift_bin', 'Mean_petroRad_r']\n",
    "\n",
    "# Define the model function A + Bz\n",
    "def size_model(z, A, B):\n",
    "    return A + B*z\n",
    "\n",
    "# Extract the midpoint of the redshift bins as numeric values\n",
    "x_data = binned_data['Redshift_bin'].apply(lambda x: x.mid).astype(float)\n",
    "y_data = np.log(binned_data['Mean_petroRad_r'].values)\n",
    "\n",
    "# Perform the curve fitting\n",
    "params, covariance = curve_fit(size_model, x_data, y_data)\n",
    "A_fit, B_fit = params\n",
    "\n",
    "# Generate a smooth curve for the fit\n",
    "z_fit = np.linspace(min(x_data), max(x_data), 100)\n",
    "petroRad_fit = size_model(z_fit, A_fit, B_fit)\n",
    "\n",
    "# Plot the original data and the fit\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(x_data, y_data, 'o', label=\"Binned Data (Log of Mean PetroRad_r)\", markersize=8)\n",
    "plt.plot(z_fit, petroRad_fit, '-', label=f\"Fit: $A + Bz$ (A = {A_fit:.2f}, B = {B_fit:.2f})\", linewidth=2)\n",
    "plt.xlabel(\"Redshift (z)\", fontsize=14)\n",
    "plt.ylabel(\"Log of Mean PetroRad_r (arcseconds)\", fontsize=14)\n",
    "plt.title(\"Fit: Galaxy Size vs. Redshift (Log Space)\", fontsize=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.grid()\n",
    "plt.savefig(\"./Drawing_For_Publications/Kapahi_SDSSMean.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "198e02d4-5413-4be4-9c46-22b91c9c7a77",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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