{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果某质量为m的天体，从无穷远处到被黑洞吸积到最小稳定轨道（3Rs），释放的能量是多少?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$R_s = \\frac{2GM_{BH}}{c^2}$ <p>\n",
    "$\\Delta E = \\frac{GM_{BH}m}{3R_s} = \\frac{mc^2}{6}$ <p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果一个星系中的AGN光度超过恒星光度，其黑洞质量与恒星质量的比值最低是多少？ <p>\n",
    "• 假设该星系恒星质量的质光比~3M☉/L☉"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$L_{AGN} = L_{Edd} = 1.3 \\times 10^{38} (\\frac{M_{BH}}{M_{\\odot}})$ <p>\n",
    "$L_{star} = 3.846 \\times 10^{33} (\\frac{M_{star}}{3M_{\\odot}}) = 1.282 \\times 10^{33} (\\frac{M_{star}}{M_{\\odot}})$ <p>\n",
    "两者相当时，得 <p>\n",
    "$\\frac{M_{BH}}{M_{star}} = 10^{-5}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于作业5中的星系（或选择一个新的低红移星系），将其人为放置到更高红移处，生成在同样望远镜观测中的图像（可选多波段，并考虑K改正效应）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from astropy.io import fits\n",
    "from astropy.wcs import WCS\n",
    "\n",
    "with fits.open(\"frame-r-004874-3-0692.fits\") as hdul:\n",
    "    image_data_sdss = hdul[0].data\n",
    "    wcs_sdss = WCS(hdul[0].header)\n",
    "\n",
    "ra, dec = 40.669622, -0.013294\n",
    "cutout_size_sdss = 50\n",
    "\n",
    "center_pixel = wcs_sdss.world_to_pixel_values(ra, dec)\n",
    "x_center, y_center = int(center_pixel[0]), int(center_pixel[1])\n",
    "\n",
    "\n",
    "x_min, x_max = x_center - cutout_size_sdss, x_center + cutout_size_sdss\n",
    "y_min, y_max = y_center - cutout_size_sdss, y_center + cutout_size_sdss\n",
    "\n",
    "cutout_data_sdss = image_data_sdss[y_min:y_max, x_min:x_max].T\n",
    "cutout_data_sdss = cutout_data_sdss[:, ::-1] * 3.631e-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import LogNorm\n",
    "from matplotlib.gridspec import GridSpec\n",
    "\n",
    "fig,ax = plt.subplots(1, 1)\n",
    "\n",
    "vmin = np.percentile(cutout_data_sdss, 5)\n",
    "vmax = np.percentile(cutout_data_sdss, 99)\n",
    "\n",
    "im2 = ax.imshow(cutout_data_sdss, origin='lower', cmap='gray', vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"SDSS\")\n",
    "ax.set_xlabel(\"X\")\n",
    "ax.set_ylabel(\"Y\")\n",
    "\n",
    "cbar = fig.colorbar(im2, ax=ax, orientation='vertical', fraction=0.05, pad=0.04)\n",
    "cbar.set_label(\"Flux (Jy)\", fontsize=12)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy.cosmology import Planck18 as cosmo\n",
    "\n",
    "z_0 = 0.003793\n",
    "z_target = 2.0\n",
    "\n",
    "def K_correction(z):\n",
    "    return 5 * np.log10(1 + z)\n",
    "\n",
    "k_corr = K_correction(z_target)\n",
    "\n",
    "distance_0 = cosmo.comoving_distance(z_0).value\n",
    "distance_target = cosmo.comoving_distance(z_target).value\n",
    "\n",
    "m_0 = -2.5 * np.log10(cutout_data_sdss / 3631)\n",
    "m_z = m_0 - 5 * np.log(distance_0 / distance_target) + k_corr\n",
    "adjusted_image_data = 3631 * 10**(-m_z / 2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1, 1)\n",
    "\n",
    "vmin = np.percentile(adjusted_image_data, 5)\n",
    "vmax = np.percentile(adjusted_image_data, 99)\n",
    "\n",
    "im2 = ax.imshow(adjusted_image_data, origin='lower', cmap='gray', vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"SDSS_z\")\n",
    "ax.set_xlabel(\"X\")\n",
    "ax.set_ylabel(\"Y\")\n",
    "\n",
    "cbar = fig.colorbar(im2, ax=ax, orientation='vertical', fraction=0.05, pad=0.04)\n",
    "cbar.set_label(\"Flux (Jy)\", fontsize=12)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于作业5或者作业15中的星系，采取至少一种方法来（定量）评估该星系所处的环境。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distance from NGC 1275 to PGC 12405: 11.67 Mpc\n",
      "Distance from NGC 1275 to PGC 12441: 0.27 Mpc\n",
      "Distance from NGC 1275 to NGC 1272: 21.75 Mpc\n",
      "Distance from NGC 1275 to NGC 1273: 1.05 Mpc\n",
      "Distance from NGC 1275 to NGC 1274: 16.52 Mpc\n",
      "Distance from NGC 1275 to NGC 1277: 4.05 Mpc\n",
      "Distance from NGC 1275 to NGC 1278: 11.61 Mpc\n",
      "Distance from NGC 1275 to NGC 1279: 29.09 Mpc\n",
      "Distance from NGC 1275 to NGC 1281: 15.81 Mpc\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import astropy.units as u\n",
    "from astroquery.ned import Ned\n",
    "from astropy.coordinates import SkyCoord\n",
    "from astropy.cosmology import Planck18 as cosmo\n",
    "\n",
    "def galaxy_distance(ra, dec, z, search_radius=1.0, data_ra=None, data_dec=None, data_z=None):\n",
    "    distance_target = cosmo.comoving_distance(z)  # in Mpc\n",
    "\n",
    "    target_coord = SkyCoord(ra=ra * u.deg, dec=dec * u.deg, frame='icrs')\n",
    "    data_coords = SkyCoord(ra=data_ra * u.deg, dec=data_dec * u.deg, frame='icrs')\n",
    "\n",
    "    angular_sep = target_coord.separation(data_coords)\n",
    "\n",
    "    distances = cosmo.comoving_distance(data_z)  # in Mpc\n",
    "\n",
    "    R = np.sqrt(distance_target.value**2 + distances.value**2 - \n",
    "                2 * distance_target.value * distances.value * np.cos(angular_sep.radian))\n",
    "\n",
    "    return R\n",
    "\n",
    "#NGC 1275 in Perseus cluster\n",
    "target_name = \"NGC 1275\"\n",
    "target_result_table = Ned.query_object(target_name)\n",
    "target_ra = target_result_table['RA'][0]\n",
    "target_dec = target_result_table['DEC'][0]\n",
    "target_z = target_result_table['Redshift'][0]\n",
    "\n",
    "# Surrounding galaxies in SDSS\n",
    "object_names = [\"PGC 12405\", \"PGC 12441\", \"NGC 1272\", \"NGC 1273\", \"NGC 1274\", \"NGC 1277\", \"NGC 1278\", \"NGC 1279\", \"NGC 1281\"]\n",
    "\n",
    "data_ra = []\n",
    "data_dec = []\n",
    "data_z = []\n",
    "\n",
    "for object_name in object_names:\n",
    "    result_table = Ned.query_object(object_name)\n",
    "    \n",
    "    ra = result_table['RA'][0]\n",
    "    dec = result_table['DEC'][0]\n",
    "    redshift = result_table['Redshift'][0]\n",
    "    \n",
    "    data_ra.append(ra)\n",
    "    data_dec.append(dec)\n",
    "    data_z.append(redshift)\n",
    "\n",
    "data_ra = np.array(data_ra)\n",
    "data_dec = np.array(data_dec)\n",
    "data_z = np.array(data_z)\n",
    "\n",
    "distances = galaxy_distance(target_ra, target_dec, target_z, \n",
    "                            search_radius=5.0, \n",
    "                            data_ra=data_ra, \n",
    "                            data_dec=data_dec, \n",
    "                            data_z=data_z)\n",
    "\n",
    "for i, name in enumerate(object_names):\n",
    "    print(f\"Distance from {target_name} to {name}: {distances[i]:.2f} Mpc\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从sdss巡天图中找出Perseus中心星系NGC 1275周围的几个星系，但算出的与NGC 1275的距离似乎有点远，基本超出了星系团的范围"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
