{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy.io import fits\n",
    "from os import path\n",
    "from mgefit.find_galaxy import find_galaxy\n",
    "from astropy.wcs import WCS\n",
    "from astropy import units as u\n",
    "from astropy.coordinates import SkyCoord,ICRS\n",
    "import astropy.constants as constants\n",
    "from scipy.integrate import quad\n",
    "import sympy as sp\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于同一个星系，画出地面望远镜（SDSS or DESI）和空间望远镜（Hubble）的（尽量同一波段）fits图像的对比\n",
    "\n",
    "定出星系的中心（流量最高点）\n",
    "\n",
    "• 计算其赤经赤纬\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pix2radec_legacy(x,y):\n",
    "    xcen_ra_ip = y\n",
    "    ycen_dec_ip = x\n",
    "    file = './NGC1300_DESI_R.fits'\n",
    "    f = fits.open(file)\n",
    "    w = WCS(f[0].header)\n",
    "    sky = w.pixel_to_world(xcen_ra_ip,ycen_dec_ip)   \n",
    "    hmsdms = sky.to_string('hmsdms')\n",
    "    ra = hmsdms.split(\" \")[0]\n",
    "    dec = hmsdms.split(\" \")[1]\n",
    "    print('ra,dec=',ra,dec) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pix2radec_Hubble(x,y):\n",
    "    xcen_ra_ip = y\n",
    "    ycen_dec_ip = x\n",
    "    file = './NGC1300_f606w.fits'\n",
    "    f = fits.open(file)\n",
    "    w = WCS(f[1].header)\n",
    "    sky = w.pixel_to_world(xcen_ra_ip,ycen_dec_ip)   \n",
    "    hmsdms = sky.to_string('hmsdms')\n",
    "    ra = hmsdms.split(\" \")[0]\n",
    "    dec = hmsdms.split(\" \")[1]\n",
    "    print('ra,dec=',ra,dec) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Pixels used: 15366\n",
      " Peak Img[j, k]: 400 400\n",
      " Mean (j, k): 399.26 399.04\n",
      " Theta (deg): 168.6\n",
      " Astro PA (deg): 101.4\n",
      " Eps: 0.437\n",
      " Major axis (pix): 98.8\n",
      "ra,dec= 03h19m41.03669759s -19d24m40.05179998s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "path = './NGC1300_DESI_R'\n",
    "hdu_list = fits.open(path+'.fits', cache=True)\n",
    "img = hdu_list[0].data\n",
    "f = find_galaxy(img, fraction=0.03, plot=1)\n",
    "xcen = f.xpeak\n",
    "ycen = f.ypeak\n",
    "pix2radec_legacy(xcen,ycen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Pixels used: 23147\n",
      " Peak Img[j, k]: 499 577\n",
      " Mean (j, k): 493.72 573.84\n",
      " Theta (deg): 178.2\n",
      " Astro PA (deg): 91.8\n",
      " Eps: 0.226\n",
      " Major axis (pix): 106.3\n",
      "ra,dec= 03h19m41.0400642s -19d24m39.83864201s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "path = './NGC1300_f606w'\n",
    "hdu_list = fits.open(path+'.fits', cache=True)\n",
    "img = hdu_list[1].data\n",
    "f = find_galaxy(img, fraction=0.03, plot=1)\n",
    "xcen = f.xpeak\n",
    "ycen = f.ypeak\n",
    "pix2radec_Hubble(xcen,ycen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 画在相同空间坐标系下才会更直观"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1个本地（红移为0 ）重子物质为10^11 Msun的星系，\n",
    "假设其物质密度分布为指数盘形式，指数盘的scalelength 为 3Kpc，该星系所在的暗物质晕的质量为\n",
    "10^12Msun，暗物质的物质密度轮廓服从NFW分布\n",
    "（c=10），该星系的运动为旋转的盘，请画出该星系的\n",
    "旋转曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "M_b = 1e11\n",
    "M_dm = 1e12\n",
    "l_scale = 3\n",
    "G = constants.G\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "217.64789094791217\n"
     ]
    }
   ],
   "source": [
    "#计算暗物质profile\n",
    "H = 0.06774*(u.km/u.s/u.kpc)#km/s/kpc\n",
    "c= 10\n",
    "M = (M_b+M_dm)*u.Msun\n",
    "#Vc = 10*r200*H\n",
    "#GM = 100*(r200**3)*H*2\n",
    "#r200**3 = GM/(100*(H**2))\n",
    "\n",
    "r200 = (G*M/(100*(H**2)))**(1/3)\n",
    "rs = (r200/c).to_value(u.kpc)\n",
    "print(r200.to_value(u.kpc))\n",
    "\n",
    "delta0 = (200/3)*(c**3/(np.log(1+c)-(c/(1+c))))\n",
    "\n",
    "def rou(r):\n",
    "    return r**2*delta0/(r/rs*(1+r/rs)**2)\n",
    "result, error = quad(rou, 0, 217)  \n",
    "\n",
    "rou_crit = M_dm/(4*np.pi*result) \n",
    "#rou_r = rou_crit*delta0//((r/rs)*((1+r/rs)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "#计算重子物质profile\n",
    "def f(r):\n",
    "    return r*np.exp(-r/l_scale)\n",
    "result, error = quad(f, 0, 217)  \n",
    "I_b_0 = M_b/(2*np.pi*result) #Msun\n",
    "#I_b(r) = I_b_0*np.exp(-r/l_scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Name   = Gravitational constant\n",
      "  Value  = 6.6743e-11\n",
      "  Uncertainty  = 1.5e-15\n",
      "  Unit  = m3 / (kg s2)\n",
      "  Reference = CODATA 2018\n",
      "132712440000.0\n",
      "132712440000.0 km3 / (s2 solMass)\n"
     ]
    }
   ],
   "source": [
    "G = constants.G\n",
    "print(G)\n",
    "print(G.to_value(((u.km)**3/u.Msun/(u.s)**2)))\n",
    "G = 132712440000 *(u.km)**3/u.Msun/(u.s)**2\n",
    "print(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-142-a1e48ea3a65e>:2: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  return rou_crit*delta0/(r/rs)/(1+r/rs)**2\n",
      "<ipython-input-142-a1e48ea3a65e>:6: RuntimeWarning: invalid value encountered in scalar multiply\n",
      "  return 4*np.pi*r**2*dm_density(r)+2*np.pi*r*bm_density(r)\n",
      "<ipython-input-142-a1e48ea3a65e>:14: IntegrationWarning: Extremely bad integrand behavior occurs at some points of the\n",
      "  integration interval.\n",
      "  M_1, error = quad(Mtot, 0, r1)\n"
     ]
    }
   ],
   "source": [
    "def dm_density(r):\n",
    "    return rou_crit*delta0/(r/rs)/(1+r/rs)**2\n",
    "def bm_density(r):\n",
    "    return I_b_0*np.exp(-r/l_scale)\n",
    "def Mtot(r):\n",
    "    return 4*np.pi*r**2*dm_density(r)+2*np.pi*r*bm_density(r)\n",
    "\n",
    "bins = 2170\n",
    "rmax = 217\n",
    "Var = np.array([])\n",
    "rar = np.array([])\n",
    "for i in range(bins):\n",
    "    r1 = i*rmax/bins\n",
    "    M_1, error = quad(Mtot, 0, r1) \n",
    "    M_1 = M_1*u.Msun\n",
    "    V = np.sqrt(G * M_1/(r1*u.kpc))\n",
    "    Var = np.append(Var,V.to_value(u.km/u.s))\n",
    "    rar = np.append(rar,r1)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'V[km/s]')"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5),dpi=100) \n",
    "plt.scatter(rar,Var,c='k',s=2)\n",
    "plt.xticks(size=20)\n",
    "plt.yticks(size=20)\n",
    "plt.xlabel('r[kpc]',size=20)\n",
    "plt.ylabel('V[km/s]',size=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 可以看一下各个不同的组分贡献的旋转速度分别是多少，盘不是三维的"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于Sersic指数分别是n=1，3，4的三个星系来说，其R90/R50分别是多少？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "157.07963267948776\n",
      "9 0\n",
      "2.2222222222222223\n"
     ]
    }
   ],
   "source": [
    "#设rscale = 5,且三个星系I0一致\n",
    "rscale = 5\n",
    "def n1(r):\n",
    "    return 2*np.pi*r*np.exp(-(r/rscale)**(1/1))\n",
    "\n",
    "All, error = quad(n1, 0, np.inf) \n",
    "print(All)\n",
    "flag = 1\n",
    "for i in range(200):\n",
    "    I, error = quad(n1, 0, i) \n",
    "    if (I >=All*0.5)&(flag==1):\n",
    "        r50 = i\n",
    "        flag = 0    \n",
    "        print(r50,flag)   \n",
    "    if I >=All*0.9:\n",
    "        r90 = i\n",
    "        break\n",
    "print(r90/r50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22619467.10584954\n",
      "4.37353171495693\n"
     ]
    }
   ],
   "source": [
    "rscale = 5\n",
    "def n3(r):\n",
    "    return 2*np.pi*r*np.exp(-(r/rscale)**(1/3))\n",
    "\n",
    "All, error = quad(n3, 0, np.inf) \n",
    "print(All)\n",
    "flag = 1\n",
    "for i in range(10000):\n",
    "    I, error = quad(n3, 0, i) \n",
    "    if (I >=All*0.5)&(flag==1):\n",
    "        r50 = i\n",
    "        flag = 0      \n",
    "    if I >=All*0.9:\n",
    "        r90 = i\n",
    "        break\n",
    "print(r90/r50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.549023008440282\n"
     ]
    }
   ],
   "source": [
    "\n",
    "rscale = 5\n",
    "def n4(r):\n",
    "    return 2*np.pi*r*np.exp(-(r/rscale)**(1/4))\n",
    "\n",
    "All, error = quad(n4, 0, np.inf) \n",
    "for i in range(90000,100000):\n",
    "    I, error = quad(n4, 0, i)   \n",
    "    if I >=All*0.9:\n",
    "        r90 = i\n",
    "        break\n",
    "flag = 1\n",
    "for i in range(10000,20000):\n",
    "    I, error = quad(n4, 0, i) \n",
    "    if (I >=All*0.5)&(flag==1):\n",
    "        r50 = i\n",
    "        flag = 0   \n",
    "print(r90/r50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当rscale=5时，n = 1,3,4 的星系，r90/r50 分别为 2.2，4.375，5.5\n",
    "\n",
    "我手算了一下n=1的情况，就是积分[0,r]，对2* np.pi* r* np.exp(-(r/rs)**(1/1))做积分，\n",
    "\n",
    "最后算出来是2 * np.pi * rscale ** 2* [1-(1+r/rs)*np.exp(-r/rs)]\n",
    "\n",
    "然后r趋向于无穷时等于2 * np.pi *rs**2\n",
    "\n",
    "所以令上述结果等于0.5 * 2 * np.pi*rs**2 \n",
    "\n",
    "和 0.9 * 2 * np.pi*rs**2可以得到一个没有解析解的微分方程\n",
    "\n",
    "原则上应该是给出rscale的值就能获得一个数值解..我感觉是这么做..\n",
    "\n",
    "然后n = 其他值的时候积分也算不出来解析解。。感觉是给定n和rs，求无穷,50%,90%的数值解。\n",
    "或许有某些特殊函数能解..但我没有查询到.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# good n~3,4 是只有数值解"
   ]
  }
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