{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e8feea42",
   "metadata": {},
   "outputs": [],
   "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 定出星系的中心（流量最高点） • 计算其赤经赤纬"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "49e24037",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filename: 149.74358_2.125144_sci.fits\n",
      "No.    Name      Ver    Type      Cards   Dimensions   Format\n",
      "  0  PRIMARY       1 PrimaryHDU     371   ()      \n",
      "  1  SCI           1 ImageHDU        81   (75, 75)   float32   \n",
      "最高流量点的位置：x = 33, y = 44\n",
      "赤经 (RA)：34.0 度\n",
      "赤纬 (Dec)：45.0 度\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: FITSFixedWarning: The WCS transformation has more axes (2) than the image it is associated with (0) [astropy.wcs.wcs]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#task5.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",
    "#• 定出星系的中心（流量最高点）\n",
    "#• 计算其赤经赤纬\n",
    "\n",
    "\n",
    "from astropy.io import fits\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy.wcs import WCS\n",
    "import numpy as np\n",
    "# 打开 FITS 文件\n",
    "file_path = '149.74358_2.125144_sci.fits'  # 替换为你的 FITS 文件路径\n",
    "with fits.open(file_path) as hdul:\n",
    "    # 打印文件信息，查看可用的扩展和数据\n",
    "    hdul.info()\n",
    "\n",
    "    # 加载主数据\n",
    "    image_data = hdul[1].data\n",
    "    header = hdul[0].header \n",
    "\n",
    "\n",
    "# 找到图像数据中最大值的位置\n",
    "y, x = np.unravel_index(np.argmax(image_data), image_data.shape)\n",
    "print(f\"最高流量点的位置：x = {x}, y = {y}\")\n",
    "\n",
    "\n",
    "\n",
    "# 使用头信息创建 WCS 对象\n",
    "wcs = WCS(header)\n",
    "\n",
    "# 将像素坐标转换为赤经和赤纬\n",
    "ra, dec = wcs.wcs_pix2world(x, y, 0)\n",
    "print(f\"赤经 (RA)：{ra} 度\")\n",
    "print(f\"赤纬 (Dec)：{dec} 度\")\n",
    "# 绘制图像\n",
    "plt.imshow(image_data, cmap='gray')  # 使用灰度配色\n",
    "plt.scatter(x, y, color='red', marker='x', s=100, label='流量最高点')  # 标记最高点\n",
    "plt.colorbar()  # 添加颜色条\n",
    "plt.title('COSMOS-web galaxy image')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b8040f0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 常数\n",
    "G = 4.30091e-6  # 引力常数，(kpc/M_sun) (km/s)^2\n",
    "Msun = 1.989e30  # 太阳质量 (kg)\n",
    "\n",
    "# 星系参数\n",
    "M_disk = 1e11  # 盘质量 (M_sun)\n",
    "R_s = 3.0  # 盘的尺度长度 (kpc)\n",
    "\n",
    "# NFW 暗物质晕参数\n",
    "M_halo = 1e12  # 晕质量 (M_sun)\n",
    "c = 10  # NFW 浓缩参数\n",
    "R_vir = 200  # 暂定为 200 kpc 的晕半径\n",
    "R_s_halo = R_vir / c  # NFW 模型的特征半径 (kpc)\n",
    "\n",
    "# 计算 NFW 模型的特征密度 rho_0\n",
    "rho_0 = M_halo / (4 * np.pi * R_s_halo**3 * (np.log(1 + c) - c / (1 + c)))\n",
    "\n",
    "# 质量分布和旋转速度\n",
    "def M_disk_function(R):\n",
    "    return M_disk * (1 - np.exp(-R / R_s) * (1 + R / R_s))\n",
    "\n",
    "def V_disk(R):\n",
    "    return np.sqrt(G * M_disk_function(R) / R)\n",
    "\n",
    "def M_NFW_function(r):\n",
    "    return 4 * np.pi * rho_0 * R_s_halo**3 * (np.log(1 + r / R_s_halo) - (r / R_s_halo) / (1 + r / R_s_halo))\n",
    "\n",
    "def V_NFW(r):\n",
    "    return np.sqrt(G * M_NFW_function(r) / r)\n",
    "\n",
    "# 计算总旋转曲线\n",
    "R = np.linspace(0.1, 50, 1000)  # 半径范围 (kpc)\n",
    "V_total = np.sqrt(V_disk(R)**2 + V_NFW(R)**2)\n",
    "\n",
    "# 绘图\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(R, V_disk(R), label='Disk', color='blue')\n",
    "plt.plot(R, V_NFW(R), label='NFW Halo', color='green')\n",
    "plt.plot(R, V_total, label='Total', color='red')\n",
    "plt.xlabel('Radius (kpc)')\n",
    "plt.ylabel('Velocity (km/s)')\n",
    "plt.title('Rotation Curve of the Galaxy')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b7c9a428",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sérsic 指数 n = 1: R90/R50 ≈ 2.32\n",
      "Sérsic 指数 n = 3: R90/R50 ≈ 1.64\n",
      "Sérsic 指数 n = 4: R90/R50 ≈ 1.53\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#task_7. 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？\n",
    "import numpy as np\n",
    "from scipy.special import gammaincinv\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义函数来计算 R90/R50 的比值\n",
    "def compute_R90_R50_ratio(n):\n",
    "    # 计算 b_n，使用近似公式 b_n ≈ 2n - 1/3\n",
    "    b_n = 2 * n - 1 / 3\n",
    "    \n",
    "    # 计算包含 50% 和 90% 光度的归一化半径\n",
    "    R50 = gammaincinv(2 * n, 0.5)  # 包含 50% 光度的半径\n",
    "    R90 = gammaincinv(2 * n, 0.9)  # 包含 90% 光度的半径\n",
    "    \n",
    "    # 计算比值\n",
    "    return R90 / R50\n",
    "\n",
    "# 不同的 Sérsic 指数\n",
    "n_values = [1, 3, 4]\n",
    "ratios = [compute_R90_R50_ratio(n) for n in n_values]\n",
    "\n",
    "# 输出结果\n",
    "for n, ratio in zip(n_values, ratios):\n",
    "    print(f\"Sérsic 指数 n = {n}: R90/R50 ≈ {ratio:.2f}\")\n",
    "\n",
    "# 可视化 R90/R50 比值随 n 的变化\n",
    "n_range = np.linspace(0.5, 5, 100)\n",
    "ratios_range = [compute_R90_R50_ratio(n) for n in n_range]\n",
    "\n",
    "plt.plot(n_range, ratios_range, label=\"R90/R50 vs. Sérsic Index\")\n",
    "plt.scatter(n_values, ratios, color='red', label=\"Specific n Values\")\n",
    "plt.xlabel(\"Sérsic Index (n)\")\n",
    "plt.ylabel(\"R90/R50\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.title(\"R90/R50 Ratio for Different Sérsic Indices\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "819af2e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#作业7\n",
    "import numpy as np\n",
    "from scipy.integrate import quad\n",
    "def sersic_profile(r, n, I0, alpha):\n",
    "    return I0 * np.exp(-(r / alpha)**(1/n))\n",
    "\n",
    "def total_flux(n, I0, alpha):\n",
    "    integral, _ = quad(lambda r: 2 * np.pi * r * sersic_profile(r, n, I0, alpha), 0, np.inf)\n",
    "    return integral\n",
    "\n",
    "def radius_ratio(n, I0, alpha):\n",
    "    R50 = quad(lambda r: 2 * np.pi * r * sersic_profile(r, n, I0, alpha), 0, alpha/2)[0]\n",
    "    R90 = quad(lambda r: 2 * np.pi * r * sersic_profile(r, n, I0, alpha), 0, alpha * 0.9)[0]\n",
    "    return R90 / R50\n",
    "\n",
    "n_values = [1, 3, 4]\n",
    "I0 = 1  # 假设为1\n",
    "alpha = 1  # 假设为1\n",
    "\n",
    "for n in n_values:\n",
    "    ratio = radius_ratio(n, I0, alpha)\n",
    "    print(f\"Sérsic指数n={n}时，R90/R50={ratio}\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
