HajimeKawahara/exojax

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rigid Stellar Rotation and Gaussian Convolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The planet/stellar spectrum we observe is an integrated emission from the top of the atmosphere over (parts of) the planet/stellar sphere. The planet/star spin rotation yields a Doppler broadening of the molecular/atomic line. We here demonstrate to include a rigid rotation broadening into the simulated spectrum. \n",
    "\n",
    "In practice, we use a specgrograph to observe the spectrum. The response (known as instrumental profile; IP) by the spectrograph also makes the instrumental broadening of the spectrum. \n",
    "\n",
    "These effects are essentially a convolution of the kernel to the (raw) spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:36.811808Z",
     "iopub.status.busy": "2024-01-16T23:29:36.811599Z",
     "iopub.status.idle": "2024-01-16T23:29:38.165752Z",
     "shell.execute_reply": "2024-01-16T23:29:38.165086Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from exojax.utils.grids import wavenumber_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:38.168441Z",
     "iopub.status.busy": "2024-01-16T23:29:38.168184Z",
     "iopub.status.idle": "2024-01-16T23:29:38.177416Z",
     "shell.execute_reply": "2024-01-16T23:29:38.177034Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xsmode =  premodit\n",
      "xsmode assumes ESLOG in wavenumber space: mode=premodit\n",
      "======================================================================\n",
      "We changed the policy of the order of wavenumber/wavelength grids\n",
      "wavenumber grid should be in ascending order and now \n",
      "users can specify the order of the wavelength grid by themselves.\n",
      "Your wavelength grid is in ***  descending  *** order\n",
      "This might causes the bug if you update ExoJAX. \n",
      "Note that the older ExoJAX assumes ascending order as wavelength grid.\n",
      "======================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kawahara/exojax/src/exojax/utils/grids.py:145: UserWarning: Resolution may be too small. R=460768.77729497064\n",
      "  warnings.warn('Resolution may be too small. R=' + str(resolution),\n"
     ]
    }
   ],
   "source": [
    "nu_grid,wav,res=wavenumber_grid(23000,23100,2000,unit=\"AA\",xsmode=\"premodit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test using a delta function -like spectrum as an input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:38.200992Z",
     "iopub.status.busy": "2024-01-16T23:29:38.200826Z",
     "iopub.status.idle": "2024-01-16T23:29:38.202971Z",
     "shell.execute_reply": "2024-01-16T23:29:38.202658Z"
    }
   },
   "outputs": [],
   "source": [
    "#1 - delta function like\n",
    "F=np.ones_like(nu_grid)\n",
    "F[1000]=0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rigid rotation is characterized by a single parameter, Vsini, which is the product of the velocity at the planet/stellar equator and sine of the inclination of the spin axis to the observer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:38.204522Z",
     "iopub.status.busy": "2024-01-16T23:29:38.204396Z",
     "iopub.status.idle": "2024-01-16T23:29:38.206400Z",
     "shell.execute_reply": "2024-01-16T23:29:38.205985Z"
    }
   },
   "outputs": [],
   "source": [
    "vsini=100.0 #km/s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use exojax.spec.response.rigidrot for the rigid rotation, but, for the retrieval, we need a more efficient convolution. We try to the latter here. We define the maximum vsini we will consider (important for retrieval! but now just set the same value as visini) the velocity grid for the convilution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:38.207984Z",
     "iopub.status.busy": "2024-01-16T23:29:38.207797Z",
     "iopub.status.idle": "2024-01-16T23:29:39.505142Z",
     "shell.execute_reply": "2024-01-16T23:29:39.504596Z"
    }
   },
   "outputs": [],
   "source": [
    "from exojax.spec.response import ipgauss_sampling\n",
    "from exojax.spec.spin_rotation import convolve_rigid_rotation\n",
    "from exojax.utils.grids import velocity_grid\n",
    "vsini_max = 100.0\n",
    "vr_array = velocity_grid(res, vsini_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:39.507119Z",
     "iopub.status.busy": "2024-01-16T23:29:39.506948Z",
     "iopub.status.idle": "2024-01-16T23:29:40.440081Z",
     "shell.execute_reply": "2024-01-16T23:29:40.439422Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "Frot = convolve_rigid_rotation(F, vr_array, vsini, u1=0.0, u2=0.0)\n",
    "plt.plot(wav,Frot,lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You find the extreme drops at the right and left sides of the spectrum. This is due to the convolution of the rotation kernel to the edges.\n",
    "So, you need to set some margin to avoid to use the edges in the analysis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:40.443162Z",
     "iopub.status.busy": "2024-01-16T23:29:40.442987Z",
     "iopub.status.idle": "2024-01-16T23:29:40.537622Z",
     "shell.execute_reply": "2024-01-16T23:29:40.537203Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(wav,Frot,lw=1)\n",
    "plt.xlim(23035,23065)\n",
    "plt.ylim(0.99,1.01)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We confirmed that the rotation convolution was applied to the spectrum. \n",
    "The parameters of u1 and u2 are the quadratic Limb darkening coefficients.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:40.540097Z",
     "iopub.status.busy": "2024-01-16T23:29:40.539652Z",
     "iopub.status.idle": "2024-01-16T23:29:40.655229Z",
     "shell.execute_reply": "2024-01-16T23:29:40.654736Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Frot_ld = convolve_rigid_rotation(F, vr_array, vsini, u1=0.6, u2=0.4)\n",
    "plt.plot(wav,Frot,lw=1,label=\"u1=0,u2=0\")\n",
    "plt.plot(wav,Frot_ld,lw=2,label=\"u1=0.6,u2=0.4\")\n",
    "plt.xlim(23035,23065)\n",
    "plt.ylim(0.99,1.01)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also apply a Gaussian covolution and velocity shift to the spectrum. It should be noted that beta is the standard deviation of a Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:40.657486Z",
     "iopub.status.busy": "2024-01-16T23:29:40.657094Z",
     "iopub.status.idle": "2024-01-16T23:29:40.921939Z",
     "shell.execute_reply": "2024-01-16T23:29:40.921329Z"
    }
   },
   "outputs": [],
   "source": [
    "beta1=20.0 #std of gaussian\n",
    "beta2=50.0\n",
    "RV=30.0\n",
    "Fx=ipgauss_sampling(nu_grid,nu_grid,Frot,beta1,0.0,vr_array)\n",
    "Fxx=ipgauss_sampling(nu_grid,nu_grid,Frot,beta2,RV,vr_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-01-16T23:29:40.923897Z",
     "iopub.status.busy": "2024-01-16T23:29:40.923726Z",
     "iopub.status.idle": "2024-01-16T23:29:41.161677Z",
     "shell.execute_reply": "2024-01-16T23:29:41.161290Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(wav[::-1],Frot,lw=1,label=\"Vsini=100km/s\")\n",
    "plt.plot(wav[::-1],Fx,lw=1,ls=\"dashed\",label=\"Vsini=100km/s $\\\\ast \\\\beta$=20km/s\")\n",
    "plt.plot(wav[::-1],Fxx,lw=1,ls=\"dotted\",label=\"Vsini=100km/s $\\\\ast \\\\beta$=50km/s, RV=30km/s\")\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.xlabel(\"wavelength $\\AA$\")\n",
    "plt.xlim(23030,23070)\n",
    "plt.ylim(0.99,1.005)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.8 ('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": "3.10.9"
  },
  "vscode": {
   "interpreter": {
    "hash": "72bc7f8b1808a6f5ada3c6a20601509b8b1843160436d276d47f2ba819b3753b"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}