Skip to content

Instantly share code, notes, and snippets.

@bmorris3
Created December 14, 2023 14:06
Show Gist options
  • Save bmorris3/42094aad66ead6cae322280f18140b66 to your computer and use it in GitHub Desktop.
Save bmorris3/42094aad66ead6cae322280f18140b66 to your computer and use it in GitHub Desktop.
Light curve fitting demo notebook for @nnicolesanchez
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"id": "44b528fb-8c45-4610-beff-adbd27b22de6",
"metadata": {},
"source": [
"# Measure the radius of a transiting exoplanet:\n",
"\n",
"Search for part of the Kepler light curve of HAT-P-7 b, a hot Jupiter:"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "f20564fd-d735-4cca-8765-cf06a33f8447",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from scipy.optimize import minimize\n",
"\n",
"import astropy.units as u\n",
"from lightkurve import search_lightcurve\n",
"\n",
"lc_search = search_lightcurve(\"HAT-P-7\", mission=\"Kepler\", author=\"Kepler\", quarter=1, cadence='short')"
]
},
{
"cell_type": "markdown",
"id": "3daad546-37d0-4c70-bc80-a6d69996f517",
"metadata": {},
"source": [
"Download the light curve:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "45d93646-bbda-45c8-a217-9350daade652",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"lc = lc_search.download_all()[0]"
]
},
{
"cell_type": "markdown",
"id": "8bcdf435-2ca2-42e7-9035-b521b11e71e7",
"metadata": {},
"source": [
"Normalize the light curve by its mean:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "f8eb65d6-6a31-42c1-97b5-dfb2ea26f9dd",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"lc = lc.normalize().remove_nans()"
]
},
{
"cell_type": "markdown",
"id": "5e21bab8-b29f-45f5-a690-487543cc13c5",
"metadata": {},
"source": [
"Plot the light curve:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "6a4ddeb4-f1d2-45ab-9aa2-7b9e761e6c60",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"<AxesSubplot: xlabel='Time - 2454833 [BKJD days]', ylabel='Normalized Flux'>"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 848.5x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lc.plot()"
]
},
{
"cell_type": "markdown",
"id": "260c0ae7-7a0d-42d2-943e-e1f196486a4d",
"metadata": {},
"source": [
"This function will compute a model of a planet transiting its star, from [Mandel & Agol 2002](https://ui.adsabs.harvard.edu/abs/2002ApJ...580L.171M/abstract):"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "c73e221f-a99e-45dc-b470-4987be9bf274",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def transit_model(midpt, rprs, cosi, ars, flux, p, t):\n",
" '''\n",
" This function computes the primary transit shape using a uniform \n",
" limb-darkening equation, as provided by Mandel & Agol (2002).\n",
"\n",
" Parameters\n",
" ----------\n",
" midpt: Center of eclipse\n",
" rprs: Planet radius / stellar radius\n",
" cosi: Cosine of the inclination\n",
" ars: Semi-major axis / stellar radius\n",
" flux: Flux offset from 0\n",
" t: Array of phase/time points\n",
" p: Period in same units as t\n",
"\n",
" Returns\n",
" -------\n",
" This function returns the flux for each point in t.\n",
"\n",
" References\n",
" ----------\n",
" \n",
" Mandel & Agol (2002)\n",
" /home/esp01/doc/Mandel+Agol-2002_eq8.pdf\n",
" /home/esp01/code/MandelAgol/occultnl.pro\n",
" Adapted from https://github.com/kevin218/POET/\n",
" '''\n",
" \n",
" # Set exception case for avoiding invalid boundreis\n",
" if(abs(rprs - .5) < .001):\n",
" rprs = .5\n",
" \n",
" #COMPUTE z(t) FOR TRANSIT ONLY (NOT ECLIPSE) AND Sigma*4\n",
" #NOTE: z(t) ASSUMES A CIRCULAR ORBIT\n",
" z = ars * np.sqrt(np.sin(2 * np.pi * (t - midpt)/p)**2 + (cosi * np.cos(2 * np.pi * (t - midpt)/p))**2)\n",
" z[np.where(((t - midpt)%p > p/4.) & ((t - midpt)%p < p * 3./4))] = ars\n",
" \n",
" #CALCULATE TRANSIT SHAPE WITH LIMB-DARKENING\n",
" y = np.ones(len(t))\n",
" if rprs == 0:\n",
" return y*flux\n",
" \n",
" # Where planet is not in transit\n",
" miss = np.where(z > (1+rprs))\n",
" y[miss] = 1\n",
" \n",
" # Where planet is in ingress/egress\n",
" iingress = np.where( np.logical_and( np.logical_and( (1-rprs) < z, z <= (1+rprs) ), z > (rprs- 1)) )[0]\n",
" kap1 = np.arccos((1 - rprs**2 + z[iingress]**2) / 2 / z[iingress])\n",
" kap0 = np.arccos((rprs**2 + z[iingress]**2 - 1) / 2 / rprs / z[iingress])\n",
" lambdae = (rprs**2 * kap0 + kap1 - 0.5 * np.sqrt(4 * z[iingress]**2 - (1 + z[iingress]**2 - rprs**2)**2)) / np.pi\n",
" y[iingress] = 1 - lambdae\n",
" \n",
" # Where planet is in transit\n",
" itrans = np.where(z <= (1-rprs))\n",
" y[itrans] = 1 - rprs**2\n",
" \n",
" # If planet covers source\n",
" cover = np.where(z <= rprs - 1)\n",
" y[cover] = 0\n",
" \n",
" return y*flux\n",
" "
]
},
{
"cell_type": "markdown",
"id": "7dda2184-e65a-4c94-b3a6-3c308fba0668",
"metadata": {
"tags": []
},
"source": [
"Let's evaluate the model at each time in the Kepler light curve:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "16f23924-c475-4340-87a8-914c4c2df579",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# These values have been published in the literature, and you can find\n",
"# them in databases like the NASA Exoplanet Archive here: \n",
"# https://exoplanetarchive.ipac.caltech.edu/overview/HAT-P-7%20b#planet_HAT-P-7-b_collapsible\n",
"\n",
"midtransit_time = 2455430.58123\n",
"rp_rs = 0.07809\n",
"a_rs = 4.03\n",
"inclination = 82.2\n",
"period = 2.20473657\n",
"\n",
"# these are the times of the Kepler measurements:\n",
"times = lc.time.jd\n",
"\n",
"# this is the transit model evaulated at `times`:\n",
"transit = transit_model(midtransit_time, rp_rs, np.cos(np.radians(inclination)), a_rs, 1, period, times)"
]
},
{
"cell_type": "markdown",
"id": "8ff551b5-5459-43fa-b121-1e8203b28901",
"metadata": {},
"source": [
"and plot the model on the data:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "ec62a31e-735c-4ded-89d1-1e40d9bc2b5f",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0.5, 0, 'Time (JD)'), Text(0, 0.5, 'Relative flux')]"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(times, lc.flux, label='Kepler')\n",
"plt.plot(times, transit, label='Model')\n",
"plt.legend()\n",
"plt.gca().set(\n",
" xlabel='Time (JD)',\n",
" ylabel='Relative flux'\n",
")"
]
},
{
"cell_type": "markdown",
"id": "0e1fff22-dfd9-4b66-a475-3b309a109e9d",
"metadata": {},
"source": [
"Now let's fit the transit model to the Kepler observations:"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "d648a896-7a7e-48ff-8ed9-8417771687ea",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def fittable_model(rp_rs):\n",
" return transit_model(\n",
" midtransit_time, rp_rs, \n",
" np.cos(np.radians(inclination)), \n",
" a_rs, 1, period, times\n",
" )\n",
" \n",
"def chi2(rp_rs):\n",
" return np.nansum(\n",
" (fittable_model(rp_rs) - lc.flux.value)**2 / lc.flux_err.value**2\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "d4cc6a28-b0f3-47ad-be79-b23a444c477f",
"metadata": {},
"source": [
"The best-fit $R_p/R_\\star$ minimizes the $\\chi^2$:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "8b9fd0a4-0632-4462-8309-048fb092bc73",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"initial_params = [rp_rs]\n",
"fit_result = minimize(chi2, initial_params, method='powell')\n",
"\n",
"best_fit_rp_rs = fit_result.x[0]"
]
},
{
"cell_type": "markdown",
"id": "3a91e8f7-b759-42a8-bbf0-da80a5816a2a",
"metadata": {},
"source": [
"Compare with literature measurement from by [Wong et al. 2016](https://ui.adsabs.harvard.edu/abs/2016ApJ...823..122W/abstract):"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "6a6ee9d3-2fe2-4e23-8bc2-57192598c6da",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fractional error = (literature - ours) / literature) = 0.01\n"
]
}
],
"source": [
"literature_rp_rs = 0.07809\n",
"\n",
"fractional_error = abs(literature_rp_rs - best_fit_rp_rs) / literature_rp_rs\n",
"\n",
"print(f\"Fractional error = (literature - ours) / literature) = {fractional_error :.2f}\")"
]
},
{
"cell_type": "markdown",
"id": "faacfd81-66b3-4be3-b9ca-3e130d2ce7a4",
"metadata": {},
"source": [
"We got pretty close to the \"correct\" answer!\n",
"\n",
"Now if we know the stellar radius from other measurements, we can compute the planet's radius in units of Jupiter radii:"
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "a892d837-9a95-4741-a044-3fa7144cdadc",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"We find that the planet's radius is: 1.54 Jupiter radii\n"
]
}
],
"source": [
"stellar_radius = 2 * u.R_sun\n",
"\n",
"planet_radius = best_fit_rp_rs * stellar_radius\n",
"\n",
"print(f\"We find that the planet's radius is: {planet_radius.to_value(u.R_jup) :.2f} Jupiter radii\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "944dd813-a9c4-4c84-939d-d72d9c0c75cc",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.10.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment