{ "cells": [ { "cell_type": "markdown", "id": "a47326c5", "metadata": {}, "source": [ "# Fit a model to observations\n", "\n", "In the **Quickstart example** notebook we saw a quick introduction to forward modeling the upper atmosphere and He triplet signal of HD 209458 b. In this notebook we will go over an advanced-level tutorial on retrieving the properties of the upper atmosphere of HAT-P-11 b using ``p-winds`` models." ] }, { "cell_type": "code", "execution_count": 1, "id": "39455c13", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/leonardo/GitHub/p-winds/p_winds/transit.py:17: SyntaxWarning: The transit module has significant syntax changes since version 0.6. Consult the documentation.\n", " warn('The transit module has significant syntax changes since version 0.6. '\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.pylab as pylab\n", "import astropy.constants as c\n", "import astropy.units as u\n", "from astropy.convolution import convolve\n", "from scipy.optimize import minimize\n", "from p_winds import parker, hydrogen, helium, transit, microphysics\n", "\n", "# Uncomment the next line if you have a MacBook with retina screen\n", "# %config InlineBackend.figure_format = 'retina'\n", "pylab.rcParams['figure.figsize'] = 9.0,6.5\n", "pylab.rcParams['font.size'] = 18" ] }, { "cell_type": "markdown", "id": "fb4efbda", "metadata": {}, "source": [ "Let's start with the observation of the He triplet transmission spectrum of HAT-P-11 b using the CARMENES spectrograph. This data is openly available in the [DACE platform](https://dace.unige.ch/openData/). But we will retrieve it from a [public Gist](https://gist.github.com/ladsantos/a8433928e384819a3632adc469bed803) for convenience." ] }, { "cell_type": "code", "execution_count": 2, "id": "f06da648", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The observed transmission spectrum\n", "data_url = 'https://gist.githubusercontent.com/ladsantos/a8433928e384819a3632adc469bed803/raw/a584e6e83073d1ad3444248624927838588f22e4/HAT-P-11_b_He.dat'\n", "# We skip 2 rows instead of 1 to have an odd number of rows and allow a fast convolution later\n", "He_spec = np.loadtxt(data_url, skiprows=2)\n", "wl_obs = He_spec[:, 0] # Angstrom\n", "f_obs = 1 - He_spec[:, 1] * 0.01 # Normalized flux\n", "u_obs = He_spec[:, 2] * 0.01 # Flux uncertainty\n", "\n", "# Convert in-vacuum wavelengths to in-air\n", "s = 1E4 / np.mean(wl_obs)\n", "n = 1 + 0.0000834254 + 0.02406147 / (130 - s ** 2) + 0.00015998 / (38.9 - s ** 2)\n", "wl_obs /= n\n", "\n", "# We will also need to know the instrumental profile that\n", "# widens spectral lines. We take the width from Allart et al. (2018),\n", "# the paper describing the HAT-P-11 b data.\n", "def gaussian(x, mu=0.0, sigma=1.0):\n", " return 1 / sigma / (2 * np.pi) ** 0.5 * np.exp(-0.5 * (x - mu) ** 2 / sigma ** 2)\n", "\n", "instrumental_profile_width_v = 3.7 # Instrumental profile FWHM in km / s (assumed Gaussian)\n", "sigma_wl = instrumental_profile_width_v / \\\n", " c.c.to(u.km / u.s).value * np.mean(wl_obs) # Same unit as wl_obs\n", "instrumental_profile = gaussian(wl_obs, np.mean(wl_obs), sigma=sigma_wl)\n", "\n", "plt.errorbar(wl_obs, f_obs, yerr=u_obs)\n", "plt.xlabel(r'Wavelength (${\\rm \\AA}$)')\n", "plt.ylabel('Normalized flux')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fa59a54f", "metadata": {}, "source": [ "Now we set up the simulation. This is quite a dense cell of configurations, but you should be familiar with all of it if you followed the quickstart example." ] }, { "cell_type": "code", "execution_count": 3, "id": "6d98ff3a", "metadata": {}, "outputs": [], "source": [ "# Set up the simulation\n", "\n", "# Fixed parameters of HAT-P-11 b (not to be sampled)\n", "R_pl = 0.389 # Planetary radius (Jupiter radii)\n", "M_pl = 0.09 # Planetary mass (Jupiter masses)\n", "a_pl = 0.05254 # Semi-major axis (au)\n", "planet_to_star_ratio = 0.057989\n", "impact_parameter = 0.132\n", "h_he = 0.9 # H/He fraction (assumed for now, but can be a free parameter)\n", "mean_f_ion = 0.90 # Initially assumed, but the model relaxes for it\n", "\n", "# Physical constants\n", "m_h = c.m_p.to(u.g).value # Hydrogen atom mass in g\n", "m_He = 4 * 1.67262192369e-27 # Helium atomic mass in kg\n", "k_B = 1.380649e-23 # Boltzmann's constant in kg / (m / s) ** 2 / K\n", "\n", "# Free parameters (to be sampled with the optimization algorithm)\n", "# The reason why we set m_dot and T in log is because\n", "# we will fit for them in log space\n", "log_m_dot_0 = np.log10(6E10) # Planetary mass loss rate (g / s)\n", "log_T_0 = np.log10(8000) # Atmospheric temperature (K)\n", "v_wind_0 = -2E3 # Line-of-sight wind velocity (m / s)\n", "\n", "# Altitudes samples (this can be a very important setting)\n", "r = np.logspace(0, np.log10(20), 100)\n", "\n", "# First guesses of fractions (not to be fit, but necessary for the calculation)\n", "initial_f_ion = 0.0 # Fraction of ionized hydrogen\n", "initial_f_he = np.array([1.0, 0.0]) # Fraction of singlet, triplet helium\n", "\n", "# Model settings\n", "relax_solution = True # This will iteratively relax the solutions until convergence\n", "sample_phases = np.linspace(-0.50, 0.50, 5) # Phases that we will average to obtain the final spectrum\n", "# The phases -0.5 and +0.5 correspond to the times of first and fourth transit contact\n", "w0, w1, w2, f0, f1, f2, a_ij = microphysics.he_3_properties()\n", "w_array = np.array([w0, w1, w2]) # Central wavelengths of the triplet\n", "f_array = np.array([f0, f1, f2]) # Oscillator strengths of the triplet\n", "a_array = np.array([a_ij, a_ij, a_ij]) # This is the same for all lines in then triplet\n", "n_samples = len(sample_phases)\n", "transit_grid_size = 100 # Also very important to constrain computation time\n", "supersampling = 5 # This is used to improve the hard pixel edges in the ray tracing" ] }, { "cell_type": "markdown", "id": "4cb69d50", "metadata": {}, "source": [ "The full spectrum of HAT-P-11 until 2600 Å is not known. But we can use a proxy for which we do have a full spectrum: HD 40307. It has a similar size, spectral type, effective temperature, and surface gravity as HAT-P-11. We take the spectrum from the [MUSCLES database](https://archive.stsci.edu/prepds/muscles/). The original file is fairly large, so for convenience we also retrieve the relevant section of the spectrum from a public Gist (already scaled to correspond to the irradiation at the planet HAT-P-11 b)." ] }, { "cell_type": "code", "execution_count": 4, "id": "83c456a2", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data_url = 'https://gist.githubusercontent.com/ladsantos/c7d1aae1ecc755bae9f1c8ef1545cf8d/raw/cb444d9b4ff9853672dab80a4aab583975557449/HAT-P-11_spec.dat'\n", "spec = np.loadtxt(data_url, skiprows=1)\n", "host_spectrum = {'wavelength': spec[:, 0], 'flux_lambda': spec[:, 1],\n", " 'wavelength_unit': u.angstrom,\n", " 'flux_unit': u.erg / u.s / u.cm ** 2 / u.angstrom}\n", "\n", "plt.loglog(host_spectrum['wavelength'], host_spectrum['flux_lambda'])\n", "plt.xlabel(r'Wavelength (${\\rm \\AA}$)')\n", "plt.ylabel(r'Flux density (erg s$^{-1}$ cm$^{-2}$ ${\\rm \\AA}^{-1}$)')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4fc80f5d", "metadata": {}, "source": [ "Before we start fitting the observed data to models, we have to do a few sanity checks and assess if all the moving parts of ``p-winds`` will work well for the configuration you set in the cell above. Most numerical issues are caused when using the ``scipy.integrate`` routines.\n", "\n", "We start by assessing if the atmospheric model behaves well." ] }, { "cell_type": "code", "execution_count": 5, "id": "5537fd15", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Calculate the model\n", "def atmospheric_model(theta):\n", " log_m_dot, log_T = theta\n", " m_dot = 10 ** log_m_dot\n", " T = 10 ** log_T\n", " \n", " vs = parker.sound_speed(T, h_he, mean_f_ion) # Speed of sound (km/s, assumed to be constant)\n", " rs = parker.radius_sonic_point(M_pl, vs) # Radius at the sonic point (jupiterRad)\n", " rhos = parker.density_sonic_point(m_dot, rs, vs) # Density at the sonic point (g/cm^3)\n", " r_array = r * R_pl / rs # altitudes in unit of radius at the sonic point\n", " v_array, rho_array = parker.structure(r_array) # velocities and densities in units at the sonic point\n", " \n", " f_r = hydrogen.ion_fraction(r, R_pl, T, h_he,\n", " m_dot, M_pl, mean_f_ion,\n", " spectrum_at_planet=host_spectrum,\n", " initial_f_ion=initial_f_ion, \n", " relax_solution=relax_solution)\n", "\n", " # Update the structure for the revised ion fraction\n", " updated_mean_f_ion = np.mean(f_r)\n", " vs = parker.sound_speed(T, h_he, updated_mean_f_ion)\n", " rs = parker.radius_sonic_point(M_pl, vs)\n", " rhos = parker.density_sonic_point(m_dot, rs, vs)\n", " r_array = r * R_pl / rs\n", " v_array, rho_array = parker.structure(r_array)\n", " \n", " # Calculate the helium population\n", " f_he_1, f_he_3 = helium.population_fraction(r, v_array, rho_array, f_r,\n", " R_pl, T, h_he, vs, rs, rhos, host_spectrum,\n", " initial_state=initial_f_he, relax_solution=relax_solution)\n", "\n", " # Number density of helium nuclei\n", " n_he = (rho_array * rhos * (1 - h_he) / (1 + 4 * (1 - h_he)) / m_h)\n", " \n", " # Number density distribution of helium\n", " n_he_1 = f_he_1 * n_he\n", " n_he_3 = f_he_3 * n_he\n", " n_he_ion = (1 - f_he_1 - f_he_3) * n_he\n", " \n", " # Return the important outputs (number densities [cm ** -3] of helium and \n", " # the profile of velocities of the outflow [km / s])\n", " return n_he_1, n_he_3, n_he_ion, v_array * vs\n", "\n", "# Let's test if the model function is working\n", "theta = (log_m_dot_0, log_T_0)\n", "y0 = (initial_f_ion, initial_f_he)\n", "n_he_1, n_he_3, n_he_ion, v_array = atmospheric_model(theta)\n", "\n", "plt.semilogy(r, n_he_1, color='C0', label='He singlet')\n", "plt.semilogy(r, n_he_3, color='C1', label='He triplet')\n", "plt.semilogy(r, n_he_ion, color='C2', label='He ionized')\n", "plt.xlabel(r'Radius (R$_\\mathrm{pl}$)')\n", "plt.ylabel('Number density (cm$^{-3}$)')\n", "plt.xlim(1, 10)\n", "plt.ylim(1E-2, 1E10)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "23759e18", "metadata": {}, "source": [ "Seems to be working fine. Now we do a sanity check for the radiative transfer. There is not a lot of things that can break here, but we do it anyway." ] }, { "cell_type": "code", "execution_count": 9, "id": "e975a383", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The transmission spectrum model\n", "def transmission_model(wavelength_array, v_wind, n_he_3_distribution, log_T, v_array):\n", "\n", " # Set up the transit configuration. We use SI units to avoid too many \n", " # headaches with unit conversion\n", " R_pl_physical = R_pl * 71492000 # Planet radius in m\n", " r_SI = r * R_pl_physical # Array of altitudes in m\n", " v_SI = v_array * 1000 # Velocity of the outflow in m / s\n", " n_he_3_SI = n_he_3_distribution * 1E6 # Volumetric densities in 1 / m ** 3\n", "\n", " # Set up the ray tracing\n", " f_maps = []\n", " t_depths = []\n", " r_maps = []\n", " for i in range(n_samples):\n", " flux_map, transit_depth, r_map = transit.draw_transit(\n", " planet_to_star_ratio,\n", " impact_parameter=impact_parameter,\n", " supersampling=supersampling,\n", " phase=sample_phases[i],\n", " planet_physical_radius=R_pl_physical,\n", " grid_size=transit_grid_size\n", " )\n", " f_maps.append(flux_map)\n", " t_depths.append(transit_depth)\n", " r_maps.append(r_map)\n", " # Do the radiative transfer\n", " spectra = []\n", "\n", " for i in range(n_samples):\n", " spec = transit.radiative_transfer_2d(f_maps[i], r_maps[i], \n", " r_SI, n_he_3_SI, v_SI, w_array, f_array, a_array,\n", " wavelength_array, 10 ** log_T, m_He, bulk_los_velocity=v_wind,\n", " wind_broadening_method='formal')\n", " # We add the transit depth because ground-based observations\n", " # lose the continuum information and they are not sensitive to\n", " # the loss of light by the opaque disk of the planet, only\n", " # by the atmosphere\n", " spectra.append(spec + t_depths[i])\n", "\n", " spectra = np.array(spectra)\n", " # Finally we take the mean of the spectra we calculated for each phase\n", " spectrum = np.mean(spectra, axis=0)\n", " return spectrum\n", "\n", "# Here we divide wl_obs by 1E10 to convert angstrom to m\n", "t_spectrum = transmission_model(wl_obs / 1E10, v_wind_0, n_he_3, log_T_0, v_array)\n", "plt.errorbar(wl_obs, f_obs, yerr=u_obs)\n", "plt.plot(wl_obs, t_spectrum, color='k', lw=2)\n", "plt.xlabel(r'Wavelength (${\\rm \\AA}$)')\n", "plt.ylabel('Normalized flux')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ebff07be", "metadata": {}, "source": [ "Alright, it seems that our first guess was not very good. But we shall soon make this an actual fit. For now, let's write a cascading model that combines both the atmosphere and the radiative transfer. This function will also convolve our predicted spectrum with the instrumental profile.\n", "\n", "Also, in the next cell you can do a trial-and-error process to have a better starting guess for the escape rate and the temperature. It took me a minute to find out that the escape rate `1E10` g / s and temperature `6000` K are a much better first guess to fit the data." ] }, { "cell_type": "code", "execution_count": null, "id": "39b0d119", "metadata": {}, "outputs": [], "source": [ "def cascading_model(theta, wavelength_array):\n", " log_m_dot, log_T, v_wind = theta\n", " n_he_1, n_he_3, n_he_ion, v = atmospheric_model((log_m_dot, log_T))\n", " t_spec = transmission_model(wavelength_array, v_wind, n_he_3, log_T, v)\n", " t_spec_conv = convolve(t_spec, instrumental_profile, boundary='extend')\n", " return t_spec_conv\n", "\n", "# First guess\n", "theta0 = (log_m_dot_0, \n", " log_T_0, \n", " v_wind_0)\n", "\n", "t_spec = cascading_model(theta0, wl_obs / 1E10)\n", "\n", "plt.errorbar(wl_obs, f_obs, yerr=u_obs)\n", "plt.plot(wl_obs, t_spec, color='k', lw=2)\n", "plt.xlabel(r'Wavelength (${\\rm \\AA}$)')\n", "plt.ylabel('Normalized flux')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "eba5b671", "metadata": {}, "source": [ "Great, it seems that the cascading model is also working well. We will fit it to the observations using a maximum likelihood estimation. The log-likelihood is defined as:\n", "\n", "$$\n", "\\ln{p(y | x, \\sigma, \\log{\\dot{m}}, \\log{T}, v_{\\rm wind})} = -\\frac{1}{2} \\sum_n \\left[ \\frac{\\left(y_n - y_{\\rm model}\\right)^2}{\\sigma^2} + \\ln{\\left(2\\pi \\sigma^2 \\right)} \\right]\n", "$$\n", "\n", "We do one sneaky trick in the calculation of log-likelihood here to avoid some numerical issues. The problem is that the solvers, which calculates the steady-state ionization of He, for some reason, can ocassionally become numerically unstable in some very specific cases and lose precision, yielding a `RuntimeError`. These solutions are of no use to us, but we do not want them to stop our optimization. So we discard them by making the log-likelihood function return `-np.inf` in those cases." ] }, { "cell_type": "code", "execution_count": null, "id": "8c6fa1b8", "metadata": {}, "outputs": [], "source": [ "def log_likelihood(theta, x, y, yerr):\n", " try:\n", " model = cascading_model(theta, x)\n", " sigma2 = yerr ** 2\n", " return -0.5 * np.sum((y - model) ** 2 / sigma2 + np.log(sigma2))\n", " except RuntimeError:\n", " return -np.inf" ] }, { "cell_type": "markdown", "id": "d9135eab", "metadata": {}, "source": [ "With all that set, we use `scipy.optimize.minimize()` to maximize the likelihood of our solution and find the best fit. This calculation takes a few minutes to run on a computer with a 3.1 GHz CPU, so I commented the line that actually does this calculation as to not use the resources of online platforms that compile this notebook and upset the powers that be. But you should try running it in your own computer. \n", "\n", "In some cases you may run into runtime warnings, but the result should be robust. The actual computation time depends on how bad the first guess was, so you will probably save some time if you do a first fit by eye and than optimize it. You can also try changing the `method` option of `minimize()`." ] }, { "cell_type": "code", "execution_count": null, "id": "4f96d1f3", "metadata": {}, "outputs": [], "source": [ "nll = lambda *args: -log_likelihood(*args)\n", "args = (wl_obs / 1E10, f_obs, u_obs)\n", "# %time soln = minimize(nll, theta0, args=args, method='Nelder-Mead')\n", "# log_mdot_ml, logT_ml, v_wind_ml = soln.x" ] }, { "cell_type": "markdown", "id": "df6c88fb", "metadata": {}, "source": [ "When I started from a very good guess (`m_dot = 1E10`, `T_0 = 6000`, `v_wind_0 = -2000.0`), `minimize()` converges to a best fit solution of $\\dot{m} = 4.7 \\times 10^{10}$ g s$^{-1}$, $T = 7600$ K, and $v_{\\rm wind} = -1.9$ km s$^{-1}$ in about 5 minutes in a 3.1 GHz CPU with four threads." ] }, { "cell_type": "code", "execution_count": null, "id": "7cac7265", "metadata": {}, "outputs": [], "source": [ "theta_ml = (np.log10(4.7E10), np.log10(7600), -1.9E3)\n", "\n", "t_spec = cascading_model(theta_ml, wl_obs / 1E10)\n", "\n", "plt.errorbar(wl_obs, f_obs, yerr=u_obs)\n", "plt.plot(wl_obs, t_spec, color='k', lw=2)\n", "plt.xlabel(r'Wavelength (${\\rm \\AA}$)')\n", "plt.ylabel('Normalized flux')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }