{ "cells": [ { "cell_type": "markdown", "id": "7a2cd18c", "metadata": {}, "source": [ "# Divide by a black body\n", "\n", "Often in real-world astronomical applications, we want to see how a stellar spectrum varies in wavelength without the large and omnipresent crest of the black body curve.\n", "\n", "In this tutorial we show how to remove the black body curve from a precomputed model spectrum." ] }, { "cell_type": "code", "execution_count": 1, "id": "1bff4637", "metadata": {}, "outputs": [], "source": [ "from gollum.phoenix import PHOENIXSpectrum\n", "from gollum.precomputed_spectrum import PrecomputedSpectrum\n", "from astropy.modeling.physical_models import BlackBody\n", "import astropy.units as u\n", "import numpy as np\n", "%config InlineBackend.figure_format='retina'" ] }, { "cell_type": "code", "execution_count": 2, "id": "57a2e0ff", "metadata": {}, "outputs": [], "source": [ "T_eff = 5_700" ] }, { "cell_type": "code", "execution_count": 3, "id": "5e0d7fcb", "metadata": {}, "outputs": [], "source": [ "original_spectrum = PHOENIXSpectrum(teff=T_eff, logg=4.5, metallicity=0,\n", " wl_lo=0, wl_hi=1e10) # Get the whole spectrum" ] }, { "cell_type": "markdown", "id": "979b0e04", "metadata": {}, "source": [ "The PHOENIX spectra have units of $\\frac{\\mathrm{erg}}{\\mathrm{s\\;cm^2 \\;cm}}$" ] }, { "cell_type": "code", "execution_count": 4, "id": "64e6e428", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\mathrm{\\frac{erg}{s\\,cm^{3}}}$" ], "text/plain": [ "Unit(\"erg / (cm3 s)\")" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "original_spectrum.flux.unit" ] }, { "cell_type": "code", "execution_count": 5, "id": "e165c383", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$5.5922428 \\times 10^{-15} \\; \\mathrm{\\frac{erg}{s\\,cm^{3}}}$" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "original_spectrum.flux.min()" ] }, { "cell_type": "markdown", "id": "10288aa0", "metadata": {}, "source": [ "### Make a black body spectrum with the same temperature" ] }, { "cell_type": "code", "execution_count": 6, "id": "5f14268b", "metadata": {}, "outputs": [], "source": [ "blackbody_model = BlackBody(temperature=T_eff*u.Kelvin)\n", "blackbody_flux_per_sr = blackbody_model(original_spectrum.wavelength)" ] }, { "cell_type": "markdown", "id": "247006ed", "metadata": {}, "source": [ "The Black Body spectra have units of $\\frac{\\mathrm{erg}}{\\mathrm{s\\;cm^2 \\;Hz \\;sr}}$. To convert between the two conventions we have to do two things. First we have to pretend we are standing on the surface of the star, and multiply by $\\pi$ steradians. Second, we have to convert flux density in per frequency to per wavelength units. We can do that with astropy's `equivalencies` kwarg." ] }, { "cell_type": "code", "execution_count": 7, "id": "a27c90f8", "metadata": {}, "outputs": [], "source": [ "blackbody_flux_per_Hz = blackbody_flux_per_sr * np.pi * u.steradian" ] }, { "cell_type": "code", "execution_count": 8, "id": "e050f4f5", "metadata": {}, "outputs": [], "source": [ "blackbody_flux = blackbody_flux_per_Hz.to(original_spectrum.flux.unit, \n", " equivalencies=u.spectral_density(original_spectrum.wavelength))" ] }, { "cell_type": "code", "execution_count": 9, "id": "a04d7688", "metadata": {}, "outputs": [], "source": [ "blackbody = PrecomputedSpectrum(flux=blackbody_flux, \n", " spectral_axis=original_spectrum.wavelength)" ] }, { "cell_type": "code", "execution_count": 10, "id": "b158b8d8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 269, "width": 618 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = original_spectrum.plot()\n", "blackbody.plot(ax=ax)\n", "ax.set_ylim(1e0, 1e16)\n", "ax.set_yscale('log')\n", "ax.set_ylabel('Flux (erg/s/cm$^3$)');" ] }, { "cell_type": "markdown", "id": "de95c7b3", "metadata": {}, "source": [ "The plot spans 16 orders of magnitude-- a huge dynamic range! Notice that the spectra have similar---but not identical---broadband spectral shapes. They should have the identical area under the curve, by the definition of effective temperature. Let's see if they do!" ] }, { "cell_type": "code", "execution_count": 11, "id": "2b0fccdc", "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import trapezoid" ] }, { "cell_type": "code", "execution_count": 12, "id": "afe2110c", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$0.99048532 \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "original_flux = trapezoid(original_spectrum.flux, x=original_spectrum.wavelength.to(u.cm))\n", "black_body_flux = trapezoid(blackbody.flux, x=original_spectrum.wavelength.to(u.cm))\n", "\n", "original_flux/black_body_flux" ] }, { "cell_type": "markdown", "id": "9de97390", "metadata": {}, "source": [ "The two spectral models have the same flux to within 1%, which is close enough to identical given that more spectrum resides outside the extent of the plot, and numerical artifacts limitations in the spectral modeling procedure. Let's compute the ratio spectrum to see how flat the spectrum looks. We'll first plot it over the same dynamic range as before to emphasize how much more compressed it is." ] }, { "cell_type": "code", "execution_count": 13, "id": "fc9ba890", "metadata": {}, "outputs": [], "source": [ "ratio_spectrum = original_spectrum.divide(blackbody)" ] }, { "cell_type": "markdown", "id": "999ba02b", "metadata": {}, "source": [ "The resulting spectrum is a ratio of fluxes with the same units, so it is dimensionless." ] }, { "cell_type": "code", "execution_count": 14, "id": "8c0b1d06", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ratio_spectrum.flux.unit == u.dimensionless_unscaled" ] }, { "cell_type": "code", "execution_count": 15, "id": "2f432582", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 269, "width": 620 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = ratio_spectrum.plot();\n", "\n", "ax.set_ylim(1e-12, 1e4)\n", "ax.set_yscale('log')\n", "ax.set_ylabel('Normalized flux');\n", "\n", "ax.axhline(1.0, linestyle='dashed', color='k');" ] }, { "cell_type": "markdown", "id": "e67a151b", "metadata": {}, "source": [ "At this dramatic zoom level, the flux looks pretty flat (except for the extreme ultraviolet portion of the spectrum). Let's zoom in on a region of interest from $8000 - 13000\\; Å$." ] }, { "cell_type": "code", "execution_count": 16, "id": "ffea529e", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 264, "width": 624 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = ratio_spectrum.plot(ylo=0, yhi=1.15);\n", "ax.set_ylabel('Normalized flux');\n", "\n", "ax.axhline(1.0, linestyle='dashed', color='k');\n", "ax.set_xlim(8_000, 13_000);" ] }, { "cell_type": "markdown", "id": "dc91987d", "metadata": {}, "source": [ "OK, looks good! We have successfully used the blackbody curve to coarsely flatten the spectrum!" ] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }