{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Energy Densities of the Photon Targets\n", "\n", "agnpy estimates the energy densities, $u\\,/\\,({\\rm erg}\\,{\\rm cm}^{-3})$, of line and thermal emitters as a function of the distance from the central black hole (BH) along the jet axis, $u(r)$, in the reference frames comoving with the galaxy or the blob. This distance represents the distance of the blob (and of the accelerated particles) from the photon fields produced by the line and thermal emitters. When considering the external Compton scenario, comparing the energy densities of several targets at different distances might be a useful exercise to estimate which photon field is dominating the Compton scattering." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "from astropy.constants import M_sun\n", "from astropy.coordinates import Distance\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from agnpy.targets import SSDisk, SphericalShellBLR, RingDustTorus, PointSourceBehindJet\n", "from agnpy.emission_regions import Blob\n", "from agnpy.utils.plot import load_mpl_rc\n", "\n", "# matplotlib adjustments\n", "load_mpl_rc()\n", "u_label = r\"$u\\,/\\,{\\rm erg}\\,{\\rm cm}^{-3}$\"\n", "u_prime_label = r\"$u'\\,/\\,{\\rm erg}\\,{\\rm cm}^{-3}$\"\n", "r_label = r\"$r\\,/\\,{\\rm cm}$\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shakura Sunyeav Disk" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* Shakura Sunyaev accretion disk:\n", " - M_BH (central black hole mass): 1.99e+42 g\n", " - L_disk (disk luminosity): 1.00e+46 erg / s\n", " - eta (accretion efficiency): 8.33e-02\n", " - dot(m) (mass accretion rate): 1.34e+26 g / s\n", " - R_in (disk inner radius): 8.86e+14 cm\n", " - R_out (disk inner radius): 2.95e+16 cm\n" ] } ], "source": [ "M_BH = 1e9 * M_sun\n", "L_disk = 1e46 * u.Unit(\"erg s-1\")\n", "eta = 1 / 12\n", "R_tilde_in = 6\n", "R_tilde_out = 200\n", "\n", "disk = SSDisk(M_BH, L_disk, eta, R_tilde_in, R_tilde_out, R_g_units=True)\n", "print(disk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us define an array of distances over which we will calculate the integrated energy density $u$, using the `u` class method. Note that by default the energy density is computed in a stationary frame centred in the galaxy." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "r = np.logspace(15, 21) * u.cm\n", "u_disk = disk.u(r)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.loglog(r, u_disk)\n", "plt.ylabel(u_label)\n", "plt.xlabel(r_label)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let us simulate a point source behind the jet with the same luminosity as the disk. **In the limit of large\n", "distances** (specifically when the distance $r$ becomes much larger than the emitter size, $r >> R_{\\rm emitter}$), the energy density of any emitter should be approximable by the one of a point source. \n", "\n", "To test this hypothesis we create a point source (PS) approximating the disk emission. As the point source behind the jet (behind the blob, in fact) described by `agnpy` is monochromatic, we assume it has the same dimensionless energy as the photons emitted at the innermost disk radius." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ps = PointSourceBehindJet(L_disk, disk.epsilon(disk.R_in))\n", "u_ps = ps.u(r)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", " fig.canvas.print_figure(bytes_io, **kw)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_disk, label=\"SS Disk\")\n", "ax[0].loglog(r, u_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(disk.R_out.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm out}$\")\n", "ax[0].set_ylabel(u_label)\n", "ax[0].legend()\n", "\n", "deviation = u_ps / u_disk - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(disk.R_out.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u_{\\rm PS} / u_{\\rm disk} - 1$\")\n", "ax[1].set_ylim([-2, 2])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, for distances much larger than the disk external radius, the two densities tend to each other, though their ratio is never 1 (I will comment later on that). \n", "\n", "Let us see if the two energy densities are also compatible in the reference frame comoving with the blob.\n", "To compute the energy density in such a frame we just have to pass a `Blob` instance to the `u` method." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "blob = Blob()\n", "\n", "u_prime_disk = disk.u(r, blob)\n", "u_prime_ps = ps.u(r, blob)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_prime_disk, label=\"SS Disk\")\n", "ax[0].loglog(r, u_prime_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(disk.R_out.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm out}$\")\n", "ax[0].set_ylabel(u_prime_label)\n", "ax[0].legend()\n", "\n", "deviation = u_ps / u_disk - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(disk.R_out.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u'_{\\rm PS} / u'_{\\rm disk} - 1$\")\n", "ax[1].set_ylim([-2, 2])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, for $r >> R_{\\rm out}$, the two distances tend to each other.\n", "\n", "I think that the fact that the ratio between the energy densities does not converge to 1 is due to the expression for the energy density of the disk not being properly normalised with respect to the radius variable $R$. One in fact can see how, given the same luminosity, changing the external and internal radii of the disk will alter the value of $u$ at large distances. This should not be the case as, no matter how the luminosity is geometrically distributed, it should always reduce to the case of a point source at very large distances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spherical Shell Broad Line Region\n", "Let us compute the energy density of a broad line region (BLR) in the two reference frame (stationary in the galaxy and comoving with the blob) and compare it with a monochromatic point source approximating the BLR." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "blr = SphericalShellBLR(L_disk, 0.1, \"Lyalpha\", 1e17 * u.cm)\n", "\n", "# point source with the same luminosity as the BLR and line emission as the BLR\n", "ps = PointSourceBehindJet(blr.xi_line * L_disk, blr.epsilon_line)\n", "\n", "# compute the energy densities in the stationary frame\n", "u_blr = blr.u(r)\n", "u_ps = ps.u(r)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_blr, label=\"spherical shell BLR\")\n", "ax[0].loglog(r, u_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(blr.R_line.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm BLR}$\")\n", "ax[0].set_ylabel(u_label)\n", "ax[0].legend()\n", "\n", "deviation = u_ps / u_blr - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(blr.R_line.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u_{\\rm PS} / u_{\\rm BLR} - 1$\")\n", "ax[1].set_ylim([-1, 1])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# compute the energy densities in the frame comoving with the blob\n", "u_prime_blr = blr.u(r, blob)\n", "u_prime_ps = ps.u(r, blob)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_prime_blr, label=\"spherical shell BLR\")\n", "ax[0].loglog(r, u_prime_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(blr.R_line.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm BLR}$\")\n", "ax[0].set_ylabel(u_prime_label)\n", "ax[0].legend()\n", "\n", "deviation = u_prime_ps / u_prime_blr - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(blr.R_line.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u'_{\\rm PS} / u'_{\\rm BLR} - 1$\")\n", "ax[1].set_ylim([-1, 1])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, in both reference frames, the energy density of the BLR tends to the one of a point source behind the jet for large enough distances ($r >> R_{\\rm BLR}$ in this case)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ring Dust Torus\n", "Finally let us repeat the same exercise for the torus." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "dt = RingDustTorus(L_disk, 0.2, 1000 * u.K)\n", "\n", "# point source approximating the torus\n", "ps = PointSourceBehindJet(dt.xi_dt * L_disk, dt.epsilon_dt)\n", "\n", "u_dt = dt.u(r)\n", "u_ps = ps.u(r)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_dt, label=\"ring dust torus\")\n", "ax[0].loglog(r, u_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(dt.R_dt.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm DT}$\")\n", "ax[0].set_ylabel(u_label)\n", "ax[0].legend()\n", "\n", "deviation = u_ps / u_dt - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(dt.R_dt.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u_{\\rm PS} / u_{\\rm DT} - 1$\")\n", "ax[1].set_ylim([-1, 1])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# compute the energy density in the comoving frame\n", "u_prime_dt = dt.u(r, blob)\n", "u_prime_ps = ps.u(r, blob)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(\n", " 2,\n", " sharex=True,\n", " gridspec_kw={\"height_ratios\": [2, 1], \"hspace\": 0.05},\n", " figsize=(8, 6),\n", ")\n", "\n", "ax[0].loglog(r, u_prime_dt, label=\"ring dust torus\")\n", "ax[0].loglog(r, u_prime_ps, ls=\"--\", label=\"point source behind jet\")\n", "ax[0].axvline(dt.R_dt.to_value(\"cm\"), ls=\":\", color=\"gray\", label=r\"$r=R_{\\rm DT}$\")\n", "ax[0].set_ylabel(u_prime_label)\n", "ax[0].legend()\n", "\n", "deviation = u_prime_ps / u_prime_dt - 1\n", "\n", "ax[1].axhline(0, ls=\":\", color=\"gray\")\n", "ax[1].semilogx(r, deviation, ls=\"--\", color=\"tab:orange\")\n", "ax[1].axvline(dt.R_dt.to_value(\"cm\"), ls=\":\", color=\"gray\")\n", "ax[1].set_xlabel(r_label)\n", "ax[1].set_ylabel(r\"$u'_{\\rm PS} / u'_{\\rm DT} - 1$\")\n", "ax[1].set_ylim([-1, 1])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, in both reference frames and for large distances - larger than the source size, the energy density of the dust torus tends to the one of a point source behind the jet with the same luminosity." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.13 ('gammapy-0.20.1')", "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": "3.8.13" }, "vscode": { "interpreter": { "hash": "421e168cb6cfc6aca15f181c3a83240737b07be3ef1f106b08741fd3b71852a7" } } }, "nbformat": 4, "nbformat_minor": 4 }