{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Black hole rendering with SageMath\n", "\n", "### Florentin Jaffredo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "This notebook is a step-by-step implementation of a basic rendering engine in curved spacetime. The objective is to obtain a somewhat realistic image of an accretion disk around a black hole.\n", "\n", "The technique consists in launching lightlike geodesics toward the past from a single point (the virtual camera), using the [geodesic integrator](http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/integrated_curve.html) of SageMath. To reduce computation time, the spacetime is assumed be spherical symmetric; this reduces the number of required geodesics to produce an image of $n_x\\times n_y$ pixels from about $O\\left(n_x n_y\\right)$ to $O\\left(\\sqrt{n_x^2+n_y^2}\\right)$.\n", "\n", "This work relies heavily on the [SageManifolds Project](https://sagemanifolds.obspm.fr/). Advanced SageMath notions will also be used throughout this notebook, like Cython compilation and multithreading.\n", "\n", "This notebook requires a version of SageMath at least equal to 9.0:\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 10.1, Release Date: 2023-08-20'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "The code is separated into 9 parts.\n", "\n", "* Declaring the spacetime\n", "* Launching a geodesic\n", "* Launching a lot of geodesics!\n", "* Figuring out where it intersects with the accretion disk\n", "* Adding thickness to the disk\n", "* Using black-body radiation and converting spectra to RGB\n", "* First relativistic effect: Doppler effect\n", "* Second relativistic effect: aberration (forward focalisation)\n", "* Conclusion\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Configuration\n", "\n", "This notebook can be quite ressource hungry to run. For that reason different configurations options are provided. It is recommended to start with the lowest one to check that everything works properly. You can of course adapt the number of CPUs to your needs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**First configuration:** will run in less than a minute on a 4-core laptop. Produces tiny images with no details (no secondary image)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# n_cpu = 4 # 4 Go Ram minimum\n", "# n_geod = 100\n", "# nx, ny = 180, 90" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Second configuration:** will run in about 5 minutes on a workstation, produces a reasonably sized image:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n_cpu = 8 # 8 Go Ram minimum\n", "n_geod = 1000\n", "nx, ny = 720, 360" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Third configuration:** will run in 30 minutes on the Google Cloud Compute Engine. Produces a 4K image showing tiny details on the secondary disk images." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# n_cpu = 36 # 144 Go Ram minimum\n", "# n_geod = 30000\n", "# nx, ny = 4000, 2000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Additional preliminaries: display objects with $ \\LaTeX $ where possible:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Declaring the spacetime\n", "\n", "Let's start slow by declaring the spacetime we'll use for rendering: it is the ***Schwarzschild spacetime***.\n", "\n", "It is important to use a coordinate system that is regular at the horizon. Here we use the *Eddington-Finkelstein coordinates*.\n", "\n", "Let $m$ be the mass of the black hole (that we'll take equal to 2 later). \n", "\n", "We also add a restriction to ensure that nothing touches the central singularity, and we set the metric $g$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 1 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( -\\infty, +\\infty \\right)\\)" ], "text/latex": [ "$\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 1 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( -\\infty, +\\infty \\right)$" ], "text/plain": [ "t: (-oo, +oo); r: (1, +oo); th: (0, pi); ph: (-oo, +oo)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C. = M.chart(r't r:(1,+oo) th:(0,pi):\\theta ph:\\phi')\n", "C.coord_range()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "m = var('m')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[ 2*m/r - 1 2*m/r 0 0]\n", "[ 2*m/r 2*m/r + 1 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g[0,0] = -(1 - 2*m/r)\n", "g[0,1] = 2*m/r\n", "g[1,1] = 1 + 2*m/r\n", "g[2,2] = r^2\n", "g[3,3] = (r*sin(th))^2\n", "g[:]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\\)" ], "text/latex": [ "$\\displaystyle g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = (2*m/r - 1) dt⊗dt + 2*m/r dt⊗dr + 2*m/r dr⊗dt + (2*m/r + 1) dr⊗dr + r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a 3-dimensional Euclidean space $E$ to plot some results, using a map $\\phi: M \\rightarrow E$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left(x, y, z\\right) = \\left(r \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\cos\\left({\\theta}\\right)\\right) \\end{array}\\)" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left(x, y, z\\right) = \\left(r \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), r \\cos\\left({\\theta}\\right)\\right) \\end{array}$" ], "text/plain": [ "M → E^3\n", " (t, r, th, ph) ↦ (x, y, z) = (r*cos(ph)*sin(th), r*sin(ph)*sin(th), r*cos(th))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E. = EuclideanSpace()\n", "phi = M.diff_map(E, [r*sin(th)*cos(ph), r*sin(th)*sin(ph), r*cos(th)])\n", "phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Launching a geodesic\n", "\n", "[Geodesic integration](http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/integrated_curve.html) was first implemented in SageMath in 2017 and perfected in 2018 to support fast integration and event handling (used to detect the singularity in our case).\n", "\n", "To introduce the method, let's plot an orbit around a black hole.\n", "\n", "To do that, we need to find a starting point $p$ as well as an inital velocity vector $v$. It can be quite troublesome to find a suitable one, but here is a free one:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "p = M((0, 14.98, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((2, 0, 0.005, 0.05))\n", "v = v / sqrt(-g.at(p)(v, v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v$ is defined as a member of the tangent space at $p$. The last line is used to normalize $v$ as a unit timelike vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next is the definition of the geodesic. We need to pass a symbolic variable for the proper time (which will not be used). The starting point is deduced from the velocity vector (as the point where the velocity vector is defined)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "tau = var('tau')\n", "curve = M.integrated_geodesic(g, (tau, 0, 3000), v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The integration should be very fast. Don't forget to give some numerical value to $m$ here." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [], "source": [ "sol = curve.solve(step = 1, method=\"ode_int\", parameters_values={m: 2})\n", "# sol = curve.solve(step = 1, parameters_values={m: 2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the solution requires an interpolation. This is automatically done in the next line." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "interp = curve.interpolate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell plots the result using the mapping we provided previously. We also add a grey sphere at $r_s = 2m = 4$ (the event horizon) to give a scale." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = curve.plot_integrated(mapping=phi, color=\"red\", thickness=2, plot_points=3000)\n", "P += sage.plot.plot3d.shapes.Sphere(4, color='grey')\n", "P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that it look nothing like an ellipse, as we are used to in classical celestial mechanics. At this step, you can try adding an angular momentum to the black hole--in other words going from Schwarzschild to Kerr--by setting a non-zero angular momentum in the definition of the manifold ($J=1$ works fine). When this is the case, the orbits are not even included in a plane. Don't forget to revert back your changes before proceeding to the next part." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Launching a lot of geodesics!\n", "\n", "Of course one geodesic is not enough for us, we'll need at least a few hundred of them.\n", "\n", "Because we don't need to compute the equation again each time, we simply copy the previous declaration of the geodesic while changing the initial point and velocity.\n", "\n", "It will be useful here to introduce the Python module `multiprocessing` and progress bars as widgets:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import multiprocessing\n", "from ipywidgets import FloatProgress\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It wouldn't be a great idea to set \"1 job = 1 geodesic integration\". Indeed, that would mean copying the geodesic declaration a few hundred times, which would be quite slow. What is done instead is seperating geodesics into batches using the following function:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def chunks(l, n):\n", " \"\"\"Yield successive n-sized chunks from l.\"\"\"\n", " for i in range(0, len(l), n):\n", " yield l[i:i + n]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The number of batches per CPU in not very important. If set to 1, some CPUs may run faster than other ones and stay idle at the end. If too high, too much time will be spent copying the curve setting. I found 3 to be a good value." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "n_batches_per_cpu = 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also redefine the previous geodesic to our new needs: fewer steps and the ability to check for chart boundaries when integrating. The $v$ in this case will not be used; it will always be overwritten before starting any integration." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "curve = M.integrated_geodesic(g, (tau, 0, 200), v, across_charts=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using `multiprocessing`, functions can only accept a single argument. To overcome this limitation, each argument will be a tuple (curve, start index, number of curves to integrate)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "args = []\n", "start_index = 0\n", "\n", "for chunk in chunks(range(n_geod), n_geod//(n_batches_per_cpu*n_cpu)):\n", " args += [(loads(curve.dumps()), start_index, len(chunk))]\n", " start_index += len(chunk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next line prints the list of arguments. We can check that each of the 100 geodesics are correctly set. Our little trick allowed us to only define 13 geodesics (about 3 per core, as we wanted; note, the exact result here will depend on what you used for `n_cpu` at the beginning)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(Integrated geodesic in the 4-dimensional Lorentzian manifold M, 984, 16)\n", "25\n" ] } ], "source": [ "print(args[-1])\n", "print(len(args))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now comes a question: which vector can be used as the starting 4-velocity?\n", "\n", "We need a past-oriented lightlike vector pointing toward the center but with a linearly increasing angle. The 3 space components are already imposed. The time component must then be chosen so that the total vector is lightlike.\n", "\n", "Let $p$ be the initial point and $v$ the initial 4-velociy, with an unknown time coordinate $dt$ ($y$ depends on the angle, it is a known quantity)." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "dt, y, r0 = var('dt, y, r0')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "p = M((0, r0, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((dt, -1, 0, y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The norm of $v$ is currently given by:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle r_{0}^{2} y^{2} + \\frac{\\mathit{dt}^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} - \\frac{4 \\, \\mathit{dt} m}{r_{0}} + \\frac{2 \\, m + r_{0}}{r_{0}}\\)" ], "text/latex": [ "$\\displaystyle r_{0}^{2} y^{2} + \\frac{\\mathit{dt}^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} - \\frac{4 \\, \\mathit{dt} m}{r_{0}} + \\frac{2 \\, m + r_{0}}{r_{0}}$" ], "text/plain": [ "r0^2*y^2 + dt^2*(2*m - r0)/r0 - 4*dt*m/r0 + (2*m + r0)/r0" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)(v, v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to find $dt$ so that this expression is equal to 0 (lightlike condition). this is easy:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{dt} = -\\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} - 2 \\, m}{2 \\, m - r_{0}}, \\mathit{dt} = \\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} + 2 \\, m}{2 \\, m - r_{0}}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{dt} = -\\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} - 2 \\, m}{2 \\, m - r_{0}}, \\mathit{dt} = \\frac{\\sqrt{-{\\left(2 \\, m r_{0} - r_{0}^{2}\\right)} y^{2} + 1} r_{0} + 2 \\, m}{2 \\, m - r_{0}}\\right]$" ], "text/plain": [ "[dt == -(sqrt(-(2*m*r0 - r0^2)*y^2 + 1)*r0 - 2*m)/(2*m - r0), dt == (sqrt(-(2*m*r0 - r0^2)*y^2 + 1)*r0 + 2*m)/(2*m - r0)]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = g.at(p)(v, v).solve(dt)\n", "sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, there are two solutions: one past-oriented and one future-oriented. In fact, in our case it does not matter, given that the Schwartzschild spacetime is static." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next cell defines the function that will be called by `multiprocessing`. It starts by unpacking the arguments, setting an empty dictionary as the result, and defining the starting position.\n", "\n", "The initial velocity is then overwritten using the formula above, the integration is performed, and the result is added to the dictionary." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "def calc_some_geodesics(args):\n", " \"\"\"\n", " Compute nb geodesics starting at index n0\n", " \"\"\"\n", " curve, n0, nb = args\n", " res = {}\n", " r = 100\n", " posi = [0, r, pi/2, 0]\n", " p = M(posi)\n", " Tp = M.tangent_space(p)\n", " for i in range(n0, n0+nb):\n", " # starting vector\n", " dy = i*0.006/n_geod\n", " v = Tp([sol[0].rhs()(r0=r, y=dy, m=2).n(), -1, 0, dy])\n", " # overwrite the starting vector\n", " curve._initial_tangent_vector = v\n", " # integration with m=2\n", " curve.solve_across_charts(step=0.2, parameters_values={m:2})\n", " # copy and clear solution\n", " res[i] = (p.coord(), curve._solutions.copy())\n", " curve._solutions.clear()\n", " return res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`geo` will keep the numerical solutions. I like to see `pool` as a hole in which I can throw some jobs. `multiprocessing` will then magically do them for me using every resource available on the computer." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "geo = {}\n", "\n", "# progress bar display\n", "%display plain\n", "f = FloatProgress(min=0, max=n_geod)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7567c5b3a89f406f9a75df7968615cda", "version_major": 2, "version_minor": 0 }, "text/plain": [ "FloatProgress(value=0.0, max=1000.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(f)\n", "pool = multiprocessing.Pool(n_cpu)\n", "for i, some_res in enumerate(pool.imap_unordered(calc_some_geodesics, args)): # do and wait\n", " # progress bar update\n", " f.value += len(some_res)\n", " # update result\n", " geo.update(some_res)\n", "\n", "# clean exit\n", "pool.close()\n", "pool.join()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If, for any reason, you don't want to use parallel computing, you can replace the previous cell with this one:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "display(f)\n", "for arg in args:\n", " some_res = calc_some_geodesics(arg)\n", " f.value += len(some_res)\n", " geo.update(some_res)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now try to visualize those geodesics.\n", "Next cell will plot 20 of them." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# add the sphere\n", "P = sage.plot.plot3d.shapes.Sphere(4, color='grey')\n", "\n", "# cycle through the solutions\n", "for i in range(0, n_geod, 5*n_geod/100): \n", " # set solution\n", " curve._solutions = geo[i][1]\n", " # do interpolation\n", " interp = curve.interpolate()\n", " # plot the curve\n", " P += curve.plot_integrated(mapping=phi, color=[\"red\"], thickness=2, plot_points=150, \n", " label_axes=False, across_charts=True)\n", "\n", "# show the result \n", "P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that some fall inside the black hole toward the singularity. That's not an issue because the integration is automaticaly stopped when the geodesic leaves the chart domain defined in part 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intersection with the accretion disk\n", "\n", "Time to transform those simulated light-rays into an image. To do this, we first need to compute the intersection between each geodesic and the accretion disk.\n", "\n", "For this example, the disk spans from $r=8$ to $r=50$, and is tilted by an angle $\\alpha = - \\frac{\\pi}{20}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "disk_min = 12\n", "disk_max = 50\n", "alpha = -pi/20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the disk on top of the last figure.\n", "\n", "(We cheat a little bit here and use a flattened torus.)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "D = sage.plot.plot3d.shapes.Torus((disk_min+disk_max)/2,\n", " (disk_min-disk_max)/2).scale(1,1,0.01).rotateY(-pi/20)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P + D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same but tilted on the X-axis by an angle $\\beta=\\frac{\\pi}{3}$. As explained earlier, the final image will be obtained by computing for each pixel : \n", "\n", "* Which geodesic best describes the light-ray\n", "* Which angle $\\beta$ at which the disk should be tilted\n", "* The intersection between the disk and that geodesic\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P + D.rotateX(pi/3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesics are formatted in a strange way because of the solver used. The next line makes it easier to use. `geo` is now a list of list of coordinates (and not a dictionary of strange things)." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "geo = [list(geo[i][1].values())[0][0][1].tolist() for i in range(len(geo))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To detect the intersection between the disk and a geodesic, the only solution is to parse the list of successive coordinates. This is done in the following function.\n", "\n", "For each point of the curve, two rotations are performed (manually for speed purposes) before checking the point coordinates." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def intersection(curve, alpha, beta):\n", " \"\"\"\n", " Return True if the curve intersect the disk comprised between dmin and dmax\n", " tilted of angles alpha and beta\n", " \"\"\"\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n):\n", " # done in 3 lines for speed consideration\n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # conversion to cartesian:\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta) \n", " # rotation around the X-axis:\n", " y2, z2 = y2*cos(beta)-z2*sin(beta), z2*cos(beta)+y2*sin(beta) \n", " # rotation around the Y-axis:\n", " x2, z2 = x2*cos(alpha)-z2*sin(alpha), z2*cos(alpha)+x2*sin(alpha) \n", " if z!=z2: # needed to prevent a division by zero next line\n", " t = z/(z-z2) # if 0<=t<1 then the curve intersect the disk between the points i and i-1\n", " if t>=0 and t<1 and curve[i][2]>disk_min and curve[i][2]=0 and t<1 and curve[i][2]>dmin and curve[i][2]>> from scipy.misc import bytescale\n", " >>> img = np.array([[ 91.06794177, 3.39058326, 84.4221549 ],\n", " ... [ 73.88003259, 80.91433048, 4.88878881],\n", " ... [ 51.53875334, 34.45808177, 27.5873488 ]])\n", " >>> bytescale(img)\n", " array([[255, 0, 236],\n", " [205, 225, 4],\n", " [140, 90, 70]], dtype=uint8)\n", " >>> bytescale(img, high=200, low=100)\n", " array([[200, 100, 192],\n", " [180, 188, 102],\n", " [155, 135, 128]], dtype=uint8)\n", " >>> bytescale(img, cmin=0, cmax=255)\n", " array([[91, 3, 84],\n", " [74, 81, 5],\n", " [52, 34, 28]], dtype=uint8)\n", " \"\"\"\n", " if data.dtype == np.uint8:\n", " return data\n", "\n", " if high > 255:\n", " raise ValueError(\"`high` should be less than or equal to 255.\")\n", " if low < 0:\n", " raise ValueError(\"`low` should be greater than or equal to 0.\")\n", " if high < low:\n", " raise ValueError(\"`high` should be greater than or equal to `low`.\")\n", "\n", " if cmin is None:\n", " cmin = data.min()\n", " if cmax is None:\n", " cmax = data.max()\n", "\n", " cscale = cmax - cmin\n", " if cscale < 0:\n", " raise ValueError(\"`cmax` should be larger than `cmin`.\")\n", " elif cscale == 0:\n", " cscale = 1\n", "\n", " scale = float(high - low) / cscale\n", " bytedata = (data - cmin) * scale + low\n", " return (bytedata.clip(low, high) + 0.5).astype(np.uint8)\n", "\n", "def toimage(arr, high=255, low=0, cmin=None, cmax=None, pal=None,\n", " mode=None, channel_axis=None):\n", " \"\"\"Takes a numpy array and returns a PIL image.\n", " This function is only available if Python Imaging Library (PIL) is installed.\n", " The mode of the PIL image depends on the array shape and the `pal` and\n", " `mode` keywords.\n", " For 2-D arrays, if `pal` is a valid (N,3) byte-array giving the RGB values\n", " (from 0 to 255) then ``mode='P'``, otherwise ``mode='L'``, unless mode\n", " is given as 'F' or 'I' in which case a float and/or integer array is made.\n", " .. warning::\n", " This function uses `bytescale` under the hood to rescale images to use\n", " the full (0, 255) range if ``mode`` is one of ``None, 'L', 'P', 'l'``.\n", " It will also cast data for 2-D images to ``uint32`` for ``mode=None``\n", " (which is the default).\n", " Notes\n", " -----\n", " For 3-D arrays, the `channel_axis` argument tells which dimension of the\n", " array holds the channel data.\n", " For 3-D arrays if one of the dimensions is 3, the mode is 'RGB'\n", " by default or 'YCbCr' if selected.\n", " The numpy array must be either 2 dimensional or 3 dimensional.\n", " \"\"\"\n", " data = np.asarray(arr)\n", " if np.iscomplexobj(data):\n", " raise ValueError(\"Cannot convert a complex-valued array.\")\n", " shape = list(data.shape)\n", " valid = len(shape) == 2 or ((len(shape) == 3) and\n", " ((3 in shape) or (4 in shape)))\n", " if not valid:\n", " raise ValueError(\"'arr' does not have a suitable array shape for \"\n", " \"any mode.\")\n", " if len(shape) == 2:\n", " shape = (shape[1], shape[0]) # columns show up first\n", " if mode == 'F':\n", " data32 = data.astype(np.float32)\n", " image = Image.frombytes(mode, shape, data32.tobytes())\n", " return image\n", " if mode in [None, 'L', 'P']:\n", " bytedata = bytescale(data, high=high, low=low,\n", " cmin=cmin, cmax=cmax)\n", " image = Image.frombytes('L', shape, bytedata.tobytes())\n", " if pal is not None:\n", " image.putpalette(np.asarray(pal, dtype=np.uint8).tobytes())\n", " # Becomes a mode='P' automagically.\n", " elif mode == 'P': # default gray-scale\n", " pal = (np.arange(0, 256, 1, dtype=np.uint8)[:, np.newaxis] *\n", " np.ones((3,), dtype=np.uint8)[np.newaxis, :])\n", " image.putpalette(np.asarray(pal, dtype=np.uint8).tobytes())\n", " return image\n", " if mode == '1': # high input gives threshold for 1\n", " bytedata = (data > high)\n", " image = Image.frombytes('1', shape, bytedata.tobytes())\n", " return image\n", " if cmin is None:\n", " cmin = np.amin(np.ravel(data))\n", " if cmax is None:\n", " cmax = np.amax(np.ravel(data))\n", " data = (data*1.0 - cmin)*(high - low)/(cmax - cmin) + low\n", " if mode == 'I':\n", " data32 = data.astype(np.uint32)\n", " image = Image.frombytes(mode, shape, data32.tobytes())\n", " else:\n", " raise ValueError(_errstr)\n", " return image\n", "\n", " # if here then 3-d array with a 3 or a 4 in the shape length.\n", " # Check for 3 in datacube shape --- 'RGB' or 'YCbCr'\n", " if channel_axis is None:\n", " if (3 in shape):\n", " ca = np.flatnonzero(np.asarray(shape) == 3)[0]\n", " else:\n", " ca = np.flatnonzero(np.asarray(shape) == 4)\n", " if len(ca):\n", " ca = ca[0]\n", " else:\n", " raise ValueError(\"Could not find channel dimension.\")\n", " else:\n", " ca = channel_axis\n", "\n", " numch = shape[ca]\n", " if numch not in [3, 4]:\n", " raise ValueError(\"Channel axis dimension is not valid.\")\n", "\n", " bytedata = bytescale(data, high=high, low=low, cmin=cmin, cmax=cmax)\n", " if ca == 2:\n", " strdata = bytedata.tobytes()\n", " shape = (shape[1], shape[0])\n", " elif ca == 1:\n", " strdata = np.transpose(bytedata, (0, 2, 1)).tobytes()\n", " shape = (shape[2], shape[0])\n", " elif ca == 0:\n", " strdata = np.transpose(bytedata, (1, 2, 0)).tobytes()\n", " shape = (shape[2], shape[1])\n", " if mode is None:\n", " if numch == 3:\n", " mode = 'RGB'\n", " else:\n", " mode = 'RGBA'\n", "\n", " if mode not in ['RGB', 'RGBA', 'YCbCr', 'CMYK']:\n", " raise ValueError(_errstr)\n", "\n", " if mode in ['RGB', 'YCbCr']:\n", " if numch != 3:\n", " raise ValueError(\"Invalid array shape for mode.\")\n", " if mode in ['RGBA', 'CMYK']:\n", " if numch != 4:\n", " raise ValueError(\"Invalid array shape for mode.\")\n", "\n", " # Here we know data and mode is correct\n", " image = Image.frombytes(mode, shape, strdata)\n", " return image" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the above definition of `toimage`, we get the actual image from `data`:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtAAAAFoCAIAAADxRFtOAAANZElEQVR4nO3dwXrbuA4GUKffvP8r5y7S9qaJY8sSQALkOatZzExkEQD/Uop7uwEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADHeZl8AUMh79P/QiAE+mAawkfA8cZ0ZBJvQ7LCyggnjMSMJVqW7YSntEsZjJhQsQztDe4uFjJ+YVtCaFoZ+3m+3t21yxndvf+4A0IiehTa2TRiPmWLQglaF6uSMg4wzqEyHQkVCxkVGG1SjK6EQOSOcGQdFaEaYT84YwLCDufQgzCRqDGbkwSy6D+YQNSYy+GA8fQdDyRmlmIAwjHaDQUSNssxBGECjQTpRowXTEFJpMcgiZzRlLEIGnQXxRI0FGI4QS09BJFFjMUYkRNFNEEPUWJhBCdfpI7hK1NiEcQlX6CA4T9TYkKEJ5/yafQHQlbSxJ+sO5wjr8Br7DX8ZoHCcEw54gbTBZ+oBjhPQ4RBbCw+YpPCUNoEnRA0OMk/hAY9U4BFpg+NUCzwgkcN9Ng9OM1jhO30BX4kahDBe4TMdAf8nahDOkIUP3uGA36QNMqgr+CBwwO1mVyCT6oKb0z6wGTCMgcvOnHCwNWmDkdQbOxM42Jfpz3iqjm054WNHhj7TGb7sRs2zF1GDUoxg9uGRChuRNqhGTbIPgYNdmOzUpDLZhMDBFsx0KlOf7MADRBZnlNOIiczCnHCwMmmDXlQsCxM4WJbZTUfqllU5wGNBRjYLMJ1ZjBMOViNtsAaVzGIEDpZiRrMS9cxKHNqxCKOZhZnULMAJByuQNlibCmcBAgftmcXsQJ3TnYM6GjOC2ZCpTVNOOACAdLIyLTnbYHNmN+044aAfaQN0Ae0IHDRjzsIHvUAvAgedmLDwmY6gEc8B6cFghQeMcupzwkED0gY8pkeoT+CgOpMUjtApFCdwUJoZCsfpFyoTOKjL9IRX6RrKEjgoytyEc/QONXm1mXKMywoujgaLWIH5TikKklpsVFMMGARWdgojnjpUI4XYk4aZ3vnWepjpaw0flCIl2H7GKNjwln6MgkvPbhQh89lyUjVqcpWQqlElsCQVyGT2mDxN21tJ5GlaEqxB+TGTrSXDMl2tPDIsUx60o/aYw16SYcl+VioZliwVilN1TGALibVJGyubWJuUDXUoOUazbQTasIHVT6AN64eJ1BtD2S2ibN66CinK5oXESIqNcWwSITTtXyoqhIpiDJXGCDaGENr1LtUVQnWRzd8WSzr7QQj7wU/cmRD6lGxalVym2HW69CDFdp1iI48TDhLZAK6zARznXl2nZ8mjQ0lhbIWY25+nF7HpZfOZvYFwiop4Jv514zvzy6pdvIDY/9v1C+AE2wOxVBSRTPkQw9ry83ql/tBhP+inH8ppNgmiqCXCmO8hBvTk35Wa0v8jf7qaDGGfIIRCIobJfl12N87NGd8Nux7FeV2RmqE1VcRVpnmIAU80ynb7gMtTpSHKlhAtqB/OM8SjJPVh8ZzxXeoFK9cojSqKUlQOJxnfUTKasF3U+Czv4hVtlKalxVzKhpeZ2lFEjQfEjvoWKDNGUjC8wKQOlLSVLtbSSZ9IJQdarOTI46vNOcqMrux9xbRxu93e/nw0yrI6HLTegCKegRIusPGWeYbyWPjHVNXhli9CLlIhPGEux4ptuSVPNR4I/7zKO9ZW1cirlAc/MovDSRvXyRz1bViWHKEwuMMIzuAxShSPV1rYtj75iZLgHyZvnqhm2/Ng47vA+6Ds86hV/lIM/GbmppI2MsgcXShabsqAm1GbL6TNNn+M8pPA26IRsqnezSmAfRmvY0gb2WSOdlTynqz7jkzVYaJ2QY36VNRd0h3DqOrdWPG9GKYjSRuDyRwdKe99+GrzXfh+6I6kjZe8KfKGjKZ9mGaL08mzXG8taeOckPumcWZR8wuzuMsyMSeSNuaSObpT/EuyrKsxJaeL2uo052lRN1A3TacLVmI1F2Ey1nGxqaSNECG3UVvVoSMWYBHbMxNLkTbqkDnWozVas3xdmYMFeXWjGi9zrEqbdGTVmjH7ypI2apI51qZlGvlv9gXwnGG3A6ucR5Jb2OfGscrFWaC67ECNeHWjMi9z7EYr1WRdyjHX2vEwpT4PVvakrUqxHFWYZX1d/6OzPhzg+n3WpH1psQqswkzm1wI8TOnCgxU+aLdZvDQ6moHFF8bfGP5qNz54z3QWd3sQk25Jjjd6ccjBT7ThAG5yIoNpbd4V7cjbozylK5O4scFMon14V7Qpb49ynCYN5B2OGAbQboyhnXkdZB9/F1rLX+cenmTcbM7xRmsOObhI/57ghOMFRgwfzBoccmzOr7qc4EY9YabwneONBTjkIIPWfsAJxx3mCA8YKHxwyMF3Tj4ecEN+Mzg4wq/CrsSvyDKMrr9tfsJhUjCYkqtG/mMMJx+3DQOHic9p244JHvBghVdtGz62CBzGAXVsNV+KkxWYbqvwsewHNEeIFfWwf9mW6ylqUQwcYi05KJY64dDzACxgyZOPFQKHnEEXywyOZXiqQn3LfL16y+s3IBjM85SFeapCU+3mSZsL1szMEtIkfv2ysqjVMaaYpcV4Kf1IRfcCwFMt3vmoeGFyBnUE/sG3YrNxu91CF8j4oo5qM6fK9ehSCopqD89T6gtcI9OMgiqMoJmPVLQlO1DnXciFLKzCM5cJgcP8pQV7D+f4VVuKm/V7toMCh/YDgFIGH3sk/gghg75iH+c7LGkhdrEMQPpKGlkpJxw6DQCaSvqTUljgEDJYhgMJrvMmB92FP3C5Gjh0FACsLeQ90zP/rZDBwgKPN7zA0U74kpmWLOzVTnnthEPzAAC31wP6ocAhZ8CrdE1fvgEMjjv+tOVR4DAx2Y1thlheHWUfT5PHncChPeAiTdSdQw447afk8d/3fwOIYtPqxYEEBPqSPN5uGgw+uR4RKvwlSZwWu3ymK/z1Sz/AZzqCKGoJPvs1+wJgKfaYlVhNCCRwwFent5kv/6HnKR19WbWoYgAEDrjjxG5hg1mVYoAQAgfc9x63bdh+6gtca8sNdwkc8MjB/eP7v+N5Sl/f1+5gDYga8IDAAc893ktsMzt4XABqAJ4SOOCou/uKnWYfd1dfAcBBr/1tscDn786z2ezm3brDWU444KQHu44XOLp7sILSBpwjcEA6+aM+awTZ3qR1SGUna8Q8hDwCB4wmghRh+sFIAgfMJ4IMYNbBXAIH1PURRN4lkgPeP90uoCCBA9rbJI4YVtCawAHbKRJQDB/YisABAKTzPRwAQDqBAwBIJ3AAAOkEDgAgncABAKQTOACAdAIHAJBO4AAA0gkcAEA6gQMASCdwAADpBA4AIJ3AAQCkEzgAgHQCBwCQTuAAANIJHABAOoEDAEgncAAA6QQOACCdwAEApBM4AIB0AgcAkE7gAADSCRwAQDqBAwBIJ3AAAOkEDgAgncABAKQTOACAdAIHAJBO4AAA0gkcAEA6gQMASCdwAADpBA4AIJ3AAQCkEzgAgHQCBwCQTuAAANIJHABAOoEDAEgncAAA6QQOACCdwAEApBM4AIB0AgcAkE7gAADS/XqbfQUAwPL+yRvvs64CAFjR27d/+IfkAQCc9j1ePHmiInkAAAc9SBVHX+GQPACAu46EiTPvjAofALC5VwPEpV9SkTwAYCunc0PMb8VKHgCwsOtxIeVrOOQPAGgtPB8kfu+X2AEA7SQlg3FfNCp/AEBBY6LAhG82f7/d3uQPAJjk7c9ePPiHTiZ5AMAAc7f8+YHjOxEEAC6qtsFXu56vhA8AOKjypl752u4TQQDg1m0L73W1/5A8ANhQ05276WXfIX8AsKQ1tuo1PsV9IggA7ay6Ma/6ub4SPgAoa4fNeIfP+IggAsAwO2+6O3/2O+QPAALZZf9yKw4RRAB4wG76lFt0hvwBsDnb56vcsQDyB8Dy7JcXuYEjSCQAxdkOs7nDE8gfANPZ/wZzw0sQQQBS2e2mswSdyCUAX9jGurBS7UkhwCbsWK1ZvjVJIUBrNqf1WNPdvd9ubwIKkOztz7RhW1afRwQR4CU2FX6iNjhPHIEN2TY4R+WQRRyBpmwMZFBXzHc3mnizBM75qXeMe+ZSgaxANGF5hjXdqWG2I51QhPnLVhQ8HCWpcJcxCkfoFBhNcCnC+IORdBzMJ4IMYNjBXL9mXwBgL0znDsN02hAKcdQRzoyDIjQjlCN2hDDdoBSPVKAcO+V17iFUoyuhLkcdJxhqUJPehAYkj6fMMijOIxVowG76mPsD9elT6MRRxxdGGHShW6GlzZOHyQXtaFvobavkYWBBX/oXFrFw8jCnYAFeGoVFrLorr/q5YDd6GdbU+sDDYIL16GtYX4vwYRjB2vQ4bKdI/jB9YCtaHrY2OHyYOLAt7Q/8IzCCmC8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAnPU/KwXtWOgtMmEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img1 = toimage(data)\n", "img1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have seen the movie *Interstellar*, you will know that this looks a bit like a (monochrome) black hole, a very simple one for sure, but we'll improve it step by step in the following sections." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding thickness to the disk\n", "\n", "First we will be adding transpareny and thickness to the disk. For that, let's assume the disk is optically thin. This means light can only be added and never obstructed. What's more, the intensity will be proportional to the total length of emissive medium traversed.\n", "\n", "This length depends on 2 factors: the profile of the disk and the angle $\\theta$ between the disk and the light ray:\n", "\n", "$\\qquad d = \\frac{f(r)}{sin(\\theta)}$\n", "\n", "The computation of the angle $\\theta$ is not trival. The fastest way to obtain it is the perform a change of frame, which will locally (at a single point) give us a Minkowsky metric (orthonormal frame), in which angles are easy to compute.\n", "\n", "To remind you, here is our metric:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[ 2*m/r - 1 2*m/r 0 0]\n", "[ 2*m/r 2*m/r + 1 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or for a point of the disk:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m - r_{0}}{r_{0}} & \\frac{2 \\, m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r_{0}} & \\frac{2 \\, m + r_{0}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & r_{0}^{2} & 0 \\\\\n", "0 & 0 & 0 & r_{0}^{2}\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m - r_{0}}{r_{0}} & \\frac{2 \\, m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r_{0}} & \\frac{2 \\, m + r_{0}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & r_{0}^{2} & 0 \\\\\n", "0 & 0 & 0 & r_{0}^{2}\n", "\\end{array}\\right)$" ], "text/plain": [ "[(2*m - r_0)/r_0 2*m/r_0 0 0]\n", "[ 2*m/r_0 (2*m + r_0)/r_0 0 0]\n", "[ 0 0 r_0^2 0]\n", "[ 0 0 0 r_0^2]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r0, phi = var('r_0, phi')\n", "p = M((0, r0, pi/2, phi))\n", "g.at(p)[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are not that far off. Some rescaling and mixing the first two lines should do the trick." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "# default frame\n", "fr = C.frame()\n", "\n", "# create an automorphism field\n", "aut = M.automorphism_field()\n", "\n", "# some symbolic variables\n", "a, b, c = var('a, b, c')\n", "\n", "# let's try with the simplest matrix possible\n", "aut.add_comp()[:] = [[a, 0, 0, 0], [b, c, 0, 0], [0, 0, 1/r0, 0], \n", " [0, 0, 0, 1/r0]] # only b is off-diagonal\n", "fr2 = fr.new_frame(aut, 'f2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this new frame, the metric at $p$ looks like this:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{b^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{a^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} + \\frac{4 \\, a b m}{r_{0}} & \\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & \\frac{c^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{b^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{a^{2} {\\left(2 \\, m - r_{0}\\right)}}{r_{0}} + \\frac{4 \\, a b m}{r_{0}} & \\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & 0 & 0 \\\\\n", "\\frac{b c {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} + \\frac{2 \\, a c m}{r_{0}} & \\frac{c^{2} {\\left(2 \\, m + r_{0}\\right)}}{r_{0}} & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$" ], "text/plain": [ "[b^2*(2*m + r_0)/r_0 + a^2*(2*m - r_0)/r_0 + 4*a*b*m/r_0 b*c*(2*m + r_0)/r_0 + 2*a*c*m/r_0 0 0]\n", "[ b*c*(2*m + r_0)/r_0 + 2*a*c*m/r_0 c^2*(2*m + r_0)/r_0 0 0]\n", "[ 0 0 1 0]\n", "[ 0 0 0 1]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)[fr2.at(p), :]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This lets us find the values of $ a $, $ b $ and $ c $:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "c = sqrt(r/(r+2*m))\n", "a = sqrt(((r+2*m)/(r)))\n", "b = -2*a*m/(2*m+r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "aut2 = M.automorphism_field() # new automorphism field\n", "aut2.add_comp()[:] = [[a, 0, 0, 0], [b, c, 0, 0], [0, 0, 1/r, 0], [0, 0, 0, 1/(r*sin(th))]]\n", "fr3 = fr.new_frame(aut2, 'f3')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "-1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "-1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$" ], "text/plain": [ "[-1 0 0 0]\n", "[ 0 1 0 0]\n", "[ 0 0 1 0]\n", "[ 0 0 0 1]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[fr3, :]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Success!\n", "\n", "We now have an orthonormal frame everywhere (this is only possible because this frame doesn't correspond to a system of coordinates; otherwise the spacetime would be flat).\n", "\n", "Don't forget that vectors are contravariant tensors, so the components of the 4-velocity will be transformed by this matrix:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{\\sqrt{r}}{\\sqrt{2 \\, m + r}} & 0 & 0 & 0 \\\\\n", "\\frac{2 \\, m}{\\sqrt{2 \\, m + r} \\sqrt{r}} & \\frac{\\sqrt{2 \\, m + r}}{\\sqrt{r}} & 0 & 0 \\\\\n", "0 & 0 & r & 0 \\\\\n", "0 & 0 & 0 & r \\sin\\left({\\theta}\\right)\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrr}\n", "\\frac{\\sqrt{r}}{\\sqrt{2 \\, m + r}} & 0 & 0 & 0 \\\\\n", "\\frac{2 \\, m}{\\sqrt{2 \\, m + r} \\sqrt{r}} & \\frac{\\sqrt{2 \\, m + r}}{\\sqrt{r}} & 0 & 0 \\\\\n", "0 & 0 & r & 0 \\\\\n", "0 & 0 & 0 & r \\sin\\left({\\theta}\\right)\n", "\\end{array}\\right)$" ], "text/plain": [ "[ sqrt(r)/sqrt(2*m + r) 0 0 0]\n", "[2*m/(sqrt(2*m + r)*sqrt(r)) sqrt(2*m + r)/sqrt(r) 0 0]\n", "[ 0 0 r 0]\n", "[ 0 0 0 r*sin(th)]" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aut2.inverse()[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The angle $\\theta$ can now be computed using: \n", "$$\\theta = \\arctan\\left(\\frac{\\overrightarrow{v}_{\\bot}}{\\overrightarrow{v}_{\\parallel}}\\right)$$ \n", "Because this formula is using 3-vectors, it was indeed important to have been in an orthonormal frame.\n", "\n", "We also need to perform rotation of the angles $\\alpha$ and $\\beta$ for the 4-velocity. In the next cell is a Cython version optimized for speed." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, sqrt\n", "\n", "cpdef tuple spherical_to_xyz(float dr, float dtheta, float dphi, float r, \n", " float theta, float phi, float alpha, float beta):\n", " \"\"\"\n", " Convert spherical coordinates to cartesian and apply the \n", " two rotations at the same time.\n", " \"\"\"\n", " cdef float dx, dy, dz\n", " cdef float ca, cb, ct, cp\n", " cdef float sa, sb, st, sp\n", " \n", " ca = cos(alpha); sa = sin(alpha)\n", " cb = cos(beta); sb = sin(beta)\n", " ct = cos(theta); st = sin(theta)\n", " cp = cos(phi); sp = sin(phi)\n", " \n", " dx = ((-cb*ct*sa - (sa*sb*sp - ca*cp)*st)*dr + \n", " (r*cb*sa*st - (sa*sb*sp - ca*cp)*r*ct)*dtheta +\n", " (-(cp*sa*sb + ca*sp)*r*st)*dphi)\n", " \n", " dy = ((cb*sp*st - sb*ct)*dr +\n", " (r*ct*cb*sp + r*sb*st)*dtheta +\n", " (r*cp*cb*st)*dphi)\n", " \n", " dz = ((ca*cb*ct + (ca*sb*sp + cp*sa)*st)*dr +\n", " (-r*ca*cb*st+(ca*sb*sp + cp*sa)*r*ct)*dtheta +\n", " ((ca*cp*sb - sa*sp)*r*st)*dphi)\n", " \n", " return (dx, dy, dz)\n", "\n", "\n", "cpdef tuple xyz_to_spherical(float dx, float dy, float dz, float x, \n", " float y, float z):\n", " \"\"\"\n", " Convert cartesian back to spherical\n", " \"\"\"\n", " cdef r, dr, dth, dph\n", " r = sqrt(x**2+y**2+z**2)\n", " dr = (x*dx+y*dy*z*dz)/r\n", " dth = ((x*z*dx+y*z*dy)/r**2/sqrt(x**2+y**2)-sqrt(x**2+y**2)*dz)/r**2\n", " dph = -y/(x**2+y**2)*dx+x/(x**2+y**2)*dy\n", " return (dr, dth, dph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These formulas were obtained automatically by creating another chart and asking for the change of frames. Example:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -cos(beta)*cos(theta)*sin(alpha) - (sin(alpha)*sin(beta)*sin(phi) - cos(alpha)*cos(phi))*sin(theta) r*cos(beta)*sin(alpha)*sin(theta) - (sin(alpha)*sin(beta)*sin(phi) - cos(alpha)*cos(phi))*r*cos(theta) -(cos(phi)*sin(alpha)*sin(beta) + cos(alpha)*sin(phi))*r*sin(theta)]\n", "[ cos(beta)*sin(phi)*sin(theta) - cos(theta)*sin(beta) r*cos(beta)*cos(theta)*sin(phi) + r*sin(beta)*sin(theta) r*cos(beta)*cos(phi)*sin(theta)]\n", "[ cos(alpha)*cos(beta)*cos(theta) + (cos(alpha)*sin(beta)*sin(phi) + cos(phi)*sin(alpha))*sin(theta) -r*cos(alpha)*cos(beta)*sin(theta) + (cos(alpha)*sin(beta)*sin(phi) + cos(phi)*sin(alpha))*r*cos(theta) (cos(alpha)*cos(phi)*sin(beta) - sin(alpha)*sin(phi))*r*sin(theta)]\n" ] } ], "source": [ "def print_formulas(): # enclosed in a function to prevent altering the namespace\n", " alpha, beta = var('alpha, beta')\n", " spher. = E.chart()\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta) # normal Spherical->Cartesian transformation\n", " y, z = y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta) # first rotation\n", " x, z = x*cos(alpha)-z*sin(alpha), z*cos(alpha)+x*sin(alpha) # second rotation\n", " spher.transition_map(E.default_chart(), [x, y, z])\n", " print(list(E.changes_of_frame().values())[0][spher.frame(),:, spher])\n", "\n", "print_formulas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The thickness of the disk will follow this profile, obtained from my high level understanding of black holes mechanics (i.e. it's mostly random, but looks nice)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport exp, erf\n", "\n", "cpdef float profile(float x, float disk_min, float disk_max):\n", " cdef float y \n", " # we really don't want negative values\n", " if xdisk_max:\n", " return 0\n", " y = (exp(-(disk_min-20-x)**2/400)*(x-disk_min)**2*(disk_max-x)**2/10000 +\n", " exp(-(32-x)**2/70)/2*(x-disk_min)**2*(disk_max-x)**2/150000)\n", " return max(y, 0)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(lambda x, d1=disk_min, d2=disk_max: profile(x, d1, d2), \n", " xmin=0, xmax=60, ymin=0, ymax=1.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now rewrite the function `intersection` taking everything into account. This time it directly returns an RGB value." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float R, G, B\n", " cdef float dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th\n", " R, G, B = 0., 0., 0. # return values\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]= 255:\n", " R = 255\n", " return R, G, B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also have to rewrite `render_row` to accept an RGB value." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "def render_row(x):\n", " \"\"\"\n", " Render a single row of the image\n", " \"\"\"\n", " res = np.zeros((ny,3)) # result row in RGB format\n", " for y in range(ny):\n", " beta = atan2(y-ny/2,x) # beta angle \n", " r = sqrt(x**2+(y-ny/2)**2) # pixel distance to the center of the image\n", " ind_geo = int(r/400*n_geod*720/nx) # index of the geodesic to use. values are obtained by trial and error.\n", " if ind_geo" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "img2 = toimage(data)\n", "img2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Much more beautiful! \n", "\n", "But enough of red black holes, let's add real spectra into the mix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Black body spectrum\n", "\n", "It's quite easy to associate a spectrum to each light ray, but it's also important to be able to convert it back to displayable colors.\n", "\n", "This part shows how to do that, using the CIE standard XYZ function. This function should contain all information about a spectrum that is relevant to the human eye. They can then be converted to RGB for example. What's more, these functions are simply obtained by integrating the spectrum against a function. They are then linearly dependant on the spectrum.\n", "\n", "To compute the XYZ functions, we first need the function that defines them. I got mine from here: \n", "http://www.cvrl.org/database/data/cmfs/ciexyzjv.csv\n", "\n", "But because we are planning to add the Doppler effect, I added a lot of zeros at the beginning and the end to evntually encompass more wavelengths (I went from 5 to 3000 nm, instead of 380-780 for visible light)." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "from six.moves.urllib.request import urlretrieve # valid for both Python 2 and Python 3\n", "urlretrieve(\"http://www.cvrl.org/database/data/cmfs/ciexyzjv.csv\", \n", " \"ciexyzjv.csv\")\n", "ciexyz = np.genfromtxt(\"ciexyzjv.csv\", delimiter=\",\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is what they look like. Y can be seen as the luminosity of a normalized spectrum (e.g. for the same light intensity, green will appear much brighter to the human eye than purple). The other two don't really have an interpretation." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(ciexyz[:,0],ciexyz[:,3], label='Z')\n", "plt.plot(ciexyz[:,0],ciexyz[:,2], label='Y')\n", "plt.plot(ciexyz[:,0],ciexyz[:,1], label='X')\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we need to compute the black body spectrum for a given temperature, using Planck's law. \n", "I already include the Doppler effect in the formula." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport exp\n", "\n", "cpdef float blackbody(float nu, float T, float doppler):\n", " \"\"\"\n", " Spectral power emmited at frequency nu by a black-body at \n", " temperature T per square meter par steradian\n", " \"\"\"\n", " cdef float h = 6.62e-34\n", " cdef float k = 1.38e-23\n", " cdef float c = 3e8\n", " cdef float h_sur_k = 4.79710144927536e-11\n", " return (2*h)*nu/c*nu/c*nu/(exp(h_sur_k*nu/doppler/T)-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact there is a small trick in the previous cell. Because of the exponent in the constants, it's fairly easy to overflow. That's why the $\\nu^3/c^2$ is written this way.\n", "\n", "Let's try at 10,000 K:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (3935: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 170 points.\n", "verbose 0 (3935: plot.py, generate_plot_points) Last error message: 'Unable to compute f(3000.0)'\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(spline([(l, blackbody(3e8/(l/1e9), 10000, 1)) for l in ciexyz[:,0]]), \n", " xmin=5, xmax=3000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, we'll use Cython to convert a temperature into XYZ. Because XYZ depends linearly on the intensity, and not RGB, the conversion will be done in post-processing. Everything is redeclared in Cython for optimization (hence all the type declarations). Even the XYZ arrays are reloaded in this Cython environment." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from __main__ import blackbody\n", "from libc.math cimport exp\n", "import numpy as np\n", "cimport numpy as np\n", "cimport cython\n", "\n", "DTYPE = float\n", "ctypedef np.float_t DTYPE_t\n", "\n", "cdef np.float_t[:] cielamb\n", "cdef np.float_t[:] ciex\n", "cdef np.float_t[:] ciey\n", "cdef np.float_t[:] ciez\n", "\n", "def init_arrays():\n", " global cielamb, ciex, ciey, ciez\n", " cdef np.ndarray[np.float_t, ndim=2] ciexyz = np.genfromtxt('ciexyzjv.csv', delimiter=\",\") \n", " cielamb = ciexyz[:, 0]\n", " ciex = ciexyz[:, 1]\n", " ciey = ciexyz[:, 2]\n", " ciez = ciexyz[:, 3]\n", " \n", "init_arrays()\n", "\n", "cpdef tuple temp_to_XYZ(float T, float doppler):\n", " cdef int nl = len(cielamb)\n", " cdef np.ndarray[np.float_t, ndim=1] sp = np.zeros(nl)\n", " cdef int i\n", " cdef float x, y, z\n", " for i in range(nl):\n", " sp[i] = blackbody(3e8/(cielamb[i]/1e9), T, doppler)\n", " x = np.dot(sp, ciex)\n", " y = np.dot(sp, ciey)\n", " z = np.dot(sp, ciez)\n", " return (x, y, z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's convert it to RGB, using one of the many formulas, just to see how it looks:" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "def xyz_to_rgb(*args):\n", " # constants\n", " fact = 3e-8 # arbitrary\n", " gamma = 1/2.2\n", " mat = [[3.24047, -1.53715, -0.498835],\n", " [-0.96256, 1.8752, 0.041556],\n", " [0.055648, -0.204043, 1.057311]]\n", " # conversion\n", " r, g, b = np.dot(mat, np.transpose(args)/fact).tolist()\n", " # gamma correction and clipping\n", " r = min(1,max(0, r)**gamma)\n", " g = min(1,max(0, g)**gamma)\n", " b = min(1,max(0, b)**gamma)\n", " return r, g, b" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import Rectangle\n", "axes = plt.gca()\n", "axes.set_xlim([1000, 6000])\n", "for T in range(1000, 6000, 200):\n", " # plot a rectangle at a color obtained from the temperature\n", " axes.add_patch(Rectangle((T, 0), 200, 1, facecolor=xyz_to_rgb(*temp_to_XYZ(T, 1))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this formula, it becomes bright very quickly. Adjusting the $\\gamma$ correction could help.\n", "\n", "We can now add it to our black hole ray tracer:" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, doppler, factor,\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img3 = toimage(data_rgb)\n", "img3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First relativistic effect: Doppler effect\n", "\n", "Everything has been so far done in such a way as to make this part easy. All we have to do is evalute the Doppler factor.\n", "\n", "To compute the Doppler effect due to the rotation of the disk, we need to consider the interaction between to disk and the light ray in the orthonormal frame again. The goal is to use the general formula:\n", "\n", "$$f_0 = \\frac{f_s}{\\gamma \\left(1+\\beta \\cos(\\theta)\\right)}$$\n", "\n", "To do that, we need to estimate $\\beta$ and $\\theta$. \n", "Let's first look at the equation of motion of a single particle, and impose circular motion: $dr=0$ and $\\theta=\\pi/2$" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "eqs = curve._equations_rhs[C]" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "dt, dr, dth, dph = curve._velocities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 4 equations become (note: for technical reasons the equations below display $ dt $ as $ Dt $ and $ d\\phi $ as $ Dph $; we could fix that but this is just an intermediate result so we don't bother):" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\frac{2 \\, {\\left(\\mathit{Dph}^{2} m r^{3} - \\mathit{Dt}^{2} m^{2}\\right)}}{r^{3}}\\)" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(\\mathit{Dph}^{2} m r^{3} - \\mathit{Dt}^{2} m^{2}\\right)}}{r^{3}}$" ], "text/plain": [ "2*(Dph^2*m*r^3 - Dt^2*m^2)/r^3" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "# d^2t/dtau^2 = \n", "eqs[0].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle -\\frac{2 \\, \\mathit{Dph}^{2} m r^{3} - \\mathit{Dph}^{2} r^{4} - 2 \\, \\mathit{Dt}^{2} m^{2} + \\mathit{Dt}^{2} m r}{r^{3}}\\)" ], "text/latex": [ "$\\displaystyle -\\frac{2 \\, \\mathit{Dph}^{2} m r^{3} - \\mathit{Dph}^{2} r^{4} - 2 \\, \\mathit{Dt}^{2} m^{2} + \\mathit{Dt}^{2} m r}{r^{3}}$" ], "text/plain": [ "-(2*Dph^2*m*r^3 - Dph^2*r^4 - 2*Dt^2*m^2 + Dt^2*m*r)/r^3" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2r/dtau^2 = \n", "eqs[1].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 0\\)" ], "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2th/dtau^2 = \n", "eqs[2].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 0\\)" ], "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d^2ph/dtau^2 = \n", "eqs[3].subs({th: pi/2, dr: 0, dth: 0})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In particular $d\\phi$ is constant. We also solve the second equation for $dt$\n", "(the sign depends on the directions of the rotations):" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{Dt} = -\\mathit{Dph} r \\sqrt{\\frac{r}{m}}, \\mathit{Dt} = \\mathit{Dph} r \\sqrt{\\frac{r}{m}}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{Dt} = -\\mathit{Dph} r \\sqrt{\\frac{r}{m}}, \\mathit{Dt} = \\mathit{Dph} r \\sqrt{\\frac{r}{m}}\\right]$" ], "text/plain": [ "[Dt == -Dph*r*sqrt(r/m), Dt == Dph*r*sqrt(r/m)]" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqs[1].subs({th: pi/2, dr: 0, dth: 0}).solve(dt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And so by reinjecting in the first equation $dt$ is constant, and so is $d\\phi$, like in Newtonian gravity. \n", "Their values are obtained from the normalization condition." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "p = M((0, r, pi/2, 0))\n", "Tp = M.tangent_space(p)\n", "v = Tp((r*sqrt(r/m)*dph, 0, 0, dph))" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\mathit{Dph}^{2} r^{2} + \\frac{\\mathit{Dph}^{2} {\\left(2 \\, m - r\\right)} r^{2}}{m}\\)" ], "text/latex": [ "$\\displaystyle \\mathit{Dph}^{2} r^{2} + \\frac{\\mathit{Dph}^{2} {\\left(2 \\, m - r\\right)} r^{2}}{m}$" ], "text/plain": [ "Dph^2*r^2 + Dph^2*(2*m - r)*r^2/m" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.at(p)(v,v)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\left[\\mathit{Dph} = -\\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}, \\mathit{Dph} = \\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[\\mathit{Dph} = -\\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}, \\mathit{Dph} = \\frac{\\sqrt{-\\frac{m}{3 \\, m - r}}}{r}\\right]$" ], "text/plain": [ "[Dph == -sqrt(-m/(3*m - r))/r, Dph == sqrt(-m/(3*m - r))/r]" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(g.at(p)(v,v)==-1).solve(dph)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the smallest circular orbit can only by at $r=3m$, with:\n", "
\n", "
\n", "\n", "$$ d\\phi = \\pm \\frac{1}{r} \\sqrt{\\frac{m}{r-3m}} \\qquad dt =\\frac{1}{\\sqrt{r}\\sqrt{r-3m}} $$\n", "\n", "We can see that:\n", "\n", "If we switch to the orthonormal frame (just multiply $d\\phi$ by $r$, as seen in the change of frame), we can see that:\n", "\n", "$$\\beta = \\frac{v}{c} = \\sqrt{\\frac{m}{r-3m}}$$\n", "\n", "To find $\\theta$, we use the formula:\n", "\n", "$$\\theta = \\arccos\\left(\\frac{\\overrightarrow{v_1}\\cdot \\overrightarrow{v_2}}{||\\overrightarrow{v_1}||\\cdot||\\overrightarrow{v_2}||}\\right)$$\n", "\n", "Finally, the gravitational redshift is easier. It is simply given by the ratio of first component of the 4-velocity in the orthonormal frame between the two ends of the geodesic." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " \"\"\"\n", " Return True if the curve intersect the disk comprised between dmin \n", " and dmax tilted of angles alpha and beta\n", " \"\"\"\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dt, dt0, dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, rho, doppler, beta_rel\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " dt0 = curve[1][1]-curve[0][1]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "data_rgb = XYZ_to_RGB(data)\n", "img4 = toimage(data_rgb)\n", "img4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second relativistic effect: aberration (forward focalisation)\n", "\n", "One last thing we didn't take into account is that a moving object that emits isotropic light at rest doesn't do so when in motion. The classical aberration formula reads:\n", "\n", "$$\\theta' = \\arccos \\left( \\frac{\\cos \\theta -\\beta}{1-\\beta \\cos \\theta} \\right)$$\n", "\n", "In the rest frame, the number of light rays emanating from the object at an angle $\\theta'$ is constant, equal to $\\frac{dN}{d\\theta'}$.\n", "\n", "By using chain derivation, in the moving frame :\n", "\n", "$$\\frac{dN}{d\\theta} = \\frac{dN}{d\\theta'} \\frac{d\\theta'}{d\\theta}$$\n", "\n", "As we can see, the number of rays per unit angle is multiplied by $\\frac{d\\theta'}{d\\theta}$. Let's plot this function for multiple values of $\\beta$." ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [], "source": [ "beta = var('beta')" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [], "source": [ "thp = acos((cos(th)-beta)/(1-beta*cos(th)))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle -\\frac{\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)} \\beta \\sin\\left({\\theta}\\right)}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + \\frac{\\sin\\left({\\theta}\\right)}{\\beta \\cos\\left({\\theta}\\right) - 1}}{\\sqrt{-\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)}^{2}}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + 1}}\\)" ], "text/latex": [ "$\\displaystyle -\\frac{\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)} \\beta \\sin\\left({\\theta}\\right)}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + \\frac{\\sin\\left({\\theta}\\right)}{\\beta \\cos\\left({\\theta}\\right) - 1}}{\\sqrt{-\\frac{{\\left(\\beta - \\cos\\left({\\theta}\\right)\\right)}^{2}}{{\\left(\\beta \\cos\\left({\\theta}\\right) - 1\\right)}^{2}} + 1}}$" ], "text/plain": [ "-((beta - cos(th))*beta*sin(th)/(beta*cos(th) - 1)^2 + sin(th)/(beta*cos(th) - 1))/sqrt(-(beta - cos(th))^2/(beta*cos(th) - 1)^2 + 1)" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display latex\n", "diff(thp,th)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "aberration = abs(diff(thp,th)) # abs needed if we want negative angles" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = plot(aberration.subs(beta=0.), [-pi*.99,pi*.99])\n", "for i in range(1,10):\n", " P += plot(aberration.subs({beta: 0.1*i}), [-pi*.99,pi*.99])\n", "P.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the effect does focus rays toward the direction of motion. One can also check that the integral does not depend on $\\beta$.\n", "\n", "This is a fast cython implementation:" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin ,sqrt\n", "\n", "cpdef float focalisation_factor(float th, float beta):\n", " # uses an other expression stricly equal, but faster to compute.\n", " return (cos(th)*(cos(th)+beta)+sin(th)**2)/\\\n", " (sin(th)**2*sqrt(1-beta**2)+1/sqrt(1-beta**2)*(beta+cos(th))**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, this is the final code for the intersection: " ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "%%cython\n", "from libc.math cimport cos, sin, acos, sqrt, abs, atan2\n", "cimport cython\n", "from __main__ import profile\n", "from __main__ import xyz_to_spherical\n", "from __main__ import spherical_to_xyz\n", "from __main__ import temp_to_XYZ\n", "from __main__ import focalisation_factor\n", "\n", "@cython.boundscheck(False)\n", "@cython.wraparound(False)\n", "cpdef tuple intersection(list curve, float m, float alpha, float beta, \n", " float dmin, float dmax):\n", " cdef float x, y, z\n", " cdef float x2, y2, z2\n", " cdef float r, theta, phi\n", " cdef int n, i\n", " cdef float t\n", " cdef float sinalpha, cosalpha\n", " cdef float sinbeta, cosbeta\n", " cdef float X, Y, Z\n", " cdef float X0, Y0, Z0\n", " cdef float dt, dt0, dr, dtheta, dphi\n", " cdef float dx, dy, dz\n", " cdef float th, rho, doppler, beta_rel\n", " X, Y, Z = 0., 0., 0. # return values\n", " # 20 percent speed gain\n", " sinalpha = sin(alpha)\n", " cosalpha = cos(alpha)\n", " sinbeta = sin(beta)\n", " cosbeta = cos(beta)\n", " n = len(curve)\n", " r, theta, phi = curve[0][2:5]\n", " dt0 = curve[1][1]-curve[0][1]\n", " # rotations\n", " x, y, z = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " x, y, z = x, y*cos(beta)-z*sin(beta), z*cos(beta)+y*sin(beta)\n", " z = z*cos(alpha)+x*sin(alpha)\n", " for i in range(1, n): \n", " r = curve[i][2]\n", " theta = curve[i][3]\n", " phi = curve[i][4]\n", " # rotations\n", " x2, y2, z2 = r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)\n", " y2, z2 = y2*cosbeta-z2*sinbeta, z2*cosbeta+y2*sinbeta\n", " x2, z2 = x2*cosalpha-z2*sinalpha, z2*cosalpha+x2*sinalpha\n", " if z!=z2:\n", " t = z/(z-z2)\n", " if t>=0 and t<1 and curve[i][2]>dmin and curve[i][2]" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%display plain\n", "data = np.zeros( (ny, nx, 3), dtype=float )\n", "render()\n", "data_rgb = XYZ_to_RGB(data)\n", "img5 = toimage(data_rgb)\n", "# img5.save(\"my_home_made_black_hole.png\") # uncomment to save\n", "img5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference with the previous image seems small, but that's only because the translation to RGB introduces luminosity clipping. In fact, the white area is twice as bright in the new picture." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "Here is a small recap of all the steps we went through:\n", "\n", "### Geometric image:" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Disk thickness:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Black body object:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Doppler effect added:" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relativistic aberration added:" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "img5" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.1", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 2 }