{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Outline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following features of impulse response simulator have been implemented in this notebook.\n", "\n", "1- Find lag-frequency spectrum of a simple delta impulse response.\n", "\n", "2- Find lag-frequency spectrum of a _more_ realistic impulse response based on real physical principles.\n", "\n", "3- Compute lag-frequency spectrum of delta impulse responses with same intensities and varying positions at different energy levels.\n", "\n", "4- Compute lag-frequency spectrum of delta impulse responses with same positions and varying intensities at different energy levels." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import libraries and obtain data." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from stingray import Crossspectrum, Lightcurve, sampledata\n", "import numpy as np\n", "from scipy import signal\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define variability signal." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lc = sampledata.sample_data()\n", "s = lc.counts" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lag-frequency Spectrum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simple Delta Impulse Response" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a delta impulse response with a delay of 10." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "delay = int(10/lc.dt)\n", "h_zeros = np.zeros(delay)\n", "h = np.append(h_zeros, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Find output signal by taking convolution of variability signal and impulse response." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "output = signal.fftconvolve(s, h)\n", "# To make two counts of equal size, remove last 'delay' entries and avoid first zeros\n", "output = output[delay:-delay]\n", "s_mod = s[delay:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize input and output signals." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(s_mod[-80:],'r',output[-80:],'g')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make lightcurves using `Lightcurve` class." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "time = lc.time[delay:]\n", "lc1 = Lightcurve(time, s_mod)\n", "lc2 = Lightcurve(time, output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute crossspectrum." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cross = Crossspectrum(lc2, lc1)\n", "# Rebin the cross spectrum for ease of visualization\n", "cross = cross.rebin(0.0075)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate time lag." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "lag = np.angle(cross.power)/ (2 * np.pi * cross.freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot lag." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "\n", "# Plot lag-frequency spectrum.\n", "plt.plot(cross.freq, lag, 'r')\n", "\n", "# Find cutoff points\n", "v_cutoff = 1.0/(2*10.0)\n", "h_cutoff = lag[int((v_cutoff-0.0075)*1/0.0075)]\n", "\n", "plt.axvline(v_cutoff, color='g',linestyle='--')\n", "plt.axhline(h_cutoff, color='g', linestyle='-.')\n", "\n", "# Define axis\n", "plt.axis([0,0.2,-15,15])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to Uttley et al, the lag-frequency spectrum shows a constant delay until the frequency (1/2*time_delay) which is represented by the green vertical line in the above figure. After this point, the phase warps and the lag becomes negative. This is given in page 43 of review." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### More realistic impulse response" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The response of refelection from an accretion disk to an instantaneous flash follows the _top-hat function_ to first\n", "order approximation. The response shows an initial steep rise some time after the initial flash (slope depending on\n", "the light travel time to the disk) and then gradually decays, as parts of the accretion disk farther away from the \n", "source receieve radiations at later times.\n", "\n", "The secondary peak is caused due to the bending of light in strong gravitational field around the black hole. This is the re-emergence of photons reflected from the far side of accretion disk that although would be classically blocked from our view, are lensed by strong gravitational field around black hole into our line of sight. \n", "\n", "Below, we obtain an impulse response similar to one in Utley et al.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Primary peak time, secondary peak time, end time\n", "t1, t2, t3 = 3, 4, 10\n", "# Peaks' values\n", "p1, p2 = 1, 1.4\n", "# Rise and decay slopes\n", "rise, decay = 0.6, 0.1\n", "\n", "# Append zeros before start time\n", "h_primary = np.append(np.zeros(int(t1/lc.dt)), p1)\n", "\n", "# Create a rising exponential of user-provided slope that ends at secondary peak time and secondary peak\n", "# value\n", "x = np.linspace(int(t1/lc.dt), int(t2/lc.dt), int((t2-t1)/lc.dt))\n", "h_rise = np.exp(rise*x)\n", "# Find a factor for scaling\n", "factor = np.max(h_rise)/(p2-p1)\n", "h_secondary = (h_rise/factor) + p1\n", "\n", "# Create a decaying exponential until the end time\n", "x = np.linspace(int(t2/lc.dt), int(t3/lc.dt), int((t3-t2)/lc.dt))\n", "h_decay = (np.exp((-decay)*(x-4/lc.dt)))\n", "\n", "# Add the three responses\n", "h = np.append(h_primary, h_secondary)\n", "h = np.append(h, h_decay)\n", "\n", "# Plot\n", "plt.plot(h,'y')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obtain output through convolution." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "delay = (int(t3/lc.dt))\n", "output = signal.fftconvolve(s, h)\n", "output = output[delay:-delay]\n", "s_mod = s[delay:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Form light curves." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "time = lc.time[delay:]\n", "lc1 = Lightcurve(time, s_mod)\n", "lc2 = Lightcurve(time, output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Find cross spectrum and compute lags." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cross = Crossspectrum(lc2, lc1)\n", "cross = cross.rebin(0.0075)\n", "lag = np.angle(cross.power)/ (2 * np.pi * cross.freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot results." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "\n", "# Plot lag-frequency spectrum.\n", "plt.plot(cross.freq, lag, 'r')\n", "\n", "# Define the x-position of vertical line\n", "v_cutoff = 1.0/(2*t2)\n", "h_cutoff = lag[int((v_cutoff-0.0075)*1/0.0075)]\n", "\n", "plt.axvline(v_cutoff, color='g', linestyle='--')\n", "plt.axhline(h_cutoff, color='g', linestyle='-.')\n", "\n", "# Define axis\n", "plt.axis([0,0.2,-10,10])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Energy Dependence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### With same intensity and varying position" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create different lags for different energy channels, we create delta impulses of same intensity at different positions." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "energies = np.array([4.5,8.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create impulse responses for all energy channels." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "h_zeros = [np.zeros(int(i/lc.dt)) for i in energies]\n", "responses = [np.append(h, 1) for h in h_zeros]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "delays = [int(i/lc.dt) for i in energies]\n", "outputs = [signal.fftconvolve(s, h)[d:-d] for h,d in zip(responses,delays)]\n", "s_mods = [s[d:] for d in delays]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make light curves." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "t_mods = [lc.time[d:] for d in delays]\n", "lc_input = [Lightcurve(t_mod, s_mod) for t_mod, s_mod in zip(t_mods,s_mods)]\n", "lc_output = [Lightcurve(t_mod, output) for t_mod, output in zip(t_mods,outputs)]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cross_spectrums = [Crossspectrum(lc2, lc1).rebin(0.0075) for lc1,lc2 in zip(lc_input,lc_output)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute lags and cutoffs." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lags = [np.angle(cross.power)/ (2 * np.pi * cross.freq) for cross in cross_spectrums]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get cutoff points for all energy channels." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "v_cutoffs = [1.0/(2*energy) for energy in energies]\n", "h_cutoffs = [lag[int((v_cutoff-0.0075)*1/0.0075)] for lag, v_cutoff in zip(lags, v_cutoffs)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot lag-frequency spectrum for all energy channels." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plots = []\n", "colors = ['r','g']\n", "\n", "# Plot lag-frequency spectrum\n", "for i in range(0,len(lags)):\n", " plots += plt.plot(cross_spectrums[i].freq, lags[i], colors[i], label=str(energies[i])+'keV')\n", " plt.axvline(v_cutoffs[i],color=colors[i],linestyle='--')\n", " plt.axhline(h_cutoffs[i], color=colors[i], linestyle='-.')\n", "\n", "# Define axes and add labels\n", "plt.axis([0,0.2,-20,20])\n", "plt.legend()\n", "plt.xlabel('Frequencies (Hz)')\n", "plt.ylabel('Lags')\n", "plt.title('Energy Dependent Frequency-lag Spectrum')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note:\n", "\n", "Currently, lag-energy spectrum isn't plotted and hence I am unable to verify results from Uttley et al. However, as soon as it is implemented in library project, I will test it here as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### With same position and varying intensity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we use delta impulse responses whose position remains same but intensity varies. \n", "\n", "Again, first we define energies and then create impulse responses, and subsequently using convolution, obtain the output light curves." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "energies = np.array([4.5,8.5])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "h_zeros = np.zeros(int(10/lc.dt))\n", "responses = [np.append(h_zeros, i+1) for i in range(0,len(energies))]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "delay = int(10/lc.dt)\n", "outputs = [signal.fftconvolve(s, h)[delay:-delay] for h in responses]\n", "s_mod = s[delay:]" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "t_mod = lc.time[delay:]\n", "lc_input = Lightcurve(t_mod, s_mod)\n", "lc_output = [Lightcurve(t_mod, output) for output in outputs]" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cross_spectrums = [Crossspectrum(lc2, lc_input).rebin(0.0075) for lc2 in lc_output]" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "lags = [np.angle(cross.power)/ (2 * np.pi * cross.freq) for cross in cross_spectrums]" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "v_cutoff = 1.0/(2.0*10)\n", "h_cutoff = lags[0][int((v_cutoff-0.0075)*1/0.0075)]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plots = []\n", "colors = ['r','g']\n", "\n", "# Plot lag-frequency spectrum\n", "for i in range(0,len(lags)):\n", " plots += plt.plot(cross_spectrums[i].freq, lags[i], colors[i], label=str(energies[i])+'keV')\n", "\n", "# Draw horizontal and vertical line\n", "plt.axvline(v_cutoff, color='g', linestyle='--')\n", "plt.axhline(h_cutoff, color='g', linestyle='-.')\n", "\n", "\n", "# Define axis\n", "plt.axis([0,0.2,-25,25])\n", "plt.legend()\n", "plt.xlabel('Frequencies (Hz)')\n", "plt.ylabel('Lags')\n", "plt.title('Energy Dependent Frequency-lag Spectrum')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected (and also demonstrated in Utley et al), the shape of lag-frequency spectrum for both energy channels is similar.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 0 }