{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "g3Jx1sf_V8ET" }, "source": [] }, { "cell_type": "markdown", "metadata": { "id": "SRK793m0V9Ee" }, "source": [ "## Necessary Packages and Functions " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "LEys9dAFmg2d" }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as sts\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "2trB_l7k2eW2" }, "outputs": [], "source": [ "import matplotlib.animation as animation\n", "from IPython.display import HTML\n", "from IPython.display import clear_output\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "jtiUyqMO3C2h" }, "outputs": [], "source": [ "def make_animation(draw_function, frames, interval, filename=None,\n", " verbose=False, figure_params=None):\n", " \"\"\"\n", " Write an animated GIF to file using matplotlib and ImageMagick.\n", " Inputs:\n", " draw_function (callable) The function to call, once per frame,\n", " to render to the current matplotlib figure. This function's call\n", " signature must be\n", " draw_function(current_frame_number, total_frame_count)\n", " The first frame is 0 and the last frame is total_frame_count-1.\n", " frames (int) The number of frames to generate.\n", " interval (float) The number of milliseconds to wait between frames\n", " in the animation. Set this to 40 for a fairly standard frame rate\n", " of 25fps (1 second / 40 (milliseconds per frame) = 25 frames per\n", " second).\n", " filename (str) The path to the file to write to. If none is provided,\n", " the animation will be written to a random filename, prefixed with\n", " \"animate_\" in the current directory. Default: None.\n", " verbose (bool) Whether to print the current frame number to the\n", " console as the animation is being created. This will clear other\n", " console output. Default: False.\n", " figure_params (dict) The keyword arguments to pass to matplotlib\n", " when creating a new figure for this animation. Use it to set the\n", " figure size and other figure properties. Default: None.\n", " Returns: A display object that will inject HTML for displaying the\n", " animated GIF into the notebook.\n", " \"\"\"\n", " from matplotlib import pyplot, animation\n", " from IPython.display import HTML, display, clear_output\n", " import random\n", "\n", " if filename is None:\n", " filename = 'animate_%06i.gif' % random.randint(0, 999999)\n", " # Create figure\n", " if figure_params is None:\n", " figure_params = {}\n", " figure = pyplot.figure(**figure_params)\n", " # Wrap draw_function if we need to print to console\n", " if verbose:\n", " old_draw_function = draw_function\n", " def draw_function(current_frame_number, total_frame_count):\n", " old_draw_function(current_frame_number, total_frame_count)\n", " print('Processed frame', current_frame_number + 1, '/', total_frame_count)\n", " clear_output(wait=True)\n", " if current_frame_number + 1 == total_frame_count:\n", " print('Writing animation to file...')\n", " clear_output(wait=True)\n", " # Generate animation\n", " anim = animation.FuncAnimation(\n", " figure, draw_function, frames=frames, interval=interval,\n", " init_func=lambda: None, fargs=(frames,))\n", " #anim.save(filename, writer='imagemagick')\n", " # Close the animation figure so the last frame does not get displayed\n", " # in the notebook.\n", " #pyplot.close()\n", " # Return display object for the animated GIF\n", " #return display(HTML(''))\n", " ret = display(HTML(anim.to_html5_video()))\n", " pyplot.close()\n", " return ret" ] }, { "cell_type": "markdown", "metadata": { "id": "S48Nt1JUWGWb" }, "source": [ "## Empirical Simulation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "vO6GovHWSKD4" }, "outputs": [], "source": [ "## Declaring the constants and units \n", "\n", "G = 6.67*10**(-11) # m**3/(kg s**2)\n", "M_sun = 2*10**30 # kg\n", "v_star = 3*10**3 # m/s\n", "AU = 1.5*10**11 # m\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Vhf3xf85RjIV" }, "outputs": [], "source": [ "class Star:\n", " '''\n", " Class with all the properties of a star.\n", " x: x axis position\n", " y: y axis position\n", " vx: x component of velocity\n", " vy: y component of velocity\n", " '''\n", " def __init__(self, x, y, vx, vy, mass = 1, radius = 0.1):\n", " self.x = [x]\n", " self.y = [y]\n", " self.vx = [vx]\n", " self.vy = [vy]\n", " self.mass = mass\n", " self.radius = radius\n", " self.ax = []\n", " self.ay = []\n", " self.momentum_x = self.vx[-1]*self.mass\n", " self.momentum_y = self.vy[-1]*self.mass" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "6d4fs1i4PWNB" }, "outputs": [], "source": [ "def truncnorm(mean, sigma, lower = 0):\n", " '''\n", " Function to generate a trancated normal distribution with mean = mean \n", " and sigma and sigma which will only generate non-negative value\n", " '''\n", " myclip_a = lower\n", " myclip_b = 10**30\n", " my_mean = mean\n", " ## if sigma is 0, replace it with a low number to avoid division by 0\n", " my_std = max(sigma, 10**-30) \n", "\n", " a, b = (myclip_a - my_mean) / my_std, (myclip_b - my_mean) / my_std\n", " return sts.truncnorm(a, b, loc = my_mean, scale = my_std)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "8i0O3gK6OTeS", "outputId": "d89472ae-2f47-4d2a-a610-02874ae92aa2" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0,5,20)\n", "dist = truncnorm(mean = 1, sigma = 1)\n", "plt.plot(x, dist.pdf(x))\n", "plt.plot(x, sts.norm.pdf(x, 1, 1))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "ISewFc8smf1u" }, "outputs": [], "source": [ "class Cluster:\n", " '''\n", " System of group of stars, initial with the size of the grid\n", " '''\n", " def __init__(self, size):\n", " self.size = size\n", " self.stars = [] # list of all the current stars\n", " self.merged_stars = [] # list of stars who were merged\n", " self.n_merged_star = 0\n", "\n", " def initialize(self, density, mean_v, sigma_v = 0.01, explode = True, n_star = None):\n", " '''\n", " Initializing a random sample of stars. \n", " explode: if True then generate a exploding system\n", " density: density of the stars in the given area\n", " mean_v: mean of the velocity distribution of all the stars\n", " sigma_v: sigma of the velocity distribution of all the stars\n", " '''\n", " self.binary = False\n", " \n", " self.density = density\n", " self.time = [0]\n", " \n", " if explode: # same outward velociy and normal initial distribution of position \n", " self.area = np.pi*self.size**2\n", " self.n_star = int(round(self.density*self.area))\n", " \n", " # normal initial distribution of position\n", " star_x = sts.norm(0, self.size/2).rvs(size=self.n_star)\n", " star_y = sts.norm(0, self.size/2).rvs(size=self.n_star)\n", "\n", " self.center_of_mass_x = np.mean(star_x)\n", " self.center_of_mass_y = np.mean(star_y)\n", "\n", " for x,y in zip(star_x, star_y):\n", " d_x = x - self.center_of_mass_x\n", " d_y = y - self.center_of_mass_y\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", "\n", " # generate velocity from the distribution\n", " v = truncnorm(mean_v, sigma_v).rvs()\n", " vx = v * d_x / dist\n", " vy = v * d_y / dist\n", " \n", " self.stars.append(Star(x, y, vx, vy))\n", " \n", " if not explode: # uniform initial distribution of position and velocity\n", " self.area = (2*self.size)**2\n", " self.n_star = int(round(self.density*self.area))\n", " \n", " # uniform initial distribution of position\n", " star_x = np.random.uniform(-self.size, self.size, size=self.n_star)\n", " star_y = np.random.uniform(-self.size, self.size, size=self.n_star)\n", " \n", " self.center_of_mass_x = np.mean(star_x)\n", " self.center_of_mass_y = np.mean(star_y)\n", "\n", " # uniform initial distribution of velocity\n", " star_vx = np.random.uniform(mean_v-2*sigma_v, mean_v+2*sigma_v, size=self.n_star)\n", " star_vy = np.random.uniform(mean_v-2*sigma_v, mean_v+2*sigma_v, size=self.n_star)\n", " \n", " for x,y, vx, vy in zip(star_x, star_y, star_vx, star_vy):\n", " self.stars.append(Star(x, y, vx, vy))\n", "\n", " # every star is of 1 M_sun\n", " self.total_mass = 1*self.n_star\n", " \n", " \n", " # calculate the acceleration at time = 0 \n", " for star in self.stars:\n", " star.ax.append(0)\n", " star.ay.append(0)\n", " for other_star in self.stars:\n", " d_x = other_star.x[-1] - star.x[-1]\n", " d_y = other_star.y[-1] - star.y[-1]\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " if (star != other_star):\n", " acc = (G*other_star.mass*M_sun / \n", " (dist*AU)**2 )\n", "\n", " # unit of ax, ay: m/s**2\n", " star.ax[-1] += acc * d_x / dist\n", " star.ay[-1] += acc * d_y / dist\n", " \n", "\n", " def initialize_binary(self, distance, mean_v, n_star = 2, sigma_v = 0.001, mass_ratio = 1):\n", " \"\"\"\n", " Initializing a binary system.\n", " distance: distance between the two stars in AU\n", " mean_v: mean of the velocity distribution fo less massive star, star 1\n", " sigma_v: SD of the velocity distribution fo less massive star, star 1\n", " mass_ratio: mass_star0/ mass_star1. As star 0 is more massive, mass_ratio \n", " is alwasws equal or more than 1.\n", " \"\"\"\n", " self.binary = True\n", " self.n_star = n_star\n", " self.time = [0]\n", " \n", " \n", " # star 0 is the massive star, mean_v is the velocity of less massive star 1\n", " vel_1 = truncnorm(mean_v, sigma_v).rvs()\n", " vel_0 = truncnorm(mean_v, sigma_v).rvs() * np.sqrt(1/mass_ratio)\n", " \n", " # set the position only in x axis and velocity only in y axis\n", " self.stars.append(Star(0+distance/2, 0, 0, +vel_0))\n", " self.stars.append(Star(0-distance/2, 0, 0, -vel_1))\n", " \n", " # star 0 is the massive star\n", " self.stars[0].mass = mass_ratio \n", " # radius will depend on the stars mass\n", " self.stars[0].radius = ((self.stars[0].mass * 4*np.pi*self.stars[0].radius**2)\n", " /(4*np.pi))**0.5\n", " \n", " self.center_of_mass_x = 0\n", " self.center_of_mass_y = 0\n", " \n", " # star_1 has 1 M_sun\n", " self.total_mass = 1 + mass_ratio\n", " \n", " # distance between the stars\n", " self.dist = [distance]\n", " \n", " # calculate the acceleration at time = 0 \n", " for star in self.stars:\n", " star.ax.append(0)\n", " star.ay.append(0)\n", " for other_star in self.stars:\n", " d_x = other_star.x[-1] - star.x[-1]\n", " d_y = other_star.y[-1] - star.y[-1]\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " if (star != other_star):\n", " acc = (G*other_star.mass*M_sun / \n", " ((dist*AU)**3) )\n", "\n", " # unit of ax, ay: m/s**2\n", " star.ax[-1] += acc * d_x\n", " star.ay[-1] += acc * d_y\n", " \n", " def merge(self, star1, star2):\n", " # update the velocity to conserve momentum\n", " star1.vx[-1] = (star1.momentum_x + star2.momentum_x) / (star1.mass + star2.mass)\n", " star1.vy[-1] = (star1.momentum_y + star2.momentum_y) / (star1.mass + star2.mass)\n", "\n", " star1.mass += star2.mass\n", " star1.radius = ((4*np.pi*star1.radius**2 + \n", " 4*np.pi*star2.radius**2)/(4*np.pi))**0.5\n", " \n", " self.stars.remove(star2)\n", " self.n_star -= 1\n", " self.merged_stars.append(star2)\n", " self.n_merged_star += 1\n", "\n", " def update(self):\n", " # select an appropriate timestep depending on the max_v and max_acc\n", " max_ax = max([star.ax[-1] for star in self.stars])\n", " max_ay = max([star.ay[-1] for star in self.stars])\n", "\n", " max_vx = max([star.vx[-1] for star in self.stars])\n", " max_vy = max([star.vy[-1] for star in self.stars])\n", " \n", " # see the details of chooing timestep in the paper \n", " # 10**-15 are added to avoid division by zero\n", " # unit of timestep: s\n", " self.timestep = min( np.sqrt(AU/max(max_ax, max_ay, 10**(-15)))/10,\n", " AU/(max(max_vx, max_vy, 10**(-15)) * v_star)/10 )\n", " \n", " timestep = self.timestep\n", " self.time.append(self.time[-1] + timestep)\n", "\n", " # Update the position first using leapfrog equation\n", " # unit of x,y: AU\n", " for star in self.stars:\n", " star.x.append(star.x[-1] + (star.vx[-1]*v_star) * timestep / AU + \\\n", " star.ax[-1]/2*(timestep)**2 / AU)\n", " star.y.append(star.y[-1] + (star.vy[-1]*v_star) * timestep / AU + \\\n", " star.ay[-1]/2*(timestep)**2 / AU) \n", "\n", " \n", " # next, update the acceleration\n", " next_stars = self.stars.copy() \n", " \n", " for star in next_stars:\n", " star.ax.append(0)\n", " star.ay.append(0)\n", " for other_star in self.stars:\n", " d_x = other_star.x[-1] - star.x[-1]\n", " d_y = other_star.y[-1] - star.y[-1]\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " if (star != other_star):\n", " acc = (G*other_star.mass*M_sun / \n", " (dist*AU)**2 )\n", "\n", " # unit of ax, ay: m/s**2\n", " star.ax[-1] += acc * d_x / dist\n", " star.ay[-1] += acc * d_y / dist\n", " \n", " \n", " # Finally update the velocity using leapfrog method\n", " # unit of vx, vy: v_star\n", " for star in next_stars:\n", " star.vx.append(star.vx[-1] + (np.mean(star.ax[-2:])*timestep)/v_star)\n", " star.vy.append(star.vy[-1] + (np.mean(star.ay[-2:])*timestep)/v_star)\n", "\n", "\n", " self.stars = next_stars\n", " \n", " # check if any two stars are closer than twice their radius, if yes, merge them\n", " for star in self.stars:\n", " for other_star in self.stars:\n", " d_x = other_star.x[-1] - star.x[-1]\n", " d_y = other_star.y[-1] - star.y[-1]\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " if (star != other_star and dist < star.radius*2):\n", " self.merge(star, other_star)\n", "\n", " # update the position of center of mass\n", " star_mx = [star.mass*star.x[-1] for star in self.stars]\n", " star_my = [star.mass*star.y[-1] for star in self.stars]\n", " self.center_of_mass_x = np.sum(star_mx)/self.total_mass\n", " self.center_of_mass_y = np.sum(star_my)/self.total_mass\n", " \n", " # if it is binary star simulation, update the distance between stars\n", " if self.binary:\n", " if self.n_star > 1:\n", " d_x = self.stars[0].x[-1] - self.stars[1].x[-1]\n", " d_y = self.stars[0].y[-1] - self.stars[1].y[-1]\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " self.dist.append(dist)\n", "\n", " def display(self):\n", " '''\n", " Display the star system\n", " '''\n", " plt.figure(figsize=(8,8))\n", "\n", " x, y, r = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars], [star.radius for star in cluster.stars]\n", " size = self.size*100 * np.array(r)**2\n", " plt.scatter(x, y, s = size)\n", " plt.title('Star clusters at t = '+str(np.round(cluster.time[-1], 2)))\n", " plt.show()\n", "\n", " def display_plot(self, parameter = ['xy']):\n", " \"\"\"\n", " Display how the different paramters of the star cluster changes over time.\n", " \"\"\"\n", " for param in parameter:\n", " if param == 'xy':\n", " for star in self.stars:\n", " plt.plot(star.x, star.y)\n", " plt.title('Position from the origin (0,0)')\n", " for star in self.merged_stars:\n", " plt.plot(star.x, star.y)\n", " plt.xlabel('position in x (AU)')\n", " plt.ylabel('position in y (AU)')\n", " plt.show()\n", "\n", " elif param == 'vx':\n", " for star in self.stars:\n", " plt.plot(self.time, star.vx)\n", " plt.title('Velocity_x')\n", " for star in self.merged_stars:\n", " n_data = len(star.x)\n", " plt.plot(self.time[:n_data], star.vx)\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Velocity in x (v_star)')\n", " plt.show()\n", "\n", " elif param == 'vy':\n", " for star in self.stars:\n", " plt.plot(self.time, star.vy)\n", " plt.title('Velocity_y')\n", " for star in self.merged_stars:\n", " n_data = len(star.y)\n", " plt.plot(self.time[:n_data], star.vy)\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Velocity in y (v_star)')\n", " plt.show()\n", " \n", " elif param == 'v':\n", " for star in self.stars:\n", " v = np.sqrt(np.array(star.vx)**2+np.array(star.vy)**2)\n", " plt.plot(self.time, v)\n", " plt.title('Velocity')\n", " for star in self.merged_stars:\n", " n_data = len(star.x)\n", " v = np.sqrt(np.array(star.vx)**2+np.array(star.vy)**2)\n", " plt.plot(self.time[:n_data], v)\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Velocity (v_star)')\n", " plt.show()\n", " \n", " elif param == 'ax':\n", " for star in self.stars:\n", " plt.plot(self.time[1:], star.ax[1:], 'o')\n", " plt.title('Acceleration_x')\n", " for star in self.merged_stars:\n", " n_data = len(star.x)\n", " plt.plot(self.time[1:n_data], star.ax[1:], 'o') \n", " plt.xlabel('Time')\n", " plt.ylabel('Acceleration in x (m/s^2)')\n", " plt.show()\n", "\n", " elif param == 'ay':\n", " for star in self.stars:\n", " plt.plot(self.time[1:], star.ay[1:], 'o')\n", " plt.title('Acceleration_y')\n", " for star in self.merged_stars:\n", " n_data = len(star.x)\n", " plt.plot(self.time[1:n_data], star.ay[1:], 'o')\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Acceleration in y (m/s^2)')\n", " plt.show()\n", " \n", " elif param == 'a':\n", " for star in self.stars:\n", " a = np.sqrt(np.array(star.ax)**2+np.array(star.ay)**2)\n", " plt.plot(self.time[1:], a[1:])\n", " plt.title('Acceleration')\n", " for star in self.merged_stars:\n", " n_data = len(star.x)\n", " v = np.sqrt(np.array(star.ax)**2+np.array(star.ay)**2)\n", " plt.plot(self.time[1:n_data], a[1:])\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Acceleration $(m/s^2)$')\n", " plt.show()\n", " \n", " elif param == 'dist':\n", " n_data = len(self.dist)\n", " plt.title('Distance Between Stars')\n", " plt.plot(self.time[:n_data], self.dist)\n", " plt.xlabel('Time (s)')\n", " plt.ylabel('Distance (AU)')\n", " plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "id": "z9vGySS8Nc9_" }, "source": [ "## Same Mass Binary Star:\n", "Distance, $d = 20 AU$\n", "\n", "$m_{star 1}= 1 M_{sun}$, $m_{star 2}= 1 M_{sun}$\n", "\n", "\n", "initial_vel = $\\sqrt{\\frac{G M_{sun} }{(20 AU)}} \\frac{1}{v_{star}}$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 557 }, "id": "QhGMTm9zRh-F", "outputId": "13a5b1ad-be54-4234-9ab5-eda42de097ab" }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(50)\n", "\n", "dist = 20\n", "vel = np.sqrt(0.5*G*M_sun/(dist*AU))/v_star\n", "\n", "cluster.initialize_binary(distance = dist, mean_v=vel, sigma_v = vel/100, mass_ratio = 1)\n", "\n", "fig = plt.figure()\n", "\n", "\n", "ax = plt.axes(xlim=(-30, 70), ylim=(-30, 70))\n", "x, y = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars] \n", "scat = ax.scatter(x, y)\n", "\n", "def animate(j):\n", " cluster.update()\n", " if (j % 25 == 0):\n", " x, y,r = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars], [star.radius for star in cluster.stars]\n", " scat.set_offsets(np.c_[x,y])\n", " scat.set_sizes(200*np.array(r)**2*10)\n", " return scat,\n", "\n", "anim = animation.FuncAnimation(fig, animate,\n", " frames=500, \n", " interval=20)\n", "\n", "HTML(anim.to_html5_video())\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 998 }, "id": "WgzIRjG4tEyg", "outputId": "8428eb8e-c2c5-41bc-aba4-91979c53609b", "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.5717411906450662\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(50)\n", "\n", "dist = 20\n", "vel = np.sqrt(0.5*G*M_sun/(dist*AU))/v_star\n", "\n", "cluster.initialize_binary(distance = 20, mean_v=vel, sigma_v = vel/100, mass_ratio = 1)\n", "\n", "print(vel)\n", "\n", "cluster.display()\n", "\n", "while(cluster.time[-1] < 10**10 and cluster.n_star > 1 and cluster.dist[-1] < 10**3):\n", " cluster.update()\n", " \n", "cluster.display()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 1000 }, "id": "Mspqomj9tEyh", "outputId": "dafe81ab-f273-4c32-c3c7-08305ad145a9", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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", 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", 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", 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", 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", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster.display_plot(['xy', 'dist', 'vx','vy','v','a'])" ] }, { "cell_type": "markdown", "metadata": { "id": "MfVv7f5qONln" }, "source": [ "## Different mass binary system\n", "$m_{star 1}= 1 M_{sun}$, $m_{star 2}= 5 M_{sun}$\n", "\n", "$d = 15 AU$\n", "\n", "$v_{star 1}= 0$, $v_{star 2}= \\sqrt{\\frac{G \\, 5\\,M_{sun} }{(15 AU)}} \\frac{1}{v_{star}}$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 578 }, "id": "aqGhmqDy8HWj", "outputId": "682bfadd-42d2-492b-c1ea-f0eb77ee52d0" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.514520145318824\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 20, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(50)\n", "\n", "dist = 20\n", "vel = np.sqrt(0.5*G*5*M_sun/(dist*AU))/v_star\n", "\n", "cluster.initialize_binary(distance = dist, mean_v=vel, sigma_v = vel/100, mass_ratio = 5)\n", "\n", "print(vel)\n", "\n", "fig = plt.figure()\n", "\n", "ax = plt.axes(xlim=(-30, 70), ylim=(-30, 60))\n", "x, y = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars] \n", "scat = ax.scatter(x, y)\n", "\n", "def animate(j):\n", " cluster.update()\n", " if (j % 25 == 0):\n", " #cluster.display()\n", " #print([(star.ax, star.ay) for star in cluster.stars])\n", " x, y,r = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars], [star.radius for star in cluster.stars]\n", " scat.set_offsets(np.c_[x,y])\n", " scat.set_sizes(200*np.array(r)**2*10)\n", " return scat,\n", "\n", "anim = animation.FuncAnimation(fig, animate,\n", " frames=1000, \n", " interval=20)\n", "\n", "HTML(anim.to_html5_video())\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "lNqmGPGa-TQF" }, "outputs": [], "source": [ "cluster.display_plot()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 998 }, "id": "AFDHeHPFz0Wk", "outputId": "17afae1c-8dcd-4f53-dbfe-5b546fa0d725", "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.514520145318824\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(50)\n", "\n", "dist = 20\n", "vel = np.sqrt(0.5*G*5*M_sun/(dist*AU))/v_star\n", "\n", "cluster.initialize_binary(distance = 20, mean_v=vel, sigma_v = vel/100, mass_ratio = 5)\n", "\n", "print(vel)\n", "\n", "cluster.display()\n", "\n", "while(cluster.time[-1] < 10**10 and cluster.n_star > 1 and cluster.dist[-1] < 10**3):\n", " cluster.update()\n", " \n", "cluster.display()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 1000 }, "id": "tP_vjCYJz0Wq", "outputId": "69a68e6e-4fc3-4390-b7f9-cbd9dda14e12", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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", 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", 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", 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", 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", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster.display_plot(['xy', 'dist', 'vx','vy','v','a'])" ] }, { "cell_type": "markdown", "metadata": { "id": "DpTIFBBtPAqy" }, "source": [ "## Exploding away from the center of mass" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 573 }, "id": "sFQHIjnuRmif", "outputId": "616f2f96-21b3-439b-b728-65047772d20f" }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 23, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(25)\n", "\n", "mean_v = 2\n", "sigma_v = mean_v/100\n", "\n", "cluster.initialize(0.01, mean_v = mean_v, sigma_v=sigma_v)\n", "\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(xlim=(-50, 50), ylim=(-50, 50))\n", "x, y = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars] \n", "scat = ax.scatter(x, y)\n", "\n", "\n", "\n", "def animate(j):\n", " cluster.update()\n", " if (j % 25 == 0):\n", " x, y,r = [star.x[-1] for star in cluster.stars], [star.y[-1] for star in cluster.stars], [star.radius for star in cluster.stars]\n", " scat.set_offsets(np.c_[x,y])\n", " scat.set_sizes(200*np.array(r)**2*10)\n", " plt.title('Star clusters at t = '+str(np.round(cluster.time[-1], 2)))\n", " return scat,\n", "\n", "anim = animation.FuncAnimation(fig, animate,\n", " frames=500, \n", " interval=20)\n", "\n", "HTML(anim.to_html5_video())\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 981 }, "id": "myr9TM9N5_eT", "outputId": "bf385052-a033-4fa7-dfce-656f377b1249", "scrolled": false }, "outputs": [ { "data": { "image/png": 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m47rql1Wa/84WtWRcyYTptEnl+slFxxNpAD3evS+v0fV/eEMuKZUw3fSnxZr3xVM0alCfuEc7aGK/ihsH5sklmzT/nS2qa0qrqSWj+qa0nlpSreff2RL3aADQJQ3Nad1w30I1tGTU2JJRbVNa2+qa9L2H3op7tIOKQPdQr67errqmdKtljS1pvbZ6R0wTAUD3WLOtXm3PA2ZcWrBqWyzzxIVA91BHDOuvvsXJVstKUkkdMawspokAoHuMHFSqtHurZWbS5JEDYpooHgS6hzrz6OEaX97v/Uj3LU7qqBEDNGPSoTFPBgBd07c4pa+eeaRKixJKmFSSSqisJKWvzTwy7tEOKvM2P6XEqbKy0quqquIeo8dobEnrT6+v18K1OzR19CB97NgRKkryMxeAwvD6mu16ZOEGDepbpE8dX6GhZSVxj5QXZrbA3Sv3WE6gAQCIT0eB5nALAIAAEWgAAAJEoAEACBCBBgAgQAQaAIAAEWgAAAJEoAEACBCBBgAgQAQaAIAAEWgAAAJEoAEACBCBBgAgQKm4BwAAIHRPv12tmx9crPU1DTplwlDdePZkHdq/NK/bJNAAAOzFK6u26XO/qlJDc0aS9PDCDVq0boee+NIMJRKWt+1yihsAgL2Y+9wKNUZxlqSWjGtTTaNeWb0tr9vlCBo9yoKV23TXCyvlLl104hhVjhsS90gdSmdcCZPM8vcTNoD8q2tMy9ssMzPVNaXzul0CjR5j3qtr9bX/eUMNzdkviocWrtfN507RrA+Minmy1jbsaNA//fYVvbhiq/oUJfW5vzlcXzx9AqEGeqjzp43WX5dvUX3z7iAnEtL0w/J7gMApbvQYNz24WPXN2Z9kXVJ9c0b/98HFcY/Virvrkttf0IsrtirjUm1TWj99erl+V7U67tEAHKCPTh6mz884XKVFCRUnExo9uI9+feWJKkkl87pdjqDRY1TvbNxj2eadjXL3YI5OV2yu1eptdcrknA+rb07rjudX6vxpY+IbDMABMzP9w+kT9bkPj9euhhYN6Vd8UL7nEGgcMHfXH15eq7nPrVDGXZd+cJxmTxudt3+4UyoG6bXV299/LsgkTakYGEycJSnRwSzJPF7pCeDgKEklVVKW36PmXJzixgGb+9y7+sZ9C7VoXY0Wr9+p7/zxTd36xNK8be/7503RoL5FKitJqawkpUF9i/T986bmbXsHYtzQfppQXqZUTpD7FCV15SmHxTgVgJ7I3NtemxafyspKr6qqinsMdNLx331MW2ubWi3rW5zUom+fmbej2saWtP66bIsk6eQJh+T9OaADsWVXo66/9w09taRa/UtS+uLpE3T5yQQaQPvMbIG7V7ZdziluHLBdjS17LGtoTivjUjJPZ3RLUkmdduSh+XnwbnJIWYnmXLLH1xoA7BdOceOAzZhU3upUbtKkk8YfwvOtANANCDQO2M3nTtHRIweoJJVQaVFCRwzrrx9ecFzcYwFAQeAUNw7YkH7Fuv8Lp2j11jpl3DX2kH5xjwQABYNAo8tGD+kb9wgAUHA4xQ0AQIAINAAAASLQAAAEiEADABAgAg0AQIAINAAAASLQAAAEiEADABAgAg0AQIAINAAAASLQAAAEiEADABAgAg0AQIAINAAAASLQAAAEiEADABAgAg0AQIAINAAAASLQAAAEiEADABAgAg0AQIBScQ+QD+mM66klm/TmuhodPWqAZhxxqBIJi3ssAAA6reACnc64/u72F/Ta6u2qb0qrT3FSx48ZrF9+djqRBgD0GAV3ivvPb23Sa6u3q64pLZdU15TWy6u26em3q+MeDQCATiu4QC9at0N1TelWyxqa03pzfU1MEwEAsP8KLtCTRwxQ3+Jkq2WlRUlNHjEgpokAANh/BRfo048apikVA9W3OCmT1Dd6DvrDR5THPRoAAJ1WcBeJJROmO686SX9+a5MWr6/R0SMHaMYkruIGAPQsBRdoKRvpj0wepo9MHhb3KAAAHJCCO8UNAEAhINAAAASIQAMAECACDQBAgAg0AAABItAAAASIQEO1jS1au71emYzHPQoAINKlQJvZeWa2yMwyZlbZZt31ZrbMzJaY2ZldGxP54O66+aHFOv67j+n0Hzylk2/+s15etS3usQAA6voR9EJJ50p6JnehmU2WNFvS0ZJmSrrNzJJ7fjri9MDr63XHX1eqsSWjhuaMNtQ06PK5L6qhOb3vTwYA5FWXAu3ui919STurZkm6290b3X2FpGWSpndlW+h+v1+wRvVtYpxxqepdjqIBIG75eg56lKTVObfXRMsQkIF9itT2Hcoz7iorLch3gAWAHmWf34nN7HFJw9tZdYO739/VAczsaklXS9KYMWO6+nB589yyzbr1iaXaUtuks6eM1DUzxqsk1bPP2l916mF67M0Nqm/OSJKKEqaKwX00tWJgzJMBAPYZaHc/4wAed62k0Tm3K6Jl7T3+HElzJKmysjLIy4ifW7ZZV97xkhqikP30qWVatH6H5lxSuY/PDNuUikG6/fJpuuXhJVq3o14zJh2q62YeKTN+8xcAxC1f5zLnSbrLzP5d0khJEyW9mKdt5d2tTyx9P86S1NCS0dNLqrWxpkHDBpTGOFnXnXz4UN177dC4xwAAtNGlQJvZpyT9SFK5pD+Z2avufqa7LzKzeyS9KalF0rXu3mMvDd5a27THsmTCtKO+uccHGsBuT79drW/NW6S12+t17KiBuvncYzVxWP+4x0Iv1dWruO919wp3L3H3Ye5+Zs66m9z9cHef5O4PdX3U+Jw9daRKi1rvqrKSlCaUl8U0EYDutmTDTn3uV1VasblWTS0Zvbxymz7zs+dV39Rjjy3Qw/FOYp3wuQ+P14ePKFdJKqG+xUkd2r9Ecy+fpkSC52qBQvHbl1apqWX3U1kuqSWT0ZNLNsU3FHo1Xk/TCSWppH5+SaU21jRoR32zJpSXEWegwKTbe6tbl1p4C1zEhCPo/TBsQKmOGNafOAMF6NMnVKg41eZbokmnTSqPZyD0egQaAJR92eG/nTtFh/Qrlpk0fmg/3XnVSepfWhT3aOilOMUNoNeb99o6zXlmuZpaMvrCaYfrwuljVVrcs9+ICD0fgQYC9vqa7brpT4u1vHqXpo8bohs+MVmjBvWJe6yCctcLK/XdBxa//77033vkba3b0aAbPj455snQ23GKGwjUqi11mj1nvl5YsVWbdzXp4UUbdM5PnlNjCy/76U4/+vOyVr80pr45rV8+v1LN6cxePgvIPwINBOruNi/7ybhU39SiJ9+qjnGqwrOroWWPZS0ZJ9CIHYEGAlXT0LzHS38yLtU27hkUHLgzJg9TUXL3KzOSZppSMVB9i3kGEPEi0ECgZh03SqVFrS9UyrhrBi/76Vbf+uTR+sDowSpJJVRalNBh5f3044uOj3ssgIvEEJadDc26c/5KLVi5XSeMHaSLTxrba1/mMm3cEP3zmZP0/UeXKOOuPkVJ/fCC43RIWUncoxWUgX2KdM81H9S67fVqaslo7CF9+Y1uCIK5h/MuOZWVlV5VVRX3GIhJQ3NaZ/3ns1q3vV6NLRmVphIaMaiPHvrHU/c4kuxNGprT2lLbpOEDSpXkTXKAgmNmC9x9j99fzCluBOORRRu0saZBjdGFUQ0tGW2sadAjizbEPFm8SouSGjWoD3EGehkCjWCs3lqnhubWLyFqaE5r1Za6mCYCgPgQaATjxPGHqCTV+lR2SSqpE8cfEtNEABAfAo1gVI4drM+cUKGSVEJlJUmVpBL69PEVmjZucNyjAcBBx1XcCIaZ6bvnHKMrPjROi9fv1FEj+mt8eVncYwFALAg0gjO+vIwwA+j1OMUNAECACDQAAAEi0AAABIhAAwAQIAINAECACDQAAAEi0AAABIhAAwAQIAIN4KBaunGnXl29XelMOL/qFggR7yQG4KDYUd+sS29/QW9v3KVEQupTlNSvrzpRRw4fEPdoQJA4ggZwUPzrg4v15voa1TenVduY1uZdTbrmVwvkzpE00B4CDeCgeHzxRjWnW8d43Y4GVe9sjGkiIGwEGsBBMbSsZI9lJqmslGfagPYQaAAHxVc+OkmlRbu/5fQpSuriE8eobzGBBtrDVwaAg+KMycM097Jp+vkz72hnQ7MumDZa550wOu6xgGARaAAHzckThurkCUPjHgPoETjFDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAEKAuBdrMbjGzt8zsdTO718wG5ay73syWmdkSMzuz66MCANB7dPUI+jFJx7j7FElvS7peksxssqTZko6WNFPSbWaW7OK2AADoNboUaHd/1N1bopvzJVVEH8+SdLe7N7r7CknLJE3vyrYAAOhNuvM56M9Keij6eJSk1Tnr1kTLAABAJ6T2dQcze1zS8HZW3eDu90f3uUFSi6Q793cAM7ta0tWSNGbMmP39dAAACtI+A+3uZ+xtvZldLukTkk53d48Wr5U0OuduFdGy9h5/jqQ5klRZWent3QcAgN6mq1dxz5T0VUmfdPe6nFXzJM02sxIzO0zSREkvdmVbAAD0Jvs8gt6HH0sqkfSYmUnSfHe/xt0Xmdk9kt5U9tT3te6e7uK2AADoNboUaHefsJd1N0m6qSuPDwBAb8U7iQEAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQBAgAg0AAABItAAAASIQAMAECACDQB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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster = Cluster(25)\n", "\n", "mean_v = 2\n", "sigma_v = mean_v/100\n", "\n", "cluster.initialize(0.01, mean_v = mean_v, sigma_v=sigma_v)\n", "\n", "cluster.display()\n", "\n", "while(cluster.time[-1] < 10**10 and cluster.n_star > 1):\n", " cluster.update()\n", " \n", "cluster.display()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 851 }, "id": "N9sx3o5J5_eV", "outputId": "dc9cd032-df96-4e69-eb26-e59c3ab9f1b3", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "cluster.display_plot(['xy', 'vx','vy'])" ] }, { "cell_type": "markdown", "metadata": { "id": "1IDPoqiFPcIr" }, "source": [ "## Varying the initial velocity for exploding Model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "RVvqTqJuVHUV", "outputId": "7dea3041-50cb-4230-d47d-ab522f90f1e8" }, "outputs": [ { "data": { "text/plain": [ "(array([-3. , -2.5, -2. , -1.5, -1. , -0.5, 0. , 0.5, 1. , 1.5, 2. ]),\n", " [0.001,\n", " 0.0031622776601683794,\n", " 0.01,\n", " 0.03162277660168379,\n", " 0.1,\n", " 0.31622776601683794,\n", " 1.0,\n", " 3.1622776601683795,\n", " 10.0,\n", " 31.622776601683793,\n", " 100.0])" ] }, "execution_count": 439, "metadata": { "tags": [] }, "output_type": "execute_result" } ], "source": [ "v_means = [10**i for i in np.linspace(-3,2, 11)]\n", "np.log10(v_means), v_means" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "DbmoYRx_VHUi" }, "outputs": [], "source": [ "cluster = Cluster(25)\n", "def check_inside(cluster, check_radius = cluster.size*2):\n", " '''\n", " check the fraction of stars and fraction of total mass\n", " within the check_radius of the center of mass\n", " '''\n", " n_star_inside = 0\n", " mass_star_inside = 0\n", " \n", " for star in cluster.stars:\n", " d_x = star.x[-1] - cluster.center_of_mass_x\n", " d_y = star.y[-1] - cluster.center_of_mass_y\n", " dist = np.sqrt(d_x**2 + d_y**2)\n", " if dist < check_radius:\n", " mass_star_inside += star.mass\n", " n_star_inside += 1\n", "\n", " return n_star_inside/cluster.n_star, mass_star_inside/cluster.total_mass" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "yyQmFy0tU4BK" }, "outputs": [], "source": [ "cluster = Cluster(25)\n", "def check_radius(cluster):\n", " '''\n", " find the mean and median of the distances of the stars\n", " from the center of mass of the system\n", " '''\n", " d_x = [star.x[-1] - cluster.center_of_mass_x for star in cluster.stars]\n", " d_y = [star.y[-1] - cluster.center_of_mass_y for star in cluster.stars]\n", " \n", " dist = np.sqrt(np.array(d_x)**2 + np.array(d_y)**2)\n", "\n", " return np.mean(dist), np.median(dist)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "fgccxz74VHUk" }, "outputs": [], "source": [ "def confidence_interval(data):\n", " '''\n", " Returns the upper limit value of \n", " 95% confidence interval\n", " '''\n", " mean = np.mean(data)\n", " std = np.std(data)\n", " se = std/np.sqrt(len(data))\n", " upper95 = mean + 1.94*se\n", " return upper95" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "-NesvdFoVHUl", "outputId": "7b06d9cd-43ce-472d-8017-e44193ff77e3" }, "outputs": [ { "data": { "text/plain": [ "[0.001,\n", " 0.0031622776601683794,\n", " 0.01,\n", " 0.03162277660168379,\n", " 0.1,\n", " 0.31622776601683794,\n", " 1.0,\n", " 3.1622776601683795,\n", " 10.0,\n", " 31.622776601683793,\n", " 100.0]" ] }, "execution_count": 430, "metadata": { "tags": [] }, "output_type": "execute_result" } ], "source": [ "v_means" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 1000 }, "id": "AB-2LnQmVHUl", "outputId": "5cc58d77-c57c-447c-f4b3-c5ec5539c50e" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v = 0.001: Trial: 5 complete...\n", "v = 0.001: Trial: 10 complete...\n", "v = 0.001: Trial: 15 complete...\n", "v = 0.001: Trial: 20 complete...\n", "v = 0.0031622776601683794: Trial: 5 complete...\n", "v = 0.0031622776601683794: Trial: 10 complete...\n", "v = 0.0031622776601683794: Trial: 15 complete...\n", "v = 0.0031622776601683794: Trial: 20 complete...\n", "v = 0.01: Trial: 5 complete...\n", "v = 0.01: Trial: 10 complete...\n", "v = 0.01: Trial: 15 complete...\n", "v = 0.01: Trial: 20 complete...\n", "v = 0.03162277660168379: Trial: 5 complete...\n", "v = 0.03162277660168379: Trial: 10 complete...\n", "v = 0.03162277660168379: Trial: 15 complete...\n", "v = 0.03162277660168379: Trial: 20 complete...\n", "v = 0.1: Trial: 5 complete...\n", "v = 0.1: Trial: 10 complete...\n", "v = 0.1: Trial: 15 complete...\n", "v = 0.1: Trial: 20 complete...\n", "v = 0.31622776601683794: Trial: 5 complete...\n", "v = 0.31622776601683794: Trial: 10 complete...\n", "v = 0.31622776601683794: Trial: 15 complete...\n", "v = 0.31622776601683794: Trial: 20 complete...\n", "v = 1.0: Trial: 5 complete...\n", "v = 1.0: Trial: 10 complete...\n", "v = 1.0: Trial: 15 complete...\n", "v = 1.0: Trial: 20 complete...\n", "v = 3.1622776601683795: Trial: 5 complete...\n", "v = 3.1622776601683795: Trial: 10 complete...\n", "v = 3.1622776601683795: Trial: 15 complete...\n", "v = 3.1622776601683795: Trial: 20 complete...\n", "v = 10.0: Trial: 5 complete...\n", "v = 10.0: Trial: 10 complete...\n", "v = 10.0: Trial: 15 complete...\n", "v = 10.0: Trial: 20 complete...\n", "v = 31.622776601683793: Trial: 5 complete...\n", "v = 31.622776601683793: Trial: 10 complete...\n", "v = 31.622776601683793: Trial: 15 complete...\n", "v = 31.622776601683793: Trial: 20 complete...\n", "v = 100.0: Trial: 5 complete...\n", "v = 100.0: Trial: 10 complete...\n", "v = 100.0: Trial: 15 complete...\n", "v = 100.0: Trial: 20 complete...\n" ] } ], "source": [ "n_trials = 20\n", "mean_radius_mean = []\n", "median_radius_mean = []\n", "avg_n_merged_star_mean = []\n", "\n", "mean_radius_upper95 = []\n", "median_radius_upper95 = []\n", "avg_n_merged_star_upper95 = []\n", "\n", "for v in v_means:\n", " mean_radius = []\n", " median_radius = []\n", " avg_n_merged = []\n", " for i in range(n_trials):\n", " cluster = Cluster(size = 25)\n", " mean_v = v\n", " sigma_v = mean_v/100\n", " cluster.initialize(density = 0.01, mean_v = mean_v, sigma_v=sigma_v)\n", "\n", " while(cluster.time[-1] < 10**8 and cluster.n_star > 1):\n", " cluster.update()\n", "\n", " mean_r, median_r = check_radius(cluster)\n", " mean_radius.append(mean_r)\n", " median_radius.append(median_r)\n", " \n", " # stop running when all the stars merged or there is no star within 2*cluster size\n", " # otherwise run until time = 10**12\n", " while(cluster.time[-1] < 10**12 and check_inside(cluster)[0] != 0 and cluster.n_star > 1):\n", " cluster.update()\n", " \n", " avg_n_merged.append(cluster.n_merged_star/(cluster.n_merged_star+cluster.n_star))\n", " \n", " if ((i+1)%5 == 0):\n", " print(f'v = {v}: Trial: {i+1} complete...')\n", "\n", " mean_radius_mean.append(np.mean(mean_radius))\n", " median_radius_mean.append(np.mean(median_radius))\n", " avg_n_merged_star_mean.append(np.mean(avg_n_merged))\n", "\n", " mean_radius_upper95.append(confidence_interval(mean_radius))\n", " median_radius_upper95.append(confidence_interval(median_radius))\n", " avg_n_merged_star_upper95.append(confidence_interval(avg_n_merged))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "40iDFiS5VHUn", "scrolled": true }, "outputs": [], "source": [ "mean_radius_error = np.array(mean_radius_upper95) - np.array(mean_radius_mean)\n", "median_radius_error = np.array(median_radius_upper95) - np.array(median_radius_mean)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "pPC5MlfdVHUn", "outputId": "a86a9765-37a5-4b35-9af8-bfad17fc66ad" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,8))\n", "plt.errorbar(v_means, mean_radius_mean, mean_radius_error, label = 'Mean Distance')\n", "plt.errorbar(v_means, median_radius_mean, median_radius_error, label = 'Median Distance')\n", "plt.xscale('log')\n", "plt.xlabel('Mean Velocity, $\\mu_v$ (v_star)', fontsize=12)\n", "plt.title('Mean and Median of the Distance of the stars from the the center of mass when time = $10^{8}$ s', fontsize=12)\n", "plt.ylabel('Distance from Center of Mass (AU)', fontsize=12)\n", "theoritical_v = np.sqrt(2*G*cluster.total_mass*M_sun/(cluster.size*AU))/v_star\n", "plt.axvline(theoritical_v, linestyle = \":\", label = 'Theoretical Estimate')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 269 }, "id": "Xr9_UYxqVHUo", "outputId": "3b66f675-0ce8-4d7d-ccb8-5b9045a1a1ba", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "avg_n_merge_error = np.array(avg_n_merged_star_upper95) - np.array(avg_n_merged_star_mean)\n", "\n", "plt.figure(figsize=(10,8))\n", "plt.errorbar(v_means, avg_n_merged_star_mean, avg_n_merge_error)\n", "plt.xlabel('Mean Velocity, $\\mu_v$ (v_star)', fontsize=12)\n", "plt.ylabel('Average fraction of merging', fontsize=12)\n", "plt.title('Average Fraction of Merged Star When Time = $10^{12}$ s', fontsize=12)\n", "theoritical_v = np.sqrt(2*G*cluster.total_mass*M_sun/(cluster.size*AU))/v_star\n", "plt.axvline(theoritical_v, linestyle = \":\", label = 'Theoretical Estimate')\n", "plt.xscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "UbhWqIVkxwmn", "outputId": "0e5f004f-35fa-4bc5-9012-20670742f05f" }, "outputs": [ { "data": { "text/plain": [ "12.57392952516053" ] }, "execution_count": 29, "metadata": { "tags": [] }, "output_type": "execute_result" } ], "source": [ "np.sqrt(2*G*20*M_sun/(25*AU))/v_star" ] }, { "cell_type": "markdown", "metadata": { "id": "u_FhI-ydVaXQ" }, "source": [ "## Varying the velocity for Binary Star System \n", "\n", "Distance = 20 AU\n", "\n", "Mass1 = Mass2 = 1 M_sun" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "NGHzqw_8obv-", "outputId": "639e78b3-e2dd-4e72-efbe-dbbccaa9eb0d" }, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. ])" ] }, "execution_count": 10, "metadata": { "tags": [] }, "output_type": "execute_result" } ], "source": [ "v_means = np.linspace(0, 5, 11)\n", "v_means" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "H8gvmQfntEyx", "outputId": "4ea961e2-3c81-4b68-fa2a-3b5a080a0a10" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v = 0.0: Trial: 5 complete...\n", "v = 0.0: Trial: 10 complete...\n", "v = 0.0: Trial: 15 complete...\n", "v = 0.0: Trial: 20 complete...\n", "v = 0.5: Trial: 5 complete...\n", "v = 0.5: Trial: 10 complete...\n", "v = 0.5: Trial: 15 complete...\n", "v = 0.5: Trial: 20 complete...\n", "v = 1.0: Trial: 5 complete...\n", "v = 1.0: Trial: 10 complete...\n", "v = 1.0: Trial: 15 complete...\n", "v = 1.0: Trial: 20 complete...\n", "v = 1.5: Trial: 5 complete...\n", "v = 1.5: Trial: 10 complete...\n", "v = 1.5: Trial: 15 complete...\n", "v = 1.5: Trial: 20 complete...\n", "v = 2.0: Trial: 5 complete...\n", "v = 2.0: Trial: 10 complete...\n", "v = 2.0: Trial: 15 complete...\n", "v = 2.0: Trial: 20 complete...\n", "v = 2.5: Trial: 5 complete...\n", "v = 2.5: Trial: 10 complete...\n", "v = 2.5: Trial: 15 complete...\n", "v = 2.5: Trial: 20 complete...\n", "v = 3.0: Trial: 5 complete...\n", "v = 3.0: Trial: 10 complete...\n", "v = 3.0: Trial: 15 complete...\n", "v = 3.0: Trial: 20 complete...\n", "v = 3.5: Trial: 5 complete...\n", "v = 3.5: Trial: 10 complete...\n", "v = 3.5: Trial: 15 complete...\n", "v = 3.5: Trial: 20 complete...\n", "v = 4.0: Trial: 5 complete...\n", "v = 4.0: Trial: 10 complete...\n", "v = 4.0: Trial: 15 complete...\n", "v = 4.0: Trial: 20 complete...\n", "v = 4.5: Trial: 5 complete...\n", "v = 4.5: Trial: 10 complete...\n", "v = 4.5: Trial: 15 complete...\n", "v = 4.5: Trial: 20 complete...\n", "v = 5.0: Trial: 5 complete...\n", "v = 5.0: Trial: 10 complete...\n", "v = 5.0: Trial: 15 complete...\n", "v = 5.0: Trial: 20 complete...\n" ] } ], "source": [ "n_trials = 20\n", "dist_mean = []\n", "dist_upper95 = []\n", "\n", "for v in v_means:\n", " dist_list = []\n", "\n", " for i in range(n_trials):\n", " cluster = Cluster(size = 25)\n", " dist = 20\n", " mean_v = v\n", " sigma_v = mean_v/100\n", " cluster.initialize_binary(distance = dist, mean_v=mean_v, sigma_v = sigma_v, mass_ratio = 1)\n", " \n", " # stop running when all the stars merged or distance between the stars are 200 AU\n", " # otherwise run until time = 10**10 s\n", " while(cluster.time[-1] < 10**10 and cluster.n_star > 1 and cluster.dist[-1] < 200):\n", " cluster.update()\n", " \n", " if cluster.n_star == 1: \n", " dist_list.append(0)\n", " else:\n", " dist_list.append(cluster.dist[-1])\n", " \n", " if ((i+1)%5 == 0):\n", " print(f'v = {v}: Trial: {i+1} complete...')\n", "\n", " dist_mean.append(np.mean(dist_list))\n", " dist_upper95.append(confidence_interval(dist_list))\n", " \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 523 }, "id": "7kD-cQB39c_P", "outputId": "bf41e586-1459-459f-d168-02eccfd0cc6f" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "dist_error = np.array(dist_upper95) - np.array(dist_mean)\n", "\n", "plt.figure(figsize=(10,8))\n", "plt.errorbar(v_means, dist_mean, dist_error)\n", "plt.xlabel('Mean Velocity, $\\mu_v$ (v_star)', fontsize=12)\n", "plt.ylabel('Distance between the stars (AU)', fontsize=12)\n", "plt.title('Distance between the stars When Time = $10^{10}$ s or Distance = 200', fontsize=12)\n", "distance = 20\n", "theoritical_v = np.sqrt(G*M_sun/(2*distance*AU))/v_star\n", "plt.axvline(theoritical_v, linestyle = \":\", label = 'Theoretical Estimate')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "tpVKb0JH-AYZ", "outputId": "df919826-c200-479f-c2e2-8201ae608bbb" }, "outputs": [ { "data": { "text/plain": [ "1.5717411906450662" ] }, "execution_count": 30, "metadata": { "tags": [] }, "output_type": "execute_result" } ], "source": [ "np.sqrt(G*M_sun/(2*distance*AU))/v_star" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "3CudyD_N0RPf" }, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [ "MfVv7f5qONln", "DpTIFBBtPAqy" ], "include_colab_link": true, "name": "CS166_Final_Project_Final.ipynb", "provenance": [], "toc_visible": true }, "kernelspec": { "display_name": "Python 3.6.8 ('base')", "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": "3.6.8" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "vscode": { "interpreter": { "hash": "5c9af5bf861f622e259cbb5c3fcf8912a684acabc7d57c0ec1c076ab03a2eda7" } } }, "nbformat": 4, "nbformat_minor": 1 }