{ "cells": [ { "cell_type": "code", "execution_count": 11, "id": "8a004a62", "metadata": { "ExecuteTime": { "end_time": "2024-10-19T06:10:35.301605Z", "start_time": "2024-10-19T06:10:35.270185Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "45019e81", "metadata": {}, "source": [ "作业11\n", "\n", "假设在红移为1处去观测一个现在红移为2的星系，其红移为多少？" ] }, { "cell_type": "code", "execution_count": 2, "id": "0dbb60e9", "metadata": { "ExecuteTime": { "end_time": "2024-10-19T02:48:08.420574Z", "start_time": "2024-10-19T02:48:08.390485Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "红移为: 0.5\n" ] } ], "source": [ "z1 = 1\n", "z2 = 2\n", "\n", "a1 = 1/(z1+1)\n", "a2 = 1/(z2+1)\n", "\n", "a_new = a2/a1\n", "z_new = 1/a_new-1\n", "\n", "print('红移为:',z_new)" ] }, { "cell_type": "markdown", "id": "55cca51b", "metadata": {}, "source": [ "假设宇宙的膨胀是一个线性过程，请根据今天的哈勃常数估算宇宙的年龄。" ] }, { "cell_type": "code", "execution_count": null, "id": "c791d649", "metadata": { "ExecuteTime": { "end_time": "2024-10-19T03:03:37.712505Z", "start_time": "2024-10-19T03:03:37.693587Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "13.995464852607707\n", "2.2683084899546342e-18\n", "宇宙年龄为: 13.9955 Gyr\n" ] } ], "source": [ "H_z = 70/3.086/1e19 #s\n", "\n", "#a正比t\n", "\n", "#a = t\n", "\n", "#a的导数为常数\n", "a_dot = 1\n", "#哈勃常数正比于1/t\n", "\n", "#H_z = 1/a\n", "#H_z = 1/t\n", "\n", "t = 1/H_z/3.15/1e7/1e9#Gyr\n", "print(t)\n", "print(H_z)\n", "print('宇宙年龄为: {:.4f} Gyr'.format(t))\n" ] }, { "cell_type": "markdown", "id": "187da9b0", "metadata": {}, "source": [ "作业12\n", "\n", "一团1000个太阳质量的中性气体云（全部为H原子）, 温度为30K，当云的密度大于多少时，气体云将发生塌缩？塌缩（自由下落）时标为多少？\n", "\n", "• 云塌缩：势能 > 热能" ] }, { "cell_type": "code", "execution_count": 27, "id": "d7376d2e", "metadata": { "ExecuteTime": { "end_time": "2024-10-19T03:20:23.992513Z", "start_time": "2024-10-19T03:20:23.961136Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "数密度: 2.4300 cm-3\n", "下落时间为: 0.0235 Gyr\n" ] } ], "source": [ "#Jeans质量\n", "#M = 30*((T/10)**(3/2))*((100/n)**(1/2))\n", "#T = 30\n", "\n", "#1000 = 30*3**(3/2)*((100/n)**(1/2))\n", "\n", "#(100/n)**(1/2) = 1000/30/(3**(3/2))\n", "#100/n = (1000/30/(3**(3/2)))**2\n", "\n", "#数密度\n", "n = 100/((1000/30/(3**(3/2)))**2) #cm-3\n", "#坍缩时间\n", "rou = n*3.32*1e-24 #cm-3 g\n", "G = 6.67*1e-8 #cm3 g-3 s-2\n", "t = np.sqrt(3*np.pi/32/G/rou)/3.15/1e7/1e9\n", "\n", "print('数密度: {:.4f} cm-3'.format(n))\n", "print('下落时间为: {:.4f} Gyr'.format(t))" ] }, { "cell_type": "markdown", "id": "975c09f2", "metadata": {}, "source": [ "这团气体中能形成的最大质量的恒星的质量是多少？\n", "\n", "假设分子云中的恒星形成遵循Salpter初始质量函数（最小质量的恒星为0.08太阳质量）" ] }, { "cell_type": "code", "execution_count": 40, "id": "4e9256b4", "metadata": { "ExecuteTime": { "end_time": "2024-10-19T04:39:17.535526Z", "start_time": "2024-10-19T04:39:17.515210Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "在小质量星（m<0.5）总质量占比25%的情况下最大质量为7.7 M_sun\n" ] } ], "source": [ "#取不同alpha时http://cluster.shao.ac.cn/~shen/Lecture/IMF.pdf的（3）式有不同的指数形式\n", "\n", "#0.08~0.5的质量 alpha = 1.3\n", "\n", "#M_1 = k2/0.3*((0.08**(-0.3))-(0.5**(-0.3)))\n", "#M_1 = 3*k2 #1式\n", "\n", "#0.5~最大质量的质量 alpha = 2.3\n", "\n", "#M_2 = k2/1.3*((M_max**(-1.3))-(0.5**(-1.3))) #2式\n", "\n", "#M_1+M_2 = 1000 #M_sun 3式\n", "\n", "#1式除2式 带入3式\n", "\n", "#1000/M2-1 = 3.9/((0.5**(-1.3))-(M_max**(-1.3))\n", " \n", "#假设小质量星占25%,则M2 = 750\n", "#可得\n", "M_max = 7.7 #M_sun\n", "\n", "print('在小质量星（m<0.5）总质量占比25%的情况下最大质量为{:.1f} M_sun'.format(M_max))" ] }, { "cell_type": "markdown", "id": "6b662cfb", "metadata": {}, "source": [ "#思路挺好，差一点\n", "#Mtot(M>M*)/Mtot(M" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = np.loadtxt('bc2003_hr_m162_salp_ssp.4color.txt',skiprows=29)\n", "t = data[:,0] #Gyr\n", "Lv = 1/data[:,5] #V波段光度\n", "\n", "#从0到t积分\n", "M_t = 3*(1-np.exp(-t/3))\n", "\n", "M_L_ratio = M_t/Lv\n", "\n", "plt.figure(dpi=100,figsize=(7,4))\n", "plt.scatter(t,M_L_ratio)\n", "plt.xlabel('t[Gyr]',size=12)\n", "plt.ylabel('M/Lv',size=12)" ] }, { "cell_type": "code", "execution_count": null, "id": "d6c98f04", "metadata": {}, "outputs": [], "source": [ "### 这个文件的各列的意思理解不到位" ] }, { "cell_type": "code", "execution_count": null, "id": "213194ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "5a173cf3", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "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": "3.8.17" } }, "nbformat": 4, "nbformat_minor": 5 }