EVENT_RATE_N_exp_exclusion_M31.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "5a2cb4ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import special\n",
    "from scipy import integrate\n",
    "from scipy.integrate import quad\n",
    "import astropy.constants as cte #cte\n",
    "import astropy.units as unt  #unt\n",
    "from tqdm.auto import tqdm\n",
    "import sympy as sp\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "pc    = cte.pc.to_value()\n",
    "kpc   = cte.kpc.to_value()\n",
    "c     = cte.c.to_value()\n",
    "MSun  = cte.M_sun.to_value()\n",
    "G_num = cte.G.to_value()\n",
    "time  = 3600 # es una hora en segundos\n",
    "rs    = 21.5*kpc\n",
    "d_s   = 770*kpc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4d5decde",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rE(m, d):\n",
    "    D   = d*(1-d/d_s)\n",
    "    arg = 4*G_num*(m*MSun)*D/c**2\n",
    "    rE  = np.sqrt(abs(arg)) #R_E al cuadrado\n",
    "    return rE\n",
    "\n",
    "def v_r(tE, rE, y):\n",
    "    te = tE*time #3600 es una hora en segundos\n",
    "    return 2*rE*np.sqrt(1-y**2)/te\n",
    "\n",
    "def r_MW(d,l,b):\n",
    "    '''\n",
    "    Distancia de PBH al centro de MW, en terminos de d. \n",
    "    \n",
    "    d: distancia observador-lente.\n",
    "    '''\n",
    "    R_0  = 8.5*kpc\n",
    "    r_mw = np.sqrt(R_0**2 + d**2 - 2*R_0*d*np.cos(math.radians(l))*np.cos(math.radians(b))) \n",
    "    return r_mw\n",
    "\n",
    "def r_M31(d):\n",
    "    '''\n",
    "    Distancia para PBH del centro de M31. Ecuacion 10.\n",
    "    \n",
    "    d_s: distancia del observador a la fuente.\n",
    "    '''\n",
    "    r_m31 = d_s - d\n",
    "    return r_m31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "14e8e986",
   "metadata": {},
   "outputs": [],
   "source": [
    "def density_DM(d,l,b):\n",
    "    \n",
    "    '''\n",
    "    Densidad de DM en MW.\n",
    "    '''\n",
    "    term1 =  rho_c_MW\n",
    "    term2 = (r_MW(d,l,b) / r_s_MW)\n",
    "    term3 = (1 + r_MW(d,l,b) / r_s_MW)**2\n",
    "    return (term1 /(term2 * term3)) #+  (term4 / (term5 * term6)) \n",
    "\n",
    "def M_nfw(rho_0,d):\n",
    "    l       = 121.2 # degree\n",
    "    b       = -21.6 # degree\n",
    "    R_0     = 8.5*kpc\n",
    "    rs      = 21.5*kpc\n",
    "    C       = r_MW(d,l,b)/rs\n",
    "    return 4*np.pi*rho_0*rs**3*(np.log(1+C)-C/(1+C))\n",
    "\n",
    "def vc(d,M_nfw):\n",
    "    l       = 121.2 # degree\n",
    "    b       = -21.6 # degree\n",
    "    return np.sqrt(abs(G_num*M_nfw/r_MW(d,l,b)))\n",
    "\n",
    "@np.vectorize\n",
    "def integrand_HSC(d,y,t,m):\n",
    "    '''\n",
    "    integrando tasa de eventos en MW.\n",
    "    '''\n",
    "    rho_0   = rho_c_MW\n",
    "    exp_fac = np.exp(-v_r(t,rE(m,d),y)**2/vc(d,M_nfw(rho_0,d))**2)\n",
    "    M       = m*MSun\n",
    "    tE      = t*time\n",
    "    E       = 7*time*t #3600 es una hora en segundos\n",
    "    return 2*exp_fac*density_DM(d,l,b)*v_r(t,rE(m,d),y)**4/(np.sqrt(1-y**2)*M*vc(d,M_nfw(rho_0,d))**2)*(3600**2)                             "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "e8ce32d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# M31 \n",
    "def density_DM2(d,l,b):\n",
    "    \n",
    "    '''\n",
    "    Densidad de DM en M31.\n",
    "    '''\n",
    "    term4 = rho_c_M31               \n",
    "    term5 = (r_M31(d) / r_s_M31)\n",
    "    term6 = (1 + r_M31(d) / r_s_M31)**2\n",
    "    return  (term4 / (term5 * term6)) \n",
    "\n",
    "def M_nfw2(rho_0,d,rs):\n",
    "    '''\n",
    "    Función debajo de la ecuacion (13).\n",
    "    '''\n",
    "    l       = 121.2 # degree\n",
    "    b       = -21.6 # degree\n",
    "    C       = r_M31(d)/rs\n",
    "    return  4*np.pi*rho_0*rs**3*(np.log(1+C)-C/(1+C))\n",
    "\n",
    "def vc2(d,M_nfw2):\n",
    "    '''\n",
    "    velocidad de dispersion en M31. Ecuacion (13).\n",
    "    '''\n",
    "    return np.sqrt(abs(G_num*M_nfw2/r_M31(d)))\n",
    "\n",
    "@np.vectorize\n",
    "def integrand_HSC2(d,y,t,m):\n",
    "    rho_0   = rho_c_M31\n",
    "    exp_fac = np.exp(-v_r(t,rE(m,d),y)**2/vc2(d,M_nfw2(rho_0,d,r_s_M31))**2)\n",
    "    M       = m*MSun\n",
    "    tE      = t*time\n",
    "    E       = 7*time*t #3600 es una hora en segundos\n",
    "    return 2*exp_fac*density_DM2(d,l,b)*v_r(t,rE(m,d),y)**4/(np.sqrt(1-y**2)*M*vc2(d,M_nfw2(rho_0,d,r_s_M31))**2)*(3600**2)                             "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "0826985e",
   "metadata": {},
   "outputs": [],
   "source": [
    "d         = sp.Symbol('d')\n",
    "d_s       = sp.Symbol('d_s')\n",
    "rho_c_MW  = 4.88 * 10**6 * (MSun/kpc**3)\n",
    "rho_c_M31 = 4.96 * 10**6 * (MSun/kpc**3)\n",
    "r_s_MW    = 21.5 * kpc\n",
    "r_s_M31   = 25 * kpc\n",
    "d_s       = 770 * kpc\n",
    "l         = 121.2 # degree\n",
    "b         = -21.6 # degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "ec9d145c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TASA DE EVENTOS DE HSC\n",
    "\n",
    "# @np.vectorize\n",
    "def dG_dt_HSC(t,M):\n",
    "    ti  = t[0]\n",
    "    tf  = t[1]\n",
    "    t   = np.logspace(ti,tf,25)\n",
    "#     t   = np.linspace(10**ti,10**tf,50)\n",
    "    I_k = np.zeros([len(t)])\n",
    "    for i in tqdm(range(len(t))):\n",
    "        I_j = integrate.dblquad(lambda y, d: integrand_HSC(d,y,t[i],M), 0, d_s, lambda d: 0, lambda d: 1,epsrel=1e-20)\n",
    "        I_j2 = integrate.dblquad(lambda y, d: integrand_HSC2(d,y,t[i],M), 0, d_s, lambda d: 0, lambda d: 1,epsrel=1e-20)\n",
    "        I_k[i] = I_j[0]+ I_j2[0]\n",
    "    return I_k,t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "518dbcf0",
   "metadata": {},
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      "c:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py:879: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n"
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      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
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      "\u001b[1;32m<ipython-input-27-242971e7319e>\u001b[0m in \u001b[0;36mdG_dt_HSC\u001b[1;34m(t, M)\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mtqdm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m         \u001b[0mI_j\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdblquad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mintegrand_HSC\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0md\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md_s\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m         \u001b[0mI_j2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdblquad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mintegrand_HSC2\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0md\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md_s\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m         \u001b[0mI_k\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mI_j\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m+\u001b[0m \u001b[0mI_j2\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mI_k\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mdblquad\u001b[1;34m(func, a, b, gfun, hfun, args, epsabs, epsrel)\u001b[0m\n\u001b[0;32m    599\u001b[0m                 hfun(args[0]) if callable(hfun) else hfun]\n\u001b[0;32m    600\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 601\u001b[1;33m     return nquad(func, [temp_ranges, [a, b]], args=args,\n\u001b[0m\u001b[0;32m    602\u001b[0m             opts={\"epsabs\": epsabs, \"epsrel\": epsrel})\n\u001b[0;32m    603\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mnquad\u001b[1;34m(func, ranges, args, opts, full_output)\u001b[0m\n\u001b[0;32m    823\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    824\u001b[0m         \u001b[0mopts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mopt\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32melse\u001b[0m \u001b[0m_OptFunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mopt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mopts\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 825\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_NQuad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mranges\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopts\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    826\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    827\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mintegrate\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    877\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    878\u001b[0m             \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpartial\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdepth\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdepth\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 879\u001b[1;33m         quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n\u001b[0m\u001b[0;32m    880\u001b[0m                       **opt)\n\u001b[0;32m    881\u001b[0m         \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mquad_r\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mquad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)\u001b[0m\n\u001b[0;32m    349\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    350\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 351\u001b[1;33m         retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,\n\u001b[0m\u001b[0;32m    352\u001b[0m                        points)\n\u001b[0;32m    353\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36m_quad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points)\u001b[0m\n\u001b[0;32m    461\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mpoints\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    462\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0minfbounds\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 463\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_qagse\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    464\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    465\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_qagie\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mbound\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0minfbounds\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mintegrate\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    877\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    878\u001b[0m             \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpartial\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdepth\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdepth\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 879\u001b[1;33m         quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n\u001b[0m\u001b[0;32m    880\u001b[0m                       **opt)\n\u001b[0;32m    881\u001b[0m         \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mquad_r\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36mquad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)\u001b[0m\n\u001b[0;32m    349\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    350\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 351\u001b[1;33m         retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,\n\u001b[0m\u001b[0;32m    352\u001b[0m                        points)\n\u001b[0;32m    353\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py\u001b[0m in \u001b[0;36m_quad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points)\u001b[0m\n\u001b[0;32m    461\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mpoints\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    462\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0minfbounds\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 463\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_qagse\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    464\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    465\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_qagie\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mbound\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0minfbounds\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-27-242971e7319e>\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(y, d)\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mtqdm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m         \u001b[0mI_j\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdblquad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mintegrand_HSC\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0md\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md_s\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 12\u001b[1;33m         \u001b[0mI_j2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdblquad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mintegrand_HSC2\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0md\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mM\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0md_s\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     13\u001b[0m         \u001b[0mI_k\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mI_j\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m+\u001b[0m \u001b[0mI_j2\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mI_k\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   2111\u001b[0m             \u001b[0mvargs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mextend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0m_n\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0m_n\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mnames\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2112\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2113\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_vectorize_call\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mvargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2114\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2115\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_get_ufunc_and_otypes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36m_vectorize_call\u001b[1;34m(self, func, args)\u001b[0m\n\u001b[0;32m   2189\u001b[0m             \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2190\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2191\u001b[1;33m             \u001b[0mufunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0motypes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_ufunc_and_otypes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2192\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2193\u001b[0m             \u001b[1;31m# Convert args to object arrays first\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36m_get_ufunc_and_otypes\u001b[1;34m(self, func, args)\u001b[0m\n\u001b[0;32m   2143\u001b[0m             \u001b[1;31m# Assumes that ufunc first evaluates the 0th elements in the input\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2144\u001b[0m             \u001b[1;31m# arrays (the input values are not checked to ensure this)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2145\u001b[1;33m             \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2146\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mbuiltins\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0many\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2147\u001b[0m                 raise ValueError('cannot call `vectorize` on size 0 inputs '\n",
      "\u001b[1;32mc:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m   2143\u001b[0m             \u001b[1;31m# Assumes that ufunc first evaluates the 0th elements in the input\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2144\u001b[0m             \u001b[1;31m# arrays (the input values are not checked to ensure this)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2145\u001b[1;33m             \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2146\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mbuiltins\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0many\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2147\u001b[0m                 raise ValueError('cannot call `vectorize` on size 0 inputs '\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "m = [1e-7,1e-8,1e-9,1e-10,1e-11,1e-12]\n",
    "# m = [1e-7,1e-8,1e-9,1e-10,1e-11,1e-12,1e-6,1e-5,1e-4]\n",
    "\n",
    "\n",
    "dgdt,t = dG_dt_HSC([-2,1],1e-7)\n",
    "dgdt1,t = dG_dt_HSC([-2,1],1e-8)\n",
    "dgdt2,t = dG_dt_HSC([-2,1],1e-9)\n",
    "dgdt3,t = dG_dt_HSC([-2,1],1e-10)\n",
    "dgdt4,t = dG_dt_HSC([-2,1],1e-11)\n",
    "dgdt5,t = dG_dt_HSC([-2,1],1e-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a67cda19",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=plt.axes()\n",
    "\n",
    "plt.ylim(1e-8,1e-2)\n",
    "plt.loglog(t,dgdt,linestyle='-',lw=3,color='black',label='$10^{-7}M_{\\odot}$')\n",
    "plt.loglog(t,dgdt1,linestyle='dotted',lw=3,color='black',label='$10^{-8}M_{\\odot}$')\n",
    "plt.loglog(t,dgdt2,linestyle='-.',lw=3,color='black',label='$10^{-9}M_{\\odot}$')\n",
    "plt.loglog(t,dgdt3,linestyle='dashed',lw=3,color='black',label='$10^{-10}M_{\\odot}$')\n",
    "# plt.loglog(t,dgdt4,linestyle='--',lw=3,color='black',label='$1M_{\\odot}$')\n",
    "# plt.loglog(t,dgdt5,linestyle='-',lw=3,color='black',label='$1M_{\\odot}$')\n",
    "plt.axvline(x=1/60*3,ymin=0,ymax=1,color='orange')\n",
    "plt.axvline(x=4,ymin=0,ymax=1,color='orange')\n",
    "plt.axvspan(1/60*3, 4, alpha=0.3, color='y')\n",
    "\n",
    "plt.ylabel(r'$\\frac{d\\Gamma}{d\\hat{t}}$(eventos/hora/hora)',fontsize=30)\n",
    "plt.xlabel(r'$\\hat{t}$ [horas]',fontsize=30)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')\n",
    "plt.legend(loc='best',fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "88f6a562",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fd98bc7490>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import InterpolatedUnivariateSpline\n",
    "import pandas as pd\n",
    "\n",
    "eficiencia_hsc= pd.read_csv(\"eficiency_HSC.txt\", decimal='.', sep=';')\n",
    "eficiencia_hsc = eficiencia_hsc.values\n",
    "t_efi = eficiencia_hsc[:,0]\n",
    "Efi = eficiencia_hsc[:,1]\n",
    "\n",
    "t_efi = list(t_efi)\n",
    "Efi = list(Efi)\n",
    "\n",
    "tck = InterpolatedUnivariateSpline(t_efi, Efi,k=1)\n",
    "\n",
    "x= np.linspace(0,200,500)\n",
    "\n",
    "def eficy(x):\n",
    "    \n",
    "    if x>6.85:\n",
    "        efichi = 0\n",
    "    elif x<0.032:\n",
    "        efichi = 0\n",
    "    else:\n",
    "        efichi = tck(x)\n",
    "    return efichi\n",
    "\n",
    "def funcion(t):\n",
    "    efic = []\n",
    "    for T in t:\n",
    "        efic.append(float(eficy(T)))\n",
    "    return efic\n",
    "\n",
    "eficiencia = []\n",
    "\n",
    "t=[-2,1]\n",
    "ti  = t[0]\n",
    "tf  = t[1]\n",
    "hat_t   = np.logspace(ti,tf,25)\n",
    "\n",
    "for t in hat_t:\n",
    "    eficiencia.append(eficy(t))\n",
    "\n",
    "plt.ylabel('Eficiencia')    \n",
    "plt.xlabel('$\\hat{t}(horas)$')\n",
    "plt.semilogx(hat_t, eficiencia,'green')\n",
    "plt.semilogx(eficiencia_hsc[:,0],eficiencia_hsc[:,1],'o')"
   ]
  },
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      "c:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py:879: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n"
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    {
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    {
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   ],
   "source": [
    "from scipy.integrate import simps\n",
    "E=7e+4\n",
    "# M =  [1e-2,1e-3,1e-4,1e-5,1e-6,1e-7,1e-8,1e-9,1e-10,1e-11,1e-12,1e-13,1e-14]\n",
    "M = np.logspace(-14,-2,50)\n",
    "N = []\n",
    "\n",
    "for i in tqdm(range(len(M))):\n",
    "    G,tE = dG_dt_HSC([-2,1],M[i])\n",
    "    int_G = simps(G*0.5*eficiencia,tE)\n",
    "    N.append(int_G)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "fc1df294",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.59257853e+00 2.79735587e+00 4.91156375e+00 8.61725514e+00\n",
      " 1.50993542e+01 2.63978387e+01 4.59716148e+01 7.95285839e+01\n",
      " 1.36058817e+02 2.28628349e+02 3.73804291e+02 5.88220504e+02\n",
      " 8.82348810e+02 1.25369195e+03 1.67984870e+03 2.11270186e+03\n",
      " 2.47818693e+03 2.68995504e+03 2.68811827e+03 2.47778914e+03\n",
      " 2.12720810e+03 1.73385389e+03 1.37025289e+03 1.06248708e+03\n",
      " 8.15515022e+02 6.20248990e+02 4.67190754e+02 3.46810471e+02\n",
      " 2.52605115e+02 1.78883284e+02 1.21944888e+02 7.87797467e+01\n",
      " 4.74661087e+01 2.60827753e+01 1.28390700e+01 5.67642221e+00\n",
      " 2.34031098e+00 9.68907962e-01 4.09203096e-01 1.72525665e-01\n",
      " 7.27837851e-02 3.08485995e-02 1.30948306e-02 5.45474171e-03\n",
      " 2.13893872e-03 7.26344089e-04 1.80752713e-04 3.33098855e-05\n",
      " 8.23880233e-06 2.28189911e-06]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.loglog(M,np.array(N)*7*8.7e+7,'-.')\n",
    "\n",
    "#redefino un vector que reemplace los valores menores a uno en el numero esperado de eventos por 1\n",
    "N2 = []\n",
    "for i in range(len(N)):\n",
    "    n = N[i]*7*8.7e+7\n",
    "    if n<1:\n",
    "        n=1\n",
    "    N2.append(n) \n",
    "print(np.array(N)*7*8.7e+7)\n",
    "    \n",
    "plt.figure(figsize=(8,6))\n",
    "ax=plt.axes()\n",
    "\n",
    "plt.semilogx(M,np.array(N2), linestyle='-', lw=3, color='black')\n",
    "\n",
    "plt.xlabel(r'$M [M_{\\odot}]$',fontsize=30)\n",
    "plt.ylabel(r'N expected (HSC)',fontsize=30)\n",
    "# plt.legend(loc='best',fontsize=20)\n",
    "\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "57bac3ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=plt.axes()\n",
    "\n",
    "plt.ylim(1e-4,1)\n",
    "plt.xlim(1e-15,1e-3)\n",
    "plt.loglog(M,4.74/(7*8.7e+7*np.array(N)),lw=3,color='red',linestyle='-')\n",
    "b = np.loadtxt('Microlensing-copy1.txt')\n",
    "\n",
    "plt.loglog(b[:,0],b[:,1],color='black',alpha=0.1,linestyle='-',lw=3)\n",
    "plt.fill_between(b[:,0],b[:,1],1,color='black', alpha=0.1,label='Old Constraints')\n",
    "\n",
    "plt.fill_between(M,4.74/(7*8.7e+7*np.array(N)),1, color='red',alpha=0.1)\n",
    "\n",
    "plt.xlabel(r'$M [M_{\\odot}]$',fontsize=30)\n",
    "plt.ylabel(r'$f_{DM}$',fontsize=30)\n",
    "plt.legend(loc='best',fontsize=20)\n",
    "\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')\n",
    "\n",
    "np.savetxt('N_m31.txt', N2)\n",
    "np.savetxt('constraints_m31.txt', 4.74/(7*8.7e+7*np.array(N)))\n",
    "\n",
    "# M = np.logspace(-14,-2,50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "63f5f43f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$t_E$')"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "eff = np.array([1117., 1822., 2547., 3357., 5042., 7388., 9667., 9714., 9459.])\n",
    "te = np.array([1,5,10,20,30,60,90,200,500])\n",
    "\n",
    "from scipy.interpolate import InterpolatedUnivariateSpline\n",
    "tck = InterpolatedUnivariateSpline(te, eff,w=None,k=1)\n",
    "x= np.linspace(0,500,1000)\n",
    "\n",
    "def eff_lsst_01(x):\n",
    "    efichi = tck(x)\n",
    "    return efichi\n",
    "\n",
    "def eff_lsst(t):\n",
    "    efic = []\n",
    "    for T in t:\n",
    "        efic.append(float(eff_lsst_01(T/24))/10000)\n",
    "    return efic\n",
    "\n",
    "plt.plot(x,eff_lsst(x),label='LSST (baseline)')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Eficiencia')    \n",
    "plt.xlabel('$t_E$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "87c09976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4de5e1eb7d6b47059567dba597abf6d2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c9422faf3b1945b68524dd52185512c3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/25 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "09578b5f36124cffb6c1c0cbcd9d737d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/25 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2a1f8acad2d347caba47ec3f93c6056c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "686ab62e596e43ddb1cb07ccb408bde0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e4ac51cff0074041bea808fbfa100ade",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c4aa9ae02be0454a98ca31810e0fff88",
       "version_major": 2,
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      "c:\\users\\aniba\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\scipy\\integrate\\quadpack.py:879: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n"
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   ],
   "source": [
    "from scipy.integrate import simps\n",
    "E=7e+4\n",
    "M2 = np.logspace(-16,-2,50)\n",
    "N_lsst = []\n",
    "N_lsst2 = []\n",
    "\n",
    "for i in tqdm(range(len(M))):\n",
    "    G,tE  = dG_dt_HSC([-2,1],M2[i])\n",
    "#     int_G = simps(G*0.5, t)\n",
    "#     N_lsst.append(int_G)\n",
    "    for j in range(len(tE)):\n",
    "        if tE[j]>4:\n",
    "            G[j] = 0\n",
    "        elif tE[j]<0.016:\n",
    "            G[j] = 0\n",
    "    int_G = simps(E*G*0.5,tE)\n",
    "    N_lsst2.append(int_G)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "13b1f430",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=plt.axes()\n",
    "\n",
    "plt.semilogx(M2,np.array(N_lsst2)*7*8.7e+7/E, linestyle='-', lw=3, color='black')\n",
    "\n",
    "plt.xlabel(r'$M [M_{\\odot}]$',fontsize=30)\n",
    "plt.ylabel(r'N expected (M31-LSST)',fontsize=30)\n",
    "\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "f303354c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M31 = np.loadtxt('constraints_m31.txt')\n",
    "\n",
    "M = np.logspace(-14,-2,50)\n",
    "M2 = np.logspace(-16,-2,50)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "ax=plt.axes()\n",
    "\n",
    "plt.ylim(1e-5,1)\n",
    "plt.xlim(1e-15,1e1)\n",
    "#------------------------old constraints------------------------------\n",
    "b = np.loadtxt('Microlensing-copy1.txt')\n",
    "plt.loglog(b[:,0],b[:,1],color='black',alpha=0.1,linestyle='-',lw=3)\n",
    "plt.fill_between(b[:,0],b[:,1],1,color='black', alpha=0.1)\n",
    "#---------------------------------------------------------------------\n",
    "plt.loglog(M2,4.74/(np.array(N_lsst2)*7*8.7e+7/E),lw=3,color='red',linestyle='-')\n",
    "plt.fill_between(M2,4.74/(np.array(N_lsst2)*7*8.7e+7/E),1, color='red',alpha=0.1)\n",
    "\n",
    "plt.loglog(M,4.74/(7*8.7e+7*np.array(N)),lw=3,color='blue',linestyle='-')\n",
    "plt.fill_between(M,4.74/(7*8.7e+7*np.array(N)),1, color='blue',alpha=0.1)\n",
    "\n",
    "plt.text(1e-11, 3e-1, 'HSC', fontsize=20)\n",
    "plt.text(1e-13, 1e-4, 'LSST', fontsize=20)\n",
    "#--------------------------------------------------------------------\n",
    "plt.xlabel(r'$M [M_{\\odot}]$',fontsize=30)\n",
    "plt.ylabel(r'$f_{DM}$',fontsize=30)\n",
    "# plt.legend(loc='best',fontsize=20)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.tick_params(which='both', width=2)\n",
    "ax.tick_params(which='major', length=9)\n",
    "ax.tick_params(which='minor', length=5, color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "8454527a",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'N2_lsst' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-46-93184ccc051f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msavetxt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'N_m31_lsst.txt'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mN2_lsst\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msavetxt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'constraints_m31_lsst.txt'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4.74\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mN2_lsst\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'N2_lsst' is not defined"
     ]
    }
   ],
   "source": [
    "np.savetxt('N_m31_lsst.txt', N2_lsst)\n",
    "np.savetxt('constraints_m31_lsst.txt', 4.74/(np.array(N2_lsst)))\n"
   ]
  }
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