hamogu intial commit of code for figures  about 10 years ago

Commit id: 8892c853c829085668251671371bcabd87833f31

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{  "metadata": {  "name": "jet_recol_shocks"  },  "nbformat": 3,  "nbformat_minor": 0,  "worksheets": [  {  "cells": [  {  "cell_type": "code",  "collapsed": false,  "input": [  "import numpy as np\n",  "from scipy.integrate import odeint\n",  "from matplotlib import pyplot as plt"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 4  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "class ODEnotsolvedException(Exception):\n",  " '''Exception to indicate that the ODE needs to be solved before properties of the solution are available'''\n",  " pass\n",  "\n",  "\n",  "class StellarWindShock(object):\n",  " '''This class describes a shock front formed due to confinement by an external presure.\n",  "\n",  " An object of this class describes one specific combination of stellar wind parameters\n",  " and external presure profile. This class provides methods to solve the ordinary\n",  " differential equation that governs the shape of the shock front, which forms due to\n",  " the external presure from the expanding disk wind.\n",  "\n",  " ..note::\n",  " This class accepts all lengths scales input in units of AU and all other parameters\n",  " (velocity, mass flux, presure) in cgs units.\n",  " The possibility for user error would be greatly decreased by using a module that \n",  " tracks the units (e.g. ``astropy.units``) but the scipy ODE solver does not work well\n",  " with any such scheme. Thus, BEWARE of the UNITS!\n",  " '''\n",  " def __init__(self, p_ext, v_inf, m_dot):\n",  " '''\n",  " Parameters\n",  " ----------\n",  " p_ext: function or callable object\n",  " ``p_ext`` must accept a height (in AU) and return a presure (in cgs units)\n",  " v_inf: float\n",  " wind speed (in cgs units)\n",  " It is assumed that the stellar wind reaches its final wind speed before any\n",  " interaction with the disk wind occurs.\n",  " m_dot: float\n",  " Spherically integrated stellar mass loss rate (in cgs units)\n",  " '''\n",  " self.p_ext = p_ext\n",  " self.v_inf = v_inf\n",  " self.m_dot = m_dot\n",  " \n",  "\n",  " def R0(self, z):\n",  " '''Eqn 14'''\n",  " const = self.m_dot * self.v_inf / (4.*np.pi* self.p_ext(z))\n",  " # const from cgs in AU \n",  " return np.sqrt(const)/(1.5e13)\n",  " \n",  " def __call__(self, omega, z):\n",  " r = np.sqrt(omega**2+z**2)\n",  " R0 = self.R0(z)\n",  " r = np.clip(r, 0, R0)\n",  " return np.tan(np.arctan2(omega, z) - np.arcsin(r/R0))\n",  " \n",  "\n",  " def start(self):\n",  " '''gives equilibrium solution at z=0\n",  "\t \n",  " Returns\n",  "\t -------\n",  " d : float\n",  " omega (in AU) for equilibrium solution at z=0\n",  " '''\n",  " return self.R0(0.)\n",  "\n",  " \n",  " def solve(self, omega0, z):\n",  " '''solve ODE starting at omega=omega0 for z = z[0]\n",  "\n",  " Parameters\n",  " ----------\n",  " omega0: float\n",  " distance from star (in AU) along the radial direction of the\n",  " cylindrical coordinate system where to start the integration\n",  " z: np.array\n",  " grid in z direction (in AU)\n",  " '''\n",  " if omega0 > self.start():\n",  " raise ValueError('omega0 {0:5.2f} is outside the range that the stellar wind can physically reach {1:5.2f}'.format(omega0, self.start()))\n",  " self.z = z\n",  " self.omega0 = omega0\n",  " res, info = odeint(self, omega0, z, full_output = True)\n",  " self.res = res.flatten()\n",  " self.odeinfo = info\n",  "\n",  " # This is to cut solution after shock merged z-axis\n",  " if np.any(self.res < 0.001):\n",  " ngood = np.min(np.where(self.res<0.001)[0])\n",  " self.res = self.res[0:ngood]\n",  " self.z = self.z[0:ngood]\n",  " \n",  " @property\n",  " def v_shock(self):\n",  " '''pre-shock wind velocity component perpendicular to shock front'''\n",  " try:\n",  " v_shock = self.v_inf * np.sin(np.arctan2(self.res, self.z) - np.arctan(self(self.res, self.z)))\n",  " except AttributeError:\n",  " raise ODEnotsolvedException(\"ODE needs to be solved first\")\n",  " return v_shock\n",  " \n",  " @property\n",  " def T_postshock(self):\n",  " '''Post-shock temperature in K'''\n",  " return 3/20.*1.4*1.67e-24/1.38e-16*self.v_shock**2\n",  "\n",  " def plot(self):\n",  " f = plt.figure(figsize=(10,3))\n",  " ax1 = f.add_subplot(131)\n",  " ax2 = f.add_subplot(132, sharey = ax1)\n",  " ax3 = f.add_subplot(133, sharey = ax1)\n",  " fig.subplots_adjust(hspace=0, wspace=0)\n",  " \n",  " ax3.plot(self.v_shock/1e5, self.z, label = '$v_{shock}$')\n",  " ax3.set_xlim([0, None])\n",  " ax2.plot(self.res, self.z)\n",  " ax2.plot(np.sqrt(self.R0(self.z)**2 - self.z**2), self.z)\n",  " ax3.set_xlabel('velocity (km/s)')\n",  " ax2.set_xlabel('$\\omega$ (AU)')\n",  " ax2.set_title('Shock location')\n",  " ax3.set_title('Shock velocity')\n",  " ax3.annotate('Mass loss : '+str(self.m_dot/2e33*3.16e7)+' $M_\\odot$/yr',xy=(10,3))\n",  " ax3.annotate('v_inf: '+str(self.v_inf/1e5)+' km/s',xy=(10,5))\n",  " \n",  " ax1.plot(self.p_ext(z),z)\n",  " ax1.set_title('External presure')\n",  " ax1.set_ylabel('Height (AU)')\n",  " ax1.set_xlabel('presure [ba]')\n",  " #ax2.set_xlim([0, self.start()])"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 56  },  {  "cell_type": "heading",  "level": 3,  "metadata": {},  "source": [  "Test the code"  ]  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "In order to check that the equations that are developed in the paper are correctly implemented, we solve them here for a simple test problem."  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "class ConstantPres(object):\n",  " '''A constant pressure'''\n",  " def __init__(self, p_const):\n",  " '''\n",  " Parameters\n",  " ---------- \n",  " p_inf : float\n",  " presure\n",  " '''\n",  " self.p_const = p_const\n",  " \n",  " def __call__(self, z):\n",  " '''\n",  " Parameters\n",  " ----------\n",  " z : array-like\n",  " same dimension as z_1\n",  " '''\n",  " return self.p_const + np.zeros_like(z)"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 57  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "#ode = StellarWindShock(lambda z: 1e-7*(20-z+1), 5e7, 12e14)\n",  "ode = StellarWindShock(ConstantPres(1e-6), 1e7, 12e14)\n",  "z = np.arange(0, ode.start(), .01)\n",  "ode.solve(ode.start(), z)\n",  "ode.plot()\n",  "fig = plt.gcf()\n",  "fig.axes[2].set_xlim([0,110])\n",  "fig.axes[0].set_xlim([-1,1])"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "output_type": "pyout",  "prompt_number": 58,  "text": [  "(-1, 1)"  ]  },  {  "output_type": "display_data",  "png": 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JHanC4JggQ2NwBWPXrl2RkpKC48ePIzw8HD169IBCod2Tvu/du6fabRsXFwch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\nfUOONFMoAC7GspNDf5RDBpK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}  ],  "prompt_number": 58  },  {  "cell_type": "heading",  "level": 3,  "metadata": {},  "source": [  "Evaluating the position and properties of the shock front"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "class PowerPres(object):\n",  " '''A powerlaw pressure function'''\n",  " def __init__(self, p_inf, p_1, eta, z_1):\n",  " '''\n",  " Parameters\n",  " ---------- \n",  " p_inf : float\n",  " presure at infinity\n",  " p_1 : float\n",  " presure at z_1\n",  " eta : float\n",  " exponent of power law\n",  " z_1 : float\n",  " normalisation of z (in our case in AU)\n",  " '''\n",  " self.p_inf = p_inf\n",  " self.p_1 = p_1\n",  " self.eta = eta\n",  " self.z_1 = z_1\n",  " \n",  " def __call__(self, z):\n",  " '''\n",  " Parameters\n",  " ----------\n",  " z : array-like\n",  " same dimension as z_1\n",  " '''\n",  " return self.p_inf + self.p_1 * ((self.z_1 + z)/self.z_1)**(-self.eta)\n",  "\n",  "class ExpPres(object):\n",  " '''an explonential pressure function'''\n",  " def __init__(self, p_0, h, p_inf = 0.):\n",  " '''\n",  " Parameters\n",  " ---------- \n",  " p_0 : float\n",  " pressure at x=0\n",  " h : float\n",  " scaleheight of exponential (in our case in AU)\n",  " p_inf : float, optional\n",  " pressure at infinity (additive to powerlaw)\n",  " '''\n",  " self.p_0 = p_0\n",  " self.h = h\n",  " self.p_inf = p_inf\n",  " \n",  " def __call__(self, z):\n",  " '''\n",  " Parameters\n",  " ----------\n",  " z : array-like\n",  " same dimension as z_1\n",  " '''\n",  " return self.p_inf + self.p_0 * np.exp(-z/self.h)\n",  " "  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 59  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "z = np.arange(0,15., .01)"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 60  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "pexp = ExpPres(1e-7, 10., p_inf = 1e-7)\n",  "\n",  "ode = StellarWindShock(ConstantPres(1e-7), 5e7, 12e14)\n",  "ode.solve(4, z)\n",  "ode.plot()\n",  "fig = plt.gcf()\n",  "ax = fig.axes[1]\n",  "ax.set_xlim([0,15])"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "output_type": "stream",  "stream": "stdout",  "text": [  "Excess work done on this call (perhaps wrong Dfun type).\n",  "Run with full_output = 1 to get quantitative information.\n"  ]  },  {  "output_type": "pyout",  "prompt_number": 61,  "text": [  "(0, 15)"  ]  },  {  "output_type": "display_data",  "png": 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zfPlyzp8/T0xMDMuWLcPf359OnTqxfbtMfCiEyD8+/BB27YIdO3LfRjH7Yqzu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\nnDhx4rnrZIxp6nnsE0olcOUKcPJk+62mBoiKAo4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88w6lpqYSUfsvKnTk3dTUROPGjdNv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\nY32IB2OMMcYYY33o/wBaZZWtDpT+UQAAAABJRU5ErkJggg==\n"  }  ],  "prompt_number": 61  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "grid = np.mgrid[0:15:0.1,0:12:.1]\n",  "plt.contourf(grid[0,:,:], grid[1,:,:], ode(grid[0,:,:], grid[1,:,:]),[-1e3,-1,0,1,10,1e3], colors=['b','g','y','orange','r'])\n",  "plt.colorbar()\n",  "#plt.plot(ode.sphereofwind(grid[1,0,:]), grid[1,0,:],'k')"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "output_type": "pyout",  "prompt_number": 62,  "text": [  ""  ]  },  {  "output_type": "display_data",  "png": 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}  ],  "prompt_number": 62  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "pext = PowerPres(1e-7, 1e-6, 3, 5.)\n",  "ode = StellarWindShock(pext, 5e7, 12e14)\n",  "\n",  "ode.solve(1, z)\n",  "ode.plot()"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "output_type": "stream",  "stream": "stdout",  "text": [  "Excess work done on this call (perhaps wrong Dfun type).\n",  "Run with full_output = 1 to get quantitative information.\n"  ]  },  {  "output_type": "display_data",  "png": 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du4Zdu3ahR48ecktmZapVC3j+XOgoCFFdEglfvf/OHSAsDGjRAnj4UOioSEGq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\nlwexWMzpE4lEkMlknI2FhYWQyWSc7Up7CwsLuTwVFRXB2to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AREREIDs7G8bGxmrtfOut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\nze8AAAAASUVORK5CYII=\n"  }  ],  "prompt_number": 63  },  {  "cell_type": "heading",  "level": 4,  "metadata": {},  "source": [  "Same external presure, different starting points of integration"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "pexp = ExpPres(1e-6, 2., p_inf = 1e-8)\n",  "z = np.arange(0,40., .01)\n",  "\n",  "f = plt.figure(figsize=(10,5))\n",  "ax1 = f.add_subplot(131)\n",  "ax2 = f.add_subplot(132, sharey = ax1)\n",  "ax3 = f.add_subplot(133, sharey = ax1)\n",  " \n",  "\n",  "for omega0 in [0.01, 0.1,1, 3]:\n",  " ode = StellarWindShock(pexp, 5e7, 12e14)\n",  " ode.solve(omega0, z)\n",  "\n",  " ax1.plot(ode.v_shock/1e5, ode.z, label = omega0)\n",  " ax2.plot(ode.res, ode.z)\n",  " ax3.plot(ode.p_ext(z), z)\n",  " \n",  "ax1.set_xlabel('velocity (km/s)')\n",  "ax2.set_xlabel('$\\omega$ (AU)')\n",  "ax1.set_ylabel('Height (AU)') \n",  "ax1.set_title('Shock velocity')\n",  "ax2.set_title('Shock location')\n",  "ax3.set_title('External presure')\n",  "ax3.set_xlabel('presure [ba]')\n",  " "  ],  "language": "python",  "metadata": {},  "outputs": [  {  "output_type": "stream",  "stream": "stdout",  "text": [  "Excess work done on this call (perhaps wrong Dfun type).\n",  "Run with full_output = 1 to get quantitative information.\n",  "Excess work done on this call (perhaps wrong Dfun type)."  ]  },  {  "output_type": "stream",  "stream": "stdout",  "text": [  "\n",  "Run with full_output = 1 to get quantitative information.\n",  "Excess work done on this call (perhaps wrong Dfun type)."  ]  },  {  "output_type": "stream",  "stream": "stdout",  "text": [  "\n",  "Run with full_output = 1 to get quantitative information.\n"  ]  },  {  "output_type": "pyout",  "prompt_number": 64,  "text": [  ""  ]  },  {  "output_type": "display_data",  "png": 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7l77nzpGSnc284GCecnbWOlKhYy59osPo0eQAG/72B48QWjCXusVol19v3LiR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\nwFRvbx73beC4vlbAHO3xcv2hMTGs+HoDT9rp+MjWhTG3xBk5SklSqOU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9lesiurHyzk/o\n3L6eJWuysuChhyA5GVasgF69jFL/xn/Gzz3v78/jvr5yhqsRqaE9qiEGU9Bqa/hg5TdsTUnkTGdX\nTgSF4J6fT0D6GYL0toy85jpuubEf1jbqWSFAUk97lEldG5OcDNOmV3DU6yVE9zV8deeXXN/1+oad\nvGmTspr/vn3QxfyLbBbpdIw5fBg3W1uzrvyvhvaohhgaqrIS5rxRzKIDs2h31Ro+uv1dxna/4+Kk\nSqtVvl3MmwfTpyvj6Iwwo7pSr+e5pCS+y8tjZUQEAyx02741U0N7VEMM5lBWXsmnX//AjuRE0pwd\nOB4Ugq1OR0jyaXzKtcR0CWTiqFvw8VbfGp9tiVrao0zq2oicHJj7uo6le1ZgPWgWt0Rez/u3vHfp\n1fsvtG6dcjXlm29gQD23z8zEEpuuq6E9qiGGKxECVn6pY8aKj6noM4fbIoez+NY3L25jQsCvv8Lj\nj0NAACxapCxqbQT7SkuZmJhItJMTS0JDVbtLSUunhvaohhgsQa/T89WGLfy6fzfpNgbSvb1I7eJH\n18x0fLKz8NVa0S+0O3ffdjNOjnL8qLmopT3KpK6V27sX3l5cyHdnPsGm//v09AvinWHzGjZ+DiA/\nX7nl+uuv8NVX0NvyC2lWGQyMPHSIKEdHFoSYft0nNbRHNcRwKULA5i0G/u+97zgT/B/C/d35dNw7\n9PKu5zbq1q3KFbnsbHjrLRg50ihrz1UbDMw7c4bFGRksDAlhgqdns8uULk0N7VENMahFRlYeK9dv\nZH9mEpntbTnj40dOp84En0nGKzcPT50VPX0CGXfLYPx95FI+pqCW9iiTulYoORlWrq7m020byXb/\nEhH0CyO7jeTZGx6jd5cGJmVFRfDRR8oOEmPHwty5oKLbWIU1NfTdt495QUGMMcIMyctRQ3tUQwwX\nEgI2bNTz5NKvSPWfSxcPexaOnsWosBF1b7UKoSRzc+fCqVPKIsJ3322UnSEA4ouKeOjECSLat+fd\nkBD87OtZJkUyKjW0RzXEoGaHjiXx9S+/caIgixx7G7I8PUnt4otnfi4+WZl4lFYS2N6NQX36MuT6\nvnKMXjOppT3KpK4V0Gphxw5Y+0smPxz9hSynn9EEbyLcrScPXTuBsZFjGnabVQjYswc++wxWroRb\nblFmIUZGmv6PaIJtRUWMT0zkZN++OJhwWzE1tEc1xHBOeTl89EU+b21aRn7gBwS4e7HgtpcZFjq0\nbjKn1cLXXyuLB5eXKzNbp0wx2k4kWdXVvJiczObCQt4NDeU2Fe4b3FqpoT2qIYaWprikjK82bObv\nU4lkGKrI6ejKGR8/qm3t8M9Kp3N+Pp2r9Pg7utEvqicjB10r189rILW0R5nUtUAlJbB7t2DjjlQ2\nn/iLo6V/YRO8FdEhnX6eg5nQ52ZuCRt66a2XzqfTwd9/w08/werVyu8mTIAHHgAfH9P+IUYw9MAB\npnh5mfR2mxrao6VjEAIOHDQw97O/WJ++FNHtO673GskrIx+mn19s3WTuxAlYtkz5chAeDk8+CcOG\ngZEmtpTp9bydlsZ76elM9fbm5a5d5VIlZmbp9qiWGFqLnXuPsGnHTk7mZZJjbSDf1YUMry4UdXDG\nPzsDj9xcOpVX0cXWkZigbowcOAAvj46WDltV1NIeZVKncnl5yofpHwdS2HH6EIdyDpJnsx+rrjuw\nsxP0cL2WYVH9GRLRn95demNjdYUPN51OWWtixw7YvFnZI8zPT9kdYuxYZcxcC1r64Z20NFKqqng3\nNNRkdaihPVoqhtOnBQu+PMjqI6so8l1NR8cOTOszmSfi7q27vVduLnz/vbIkycmTyrZe995r1Ku8\n1QYDy7KzeTUlhThXV+YGBREgb7VaRFvuE23JyeR0ftiyjaPpKWRTTb6zI9keXmS6e9K5uBDPnLN0\nLC7GrVpPF3tnoroGM/SGfm1y3J5a2mObSOri4+OJi4szWnnGLlOng6++isfJLZZdJ05zKOMUx3NP\nkVZxAq3rYfA4jL3GhQCHnvT27cnAqJ4MCOxHV5eul117K37TJuI8PZVN0ffvh127lJkTvr4QGws3\n3aRs+eXtbfa/2VhlvpaaSn5NDfP/mTBhihjV0FmNFcOVnh+dDuK3V/LRr3+wJW0Dhe4/4eik59bg\n8Tw9dALRXj3+LSc4WEnk1q1TlrkZOlQZK3fLLdDAWacNeb0q9Ho+zsrirbQ0oh0dmR0QQJ96tvky\n1mvfWssxZlmtqU80hCneV9RQV1PrKyuvZNO23fx95AhnSvPJtzJQ5OxIbid3Mjy8cC0rxTMnm45F\nRbhV6fCydSTY2xd7fTUP3jfJLOP3zP08qqFPAFjknsXPP//M448/jl6vZ9q0aTz33HMmrc/SyUh5\nOaSlCY6nlnAkLZ2T2emkFKSTXpJOTnUapban4fg+NIOqcdYH4u0cQkRgCJOCYhgQNpGenj1wc3Cr\nv3CDATIzldkRyclw+jQcPQqHDxN/6hRxoaHK1ZKePeHFF5Utvpo44cHSz+OFKvR6lmVn89F5y2GY\nuyMbi7n6xIXPj1YLf+4uZ/X2XfyRvJ3TNdsxdNmJr10M44bdwv1x3xLj3UP58lBcrCRxv/1G/OrV\nxBkMMGIEPPGE8uWgCdtvXe71ytZq+Sgzkw8yM7nG2Znvo6K4ukOHJpVlrJhacjnGLsvUzP05cTky\nqavLydGB0TffwOibb7joscrKarb8tZdd6QWkVEO+FSS0F2zRlJPy+2ae8ffEOzeHToX5uJSU4VJj\noLNte4I9fYiN7kH/qyKNkvS1pLZuTGZP6vR6PY888gi//fYbPj4+9OnTh1GjRhEREWHuUJrMYFAW\nWD123EBSZiFJZ3M5k5dLRlEuZ8tyyavIpVCbS3FNLuXkoG+fAS7pWGnAyeCHm7UvXh6+XB3mS4RP\nH/qG3sUvy35k/qz5WFud15j1emWBuaNJyqr7534yMyElRUniUlPBzQ0CA5WfoCC4/Xb4z3+UJUhe\nfdViz5Mp5dfUMPbIEa53ceFGt0skvC2EufpERQUkp1Xz7Pvb2JV6gONFB8m1TgD3RDxFNH16XMcL\nvR9lVPQa3Gw7KLfpf9wJu9+F3bshKUnZ73fQIKWNffCB0cbJnSOEYEdJCYszMvipoIA7PTzYFB1N\nlJm2pJPUoTV8TrRVDg7tGD6wP8MHXrw3+Owz6dwVEsm2Ai2JlUWcrYFCaw1ZDvCHVQXzspIo35z1\nT9KXh0tpGS7Vetys2tHFtRPd/Ltybe9oAv28LPCXtQxmT+p2795NSEgIAQEBANx11118//33Ju2s\nBoNykaG0XEdBaQVF5ZUUl1dSXFFJcXkFJZWVlFRWUlRWSVFFOUWVxRRXFVOqLaFMV0yFoZgqUYJW\nU0yNdTF6m2LYk82b9nOx1jthr3fHUeOOi40HnZzd8fdyJ9YlkACPvnTr0pmIju74WbvSoUYDpaXK\nciEFBcrPsQL4awu7ftuOddJ45Xf5+co6Xnl50LGjcnv0/J+oKGV9r8BAZfHW9u3r/8PXrTPZc2op\nFXo9K7KzmZOayiRPT+YFBVk6pGYzRp/Q6yEnT8fJjHxOZeZw+mwOJ7IyOV2QRFZlEoUkUe2YhOZU\nLp08fifULZq7evTk1oDh9LPthH1KGiQmwvzPIPEF5YpvUJByZbdvX2XHhx49/p25Onu2URO6pMpK\nVp49yxdnzyKAh318WNytG65yAkSbZInPCck8wkP8CQ/xv+TjSSmZxBfu5WhlIdlaKLSCk/aCvXZa\nCqryyDl6gHb7/8ajIA/X4iI6lJXTQavDFVs8nVwI8fHjml49EAbL3wq1CGFmX3/9tZg2bVrt/3/+\n+efikUceqXMMIH/kj6p+ZJ+QP/Kn7o/sE/JH/tT9UQOzfw1uyKbaQgWDDSXJXGSfkKS6ZJ+QpKYx\nz47o5/Hx8SEtLa32/9PS0vD19TV3GJKkGrJPSFJdsk9IUtOYPanr3bs3J0+eJCUlBa1Wy5o1axg1\napS5w5Ak1ZB9QpLqkn1CkprG7LdfbWxseP/99xk6dCh6vZ6pU6fKwa9Smyb7hCTVJfuEJDWRhcf0\nXWTjxo0iLCxMhISEiHnz5jWpjK5du4oePXqImJgY0adPHyGEEPn5+WLQoEEiNDRUDB48WBQWFl62\njHvvvVd4eHiIqKio2t9drozXXntNhISEiLCwMPHLL780qLxZs2YJHx8fERMTI2JiYsRPP/3U4PKE\nEOLMmTMiLi5OdO/eXURGRopFixY1K85LldecOCsrK0Xfvn1FdHS0iIiIEM8//3yzYrxUec19LnU6\nnYiJiREjRoxoVnymYIw+UV/7a4pLtZGmuNRr2RQXvn5NVd97R1MUFhaKMWPGiPDwcBERESF27NjR\npHKOHTtW26ZjYmKEs7Nzk5/z1157TXTv3l1ERUWJ8ePHi6qqqiaVs3DhQhEVFSUiIyPFwoUL6z2m\nIW320UcfFSEhIaJnz55i3759Vzz3Un1y48aNonPnzsLW1lZ07ty5Tp/cs2ePiIqKEi4uLsLFxaW2\nrqqqKjFu3Djh7e0t7O3tRUBAQG1dy5cvF0FBQcLBwUF4enqarK6EhATRr18/ERYWJpycnIS3t/dF\n7zX33HOPsLW1Fba2tmLq1KkX1RUSEiKio6Nrn8edO3eKcePG1b4/BQcH13kei4uLhbe3t/Dz8zP5\n85iamiri4uKEo6OjsLOzEwMGDDBJXQaDQTz66KMiLCxMODo6CldX12Y/j5988ono1auXsLGxETNn\nzqzTHpcvXy5CQ0NFUFCQiIyMbNRnxPn1zZgxo/b3f/zxR219a9eurf39uTYSGRkpevbsKdasWSOu\nRFVJnU6nE8HBwSI5OVlotVoRHR0tjh492uhyAgICRH5+fp3fPfPMM+KNN94QQggxb95zFT0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dnZ2TGBQMDl4+nTp5lUKuWG0+Dz+S3yMTo6mtna2vZ6Ph4+fJg5OjoyY2NjZmpqyvz9/XstrmXL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\n0gf8B26PJoV0i5NVAAAAAElFTkSuQmCC\n"  }  ],  "prompt_number": 64  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "The starting point of the integration really makes a difference. If the radius of the stellar wind zone of influence is larger initially, the shock will encompass a much bigger volume, reach to larger heights and, at least for this presure profile, reach much larger velocities and thus X-ray temperatures."  ]  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "to do\n",  "implent test cases to test implementations constantp and circle, calcualte radius of circle by hand and hardcode here. as regression test and azamepl"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [],  "language": "python",  "metadata": {},  "outputs": []  }  ],  "metadata": {}  }  ]  }