{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bbbaafbb-fd7d-4b73-a970-93506ba35d71",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Example use case: Common-envelope evolution\n",
    "\n",
    "In this notebook we look at how common-envelope evolution (CEE) alters binary-star orbits. We construct a population of low- and intermediate-mass binaries and compare their orbital periods before and after CEE. Not all stars evolve into this phase, so we have to run a whole population to find those that do. We then have to construct the pre- and post-CEE distributions and plot them.\n",
    "\n",
    "First, we import a few required Python modules. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bf6b8673-a2b5-4b50-ad1b-e90671f57470",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from binarycpython.utils.functions import temp_dir\n",
    "from binarycpython.utils.grid import Population\n",
    "TMP_DIR = temp_dir(\"notebooks\", \"notebook_comenv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f268eff3-4e08-4f6b-8b59-f22dba4d2074",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Setting up the Population object\n",
    "We set up a new population object. Our stars evolve to $13.7\\text{ }\\mathrm{Gyr}$, the age of the Universe, and we assume the metallicity $Z=0.02$. We also set the common-envelope ejection efficiency $\\alpha_\\mathrm{CE}=1$ and the envelope structure parameter $\\lambda=0.5$. More complex options are available in *binary_c*, such as $\\lambda$ based on stellar mass, but this is just a demonstration example so let's keep things simple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "79ab50b7-591f-4883-af09-116d1835a751",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adding: log_dt=10 to grid_options\n",
      "adding: max_evolution_time=13700 to BSE_options\n",
      "adding: metallicity=0.02 to BSE_options\n",
      "adding: alpha_ce=1.0 to BSE_options\n",
      "adding: lambda_ce=0.5 to BSE_options\n"
     ]
    }
   ],
   "source": [
    "# Create population object\n",
    "population = Population()\n",
    "population.set(\n",
    "    # grid options\n",
    "    tmp_dir = TMP_DIR,\n",
    "    verbosity = 1,\n",
    "    log_dt = 10, # log every 10 seconds\n",
    "\n",
    "    # binary-star evolution options\n",
    "    max_evolution_time=13700,  # maximum stellar evolution time in Myr (13700 Myr == 13.7 Gyr)\n",
    "    metallicity=0.02, # 0.02 is approximately Solar metallicity \n",
    "    alpha_ce = 1.0,\n",
    "    lambda_ce = 0.5,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9a65554-36ab-4a04-96ca-9f1422c307fd",
   "metadata": {},
   "source": [
    "## Stellar Grid\n",
    "We now construct a grid of stars, varying the mass from $1$ to $6\\text{ }\\mathrm{M}_\\odot$. We avoid massive stars for now, and focus on the (more common) low- and intermediate-mass stars. We also limit the period range to $10^4\\text{ }\\mathrm{d}$ because systems with longer orbital periods will probably not undergo Roche-lobe overflow and hence common-envelope evolution is impossible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "47979841-2c26-4b26-8945-603d013dc93a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Added grid variable: {\n",
      "    \"name\": \"lnm1\",\n",
      "    \"longname\": \"Primary mass\",\n",
      "    \"valuerange\": [\n",
      "        1,\n",
      "        6\n",
      "    ],\n",
      "    \"resolution\": \"10\",\n",
      "    \"spacingfunc\": \"const(math.log(1), math.log(6), 10)\",\n",
      "    \"precode\": \"M_1=math.exp(lnm1)\",\n",
      "    \"probdist\": \"three_part_powerlaw(M_1, 0.1, 0.5, 1.0, 150, -1.3, -2.3, -2.3)*M_1\",\n",
      "    \"dphasevol\": \"dlnm1\",\n",
      "    \"parameter_name\": \"M_1\",\n",
      "    \"condition\": \"\",\n",
      "    \"gridtype\": \"centred\",\n",
      "    \"branchpoint\": 0,\n",
      "    \"grid_variable_number\": 0\n",
      "}\n",
      "Added grid variable: {\n",
      "    \"name\": \"q\",\n",
      "    \"longname\": \"Mass ratio\",\n",
      "    \"valuerange\": [\n",
      "        \"0.1/M_1\",\n",
      "        1\n",
      "    ],\n",
      "    \"resolution\": \"10\",\n",
      "    \"spacingfunc\": \"const(1/M_1, 1, 10)\",\n",
      "    \"precode\": \"M_2 = q * M_1\",\n",
      "    \"probdist\": \"flatsections(q, [{'min': 1/M_1, 'max': 1.0, 'height': 1}])\",\n",
      "    \"dphasevol\": \"dq\",\n",
      "    \"parameter_name\": \"M_2\",\n",
      "    \"condition\": \"\",\n",
      "    \"gridtype\": \"centred\",\n",
      "    \"branchpoint\": 0,\n",
      "    \"grid_variable_number\": 1\n",
      "}\n",
      "Added grid variable: {\n",
      "    \"name\": \"log10per\",\n",
      "    \"longname\": \"log10(Orbital_Period)\",\n",
      "    \"valuerange\": [\n",
      "        0.15,\n",
      "        5.5\n",
      "    ],\n",
      "    \"resolution\": \"10\",\n",
      "    \"spacingfunc\": \"const(0.15, 4, 10)\",\n",
      "    \"precode\": \"orbital_period = 10.0 ** log10per\\nsep = calc_sep_from_period(M_1, M_2, orbital_period)\\nsep_min = calc_sep_from_period(M_1, M_2, 10**0.15)\\nsep_max = calc_sep_from_period(M_1, M_2, 10**4)\",\n",
      "    \"probdist\": \"sana12(M_1, M_2, sep, orbital_period, sep_min, sep_max, math.log10(10**0.15), math.log10(10**4), -0.55)\",\n",
      "    \"dphasevol\": \"dlog10per\",\n",
      "    \"parameter_name\": \"orbital_period\",\n",
      "    \"condition\": null,\n",
      "    \"gridtype\": \"centred\",\n",
      "    \"branchpoint\": 0,\n",
      "    \"grid_variable_number\": 2\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "import binarycpython.utils.distribution_functions\n",
    "# Set resolution and mass range that we simulate\n",
    "resolution = {\"M_1\": 10, \"q\" : 10, \"per\": 10} \n",
    "massrange = [1, 6] \n",
    "logperrange = [0.15, 4]\n",
    "\n",
    "population.add_grid_variable(\n",
    "    name=\"lnm1\",\n",
    "    longname=\"Primary mass\",\n",
    "    valuerange=massrange,\n",
    "    resolution=\"{}\".format(resolution[\"M_1\"]),\n",
    "    spacingfunc=\"const(math.log({min}), math.log({max}), {res})\".format(min=massrange[0],max=massrange[1],res=resolution[\"M_1\"]),\n",
    "    precode=\"M_1=math.exp(lnm1)\",\n",
    "    probdist=\"three_part_powerlaw(M_1, 0.1, 0.5, 1.0, 150, -1.3, -2.3, -2.3)*M_1\",\n",
    "    dphasevol=\"dlnm1\",\n",
    "    parameter_name=\"M_1\",\n",
    "    condition=\"\",  # Impose a condition on this grid variable. Mostly for a check for yourself\n",
    ")\n",
    "\n",
    "# Mass ratio\n",
    "population.add_grid_variable(\n",
    "     name=\"q\",\n",
    "     longname=\"Mass ratio\",\n",
    "     valuerange=[\"0.1/M_1\", 1],\n",
    "     resolution=\"{}\".format(resolution['q']),\n",
    "     spacingfunc=\"const({}/M_1, 1, {})\".format(massrange[0],resolution['q']),\n",
    "     probdist=\"flatsections(q, [{{'min': {}/M_1, 'max': 1.0, 'height': 1}}])\".format(massrange[0]),\n",
    "     dphasevol=\"dq\",\n",
    "     precode=\"M_2 = q * M_1\",\n",
    "     parameter_name=\"M_2\",\n",
    "     condition=\"\",  # Impose a condition on this grid variable. Mostly for a check for yourself\n",
    " )\n",
    "\n",
    "# Orbital period\n",
    "population.add_grid_variable(\n",
    "    name=\"log10per\", # in days\n",
    "    longname=\"log10(Orbital_Period)\",\n",
    "    valuerange=[0.15, 5.5],\n",
    "    resolution=\"{}\".format(resolution[\"per\"]),\n",
    "    spacingfunc=\"const({}, {}, {})\".format(logperrange[0],logperrange[1],resolution[\"per\"]),\n",
    "    precode=\"\"\"orbital_period = 10.0 ** log10per\n",
    "sep = calc_sep_from_period(M_1, M_2, orbital_period)\n",
    "sep_min = calc_sep_from_period(M_1, M_2, 10**{})\n",
    "sep_max = calc_sep_from_period(M_1, M_2, 10**{})\"\"\".format(logperrange[0],logperrange[1]),\n",
    "    probdist=\"sana12(M_1, M_2, sep, orbital_period, sep_min, sep_max, math.log10(10**{}), math.log10(10**{}), {})\".format(logperrange[0],logperrange[1],-0.55),\n",
    "    parameter_name=\"orbital_period\",\n",
    "    dphasevol=\"dlog10per\",\n",
    " )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "163f13ae-fec1-4ee8-b9d4-c1b75c19ff39",
   "metadata": {},
   "source": [
    "## Logging and handling the output\n",
    "\n",
    "We now construct the pre- and post-common envelope evolution data for the first common envelope that forms in each binary. We look at the comenv_count variable, we can see that when it increases from 0 to 1 we have found our object. If this happens, we stop evolution of the system to save CPU time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0c986215-93b1-4e30-ad79-f7c397e9ff7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adding: C_logging_code=\n",
      "\n",
      "/*\n",
      " * Detect when the comenv_count increased \n",
      " */\n",
      "if(stardata->model.comenv_count == 1 && \n",
      "   stardata->previous_stardata->model.comenv_count == 0)\n",
      "{\n",
      "   /*\n",
      "    * We just had this system's first common envelope:\n",
      "    * output the time at which this happens, \n",
      "    * the system's probability (proportional to the number of stars),\n",
      "    * the previous timestep's (pre-comenv) orbital period (days) and\n",
      "    * the current timestep (post-comenv) orbital period (days)\n",
      "    */\n",
      "    Printf(\"COMENV %g %g %g %g\\n\",\n",
      "           stardata->model.time,\n",
      "           stardata->model.probability,\n",
      "           stardata->previous_stardata->common.orbit.period * YEAR_LENGTH_IN_DAYS,\n",
      "           stardata->common.orbit.period * YEAR_LENGTH_IN_DAYS);\n",
      "           \n",
      "    /*\n",
      "     * We should waste no more CPU time on this system now we have the\n",
      "     * data we want.\n",
      "     */\n",
      "    stardata->model.evolution_stop = TRUE;\n",
      "}\n",
      " to grid_options\n"
     ]
    }
   ],
   "source": [
    "custom_logging_statement = \"\"\"\n",
    "\n",
    "/*\n",
    " * Detect when the comenv_count increased \n",
    " */\n",
    "if(stardata->model.comenv_count == 1 && \n",
    "   stardata->previous_stardata->model.comenv_count == 0)\n",
    "{\n",
    "   /*\n",
    "    * We just had this system's first common envelope:\n",
    "    * output the time at which this happens, \n",
    "    * the system's probability (proportional to the number of stars),\n",
    "    * the previous timestep's (pre-comenv) orbital period (days) and\n",
    "    * the current timestep (post-comenv) orbital period (days)\n",
    "    */\n",
    "    Printf(\"COMENV %g %g %g %g\\\\n\",\n",
    "           stardata->model.time,\n",
    "           stardata->model.probability,\n",
    "           stardata->previous_stardata->common.orbit.period * YEAR_LENGTH_IN_DAYS,\n",
    "           stardata->common.orbit.period * YEAR_LENGTH_IN_DAYS);\n",
    "           \n",
    "    /*\n",
    "     * We should waste no more CPU time on this system now we have the\n",
    "     * data we want.\n",
    "     */\n",
    "    stardata->model.evolution_stop = TRUE;\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "population.set(\n",
    "    C_logging_code=custom_logging_statement\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae1f1f0c-1f8b-42d8-b051-cbf8c6b51514",
   "metadata": {},
   "source": [
    "The parse function must now catch lines that start with \"COMENV\" and process the associated data. We set up the parse_data function to do just this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fd197154-a8ce-4865-8929-008d3483101a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adding: parse_function=<function parse_function at 0x14736bebc040> to grid_options\n"
     ]
    }
   ],
   "source": [
    "from binarycpython.utils.functions import bin_data,datalinedict\n",
    "import re\n",
    "\n",
    "# log-period distribution bin width (dex)\n",
    "binwidth = 0.5 \n",
    "\n",
    "def parse_function(self, output):\n",
    "    \"\"\"\n",
    "    Parsing function to convert HRD data into something that Python can use\n",
    "    \"\"\"\n",
    "    \n",
    "    # list of the data items\n",
    "    parameters = [\"header\", \"time\", \"probability\", \"pre_comenv_period\", \"post_comenv_period\"]\n",
    "    \n",
    "    # Loop over the output.\n",
    "    for line in output.splitlines():\n",
    "        \n",
    "        # obtain the line of data in dictionary form \n",
    "        linedata = datalinedict(line,parameters)\n",
    "            \n",
    "        # choose COMENV lines of output\n",
    "        if linedata[\"header\"] == \"COMENV\":\n",
    "            # bin the pre- and post-comenv log10-orbital-periods to nearest 0.5dex\n",
    "            binned_pre_period = bin_data(math.log10(linedata[\"pre_comenv_period\"]), binwidth)\n",
    "            \n",
    "            # but check if the post-comenv period is finite and positive: if \n",
    "            # not, the system has merged and we give it an aritifical period\n",
    "            # of 10^-100 days (which is very much unphysical)\n",
    "            if linedata[\"post_comenv_period\"] > 0.0:\n",
    "                binned_post_period = bin_data(math.log10(linedata[\"post_comenv_period\"]), binwidth)\n",
    "            else:\n",
    "                binned_post_period = bin_data(-100,binwidth) # merged!\n",
    "                \n",
    "            # make the \"histograms\"\n",
    "            self.grid_results['pre'][binned_pre_period] += linedata[\"probability\"]\n",
    "            self.grid_results['post'][binned_post_period] += linedata[\"probability\"]\n",
    "\n",
    "    # verbose reporting\n",
    "    #print(\"parse out results_dictionary=\",self.grid_results)\n",
    "    \n",
    "# Add the parsing function\n",
    "population.set(\n",
    "    parse_function=parse_function,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91509ce5-ffe7-4937-aa87-6d7baac9ac04",
   "metadata": {},
   "source": [
    "## Evolving the grid\n",
    "Now we actually run the population. This may take a little while. You can set amt_cores higher if you have a powerful machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8ea376c1-1e92-45af-8cab-9d7fdca564eb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adding: amt_cores=4 to grid_options\n",
      "Creating and loading custom logging functionality\n",
      "Generating grid code\n",
      "Generating grid code\n",
      "Constructing/adding: lnm1\n",
      "Constructing/adding: q\n",
      "Constructing/adding: log10per\n",
      "Saving grid code to grid_options\n",
      "Writing grid code to /tmp/binary_c_python/notebooks/notebook_comenv/binary_c_grid_ad303100d719457c83256568f9a9887c.py\n",
      "Loading grid code function from /tmp/binary_c_python/notebooks/notebook_comenv/binary_c_grid_ad303100d719457c83256568f9a9887c.py\n",
      "Grid code loaded\n",
      "Grid has handled 1000 stars\n",
      "with a total probability of 0.0645905996773004\n",
      "Total starcount for this run will be: 1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:07:39,950 DEBUG    Process-2] --- Setting up processor: process-0\n",
      "[2021-09-12 18:07:39,953 DEBUG    Process-3] --- Setting up processor: process-1\n",
      "[2021-09-12 18:07:39,959 DEBUG    Process-4] --- Setting up processor: process-2\n",
      "[2021-09-12 18:07:39,962 DEBUG    MainProcess] --- setting up the system_queue_filler now\n",
      "[2021-09-12 18:07:39,965 DEBUG    Process-5] --- Setting up processor: process-3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process 0 started at 2021-09-12T18:07:39.965721.\tUsing store memaddr <capsule object \"STORE\" at 0x14736bee47e0>\n",
      "Process 1 started at 2021-09-12T18:07:39.970949.\tUsing store memaddr <capsule object \"STORE\" at 0x14736bee4870>\n",
      "Process 2 started at 2021-09-12T18:07:39.978355.\tUsing store memaddr <capsule object \"STORE\" at 0x14736bee4f30>\n",
      "Process 3 started at 2021-09-12T18:07:39.983689.\tUsing store memaddr <capsule object \"STORE\" at 0x14736bee4870>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:07:40,066 DEBUG    MainProcess] --- Signaling stop to processes\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating grid code\n",
      "Generating grid code\n",
      "Constructing/adding: lnm1\n",
      "Constructing/adding: q\n",
      "Constructing/adding: log10per\n",
      "Saving grid code to grid_options\n",
      "Writing grid code to /tmp/binary_c_python/notebooks/notebook_comenv/binary_c_grid_ad303100d719457c83256568f9a9887c.py\n",
      "Loading grid code function from /tmp/binary_c_python/notebooks/notebook_comenv/binary_c_grid_ad303100d719457c83256568f9a9887c.py\n",
      "Grid code loaded\n",
      "163/1000  16.3% complete 18:07:49 ETA=   51.5s tpr=6.16e-02 ETF=18:08:41 mem:594.9MB\n",
      "322/1000  32.2% complete 18:07:59 ETA=   42.9s tpr=6.33e-02 ETF=18:08:42 mem:538.2MB\n",
      "465/1000  46.5% complete 18:08:09 ETA=   38.1s tpr=7.12e-02 ETF=18:08:47 mem:538.2MB\n",
      "586/1000  58.6% complete 18:08:19 ETA=   34.3s tpr=8.29e-02 ETF=18:08:54 mem:540.0MB\n",
      "682/1000  68.2% complete 18:08:30 ETA=   34.0s tpr=1.07e-01 ETF=18:09:04 mem:540.1MB\n",
      "784/1000  78.4% complete 18:08:40 ETA=   21.2s tpr=9.81e-02 ETF=18:09:01 mem:541.8MB\n",
      "872/1000  87.2% complete 18:08:50 ETA=   15.0s tpr=1.17e-01 ETF=18:09:05 mem:546.1MB\n",
      "963/1000  96.3% complete 18:09:00 ETA=    4.2s tpr=1.14e-01 ETF=18:09:04 mem:546.9MB\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:09:06,366 DEBUG    Process-5] --- Process-3 is finishing.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process 3 finished:\n",
      "\tgenerator started at 2021-09-12T18:07:39.964604, done at 2021-09-12T18:09:06.370832 (total: 86.406228s of which 86.24177551269531s interfacing with binary_c).\n",
      "\tRan 222 systems with a total probability of 0.014137215791516371.\n",
      "\tThis thread had 0 failing systems with a total probability of 0.\n",
      "\tSkipped a total of 0 systems because they had 0 probability\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:09:06,374 DEBUG    Process-5] --- Process-3 is finished.\n",
      "[2021-09-12 18:09:06,979 DEBUG    Process-3] --- Process-1 is finishing.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process 1 finished:\n",
      "\tgenerator started at 2021-09-12T18:07:39.953039, done at 2021-09-12T18:09:06.982866 (total: 87.029827s of which 86.82909393310547s interfacing with binary_c).\n",
      "\tRan 273 systems with a total probability of 0.01877334232598154.\n",
      "\tThis thread had 0 failing systems with a total probability of 0.\n",
      "\tSkipped a total of 0 systems because they had 0 probability\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:09:06,985 DEBUG    Process-3] --- Process-1 is finished.\n",
      "[2021-09-12 18:09:07,174 DEBUG    Process-2] --- Process-0 is finishing.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process 0 finished:\n",
      "\tgenerator started at 2021-09-12T18:07:39.949775, done at 2021-09-12T18:09:07.176660 (total: 87.226885s of which 87.02672934532166s interfacing with binary_c).\n",
      "\tRan 268 systems with a total probability of 0.016469813170514686.\n",
      "\tThis thread had 0 failing systems with a total probability of 0.\n",
      "\tSkipped a total of 0 systems because they had 0 probability\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:09:07,179 DEBUG    Process-2] --- Process-0 is finished.\n",
      "[2021-09-12 18:09:07,233 DEBUG    Process-4] --- Process-2 is finishing.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process 2 finished:\n",
      "\tgenerator started at 2021-09-12T18:07:39.958802, done at 2021-09-12T18:09:07.236252 (total: 87.27745s of which 87.0905077457428s interfacing with binary_c).\n",
      "\tRan 237 systems with a total probability of 0.015210228389288167.\n",
      "\tThis thread had 0 failing systems with a total probability of 0.\n",
      "\tSkipped a total of 0 systems because they had 0 probability\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[2021-09-12 18:09:07,238 DEBUG    Process-4] --- Process-2 is finished.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population-ad303100d719457c83256568f9a9887c finished! The total probability was: 0.06459059967730076. It took a total of 87.54819011688232s to run 1000 systems on 4 cores\n",
      "There were no errors found in this run.\n"
     ]
    }
   ],
   "source": [
    "# set number of threads\n",
    "population.set(\n",
    "    # set number of threads (i.e. number of CPU cores we use)\n",
    "    amt_cores=4,\n",
    "    )\n",
    "\n",
    "# Evolve the population - this is the slow, number-crunching step\n",
    "analytics = population.evolve()  \n",
    "\n",
    "# Show the results (debugging)\n",
    "#print (population.grid_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91ab45c7-7d31-4543-aee4-127ab58e891f",
   "metadata": {},
   "source": [
    "After the run is complete, some technical report on the run is returned. I stored that in `analytics`. As we can see below, this dictionary is like a status report of the evolution. Useful for e.g. debugging. We check this, and then set about making the plot of the orbital period distributions using Seaborn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e1f0464b-0424-4022-b34b-5b744bc2c59d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'population_name': 'ad303100d719457c83256568f9a9887c', 'evolution_type': 'grid', 'failed_count': 0, 'failed_prob': 0, 'failed_systems_error_codes': [], 'errors_exceeded': False, 'errors_found': False, 'total_probability': 0.06459059967730076, 'total_count': 1000, 'start_timestamp': 1631462859.9342952, 'end_timestamp': 1631462947.4824853, 'total_mass_run': 4680.235689312421, 'total_probability_weighted_mass_run': 0.22611318083528567, 'zero_prob_stars_skipped': 0}\n"
     ]
    }
   ],
   "source": [
    "print(analytics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "05c6d132-abee-423e-b1a8-2039c8996fbc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'merged': 0.035263029200000025, 'unmerged': 0.019388724199999995}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of stars')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a plot of the distributions\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import copy\n",
    "pd.set_option(\"display.max_rows\", None, \"display.max_columns\", None)\n",
    "from binarycpython.utils.functions import pad_output_distribution\n",
    "\n",
    "# set up seaborn for use in the notebook\n",
    "sns.set(rc={'figure.figsize':(20,10)})\n",
    "sns.set_context(\"notebook\",\n",
    "                font_scale=1.5,\n",
    "                rc={\"lines.linewidth\":2.5})\n",
    "\n",
    "pd.set_option(\"display.max_rows\", None, \"display.max_columns\", None)\n",
    "\n",
    "# remove the merged objects\n",
    "probability = { \"merged\" : 0.0, \"unmerged\" : 0.0}\n",
    "\n",
    "# copy the results so we can change the copy\n",
    "results = copy.deepcopy(population.grid_results)\n",
    "\n",
    "for distribution in ['post']:    \n",
    "    for logper in population.grid_results[distribution]:\n",
    "        dprob = results[distribution][logper]\n",
    "        if logper < -90:\n",
    "            # merged system\n",
    "            probability[\"merged\"] += dprob\n",
    "            del results[distribution][logper]\n",
    "        else:\n",
    "            # unmerged system\n",
    "            probability[\"unmerged\"] += dprob\n",
    "print(probability)\n",
    "    \n",
    "# pad the final distribution with zero\n",
    "for distribution in population.grid_results:    \n",
    "    pad_output_distribution(results[distribution],\n",
    "                            binwidth)\n",
    "    \n",
    "# make pandas dataframe \n",
    "plot_data = pd.DataFrame.from_dict(results, orient='columns')\n",
    "\n",
    "# make the plot\n",
    "p = sns.lineplot(data=plot_data)\n",
    "p.set_xlabel(\"$\\log_{10} (P_\\mathrm{orb} / \\mathrm{day})$\")\n",
    "p.set_ylabel(\"Number of stars\")\n",
    "#p.set(xlim=(-5,5)) # might be necessary?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4740c93-d01e-4ca1-8766-c2fb4ddca2e4",
   "metadata": {},
   "source": [
    "You can see that common-envelope evolution shrinks stellar orbits, just as we expect. Pre-CEE, most orbits are in the range $10$ to $1000\\text{ }\\mathrm{d}$, while after CEE the distribution peaks at about $1\\text{ }\\mathrm{d}$. Some of these orbits are very short: $\\log_{10}(-2) = 0.01\\text{ }\\mathrm{d}\\sim10\\text{ }\\mathrm{minutes}$. Such systems are prime candidates for exciting astrophysics: novae, type Ia supernovae and gravitational wave sources."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57faf043-3809-427a-b378-2355ce8c2691",
   "metadata": {},
   "source": [
    "Things to try:\n",
    "* Extend the logging to output more data than just the orbital period.\n",
    "* What are the stellar types of the post-common envelope systems? Are they likely to undergo novae or a type-Ia supernova?\n",
    "* What are the lifetimes of the systems in close ($<1\\text{ }\\mathrm{d}$) binaries? Are they likely to merge in the life of the Universe?\n",
    "* How much mass is lost in common-envelope interactions?\n",
    "* Extend the grid to massive stars. Do you see many NS and BH compact binaries?\n",
    "* Try different $\\alpha_\\mathrm{CE}$ and $\\lambda_\\mathrm{CE}$ options...\n",
    "* ... and perhaps increased resolution to obtain smoother curves.\n",
    "* Why do long-period systems not reach common envelope evolution?"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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