ExploringGalacticVariability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0a74b023-3d28-4249-a0bc-9045e95f60c2",
   "metadata": {},
   "source": [
    "## Galactic Variability Timescales Figures of Merit ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ae48071d-d7b3-4c8e-bb9b-b30db12c6f42",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import healpy as hp\n",
    "import astropy.units as u\n",
    "from astropy.coordinates import SkyCoord\n",
    "from matplotlib.patches import Rectangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b1bf3e0a-a9a4-4ae3-9d2d-1068c95d9237",
   "metadata": {},
   "outputs": [],
   "source": [
    "NSIDE = 64"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d59ec79f-7c98-4390-9a9b-0b2224ba9d30",
   "metadata": {},
   "source": [
    "This notebook is designed to present Figures of Merit (FoM) that *very approximately* explore how different categories of galactic variability will benefit or suffer depending on the combination of survey footprint and total number of visits dedicated to this survey region.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de85913c-224b-404a-9078-f9b23e07a141",
   "metadata": {},
   "source": [
    "**Assumptions:**\n",
    "* The distribution of the visits are uniform in time, i.e. intervals between visits are constant\n",
    "* Equal numbers of visits are obtained in all 6 filters, repeating sequentially, so that color information is obtained"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f99df81-b0ad-4dbf-9285-f1d9cb1f7015",
   "metadata": {},
   "source": [
    "**MAJOR CAVEAT:** this dramatically simplifies the requirements of the science involved, particularly in the distribution of the visits throughout the survey and the relative time allocated to obtaining data in different filters.  This is an unsafe and potentially misleading assumption and caution is strongly advised in interpreting the results on this basis alone. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff8b6232-5a2e-4719-b615-5543805e3f90",
   "metadata": {},
   "source": [
    "### Categorizing variability according to timescale ###\n",
    "\n",
    "We group all types of galactic stellar variabililty into either transient and periodic phenomena, and consider four very broad categories based on the characteristic *timescale of variability* $\\tau_{var}$, since this is the key characteristic affected by changes in lightcurve time sampling when more or fewer visits to a given pointing are made in the course of the survey.  \n",
    "For transient phenomena, the timescale of variability refers to typical duration of the transient signal, such as the duration of an outburst or explosion, or the Einstein crossing timescale in microlensing.  \n",
    "For periodic phenomena, the timescale of variability is considered to be the primary periodicity of the object, typically the rotation or orbital period.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "802586f1-ff13-4032-9666-f754653d4c3c",
   "metadata": {},
   "source": [
    "Galactic variability can then be grouped into the following categories according to $\\tau_{var}$:\n",
    "* $<$10 days: including exoplanet & White Dwarf transits, stellar flares, short period stellar binaries, pulsating stars (inc. RR Lyrae, Cepheids), some point-source microlensing (e.g., by free-floating planets, bound planet anomalies, brown dwarfs), most binary microlensing, variability in young stars, short-term accretion variability\n",
    "* 10-100 days: includes point-source microlensing by galactic stellar-mass lenses (but not binary-lens anomalies), intermediate stellar pulsation periods, disk instability in Cataclysmic Variables, novae\n",
    "* 100-365 days: includes microlensing by black holes, long-timescale pulsations, \n",
    "* $>$365 days: includes long-period variables, e.g. Miras"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96ec5485-02a0-4b33-8b76-d47d46832457",
   "metadata": {},
   "source": [
    "Although LSST will generate an alert whenever an object varies by more than 5$\\sigma$ from the reference flux, for most of Galactic science this is insufficient to reliably detect variability and certainly inadequate to meaningfully classify it.  \n",
    "\n",
    "Based on previous follow-up experience we require a minimum of 5 observations taken within $\\tau_{var}$ to consider a variable target \"detectable\" in the sense of being able to accurately extract targets of interest from the LSST datastream (for comparison we understand the ZTF estimate that 10 observations are required).  Note that this neglects requirements for multi-color observations in order to simplify the problem.  \n",
    "\n",
    "Applying this requirement to transient phenomena, we derive a maximum-useful observation interval, $\\tau_{obs} = \\tau_{var} / 5$ for the four categories above:\n",
    "* $\\tau_{var} < $10 days, $\\tau_{obs}$ = 2days\n",
    "* 10 $<$ $\\tau_{var} < $100 days, $\\tau_{obs}$ = 2 - 20 days\n",
    "* 100 $<$ $\\tau_{var} < $365 days, $\\tau_{obs}$ = 20 - 73 days\n",
    "* $\\tau_{var} > $365 days, $\\tau_{obs}$ = 73days"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28254d11-2e53-4451-b4be-dbeacfe267e2",
   "metadata": {},
   "source": [
    "It is often assumed that periodic variables will automatically be detected over the lifetime of LSST.   More precisely, an accurate period, $P$, should be recovered if at least ~5 observations are obtained spanning a range of different phases of the variability period, and this is indeed likely to be true for all $\\tau_{var}$ categories by the end of the 10yr survey.  However, *the early identification of periodic variables is critical to the accurate classification of transients*, so waiting until year 10 to identify all periodic variables would severely limit the transient science that can be done, as well as delaying variable star science.  \n",
    "\n",
    "On the assumption that Galactic Plane visits are uniformly distributed throughout the survey, we therefore consider the detection of periodic variables based on observations taken *only within the first year*.  The maximum-useful observation interval is then set by requiring $\\tau_{obs} = P / 5$, leading to the same $\\tau_{obs}$ categories as above."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f09b43-38ba-4525-a106-de6867f15c99",
   "metadata": {},
   "source": [
    "### Galactic Plane Survey Footprint ###\n",
    "\n",
    "To first order, the spatial distribution of all of these classes of variable follows the distribution of stars in the Milky Way, which we represent using the TVS/SMWLV Galactic Plane priority map.  This map assigns a numerical priority to each HEALpix in the sky according to that pixels importance in Galactic Plane science (as described in Street et al. 2021 https://docushare.lsst.org/docushare/dsweb/Get/Document-37639/Galactic_Plane_Footprint.pdf).\n",
    "\n",
    "Note that the SDSS-i band map is used here as the most generally-applicable and inclusive reference.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e5eb6a14-6f1b-4423-b24c-a4d3c1b8acb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "footprint_maps_dir = os.getenv('FOOTPRINT_MAPS_DIR')\n",
    "GP_footprint = hp.read_map(os.path.join(footprint_maps_dir,'GalPlane_priority_map_i.fits'), dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "40e0ef65-ca33-453f-bffa-d89c8e66c140",
   "metadata": {},
   "outputs": [],
   "source": [
    "def galPlane_survey_footprint(healpix_priority_minimum_threshold = 0.25):\n",
    "    galwfd = np.where(GP_footprint >= healpix_priority_minimum_threshold,1,0)\n",
    "    return galwfd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "372a105d-0fc2-4db7-b0af-667d525c31b7",
   "metadata": {},
   "source": [
    "To give illustrative examples, the following plots show how the survey footprint changes when we include only the higher-priority areas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ab860902-7441-46ae-8d26-59f3b55280d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resolution of HEALpix map: 0.9deg per HEALpix\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 612x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold = 0.25)\n",
    "hp.mollview(galwfd, max=1)\n",
    "print('Resolution of HEALpix map: '+str(round(hp.nside2resol(NSIDE, arcmin=True) / 60,1))+'deg per HEALpix')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3accdb47-3bf9-4cc9-bd63-d690ae8b5b64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 612x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold = 0.5)\n",
    "hp.mollview(galwfd, max=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7c74784-eeef-4fd8-bf07-6166f3024724",
   "metadata": {},
   "source": [
    "One dimension of survey strategy optimization is to consider larger vs smaller footprints in the Galactic Plane, which can be done by lowering or increasing (respectively) the healpix_priority_minimum_threshold.  We estimate the total survey area included in the Galactic Plane as a function of healpix_priority_minimum_threshold as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b063b5be-d2a4-4bbb-96c2-54f0e8a92458",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_GP_survey_area(galwfd, nside=64):\n",
    "    gp_area = galwfd.sum() * hp.nside2pixarea(nside, degrees=True)\n",
    "    return gp_area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "94baa677-6c90-4d47-ab44-69ae99fb40d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "priority_range = np.arange(0.1,1.0,0.1)\n",
    "survey_area = np.zeros(len(priority_range))\n",
    "for i in range(0,len(priority_range),1):\n",
    "    galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold=priority_range[i])\n",
    "    survey_area[i] = estimate_GP_survey_area(galwfd)\n",
    "data = np.column_stack((priority_range,survey_area))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f194faae-b4ec-49b7-9cab-7f47d5c7ef7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Survey area (sq deg)')"
      ]
     },
     "execution_count": 8,
     "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": [
    "plt.plot(data[:,0], data[:,1])\n",
    "plt.grid(alpha=0.2)\n",
    "plt.xlabel('HEALpix priority minimum threshold')\n",
    "plt.ylabel('Survey area (sq deg)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "666eb977-76d9-4a03-9cf6-5903262aa39f",
   "metadata": {},
   "source": [
    "### Survey Time Requirements ###"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea1d28c1-6dc4-4a9d-a47e-01e84cc07535",
   "metadata": {},
   "source": [
    "To estimate the time required to survey a given region, we calculate the observing time required for a single visit, based on 2x15s exposures, with a mean visit time of 42.2s (from https://www.lsst.org/scientists/keynumbers).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c46107ec-af7a-4c97-9f86-5fc8db7e17e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_survey_time(nvisits_per_pointing,survey_area):\n",
    "    \"\"\"Estimates the total on-sky observing time used to survey a footprint of a given area, \n",
    "    for the number of visits indicated.  Estimate is returned in units of hours.\"\"\"\n",
    "    mean_visit_time = 42.2/3600.0  # secs -> hours\n",
    "    npointings = survey_area / 9.6 # Estimated from the Rubin FOV=9.6 sq deg\n",
    "    survey_time = mean_visit_time * nvisits_per_pointing * npointings\n",
    "    return survey_time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2679a1de-5d5e-4b6d-b132-f9e9848dc0c4",
   "metadata": {},
   "source": [
    "To build intuition, let's calculate the amount of time required to survey the Galactic Plane to different HEALpix priority levels, assuming the default 825 visits per field, and compare this with a rough estimate of the total observing time for the LSST survey:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e2eb90e8-69ad-4edd-bffd-64e86c6821fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.00000000e-01 1.30048550e+04 1.31008110e+04]\n",
      " [2.00000000e-01 5.17508462e+03 5.21326883e+03]\n",
      " [3.00000000e-01 5.17172744e+03 5.20988689e+03]\n",
      " [4.00000000e-01 1.95051843e+03 1.96491028e+03]\n",
      " [5.00000000e-01 1.48806763e+03 1.49904730e+03]\n",
      " [6.00000000e-01 1.48722834e+03 1.49820181e+03]\n",
      " [7.00000000e-01 4.94343957e+02 4.97991460e+02]\n",
      " [8.00000000e-01 4.86790314e+02 4.90382083e+02]\n",
      " [9.00000000e-01 4.54897156e+02 4.58253602e+02]]\n"
     ]
    }
   ],
   "source": [
    "survey_time = np.zeros(len(priority_range))\n",
    "for i in range(0,len(priority_range),1):\n",
    "    survey_time[i] = calc_survey_time(825, survey_area[i])\n",
    "data = np.column_stack((priority_range,survey_area,survey_time))\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1b25f311-2385-4680-b51c-72ca29cbd79e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of hours of observations in LSST = 26280.0hrs\n",
      "Estimate number of hours available for non-WFD observations = 2628.0hrs\n"
     ]
    }
   ],
   "source": [
    "nyears = 10.0\n",
    "ndays_per_year = 365.0\n",
    "nhours_per_night = 9.0\n",
    "clear_fraction = 0.8\n",
    "total_lsst_survey_time = nyears * ndays_per_year * nhours_per_night * clear_fraction\n",
    "print('Total number of hours of observations in LSST = '+str(total_lsst_survey_time)+'hrs')\n",
    "available_lsst_fraction = 0.1\n",
    "available_survey_time = total_lsst_survey_time * available_lsst_fraction\n",
    "print('Estimate number of hours available for non-WFD observations = '+str(available_survey_time)+'hrs')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "33f6446e-f0c1-46de-9b17-40fa922e54ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1712845d0>"
      ]
     },
     "execution_count": 12,
     "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": [
    "plt.plot(data[:,0], data[:,2])\n",
    "plt.grid(alpha=0.2)\n",
    "plt.plot([data[:,0].min(),data[:,0].max()],[total_lsst_survey_time]*2,'r-',label='Total LSST survey time')\n",
    "plt.plot([data[:,0].min(),data[:,0].max()],[available_survey_time]*2,'m-.',label='Available survey time')\n",
    "plt.xlabel('HEALpix priority minimum threshold')\n",
    "plt.ylabel('Survey time required (hours)')\n",
    "plt.title('Time required for 825 visits to all pointings in different Galactic Plane footprints')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b87c79f2-2d24-471b-a820-47c23869b636",
   "metadata": {},
   "source": [
    "### Impact of Number of Observations on Scientific Yield ###\n",
    "\n",
    "If the total amount of Rubin observing time dedicated to surveying the Galactic Plane has to be reduced due to other scheduling pressures, what impact will this have on galactic variability science?\n",
    "\n",
    "For simplicity, we assume that if the total number of visits to a field is reduced, the remaining visits are distributed uniformly (in time and in filter selection) and so the interval between visits increases.  We can therefore *roughly* gauge the scientific impact of this change by comparing the inter-visit interval with $\\tau_{var}$ and $\\tau_{obs}$.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3896db23-6b2c-4d5c-934a-785e122e0bc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ensure_array(entry):\n",
    "    if type(entry) == type(50) or type(entry) == type(50.0):\n",
    "        entry = [entry]\n",
    "    if type(entry) == list:\n",
    "        entry = np.array(entry)\n",
    "    return entry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c1fc285f-0b9c-48d4-bf20-5f0292265229",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_visit_interval(nvisits):\n",
    "    \"\"\"Function to estimate the interval between visits to a given pointing \n",
    "    based on the total number of visits over the lifetime of the survey.  \n",
    "    This assumes that:\n",
    "    - Any given field is observable from site for an average of 8 months per year\n",
    "    - The survey lifetime is 10 years\n",
    "    - Visits to the field are uniformly distributed\n",
    "    \"\"\"\n",
    "    nvisits = ensure_array(nvisits)\n",
    "    \n",
    "    # Estimate the total period of time for which a field can be observed by Rubin\n",
    "    # over the lifetime of LSST.  Units of hours\n",
    "    total_time_field_observable = 10.0 * 365.25 * 24.0\n",
    "    time_observable = np.zeros(len(nvisits))\n",
    "    time_observable.fill(total_time_field_observable)\n",
    "    \n",
    "    # Average interval between visits in hours\n",
    "    visit_interval = time_observable / nvisits\n",
    "    \n",
    "    return visit_interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "840de38a-511e-4a02-8b5e-b85519f3c685",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_nvisits(visit_interval):\n",
    "    \"\"\"Function to estimate the number of visits over the lifetime of the survey, \n",
    "    based on the interval between them.   \n",
    "    This assumes that:\n",
    "    - Any given field is observable from site for an average of 8 months per year\n",
    "    - The survey lifetime is 10 years\n",
    "    - Visits to the field are uniformly distributed\n",
    "    \"\"\"\n",
    "    visit_interval = ensure_array(visit_interval)\n",
    "    \n",
    "    # Estimate the total period of time for which a field can be observed by Rubin\n",
    "    # over the lifetime of LSST.  Units of hours\n",
    "    total_time_field_observable = 10.0 * 365.25 * 24.0\n",
    "    time_observable = np.zeros(len(visit_interval))\n",
    "    time_observable.fill(total_time_field_observable)\n",
    "    \n",
    "    # Average number of visits\n",
    "    nvisits = time_observable / visit_interval\n",
    "    \n",
    "    return nvisits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "19e4ffbd-f166-44ad-b53a-aec9e56998cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Zoom into short observation intervals')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "min_nvisits = 10\n",
    "max_nvisits = 1000\n",
    "nvisits_range = np.arange(min_nvisits,max_nvisits,10)\n",
    "visit_intervals = estimate_visit_interval(nvisits_range) / 24.0\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(15,5))\n",
    "ax1.plot(nvisits_range, visit_intervals)\n",
    "ax1.grid(alpha=0.2)\n",
    "ax1.set_xlabel('Nvisits per pointing')\n",
    "ax1.set_ylabel('Interval between visits [days]')\n",
    "ax1.fill_between(nvisits_range, 0.0, 2.0, facecolor='green', alpha=0.2, label='$\\\\tau_{obs}$ < 2days')\n",
    "ax1.fill_between(nvisits_range, 2.0, 20.0, facecolor='m', alpha=0.2, label='2 < $\\\\tau_{obs}$ < 20days')\n",
    "ax1.fill_between(nvisits_range, 20.0, 73.0, facecolor='b', alpha=0.2, label='20 < $\\\\tau_{obs}$ < 73days')\n",
    "ax1.fill_between(nvisits_range, 73.0, visit_intervals.max(), facecolor='r', alpha=0.2, label='$\\\\tau_{obs}$ > 73days')\n",
    "(xmin,xmax,ymin,ymax) = ax1.axis()\n",
    "ax1.axis([xmin,xmax,0.0,visit_intervals.max()])\n",
    "ax1.legend()\n",
    "ax1.set_title('Full range of observation intervals')\n",
    "\n",
    "\n",
    "ax2.plot(nvisits_range, visit_intervals)\n",
    "ax2.grid(alpha=0.2)\n",
    "ax2.set_xlabel('Nvisits per pointing')\n",
    "ax2.set_ylabel('Interval between visits [days]')\n",
    "ax2.fill_between(nvisits_range, 0.0, 2.0, facecolor='green', alpha=0.2, label='$\\\\tau_{obs}$ < 2days')\n",
    "ax2.fill_between(nvisits_range, 2.0, 20.0, facecolor='m', alpha=0.2, label='2 < $\\\\tau_{obs}$ < 20days')\n",
    "(xmin,xmax,ymin,ymax) = ax2.axis()\n",
    "ax2.axis([xmin,xmax,0.0,20.0])\n",
    "ax2.legend()\n",
    "ax2.set_title('Zoom into short observation intervals')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82260d46-76c6-45cc-af63-c52601ca0d8f",
   "metadata": {},
   "source": [
    "The plot above illustrates which categories of galactic plane science will be served, given different numbers of total visits, assuming they are distributed uniformly in time and filter selection. **However caution is urged in interpreting these plots** The four $\\tau_{obs}$ categories are not considered scientifically equal in the sense that the **majority of high-impact science is contained within the category $\\tau_{obs} < 2$ days.**  \n",
    "\n",
    "If LSST does not provide sufficient numbers of visits to achieve this science, it is possible that some of it may still be achieved through real-time follow-up observations at higher cadence.  This has been demonstrated with microlensing for example, if the survey provides sufficient observations to alert new discoveries at an early stage of the event.  **But we stress that follow-up observations cannot fully compensate for the loss of Rubin observations** particularly at fainter magnitudes, as inadequate time is available at follow-up facilities of sufficient aperture and instrumentation, and the scientific yield of the survey would be substantially diminished."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be1658bd-bac6-47ee-903d-fb36762d2d29",
   "metadata": {},
   "source": [
    "### Impact of Survey Footprint Area ###\n",
    "\n",
    "From the plots above, we note that nvisits~500/pointing provides a rough rule-of-thumb as the minimum viable number of visits that would enable science in all four $\\tau_{var}$ categories.  We combine this with the Galactic Plane priority map to estimate the total survey time required for different footprints. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "00f9890e-8429-4e6b-9e27-40d8aed70c90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17146da50>"
      ]
     },
     "execution_count": 17,
     "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": [
    "priority_range = np.arange(0.1,1.0,0.01)\n",
    "survey_area = np.zeros(len(priority_range))\n",
    "survey_time = np.zeros(len(priority_range))\n",
    "for i in range(0,len(priority_range),1):\n",
    "    galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold=priority_range[i])\n",
    "    survey_area[i] = estimate_GP_survey_area(galwfd)\n",
    "    survey_time[i] = calc_survey_time(500, survey_area[i])\n",
    "data = np.column_stack((priority_range,survey_area,survey_time))\n",
    "plt.plot(data[:,0], data[:,2])\n",
    "plt.grid(alpha=0.2)\n",
    "plt.plot([data[:,0].min(),data[:,0].max()],[total_lsst_survey_time]*2,'r-',label='Total LSST survey time')\n",
    "plt.plot([data[:,0].min(),data[:,0].max()],[available_survey_time]*2,'m-.',label='Available survey time')\n",
    "plt.xlabel('HEALpix priority minimum threshold')\n",
    "plt.ylabel('Survey time required (hours)')\n",
    "plt.title('Time required for 500 visits to all pointings in different Galactic Plane footprints')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b526f29c-4c5b-487f-9400-0b5f1360913c",
   "metadata": {},
   "source": [
    "This plot implies that using a HEALpix-priority threshold of 0.4 to select fields in the Galactic Plane might be surveyed to an adequate cadence by LSST to enable all of the science considered here.  To illustrate that footprint graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "eb90e436-0b1f-47a0-b7b5-aa6d3a191f0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rstreet1/software/lsst_tvs_venv/lib/python3.7/site-packages/healpy/projaxes.py:920: MatplotlibDeprecationWarning: You are modifying the state of a globally registered colormap. In future versions, you will not be able to modify a registered colormap in-place. To remove this warning, you can make a copy of the colormap first. cmap = copy.copy(mpl.cm.get_cmap(\"viridis\"))\n",
      "  newcm.set_over(newcm(1.0))\n",
      "/Users/rstreet1/software/lsst_tvs_venv/lib/python3.7/site-packages/healpy/projaxes.py:921: MatplotlibDeprecationWarning: You are modifying the state of a globally registered colormap. In future versions, you will not be able to modify a registered colormap in-place. To remove this warning, you can make a copy of the colormap first. cmap = copy.copy(mpl.cm.get_cmap(\"viridis\"))\n",
      "  newcm.set_under(bgcolor)\n",
      "/Users/rstreet1/software/lsst_tvs_venv/lib/python3.7/site-packages/healpy/projaxes.py:922: MatplotlibDeprecationWarning: You are modifying the state of a globally registered colormap. In future versions, you will not be able to modify a registered colormap in-place. To remove this warning, you can make a copy of the colormap first. cmap = copy.copy(mpl.cm.get_cmap(\"viridis\"))\n",
      "  newcm.set_bad(badcolor)\n",
      "/Users/rstreet1/software/lsst_tvs_venv/lib/python3.7/site-packages/healpy/projaxes.py:211: MatplotlibDeprecationWarning: Passing parameters norm and vmin/vmax simultaneously is deprecated since 3.3 and will become an error two minor releases later. Please pass vmin/vmax directly to the norm when creating it.\n",
      "  **kwds\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 612x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold = 0.4)\n",
    "hp.mollview(galwfd, max=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "429a4f20-559a-4a38-a63b-5565c949bc34",
   "metadata": {},
   "source": [
    "### Galactic Science Figure of Merit ###\n",
    "\n",
    "A very approximate rule of thumb for galactic science may be derived by combining the above metrics for survey footprint and number of visits per pointing.  To give a sense of scale, we normalize this FoM using intermediate values for survey footprint area of 2000 sq deg. and nvisits_per_pointing of 500, based on the analysis above.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f63a0382-99a0-452b-81da-807b15d8016c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def GP_FoM_tau_footprint(nvisits_per_pointing,survey_area):\n",
    "    \n",
    "    visit_intervals = estimate_visit_interval(nvisits_per_pointing) / 24.0\n",
    "    FoM = survey_area / visit_intervals\n",
    "    \n",
    "    minimum_visit_interval = estimate_visit_interval(500) / 24.0\n",
    "    fiducial_FoM = 2000.0 / minimum_visit_interval\n",
    "    \n",
    "    norm_FoM = FoM/fiducial_FoM\n",
    "    \n",
    "    return norm_FoM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "808eafbe-5d65-4a96-ba8a-9a653d777b1c",
   "metadata": {},
   "source": [
    "We then compute this FoM for a range of survey parameters, spanning ranges of number of visits/pointing and total survey footprint area in the Galactic Plane region.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "023b7792-3fed-4f97-8a6e-99cd67e013e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_yval(visit_interval, min_nvisits, max_nvisits, scale_min, scale_max):\n",
    "    \"\"\"Function to map y-axis parameter values to y-axis scale in the 2D FoM plot\"\"\"\n",
    "    \n",
    "    nvisits = estimate_nvisits(visit_interval)\n",
    "    #print('Visit interval='+str(visit_interval)+' -> nvisits='+str(nvisits))\n",
    "    #print('SCALE: '+str(scale_min)+' '+str(scale_max))\n",
    "    #print('PARAMETER: '+str(min_nvisits)+' '+str(max_nvisits))\n",
    "    \n",
    "    scale_grad = (scale_max - scale_min) / (max_nvisits - min_nvisits)\n",
    "    \n",
    "    scale_value = scale_min + scale_grad*nvisits\n",
    "    #print('Scale gradient: '+str(scale_grad))\n",
    "    #print('Value on scale: '+str(scale_value))\n",
    "    \n",
    "    return scale_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "507eb73b-c25c-41cf-89ed-2ddbb7ed757d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rstreet1/software/lsst_tvs_venv/lib/python3.7/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Rectangle at 0x171317590>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "min_nvisits = 1\n",
    "max_nvisits = 2000\n",
    "nvisits_range = np.arange(min_nvisits,max_nvisits,10)\n",
    "visit_intervals = estimate_visit_interval(nvisits_range) / 24.0\n",
    "min_priority = 0.1\n",
    "max_priority = 1.0\n",
    "priority_range = np.arange(min_priority, max_priority,0.01)\n",
    "FoM = np.zeros((len(priority_range),len(nvisits_range)))\n",
    "survey_time = np.zeros((len(priority_range),len(nvisits_range)))\n",
    "for i in range(0,len(priority_range),1):\n",
    "    galwfd = galPlane_survey_footprint(healpix_priority_minimum_threshold=priority_range[i])\n",
    "    survey_area = estimate_GP_survey_area(galwfd)\n",
    "    survey_time[i,:] = calc_survey_time(500, survey_area)\n",
    "    FoM[i,:] = GP_FoM_tau_footprint(nvisits_range,survey_area)\n",
    "FoM = np.flip(FoM,1)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(15,6))\n",
    "im = ax.imshow(FoM, interpolation='none')\n",
    "ax.set_xlabel('HEALpix priority minimum threshold')\n",
    "ax.set_ylabel('Nvisits/pointing')\n",
    "(xmin,xmax,ymin,ymax) = plt.axis()\n",
    "priority_intervals = np.arange(min_priority, max_priority, 0.1)\n",
    "nvisits_intervals = np.arange(min_nvisits,max_nvisits,100)\n",
    "plt.xticks(np.linspace(xmin,xmax,len(priority_intervals)), [str(round(p,1)) for p in priority_intervals])\n",
    "plt.yticks(np.linspace(ymin,ymax,len(nvisits_intervals)), [str(round(n)) for n in nvisits_intervals])\n",
    "plt.colorbar(im)\n",
    "plt.title('Normalized Galactic Science Figure of Merit for different survey parameters')\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "yincr = max_nvisits - min_nvisits\n",
    "y2entries = np.array([0.1,0.25, 0.5, 0.75])\n",
    "y2values = min_nvisits + y2entries*yincr\n",
    "y2range = estimate_visit_interval(y2values) / 24.0\n",
    "\n",
    "ax2.set_ylabel('Interval between visits [days]')\n",
    "ax2.set_yticks(y2entries)\n",
    "ax2.set_yticklabels([str(round(n,1)) for n in y2range])\n",
    "#ax2.invert_yaxis()\n",
    "(xmin2,xmax2,ymin2,ymax2) = ax2.axis()\n",
    "val_max = estimate_visit_interval(min_nvisits ) / 24.0\n",
    "val_min = estimate_visit_interval(max_nvisits) / 24.0\n",
    "\n",
    "# Box for tau_obs < 2.0 days [converted to hrs] - green line\n",
    "sval = calc_yval(2.0*24.0, max_nvisits, min_nvisits, ymin, ymax)\n",
    "rect = Rectangle((xmin, 0.0), (xmax-xmin), sval, linewidth=2, edgecolor='g', facecolor='none')\n",
    "ax.add_patch(rect)\n",
    "\n",
    "# Box for 2.0 < tau_obs < 20.0 days [converted to hrs] - magenta line\n",
    "sval1 = calc_yval(2.0*24.0, min_nvisits, max_nvisits, ymin, ymax)\n",
    "sval2 = calc_yval(20.0*24.0, min_nvisits, max_nvisits, ymin, ymax)\n",
    "dsval = sval2 - sval1\n",
    "rect = Rectangle((xmin, sval1), (xmax-xmin), dsval, linewidth=2, edgecolor='m', facecolor='none')\n",
    "ax.add_patch(rect)\n",
    "\n",
    "# Box for 20.0 < tau_obs < 73.0 days [converted to hrs] - blue line\n",
    "sval1 = calc_yval(20.0*24.0, min_nvisits, max_nvisits, ymin, ymax)\n",
    "sval2 = calc_yval(73.0*24.0, min_nvisits, max_nvisits, ymin, ymax)\n",
    "dsval = sval2 - sval1\n",
    "rect = Rectangle((xmin, sval1), (xmax-xmin), dsval, linewidth=2, edgecolor='b', facecolor='none')\n",
    "ax.add_patch(rect)\n",
    "\n",
    "# Box for tau_obs > 73.0 days [converted to hrs] - red line\n",
    "sval1 = calc_yval(73.0*24.0, min_nvisits, max_nvisits, ymin, ymax)\n",
    "sval2 = min(calc_yval(1000.0*24.0, min_nvisits, max_nvisits, ymin, ymax), ymin)\n",
    "dsval = sval2 - sval1\n",
    "rect = Rectangle((xmin, sval1), (xmax-xmin), 2, linewidth=2, edgecolor='r', facecolor='none')\n",
    "ax.add_patch(rect)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5baa4ab2-a0a2-4c13-82ac-a97e35b0a375",
   "metadata": {},
   "source": [
    "The figure above shows the normalized FoM calculated for a range of survey designs, where the colorbar indicates values of the FoM - higher values are better for the scientific return. \n",
    "\n",
    "The x-axis is inversely proportional to survey area.  \n",
    "\n",
    "The left-hand y-axis represents the number of pointings per field and the right-hand y-axis displays the corresponding interval between sequential observations.  \n",
    "\n",
    "The superimposed lines indicate the approximate regions where the interval between visits meets the requirements of the $\\tau_{obs}$ categories; the color of the box outlines correspond to the plot colors used in the plots of interval between obs vs. Nvisits.  \n",
    "\n",
    "Survey parameters above these lines should (to first order) serve the needs of the science cases within the corresponding variability timescale category and those with longer $\\tau_{obs}$, though the caveats above are again strongly emphasized.  Surveys with larger areas (i.e. a lower priority map threshold) will return proportionally higher science return by including more potential targets.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "271a8bf9-586b-4fb0-9486-0757502f2f6d",
   "metadata": {},
   "source": [
    "### Interpretation ###\n",
    "\n",
    "Rather than interpret these lines as hard-and-fast rules, we stress that the goal of these plots is to give an intuition regarding the survey designs that most suit the needs of a range of Galactic Plane science.  In general, smaller numbers of visits/pointing will restrict the science return to the longer categories of variability only.  However, a trade-off must be made regarding the total area surveyed, since much of the science interest in LSST is precisely because it will probe larger regions than could hitherto be explored, and for this reason we recommend a maximum priority threshold of ~0.4 (or lower) be used to select sky regions from the priority maps provided.  \n",
    "\n",
    "However, we again note that further optimizations are possible, including using the priority maps to optimize the filter selection used. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ddfee59",
   "metadata": {},
   "source": [
    "## Evaluating Survey Cadence and Season Length"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54fb8da8",
   "metadata": {},
   "source": [
    "In the discussion above we have considered only a fixed median visit interval ($\\Delta\\tau_{med}$), on the assumption that the observational cadence of every strategy will be uniform throughout the survey lifetime.  However, some survey strategies have highly non-uniform visit intervals, particularly the rolling cadence strategies.  To take this into account, the Figure of Merit above needs some refinement.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b39a8fad",
   "metadata": {},
   "source": [
    "Firstly, we design a metric to evaluate the scientific benefit of sequential observations taken at an interval of $\\Delta t$, by comparing this with $\\tau_{obs}$ for the four categories of variability.  Observations taken at intervals less than or equal to $\\tau_{obs}$ are by definition of high value, and return a metric value of 1.  Observations taken at intervals greater than $\\tau_{obs}$ are usually of some value, but the value deteriorates quite quickly with increasingly large gaps relative to $\\tau_{obs}$.  We represent this as an exponential decay function with a decay constant of 1/$\\tau_{obs}$ in the metric below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f7f6f629",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_visit_interval_metric(delta_t, tau_obs):\n",
    "    K = 1.0/tau_obs\n",
    "    \n",
    "    if type(delta_t) == type(5.0):\n",
    "        delta_t = np.array([delta_t])\n",
    "    \n",
    "    metric = np.zeros(len(delta_t))\n",
    "    idx = np.where(delta_t <= tau_obs)[0]\n",
    "    if len(idx) > 0:\n",
    "        metric[idx] = 1.0\n",
    "    \n",
    "    idx = np.where(delta_t > tau_obs)[0]\n",
    "    if len(idx) > 0:\n",
    "        metric[idx] = np.exp(-K*(delta_t[idx] - tau_obs))\n",
    "\n",
    "    return metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6b304055",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x173089490>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau_obs_range = [2.0, 10.0, 73.0]\n",
    "median_visit_intervals = np.array([1.0, 2.0, 4.0, 6.0, 8.0, 10.0, 50.0, 75.0, 100.0, 150.0, 200.0, 365.0])\n",
    "median_visit_intervals = np.arange(1.0, 365.0, 1.0)\n",
    "formats = ['r-','m-','b-']\n",
    "\n",
    "fig,ax = plt.subplots(1, 1, figsize=(10,10))\n",
    "for i,tau_obs in enumerate(tau_obs_range):\n",
    "    metric_data = calc_visit_interval_metric(median_visit_intervals, tau_obs)\n",
    "    ax.plot(median_visit_intervals, metric_data, formats[i], \n",
    "            label='$\\\\tau_{obs}$='+str(tau_obs)+'days')\n",
    "ax.set_xlabel('Median visit interval [days]')\n",
    "ax.set_ylabel('Metric')\n",
    "ax.set_title('Timescale metric calculated for different categories of variability timescale')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e816e0",
   "metadata": {},
   "source": [
    "Some survey strategies consist of a set of regular visits to a given field for a period we refer to as a \"season\", interspaced by much larger gaps between observing seasons; this is particularly true for the rolling cadence proposals.  To evaluate this, we modify the metric above to consider not just $\\Delta\\tau_{med}$ but also the maximum interval between visits, $\\Delta\\tau_{max}$.  We derive the median visit intervals as above, and simulate a range of maximum visit intervals up to a limit of 3 years to explore the behaviour of the proposed metric.  This limit was chosen based on the maximum length of the rolling cadence \"season\" currently being explored, that is dividing the sky into 3 regions.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df649747",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_visit_interval_season_metric(delta_t_median, delta_t_max, tau_obs):\n",
    "    K = 1.0/tau_obs\n",
    "    \n",
    "    if type(delta_t_median) == type(5.0):\n",
    "        delta_t = np.array([delta_t_median])\n",
    "    \n",
    "    if type(delta_t_max) == type(5.0):\n",
    "        delta_t = np.array([delta_t_max])\n",
    "    \n",
    "    terms = []\n",
    "    for dt in [delta_t_median, delta_t_max]:\n",
    "        term = np.zeros(len(dt))\n",
    "        idx = np.where(dt <= tau_obs)[0]\n",
    "        if len(idx) > 0:\n",
    "            term[idx] = 1.0\n",
    "\n",
    "        idx = np.where(dt > tau_obs)[0]\n",
    "        if len(idx) > 0:\n",
    "            term[idx] = np.exp(-K*(delta_t[idx] - tau_obs))\n",
    "        terms.append(term)\n",
    "    terms = np.array(terms)\n",
    "    metric = np.prod(terms, axis=1)\n",
    "    print(metric)\n",
    "    \n",
    "    return metric"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}