DP03_04a_Introduction_to_Phase_Curves.ipynb

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   "metadata": {},
   "source": [
    "<img align=\"left\" src = https://project.lsst.org/sites/default/files/Rubin-O-Logo_0.png width=250 style=\"padding: 10px\"> \n",
    "<br>\n",
    "<b>Phase Curve of Solar System Objects</b> <br>\n",
    "Contact authors: Christina Williams and Yumi Choi<br>\n",
    "Last verified to run: 2024-05-01 <br>\n",
    "LSST Science Piplines version: Weekly 2024_16 <br>\n",
    "Container Size: medium <br>\n",
    "Targeted learning level: intermediate <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9da1a210-d858-42fe-8591-570965b8be1a",
   "metadata": {},
   "source": [
    "**Description:** Explore phase curves for DP0.3 solar system objects. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80a0baf5-51ad-40ec-8991-060a7b27c289",
   "metadata": {},
   "source": [
    "**Skills:** Use the TAP service and ADQL to access the DP0.3 tables. Join information from multiple DP0.3 tables. Plot phase curves."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "393da88f-7978-4920-aa4a-a9830df6eed9",
   "metadata": {},
   "source": [
    "**LSST Data Products:** TAP tables dp03_catalogs_10yr.SSObject, dp03_catalogs_10yr.MPCORB, dp03_catalogs_10yr.DiaSource, dp03_catalogs_10yr.SSSource"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c67fab9-136a-4adc-bb42-142b91ab69dd",
   "metadata": {},
   "source": [
    "**Packages:** lsst.rsp.get_tap_service"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f72b27f",
   "metadata": {},
   "source": [
    "**Credit:**\n",
    "Inspired by a jupyter notebook developed by Queen's University Belfast Planet Lab (including Brian Rogers, Niall McElroy, and Meg Schwamb). References: <a href=\"https://ui.adsabs.harvard.edu/abs/2010Icar..209..542M/abstract\">Muinonen et al. (2010)</a> and <a href=\"http://astronotes.co.uk/blog/2018/05/28/determining-the-h-g-parameters-of-atlas-asteroid-phase-curves.html\">David Young's webpage.</a> Please consider acknowledging them if this notebook is used for the preparation of journal articles, software releases, or other notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a400d1bb-e1ec-4160-bd41-bc7ca953a97c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-07-27T17:55:39.523317Z",
     "iopub.status.busy": "2023-07-27T17:55:39.522902Z",
     "iopub.status.idle": "2023-07-27T17:55:40.035942Z",
     "shell.execute_reply": "2023-07-27T17:55:40.034503Z",
     "shell.execute_reply.started": "2023-07-27T17:55:39.523290Z"
    },
    "tags": []
   },
   "source": [
    "**Get Support:** Find DP0 documentation and resources at <a href=\"https://dp0.lsst.io\">dp0.lsst.io</a>. Questions are welcome as new topics in the <a href=\"https://community.lsst.org/c/support/dp0\">Support - Data Preview 0 Category</a> of the Rubin Community Forum. Rubin staff will respond to all questions posted there."
   ]
  },
  {
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snQm8jGX7xy97spV9yZ7s2SoV2ZJEQqnQLgohr1YphbKWvNmFlDZpU9kKiUL7YkslsqUQ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70fvE/RY0bRdq7vArHyZzNJB1Qmd+/eLQ/OXNuBaiTq4hB9BylzJXAYC6Jy8T+bJoGD8iPqvaDK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\nAAmQAAmQAAmQAAl4R+D/AIHPOWf+5R8zAAAAAElFTkSuQmCC\n"
    }
   },
   "cell_type": "markdown",
   "id": "cfc73be0",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 1. Introduction\n",
    "\n",
    "This notebook explores the properties of solar system bodies in the DP0.3 dataset by using the science example of constructing and exploring their phase curves. \n",
    "\n",
    "The DP0.3 catalogs contain both real and simulated solar system objects (including asteroids, near-Earth objects, Trojans, trans-Neptunian objects, comets). These objects change position between each Rubin image. In the DP0.3 catalogs, the intrinsic properties and orbital parameters are known, and are used to estimate what the measurements would be in a given image, and how they change between images. From these simulated observations, it is possible to reconstruct their intrinsic properties and orbital parameters in the same way as will be done using the real LSST data. An important way to characterize intrinsic properties of a solar system object is by measuring its \"phase curve\", which is the object brightness as a function of its \"solar phase angle\" (the angle made between the line of sight from the object to the Sun, and the line of sight from the object to Earth; see Figure 1.\n",
    "\n",
    "                                            \n",
    "![data/Buchheim2010.png](attachment:d51223c2-2573-4477-ac49-2b4f757f1681.png)\n",
    "\n",
    "\n",
    "Figure 1: Diagram showing the definition of phase angle $\\alpha$, credit [Buchheim 2010](https://articles.adsabs.harvard.edu/pdf/2010SASS...29..101B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3eaef36-ed53-450e-a3d6-5a2573469c50",
   "metadata": {},
   "source": [
    "In order to reveal the intrinsic properties of the asteroid (such as its surface properties and albedo, which helps determine its class of solar system body), we first must turn apparent magnitudes as a function of time (what is measured by LSST data) into \"reduced magnitude\", which takes into account the relative distances between the asteroid and the Sun/Earth (heliocentric/topocentric distances) at each observation. Reduced magnitude is normalized such that it is the brightness of an asteroid as if it is observed at 1 astronomical unit (au) from both the Sun and the Earth (i.e. unit topocentric and heliocentric distance). Note that rotation curves or complex geometry of solar system objects are not included in DP0.3 simulations. Thus, any changes over time in an object’s apparent magnitude are due only to changes in its distance and phase angle. Phase curves can be constructed for each filter.\n",
    "\n",
    "Modeling the phase curve (reduced magnitude $H(α)$ as a function of phase angle $α$) enables measurement of the absolute magnitude, $H$, defined as the brightness at 0 phase angle. The functional form can depend on the data quality and type of object targeted. In this tutorial, we will mention three functional forms that are relevant for understanding the DP0.3 data products. These are the `HG_model`, `HG1G2_model`, and `HG12_model`. The `HG_model` is the simplest model (see [Bowell et al. 1989](https://ui.adsabs.harvard.edu/abs/1989aste.conf..524B/abstract)), and has the form:\n",
    "\n",
    "$$H(α)=H−2.5log_{10}[(1−G)Φ_1(α)+GΦ_2(α)],$$\n",
    "\n",
    "where $Φ_n$ are basis functions (which allow for one to model non-linearity in the data, but maintain linearity in the fitted parameters). $Φ_n$ are normalized to unity at α=0 deg. This model provides a best fit for the slope parameter $G$ (from which surface properties can then be derived) and the absolute magnitude $H$. The `HG_model` $G$ and $H$ values are stored in the `dp03_catalogs_10yr.MPCORB` table. \n",
    "\n",
    "To better accommodate various observational effects (e.g., photometric quality, incomplete phase angle sampling) the more sophisticated `HG1G2_model` (a linear three-parameter function) and its nonlinear two-parameter version `HG12_model` were developed (see [Muinonen et al. 2010](https://ui.adsabs.harvard.edu/abs/2010Icar..209..542M/abstract)). The `HG1G2_model` has the form\n",
    "\n",
    "$$H(α)=H−2.5log_{10}[G_1Φ_1(α)+G_2Φ_2(α) + (1-G_1-G_2)Φ_3(α)],$$\n",
    "\n",
    "which now has three free parameters, $H$, $G_1$ and $G_2$. However, a third representation, the `HG12_model`, is generally very effective for deriving reliable values of absolute magnitude when the phase angle sampling is not optimal (e.g., poor phase angle coverage at a range of phase angle). Thus, the LSST data products will compute estimated parameters of the `HG12_model` and this will be the focus of this tutorial. The `HG12_model` expresses the $G_1$ and $G_2$ parameters as a piecewise linear function of a single parameter, $G_{12}$, \n",
    "\n",
    "for $G_{12}$ > 0.2\n",
    "$$G_1 = 0.9529\\times G_{12} + 0.02162$$\n",
    "$$G_2 = -0.6125\\times G_{12} + 0.5572$$\n",
    "for $G_{12}$ < 0.2\n",
    "$$G_1 = 0.7527\\times G_{12} + 0.06164$$\n",
    "$$G_2 = -0.9612\\times G_{12} + 0.6270$$\n",
    "\n",
    "This notebook will demonstrate how to plot the phase curve of solar system bodies using the DP0.3 simulated catalogs. Section 2 compares the phase curves for three different types of objects at different orbital radii from the Sun, and compares the data to the LSST pipeline measured phase curve parameters, `H`, and `G12`. Section 3 aggregates the phase curve fits for a number of solar system bodies in DP0.3 and shows how the quality of the fit depends on LSST observations (which additionally provides some insight into expectations for real LSST data)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bf722b4-8227-441f-9f3e-0f8140040fc1",
   "metadata": {
    "tags": []
   },
   "source": [
    "### 1.1 Package Imports\n",
    "\n",
    "The [matplotlib](https://matplotlib.org/) (and especially sublibrary `matplotlib.pyplot`), [numpy](http://www.numpy.org/), and [scipy](https://scipy.org/) libraries are widely used Python libraries for plotting and scientific computing, and model fitting.\n",
    "\n",
    "The `lsst.rsp` package provides access to the Table Access Protocol (TAP) service for queries to the DP0 catalogs.\n",
    "\n",
    "The [seaborn](https://seaborn.pydata.org/) package provides statistical data visualization with aesthetic and informative graphics.\n",
    "\n",
    "The [sbpy](https://sbpy.org) package is an `Astropy` affiliated package for small-body planetary astronomy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cddc1458",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import CubicSpline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sbpy.photometry import HG12\n",
    "\n",
    "from lsst.rsp import get_tap_service"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c217adff-25ed-4fce-95e7-8aa04630f6cc",
   "metadata": {},
   "source": [
    "### 1.2 Define Functions and Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a4a8b3b-91cf-4729-a707-99b7b11a5b8d",
   "metadata": {},
   "source": [
    "#### 1.2.1 Set up some plotting defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c780a382-5c5e-4f20-9ffd-7aa517c37146",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.style.use('tableau-colorblind10')\n",
    "params = {'axes.labelsize': 15,\n",
    "          'font.size': 15,\n",
    "          'legend.fontsize': 12}\n",
    "plt.rcParams.update(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d85070a-bf10-4290-b63a-2b5754151fa6",
   "metadata": {
    "tags": []
   },
   "source": [
    "Set up colors and plot symbols corresponding to the $g,r,i,z$ bands since there are no $u$ and $y$ band data in the DP0.3 catalogs. These colors are the same as those used for $g,r,i,z$ bands in Dark Energy Survey (DES) publications, and are defined in <a href=\"https://github.com/DarkEnergySurvey/descolors\">this github repository</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3d5cd10e-7ab9-42a3-ac3b-d12cee04966b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "filts = ['g', 'r', 'i', 'z']\n",
    "filter_colors = {'g': '#008060', 'r': '#ff4000', 'i': '#850000', 'z': '#6600cc'}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12ab5a66-b37d-4a3b-b207-b95a68c7a7a7",
   "metadata": {},
   "source": [
    "#### 1.2.2 Define functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45f9baa6-8055-45b0-b386-eef618872ff9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-14T22:18:36.823252Z",
     "iopub.status.busy": "2023-08-14T22:18:36.822151Z",
     "iopub.status.idle": "2023-08-14T22:18:36.830853Z",
     "shell.execute_reply": "2023-08-14T22:18:36.829469Z",
     "shell.execute_reply.started": "2023-08-14T22:18:36.823212Z"
    },
    "tags": []
   },
   "source": [
    "Define a function to convert a given perihelion distance (`q`) and eccentricity (`e`) to an orbital semi-major axis (`a`). Their relationship is defined by $q = a(1-e)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2a174fc-8a02-441a-b6f8-e89da81717ba",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def calc_semimajor_axis(q, e):\n",
    "    \"\"\"\n",
    "    Given a perihelion distance and orbital eccentricity,\n",
    "    calculate the semi-major axis of the orbit.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    q: ndarray\n",
    "        Distance at perihelion, in au.\n",
    "    e: ndarray\n",
    "        Orbital eccentricity.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    a: ndarray\n",
    "        Semi-major axis of the orbit, in au.\n",
    "        q = a(1-e), so a = q/(1-e)\n",
    "    \"\"\"\n",
    "\n",
    "    return q / (1.0 - e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec51ac0b",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 2. Plot the phase curves of asteroids in DP0.3 \n",
    "\n",
    "### 2.1 Create the Rubin TAP Service Client\n",
    "\n",
    "Get an instance of the TAP service, and assert that it exists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81b8cd59-1ba3-4eaa-846f-6478ed0c3cf5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "service = get_tap_service(\"ssotap\")\n",
    "assert service is not None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf968de5-ce59-41c9-88f0-83cd88bdc083",
   "metadata": {},
   "source": [
    "### 2.2 Querying the DP0.3 SSObject and MPCORB catalogs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "171e087c-b314-48f7-8f22-6013115f2cb9",
   "metadata": {},
   "source": [
    "To plot an object's phase curve, we will need its apparent magnitudes and uncertainties across a range of observation times. Additionally, we need the phase angles of the object at those observation times, topocentric ($d_t$) and heliocentric ($d_h$) distances.\n",
    "\n",
    "To define those mock observations of solar system objects, the DP0.3 model uses the `HG_model` form of the phase curve to predict the observed parameters (apparent magnitude) for each object. These \"truth\" values are defined in the MPCORB table as `mpcH` (intrinsic absolute magnitude in $V$ band) and `mpcG` (intrinsic slope). For the purposes of DP0.3, the intrinsic slope, `mpcG`, for all objects have a constant value of 0.15.\n",
    "\n",
    "In the SSObject table, the LSST data products contain the fitted phase curve parameters based on the mock observations using the `HG12_model` (i.e., the fitted absolute magnitude `H` and slope parameter `G12` based on mock observations in $griz$ bands). Note that the value of `G12` slope will differ from `G` owing to the difference in functional form (see Section 1.2). The explanation for the absence of $u$ and $y$ bands in DP0.3 catalogs can be found in the <a href=\"https://dp0-3.lsst.io/data-products-dp0-3/data-simulation-dp0-3.html\">DP0.3 documentation</a>.\n",
    "\n",
    "Limit the query to select sources with a large number of observations that likely have good phase curve fits (in the SSObject table, this is `numObs` > 100) and with perihelion distance of less than 50 au (in the MPCORB table, `q` < 50), and then further narrow down the sample to focus on Main Belt asteroids, Jupiter Trojans, and Trans-Neptunian Obects (TNOs) for this tutorial.  \n",
    "\n",
    "Define the table returned by this query as \"unique\" since it contains the IDs of unique solar system objects. Each object has multiple individual observations in each filter in LSST. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f93c0de6-8730-4adc-a0ab-9b795d3dc4e7",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "nobs_thrh = '100'\n",
    "q_thrh = '50'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9841c6de-f012-41e7-aae7-23da5c77e4e6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "query = \"\"\"\n",
    "SELECT\n",
    "    mpc.ssObjectId, mpc.e, mpc.q, mpc.mpcG, mpc.mpcH,\n",
    "    sso.arc, sso.numObs,\n",
    "    sso.g_H, sso.g_Herr, sso.g_G12, sso.g_G12err,\n",
    "    sso.g_H_gG12_Cov, sso.g_Ndata, sso.r_H, sso.r_Herr,\n",
    "    sso.r_G12, sso.r_G12err, sso.r_H_rG12_Cov, sso.r_Ndata,\n",
    "    sso.i_H, sso.i_Herr, sso.i_G12, sso.i_G12err, sso.i_H_iG12_Cov,\n",
    "    sso.i_Ndata, sso.z_H, sso.z_Herr, sso.z_G12, sso.z_G12err,\n",
    "    sso.z_H_zG12_Cov, sso.z_Ndata\n",
    "FROM\n",
    "    dp03_catalogs_10yr.MPCORB as mpc\n",
    "INNER JOIN dp03_catalogs_10yr.SSObject as sso\n",
    "ON mpc.ssObjectId = sso.ssObjectId\n",
    "WHERE sso.numObs > {} AND mpc.q < {} ORDER by sso.ssObjectId\n",
    "\"\"\".format(nobs_thrh, q_thrh)\n",
    "\n",
    "uniqueObj = service.search(query).to_table()\n",
    "uniqueObj"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23c0099e-4761-4140-8aa9-21205abae17a",
   "metadata": {},
   "source": [
    "### 2.3 Identify Main Belt asteroids, Jupiter Trojans, and TNOs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac8fd696-22ab-49f2-acd1-8e5cf8c53a8e",
   "metadata": {},
   "source": [
    "First calculate the semi-major axis (`a`) of each object's orbit. Second, construct a Main Belt asteroid sample, a Jupiter Trojan sample, and a Trans-Neptunian Object (TNO) sample following the population definitions used by the JPL Horizons small body database query tool (https://ssd.jpl.nasa.gov/tools/sbdb_query.html): Main Belt asteroids (2.0 < `a` < 3.25 au and `q` > 1.666 au); Jupiter Trojans (4.6 < `a` < 5.5 au and `e` < 0.3), and finally TNOs which are at `a` > 30.1 au. We further limit our sample to the asteroids with `numObs` > 2000, to focus on objects with many individual observations to define its phase curve. (Note that the query for unique objects in Section 2.2 used a less-restrictive `numObs` > 100, which will used to explore the empirical properties that can influence phase curve fitting later in Section 3 and the followup tutorial notebook 04b).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17787417-b2ea-4361-888f-0525f8867f03",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "a = calc_semimajor_axis(uniqueObj['q'], uniqueObj['e'])\n",
    "\n",
    "main_belt = (a > 2.0) & (a < 3.2) & (uniqueObj['q'] > 1.666)\n",
    "main_belt_2k = (uniqueObj['numObs'] > 2000) & main_belt\n",
    "\n",
    "JT = (a > 4.6) & (a < 5.5) & (uniqueObj['e'] < 0.3)\n",
    "JT_2k = (uniqueObj['numObs'] > 2000) & JT\n",
    "\n",
    "TNO = (a > 30.1)\n",
    "TNO_2k = (uniqueObj['numObs'] > 2000) & TNO\n",
    "\n",
    "print('There are %d asteroids in this sample!' % len(a[main_belt_2k]))\n",
    "print('There are %d Jupiter Trojans in this sample!' % len(a[JT_2k]))\n",
    "print('There are %d TNOs in this sample!' % len(a[TNO_2k]))\n",
    "\n",
    "all_2k = main_belt_2k + JT_2k + TNO_2k"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87eec25f-6d14-47e5-b7f1-e0bdb7dcf774",
   "metadata": {},
   "source": [
    "Visualize the distributions of the semi-major axis `a` for the all unique objects in the 3 different populations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47510b0c-5b4a-47de-8a6a-75998d39c161",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "h = plt.hist(a[main_belt_2k], bins=25, range=(1, 7),\n",
    "             label='Main Belt asteroids', alpha=.5)\n",
    "h = plt.hist(a[JT_2k], bins=25, range=(1, 7),\n",
    "             label='Jupiter Trojans', alpha=.5)\n",
    "h = plt.hist(a[TNO_2k], bins=50, range=(1, 60), label='TNOs', alpha=.5)\n",
    "\n",
    "plt.xlabel('Semi-major axis [au]')\n",
    "plt.ylabel('Number')\n",
    "plt.yscale('log')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "977dd781-f675-4ed4-89ac-07cb6042515e",
   "metadata": {},
   "source": [
    "### 2.4 Identify individual mock observations of the solar system bodies in DP0.3 DiaSource and SSSource catalogs \n",
    "\n",
    "While there are unique solar system objects in the `SSObject` and `MPCORB` tables, these objects will be observed many times over the full LSST survey. Individual observations of each unique object in each filter are recorded in the `SSSource` and `diaSource` tables. Below, we query these tables to obtain all of the individual observed time series data (we call `indivObs`) for the solar system bodies that have >2000 observations as selected above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb665e68-f274-4c50-9b82-4899b084c33a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "query = \"\"\"\n",
    "SELECT\n",
    "    dia.ssObjectId, dia.diaSourceId, dia.mag,\n",
    "    dia.magErr, dia.band, dia.midPointMjdTai,\n",
    "    sss.phaseAngle, sss.topocentricDist, sss.heliocentricDist\n",
    "FROM\n",
    "    dp03_catalogs_10yr.DiaSource as dia\n",
    "INNER JOIN\n",
    "    dp03_catalogs_10yr.SSSource as sss\n",
    "ON\n",
    "    dia.diaSourceId = sss.diaSourceId\n",
    "WHERE\n",
    "    dia.ssObjectId\n",
    "    IN {}\n",
    "ORDER by dia.ssObjectId\n",
    "\"\"\".format(tuple(uniqueObj['ssObjectId'][all_2k]))\n",
    "\n",
    "indivObs = service.search(query).to_table()\n",
    "indivObs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e366f714-8078-40a5-9eee-65639fa293ca",
   "metadata": {},
   "source": [
    "Confirm that the number of unique objects in `indivObs` is identical to that of the asteroids with > 2000 observations in `uniqueObj`, as they should be."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "077c9400-f3fe-422d-bb2b-7ad0f2587e3d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "assert len(uniqueObj[all_2k]) == len(np.unique(indivObs['ssObjectId']))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f57f57e2-a386-46af-a527-73d397658b72",
   "metadata": {},
   "source": [
    "### 2.5 Plot the phase curve for a unique Main Belt asteroid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "392ff14e-eca1-4677-8de8-4dae0e6811bc",
   "metadata": {
    "tags": []
   },
   "source": [
    "To plot the phase curve, it is necessary to first compute the reduced magnitude $H(\\alpha)$ for each observation in each filter ($g,r,i,z$ for DP0.3), and add it as a column to the `indivObs` table of individual observations. The reduced magnitude $H(\\alpha)$ as mentioned in Introduction is the normalized apparent magnitude of an asteroid as if it is observed at 1 au from both the Sun and the Earth as a function of phase angle $\\alpha$, once accounting for the relative distances between the asteroid, and both Sun and Earth:\n",
    "\n",
    "$$H(α) = m−5log_{10}(d_t\\times\\,d_h),$$\n",
    "\n",
    "where $m$ is the apparent magnitude, and $d_t$ and $d_h$ are the topocentric and heliocentric distances of the object at the time of each observation. \n",
    "\n",
    "Note that the phase curves of solar system objects vary by observed filter, due to a combination of reflectivity of the surface and the intrinsic solar spectrum. For reference, to define the intrinsic absolute magnitude in DP0.3, the wavelength used to input the intrinsic absolute magnitude is in the $V$ band. Thus, one should not expect the absolute magnitude from any one filter to line up with the \"truth\" absolute magnitude, since none of the LSST filters include $V$ band. The conversion between each of the LSST filters and $V$ are documented for solar system bodies, and can be found in the <a href=\"https://github.com/lsst/dp0-3_lsst_io/blob/main/data-products-dp0-3/data-simulation-dp0-3.rst\">DP0.3 documentation</a>.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a387ad4-6057-4631-84fc-da9f99559b26",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "thdist = indivObs['topocentricDist']*indivObs['heliocentricDist']\n",
    "reduced_mag = indivObs['mag'] - 5.0*np.log10(thdist)\n",
    "\n",
    "indivObs.add_column(reduced_mag, name='reducedMag')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b47093f8-45bf-4bf0-9d17-bdc06eeac679",
   "metadata": {},
   "source": [
    "The cell below will plot example phase curves in all available filters (in DP0.3) $g$,$r$,$i$,$z$ for a single object referenced by its ssObjectId, here called `sId`. (Explore different objects by changing the `iObj` index to retrieve different sources). Below, it is clear that the reduced magnitude and phase curve of the source are offset from each other in each filter, reflecting the variation in brightness of asteroids in different filters. \n",
    "\n",
    "It is possible to pick an integer number between 0 and `len(uniqueObj[main_belt_2k])-1` for `iObj` below to explore other objects.\n",
    "\n",
    "The `HG12_model`-predicted phase curve is also overplotted to visualize the LSST pipeline phase curve fitting (dashed line). This demonstrates how absolute magnitude `H` is determined in the LSST data products."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "13275b12-39da-44f4-b51b-0dfeefeef3d3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "iObj = 1\n",
    "sId = uniqueObj['ssObjectId'][main_belt_2k][iObj]\n",
    "tmp = indivObs[indivObs['ssObjectId'] == sId]\n",
    "phases = np.linspace(0, 90, 100)\n",
    "\n",
    "\n",
    "for i, ifilt in enumerate(filts):\n",
    "    idx = tmp['band'] == ifilt\n",
    "\n",
    "    # Plot observations\n",
    "    plt.errorbar(tmp['phaseAngle'][idx], tmp['reducedMag'][idx],\n",
    "                 yerr=tmp['magErr'][idx], fmt='.',\n",
    "                 color=filter_colors[ifilt], alpha=0.5)\n",
    "\n",
    "    # Plot HG12 model\n",
    "    HG12_mag = HG12.evaluate(np.deg2rad(phases), \n",
    "                             uniqueObj[ifilt+'_H'][main_belt_2k][iObj], \n",
    "                             uniqueObj[ifilt+'_G12'][main_belt_2k][iObj])\n",
    "    plt.plot(phases, HG12_mag, color=filter_colors[ifilt], linestyle='--',\n",
    "             label='HG12 2-parameter model in %s' % ifilt)    \n",
    "\n",
    "\n",
    "plt.xlim(tmp['phaseAngle'].min()-5, tmp['phaseAngle'].max()+5)\n",
    "plt.ylim(tmp['reducedMag'].max()+0.5, tmp['reducedMag'].min()-0.5)\n",
    "plt.xlabel('Phase Angle [deg]')\n",
    "plt.ylabel('Reduced magnitude [mag]')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1.0), loc='upper left', ncol=1)\n",
    "plt.title('Main Belt Asteroid')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b97b3443-a858-4701-8a92-b97cad2e9fff",
   "metadata": {},
   "source": [
    "The cell below compares the phase curve of one object from each of the three populations selected in Section 2.3: the Main Belt asteroids, with the more distant Jupiter Trojans and the TNOs. The color scheme is the same as the cell above. This cell must be executed after running the above cell first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e8e4ac2-fe43-4f04-a32d-42bc28a41a59",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(13, 4))\n",
    "\n",
    "plt.subplot(131)\n",
    "for i, ifilt in enumerate(filts):\n",
    "    idx = tmp['band'] == ifilt\n",
    "\n",
    "    # Plot observations\n",
    "    plt.errorbar(tmp['phaseAngle'][idx], tmp['reducedMag'][idx],\n",
    "                 yerr=tmp['magErr'][idx], fmt='.',\n",
    "                 color=filter_colors[ifilt], alpha=0.5)\n",
    "\n",
    "    # Plot HG12 model\n",
    "    HG12_mag = HG12.evaluate(np.deg2rad(phases), \n",
    "                             uniqueObj[ifilt+'_H'][main_belt_2k][iObj],\n",
    "                             uniqueObj[ifilt+'_G12'][main_belt_2k][iObj])\n",
    "    plt.plot(phases, HG12_mag, color=filter_colors[ifilt], linestyle='--')\n",
    "\n",
    "\n",
    "plt.xlim(tmp['phaseAngle'].min()-5, tmp['phaseAngle'].max()+5)\n",
    "plt.ylim(tmp['reducedMag'].max()+0.5, tmp['reducedMag'].min()-0.5)\n",
    "plt.xlabel('Phase Angle [deg]')\n",
    "plt.ylabel('Reduced magnitude [mag]')\n",
    "plt.title('Main Belt Asteroid')\n",
    "\n",
    "plt.subplot(132)\n",
    "\n",
    "iObj = 2\n",
    "sId = uniqueObj['ssObjectId'][JT_2k][iObj]\n",
    "tmp = indivObs[indivObs['ssObjectId'] == sId]\n",
    "\n",
    "for i, ifilt in enumerate(filts):\n",
    "    idx = tmp['band'] == ifilt\n",
    "\n",
    "    # Plot observations\n",
    "    plt.errorbar(tmp['phaseAngle'][idx], tmp['reducedMag'][idx],\n",
    "                 yerr=tmp['magErr'][idx], fmt='.',\n",
    "                 color=filter_colors[ifilt], alpha=0.5)\n",
    "\n",
    "    # Plot HG12 model\n",
    "    HG12_mag = HG12.evaluate(np.deg2rad(phases),\n",
    "                             uniqueObj[ifilt+'_H'][JT_2k][iObj],\n",
    "                             uniqueObj[ifilt+'_G12'][JT_2k][iObj])\n",
    "    plt.plot(phases, HG12_mag, color=filter_colors[ifilt], linestyle='--')\n",
    "\n",
    "\n",
    "plt.xlim(tmp['phaseAngle'].min()-5, tmp['phaseAngle'].max()+5)\n",
    "plt.ylim(tmp['reducedMag'].max()+0.5, tmp['reducedMag'].min()-0.5)\n",
    "plt.xlabel('Phase Angle [deg]')\n",
    "plt.ylabel('Reduced magnitude [mag]')\n",
    "plt.title('Jupiter Trojans')\n",
    "\n",
    "plt.subplot(133)\n",
    "iObj = 3\n",
    "sId = uniqueObj['ssObjectId'][TNO_2k][iObj]\n",
    "tmp = indivObs[indivObs['ssObjectId'] == sId]\n",
    "\n",
    "for i, ifilt in enumerate(filts):\n",
    "    idx = tmp['band'] == ifilt\n",
    "\n",
    "    # Plot observations\n",
    "    plt.errorbar(tmp['phaseAngle'][idx], tmp['reducedMag'][idx],\n",
    "                 yerr=tmp['magErr'][idx], fmt='.',\n",
    "                 color=filter_colors[ifilt], alpha=0.5)\n",
    "\n",
    "plt.xlim(tmp['phaseAngle'].min()-.5, tmp['phaseAngle'].max()+.5)\n",
    "plt.ylim(tmp['reducedMag'].max()+0.5, tmp['reducedMag'].min()-0.5)\n",
    "plt.xlabel('Phase Angle [deg]')\n",
    "plt.ylabel('Reduced magnitude [mag]')\n",
    "plt.title('TNO')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aca692be-f1b7-46b0-b261-3ae66491baf6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-17T21:29:13.791091Z",
     "iopub.status.busy": "2023-08-17T21:29:13.790122Z",
     "iopub.status.idle": "2023-08-17T21:29:14.157843Z",
     "shell.execute_reply": "2023-08-17T21:29:14.157116Z",
     "shell.execute_reply.started": "2023-08-17T21:29:13.791050Z"
    },
    "tags": []
   },
   "source": [
    "Notice that the the phase coverage of objects at different semi-major axes are dramatically different. The most distant (>30.1 au) TNO will cover at most ~0-3 degrees in phase, and this is expected because they are too distant to have long phase angle coverage. Meanwhile, asteroids in the main belt will typically achieve between 0-30 degrees in terms of phase coverage. The LSST pipeline will only attempt to fit phase curves to things with more than 5 degrees of phase coverage, so the SSObject table does not include `H`, `G12` parameters for TNOs. Thus, TNOs do not have any models over-plotted. In these cases, it could be useful to independently model the phase curve using user-defined functions (e.g. for TNOs, a linear fit can be sufficient)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90bfc05-7f77-49a8-8db8-3bb1d1186471",
   "metadata": {},
   "source": [
    "### 2.6 Explore phase curve fit uncertainty in each filter\n",
    "\n",
    "For one of the Main Belt asteroids with > 2000 observations, the plot below compares the $g$- and $z$-bands to demonstrate fit uncertainty between two filters that produce different reduced magnitude quality (mostly due to difference in brightness and therefore flux uncertainties between the filters). The cell also computes the model phase curve for a given set of the best-fit phase curve parameters for the `HG12_model` stored in `SSObject` table, which is called `HG12_mag_sso`. The plot shows the uncertainty in the model parameters represented by the shaded regions. Choosing fainter or less well-sampled SSObjects increases the error region.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b072f76-a90b-4a75-89ff-65cc00c8c1cf",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "iObj = 3\n",
    "sId = uniqueObj['ssObjectId'][main_belt_2k][iObj]\n",
    "tmp = indivObs[indivObs['ssObjectId'] == sId]\n",
    "\n",
    "for ifilt in ['g', 'z']:\n",
    "    idx = tmp['band'] == ifilt\n",
    "    plt.errorbar(tmp['phaseAngle'][idx], tmp['reducedMag'][idx],\n",
    "                 yerr=tmp['magErr'][idx], fmt='o',\n",
    "                 color=filter_colors[ifilt], label=ifilt, zorder=10)\n",
    "\n",
    "    HG12_mag_sso = HG12.evaluate(np.deg2rad(phases),\n",
    "                                 uniqueObj[ifilt+'_H'][main_belt_2k][iObj],\n",
    "                                 uniqueObj[ifilt+'_G12'][main_belt_2k][iObj])\n",
    "    plt.plot(phases, HG12_mag_sso, '--', alpha=0.3, color=filter_colors[ifilt])\n",
    "\n",
    "    # Compute min/max values in reduced mag at each phase angle\n",
    "    p1 = HG12.evaluate(np.deg2rad(phases),\n",
    "                       uniqueObj[ifilt+'_H'][main_belt_2k][iObj] + 3*uniqueObj[ifilt+'_Herr'][main_belt_2k][iObj],\n",
    "                       uniqueObj[ifilt+'_G12'][main_belt_2k][iObj] + 3*uniqueObj[ifilt+'_G12err'][main_belt_2k][iObj])\n",
    "\n",
    "    p2 = HG12.evaluate(np.deg2rad(phases), \n",
    "                       uniqueObj[ifilt+'_H'][main_belt_2k][iObj] - 3*uniqueObj[ifilt+'_Herr'][main_belt_2k][iObj],\n",
    "                       uniqueObj[ifilt+'_G12'][main_belt_2k][iObj] + 3*uniqueObj[ifilt+'_G12err'][main_belt_2k][iObj])\n",
    "\n",
    "    p3 = HG12.evaluate(np.deg2rad(phases),\n",
    "                       uniqueObj[ifilt+'_H'][main_belt_2k][iObj] + 3*uniqueObj[ifilt+'_Herr'][main_belt_2k][iObj],\n",
    "                       uniqueObj[ifilt+'_G12'][main_belt_2k][iObj] - 3*uniqueObj[ifilt+'_G12err'][main_belt_2k][iObj])\n",
    "\n",
    "    p4 = HG12.evaluate(np.deg2rad(phases),\n",
    "                       uniqueObj[ifilt+'_H'][main_belt_2k][iObj] - 3*uniqueObj[ifilt+'_Herr'][main_belt_2k][iObj],\n",
    "                       uniqueObj[ifilt+'_G12'][main_belt_2k][iObj] - 3*uniqueObj[ifilt+'_G12err'][main_belt_2k][iObj])\n",
    "\n",
    "    HG_magHigh = np.maximum(np.maximum(p1, p2), np.maximum(p3, p4))\n",
    "    HG_magLow = np.minimum(np.minimum(p1, p2), np.minimum(p3, p4))\n",
    "\n",
    "    plt.fill_between(phases, HG_magLow, HG_magHigh, alpha=0.3, color=filter_colors[ifilt])\n",
    "\n",
    "plt.xlim(tmp['phaseAngle'].min()-5, tmp['phaseAngle'].max()+5)\n",
    "plt.ylim(tmp['reducedMag'].max()+0.5, tmp['reducedMag'].min()-0.5)\n",
    "plt.xlabel('Phase Angle [deg]')\n",
    "plt.ylabel('Reduced magnitude [mag]')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1.0), loc='upper left')\n",
    "plt.title('ssObjectId = %d' % sId)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "772e11d9-c007-41e5-86f3-5ee1052b18fb",
   "metadata": {},
   "source": [
    "# 3. Exploring phase curve data products from the DP0.3 SSObject and MPCORB catalogs \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40c839dd-80a3-4c7e-8255-ddeb01a92fba",
   "metadata": {},
   "source": [
    "### 3.1 Distribution of H and G12 parameters in observed filters\n",
    "\n",
    "This section explores the distribution of typical values of the `G12` slope parameter as a function of absolute magnitudes for Main Belt asteroids and Jupiter Trojans. Due to small phase angle coverage, nearly all of TNOs do not have measured phase curve parameters. Remember that the input (truth) `G` value using the `HG_model` that was used to generate the DP0.3 simulated object's observed properties was fixed across the population to a constant value of `G`=0.15. The DP0.3 automated phase curve fitting (which uses `HG12_model`) produces a nearly constant value for `G12` with a relatively small spread at bright magnitudes, and the scatter in measured `G12` starts to deviate more substantially at fainter magnitudes where its likely harder to recover the intrinsic value.\n",
    "\n",
    "> **Warnings:** the following cell produces `RuntimeWarning` messages about invalid values which can be ignored. They are due to taking the log of the occasional negative or NaN value in the catalog. Those points will not show in the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04ceaa25-e7a4-4e7d-a2bd-3750bf188d05",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(10, 8))\n",
    "gs = fig.add_gridspec(2, 2, wspace=0.1, hspace=0.2)\n",
    "axs = gs.subplots(sharex=True, sharey=True)\n",
    "axs = axs.ravel()\n",
    "\n",
    "\n",
    "for i, ifilt in enumerate(filts):\n",
    "    sns.histplot(x=uniqueObj[ifilt+'_H'], y=uniqueObj[ifilt+'_G12'],\n",
    "                 bins=100, log_scale=(False, True), ax=axs[i])\n",
    "    axs[i].scatter(uniqueObj[ifilt+'_H'][main_belt],\n",
    "                   uniqueObj[ifilt+'_G12'][main_belt],\n",
    "                   s=3, c='m', alpha=0.3, label='Main Belt asteroids')\n",
    "    axs[i].scatter(uniqueObj[ifilt+'_H'][JT],\n",
    "                   uniqueObj[ifilt+'_G12'][JT],\n",
    "                   s=3, c='k', alpha=0.1, label='Jupiter Trojans')\n",
    "    axs[i].text(10, 5, ifilt+'-band')\n",
    "    axs[i].set(xlabel=None)\n",
    "    axs[i].set(ylabel=None)\n",
    "\n",
    "axs[0].legend(loc=3, fontsize=10)\n",
    "plt.xlim(9, 25)\n",
    "plt.ylim(1e-2, 1e1)\n",
    "\n",
    "fig.supxlabel('Absolute magnitude, H [mag]')\n",
    "fig.supylabel('Slope parameter, G12')\n",
    "print(len(uniqueObj), len(uniqueObj[main_belt_2k]),\n",
    "      len(uniqueObj[JT_2k]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df408bac-a77a-4997-b946-b8f12bda924c",
   "metadata": {},
   "source": [
    "### 3.2 Phase curve fit uncertainty vs. apparent brightness of the Main Belt asteroids"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b75ee539-b0a8-4290-a59c-e5452d138600",
   "metadata": {
    "tags": []
   },
   "source": [
    "This section compares the typical apparent magnitude uncertainties per filter to see how that impacts the fit. First, compute the median apparent magnitude (i.e. as observed) and its median uncertainty in the $r$-band in this example. This enables plotting phase curve parameters vs. median apparent magnitude and its median uncertainty to see how these observational characteristics impact the resulting modeling. One can see in the plot that as objects get fainter and the median apparent magnitude uncertainty increases, so does the uncertainty in the fitted parameters of the phase curve. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eae70ca2-c3fa-4ae7-9020-aaaab89aab83",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "mag_med = []\n",
    "magSigma_med = []\n",
    "ifilt = 'r'\n",
    "\n",
    "for iobj in uniqueObj['ssObjectId'][main_belt_2k]:\n",
    "    idx = indivObs['ssObjectId'] == iobj\n",
    "    tmp = indivObs[idx]\n",
    "    idx_filt = tmp['band'] == ifilt\n",
    "\n",
    "    mag_med.append(np.ma.median(tmp['mag'][idx_filt]))\n",
    "    magSigma_med.append(np.ma.median(tmp['magErr'][idx_filt]))\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(mag_med, uniqueObj[ifilt+'_Herr'][main_belt_2k], '.', alpha=.5,\n",
    "         label=ifilt+'-band H parameter')\n",
    "plt.plot(mag_med, uniqueObj[ifilt+'_G12err'][main_belt_2k], '.', alpha=.5,\n",
    "         label=ifilt+'-band G12 parameter')\n",
    "plt.ylabel('Uncertainty in phase curve fit')\n",
    "plt.xlabel('Median apparent mag')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(magSigma_med, uniqueObj[ifilt+'_Herr'][main_belt_2k],\n",
    "         '.', alpha=.5)\n",
    "plt.plot(magSigma_med, uniqueObj[ifilt+'_G12err'][main_belt_2k],\n",
    "         '.', alpha=.5)\n",
    "plt.ylabel('Uncertainty in phase curve fit')\n",
    "plt.xlabel('Median uncertainty in apparent mag')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e16f0a8-8caa-4259-8c8c-16ccfed6ee22",
   "metadata": {},
   "source": [
    "### 3.3 Phase curve fit uncertainty vs. total number of LSST observations and perihelion distance\n",
    "\n",
    "This section explores the impact of the total number of observations for a given source (`numObs`) and the perihelion distance (`q`) on the quality of phase curve fitting in $i$-band as an example. In the left columns, it is clear that the model uncertainties decrease with number of observations of each source. So as LSST accumulates data over time, precision in the phase curve modeling will improve. The right columns show that uncertainties in the phase curve parameters modestly increase for objects with larger perihelion distances. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f572d01-6e33-4107-b125-0134ba141500",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "gs = fig.add_gridspec(2, 2, wspace=0, hspace=0.7)\n",
    "axs = gs.subplots(sharey=True)\n",
    "ifilt = 'i'\n",
    "\n",
    "sns.histplot(x=uniqueObj['numObs'], y=uniqueObj[ifilt+'_Herr'], bins=100,\n",
    "             log_scale=(False, True), ax=axs[0, 0])\n",
    "axs[0, 0].set_xlabel('Number of LSST observations')\n",
    "axs[0, 0].set_ylabel(r'$\\Delta$H in %s band' % ifilt)\n",
    "plt.ylim(1e-4, 3e1)\n",
    "\n",
    "sns.histplot(x=uniqueObj['q'], y=uniqueObj[ifilt+'_Herr'],\n",
    "             bins=100, ax=axs[0, 1])\n",
    "axs[0, 1].set_xlabel('perihelion distance [au]')\n",
    "\n",
    "sns.histplot(x=uniqueObj['numObs'], y=uniqueObj[ifilt+'_G12err'],\n",
    "             bins=100, log_scale=(False, True), ax=axs[1, 0])\n",
    "axs[1, 0].set_xlabel('Number of LSST observations')\n",
    "axs[1, 0].set_ylabel(r'$\\Delta$G12 in %s band' % ifilt)\n",
    "\n",
    "sns.histplot(x=uniqueObj['q'], y=uniqueObj[ifilt+'_G12err'],\n",
    "             bins=100, ax=axs[1, 1])\n",
    "axs[1, 1].set_xlabel('perihelion distance [au]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91ac8944-997e-4bb4-8cd8-c8817cd44253",
   "metadata": {
    "tags": []
   },
   "source": [
    "### 3.4 Number of datapoints used for phase curve fitting per band\n",
    "\n",
    "The above plots compare `numObs` (total in all bands) with model fits (per band) which may not be the ideal metric since the quality of phase curves can vary quite a bit between filters. Instead, one can look at the number of datapoints included in the phase curve modeling on a per filter basis (i.e. `rNdata` for the r-band in the `SSObject` table). The next plot looks at the distribution of the number of observations in each filter used to model the phase curve per filter. One can see that generally, $r$- and $i$-bands produce the most data points for recovering phase curves, while $g$-band produces less and $z$-band produces the fewest. Phase curves measured in $r$- and $i$-bands will thus be better sampled. \n",
    "\n",
    "Thus in the second panel, one can see that poorer sampling drives higher uncertainty in `H` using $z$-band instead of $r$-band for solar system objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a37e63c9-6d7a-47d7-afe1-8f20aad2794a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "for i, ifilt in enumerate(filts):\n",
    "    axs[0].hist(uniqueObj[ifilt+'_Ndata'], bins=100, range=(0, 1300),\n",
    "                histtype='step', color=filter_colors[ifilt], label=ifilt+'-band')\n",
    "\n",
    "axs[0].set_yscale('log')\n",
    "axs[0].set_xscale('log')\n",
    "axs[0].legend()\n",
    "axs[0].set_xlabel('Number of data points per filter')\n",
    "axs[0].set_ylabel('Number of sources')\n",
    "\n",
    "sns.histplot(x=uniqueObj['r_Herr'], y=uniqueObj['z_Herr'],\n",
    "             bins=100, log_scale=(True, True), color='b', ax=axs[1], alpha=0.7)\n",
    "\n",
    "one2one = np.arange(1e-4, 1000, .1)\n",
    "axs[1].plot(one2one, one2one, '--')\n",
    "axs[1].set_ylim(1e-4, 1e2)\n",
    "axs[1].set_xlim(1e-4, 1e2)\n",
    "axs[1].set_ylabel(r'$\\Delta$H using z-band')\n",
    "axs[1].set_xlabel(r'$\\Delta$H using r-band')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f880c4d0-6ffc-49e9-86f2-95f1b698e279",
   "metadata": {},
   "source": [
    "## 4. Excercises for the learner\n",
    "\n",
    "1. Try out the more advanced companion tutorial notebook 04b on explicitly modeling phase curves and comparing with the `HG12` model parameters stored in the DP0.3."
   ]
  }
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