TransitTutorial.ipynb

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  "metadata": {
    "colab": {
      "name": "TransitTutorial.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOZreZMrgH/jg1SQ8AIGL3V",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/aashrat/stemtoshtem/blob/master/TransitTutorial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vy9SxTSoojo0",
        "colab_type": "text"
      },
      "source": [
        "We'll need to install the kplr package (documentation found here: http://dfm.io/kplr/). The lightkurve package is more commonly used (https://docs.lightkurve.org/tutorials/02-recover-a-planet.html), but it is less compatible with google colab."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cbkf1RcEoCOO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "ffa0cac7-fe4f-4b91-f906-3d230c2df28f"
      },
      "source": [
        "pip install kplr"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: kplr in /usr/local/lib/python3.6/dist-packages (0.2.2)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from kplr) (1.12.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PJeUqfIQrH6O",
        "colab_type": "text"
      },
      "source": [
        "### Exoplanets\n",
        "To find an exoplanet, I'd first recommend going to this page: https://en.wikipedia.org/wiki/List_of_exoplanets_discovered_using_the_Kepler_space_telescope and finding an exoplanet with a Wikipedia page. I'd recommend choosing a planet with only a b-component, but if you are interested in finding a multi-planet system, message me and I can help! Once you find your planet, go to https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=cumulative and type in the planet name under Kepler name. The column next to Kepler name will give you the planet's KOI name, which you will need later. Everything after the K and the 0's is the KOI number (ex. if the table says KOO752.01, the number is 752.01).\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cPl_g8lfpkck",
        "colab_type": "text"
      },
      "source": [
        "### Kepler 5b\n",
        "Kepler 5b (https://en.wikipedia.org/wiki/Kepler-5b) is one of the first 5 confirmed exoplanets discovered by the Kepler mission. The discovery of Kepler 5b was announced in 2010. It is a hot Jupiter orbiting a subgiant star. (https://en.wikipedia.org/wiki/Kepler-5)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K--ufhZjoc-J",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#importing necessary packages\n",
        "#importing packages to handle math\n",
        "import numpy as np\n",
        "import math\n",
        "\n",
        "#importing packages to store data in tables\n",
        "import astropy\n",
        "from astropy.table import Table\n",
        "import pandas as pd\n",
        "\n",
        "#importing plotting packages\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "#plotting inline\n",
        "%matplotlib inline\n",
        "\n",
        "#importing kplr package\n",
        "import kplr"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QXC4B8o6q6tK",
        "colab_type": "text"
      },
      "source": [
        "In the cell below, *only* change the koi number (here it is 18.01) and keep everything else the same.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t5ma2_cdpnBz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#reading in kepler light curve\n",
        "client = kplr.API()\n",
        "koi = client.koi(18.01) # Find the target KOI, using your KOI number\n",
        "lcs = koi.get_light_curves(short_cadence=False) # Get list of datasets.\n",
        "f = lcs[0].open() # open the first light-curve dataset\n",
        "hdu_data = f[1].data\n",
        "time = hdu_data[\"time\"] # get the time of each observation\n",
        "flux = hdu_data[\"sap_flux\"] # get the flux\n",
        "flux_err = hdu_data[\"sap_flux_err\"] # get the error in the flux\n",
        "f.close()"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eKvWRzDGqBLl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "92a86581-1feb-4342-ffc9-89d70a901b91"
      },
      "source": [
        "#plotting the lightcurve, this is what part of a light curve looks like!\n",
        "plt.errorbar(time, flux,yerr=flux_err,fmt='.',linewidth=1,c='k',ecolor='b')\n",
        "\n",
        "#label axes\n",
        "plt.xlabel(\"time  [(UTC) - 2454833]\",size=15)\n",
        "plt.ylabel(\"flux [counts]\",size=15)\n",
        "plt.savefig('lightcurveraw.png')"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DHRx1Mf-sg1X",
        "colab_type": "text"
      },
      "source": [
        "In the cell below, you will need to change time values. There are more sophisticated methods, but we will be using visual inspection to detect transits. In the above plot, it is easy to see that the flux dips 3 times (between 122 and 124, between 126 and 128, and at around 130). Let's focus on the first transit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3KVwKpagpiaI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "f782a648-a64c-4fe2-b064-9cdd9c8e9eb6"
      },
      "source": [
        "#zooming in on first transit by eye\n",
        "plt.errorbar(time,flux,yerr=flux_err,fmt='.',linewidth=1,c='k',ecolor='b')\n",
        "#change the xlim values to the time where you approximately think the transit is. play around with this\n",
        "plt.xlim(122.6,123.2)\n",
        "\n",
        "#labeling axes\n",
        "plt.xlabel(\"time [days]\",size=15)\n",
        "plt.ylabel(\"relative flux\", size=15)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-HOtOlrntXK2",
        "colab_type": "text"
      },
      "source": [
        "We also want to normalize the flux. What this means is that the highest flux value we have is 1. There are more sophisticated values of doing this as well, but for simplicity, let's divide both the flux and the flux error by the maximum flux value we can see in the above plot. For me, this is about 60400. Change this value for your highest flux"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ONKMQ-PttuUG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "normflux = flux/60400\n",
        "normerr = flux_err/60400"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H8CLC3hjt0gr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "333dc3a4-24b5-47db-f696-e0ef340f03ea"
      },
      "source": [
        "#plot the normalized flux and error\n",
        "plt.errorbar(time,normflux,yerr=normerr,fmt='.',linewidth=1,c='k',ecolor='b')\n",
        "#change the xlim values to the time where you approximately think the transit is. play around with this\n",
        "plt.xlim(122.6,123.2)\n",
        "\n",
        "#labeling axes\n",
        "plt.xlabel(\"time [days]\",size=15)\n",
        "plt.ylabel(\"relative flux\", size=15)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "brpcvUebtC3v",
        "colab_type": "text"
      },
      "source": [
        "Now we need to define some variables based on our visual inspection and guessing!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AldStM2Zs3R5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#t0 is the middle time of the transit, where the flux is at its lowest point, \n",
        "#look at your own graph to guess this value\n",
        "t0 = 122.9\n",
        "\n",
        "#tau is half of the duration of the transit. Visually, it looks like the transit is lasting\n",
        "#from between 122.8 to 123.0. So the duration is 0.2 and half of that is 0.1\n",
        "tau = 0.1\n",
        "\n",
        "#z is essentially our time normalized, don't change anything here\n",
        "z = (time - t0)/tau\n",
        "\n",
        "#this value is a pure guess. p actually refers to the ratio of the planet's radius divided\n",
        "#by the star's radius, so if you want to calculate that from your background research,\n",
        "#that will give you a better estimate. You can also just play around with this until you\n",
        "#have a good fit\n",
        "p = 0.078"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PJ9WdgVcvixH",
        "colab_type": "text"
      },
      "source": [
        "The next few lines of code are functions to fit the transit with mathematical formulas. These formulas are shown below.\n",
        "First we have the intensity function:\n",
        "$$I(r) = 1 - (1 - \\mu ^{1/2})$$\n",
        "$$\\mu = (1-r^2)^{1/2}$$\n",
        "\n",
        "$$F(p,z) = \\frac{\\int_{0}^1I(r)[1-\\delta(p,r,z)]2rdr}{\\int_{0}^1I(r)2rdr}$$\n",
        "$$\\delta(p,r,z) = \n",
        "\\begin{cases}\n",
        "0 & r \\geq z + p \\\\\n",
        "1 & r + z \\leq p \\\\\n",
        "\\pi^{-1}arccos[(z^2-p^2+r^2)/(2zr)] & \\text{otherwise}\n",
        "\\end{cases}$$\n",
        "Don't change any of these!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JnKBmpFYwKCT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#define intensity function\n",
        "def intensity(r):\n",
        "    mu = (1 - r**2)**0.5\n",
        "    return mu**0.5\n",
        "\n",
        "#import integration\n",
        "from scipy import integrate\n",
        "\n",
        "#define delta function\n",
        "def delta(p,r,z):\n",
        "    abs(z)\n",
        "    if r >= z + p or r <= z - p:\n",
        "        return 0\n",
        "    if r + z <= p:\n",
        "        return 1\n",
        "    d = math.acos((z**2 - p**2 + r**2)/(2*z*r))/(math.pi)\n",
        "    return d\n",
        "\n",
        "#define integrands\n",
        "def numerator(r, p, z):\n",
        "    return intensity(r)*(1 - delta(p,r,z))*2*r\n",
        "def denominator(r, p, z):\n",
        "    return intensity(r)*2*r\n",
        "\n",
        "#define limbdarkening function\n",
        "def limbdarkening(p, z):\n",
        "    top = integrate.quad(numerator,0,1,args=(p,z))[0]\n",
        "    bottom = integrate.quad(denominator,0,1,args=(p,z))[0] \n",
        "    return top/bottom\n",
        "\n",
        "#define model\n",
        "def model(p,tau,t0):\n",
        "    z = (time - t0)/tau\n",
        "    modelLD = []\n",
        "    for Z in z:\n",
        "        modelLD.append(limbdarkening(p,abs(Z)))\n",
        "    return modelLD"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DRtKEuF8x4LM",
        "colab_type": "text"
      },
      "source": [
        "Below, you will plot your flux values and compare this to the model. Don't change any lines of code below, but as you plot, go back to the cell with the variables p, tau, and t0 and change these values so the red line fits the points as best as possible. \n",
        "\n",
        "**If you're interested in a more robust technique, let me know and I can show you how to implement statistical tests to see how good of a fit this is. For now, don't worry about perfect accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3uuprYPrxnI_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "4a0bc9d5-36db-453c-e11d-43aa4aa6eab5"
      },
      "source": [
        "#plot actual flux values\n",
        "plt.errorbar(z, normflux,normerr,fmt='.',linewidth=1,c='k',ecolor='b')\n",
        "#focus in specifically on transit\n",
        "plt.xlim(-4,4)\n",
        "\n",
        "#plot model with limb darkening\n",
        "plt.plot(z, model(p,tau,t0), c='r', lw=1)\n",
        "\n",
        "#label axes\n",
        "plt.xlabel(\"normalized time\",size=15)\n",
        "plt.ylabel(\"normalized flux\", size=15)\n",
        "#plt.savefig(\"transit1.png\")"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'normalized flux')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SDgdZjLEyaO-",
        "colab_type": "text"
      },
      "source": [
        "Hooray this looks like a great fit to me! Now we are going to take our final p-value and try to calculate the size of the planet. We know that its host star as a radius of 1.793 $R_\\odot$, which is 1.793 solar radiuses. The sun is 696,340 km long. \n",
        "\n",
        "**Don't change the sunradius value, but change 1.793 to however many solar radiuses your planet's host star is."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cYwOCBRKy5bR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "sunradius = 696340\n",
        "#change the value below\n",
        "hoststar = 1.793 * sunradius"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xhjcyfbXzMxq",
        "colab_type": "text"
      },
      "source": [
        "Now, let's use our p value to calculate the size of the planet and convert this to earth radiuses ($R_\\oplus$)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8SZjrx5Izft6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6c78c9f8-bf01-4ee4-fa5d-a3c6c41ffe1f"
      },
      "source": [
        "exoplanetradius = hoststar * p\n",
        "earthradius = 6378\n",
        "exoplanetradius = exoplanetradius/earthradius\n",
        "print(exoplanetradius)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "15.269039567262462\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eE6pMPiizyhF",
        "colab_type": "text"
      },
      "source": [
        "We calculated that the exoplanet is 15 times bigger than earth and has a radius of 15.27 $R_\\oplus$. This is super close to the true value of 15.55 $R_\\oplus$, which we can see on the Wikipedia page!!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dIFGvdFw0FAL",
        "colab_type": "text"
      },
      "source": [
        "## Assignment\n",
        "When you are finished, take one or more of the graphs you generated as well as the background information you found to create an image/video/powerpoint of the planet you found and your research methods. Put your final project in the google drive."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KJ1VQNM20Vup",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}