{ "cells": [ { "cell_type": "markdown", "id": "0dd17c1e-b445-436f-8d8d-5bdb74c48830", "metadata": { "jp-MarkdownHeadingCollapsed": true }, "source": [ "

Gaia Star Cluster Hertzsprung Russel Diagrams (HRD)

\n", "\n", "Here are some useful links \n", "- [European Space Agency Gaia Mission - Writing Queries Turorial](https://www.cosmos.esa.int/web/gaia-users/archive/writing-queries)\n", "- [Gaia's Hertzsprung-Russel Diagram](https://sci.esa.int/web/gaia/-/60198-gaia-hertzsprung-russell-diagram)\n", "- [Measuring the Age of a Star Cluster](https://www.e-education.psu.edu/astro801/content/l7_p6.html#:~:text=The%20HR%20diagram%20for%20stage,%2D13%20billion%20years%20old)\n", "- [Astro Prof YouTube Channel Phys 1403](https://www.youtube.com/watch?v=sDds6c7HByg)\n", "\n", "**In the examples below we will query open clusters in the Milky way and plot it in a Hertzsprung-Russel Diagram (HRD). We will also attempt to identify the Main Sequence Turnoff points for these star clusters**\n", "\n", "*adapted for the Python for Astronomy Course by Chandru Narayan using the material originally develped by Dr. Priya Hasan and the Gaia utilities*" ] }, { "cell_type": "markdown", "id": "94af65a7-d2bf-4383-a630-d71fa53ac4bf", "metadata": {}, "source": [ "# Steps to create Hertzsprung-Russel Diagram" ] }, { "cell_type": "markdown", "id": "b20a93ec-6adc-412c-a95e-6dfc70b61a86", "metadata": {}, "source": [ "- Step 1: Install the required libraries for astronomy data analysis, querying, and plotting.\n", "- Step 2: Import the necessary modules from the installed libraries.\n", "- Step 3: Query the Gaia archive for data within a specified radius around a given cluster.\n", "- Step 4a: Create a Dataframe and Cleanup data as needed.\n", "- Step 4b: Calculate absolute magnitudes and colors from the Gaia data.\n", "- Step 5: Generate HR diagrams, plotting absolute magnitude against color.\n", "- Repeat Steps 3-5 above for another Star Cluster" ] }, { "cell_type": "markdown", "id": "a9267d1f-08fb-47be-a440-0c361dfd5c15", "metadata": {}, "source": [ "## Step 1: Install necessary libraries as necessary" ] }, { "cell_type": "code", "execution_count": 1, "id": "6d25c29e-396f-4098-b71c-1e99afb93e58", "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "# pip install astropy astroquery matplotlib google" ] }, { "cell_type": "markdown", "id": "b4a8fbd1-cd0a-4c21-bf48-54b58f54db22", "metadata": {}, "source": [ "## Step 2: Import libraries" ] }, { "cell_type": "code", "execution_count": 2, "id": "121317dd-60ce-427c-a73d-f2f05acda8ce", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from astropy import units as u\n", "from astropy.coordinates import SkyCoord\n", "from astroquery.gaia import Gaia\n", "import astropy.coordinates as coord\n", "import pandas as pd" ] }, { "cell_type": "markdown", "id": "95b39153-7d0e-4b88-99d7-07d092ec9a1b", "metadata": {}, "source": [ "## Step 3: Query Gaia data" ] }, { "cell_type": "markdown", "id": "767f93cf", "metadata": {}, "source": [ "### First perform a Google Search about your target" ] }, { "cell_type": "code", "execution_count": 3, "id": "4f6cf071", "metadata": {}, "outputs": [], "source": [ "### Setup your target here\n", "target_id = 'M67'\n", "# provide approximate target distance in parsec and target size in minutes for Gaia query\n", "# change default values below\n", "target_dist = 850 # in parsec\n", "target_size = 60 # in minutes" ] }, { "cell_type": "code", "execution_count": 4, "id": "9bb6e5c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://en.wikipedia.org/wiki/Messier_67\n", "https://en.wikipedia.org/wiki/Messier_67#Description\n", "https://en.wikipedia.org/wiki/Messier_67#Planets\n", "https://en.wikipedia.org/wiki/Messier_67#Gallery\n", "https://en.wikipedia.org/wiki/Messier_object\n", "https://en.wikipedia.org/wiki/Charles_Messier\n", "https://en.wikipedia.org/wiki/Deep-sky_object\n", "https://en.wikipedia.org/wiki/Winnecke_4\n", "https://en.wikipedia.org/wiki/Messier_102\n", "https://science.nasa.gov/mission/hubble/science/explore-the-night-sky/hubble-messier-catalog/messier-67/\n" ] } ], "source": [ "try:\n", "\tfrom googlesearch import search\n", "except ImportError:\n", "\tprint(\"No module named 'google' found\")\n", "\n", "# to search\n", "query = f'{target_id} Wikipedia Astronomy'\n", "\n", "for j in search(query, tld=\"co.in\", num=10, stop=10, pause=2):\n", "\tprint(j)\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "fa0046c2-2624-4e67-a23e-4e1545b99bc7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ] }, { "cell_type": "markdown", "id": "31a3e333", "metadata": {}, "source": [ "### Perform your Query" ] }, { "cell_type": "code", "execution_count": 6, "id": "6b7f3c11-6a63-402d-8c03-ab948a98f4de", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# Parameters for API Query & HRD (20 minutes radius around Cluster center) - Change for each query!\n", "target = target_id # target to query\n", "object_radius = target_size/60 * u.deg # in deg\n", "coordinate = coord.SkyCoord.from_name(target)\n", "print(coordinate)\n", "\n", "# Define cluster coordinates and radius for Cone search\n", "radius = object_radius\n", "ra = coordinate.ra\n", "dec = coordinate.dec\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "8a8e41af-878a-403e-9212-6c01beb7e49b", "metadata": {}, "outputs": [], "source": [ "# Query strings for Gaia\n", "# Query 1\n", "query1 = f\"\"\"\n", " SELECT ra, dec, parallax, 1000/parallax as dist, phot_g_mean_mag, bp_rp\n", " FROM gaiaedr3.gaia_source \n", " WHERE parallax > 0 \n", " AND 1=CONTAINS(\n", " POINT('ICRS', ra, dec),\n", " CIRCLE('ICRS', {ra.value}, {dec.value}, {radius.value})\n", " )\n", "\"\"\"\n", "# Query 2\n", "query2 = f\"\"\"\n", " SELECT ra, dec, parallax, 1000/parallax as dist, phot_g_mean_mag, bp_rp\n", " FROM gaiaedr3.gaia_source \n", " WHERE parallax > 0 \n", " AND bp_rp > -0.75\n", " AND bp_rp < 6\n", " AND visibility_periods_used > 8\n", " AND phot_g_mean_flux_over_error > 50\n", " AND phot_bp_mean_flux_over_error > 20\n", " AND phot_rp_mean_flux_over_error > 20\n", " and phot_bp_rp_excess_factor <\n", " 1.3+0.06*power(phot_bp_mean_mag-phot_rp_mean_mag,2)\n", " and phot_bp_rp_excess_factor >\n", " 1.0+0.015*power(phot_bp_mean_mag-phot_rp_mean_mag,2)\n", " and astrometric_chi2_al/(astrometric_n_good_obs_al-5)<\n", " 1.44*greatest(1,exp(-0.4*(phot_g_mean_mag-19.5)))\n", " AND 1=CONTAINS(\n", " POINT('ICRS', ra, dec),\n", " CIRCLE('ICRS', {ra.value}, {dec.value}, {radius.value})\n", " )\n", "\"\"\" " ] }, { "cell_type": "code", "execution_count": 8, "id": "504eb037-c6e5-428f-85e1-af0477c114e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: Query finished. [astroquery.utils.tap.core]\n" ] } ], "source": [ "# create and launch async query\n", "job = Gaia.launch_job_async(query2)\n", "gaia_data = job.get_results()\n", "#print(gaia_data)" ] }, { "cell_type": "markdown", "id": "220deec4-ab47-45f7-9666-df2c4a4ccfa7", "metadata": {}, "source": [ "## Step 4a: Create a Data Frame & Cleanup Gaia Query Results data" ] }, { "cell_type": "code", "execution_count": 9, "id": "c291ccf8-ee12-4ee0-a2fd-bfb9496213f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "allstars\n", " ra dec parallax dist phot_g_mean_mag bp_rp\n", "0 133.391235 10.987632 0.906051 1103.690840 15.138968 0.925046\n", "1 133.409033 11.001376 0.298192 3353.548674 18.443552 1.123579\n", "2 133.431305 11.020590 0.416756 2399.487620 19.789114 0.762091\n", "3 133.431111 11.015676 1.177280 849.415728 17.560364 2.193853\n", "4 133.403503 11.009986 1.073133 931.850770 18.626163 2.105427\n", "... ... ... ... ... ... ...\n", "8353 131.904787 12.179726 0.830656 1203.867500 14.932704 0.750836\n", "8354 131.917027 12.198130 0.283891 3522.484053 17.067877 0.887508\n", "8355 131.936523 12.219047 0.482473 2072.655652 19.382582 0.625334\n", "8356 131.951450 12.223572 0.572090 1747.975739 14.006058 1.126587\n", "8357 131.924439 12.233467 0.461602 2166.368994 13.469939 1.203620\n", "\n", "[8358 rows x 6 columns]\n", "allstars_cleaned\n", " ra dec parallax dist phot_g_mean_mag bp_rp\n", "0 133.391235 10.987632 0.906051 1103.690840 15.138968 0.925046\n", "1 133.409033 11.001376 0.298192 3353.548674 18.443552 1.123579\n", "2 133.431305 11.020590 0.416756 2399.487620 19.789114 0.762091\n", "3 133.431111 11.015676 1.177280 849.415728 17.560364 2.193853\n", "4 133.403503 11.009986 1.073133 931.850770 18.626163 2.105427\n", "... ... ... ... ... ... ...\n", "8353 131.904787 12.179726 0.830656 1203.867500 14.932704 0.750836\n", "8354 131.917027 12.198130 0.283891 3522.484053 17.067877 0.887508\n", "8355 131.936523 12.219047 0.482473 2072.655652 19.382582 0.625334\n", "8356 131.951450 12.223572 0.572090 1747.975739 14.006058 1.126587\n", "8357 131.924439 12.233467 0.461602 2166.368994 13.469939 1.203620\n", "\n", "[8358 rows x 6 columns]\n", "allstars_masked\n", " ra dec parallax dist phot_g_mean_mag bp_rp\n", "3 133.431111 11.015676 1.177280 849.415728 17.560364 2.193853\n", "4 133.403503 11.009986 1.073133 931.850770 18.626163 2.105427\n", "17 133.397794 11.042173 1.070861 933.828389 18.950624 1.940527\n", "23 133.386143 11.059102 1.095117 913.144057 16.032089 1.120395\n", "39 133.458762 11.097318 1.200518 832.973749 12.874134 0.759347\n", "... ... ... ... ... ... ...\n", "8304 131.978834 12.058399 1.093639 914.378469 17.005825 1.781321\n", "8310 132.063985 12.071161 1.080416 925.569120 15.497908 1.315512\n", "8318 132.068331 12.116487 1.115341 896.586958 16.401670 1.422532\n", "8322 131.960436 12.107705 1.135438 880.717405 15.931160 1.221339\n", "8345 131.900446 12.147477 1.071840 932.975087 17.713017 1.800852\n", "\n", "[1538 rows x 6 columns]\n" ] } ], "source": [ "# Create a DataFrame and Cleanup specific to your target:\n", "allstars = gaia_data.to_pandas()\n", "print(\"allstars\\n\",allstars)\n", "# filter allstars\n", "allstars.dropna(inplace=True) # Drop NaN - \"not a number\"\n", "print(\"allstars_cleaned\\n\",allstars)\n", "# filter for dist between 800 & 900 pc (allstars_filtered) by creating a mask\n", "#mask = (allstars.dist >= 800) & (allstars.dist <= 900) & (allstars.bp_rp >= 0.7) & (allstars.bp_rp <= 0.8)\n", "tgt_min_dist = target_dist * 0.9 # create a range\n", "tgt_max_dist = target_dist * 1.1 # create a range\n", "mask = (allstars.dist >= tgt_min_dist) & (allstars.dist <= tgt_max_dist)\n", "allstars = allstars[mask]\n", "print(\"allstars_masked\\n\",allstars)" ] }, { "cell_type": "markdown", "id": "c3c55fcb-1eff-4599-b02d-a791368e2938", "metadata": {}, "source": [ "## Step 4b: Calculate absolute magnitude and add to DataFrame" ] }, { "cell_type": "markdown", "id": "8e2a2d86-1b4a-4cc5-a5ff-206b734dd012", "metadata": {}, "source": [ "### Review Formulas (we drived these in the Star MAgnitudes Module!)\n", "#### The quantity $\\boxed{m_{app} - m_{abs}} $ OR $ \\boxed {m - M} $ is known as the distance modulus\n", "#### Note that this quantity appears in the equations below to calculate magnitudes and distance\n", "### 1. How to calculate Magnitudes when distance (in pc) is known\n", "#### $$ \\boxed{m - M = 5 \\times log_{10}(distance) - 5} $$\n", "### 2. How to calculate Magnitudes when parallax (in arc-sec) is known\n", "#### $$ \\boxed{m - M = 5 \\times log_{10}(1/parallax) - 5} $$\n", "### 3. How to calculate Magnitudes for Gaia calculations when parallax (in milli-arc-sec or 'mas') is known\n", "##### $$ \\boxed{m -M = - 5 \\times log_{10}(parallax) + 10} $$ OR $$ \\boxed{M = m + 5 \\times log_{10}(parallax) - 10} $$\n", "#### 4. How to calculate Distance (in pc) when apparent and absolute magnitudes are known\n", "##### $$ \\boxed{distance = 10^{\\frac{m - M+5}{5}}} $$" ] }, { "cell_type": "code", "execution_count": 10, "id": "7be608f4-50ec-4903-a060-a3dbf9f8a7f9", "metadata": {}, "outputs": [], "source": [ "# Calculate absolute magnitude with parallax in mas\n", "# Make sure parallax > 0 by creating another filter\n", "\n", "distance_modulus = -5 * np.log10(allstars['parallax']) + 10\n", "abs_mag = allstars['phot_g_mean_mag'] - distance_modulus\n", "bp_rp = allstars['bp_rp']" ] }, { "cell_type": "markdown", "id": "47297628-3c9a-4bdc-911a-b08d91f74ea6", "metadata": {}, "source": [ "## Step 5: Plot HR diagram" ] }, { "cell_type": "markdown", "id": "5ba7e601-e3f5-41c0-8675-6e92810d777d", "metadata": {}, "source": [ "### Simple Plot of HRD with the Sun superimposed" ] }, { "cell_type": "code", "execution_count": 11, "id": "7c8d0baf-f920-4a0b-97a0-68ada611e358", "metadata": {}, "outputs": [], "source": [ "# sun's HRD coordinates values for plotting\n", "# google \"what is bp-rp of the sun\" bp-rp = 0.82\n", "bp_rp_sun = 0.82\n", "\n", "# we calculated the abs mag of the sun in the \"brightness of stars\" project\n", "# we will do it again below:\n", "sun_app_mag = -27 # very very bright in the sky!\n", "sun_dist_km = 150e6 #km\n", "light_speed = 3e5 #km/s\n", "seconds_in_a_year = 365*24*60*60\n", "light_year_km = seconds_in_a_year * light_speed\n", "parsec_km = light_year_km * 3.26 #km/pc\n", "sun_dist_pc = sun_dist_km / parsec_km\n", "\n", "# Use the magnitude formula above to calculate the absolute magnitude of the Sun\n", "sun_abs_mag = sun_app_mag - 5 * np.log10(sun_dist_pc) + 5\n", "#print(sun_abs_mag)" ] }, { "cell_type": "code", "execution_count": 12, "id": "d11051d7-fa74-4021-bab0-38ad87395863", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 6))\n", "plt.scatter(bp_rp, abs_mag, s=1, alpha=0.5) # plot stars\n", "plt.scatter(bp_rp_sun, sun_abs_mag, marker='+', color=\"red\") # plot sun\n", "plt.text(bp_rp_sun+0.2, sun_abs_mag, \"Red Cross is our Sun!\", color=\"red\") # mark sun\n", "plt.gca().invert_yaxis()\n", "plt.xlabel(\"BP-RP Color\")\n", "plt.ylabel(\"Absolute G Magnitude\")\n", "plt.title(f\"HR Diagram for {target}\")\n", "plt.savefig(f\"{target}.png\", dpi=140)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a39d3d3b-f336-4f55-905f-09c68dd79381", "metadata": {}, "source": [ "## Can you tell where the Main Sequence Turnoff is happening?\n", "## What does that tell you about the Age of the cluster?\n", "![](age_turnoff_point.png)\n", "## Answer Questions below" ] }, { "cell_type": "code", "execution_count": 52, "id": "ba8fdb72-bbdd-413e-9ab2-dea78a1240c4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Main Sequence cutoff for M45 is at Abs Mag 4.0\n", "This indicates that M45 is 7.1e+09 years old!\n" ] } ], "source": [ "# Write print statement below with your answer\n", "abs_mag_turnoff = 4.0\n", "turnoff_age = 7.1e9\n", "print(f'Main Sequence cutoff for {target} is at Abs Mag {abs_mag_turnoff}')\n", "print(f'This indicates that {target} is {turnoff_age:.1e} years old!')" ] }, { "cell_type": "markdown", "id": "a04a445f-d421-443b-865f-641a8b9d7cc2", "metadata": {}, "source": [ "# Repeat Steps 3 to 5 below for another Star Cluster" ] }, { "cell_type": "markdown", "id": "2bb31c28-7226-4587-94ed-ce3c66e5b36d", "metadata": {}, "source": [ "## Step 3: Query Gaia data" ] }, { "cell_type": "markdown", "id": "158a3655-8ce9-4ab1-abd2-69837e282a89", "metadata": {}, "source": [ "### First perform a Google Search about your target" ] }, { "cell_type": "code", "execution_count": 37, "id": "aa6d9afb-8c45-478d-bd58-580c369cdc4f", "metadata": {}, "outputs": [], "source": [ "### Setup your target here\n", "target_id = 'M45'\n", "# provide approximate target distance in parsec and target size in minutes for Gaia query\n", "# change default values below\n", "target_dist = 136 # in parsec\n", "target_size = 120 # in minutes" ] }, { "cell_type": "code", "execution_count": 38, "id": "3fcb25c4-f4fe-41a0-a8e2-989563be1afe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "https://upload.wikimedia.org/wikipedia/commons/4/4e/Pleiades_large.jpg?sa=X&ved=2ahUKEwjlod-Ai7qNAxU3JzQIHdvYCXMQ_B16BAgJEAI\n", "https://en.wikipedia.org/wiki/Pleiades\n", "https://simple.wikipedia.org/wiki/Pleiades\n", "https://en.wikipedia.org/wiki/File:M45-_Pleiades_(star_cluster)_(NGC1432).jpg\n", "https://astropixels.com/openclusters/M45-01.html\n", "https://en.wikipedia.org/wiki/Celaeno_(star)\n", "https://en.wikibooks.org/wiki/Messier_Index/M45\n", "http://server1.wikisky.org/starview?object=M45\n", "https://en.wikipedia.org/wiki/Messier_object\n", "https://en.wikipedia.org/wiki/Charles_Messier\n" ] } ], "source": [ "try:\n", "\tfrom googlesearch import search\n", "except ImportError:\n", "\tprint(\"No module named 'google' found\")\n", "\n", "# to search\n", "query = f'{target_id} Wikipedia Astronomy'\n", "\n", "for j in search(query, tld=\"co.in\", num=10, stop=10, pause=2):\n", "\tprint(j)\n" ] }, { "cell_type": "code", "execution_count": 39, "id": "d5fe1d8e-fa04-47b2-ae3d-9266284141a4", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "
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\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "5e89f6a2-82f2-422d-8605-4ec7d7044f90", "metadata": {}, "source": [ "### Perform your Query" ] }, { "cell_type": "code", "execution_count": 40, "id": "564459b8-0150-4067-91a0-4e5f6ef81c67", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# Parameters for API Query & HRD (20 minutes radius around Cluster center) - Change for each query!\n", "target = target_id # target to query\n", "object_radius = target_size/60 * u.deg # in deg\n", "coordinate = coord.SkyCoord.from_name(target)\n", "print(coordinate)\n", "\n", "# Define cluster coordinates and radius for Cone search\n", "radius = object_radius\n", "ra = coordinate.ra\n", "dec = coordinate.dec\n" ] }, { "cell_type": "code", "execution_count": 41, "id": "f8140568-b2f5-4f2e-bf68-d821c6fbfea2", "metadata": {}, "outputs": [], "source": [ "# Query strings for Gaia\n", "# Query 1\n", "query1 = f\"\"\"\n", " SELECT ra, dec, parallax, 1000/parallax as dist, phot_g_mean_mag, bp_rp\n", " FROM gaiaedr3.gaia_source \n", " WHERE parallax > 0 \n", " AND 1=CONTAINS(\n", " POINT('ICRS', ra, dec),\n", " CIRCLE('ICRS', {ra.value}, {dec.value}, {radius.value})\n", " )\n", "\"\"\"\n", "# Query 2\n", "query2 = f\"\"\"\n", " SELECT ra, dec, parallax, 1000/parallax as dist, phot_g_mean_mag, bp_rp\n", " FROM gaiaedr3.gaia_source \n", " WHERE parallax > 0 \n", " AND bp_rp > -0.75\n", " AND bp_rp < 6\n", " AND visibility_periods_used > 8\n", " AND phot_g_mean_flux_over_error > 50\n", " AND phot_bp_mean_flux_over_error > 20\n", " AND phot_rp_mean_flux_over_error > 20\n", " and phot_bp_rp_excess_factor <\n", " 1.3+0.06*power(phot_bp_mean_mag-phot_rp_mean_mag,2)\n", " and phot_bp_rp_excess_factor >\n", " 1.0+0.015*power(phot_bp_mean_mag-phot_rp_mean_mag,2)\n", " and astrometric_chi2_al/(astrometric_n_good_obs_al-5)<\n", " 1.44*greatest(1,exp(-0.4*(phot_g_mean_mag-19.5)))\n", " AND 1=CONTAINS(\n", " POINT('ICRS', ra, dec),\n", " CIRCLE('ICRS', {ra.value}, {dec.value}, {radius.value})\n", " )\n", "\"\"\" " ] }, { "cell_type": "code", "execution_count": 42, "id": "ce043dd6-7fc8-4e72-badc-290e990b1eb7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: Query finished. [astroquery.utils.tap.core]\n" ] } ], "source": [ "# create and launch async query\n", "job = Gaia.launch_job_async(query2)\n", "gaia_data = job.get_results()\n", "#print(gaia_data)" ] }, { "cell_type": "markdown", "id": "5c25da54-97a2-4f55-81d6-0a70f127b7f4", "metadata": {}, "source": [ "## Step 4a: Create a Data Frame & Cleanup Gaia Query Results data" ] }, { "cell_type": "code", "execution_count": 43, "id": "d765df66-5d12-45f8-a842-a9c859df51a8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "allstars\n", " ra dec parallax dist phot_g_mean_mag \\\n", "0 57.040738 25.202115 2.694236 371.162705 15.228561 \n", "1 57.036437 25.217571 0.003202 312306.424044 18.911062 \n", "2 57.029038 25.220577 0.208152 4804.179551 17.885767 \n", "3 57.036298 25.223672 0.203760 4907.726106 18.500704 \n", "4 57.061629 25.235586 0.937790 1066.336463 18.608236 \n", "... ... ... ... ... ... \n", "41345 56.177253 26.045490 0.460634 2170.919679 17.698112 \n", "41346 56.152010 26.042213 0.936664 1067.618243 16.507923 \n", "41347 56.156221 26.055469 2.952910 338.649035 14.004339 \n", "41348 56.184306 26.049957 0.234163 4270.530701 17.622841 \n", "41349 56.158642 26.068620 0.700025 1428.520492 17.756266 \n", "\n", " bp_rp \n", "0 1.636703 \n", "1 1.215275 \n", "2 0.956587 \n", "3 0.990368 \n", "4 2.049444 \n", "... ... \n", "41345 1.354347 \n", "41346 1.276431 \n", "41347 1.358456 \n", "41348 1.020552 \n", "41349 1.684143 \n", "\n", "[41350 rows x 6 columns]\n", "allstars_cleaned\n", " ra dec parallax dist phot_g_mean_mag \\\n", "0 57.040738 25.202115 2.694236 371.162705 15.228561 \n", "1 57.036437 25.217571 0.003202 312306.424044 18.911062 \n", "2 57.029038 25.220577 0.208152 4804.179551 17.885767 \n", "3 57.036298 25.223672 0.203760 4907.726106 18.500704 \n", "4 57.061629 25.235586 0.937790 1066.336463 18.608236 \n", "... ... ... ... ... ... \n", "41345 56.177253 26.045490 0.460634 2170.919679 17.698112 \n", "41346 56.152010 26.042213 0.936664 1067.618243 16.507923 \n", "41347 56.156221 26.055469 2.952910 338.649035 14.004339 \n", "41348 56.184306 26.049957 0.234163 4270.530701 17.622841 \n", "41349 56.158642 26.068620 0.700025 1428.520492 17.756266 \n", "\n", " bp_rp \n", "0 1.636703 \n", "1 1.215275 \n", "2 0.956587 \n", "3 0.990368 \n", "4 2.049444 \n", "... ... \n", "41345 1.354347 \n", "41346 1.276431 \n", "41347 1.358456 \n", "41348 1.020552 \n", "41349 1.684143 \n", "\n", "[41350 rows x 6 columns]\n", "allstars_masked\n", " ra dec parallax dist phot_g_mean_mag bp_rp\n", "6 57.064576 25.243313 6.855481 145.868687 17.047014 3.034380\n", "44 57.032048 25.315086 7.363884 135.797907 13.309442 1.716731\n", "64 57.121816 25.328998 6.907823 144.763406 17.330364 2.937561\n", "182 57.334667 25.428302 6.971480 143.441558 16.213099 2.864563\n", "355 57.648936 25.426309 7.292243 137.132019 11.730169 1.210641\n", "... ... ... ... ... ... ...\n", "40892 55.772779 25.777739 6.943416 144.021328 15.764206 2.682262\n", "40919 55.902870 25.783351 7.784496 128.460462 15.788612 2.768125\n", "40941 55.928803 25.860127 7.902433 126.543311 17.344990 3.266150\n", "41000 56.018790 25.856104 7.308381 136.829209 12.512795 1.436392\n", "41006 56.038969 25.887174 7.551490 132.424190 12.108432 1.253881\n", "\n", "[824 rows x 6 columns]\n" ] } ], "source": [ "# Create a DataFrame and Cleanup specific to your target:\n", "allstars = gaia_data.to_pandas()\n", "print(\"allstars\\n\",allstars)\n", "# filter allstars\n", "allstars.dropna(inplace=True) # Drop NaN - \"not a number\"\n", "print(\"allstars_cleaned\\n\",allstars)\n", "# filter for dist between 800 & 900 pc (allstars_filtered) by creating a mask\n", "#mask = (allstars.dist >= 800) & (allstars.dist <= 900) & (allstars.bp_rp >= 0.7) & (allstars.bp_rp <= 0.8)\n", "tgt_min_dist = target_dist * 0.9 # create a range\n", "tgt_max_dist = target_dist * 1.1 # create a range\n", "mask = (allstars.dist >= tgt_min_dist) & (allstars.dist <= tgt_max_dist)\n", "allstars = allstars[mask]\n", "print(\"allstars_masked\\n\",allstars)" ] }, { "cell_type": "markdown", "id": "606535e3-dd53-4507-b0c7-e0d8ba8b2912", "metadata": {}, "source": [ "## Step 4b: Calculate absolute magnitude and add to DataFrame" ] }, { "cell_type": "markdown", "id": "6be7b709-addd-4ac0-a9d3-4215a4078be7", "metadata": {}, "source": [ "### Review Formulas (we drived these in the Star MAgnitudes Module!)\n", "#### The quantity $\\boxed{m_{app} - m_{abs}} $ OR $ \\boxed {m - M} $ is known as the distance modulus\n", "#### Note that this quantity appears in the equations below to calculate magnitudes and distance\n", "### 1. How to calculate Magnitudes when distance (in pc) is known\n", "#### $$ \\boxed{m - M = 5 \\times log_{10}(distance) - 5} $$\n", "### 2. How to calculate Magnitudes when parallax (in arc-sec) is known\n", "#### $$ \\boxed{m - M = 5 \\times log_{10}(1/parallax) - 5} $$\n", "### 3. How to calculate Magnitudes for Gaia calculations when parallax (in milli-arc-sec or 'mas') is known\n", "##### $$ \\boxed{m -M = - 5 \\times log_{10}(parallax) + 10} $$ OR $$ \\boxed{M = m + 5 \\times log_{10}(parallax) - 10} $$\n", "#### 4. How to calculate Distance (in pc) when apparent and absolute magnitudes are known\n", "##### $$ \\boxed{distance = 10^{\\frac{m - M+5}{5}}} $$" ] }, { "cell_type": "code", "execution_count": 44, "id": "c3b1e3b0-7f5a-4d77-b9de-d1d6dc3f4d83", "metadata": {}, "outputs": [], "source": [ "# Calculate absolute magnitude with parallax in mas\n", "# Make sure parallax > 0 by creating another filter\n", "\n", "distance_modulus = -5 * np.log10(allstars['parallax']) + 10\n", "abs_mag = allstars['phot_g_mean_mag'] - distance_modulus\n", "bp_rp = allstars['bp_rp']" ] }, { "cell_type": "markdown", "id": "f886b562-c27f-4735-8c79-7f36324eb09f", "metadata": {}, "source": [ "## Step 5: Plot HR diagram" ] }, { "cell_type": "markdown", "id": "9fdf3c0b-9bb8-4d84-8e37-134a207e1296", "metadata": {}, "source": [ "### Simple Plot of HRD with the Sun superimposed" ] }, { "cell_type": "code", "execution_count": 45, "id": "97446af9-efce-45a2-8f5c-c70c959dd235", "metadata": {}, "outputs": [], "source": [ "# sun's HRD coordinates values for plotting\n", "# google \"what is bp-rp of the sun\" bp-rp = 0.82\n", "bp_rp_sun = 0.82\n", "\n", "# we calculated the abs mag of the sun in the \"brightness of stars\" project\n", "# we will do it again below:\n", "sun_app_mag = -27 # very very bright in the sky!\n", "sun_dist_km = 150e6 #km\n", "light_speed = 3e5 #km/s\n", "seconds_in_a_year = 365*24*60*60\n", "light_year_km = seconds_in_a_year * light_speed\n", "parsec_km = light_year_km * 3.26 #km/pc\n", "sun_dist_pc = sun_dist_km / parsec_km\n", "\n", "# Use the magnitude formula above to calculate the absolute magnitude of the Sun\n", "sun_abs_mag = sun_app_mag - 5 * np.log10(sun_dist_pc) + 5\n", "#print(sun_abs_mag)" ] }, { "cell_type": "code", "execution_count": 46, "id": "8723d675-46c9-43bc-affc-2c68a5103390", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 6))\n", "plt.scatter(bp_rp, abs_mag, s=1, alpha=0.5) # plot stars\n", "plt.scatter(bp_rp_sun, sun_abs_mag, marker='+', color=\"red\") # plot sun\n", "plt.text(bp_rp_sun+0.2, sun_abs_mag, \"Red Cross is our Sun!\", color=\"red\") # mark sun\n", "plt.gca().invert_yaxis()\n", "plt.xlabel(\"BP-RP Color\")\n", "plt.ylabel(\"Absolute G Magnitude\")\n", "plt.title(f\"HR Diagram for {target}\")\n", "plt.savefig(f\"{target}.png\", dpi=140)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "128e4c94-b778-4c0b-a709-7e2d5bd40e99", "metadata": {}, "source": [ "## Can you tell where the Main Sequence Turnoff is happening?\n", "## What does that tell you about the Age of the cluster?\n", "![](age_turnoff_point.png)\n", "## Answer Questions below" ] }, { "cell_type": "code", "execution_count": 51, "id": "3569ff27-5c10-4dfe-a160-68c0089e873a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Main Sequence cutoff for M45 is at Abs Mag 1\n", "This indicates that M45 is approximately 1.6e+08 years old!\n" ] } ], "source": [ "# Write print statement below with your answer\n", "abs_mag_turnoff = 1\n", "turnoff_age = 1.6e8\n", "print(f'Main Sequence cutoff for {target} is at Abs Mag {abs_mag_turnoff}')\n", "print(f'This indicates that {target} is approximately {turnoff_age:.1e} years old!')" ] }, { "cell_type": "code", "execution_count": null, "id": "88c19e23-d39b-4406-b9a8-48b49d660b83", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }