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Reload the data
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Selection by proper motion
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Convex Hull
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Assembling the query
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Selecting proper motion
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Exercise
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Summary
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<div class="section" id="transformation-and-selection">
<h1>4. Transformation and Selection<a class="headerlink" href="#transformation-and-selection" title="Permalink to this headline"></a></h1>
<p>In the previous lesson, we identified stars with the proper motion we expect for GD-1.</p>
<p>Now we’ll do the same selection in an ADQL query, which will make it possible to work with a larger region of the sky and still download less data.</p>
<div class="section" id="outline">
<h2>Outline<a class="headerlink" href="#outline" title="Permalink to this headline"></a></h2>
<p>Here are the steps in this lesson:</p>
<ol class="simple">
<li><p>Using data from the previous lesson, we’ll identify the values of proper motion for stars likely to be in GD-1.</p></li>
<li><p>Then we’ll compose an ADQL query that selects stars based on proper motion, so we can download only the data we need.</p></li>
</ol>
<p>That will make it possible to search a bigger region of the sky in a single query.
We’ll also see how to write the results to a CSV file.</p>
<p>After completing this lesson, you should be able to</p>
<ul class="simple">
<li><p>Transform proper motions from one frame to another.</p></li>
<li><p>Compute the convex hull of a set of points.</p></li>
<li><p>Write an ADQL query that selects based on proper motion.</p></li>
<li><p>Save data in CSV format.</p></li>
</ul>
</div>
<div class="section" id="reload-the-data">
<h2>Reload the data<a class="headerlink" href="#reload-the-data" title="Permalink to this headline"></a></h2>
<p>The following cells download the data from the previous lesson, if necessary, and load it into a Pandas <code class="docutils literal notranslate"><span class="pre">DataFrame</span></code>.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">os.path</span> <span class="kn">import</span> <span class="n">basename</span><span class="p">,</span> <span class="n">exists</span>
<span class="k">def</span> <span class="nf">download</span><span class="p">(</span><span class="n">url</span><span class="p">):</span>
<span class="n">filename</span> <span class="o">=</span> <span class="n">basename</span><span class="p">(</span><span class="n">url</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">exists</span><span class="p">(</span><span class="n">filename</span><span class="p">):</span>
<span class="kn">from</span> <span class="nn">urllib.request</span> <span class="kn">import</span> <span class="n">urlretrieve</span>
<span class="n">local</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">urlretrieve</span><span class="p">(</span><span class="n">url</span><span class="p">,</span> <span class="n">filename</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Downloaded &#39;</span> <span class="o">+</span> <span class="n">local</span><span class="p">)</span>
<span class="n">download</span><span class="p">(</span><span class="s1">&#39;https://github.com/AllenDowney/AstronomicalData/raw/main/&#39;</span> <span class="o">+</span>
<span class="s1">&#39;data/gd1_data.hdf&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">filename</span> <span class="o">=</span> <span class="s1">&#39;gd1_data.hdf&#39;</span>
<span class="n">centerline_df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_hdf</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s1">&#39;centerline_df&#39;</span><span class="p">)</span>
<span class="n">selected_df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_hdf</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s1">&#39;selected_df&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="selection-by-proper-motion">
<h2>Selection by proper motion<a class="headerlink" href="#selection-by-proper-motion" title="Permalink to this headline"></a></h2>
<p>Let’s review how we got to this point.</p>
<ol class="simple">
<li><p>We made an ADQL query to the Gaia server to get data for stars in the vicinity of GD-1.</p></li>
<li><p>We transformed the coordinates to the <code class="docutils literal notranslate"><span class="pre">GD1Koposov10</span></code> frame so we could select stars along the centerline of GD-1.</p></li>
<li><p>We plotted the proper motion of the centerline stars to identify the bounds of the overdense region.</p></li>
<li><p>We made a mask that selects stars whose proper motion is in the overdense region.</p></li>
</ol>
<p>At this point we have downloaded data for a relatively large number of stars (more than 100,000) and selected a relatively small number (around 1000).</p>
<p>It would be more efficient to use ADQL to select only the stars we need. That would also make it possible to download data covering a larger region of the sky.</p>
<p>However, the selection we did was based on proper motion in the <code class="docutils literal notranslate"><span class="pre">GD1Koposov10</span></code> frame. In order to do the same selection in ADQL, we have to work with proper motions in ICRS.</p>
<p>As a reminder, here’s the rectangle we selected based on proper motion in the <code class="docutils literal notranslate"><span class="pre">GD1Koposov10</span></code> frame.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pm1_min</span> <span class="o">=</span> <span class="o">-</span><span class="mf">8.9</span>
<span class="n">pm1_max</span> <span class="o">=</span> <span class="o">-</span><span class="mf">6.9</span>
<span class="n">pm2_min</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.2</span>
<span class="n">pm2_max</span> <span class="o">=</span> <span class="mf">1.0</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">make_rectangle</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y2</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the corners of a rectangle.&quot;&quot;&quot;</span>
<span class="n">xs</span> <span class="o">=</span> <span class="p">[</span><span class="n">x1</span><span class="p">,</span> <span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">x1</span><span class="p">]</span>
<span class="n">ys</span> <span class="o">=</span> <span class="p">[</span><span class="n">y1</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y1</span><span class="p">]</span>
<span class="k">return</span> <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pm1_rect</span><span class="p">,</span> <span class="n">pm2_rect</span> <span class="o">=</span> <span class="n">make_rectangle</span><span class="p">(</span>
<span class="n">pm1_min</span><span class="p">,</span> <span class="n">pm1_max</span><span class="p">,</span> <span class="n">pm2_min</span><span class="p">,</span> <span class="n">pm2_max</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>Since we’ll need to plot proper motion several times, we’ll use the following function.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">plot_proper_motion</span><span class="p">(</span><span class="n">df</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Plot proper motion.</span>
<span class="sd"> </span>
<span class="sd"> df: DataFrame with `pm_phi1` and `pm_phi2`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s1">&#39;pm_phi1&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s1">&#39;pm_phi2&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Proper motion phi1 (GD1 frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Proper motion phi2 (GD1 frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">12</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>The following figure shows:</p>
<ul class="simple">
<li><p>Proper motion for the stars we selected along the center line of GD-1,</p></li>
<li><p>The rectangle we selected, and</p></li>
<li><p>The stars inside the rectangle highlighted in green.</p></li>
</ul>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plot_proper_motion</span><span class="p">(</span><span class="n">centerline_df</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pm1_rect</span><span class="p">,</span> <span class="n">pm2_rect</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pm_phi1&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pm_phi2&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;gx&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">);</span>
</pre></div>
</div>
</div>
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<img alt="_images/04_select_15_0.png" src="_images/04_select_15_0.png" />
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<p>Now we’ll make the same plot using proper motions in the ICRS frame, which are stored in columns <code class="docutils literal notranslate"><span class="pre">pmra</span></code> and <code class="docutils literal notranslate"><span class="pre">pmdec</span></code>.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">centerline_df</span><span class="p">[</span><span class="s1">&#39;pmra&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">centerline_df</span><span class="p">[</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pmra&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;gx&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Proper motion ra (ICRS frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Proper motion dec (ICRS frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">]);</span>
</pre></div>
</div>
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<img alt="_images/04_select_17_0.png" src="_images/04_select_17_0.png" />
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</div>
<p>The proper motions of the selected stars are more spread out in this frame, which is why it was preferable to do the selection in the GD-1 frame.</p>
<p>But now we can define a polygon that encloses the proper motions of these stars in ICRS, and use that polygon as a selection criterion in an ADQL query.</p>
</div>
<div class="section" id="convex-hull">
<h2>Convex Hull<a class="headerlink" href="#convex-hull" title="Permalink to this headline"></a></h2>
<p>SciPy provides a function that computes the <a class="reference external" href="https://en.wikipedia.org/wiki/Convex_hull">convex hull</a> of a set of points, which is the smallest convex polygon that contains all of the points.</p>
<p>To use it, we’ll select columns <code class="docutils literal notranslate"><span class="pre">pmra</span></code> and <code class="docutils literal notranslate"><span class="pre">pmdec</span></code> and convert them to a NumPy array.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">points</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[[</span><span class="s1">&#39;pmra&#39;</span><span class="p">,</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]]</span><span class="o">.</span><span class="n">to_numpy</span><span class="p">()</span>
<span class="n">points</span><span class="o">.</span><span class="n">shape</span>
</pre></div>
</div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(1049, 2)
</pre></div>
</div>
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</div>
<p>NOTE: If you are using an older version of Pandas, you might not have <code class="docutils literal notranslate"><span class="pre">to_numpy()</span></code>; you can use <code class="docutils literal notranslate"><span class="pre">values</span></code> instead, like this:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">points</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[[</span><span class="s1">&#39;pmra&#39;</span><span class="p">,</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]]</span><span class="o">.</span><span class="n">values</span>
</pre></div>
</div>
<p>We’ll pass the points to <code class="docutils literal notranslate"><span class="pre">ConvexHull</span></code>, which returns an object that contains the results.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.spatial</span> <span class="kn">import</span> <span class="n">ConvexHull</span>
<span class="n">hull</span> <span class="o">=</span> <span class="n">ConvexHull</span><span class="p">(</span><span class="n">points</span><span class="p">)</span>
<span class="n">hull</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;scipy.spatial.qhull.ConvexHull at 0x7f712e3b6dc0&gt;
</pre></div>
</div>
</div>
</div>
<p><code class="docutils literal notranslate"><span class="pre">hull.vertices</span></code> contains the indices of the points that fall on the perimeter of the hull.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">hull</span><span class="o">.</span><span class="n">vertices</span>
</pre></div>
</div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([ 692, 873, 141, 303, 42, 622, 45, 83, 127, 182, 1006,
971, 967, 1001, 969, 940], dtype=int32)
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</div>
</div>
</div>
<p>We can use them as an index into the original array to select the corresponding rows.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pm_vertices</span> <span class="o">=</span> <span class="n">points</span><span class="p">[</span><span class="n">hull</span><span class="o">.</span><span class="n">vertices</span><span class="p">]</span>
<span class="n">pm_vertices</span>
</pre></div>
</div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([[ -4.05037121, -14.75623261],
[ -3.41981085, -14.72365546],
[ -3.03521988, -14.44357135],
[ -2.26847919, -13.7140236 ],
[ -2.61172203, -13.24797471],
[ -2.73471401, -13.09054471],
[ -3.19923146, -12.5942653 ],
[ -3.34082546, -12.47611926],
[ -5.67489413, -11.16083338],
[ -5.95159272, -11.10547884],
[ -6.42394023, -11.05981295],
[ -7.09631023, -11.95187806],
[ -7.30641519, -12.24559977],
[ -7.04016696, -12.88580702],
[ -6.00347705, -13.75912098],
[ -4.42442296, -14.74641176]])
</pre></div>
</div>
</div>
</div>
<p>To plot the resulting polygon, we have to pull out the x and y coordinates.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pmra_poly</span><span class="p">,</span> <span class="n">pmdec_poly</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">pm_vertices</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>This use of <code class="docutils literal notranslate"><span class="pre">transpose</span></code> is a useful NumPy idiom. Because <code class="docutils literal notranslate"><span class="pre">pm_vertices</span></code> has two columns, its <a class="reference external" href="https://en.wikipedia.org/wiki/Transpose">matrix transpose</a> has two rows, which are assigned to the two variables <code class="docutils literal notranslate"><span class="pre">pmra_poly</span></code> and <code class="docutils literal notranslate"><span class="pre">pmdec_poly</span></code>.</p>
<p>The following figure shows proper motion in ICRS again, along with the convex hull we just computed.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">centerline_df</span><span class="p">[</span><span class="s1">&#39;pmra&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">centerline_df</span><span class="p">[</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pmra&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">selected_df</span><span class="p">[</span><span class="s1">&#39;pmdec&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;gx&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pmra_poly</span><span class="p">,</span> <span class="n">pmdec_poly</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Proper motion phi1 (ICRS frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Proper motion phi2 (ICRS frame)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">]);</span>
</pre></div>
</div>
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<img alt="_images/04_select_30_0.png" src="_images/04_select_30_0.png" />
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<p>So <code class="docutils literal notranslate"><span class="pre">pm_vertices</span></code> represents the polygon we want to select.
The next step is to use it as part of an ADQL query.</p>
</div>
<div class="section" id="assembling-the-query">
<h2>Assembling the query<a class="headerlink" href="#assembling-the-query" title="Permalink to this headline"></a></h2>
<p>In Lesson 2 we used the following query to select stars in a polygonal region.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">query5_base</span> <span class="o">=</span> <span class="s2">&quot;&quot;&quot;SELECT</span>
<span class="si">{columns}</span><span class="s2"></span>
<span class="s2">FROM gaiadr2.gaia_source</span>
<span class="s2">WHERE parallax &lt; 1</span>
<span class="s2"> AND bp_rp BETWEEN -0.75 AND 2 </span>
<span class="s2"> AND 1 = CONTAINS(POINT(ra, dec), </span>
<span class="s2"> POLYGON(</span><span class="si">{point_list}</span><span class="s2">))</span>
<span class="s2">&quot;&quot;&quot;</span>
</pre></div>
</div>
</div>
</div>
<p>In this lesson we’ll make two changes:</p>
<ol class="simple">
<li><p>We’ll select stars with coordinates in a larger region.</p></li>
<li><p>We’ll add another clause to select stars whose proper motion is in the polygon we just computed, <code class="docutils literal notranslate"><span class="pre">pm_vertices</span></code>.</p></li>
</ol>
<p>Here are the coordinates of the larger rectangle in the GD-1 frame.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">astropy.units</span> <span class="k">as</span> <span class="nn">u</span>
<span class="n">phi1_min</span> <span class="o">=</span> <span class="o">-</span><span class="mi">70</span> <span class="o">*</span> <span class="n">u</span><span class="o">.</span><span class="n">degree</span>
<span class="n">phi1_max</span> <span class="o">=</span> <span class="o">-</span><span class="mi">20</span> <span class="o">*</span> <span class="n">u</span><span class="o">.</span><span class="n">degree</span>
<span class="n">phi2_min</span> <span class="o">=</span> <span class="o">-</span><span class="mi">5</span> <span class="o">*</span> <span class="n">u</span><span class="o">.</span><span class="n">degree</span>
<span class="n">phi2_max</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">u</span><span class="o">.</span><span class="n">degree</span>
</pre></div>
</div>
</div>
</div>
<p>We selected these bounds by trial and error, defining the largest region we can process in a single query.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">phi1_rect</span><span class="p">,</span> <span class="n">phi2_rect</span> <span class="o">=</span> <span class="n">make_rectangle</span><span class="p">(</span>
<span class="n">phi1_min</span><span class="p">,</span> <span class="n">phi1_max</span><span class="p">,</span> <span class="n">phi2_min</span><span class="p">,</span> <span class="n">phi2_max</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>Here’s how we transform it to ICRS, as we saw in Lesson 2.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">gala.coordinates</span> <span class="kn">import</span> <span class="n">GD1Koposov10</span>
<span class="kn">from</span> <span class="nn">astropy.coordinates</span> <span class="kn">import</span> <span class="n">SkyCoord</span>
<span class="n">gd1_frame</span> <span class="o">=</span> <span class="n">GD1Koposov10</span><span class="p">()</span>
<span class="n">corners</span> <span class="o">=</span> <span class="n">SkyCoord</span><span class="p">(</span><span class="n">phi1</span><span class="o">=</span><span class="n">phi1_rect</span><span class="p">,</span>
<span class="n">phi2</span><span class="o">=</span><span class="n">phi2_rect</span><span class="p">,</span>
<span class="n">frame</span><span class="o">=</span><span class="n">gd1_frame</span><span class="p">)</span>
<span class="n">corners_icrs</span> <span class="o">=</span> <span class="n">corners</span><span class="o">.</span><span class="n">transform_to</span><span class="p">(</span><span class="s1">&#39;icrs&#39;</span><span class="p">)</span>
</pre></div>
</div>
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</div>
<p>To use <code class="docutils literal notranslate"><span class="pre">corners_icrs</span></code> as part of an ADQL query, we have to convert it to a string.<br />
Here’s the function from Lesson 2 we used to do that.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">skycoord_to_string</span><span class="p">(</span><span class="n">skycoord</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Convert SkyCoord to string.&quot;&quot;&quot;</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">skycoord</span><span class="o">.</span><span class="n">to_string</span><span class="p">()</span>
<span class="n">s</span> <span class="o">=</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39; &#39;</span><span class="p">,</span> <span class="s1">&#39;, &#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">point_list</span> <span class="o">=</span> <span class="n">skycoord_to_string</span><span class="p">(</span><span class="n">corners_icrs</span><span class="p">)</span>
<span class="n">point_list</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;135.306, 8.39862, 126.51, 13.4449, 163.017, 54.2424, 172.933, 46.4726, 135.306, 8.39862&#39;
</pre></div>
</div>
</div>
</div>
<p>Here are the columns we want to select.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">columns</span> <span class="o">=</span> <span class="s1">&#39;source_id, ra, dec, pmra, pmdec&#39;</span>
</pre></div>
</div>
</div>
</div>
<p>Now we have everything we need to assemble the query.</p>
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<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">query5</span> <span class="o">=</span> <span class="n">query5_base</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">columns</span><span class="o">=</span><span class="n">columns</span><span class="p">,</span>
<span class="n">point_list</span><span class="o">=</span><span class="n">point_list</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">query5</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>SELECT
source_id, ra, dec, pmra, pmdec
FROM gaiadr2.gaia_source
WHERE parallax &lt; 1
AND bp_rp BETWEEN -0.75 AND 2
AND 1 = CONTAINS(POINT(ra, dec),
POLYGON(135.306, 8.39862, 126.51, 13.4449, 163.017, 54.2424, 172.933, 46.4726, 135.306, 8.39862))
</pre></div>
</div>
</div>
</div>
<p>But don’t try to run that query.
Because it selects a larger region, there are too many stars to handle in a single query.
Until we select by proper motion, that is.</p>
</div>
<div class="section" id="selecting-proper-motion">
<h2>Selecting proper motion<a class="headerlink" href="#selecting-proper-motion" title="Permalink to this headline"></a></h2>
<p>Now we’re ready to add a <code class="docutils literal notranslate"><span class="pre">WHERE</span></code> clause to select stars whose proper motion falls in the polygon defined by <code class="docutils literal notranslate"><span class="pre">pm_vertices</span></code>.</p>
<p>To use <code class="docutils literal notranslate"><span class="pre">pm_vertices</span></code> as part of an ADQL query, we have to convert it to a string.
Using <code class="docutils literal notranslate"><span class="pre">flatten</span></code> and <code class="docutils literal notranslate"><span class="pre">array2string</span></code>, we can almost get the format we need.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array2string</span><span class="p">(</span><span class="n">pm_vertices</span><span class="o">.</span><span class="n">flatten</span><span class="p">(),</span>
<span class="n">max_line_width</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
<span class="n">separator</span><span class="o">=</span><span class="s1">&#39;,&#39;</span><span class="p">)</span>
<span class="n">s</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;[ -4.05037121,-14.75623261, -3.41981085,-14.72365546, -3.03521988,-14.44357135, -2.26847919,-13.7140236 , -2.61172203,-13.24797471, -2.73471401,-13.09054471, -3.19923146,-12.5942653 , -3.34082546,-12.47611926, -5.67489413,-11.16083338, -5.95159272,-11.10547884, -6.42394023,-11.05981295, -7.09631023,-11.95187806, -7.30641519,-12.24559977, -7.04016696,-12.88580702, -6.00347705,-13.75912098, -4.42442296,-14.74641176]&#39;
</pre></div>
</div>
</div>
</div>
<p>We just have to remove the brackets.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pm_point_list</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">strip</span><span class="p">(</span><span class="s1">&#39;[]&#39;</span><span class="p">)</span>
<span class="n">pm_point_list</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39; -4.05037121,-14.75623261, -3.41981085,-14.72365546, -3.03521988,-14.44357135, -2.26847919,-13.7140236 , -2.61172203,-13.24797471, -2.73471401,-13.09054471, -3.19923146,-12.5942653 , -3.34082546,-12.47611926, -5.67489413,-11.16083338, -5.95159272,-11.10547884, -6.42394023,-11.05981295, -7.09631023,-11.95187806, -7.30641519,-12.24559977, -7.04016696,-12.88580702, -6.00347705,-13.75912098, -4.42442296,-14.74641176&#39;
</pre></div>
</div>
</div>
</div>
<div class="section" id="exercise">
<h3>Exercise<a class="headerlink" href="#exercise" title="Permalink to this headline"></a></h3>
<p>Define <code class="docutils literal notranslate"><span class="pre">query6_base</span></code>, starting with <code class="docutils literal notranslate"><span class="pre">query5_base</span></code> and adding a new clause to select stars whose coordinates of proper motion, <code class="docutils literal notranslate"><span class="pre">pmra</span></code> and <code class="docutils literal notranslate"><span class="pre">pmdec</span></code>, fall within the polygon defined by <code class="docutils literal notranslate"><span class="pre">pm_point_list</span></code>.</p>
<div class="cell tag_hide-cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Solution</span>
<span class="n">query6_base</span> <span class="o">=</span> <span class="s2">&quot;&quot;&quot;SELECT </span>
<span class="si">{columns}</span><span class="s2"></span>
<span class="s2">FROM gaiadr2.gaia_source</span>
<span class="s2">WHERE parallax &lt; 1</span>
<span class="s2"> AND bp_rp BETWEEN -0.75 AND 2 </span>
<span class="s2"> AND 1 = CONTAINS(POINT(ra, dec), </span>
<span class="s2"> POLYGON(</span><span class="si">{point_list}</span><span class="s2">))</span>
<span class="s2"> AND 1 = CONTAINS(POINT(pmra, pmdec),</span>
<span class="s2"> POLYGON(</span><span class="si">{pm_point_list}</span><span class="s2">))</span>
<span class="s2">&quot;&quot;&quot;</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="id1">
<h3>Exercise<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
<p>Use <code class="docutils literal notranslate"><span class="pre">format</span></code> to format <code class="docutils literal notranslate"><span class="pre">query6_base</span></code> and define <code class="docutils literal notranslate"><span class="pre">query6</span></code>, filling in the values of <code class="docutils literal notranslate"><span class="pre">columns</span></code>, <code class="docutils literal notranslate"><span class="pre">point_list</span></code>, and <code class="docutils literal notranslate"><span class="pre">pm_point_list</span></code>.</p>
<div class="cell tag_hide-cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Solution</span>
<span class="n">query6</span> <span class="o">=</span> <span class="n">query6_base</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">columns</span><span class="o">=</span><span class="n">columns</span><span class="p">,</span>
<span class="n">point_list</span><span class="o">=</span><span class="n">point_list</span><span class="p">,</span>
<span class="n">pm_point_list</span><span class="o">=</span><span class="n">pm_point_list</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">query6</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>SELECT
source_id, ra, dec, pmra, pmdec
FROM gaiadr2.gaia_source
WHERE parallax &lt; 1
AND bp_rp BETWEEN -0.75 AND 2
AND 1 = CONTAINS(POINT(ra, dec),
POLYGON(135.306, 8.39862, 126.51, 13.4449, 163.017, 54.2424, 172.933, 46.4726, 135.306, 8.39862))
AND 1 = CONTAINS(POINT(pmra, pmdec),
POLYGON( -4.05037121,-14.75623261, -3.41981085,-14.72365546, -3.03521988,-14.44357135, -2.26847919,-13.7140236 , -2.61172203,-13.24797471, -2.73471401,-13.09054471, -3.19923146,-12.5942653 , -3.34082546,-12.47611926, -5.67489413,-11.16083338, -5.95159272,-11.10547884, -6.42394023,-11.05981295, -7.09631023,-11.95187806, -7.30641519,-12.24559977, -7.04016696,-12.88580702, -6.00347705,-13.75912098, -4.42442296,-14.74641176))
</pre></div>
</div>
</div>
</div>
<p>Now we can run the query like this:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">astroquery.gaia</span> <span class="kn">import</span> <span class="n">Gaia</span>
<span class="n">job</span> <span class="o">=</span> <span class="n">Gaia</span><span class="o">.</span><span class="n">launch_job_async</span><span class="p">(</span><span class="n">query6</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">job</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Created TAP+ (v1.2.1) - Connection:
Host: gea.esac.esa.int
Use HTTPS: True
Port: 443
SSL Port: 443
Created TAP+ (v1.2.1) - Connection:
Host: geadata.esac.esa.int
Use HTTPS: True
Port: 443
SSL Port: 443
INFO: Query finished. [astroquery.utils.tap.core]
&lt;Table length=7345&gt;
name dtype unit description
--------- ------- -------- ------------------------------------------------------------------
source_id int64 Unique source identifier (unique within a particular Data Release)
ra float64 deg Right ascension
dec float64 deg Declination
pmra float64 mas / yr Proper motion in right ascension direction
pmdec float64 mas / yr Proper motion in declination direction
Jobid: 1615824245107O
Phase: COMPLETED
Owner: None
Output file: async_20210315120405.vot
Results: None
</pre></div>
</div>
</div>
</div>
<p>And get the results.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">candidate_table</span> <span class="o">=</span> <span class="n">job</span><span class="o">.</span><span class="n">get_results</span><span class="p">()</span>
<span class="nb">len</span><span class="p">(</span><span class="n">candidate_table</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>7345
</pre></div>
</div>
</div>
</div>
<p>We call the results <code class="docutils literal notranslate"><span class="pre">candidate_table</span></code> because it contains stars that are good candidates for GD-1.</p>
</div>
</div>
<div class="section" id="plotting-one-more-time">
<h2>Plotting one more time<a class="headerlink" href="#plotting-one-more-time" title="Permalink to this headline"></a></h2>
<p>Let’s see what the results look like.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">candidate_table</span><span class="p">[</span><span class="s1">&#39;ra&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">candidate_table</span><span class="p">[</span><span class="s1">&#39;dec&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;ra (degree ICRS)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;dec (degree ICRS)&#39;</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/04_select_62_0.png" src="_images/04_select_62_0.png" />
</div>
</div>
<p>Here we can see why it was useful to transform these coordinates. In ICRS, it is more difficult to identity the stars near the centerline of GD-1.</p>
<p>So let’s transform the results back to the GD-1 frame.
Here’s the code we used to transform the coordinates and make a Pandas <code class="docutils literal notranslate"><span class="pre">DataFrame</span></code>, wrapped in a function.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">gala.coordinates</span> <span class="kn">import</span> <span class="n">reflex_correct</span>
<span class="k">def</span> <span class="nf">make_dataframe</span><span class="p">(</span><span class="n">table</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Transform coordinates from ICRS to GD-1 frame.</span>
<span class="sd"> </span>
<span class="sd"> table: Astropy Table</span>
<span class="sd"> </span>
<span class="sd"> returns: Pandas DataFrame</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">skycoord</span> <span class="o">=</span> <span class="n">SkyCoord</span><span class="p">(</span>
<span class="n">ra</span><span class="o">=</span><span class="n">table</span><span class="p">[</span><span class="s1">&#39;ra&#39;</span><span class="p">],</span>
<span class="n">dec</span><span class="o">=</span><span class="n">table</span><span class="p">[</span><span class="s1">&#39;dec&#39;</span><span class="p">],</span>
<span class="n">pm_ra_cosdec</span><span class="o">=</span><span class="n">table</span><span class="p">[</span><span class="s1">&#39;pmra&#39;</span><span class="p">],</span>
<span class="n">pm_dec</span><span class="o">=</span><span class="n">table</span><span class="p">[</span><span class="s1">&#39;pmdec&#39;</span><span class="p">],</span>
<span class="n">distance</span><span class="o">=</span><span class="mi">8</span><span class="o">*</span><span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">,</span>
<span class="n">radial_velocity</span><span class="o">=</span><span class="mi">0</span><span class="o">*</span><span class="n">u</span><span class="o">.</span><span class="n">km</span><span class="o">/</span><span class="n">u</span><span class="o">.</span><span class="n">s</span><span class="p">)</span>
<span class="n">gd1_frame</span> <span class="o">=</span> <span class="n">GD1Koposov10</span><span class="p">()</span>
<span class="n">transformed</span> <span class="o">=</span> <span class="n">skycoord</span><span class="o">.</span><span class="n">transform_to</span><span class="p">(</span><span class="n">gd1_frame</span><span class="p">)</span>
<span class="n">skycoord_gd1</span> <span class="o">=</span> <span class="n">reflex_correct</span><span class="p">(</span><span class="n">transformed</span><span class="p">)</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">table</span><span class="o">.</span><span class="n">to_pandas</span><span class="p">()</span>
<span class="n">df</span><span class="p">[</span><span class="s1">&#39;phi1&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">skycoord_gd1</span><span class="o">.</span><span class="n">phi1</span>
<span class="n">df</span><span class="p">[</span><span class="s1">&#39;phi2&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">skycoord_gd1</span><span class="o">.</span><span class="n">phi2</span>
<span class="n">df</span><span class="p">[</span><span class="s1">&#39;pm_phi1&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">skycoord_gd1</span><span class="o">.</span><span class="n">pm_phi1_cosphi2</span>
<span class="n">df</span><span class="p">[</span><span class="s1">&#39;pm_phi2&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">skycoord_gd1</span><span class="o">.</span><span class="n">pm_phi2</span>
<span class="k">return</span> <span class="n">df</span>
</pre></div>
</div>
</div>
</div>
<p>Here’s how we use it:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">candidate_df</span> <span class="o">=</span> <span class="n">make_dataframe</span><span class="p">(</span><span class="n">candidate_table</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>And let’s see the results.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">candidate_df</span><span class="p">[</span><span class="s1">&#39;phi1&#39;</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">candidate_df</span><span class="p">[</span><span class="s1">&#39;phi2&#39;</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">&#39;ko&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;phi1 (degree GD1)&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;phi2 (degree GD1)&#39;</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/04_select_68_0.png" src="_images/04_select_68_0.png" />
</div>
</div>
<p>We’re starting to see GD-1 more clearly.
We can compare this figure with this panel from Figure 1 from the original paper:</p>
<a class="reference internal image-reference" href="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-2.png"><img alt="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-2.png" src="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-2.png" style="height: 150px;" /></a>
<p>This panel shows stars selected based on proper motion only, so it is comparable to our figure (although notice that it covers a wider region).</p>
<p>In the next lesson, we will use photometry data from Pan-STARRS to do a second round of filtering, and see if we can replicate this panel.</p>
<a class="reference internal image-reference" href="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-4.png"><img alt="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-4.png" src="https://github.com/datacarpentry/astronomy-python/raw/gh-pages/fig/gd1-4.png" style="height: 150px;" /></a>
<p>Later we’ll see how to add annotations like the ones in the figure and customize the style of the figure to present the results clearly and compellingly.</p>
</div>
<div class="section" id="summary">
<h2>Summary<a class="headerlink" href="#summary" title="Permalink to this headline"></a></h2>
<p>In the previous lesson we downloaded data for a large number of stars and then selected a small fraction of them based on proper motion.</p>
<p>In this lesson, we improved this process by writing a more complex query that uses the database to select stars based on proper motion. This process requires more computation on the Gaia server, but then we’re able to either:</p>
<ol class="simple">
<li><p>Search the same region and download less data, or</p></li>
<li><p>Search a larger region while still downloading a manageable amount of data.</p></li>
</ol>
<p>In the next lesson, we’ll learn about the database <code class="docutils literal notranslate"><span class="pre">JOIN</span></code> operation and use it to download photometry data from Pan-STARRS.</p>
</div>
<div class="section" id="best-practices">
<h2>Best practices<a class="headerlink" href="#best-practices" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p>When possible, “move the computation to the data”; that is, do as much of the work as possible on the database server before downloading the data.</p></li>
</ul>
</div>
</div>
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