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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Transit Light Curve Analysis</title>
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</head>
<body>
<div class="page-wrap">
<!-- ══ HERO ══ -->
<header class="hero">
<span class="hero-orbit" aria-hidden="true">
<svg viewBox="0 0 120 120" fill="none" xmlns="http://www.w3.org/2000/svg">
<!-- star glow -->
<circle cx="60" cy="60" r="18" fill="#f5c97a" opacity=".15"/>
<circle cx="60" cy="60" r="12" fill="#f5c97a" opacity=".25"/>
<circle cx="60" cy="60" r="7" fill="#fde68a"/>
<!-- orbit ring -->
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<circle cx="106" cy="60" r="5" fill="#5b8dee"/>
<circle cx="106" cy="60" r="3" fill="#93c5fd"/>
</g>
<!-- transit dip line -->
<path d="M 20 95 L 40 95 L 47 104 L 55 104 L 62 95 L 100 95" stroke="#5ddead" stroke-width="1.5" fill="none" stroke-linecap="round"/>
</svg>
</span>
<div class="badge">🪐 Astronomy 2025</div>
<h1>Catching <em>Shadows</em><br>of Distant Worlds</h1>
<p class="hero-sub">Data Processing in Astronomy Workshop — Time Series Analysis</p>
<div class="meta-row">
<div class="meta-chip"><span>📅</span>15 Dec 2025</div>
<div class="meta-chip"><span>🔭</span>TESS · Kepler · WASP-100</div>
<div class="meta-chip"><span>👩🏫</span>Mann Sutariya</div>
</div>
</header>
<div class="divider"></div>
<!-- ══ TOC ══ -->
<nav class="toc">
<div class="toc-title">Contents</div>
<ol>
<li><a href="#s-objective">Session Objective</a></li>
<li><a href="#s-setup">Environment Setup</a></li>
<li><a href="#s-tess">Loading TESS Data</a></li>
<li><a href="#s-pld">PLD Correction</a></li>
<li><a href="#s-bls">BLS Periodogram</a></li>
<li><a href="#s-batman">batman Transit Model</a></li>
<li><a href="#s-mcmc">MCMC Fitting</a></li>
<li><a href="#s-problem">Problem Statement</a></li>
</ol>
</nav>
<!-- ══ SECTION 1 ══ -->
<section class="section" id="s-objective">
<div class="section-head">
<span class="section-num">01</span>
<h2>Session Objective</h2>
</div>
<div class="prose">
<p>Welcome to this tutorial session! We will explore one of the most common, powerful, yet elegant astrophysical techniques to detect exoplanets around their host stars — the <strong>transit method</strong>.</p>
<div class="callout">
"In astronomy, you often learn a lot from what you <strong>can't see</strong>… especially when it causes a tiny but regular blip in what you <strong>can</strong>." 😉
</div>
<p>In this session we explore:</p>
<ul>
<li>What light curves are and how to make sense of them</li>
<li>How to detect tiny dips caused by planetary transits</li>
<li>How to model these dips using Python tools like <code>batman</code></li>
<li>How to find planet and orbital properties through this</li>
</ul>
</div>
<div class="tags">
<span class="tag tag-blue">lightkurve</span>
<span class="tag tag-blue">astropy</span>
<span class="tag tag-blue">batman-package</span>
<span class="tag tag-green">BLS</span>
<span class="tag tag-green">MCMC</span>
<span class="tag tag-orange">TESS</span>
<span class="tag tag-orange">Kepler</span>
</div>
</section>
<!-- ══ SECTION 2 ══ -->
<section class="section" id="s-setup">
<div class="section-head">
<span class="section-num">02</span>
<h2>Environment Setup</h2>
</div>
<div class="prose">
<p>Install all required packages. We pin <code>numpy==1.26.4</code> for compatibility with <code>PyTransit</code>.</p>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">bash — pip installs</span>
</div>
<pre><span class="cmt"># Upgrade pip first</span>
<span class="op">!</span>pip install <span class="op">--</span>upgrade pip
<span class="cmt"># Scientific stack</span>
<span class="op">!</span>pip install <span class="str">numpy==1.26.4</span> scipy matplotlib
<span class="cmt"># Lightkurve (NASA-supported)</span>
<span class="op">!</span>pip install lightkurve astroquery
<span class="cmt"># Exoplanet transit tools</span>
<span class="op">!</span>pip install batman-package
<span class="op">!</span>pip install <span class="str">PyTransit==2.5.18</span> <span class="cmt"># works with numpy 1.26.x</span>
<span class="op">!</span>pip install astropy</pre>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — verify installation</span>
</div>
<pre><span class="kw">import</span> <span class="mod">numpy</span> <span class="kw">as</span> np
<span class="kw">import</span> <span class="mod">lightkurve</span> <span class="kw">as</span> lk
<span class="kw">from</span> <span class="mod">astroquery.mast</span> <span class="kw">import</span> Catalogs
<span class="kw">import</span> <span class="mod">matplotlib.pyplot</span> <span class="kw">as</span> plt
<span class="fn">print</span>(<span class="str">"NumPy version:"</span>, np.__version__)
<span class="fn">print</span>(<span class="str">"Lightkurve version:"</span>, lk.__version__)</pre>
</div>
</section>
<!-- ══ SECTION 3 ══ -->
<section class="section" id="s-tess">
<div class="section-head">
<span class="section-num">03</span>
<h2>Loading TESS Data — WASP-100</h2>
</div>
<div class="prose">
<p><strong>WASP-100</strong> is a hot Jupiter host star. We load pre-downloaded TESS Pixel Files (TPF) and light curves (LC) from Google Drive to work completely offline.</p>
</div>
<div class="cards">
<div class="info-card">
<div class="ic-label">TIC ID</div>
<div class="ic-value">38846515</div>
<div class="ic-desc">TESS Input Catalog identifier</div>
</div>
<div class="info-card">
<div class="ic-label">Mission</div>
<div class="ic-value">TESS S1</div>
<div class="ic-desc">Sector 1, Full Frame Image</div>
</div>
<div class="info-card">
<div class="ic-label">Files</div>
<div class="ic-value">TPF + LC</div>
<div class="ic-desc">Target Pixel File & Light Curve</div>
</div>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — load fits files</span>
</div>
<pre><span class="kw">import</span> <span class="mod">lightkurve</span> <span class="kw">as</span> lk
<span class="kw">from</span> <span class="mod">astropy.io</span> <span class="kw">import</span> fits
abs_drive_path <span class="op">=</span> <span class="str">"/content/drive/MyDrive/NIUS/Lightcurve/"</span>
tpf_path <span class="op">=</span> abs_drive_path <span class="op">+</span> <span class="str">"tess2018206045859-s0001-0000000038846515-0120-s_tp.fits"</span>
lc_path <span class="op">=</span> abs_drive_path <span class="op">+</span> <span class="str">"tess2018206045859-s0001-0000000038846515-0120-s_lc.fits"</span>
tpf <span class="op">=</span> lk.<span class="fn">read</span>(tpf_path)
lc <span class="op">=</span> lk.<span class="fn">read</span>(lc_path)
<span class="cmt"># Read metadata from FITS header</span>
h <span class="op">=</span> fits.<span class="fn">getheader</span>(lc_path)
tic <span class="op">=</span> h.<span class="fn">get</span>(<span class="str">"TICID"</span>, <span class="str">"Unknown"</span>)
tmag <span class="op">=</span> h.<span class="fn">get</span>(<span class="str">"TESSMAG"</span>, <span class="str">"Unknown"</span>)
ra <span class="op">=</span> h.<span class="fn">get</span>(<span class="str">"RA_OBJ"</span>, <span class="str">"Unknown"</span>)
dec <span class="op">=</span> h.<span class="fn">get</span>(<span class="str">"DEC_OBJ"</span>, <span class="str">"Unknown"</span>)
<span class="fn">print</span>(<span class="str">f"Loaded TIC <span class="var">{tic}</span> — TESS mag = <span class="var">{tmag}</span>"</span>)
<span class="fn">print</span>(<span class="str">f"RA, Dec = <span class="var">{ra}</span>, <span class="var">{dec}</span>"</span>)</pre>
</div>
</section>
<!-- ══ SECTION 4 ══ -->
<section class="section" id="s-pld">
<div class="section-head">
<span class="section-num">04</span>
<h2>PLD Systematics Correction</h2>
</div>
<div class="prose">
<p><strong>Pixel Level Decorrelation (PLD)</strong> removes instrumental systematics from the raw photometry. It uses a PCA-based approach to separate astrophysical signal from spacecraft-induced trends.</p>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — aperture + PLD correction</span>
</div>
<pre><span class="kw">from</span> <span class="mod">lightkurve.correctors</span> <span class="kw">import</span> PLDCorrector
<span class="cmt"># Create aperture mask (threshold = 3σ)</span>
aperture <span class="op">=</span> tpf.<span class="fn">create_threshold_mask</span>(threshold<span class="op">=</span><span class="num">3</span>)
raw_lc <span class="op">=</span> tpf.<span class="fn">to_lightcurve</span>(aperture_mask<span class="op">=</span>aperture)
<span class="cmt"># Apply PLD correction</span>
corrector <span class="op">=</span> <span class="fn">PLDCorrector</span>(tpf)
corrected_lc <span class="op">=</span> corrector.<span class="fn">correct</span>(aperture_mask<span class="op">=</span>aperture)
<span class="cmt"># Plot raw vs corrected</span>
plt.<span class="fn">plot</span>(raw_time[q], raw_flux[q] <span class="op">/</span> np.<span class="fn">nanmedian</span>(raw_flux[q]) <span class="op">+</span> <span class="num">0.06</span>, <span class="str">'k'</span>, label<span class="op">=</span><span class="str">"Raw"</span>)
plt.<span class="fn">plot</span>(corr_time[m], corr_flux[m] <span class="op">/</span> np.<span class="fn">nanmedian</span>(corr_flux[m]), <span class="str">'g'</span>, label<span class="op">=</span><span class="str">"PLD Corrected"</span>)</pre>
</div>
</section>
<!-- ══ SECTION 5 ══ -->
<section class="section" id="s-bls">
<div class="section-head">
<span class="section-num">05</span>
<h2>Box Least Squares — Period Finding</h2>
</div>
<div class="prose">
<p>The <strong>Box Least Squares (BLS)</strong> method is designed specifically to find periodic, box-shaped decreases in brightness — exactly the shape of a planetary transit: <em>flat → sudden drop → flat → return to baseline.</em></p>
<p>See the <a href="https://docs.astropy.org/en/latest/timeseries/bls.html" target="_blank">AstroPy BLS documentation</a> for full details.</p>
</div>
<h3>Algorithm</h3>
<div class="prose">
<ol>
<li>Build a log-spaced period grid from 0.1 to 15 days</li>
<li>Compute BLS power at each period trial</li>
<li>Locate the highest power peak → best period</li>
<li>Reject harmonic aliases (P/2, 2P, P/3, …)</li>
<li>Phase-fold data at the best period and plot the transit</li>
</ol>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — BLS periodogram</span>
</div>
<pre><span class="kw">from</span> <span class="mod">astropy.timeseries</span> <span class="kw">import</span> BoxLeastSquares
<span class="cmt"># Log-spaced period grid: 0.1 → 15 days</span>
period_grid <span class="op">=</span> np.<span class="fn">exp</span>(np.<span class="fn">linspace</span>(np.<span class="fn">log</span>(<span class="num">0.1</span>), np.<span class="fn">log</span>(<span class="num">15</span>), <span class="num">50000</span>))
bls <span class="op">=</span> <span class="fn">BoxLeastSquares</span>(time, flux)
bls_power <span class="op">=</span> bls.<span class="fn">power</span>(period_grid, <span class="num">0.1</span>, oversample<span class="op">=</span><span class="num">20</span>)
<span class="cmt"># Best peak</span>
index <span class="op">=</span> np.<span class="fn">argmax</span>(bls_power.power)
bls_period <span class="op">=</span> bls_power.period[index]
bls_t0 <span class="op">=</span> bls_power.transit_time[index]
bls_depth <span class="op">=</span> bls_power.depth[index]
<span class="fn">print</span>(<span class="str">f"Best Period: <span class="var">{bls_period:.4f}</span> days"</span>)</pre>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — alias rejection</span>
</div>
<pre><span class="cmt"># Reject harmonics: P/2, 2P, P/3, 3P, 3/2P, 2/3P</span>
period_window_rtol <span class="op">=</span> <span class="num">0.01</span>
<span class="kw">for</span> i <span class="kw">in</span> s_indices:
is_alias <span class="op">=</span> <span class="fn">any</span>([
np.<span class="fn">isclose</span>(current_period, bls_period_1 <span class="op">*</span> r, rtol<span class="op">=</span>period_window_rtol)
<span class="kw">for</span> r <span class="kw">in</span> [<span class="num">1</span>, <span class="num">0.5</span>, <span class="num">2</span>, <span class="num">1/3</span>, <span class="num">3</span>, <span class="num">1.5</span>, <span class="num">2/3</span>]
])
<span class="kw">if not</span> is_alias:
bls_period_2 <span class="op">=</span> current_period
<span class="kw">break</span></pre>
</div>
</section>
<!-- ══ SECTION 6 ══ -->
<section class="section" id="s-batman">
<div class="section-head">
<span class="section-num">06</span>
<h2>batman — Transit Modelling</h2>
</div>
<div class="prose">
<p><strong>batman</strong> (Bad-Ass Transit Model cAlculatioNs) generates precise analytic transit light curves for a given set of physical parameters. We first generate synthetic light curves to understand parameter effects, then fit to real TESS data.</p>
</div>
<h3>Transit Parameters</h3>
<table class="param-table">
<thead>
<tr>
<th>Parameter</th>
<th>Symbol</th>
<th>Description</th>
<th>Typical value</th>
</tr>
</thead>
<tbody>
<tr><td>t0</td><td>t₀</td><td>Mid-transit time</td><td>1.0 days</td></tr>
<tr><td>per</td><td>P</td><td>Orbital period</td><td>2.1 days</td></tr>
<tr><td>rp</td><td>Rp/R★</td><td>Planet-to-star radius ratio</td><td>0.05–0.20</td></tr>
<tr><td>a</td><td>a/R★</td><td>Semi-major axis / stellar radius</td><td>3–30</td></tr>
<tr><td>inc</td><td>i</td><td>Orbital inclination</td><td>~90°</td></tr>
<tr><td>ecc</td><td>e</td><td>Eccentricity</td><td>0.0</td></tr>
<tr><td>u</td><td>u₁, u₂</td><td>Limb-darkening coefficients</td><td>[0.1, 0.0]</td></tr>
</tbody>
</table>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — generate artificial transit</span>
</div>
<pre><span class="kw">import</span> <span class="mod">batman</span>
times <span class="op">=</span> np.<span class="fn">linspace</span>(<span class="num">0.6</span>, <span class="num">1.4</span>, <span class="num">100</span>)
params <span class="op">=</span> batman.<span class="fn">TransitParams</span>()
params.t0 <span class="op">=</span> <span class="num">1.0</span> <span class="cmt"># mid-transit time (days)</span>
params.per <span class="op">=</span> <span class="num">2.1</span> <span class="cmt"># orbital period (days)</span>
params.rp <span class="op">=</span> <span class="num">0.2</span> <span class="cmt"># Rp / R★</span>
params.a <span class="op">=</span> <span class="num">3.2</span> <span class="cmt"># a / R★</span>
params.inc <span class="op">=</span> np.<span class="fn">degrees</span>(<span class="num">0.45</span> <span class="op">*</span> np.pi)
params.ecc <span class="op">=</span> <span class="num">0.0</span>
params.w <span class="op">=</span> <span class="num">0.0</span>
params.u <span class="op">=</span> [<span class="num">0.1</span>, <span class="num">0.0</span>]
params.limb_dark <span class="op">=</span> <span class="str">"quadratic"</span>
m <span class="op">=</span> batman.<span class="fn">TransitModel</span>(params, times)
flux <span class="op">=</span> m.<span class="fn">light_curve</span>(params)
plt.<span class="fn">plot</span>(times, flux, <span class="str">"r-"</span>)
plt.<span class="fn">title</span>(<span class="str">"Artificial Transit — batman"</span>)</pre>
</div>
<h3>Fitting to TESS Data (curve_fit)</h3>
<div class="prose">
<p>We bin the phase-folded light curve, then use <code>scipy.optimize.curve_fit</code> to optimise the four free parameters: <em>k, a/R★, inc, t0</em>.</p>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — scipy curve_fit</span>
</div>
<pre><span class="kw">from</span> <span class="mod">scipy.optimize</span> <span class="kw">import</span> curve_fit
p0 <span class="op">=</span> [<span class="num">0.1</span>, <span class="num">10.0</span>, <span class="num">87.0</span>, <span class="num">0.0</span>] <span class="cmt"># k, a/R★, inc, t0</span>
bounds_lower <span class="op">=</span> [<span class="num">0.01</span>, <span class="num">2</span>, <span class="num">60</span>, <span class="op">-</span><span class="num">0.05</span>]
bounds_upper <span class="op">=</span> [<span class="num">0.50</span>, <span class="num">30</span>, <span class="num">90</span>, <span class="num">0.05</span>]
popt, pcov <span class="op">=</span> <span class="fn">curve_fit</span>(transit_model, t_fit, f_fit,
p0<span class="op">=</span>p0, bounds<span class="op">=</span>(bounds_lower, bounds_upper),
maxfev<span class="op">=</span><span class="num">20000</span>)
k_fit, a_fit, inc_fit, t0_fit <span class="op">=</span> popt
<span class="fn">print</span>(<span class="str">f"Rp/R★ = <span class="var">{k_fit:.4f}</span>, a/R★ = <span class="var">{a_fit:.2f}</span>, inc = <span class="var">{inc_fit:.2f}</span>°"</span>)</pre>
</div>
</section>
<!-- ══ SECTION 7 ══ -->
<section class="section" id="s-mcmc">
<div class="section-head">
<span class="section-num">07</span>
<h2>MCMC — Posterior Sampling</h2>
</div>
<div class="prose">
<p><strong>Markov Chain Monte Carlo</strong> is a statistical technique used to sample the probability distribution of model parameters. Instead of giving you just one best-fit value, MCMC explores the <em>entire space</em> of possible solutions that fit the data — giving us uncertainties too.</p>
<p>We use <code>emcee</code> (the MCMC Hammer) with 32 walkers and 3000 steps, discarding the first 500 as burn-in.</p>
</div>
<div class="cards">
<div class="info-card">
<div class="ic-label">Walkers</div>
<div class="ic-value">32</div>
<div class="ic-desc">Parallel chains</div>
</div>
<div class="info-card">
<div class="ic-label">Steps</div>
<div class="ic-value">3 000</div>
<div class="ic-desc">Per walker</div>
</div>
<div class="info-card">
<div class="ic-label">Burn-in</div>
<div class="ic-value">500</div>
<div class="ic-desc">Discarded steps</div>
</div>
<div class="info-card">
<div class="ic-label">Free params</div>
<div class="ic-value">4</div>
<div class="ic-desc">k, a/R★, inc, t0</div>
</div>
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — emcee sampler</span>
</div>
<pre><span class="kw">import</span> <span class="mod">emcee</span>, <span class="mod">corner</span>
ndim, nwalkers <span class="op">=</span> <span class="num">4</span>, <span class="num">32</span>
p0 <span class="op">=</span> initial <span class="op">+</span> <span class="num">1e-4</span> <span class="op">*</span> np.random.<span class="fn">randn</span>(nwalkers, ndim)
sampler <span class="op">=</span> emcee.<span class="fn">EnsembleSampler</span>(nwalkers, ndim, log_prob,
args<span class="op">=</span>(t, f, sigma))
sampler.<span class="fn">run_mcmc</span>(p0, <span class="num">3000</span>, progress<span class="op">=</span><span class="kw">True</span>)
samples <span class="op">=</span> sampler.<span class="fn">get_chain</span>(discard<span class="op">=</span><span class="num">500</span>, thin<span class="op">=</span><span class="num">10</span>, flat<span class="op">=</span><span class="kw">True</span>)
k_m, a_m, inc_m, t0_m <span class="op">=</span> np.<span class="fn">median</span>(samples, axis<span class="op">=</span><span class="num">0</span>)
<span class="cmt"># Corner plot</span>
corner.<span class="fn">corner</span>(samples, labels<span class="op">=</span>[<span class="str">"k"</span>, <span class="str">"a/R★"</span>, <span class="str">"inc"</span>, <span class="str">"t0"</span>],
truths<span class="op">=</span>[k_m, a_m, inc_m, t0_m])</pre>
</div>
</section>
<!-- ══ SECTION 8 ══ -->
<section class="section" id="s-problem">
<div class="section-head">
<span class="section-num">08</span>
<h2>Problem Statement</h2>
</div>
<div class="prose">
<p>The following code generates a <strong>simulated transit light curve</strong> with random physical parameters. Your task is to recover <em>everything you can</em> from the noisy data.</p>
</div>
<div class="callout" style="border-left-color: var(--accent2); color: var(--accent2);">
🔬 Challenge: extract period, transit depth, duration, Rp/R★, a/R★, and inclination from the synthetic light curve below.
</div>
<div class="code-block">
<div class="code-header">
<div class="code-dots"><div class="code-dot"></div><div class="code-dot"></div><div class="code-dot"></div></div>
<span class="code-lang">python — synthetic challenge data</span>
</div>
<pre><span class="kw">from</span> <span class="mod">pytransit</span> <span class="kw">import</span> QuadraticModel
np.random.<span class="fn">seed</span>(<span class="num">42</span>) <span class="cmt"># for reproducibility</span>
<span class="cmt"># ── Random physically valid parameters ──</span>
k <span class="op">=</span> np.random.<span class="fn">uniform</span>(<span class="num">0.05</span>, <span class="num">0.15</span>) <span class="cmt"># Rp/R★</span>
ldc <span class="op">=</span> <span class="fn">list</span>(np.random.<span class="fn">uniform</span>(<span class="num">0.1</span>, <span class="num">0.4</span>, size<span class="op">=</span><span class="num">2</span>)) <span class="cmt"># limb darkening</span>
t0 <span class="op">=</span> <span class="num">0.0</span> <span class="cmt"># reference transit time</span>
p <span class="op">=</span> np.random.<span class="fn">uniform</span>(<span class="num">2.0</span>, <span class="num">5.0</span>) <span class="cmt"># period (days)</span>
a <span class="op">=</span> np.random.<span class="fn">uniform</span>(<span class="num">5.0</span>, <span class="num">15.0</span>) <span class="cmt"># a / R★</span>
<span class="cmt"># Ensure inclination produces a transit: cos(i) < (1 + k) / a</span>
cosi_max <span class="op">=</span> (<span class="num">1</span> <span class="op">+</span> k) <span class="op">/</span> a
i <span class="op">=</span> np.<span class="fn">arccos</span>(np.random.<span class="fn">uniform</span>(<span class="num">0</span>, cosi_max))
<span class="cmt"># ── Generate 5–8 transit cycles ──</span>
n_cycles <span class="op">=</span> np.random.<span class="fn">uniform</span>(<span class="num">5</span>, <span class="num">8</span>)
times <span class="op">=</span> np.<span class="fn">linspace</span>(t0 <span class="op">-</span> <span class="num">0.5</span><span class="op">*</span>p, t0 <span class="op">+</span> n_cycles<span class="op">*</span>p, <span class="num">1000</span>)
<span class="cmt"># ── Model + noise ──</span>
tm <span class="op">=</span> <span class="fn">QuadraticModel</span>()
tm.<span class="fn">set_data</span>(times)
true_flux <span class="op">=</span> tm.<span class="fn">evaluate</span>(k, ldc, t0, p, a, i, <span class="num">0.0</span>, <span class="num">0.0</span>)
noise_std <span class="op">=</span> np.random.<span class="fn">uniform</span>(<span class="num">0.0005</span>, <span class="num">0.0012</span>)
noisy_flux <span class="op">=</span> true_flux <span class="op">+</span> np.random.<span class="fn">normal</span>(<span class="num">0</span>, noise_std, size<span class="op">=</span>true_flux.shape)</pre>
</div>
<div class="tags">
<span class="tag tag-orange">seed=42</span>
<span class="tag tag-blue">BLS → period</span>
<span class="tag tag-blue">batman → Rp/R★</span>
<span class="tag tag-green">emcee → posteriors</span>
</div>
</section>
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<p>Data Processing in Astronomy Workshop</p>
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Lecture: Mann Sutariya ·
Tutorial: Prof. Bhaswati Mookerjea, Dr. Akshat Singhal & Astronomy Cell
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<p style="margin-top:10px;">
<a href="https://lightkurve.github.io/lightkurve/" target="_blank">Lightkurve docs</a> ·
<a href="https://docs.astropy.org/en/latest/timeseries/bls.html" target="_blank">AstroPy BLS</a> ·
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