ASTR 210 · Lecture 06

Differential Photometry and Light Curves

Removing common-mode effects to reveal relative variability

Learning Goals

  1. Define differential magnitude and explain why it cancels shared atmospheric and instrumental effects.
  2. Compute a light-curve dip depth from real flux ratios.
  3. Identify a poor choice of comparison star.

Reading anchor: OpenStax Astronomy 2e, Chapter 17.1 (brightness and magnitudes) and Chapter 21.4 (evidence for planets from transits).

Why This Matters

Variable-star and exoplanet-transit science rarely needs an absolute magnitude; it needs a precise relative measurement between a target and a stable comparison star in the same field, observed at the same time and airmass. Differential photometry removes clouds, seeing changes, and airmass drifts that affect both stars equally.

Opening Phenomenon

A light curve of target and comparison-star fluxes over one night shows a shallow dip in the target relative to the comparison, while the comparison star alone stays flat within measurement noise.

First question: what here is directly measured, and what is inferred from a model?

Terms for This Lecture

comparison star

Definition: A non-variable field star measured alongside a target to track transparency and instrumental changes common to both.

Why it matters here: It provides the reference needed to decide whether a target’s apparent change is intrinsic or caused by the observing system.

Relationships: The target-to-comparison flux ratio becomes a differential magnitude or normalized light curve.

Boundary / common confusion: A comparison star must be checked for stability and suitable brightness/color; sharing the field does not guarantee suitability.

Evidence We Need to Explain

Model

Quantitative Tool

\[ \Delta m = -2.5\log_{10}\!\left(\dfrac{F_{\rm target}}{F_{\rm comp}}\right) \]

Worked Example

  1. Baseline (t = 0.00): Δm = −2.5×log10(0.995/1.000) = 0.0054 mag.
  2. During the dip (t = 0.10): Δm = −2.5×log10(0.970/0.999) = 0.0320 mag.
  3. Dip depth relative to baseline: 0.0320 − (0.0054) = 0.0265 mag ≈ 27 millimagnitudes.
  4. A dip of this size (about 2.5–3% relative flux change) is comparable to a hot-Jupiter transit depth around a Sun-like star, which is why differential photometry at the millimagnitude level is central to transit science.

Visual Reasoning

Read the light curve for the target and comparison star together, not separately.

  • Why is the comparison star’s flat line essential to trusting the target’s dip?
  • What differential-magnitude value corresponds to the deepest point of the dip?
Lecture 06: Differential Photometry and Light Curvestime (fraction of night)normalized fluxtarget, t=0.00target, t=0.10 (dip)comparisonThe comparison star stays flat within 0.2% while the target dips: Δm grows from 0.005 to 0.032 mag, a 0.027-mag dip.
Target and comparison-star flux over the night, with the real dip highlighted.

Common Pitfall

Choosing a comparison star that is itself variable, blended with a neighbor, or near saturation — any of these injects a false signal into the "constant" reference and corrupts the differential light curve.

Active Learning Segment

Given a table of target and comparison fluxes at five times, compute Δm at each time and decide whether the pattern is a real dip or measurement scatter.

Lab or Observing Connection

Lab 04 (Differential Light Curve) uses the full variable-star flux table to build a light curve and test whether an observed dip exceeds the noise floor.

Synthesis

Differential photometry reveals relative variability by removing common-mode effects that would otherwise swamp a small, real signal.

References