Transit Light Source Effect (TLSE)

• TLSE is a phenomenon where stellar heterogeneities such as spots and faculae cause spectral mismatches during planetary transits.
• The effect biases exoplanet transmission spectra, leading to misestimations of planetary radii and densities, notably in active M-dwarf systems.
• Quantitative models using multi-wavelength photometry and Bayesian retrieval frameworks are crucial for correcting TLSE in exoplanet atmospheric studies.

The Transit Light Source Effect (TLSE) is a fundamental source of astrophysical systematics in exoplanet transmission spectroscopy, arising from the fact that the spectrum of the stellar region sampled during a planet’s transit can differ from the disk-averaged stellar spectrum. This spectral mismatch originates from photospheric heterogeneities—primarily cool dark spots and hot bright faculae/plages—whose distribution and spectral characteristics are typically non-uniform. The TLSE produces wavelength-dependent biases in observed transit depths, which can masquerade as or obscure genuine atmospheric features of transiting planets, and systematically bias inferred planetary radii and densities—especially for small, rocky planets orbiting active M-dwarf hosts.

1. Physical and Mathematical Foundations

Transmission spectroscopy interprets changes in stellar flux as a planet transits, under the implicit assumption that the planet is silhouetted against a photosphere with uniform spectral energy distribution (SED). However, active stellar surfaces host localized features (spots, faculae) with distinct emergent spectra, leading to deviations between the transit chord and the global disk average (Rackham et al., 2017). The defining mathematical framework is as follows:

Let:

• $F_{\lambda,\mathrm{phot}}$: Spectrum of the immaculate photosphere.
• $F_{\lambda,\mathrm{spot}}$: Spectrum of spots.
• $F_{\lambda,\mathrm{fac}}$: Spectrum of faculae.
• $f_{\mathrm{spot}}$, $f_{\mathrm{fac}}$: Covering fractions (outside transit chord).

The observed transit depth in wavelength $\lambda$ is modified by a contamination spectrum $\epsilon(\lambda)$:

$$D_{\mathrm{obs}}(\lambda) = D_{\mathrm{true}}(\lambda) \cdot \epsilon(\lambda)$$

with

$$\epsilon(\lambda) = \frac{1}{1 - f_{\mathrm{spot}}\left[1 - \frac{F_{\lambda,\mathrm{spot}}}{F_{\lambda,\mathrm{phot}}}\right] - f_{\mathrm{fac}}\left[1 - \frac{F_{\lambda,\mathrm{fac}}}{F_{\lambda,\mathrm{phot}}}\right]}$$

For "spots-only," $$\epsilon_\mathrm{spots}(\lambda) = 1/[1 - f_{\mathrm{spot}}(1 - F_{\lambda,\mathrm{spot}}/F_{\lambda,\mathrm{phot}})]$$ (Rackham et al., 2017, Murray et al., 4 Nov 2025).

The corresponding bias in transit depth,

$$\Delta D(\lambda) = D_{\mathrm{obs}}(\lambda) - D_{\mathrm{true}}(\lambda) = D_{\mathrm{true}}(\lambda) [\epsilon(\lambda) - 1]$$

This spectral distortion is not restricted to spot-dominated M dwarfs but appears, at a reduced amplitude, in G and K dwarfs as well, with the general form incorporating all three components (Rackham et al., 2018):

$$C(\lambda) = \frac{(1 - f_{\mathrm{spot}} - f_{\mathrm{fac}}) I_{\mathrm{phot}}(\lambda) + f_{\mathrm{spot}} I_{\mathrm{spot}}(\lambda) + f_{\mathrm{fac}} I_{\mathrm{fac}}(\lambda)}{I_{\mathrm{phot}}(\lambda)} - 1$$

and

$$D_{\mathrm{obs}}(\lambda) = [1 + C(\lambda)] D_{\mathrm{true}}(\lambda)$$

2. Manifestations and Observational Signatures

The TLSE can induce both broadband slopes and narrow “false features” in apparent planetary spectra. For M-dwarfs, spot/facula contamination can exceed by more than an order of magnitude the amplitude of planetary molecular absorption typical of small ($\sim$1-2$R_\oplus$) exoplanets: transmission spectral features from five scale heights in a rocky planet correspond to $$\Delta D_{\mathrm{planet}}/D_{\mathrm{planet}} \approx 1.3\%$$, whereas realistic spot/faculae populations yield measured contamination up to $5.8\%$ (3–19%) (Rackham et al., 2017).

Table: Typical TLSE contamination amplitudes for M-dwarfs (Rackham et al., 2017)

Spot Scenario	Contamination (mean)	Range
Giant spots (~5000ppm)	0.4%	0.2–0.9%
Solar-like spots (~400ppm)	5.0%	2.6–16%
Spots + faculae (giant)	–0.4%	–0.3– –0.9%
Spots + faculae (solar-like)	+5.8%	3.0–19%

In the FGK regime, the maximal contamination is generally lower but can reach up to 100–350 ppm in late-K dwarfs, with broader visual slopes or atomic line signatures (notably Na D in G9V–K dwarfs) and TiO/VO features for very active hosts (Rackham et al., 2018). For inactive FGK stars, contamination in molecular bands (e.g., CH$_4$, CO, H$_2$O) remains undetectable at $<30$ ppm.

3. Stellar Heterogeneity Mapping and Parameter Estimation

The mapping from photometric variability to surface coverage fractions is non-trivial. The rotational modulation amplitude $A$ reveals only the non-axisymmetric component of heterogeneities. Monte Carlo models demonstrate that $A$ scales sublinearly with covering fraction:

$A \simeq C \sqrt{f_{\mathrm{spot}}}$

with $C \sim 0.02$–$0.11$ (M-dwarfs), $C_0 \sim 0.05$ (FGK dwarfs) (Rackham et al., 2017, Rackham et al., 2018). Linear models ($A \propto f_{\mathrm{spot}}$) systematically underestimate $f_{\mathrm{spot}}$ by up to an order of magnitude, particularly in the small-spot regime. Axisymmetric distributions can produce substantial surface coverage—$f_{\mathrm{spot}} \approx 8^{+18}_{-7}\%$ and $f_{\mathrm{fac}} \approx 54^{+16}_{-46}\%$ for TRAPPIST-1—at very modest $A \sim 1$\%.

High-precision multi-wavelength photometry, rotational modulation, and spectroscopic decomposition (e.g., for AU Mic, $T_{\mathrm{spot}}=3000\pm70$ K, $f_{\mathrm{spot}}=0.39\pm0.04$, with ~5% modulation) offer orthogonal constraints on both temperature and coverage (Waalkes et al., 2023).

4. Light Curve Effects: Spot Crossing Events and Systematics

When the transit chord crosses an active region (“starspot-crossing event," SCE), additional time-dependent features are imprinted on the light curve. Analysis of synthetic SCEs using the starry formalism shows that for SNR ≥ 4, the typical recovered transit depth bias is 78.3 ppm (0.78%), with 80% of events within 0.6% (Murray et al., 4 Nov 2025). Spot longitude is well-constrained ($>$80% within 1$^\circ$), but spot contrast and size are degenerate.

Masking SCEs is sub-optimal for contamination factors $\epsilon > 1.3\%$; fitting for spot parameters yields improved results in $>95\%$ of realizations, but for $c_{\mathrm{spot}}<5\%$ or $f_{\mathrm{spot}}<2\%$, fits can over-correct the TLSE. Modeling SCEs inflates uncertainties in transit depth by up to $10-100\times$ the photon-noise limit for JWST-like data.

Grid-based priors, filtered via observables $$(t_{\mathrm{spot}}, \Delta t_{\mathrm{spot}}, \Delta D_{\mathrm{spot}})$$, enable efficient and robust posterior sampling for SCE events. These constraints help regularize the inherent degeneracy among spot size, latitude, and contrast.

5. Correction, Retrieval, and Mitigation Strategies

Quantitative correction of TLSE in transmission spectra requires:

• Robust estimation of covering fractions and spectral contrasts for each heterogeneity type.
• Forward modeling: prediction of the contaminated disk-integrated spectrum using component spectra ($F_{\mathrm{phot}}(\lambda,T_{phot})$, $F_{\mathrm{spot}}(\lambda,T_{spot})$, $F_{\mathrm{fac}}(\lambda,T_{fac})$) and fractional areas (Piaulet-Ghorayeb, 25 Aug 2025).
• Application of the contamination spectrum to infer the intrinsic planet signal:

$$D_{\mathrm{true}}(\lambda) = \frac{D_{\mathrm{obs}}(\lambda)}{\epsilon(\lambda)}$$

• Bayesian retrieval frameworks (e.g., STCTM) parameterize temperatures, covering fractions, and optionally joint planetary atmospheric properties. Priors are optimally constrained by out-of-transit spectroscopy via submodules such as exotune, reducing parameter degeneracy.

For observational campaigns, multi-band simultaneous photometry, careful monitoring of rotational variability, and high-S/N time-resolved spectroscopy are indispensable. Spot/facula occultations provide empirical leverages on region contrasts and geometries. Joint modeling of planetary and stellar signals, ideally marginalizing over stellar activity parameters, yields robust atmospheric constraints.

6. Quantitative Effects on Radius and Density Determinations

The planet radius $R_p$ and bulk density $\rho$ are systematically biased by TLSE. For small contamination,

$\Delta R / R \approx \frac{\epsilon - 1}{2}$

$$\Delta \rho / \rho \approx -\frac{3}{2}(\epsilon - 1)$$

As demonstrated in the TRAPPIST-1 system, an observed mean contamination of $\Delta R / R \approx 1.1\%^{+2.5\%}_{-1.0\%}$ corresponds to a $\Delta \rho / \rho$ underestimate of $-3\%^{+3\%}_{-8\%}$ (Rackham et al., 2017). In the AU Mic system, spot-induced contamination can constitute $25-75\%$ of the measured planet transit depths, yielding physical overestimates up to $\sim$1.7 $R_\oplus$ for AU Mic b (Waalkes et al., 2023).

7. Current Status, Practical Outlook, and Future Prospects

Empirical analyses of Spitzer and HST/WFC3 transits of TRAPPIST-1 indicate that, in the near- and mid-infrared, TLSE biases are currently limited to $<300$ ppm, which is sub-dominant to molecular features for many anticipated JWST targets (Morris et al., 2018). Nonetheless, undetected magnetic features of a few megameters in size cannot be excluded. Forthcoming optical-infrared spectrographs and next-generation monitoring will reduce these floors, and Bayesian frameworks such as STCTM will play an increasing role (Piaulet-Ghorayeb, 25 Aug 2025).

In summary, the TLSE represents an unavoidable astrophysical systematic for exoplanet atmospheric inference, especially in active-star regimes. Mitigation demands detailed modeling of stellar heterogeneity, synthesis of multi-modal observational constraints, and marginalization over contamination in retrieval analyses. As sensitivity and wavelength coverage improve, particularly with facilities like JWST/NIRSpec, the community is equipped to resolve TlSE at the $<10^{-4}$ level and recover robust planetary atmospheric signatures.