A New Strategy for Using Spectroscopic Phase Curves to Characterize Non-Transiting Planets

TL;DR

The paper tackles the challenge of characterizing atmospheres of non-transiting exoplanets by introducing the Variable Planetary Infrared Excess (VPIE) technique, which uses empirical stellar normalization to isolate planetary emission in combined-light spectroscopic time series. By modeling stellar variability with a small set of basis spectra derived from short-wavelength data and analyzing long-wavelength residuals, VPIE obtains phase-resolved planetary information without relying on physics-based stellar models. Through JWST-based simulations of TOI-519 b, GJ 876 d, and Proxima Centauri b, the study demonstrates that VPIE can constrain planetary radius and atmospheric heat-redistribution regimes, with performance improving for brighter targets and longer-wavelength coverage. The work suggests VPIE as a promising framework for studying non-transiting planets around nearby M-dwarfs and outlines pathways for instrument design and methodological refinements to extend its applicability to cooler, potentially habitable worlds.

Abstract

We introduce a new time-series analysis strategy for combined-light exoplanet spectroscopic phase curves called the Variable Planetary Infrared Excess (VPIE) method. VPIE can be used to extract information about the planetary flux contribution without the need for the planet to transit, or use of a stellar spectral model. VPIE utilizes a linear combination of a small set of individual spectra to produce an empirical model of the stellar contribution at each time step, thereby normalizing each spectrum and leaving only an imprint of the planet's flux in the residual data. We demonstrate the effectiveness of VPIE through simulated James Webb Space Telescope (JWST) observations of three known exoplanet orbiting late-type M stars: the warm giant TOI-519 b, the warm sub-Neptune GJ 876 d, and the temperate super-Earth Proxima Centauri b. Our results indicate that though VPIE loses sensitivity for very high redistribution values, it can successfully distinguish between various atmospheric circulation regimes (zero, moderate, or high heat redistribution) and constrain planetary radii for non-unity day-night temperature ratios. While performance for cooler targets may be limited by JWST spectroscopic capabilities at longer wavelengths, future VPIE improvements or new instrumentation could enable characterization of potentially habitable planets. VPIE offers a promising new framework for pulling back the veil on the population of non-transiting planets around nearby M-stars that are otherwise inaccessible to current techniques.

Figures (8)

• Figure 1: Known potentially-rocky exoplanets within 20 pc. The vast majority of the closest planets are non-transiting and their atmospheres cannot be characterized with currently-available techniques. Data from the NASA Exoplanet Archive, accessed on output/nearby_mdwarfs_date.txt.
• Figure 2: Basis spectra reconstruction. Top: Spectral time-series comprising a VPIE observation. The planetary spectrum has been multiplied by $10^4$ for visibility; the sinusoidal shape of the variability caused by the planet can be clearly seen in the LW portion of the spectrum. The SW stellar spectrum also varies with time; the red-blue image on the $x$-$y$ plane shows variations from the mean spectrum. Middle: The best basis for the dataset shown in top panel, found by minimizing the BIC. Bottom: Reconstruction of the dataset shown in top panel using only the basis spectra (dashed lines), plotted along with the original data (solid lines). Note that solid and dashed lines converge in the SW portion of the spectrum, but in the LW region the spectra are significantly different; this is because the fitting procedure was not given any information about the time-series behavior of the planet. The planet's imprint on the residuals is shown in red and blue on the $x$-$y$ plane; note the difference in the scale bar values.
• Figure 3: Example residual curves ($\bm{f} - \tilde{\bm{f}}$) at in the LW spectral region for three heat-redistribution scenarios. The mismatch between two models is measured by $\chi^2_\mathrm{red}$, which is computed here between the "No heat redistribution" ($T_\mathrm{night}/T_\mathrm{day}\approx 0$) scenario and the other two. It is clear that "Full heat redistribution" ($T_\mathrm{night}/T_\mathrm{day}\approx 1$) fits poorly, and, as expected, $\chi^2_\mathrm{red}$ tells us that the two phase curves do not match with a high statistical significance ($\sim 300$). The "Moderate heat redistribution" ($T_\mathrm{night}/T_\mathrm{day}\approx 1/2$) scenario, however, traces the baseline phase curve well, and $\chi^2_\mathrm{red}$ tells us that these two models agree within $3\sigma$. Only the longest wavelength channel is plotted here, but $\chi^2_\mathrm{red}$ is calculated using the whole $4-5\;\mathrm{\mu m}$ range. The time axis has been binned into 3-pixel bins compared to the original lightcurve to reduce correlated noise. The data is drawn from the example described in Section \ref{['subsec:gj876']}.
• Figure 4: PIE phase curve and VPIE analysis of the warm giant planet TOI-519 b. a) Thermal emission phase curve with $T_\mathrm{night}/T_\mathrm{day} = 0.5$ over one orbit in the spectra range $0.6-5\;\mathrm{\mu m}$. b) Stellar variability. Left axis (blue line) shows the normalized white light curve of the star over the observation. The right axis shows the best-fit coefficients of the basis spectra ($a_k$ in equation (\ref{['eq:def-frec']})). c) VPIE residual pattern. This is the signal which can be matched with a model to infer planetary properties. d) Binned VPIE residual pattern. Same as (c), but binned by 6 pixels in wavelength and 4 pixels in time in order to remove correlated noise.
• Figure 5: Heat distribution and planet radius mismatch for TOI-519 b. a) Zero variability in the planetary lightcurve, but the eclipse is considered in the analysis; By including the eclipsing epochs in the VPIE analysis the radius of the planet is constrained. b) Same as (c), but the $T_\mathrm{night}/T_\mathrm{day}$ of the ground-truth is 0.5. c) Same as (a), but the eclipse is removed from the data before analysis. This case simulates a non-transiting planet; in the absence of an eclipse, the minimum $\chi_\mathrm{red}^2$ is degenerate between heat redistribution and planet radius. At the true $\sim R_\mathrm{J}$ radius of TOI-519 b, the moderate-redistribution model is rejected at $10\sigma$. d) Same as (c), but the $T_\mathrm{night}/T_\mathrm{day}$ of the ground-truth is 0.5. In each panel, the star indicates the ground-truth used in calculating $\chi_\mathrm{red}^2$.