ESPRESSO Transit Follow-up Sub-program

• The sub-program employs ultra-precise radial velocity measurements to determine planetary masses, radii, and compositions with accuracies around 16% and precisions near 23%.
• Tailored scheduling strategies and uniform phase coverage minimize biases, enabling unbiased dynamical characterization of rocky and sub-Neptune exoplanets.
• A high-resolution ESPRESSO setup combined with Bayesian inference effectively separates planetary signals from stellar activity and instrumental noise.

Searching arXiv for the cited ESPRESSO transit follow-up papers. The ESPRESSO Transit Follow-up Sub-program is one of the ESPRESSO Guaranteed Time Observations initiatives on ESO’s VLT, dedicated to confirming and precisely characterizing small transiting planets discovered by K2 and TESS through ultra-precise radial velocities. Its stated aims include delivering dynamical masses, radii, ephemerides, and bulk compositions for a hand-picked sample of TESS discoveries; mapping the rocky–gaseous transition as a function of insolation, orbital period, and host-star properties; identifying additional non-transiting companions; and selecting the most favorable systems for atmospheric characterization (Hobson et al., 26 May 2026, Sozzetti et al., 2021).

1. Scientific scope and target definition

The sub-program is designed around small planets, from rocky planets to sub-Neptunes. In the broader WG3 overview, the primary “rocky” sample consists of planets with $R_p \lesssim 2 R_\oplus$, $V \lesssim 14.5$ mag, and no prior mass measurement, while the secondary “volatile-rich” sample consists of sub-Neptune candidates with $R_p \lesssim 4 R_\oplus$ in the medium-insolation window $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$ (Hobson et al., 26 May 2026). An earlier target-selection description emphasizes TESS Objects of Interest orbiting stars brighter than $V \approx 10$, with spectral types F5–K, low projected rotation $(v \sin i < 5\ \mathrm{km\ s^{-1}})$, and minimal photometric activity $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$ (Sozzetti et al., 2021).

These criteria reflect the instrumental logic of the program. Bright, slowly rotating stars optimize radial-velocity information content, while short- to moderate-period planets with expected semi-amplitudes of order $1$–$5\ \mathrm{m\ s^{-1}}$ are well matched to ESPRESSO’s precision domain (Sozzetti et al., 2021). The program therefore occupies a specific regime in exoplanet follow-up: not transit discovery itself, but high-precision dynamical characterization of already identified candidates, especially where mass precision is needed to distinguish rocky, water-rich, and H–He-bearing planets.

By 2026, the sub-program had characterized 65 planets in 30 systems, including 54 published planets and 11 new or updated cases in that overview. The observational parent sample comprised 50 stars, of which 35 were followed long enough to yield precise masses; among the resulting planets, 51 transiting planets had well-measured masses and radii, with mass error $\lesssim 25\%$ and radius error $V \lesssim 14.5$0 (Hobson et al., 26 May 2026). This establishes the program as a homogeneous precision-RV sample rather than an isolated collection of case studies.

2. Instrumental configuration and observing practice

The instrumental basis of the sub-program is ESPRESSO in 1-UT high-resolution mode, with resolving power quoted as $V \lesssim 14.5$1 in the program overview and $V \lesssim 14.5$2 in individual target analyses, using simultaneous Fabry–Pérot calibration (Hobson et al., 26 May 2026, Damasso et al., 2023). In the HIP 29442 analysis, the wavelength coverage is $V \lesssim 14.5$3–$V \lesssim 14.5$4, fibre B is illuminated with a Fabry–Pérot etalon for drift measurements, and the cross-correlation mask is a G9 template (Damasso et al., 2023). The observational strategy is magnitude-dependent: $V \lesssim 14.5$5 exposures for $V \lesssim 14.5$6, $V \lesssim 14.5$7 in slow readout for $V \lesssim 14.5$8–$V \lesssim 14.5$9, $R_p \lesssim 4 R_\oplus$0 for $R_p \lesssim 4 R_\oplus$1–$R_p \lesssim 4 R_\oplus$2, $R_p \lesssim 4 R_\oplus$3 for $R_p \lesssim 4 R_\oplus$4, and multiple short reads for ultra-bright stars with $R_p \lesssim 4 R_\oplus$5 (Hobson et al., 26 May 2026).

The program aims for typical per-exposure photon-noise RV precision $R_p \lesssim 4 R_\oplus$6, reaching down to $R_p \lesssim 4 R_\oplus$7 on bright targets, and was designed to build a homogeneous sample with RV precision down to $R_p \lesssim 4 R_\oplus$8 over multi-year baselines (Hobson et al., 26 May 2026). In the HIP 29442 system, 83 unique visits from 9 October 2019 to 24 March 2022, all with $R_p \lesssim 4 R_\oplus$9 exposures, achieved median photon-noise limited precision $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$0 and overall RV scatter $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$1 (Damasso et al., 2023). In HD 5278, 43 ESPRESSO visits over 403 days, each with fixed $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$2 exposure, yielded a median internal uncertainty of $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$3, with simultaneous FP calibration measuring instrumental drifts well below $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$4 (Sozzetti et al., 2021).

Cadence is similarly deliberate. The program overview reports 2–4 nights between visits over baselines of 2–36 months, with a mean baseline of $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$5 months (Hobson et al., 26 May 2026). This cadence is not merely operational convenience: it is linked to the need to resolve low-amplitude Keplerian signals, separate them from stellar activity, and support model selection between circular and eccentric orbits, one- and two-planet hypotheses, and GP or non-GP noise models.

3. Scheduling strategy and phase coverage

A distinctive methodological contribution of the sub-program is the study of scheduling for ESPRESSO follow-up of TESS targets. Three strategies were compared: a purely random scheduler (Strategy A1), a myopic uniform-in-phase scheduler (Strategy A2), and a non-myopic uniform-in-phase scheduler (Strategy B) (Cabona et al., 2020).

The random scheduler chooses uniformly among all stars satisfying the observability constraint of airmass $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$6 and Moon separation $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$7, with no equalizing rule and no phase-uniformity objective. In simulations, it produced 2–49 observations per star, with mean $50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$8, and very uneven phase coverage (Cabona et al., 2020). By contrast, the myopic uniform-in-phase scheduler operates slot by slot. At each available 24 min slot it forms the subset of stars satisfying the same observability constraint and an “equalizing” rule, namely that the star have no more prior observations than the most-observed star. If several stars tie, it selects the star whose addition maximizes

$50 S_\oplus \lesssim S_p \lesssim 200 S_\oplus$9

where $V \approx 10$0 is the orbital phase of the transiting planet at the $V \approx 10$1th observation and $V \approx 10$2 is the normalized distance in phase to the nearest neighbor, summing distances if the star has multiple transiting planets. Before every star has at least one observation, choice among as-yet unobserved stars is random. This strategy yielded 17–24 observations per star with nearly uniform phase coverage (Cabona et al., 2020).

The non-myopic version searches across all 1,102 slots for the single schedule maximizing

$V \approx 10$3

subject to the same observability constraint and the additional requirement that each of the 50 stars be observed at least 20 times. Optimization used the acebayes R-package approximate coordinate-exchange algorithm in two dimensions, slot time and star-ID; after 100 ACE runs, each of 2,204 coordinate-exchange steps, the best schedule was retained (Cabona et al., 2020).

The substantive result is that random scheduling leads to more biased, less accurate, and less precise mass estimates for transiting planets, while no significant differences were found between the myopic and non-myopic uniform-in-phase implementations. With only about 22 RV measurements per dataset, uniform-in-phase scheduling enabled an unbiased measurement of transiting-planet masses at the level of $V \approx 10$4, while keeping average relative accuracy and precision around $V \approx 10$5 and $V \approx 10$6, respectively. In the correlated stellar-activity case, the reported transiting-planet semi-amplitude metrics were $V \approx 10$7, $V \approx 10$8, $V \approx 10$9 for A2; $(v \sin i < 5\ \mathrm{km\ s^{-1}})$0, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$1, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$2 for B; and $(v \sin i < 5\ \mathrm{km\ s^{-1}})$3, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$4, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$5 for A1 (Cabona et al., 2020).

The scheduling study also frames an important correction to a common simplification. Non-circular orbits and uneven RV uncertainties make “quadrature-only” or random phase sampling sub-optimal and prone to $(v \sin i < 5\ \mathrm{km\ s^{-1}})$6–$(v \sin i < 5\ \mathrm{km\ s^{-1}})$7 degeneracies and biases; uniform-in-phase sampling minimizes nearest-neighbor gaps in phase and partially lifts those degeneracies. Over a 3 yr span and for periods below 50 d, the myopic sequential optimizer can “catch up” to the global optimizer, so the simple myopic implementation was recommended in practice (Cabona et al., 2020).

4. Reduction pipeline and Bayesian inference

The sub-program relies on a fully Bayesian analysis culture, but the literature documents more than one concrete implementation. In the program-wide overview, RVs are obtained from the ESPRESSO DRS with the CCF method, sometimes supplemented by published HIRES, HARPS, or PFS data; activity indicators include CCF FWHM, BIS, contrast, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$8, $(v \sin i < 5\ \mathrm{km\ s^{-1}})$9, H$(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$0, and Na I D; and joint photometry+RV fits are performed with juliet, combining batman transit models, radvel Keplerians, celerite or George Gaussian processes, and dynesty nested sampling (Hobson et al., 26 May 2026). In the scheduling simulations, the RV time series for a star is modeled as

$(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$1

with $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$2 combining ETC photon noise, instrumental noise $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$3, and stellar-activity noise represented either by a quasi-periodic GP or by white noise. Model selection for extra non-transiting planets is performed by iterative Bayes factors with threshold $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$4, and the computation was carried out with kima, parallelized on AWS, for about 3,000 datasets in less than 5 hr (Cabona et al., 2020).

Individual target papers expose the operational details of this framework. For HIP 29442, ESPRESSO DRS v3.0.0 performed bias subtraction, flat-fielding, order extraction, blaze correction, wavelength calibration using simultaneous ThAr lamps and Fabry–Pérot reference, instrumental drift correction from fibre B, and barycentric Earth Radial Velocity correction; the G9-mask CCF yielded RV, BIS, and FWHM, while the chromospheric $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$5-index from Ca II H&K lines was converted to $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$6 following Noyes et al. (1984) (Damasso et al., 2023). The RV model used a sum of Keplerians plus offsets and a quasi-periodic stellar-activity term,

$(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$7

with a quasi-periodic kernel

$(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$8

TESS photometry was modeled with batman transits, quadratic limb darkening, and a Matérn-3/2 GP for residual correlated noise; in practice, photometry and RVs were fit in two separate but consistent steps, with tight Gaussian priors on $(\mathrm{TESS\ rms} \lesssim 300\ \mathrm{ppm})$9 from the TESS fit when modeling the RVs (Damasso et al., 2023).

The performance metrics used in the scheduling study make explicit how inference quality is judged: for a parameter $1$0 with true value $1$1 and posterior summary $1$2, $1$3, absolute bias is $1$4, relative bias is $1$5, absolute accuracy is $1$6, relative accuracy is $1$7, absolute precision is $1$8, and relative precision is $1$9 (Cabona et al., 2020).

5. Representative systems and the ESPRESSO–TESS synergy

HIP 29442 (TOI-469) is a compact multi-planet system that illustrates the sub-program’s workflow from RV detection to transit recovery. The initial target was a validated sub-Neptune candidate around a bright K0V star, selected because it was bright enough for few-tens-cm s$5\ \mathrm{m\ s^{-1}}$0 precision and because it was scientifically important for exploring how planets populate the radius gap. The explicit goals were to confirm TOI-469.01, measure its mass to better than $5\ \mathrm{m\ s^{-1}}$1, search for additional low-mass companions in the RV residuals, and use RV ephemerides to uncover low-S/N transits in the TESS light curve (Damasso et al., 2023).

ESPRESSO frequency analysis revealed significant peaks at approximately 13.63 d, 3.54 d, and 6.44 d. After detrending the TESS PDCSAP light curve with a GP using SHOTerm+RotationTerm in celerite2, Transit Least Squares recovered the known 13.63 d transits of planet b; masking those transits and re-running TLS at the RV-informed periods recovered the 3.54 d signal of planet c with $5\ \mathrm{m\ s^{-1}}$2 and then the 6.44 d signal of planet d with $5\ \mathrm{m\ s^{-1}}$3. A refined GP+multi-transit model on the full TESS S6+S33 light curve increased the SDEs to 28.4, 18.4, and 8.9, respectively (Damasso et al., 2023). The final masses were $5\ \mathrm{m\ s^{-1}}$4, $5\ \mathrm{m\ s^{-1}}$5, and $5\ \mathrm{m\ s^{-1}}$6 for planets b, c, and d, with radii $5\ \mathrm{m\ s^{-1}}$7, $5\ \mathrm{m\ s^{-1}}$8, and $5\ \mathrm{m\ s^{-1}}$9, and bulk densities $\lesssim 25\%$0, $\lesssim 25\%$1, and $\lesssim 25\%$2 (Damasso et al., 2023). Interior-structure modeling supported planet b as a typical sub-Neptune with a pure H–He gas layer of mass $\lesssim 25\%$3 and thickness $\lesssim 25\%$4, while planets c and d were consistent with Earth-like compositions (Damasso et al., 2023).

HD 5278 (TOI-130) represents a complementary case. Using 43 ESPRESSO spectra and TESS photometry, the analysis derived a mass of $\lesssim 25\%$5 and radius $\lesssim 25\%$6 for the transiting sub-Neptune TOI-130 b, implying mean density $\lesssim 25\%$7, and discovered a second, non-transiting companion with period $\lesssim 25\%$8 d and minimum mass $\lesssim 25\%$9 (Sozzetti et al., 2021). The interior-structure retrieval for planet b yielded roughly 0.13/0.56/0.30 core/mantle/water mass fractions, plus a tiny H–He envelope contributing $V \lesssim 14.5$00 of the measured radius (Sozzetti et al., 2021).

These systems exemplify a central feature of the sub-program: high-precision RVs do not only weigh known transiting planets; they also reveal additional companions and can drive the recovery of transit signals that are weak or initially missed in TESS photometry. The documented ESPRESSO–TESS synergy is therefore bidirectional: transits provide ephemerides and radii, while RVs refine masses, uncover additional architecture, and guide photometric searches for low-S/N events (Damasso et al., 2023).

6. Population-level results and longer-term significance

At the population level, the sub-program has been used to place the small-planet sample in the context of precisely characterized planets more generally. In the medium-insolation regime $V \lesssim 14.5$01–$V \lesssim 14.5$02, the overview reports a tentative mass threshold at approximately $V \lesssim 14.5$03 for the rocky to volatile-rich composition transition: below $V \lesssim 14.5$04, planets are mostly rocky with $V \lesssim 14.5$05, whereas above $V \lesssim 14.5$06 they are volatile-rich, with H$V \lesssim 14.5$07O or H/He envelopes (Hobson et al., 26 May 2026). At higher insolation, $V \lesssim 14.5$08, a population of likely stripped massive rocky planets with masses of 6–10 $V \lesssim 14.5$09 appears, interpreted as photoevaporated cores of former sub-Neptunes (Hobson et al., 26 May 2026).

The same study reports a mass–metallicity relation in the combined WG3+PlanetS sample,

$V \lesssim 14.5$10

with $V \lesssim 14.5$11-value $V \lesssim 14.5$12, indicating that more massive small planets are hosted by more metal-rich stars (Hobson et al., 26 May 2026). It also reproduces the radius valley through

$V \lesssim 14.5$13

and finds that the mass distributions below and above the gap cross at $V \lesssim 14.5$14, consistent with the rocky–volatile threshold (Hobson et al., 26 May 2026).

The observing strategy itself became part of the scientific result. The overview states that a minimum of $V \lesssim 14.5$15 high-precision RVs is required to measure $V \lesssim 14.5$16 with $V \lesssim 14.5$17 significance, that ESPRESSO-only precision sharply reduces mass uncertainties, and that mixing in lower-precision datasets increases jitter and offset complexity (Hobson et al., 26 May 2026). For PLATO follow-up, the documented lessons are to prioritize brightness $V \lesssim 14.5$18, plan $V \lesssim 14.5$19–$V \lesssim 14.5$20 RVs per target, include simultaneous activity diagnostics, and apply GP modeling, with CCF FWHM identified as the most reliable indicator in ESPRESSO data (Hobson et al., 26 May 2026).

Taken together, these results define the ESPRESSO Transit Follow-up Sub-program as both an observational infrastructure and a methodological framework. Its contribution lies not only in confirming individual planets, but also in establishing a benchmark sample with sufficiently precise masses, radii, and compositions to support population-level statements about the rocky–volatile boundary, the radius valley, stellar-metallicity correlations, and the architecture of compact small-planet systems (Hobson et al., 26 May 2026).