A Model Selection Criterion for Multidimensional Gaussian Processes applied to RVs
Oscar Barragán
Multidimensional Gaussian Process (multi-GP) regression is widely used to disentangle stellar and planetary signals in radial velocities (RVs) by jointly modelling ancillary activity indicators. However, identifying the combination of indicators that best constrains the stellar signal in the RVs is non-trivial, as classical model comparison methods are not directly applicable when multi-GPs involve different time series combinations. In this contribution, I will present an information criterion to compare multi-GP models based on their ability to explain the RV component. I will discuss how this criterion provides a quantitative and robust framework for multi-GP model comparison, identifying the activity indicators that most effectively constrain the RV signal. Although developed in the context of RV analysis, the proposed criterion is general and applicable to multi-GP problems in which the inference focuses on a specific observable.
CALM periodogram method enables simultaneous fitting of any RV noise tracer within your planet search
Zoë de Beurs
Activity signals imprint signatures in the time- and wavelength-domain through their quasiperiodic nature and wavelength-dependent magnetic effects. Our data-driven CALM periodogram method can incorporate any activity or instrumental tracer and combine them with timing information using least-squares periodograms. By including these tracers within the periodogram search, we model the sources of RV noise concurrently within the search for planetary Doppler shifts.
We applied this novel approach to hundreds of FGKM stars observed by HARPS, making it the first systematic planet search where a noise tracer is simultaneously fit with planet periods. Our method is effective at mitigating periodogram peaks due to rotation and long-period cycles. We found several new planet candidates with some semi-amplitudes as low as 30 cm/s. This work paves the way to determining the occurrence of Earth-like planets and expands the sample of stars with modeled magnetic cycles, enabling further studies into granulation and supergranulation.
Reproducing HARPS-N solar RVs with disc-integrated MURaM_MPS-ATLAS spectra and SDO activity maps
Ryan Corzo
High-resolution spectrographs, such as HARPS-N, are advancing efforts to characterise Earth-like exoplanets, enabling RV measurements below ~1 m/s. However, the intrinsic magnetic and convective activity of exoplanet host stars, giving rise to granulation, faculae, and spots, induces RV variations that pose a fundamental barrier to exoplanet detection. To investigate how spectral lines respond to stellar activity, we construct a finite-element 'digital twin' of the Sun, and 'paint' its surface with specific intensity spectra from 3D magnetohydrodynamic simulations of the solar photosphere from the MURaM code. Using images from the Solar Dynamics Observatory (SDO), we then reproduce active-region positions across the solar disc to generate realistic solar RVs driven by magnetic activity and horizontal surface flows. We benchmark the resulting RV timeseries against ‘Sun-as-a-Star’ RVs from the SolAster code, and HARPS-N solar observations, demonstrating that the synthetic RVs are consistent with both. This paves the way for improved mitigation of stellar activity effects on exoplanet RV measurements.
Using structure functions to study supergranulation and granulation in stars other than the Sun
Jay Fitzpatrick
Characterising the variability imparted by granulation and supergranulation while making as few model assumptions about their form will be important to ensure that their removal does not bias the final time-series. Structure functions are a statistical tool to investigate the variability of a time-series by comparing the variation of points with similar separations in time across the time-series. They are particularly useful when investigating aperiodic variability and were used to identify supergranulation as a major contributor to Sun-as-a-star radial velocity time-series. We have expanded the use of structure functions on EPRV time-series to stars other than the Sun as well as developing new techniques allowing us to characterise the correlated component of the time-series. These methods will be a great addition to the community tool kit for both characterising and separating stellar and instrumental signals in a model-free way.
A scalable approach for likelihood-based coherence modeling in many-variate GPs with applications to RV planet detection
Chris Geoga
Astronomers have identified many spectroscopic indicators that could contribute to separating true Doppler shifts due to low-mass planets from spurious signals due to stellar variability. While astrophysics may motivate the covariance structure of one indicator as a function of time, it provides little insight into relationships across indicators. For this reason, coherent structures between them need to be discovered. Due to measurement gaps and irregularities, direct Fourier- or Lomb-Scargle-based coherence estimators pose difficult multiple testing questions about balancing power and false detection rates. Gaussian process (GP) models and full likeilhood methods can lessen these challenges, but large data sizes may make exact likelihood methods prohibitively expensive. To address these issues, we describe a multivariate spectral approach for specifying GP models that uses nonuniform FFT-accelerated linear algebra and naturally offers special optimizations for simple coherence structures that are concentrated at a small number of discrete frequencies. This approach has quasilinear runtime cost in data size and linear cost in the process dimension, enabling the use of GP models for, e.g., ten line-shape measurements for one thousand lines at hundreds or thousands of observation times. The same matrix structures being exploited in this algorithm also admit quasilinear-cost simulations, which may be useful for simulation studies of detection efficiency of RV surveys as a function of planet and noise properties.
Chromatic signatures of stellar activity in near-infrared radial velocities
Salomé Grouffal
Stellar activity remains the primary limitation to the detection and characterization of terrestrial exoplanets around M dwarfs. Using high-resolution SPIRou spectra, we explore the chromatic nature of activity-induced radial velocity signals at the level of individual spectral lines. Selecting lines according to their spot-to-photosphere contrast reveals two distinct families of lines producing anti-correlated RV signals, first identified in EV Lac (Larue et al. 2025) and now observed across a broader sample of active M dwarfs and young stars.
Building on this contrast analysis, we constrain spot temperature and surface coverage evolution and explain the reduced activity amplitudes observed in the near-infrared compared to the visible. We develop a method to mitigate spot-induced RV variability while preserving planetary signals. We also introduce a new activity indicator that enhances activity signatures, providing a powerful constraint for Gaussian Process activity modelling, even when activity signals are weak in the global RVs.
A physics-based model of stellar activity
Nathan Hara
Stellar activity is one of the main obstacles to the detection of small planets with radial velocity, and modelling precisely its effect is critical. While the simulations of stellar activity signatures include sophisticated physics, existing likelihood models are based on qualitative considerations. In this talk, I will present the FENRIR framework, which allows build a likelihood starting from quantitative physical hypotheses. It has several advantages: (1) it can be used on any combination of observables (RV, indicators, photometry), not necessarily sampled at the same epochs while remaining fast, as its evaluation cost scales linearly with the number of data points (2) its predictive accuracy, measured by cross-validation, is significantly better than existing models. (3) Our model explains and quantifies the non Gaussianity of stellar activity signals. (4) FENRIR enables a new form of Doppler imaging: even if the active regions are too small to be resolved individually, their average properties can be probed through the statistical properties of the signal. We demonstrate this « statistical Doppler imaging » technique using the HARPS-N RVs and SORCE photometry, and retrieve the solar obliquity with a ~ 5° precision, and discuss its application to M stars.
Tracing the Spectral Fingerprints of Magnetically Active Regions Across the Optical Spectrum
Katlyn Hobbs
Spectral Ratio Analysis (SRA) is a powerful technique for isolating the spectral signatures of stellar activity. Magnetically active regions such as faculae and spots are a dominant source of stellar activity noise in radial velocity measurements, yet their individual spectral contributions remain difficult to isolate in disk-integrated observations. To separate genuine solar signals from instrumental systematics, I will discuss how we apply SRA to contemporaneous Sun-as-a-star observations from HARPS-N, NEID, KPF SoCal, and EXPRES. Comparing signals across instruments and timescales enables us to confirm the solar origin of recovered features and decompose activity-driven variability into its constituent line-shape components, including shifts, asymmetries, and depth changes. The resulting SRA spectra reveal coherent, line-dependent variability across rotational timescales, which we correlate with facular and spot-filling factors derived from Solar Dynamics Observatory (SDO) images to directly link spectral morphology to surface magnetic structures.
Stellar granulation-induced variability across the optical spectrum
Cis Lagae
Radial velocity noise from the exoplanet hosting star, as caused by stellar activity such as granulation or faculae, hamper the detection and characterization of earth-mass exoplanets. We have build a framework that isolates and characterizes the radial velocity signature due to granulation for individual spectral lines computed from 3D stellar models. Building on this, we expanded the method to larger spectral regions, including tens of spectral lines, with the goal of mimicking real disk-integrated stellar observations. Using this method, we have quantified how granulation affects the properties and radial velocities of spectral lines differentially, from disk centre to the stellar limb. We found that certain groups of lines behave radically different than others, based on their atomic parameters and line depth. Ultimately, this work will enable us to identify key granulation noise diagnostics across the optical spectrum that can be used to reduce the granulation-induced radial velocity noise from observations.
An Exposure-averaged Gaussian Process Framework to Recover Stellar Variability in Combined Radial Velocity Data Sets
Jacob Luhn
The advent of solar data sets from several EPRV instruments enables new studies of solar and instrumental variability. One challenge when combining these time series arises from the different exposure times for each instrument, especially relevant for p-mode oscillations, where exposure times and variability timescales are comparable. As a result, each instrument traces a unique binned version of the true underlying signal, and traditional Gaussian process (GP) kernels describing the instantaneous covariance cannot be used. We present a new approach for combining multiple time series using a GP framework that accounts for individual exposure times and predicts the “latent” unobserved oscillation signal. We show that with this framework, we can model and recover instrumental drifts for each instrument, provided instruments have overlapping observations. We expect this approach will be critical for studying and characterizing both solar and instrumental variability, especially for instruments located at similar longitudes with significant overlap.
Granulation signatures in line-by-line precise RVs from first disk-resolved PoET observations
Carmen San Nicolas Martinez
We present the first results from disk-resolved solar observations of granulation obtained with the PoET telescope, focusing on time-series at disk center. To analyse these observations, we use TILARA, a template-independent line-by-line RV extraction framework based on iterative multi-Gaussian modelling of individual absorption lines. This approach enables a detailed exploration of how granulation affects spectral lines.
We classify spectral lines according to their sensitivity to granulation-driven RV variations, identifying both relatively insensitive lines and lines strongly affected by granulation. We further quantify how the induced RV shifts depend on key spectral line properties such as depth, wavelength, equivalent width, and full width at half maximum. Together, these results provide new insight into how granulation signatures are encoded across the spectrum and lay the groundwork for activity-mitigation strategies based on selective line weighting and optimized spectral masks for extreme-precision RV studies.
Visible Versus Near-Infrared Solar-type Activity Patterns
Khaled Al Moulla
In 2023, the near-infrared (NIR) NIRPS spectrograph began its symbiotic operations with the visible (VIS) HARPS spectrograph. Both instruments are connected to the HELIOS solar telescope, which delivers disk-integrated observations at a 1-minute cadence. While there exists other solar facilitates at various high-resolution spectrographs, primarily in the VIS, the NIRPS dataset is the first of its kind to achieve long-term instrumental precision at NIR wavelengths with substantial baseline to cover astrophysical signals at multiple timescales. We present an overview of the NIRPS solar data (achieving a median intra-day RV RMS of 1.5 m/s), and compare the astrophysical signals present in the RVs with their VIS counterparts. Specifically, we demonstrate how the pressure modes appear unchanged, how the granulation phenomena exhibit shorter timescales and increased scatter in the NIR, and how the unsigned magnetic flux can be extracted with high confidence in both the VIS and NIR.
From Solar to Stellar: Investigating the Spectral Impact of Supergranulation
Niamh O'Sullivan
In recent years supergranulation has emerged as one of the biggest challenges for the detection of Earth-twins in (RV) planet searches. I will present work into searching for supergranulation’s RV and spectral signature in stars other than the Sun for the first time. Looking at archival asteroseismic campaigns I will show how we have characterised supergranulation in a handful of stars, and how this can help us start our search for a supergranulation spectral indicator. I will demonstrate the need for dedicated supergranulation observational campaigns and talk about the Terra Hunting Experiment’s potential SHE survey, one of the first of these campaigns, and the preparations taken for it. I will also present preliminary work investigating supergranulation’s effect on specific spectral line groups, the first step in searching for a spectroscopic supergranulation indicator, which is urgently needed to mitigate supergranulation in RV surveys.
Measuring Granulation Jitter in 3D and Probing Depth-dependent Variability
Michael Palumbo
Temporal variability in near-surface convection creates RV jitter that varies between lines. Previous studies have attempted to quantify this differential jitter by measuring variability in lines grouped by modeled "formation temperatures." However, these codes assume a time-static, plane-parallel stellar atmosphere, neglecting the spatial variability between granules and lanes. Here, we present a method for directly inferring the "true", convectively-perturbed line contribution functions directly from the observed shape of spectral lines. We use a hydrodynamical simulation as a toy model to show that our method (which uses GPU-accelerated radiative transfer to forward-model the observed line profile) retrieves the correct depth-dependent convective flows. We then apply our method to "Sun-as-a-star" spectra to retrieve disk-integrated contribution functions. In closing, we discuss how these empirical contribution functions can be used with GP codes to map depth-dependent variability in the stellar atmosphere, moving beyond previous GP implementations on singular, CCF-derived RV time series.
CANSTAR: Mitigating stellar radial velocity jitter using orthogonal activity indices and a time-aware neural network
Jordi Blanco Pozo
We present CANSTAR (Convolutional-Attention Network for STellar Activity Removal), a novel deep-learning approach to mitigate stellar activity in RV data. It extracts line-shape distortion indices from the Cross-Correlation Function, feeding them into a hybrid convolutional neural network and transformer architecture to capture short- and long-term activity correlations. We train the network on synthetic StarSim data, achieving cm/s precision. We validate the framework across two distinct test cases.
First, using HARPS and CARMENES observations of the active stars ε Eridani and TZ Arietis, CANSTAR reduces the radial velocity RMS to 52.5% and 62.4% of uncorrected variability, significantly improving planetary parameter determination for TZ Arietis b compared to standard Gaussian Process modeling.
Second, we present preliminary results applying CANSTAR to HARPS-N solar observations using the StarSim/SunSim code, which incorporates 3D magnetohydrodynamic spectra and complex instrumental modeling, paving the way for the detection of Earth-like exoplanets around Sun-like stars.
Modeling the vertical velocity gradient to disentangle stellar activity from exoplanet signal
Varghese Reji
Extremely precise radial velocity (EPRV) measurements are critical for discovering habitable planets and estimating their masses. Modern EPRV instruments have achieved cm/s stability, however, that hasn’t translated to the discovery of earth-like planets around sun-like stars. Below a few m/s, the Doppler shift of spectral lines due to stellar activity will start dominating planetary signals. A planetary radial velocity signal should be consistent across all the heights, while a stellar activity-induced photospheric velocity, could be different at different heights of the stellar atmosphere. Based on this idea, we developed a method to disentangle stellar activity signals and planetary signals in radial velocity data. In our model, we treat the rising and falling lanes of granulation separately. We first calculate the ‘granulation contrast’, and then determine the velocity profile of both raising and falling lanes. Using Korg, a julia package for spectral synthesis, we solve the radiative transfer equation with an atmospheric model after Doppler shifting each photospheric layer by a vertical velocity profile model. To test our model, we fit this synthetic spectrum with multi epochs of disk-averaged solar spectra observed with NEID. The stellar activity parameters of our model are the coefficients of the velocity gradient polynomial. In this talk, I will present our model and its effectiveness in disentangling planetary signals from stellar activity signals.
Isolating astrophysical from instrumental variability at the pixel level in EPRV solar spectra
Ryan Rubenzahl
Discovering Earth-analog exoplanets via radial velocities is complicated by stellar and instrumental variability across all timescales. We analyzed one year of KPF, NEID, EXPRES, and HARPS-N solar RVs at the line-by-line and pixel-by-pixel (PBP) level to isolate common solar variability from uncommon instrumental drift. The common signal is modeled as a multicomponent Gaussian process (GP) to separate the time-domain signatures of oscillations, granulation, supergranulation, and active regions. The uncommon model is unique to each instrument and enables drift mapping across the detectors. We used the state space representation of GPs to efficiently handle ~100k observations while accounting for each instrument’s unique exposure time (see smolgp tutorial). We mapped the PBP solar signals to atmospheric layers using contribution functions, revealing how each solar process varies throughout the atmosphere. We aim to leverage this methodology to identify families of lines (or spectral segments) which covary to inform activity-invariant Doppler estimation.
Beating solar radial velocity jitter below 50cm/s with physics-based modeling
Sophie Stucki
Stellar magnetic activity has become the dominant limitation for RV detection of Earth analogs, whose expected signal amplitude is of the order of 10 cm/s. The Sun provides a unique benchmark to test physics-based models and assess their ability to reproduce activity-driven RV variability at the sub-m/s level.
I will present a stringent validation of the physics-based StarSim/SunSim framework using solar observations. SunSim combines SDO/HMI continuum intensity and LOS magnetogram images to derive the distribution of magnetic surface features and generate synthetic TSI and RV time series using spectra computed from 3D MHD MURaM simulations.
Comparisons with HARPS-N observations show that SunSim reproduces solar activity from daily timescales to the solar cycle, reaching residual RV scatter of 49 cm/s over three years, consistent with the intrinsic deviation of HARPS-N and comparable to state-of-the-art data-driven approaches. Beyond reproducing solar variability, injection–recovery experiments demonstrate improved planetary signal recovery through physics-based modeling, extending detectability toward lower-mass exoplanets.
Incorporating Stellar Magnetic Cycles into Gaussian Process Modelling to Improve Earth-Analogue Sensitivity
Valentina Tardugno
Despite significant advances in high-precision radial velocity instrumentation, the detection of low-amplitude signals induced by Earth-like planets remains largely limited due to stellar variability. Although Gaussian Processes (GPs) are powerful tools to model stellar activity, most applications do not account for the long-term variability induced by magnetic cycles. In this work, I incorporate information about long-term activity cycles into the Multi-GP framework, with the aim of extending detection capabilities to include Earth analogues. I investigate non-stationary GP models with a cycle function modulating the covariance kernel, and the impact of cycle-dependent contributions into the mean functions of the radial velocities and $\log{R’_{HK}}$ time series. The models are implemented using the s+leaf package, which provides computationally efficient GP inference, enabling rapid modelling and supporting larger-scale planet-search efforts. The framework is tested using injected planetary signals in simulated datasets and the 10-year daily-binned solar dataset, with model performance evaluated through leave-one-out cross-validation. I assess the impact of incorporating long-term cycle information on stellar activity mitigation, Earth-like planet detectability, and broader detection limits. These results demonstrate the potential of cycle-informed GP models to improve sensitivity to low-amplitude signals and provide a scalable framework for the next generation of radial velocity surveys.
The Extreme Stellar Signals Project IV: Results with Concurrent Solar Data
Lily Zhao
The Extreme Stellar Signals Project (ESSP) is an international research network of scientists working to further methods for mitigating stellar signals. The ESSP organizes rounds of data challenges to conduct apples-to-apples comparisons of the performance of different mitigation methods on the same data sets. Oh behalf of the collaboration, I will present results from the just finished ESSP IV round, which makes use of contemporaneous Sun-as-a-star observations taken by HARPS, HARPS-N, EXPRES, and NEID. I will highlight the different approaches of each method, their success in recovering injected planet signals, and tracers of the different components to solar activity.
Measuring Sub-Kelvin Variations in Stellar Temperature: the dTemp indicator
Charles Cadieux
This presentation introduces dTemp, a novel line-by-line differential temperature indicator capable of measuring stellar temperature variations with sub-Kelvin precision. Derived from correlated changes in the depths of spectral lines, dTemp provides a powerful new tracer of stellar magnetic activity. Several case studies are presented in which dTemp is used to mitigate stellar activity in RVs. Applied to a decade of HARPS-N solar observations, the dTemp time series is largely explained by the evolving coverage of bright/dark active regions measured from SDO data. dTemp traces supergranulation, rotation, and magnetic-cycle variability while providing a photometric proxy derived entirely from spectroscopy. Using the FENRIR multidimensional GP framework to jointly model solar RVs and dTemp, the RV residuals reach 40 cm/s over ten years, demonstrating a promising pathway toward the detection of true Earth analogs.
smolgp: Scalable Gaussian Processes for Integrated and Overlapping Measurements Via Augmented State Space Models
Soichiro Hattori
We introduce smolgp, a Python/JAX package for fast Gaussian process (GP) regression with integrated measurements and overlapping multi-instrument datasets. Traditional GP solvers require O(N³) computation when measurements are integrated or overlapping, since the covariance matrix loses any low-rank structure. Instead, smolgp uses state space representations which are solved via Kalman filtering and RTS smoothing in O(N). In this tutorial we will give an overview of state space models (SSMs), their relationship to GPs, and how integrated measurements are compatible with O(N). As SSMs by construction simultaneously model the latent state and its derivatives, they are particularly useful for models such as FF’. SSMs exactly represent any GP with rational power spectral density (PSD), and can approximate arbitrary kernels by expanding the PSD into rational functions such as the (quasi)periodic kernel favored in astronomy. We will present tutorial notebooks demonstrating each of these use cases.
Deciphering the Signal of Young Star TOI-942 using Gaussian Processes
Keith Baka
Studying young exoplanet systems is crucial to better understand the formation and evolutionary mechanisms of exoplanets, and to inform how atmospheric escape, thermal inflation, and migration shape the current population. The 50 Myr old TOI-942 system is a perfect laboratory to explore these mechanisms, with two Neptune-sized planets positioned just at the edge of the hot Neptune desert, meaning that precise mass measurements will serve as an anchor for the mass loss rate as a function of distance to the host. Therefore, we employ a multidimensional Gaussian process model to overcome semi-periodic activity signals by combining 61 ESPRESSO observations with TESS photometry and activity indicators to successfully measure the mass of TOI-942b&c. We run 24 other models and employ two analysis softwares to compare results and check consistency. We present the results of our fiducial model, as well as commentary on GP codes and a recommendation for a meta-study.
Revisiting the CoRoT-7 system with multi-dimensional GPs in the PLATO era
Pia Cortes-Zuleta
PLATO will identify Earth-like planets transiting Sun-like stars within their Habitable Zone. However, the stellar activity RV jitter will hamper their characterisation. PLATO candidates will benefit from contemporary photometry alongside RVs, offering a unique opportunity to incorporate photometry in the activity model. Here, we revisit the CoRoT-7 system—a young Sun-like star hosting three planets— using HARPS RVs and CoRoT photometry. We explore the integration of contemporaneous photometry and RVs to model stellar activity using multi-dimensional GPs. Photometry-based activity models yield planetary mass measurements comparable to those using FWHM, though the MGIC_rv metric reveals that FWHM models perform better overall. Injection-recovery tests demonstrate that both models achieve fractional mass recovery within 20% for RV semi-amplitudes above 1.5 m/s, with performance degrading for smaller amplitudes. While FWHM remains the preferred activity indicator for CoRoT-7, photometry-based models show promise for younger, more active systems or for cases of suboptimal cadence.
A benchmark for spectroscopy of infant planetary systems: the case of V1298 Tau
Mario Damasso
I will present the latest results regarding the complex challenge of measuring the masses of planets in the V1298 Tau system using radial velocities, based on nearly 400 spectra collected with HARPS-N over a time span of 4.5 years. This system is of particular interest as it raises issues concerning the extraction and modelling of radial velocities of very young and active stars, as well as serving as a benchmark for comparing planetary masses measured using different techniques.
GP Periodogram to identify and differentiate activity and Keplerian signals
Mangesh Daspute
We developed a GP periodogram using a dSHO kernel and applied it to StarSim simulated activity-induced RVs. GP periodogram identifies quasi-periodic signals like rotational periods of stars with different spot patterns, for sparsely sampled data with higher probability compared to GLS, and it is especially good at Random, ONE, and asymmetric TWO spot region configuration. It successfully detects a signal with an RMS 4 times lower than the GLS periodogram can detect in the presence of similar noise. It identifies the correct value of the rotational period instead of its harmonic more often than GLS does. It can identify and differentiate periodic and quasi-periodic signals, such as Keplerian and stellar activity, using the lifetimes and amplitudes of the GP kernel terms. GP periodogram is a new open-source tool for identifying quasi-periodic and periodic signals, and it is especially good for challenging situations like sparsely sampled and noisy data, which has contribution in harmonic and changes amplitude and phase.
Diagnosing and characterizing stellar activity signals with complex demodulation
Amna Ejaz
Stellar processes introduce quasiperiodic radial velocity variations that can mimic planetary signals. Doppler planet searches are particularly vulnerable to false positives at the stellar rotation frequency and its harmonics; examples are refuted planets HD~26965~b (Vulcan) and the previous iteration of Barnard~b. One distinguishing feature of rotational variations is that they are often modulated by the magnetic activity cycle, whereas an Earthlike planetary signal cannot be modulated by a stellar process. Here we introduce complex demodulation, which isolates the long-period wave envelope generated by a process that modulates a shorter-period oscillation, as a planet-validation tool. Complex demodulation can serve as a litmus test to differentiate between rotation and planet signals and can be performed directly on radial velocity time series without accompanying activity indicators. We demonstrate complex demodulation on synthetic data before applying it to the archival solar Bremen composite Mg II index, HARPS-N solar radial velocities, and HD 190360 radial velocities. For the solar Mg II data, we recover a modulating envelope that traces the 11-year magnetic activity cycle and includes the Gnevyshev gaps. The modulating envelope we estimate from the solar radial velocities shows amplitude variation that is consistent with the Schwabe cycle phase. In HD 190360 radial velocities, we demonstrate that a pseudowindow with sidelobes created by seasonal gaps can produce a spurious ``modulating envelope'' that reflects the time sampling rather than a physical process. Therefore, we must exercise caution when interpreting the modulating envelope. This work is the first application of complex demodulation to ground-based astronomical data.
Using (multi-)GPs to characterise planets smaller than Earth
Yoshi Nike Emilia Eschen
Gliese 12 is a metal-poor M dwarf only 12 parsec away from us that is orbited by a single transiting planet of 1 REarth, on the edge the habitable zone. This target was and still is being characterised with multiple RV instruments including ESPRESSO, MAROON-X, HARPS-N, HARPS/NIRPS and CARMENES.
In this talk I present the challenges of modelling the activity in this system by combining multiple instruments and using (multi-)GPs in combination with long-term photometric monitoring, finally obtaining a mass of 1 MEarth. This establishes Gliese 12 b in a unique position of being the only temperate planet of Earth-size and -mass around a nearby star with an accurate RV mass measurement. This study not only paves the way for future atmospheric follow-up observations probing the habitability of our Earth-like neighbour but enables us to directly test (multi-)GP models to characterise planets smaller than Earth.
ESPRESSO high-precision RVs at 40 cm/s and lessons learned
Pedro Figueira
I present an analysis of the long-term ESPRESSO GTO RV monitoring campaign of low-activity GKM dwarfs, targeting the 10 cm/s precision required to detect Earth analogues. RV variability is characterized over timescales from minutes to hours, where oscillations and granulation dominate, to years, relevant for habitable-zone planet searches around GK stars. Using multiple RV extraction techniques and spectroscopic activity indicators, instrumental effects are disentangled from stellar signals, enabling identification of the processes that set the noise floor. Granulation and magnetically driven variability are expected to be the main contributors to the long-term RV floor of ≈40 cm/s found in the data.
The interplay between convection and magnetic activity shapes the observed RV signal and limits detection sensitivity. Understanding and modeling these processes is essential to improve the robustness of future RV surveys targeting Earth-like planets. I outline several avenues for mitigating stellar noise and highlight key directions for further investigation.
The NEID Earth Twin Survey. Confirmation of a Super Earth on a 19.9 day Orbit about the Near Solar Twin 18 Scorpii
Evan Fitzmaurice
We confirm the detection of 18 Sco b, a potential super-Earth (msini~6.76 M⊕) on an eccentric, 19.9 day orbit about the closest solar twin. This signal, now independently detected with NEID in only 3 years as part of the NEID Earth Twin Survey (Gupta et al. 2025) was first identified as a candidate in Laliotis et al. 2023 using ~20 years of archival RVs. 18 Sco (HD 146233), is a nearby (~14 pc) G-dwarf that is a close solar twin based on spectroscopically determined stellar parameters (Teff = 5808±3 K, log g = 4.440±0.009, [Fe/H] = +0.041±0.003, and M* = 1.022±0.004 M☉ (Spina et al. 2016)). We will discuss the different techniques we used to ensure that the signal is planetary, not stellar activity and discuss improvements necessary to detect terrestrial planets in the habitable zones of the nearest stars.
One offset or many? Combining multi-instrument EPRV observations with multi-output GPs
Eric B. Ford
Line-by-line (LBL) analyses of EPRV spectra routinely produce dozens to thousands of RV estimates per epoch rather than a single summary RV. Because stellar activity signals vary in amplitude across spectral lines while planetary signals do not, this wealth of outputs provides new opportunities for separating planets from stellar variability. Exploiting this information raises a practical question: when combining LBL RVs from separate instruments, do we need a distinct offset for each line from each instrument?
Multi-output Gaussian processes (GPs) encode correlations across outputs, letting the data determine whether instrument differences are better captured by a common shift or a richer, output-dependent covariance structure. We apply this framework to Sun-as-a-star observations from NEID and EXPRES, comparing models with a single instrument offset against those allowing output-dependent corrections. We will discuss implications for combining datasets from multiple EPRV instruments.
A Line-by-Line SVD Framework for Mitigating Granulation in Precision RVs
Christian Hartogh
Stellar granulation limits radial-velocity (RV) measurements at the cm s⁻¹ level. Since spectral lines form at different photospheric depths, changes in their line properties trace the evolving balance between granules and intergranular lanes that produces RV variability. We use noise-free MURaM simulations to test line-depth scale factors as granulation diagnostics and to isolate their intrinsic behaviour. In this ideal regime, singular value decomposition (SVD) captures almost all variance in the simulated RVs. Feature vectors are closely related with atomic species, excitation potential, and ionisation state. We then develop a two-step SVD method: first, a granulation subspace is learned from the noise-free line responses and noisy observations are projected onto it; second, lines with large uncertainties are downweighted to produce a noise-aware decorrelation basis. Applied to synthetic spectra, the method preserves injected planetary signals while reducing granulation-driven RV scatter, and it significantly improves HARPS-N solar RVs as well.
MMLSD + SCALPELS: A Unified Framework for Enhanced RV Extraction and Stellar‑Activity Mitigation
Ancy Anna John
Detecting Earth‑twins requires modelling radial velocities (RVs) at the 10 cm/s level, yet stellar variability—driven by surface inhomogeneities—still limits achievable precision to ~1 m/s, despite modern spectrographs reaching sub‑m/s stability. Further progress therefore depends on advances in RV extraction and analysis alongside instrumentation. Conventional pipelines use CCFs built from generic line masks, with variability‑mitigation methods such as SCALPELS improving precision to ~50 cm/s. I present MMLSD, an RV‑extraction method that uses unique theoretical VALD3 masks tailored to a star’s parameters and LSD to generate optimised common profiles. MMLSD RVs timeseries exhibit a lower RMS than conventional CCFs, and applying SVD to these timeseries provides a more direct and cleaner recovery of planetary signals. Incorporating SCALPELS into the MMLSD framework further reduces RV RMS across all stars analysed. This synergy between optimised line masks and advanced variability mitigation marks a promising step toward the RV precision required for detecting Earth-twins.
Homogeneous stellar-activity treatment in a sub-Neptune mass campaign around FGK stars
Pierrot Lamontagne
Published RV masses for sub-Neptunes are drawn from disparate pipelines, stellar-activity treatments, and statistical frameworks, injecting poorly quantified systematics into the mass-radius diagram. Apparent trends may reflect methodological inconsistencies rather than genuine astrophysical signals, a problem that accumulating more data cannot resolve. I present the re-derivation of masses for 12 sub-Neptune systems totalling 21 planets orbiting FGK dwarfs under a unified hierarchical Bayesian framework. Each target is processed through four independent RV extraction pipelines (CCF, SERVAL, LBL, sBART) with homogeneous stellar-activity treatment; posteriors are combined via leave-one-out cross-validation stacking, and the noise model is selected per target through Bayesian evidence rather than imposed a priori. The number of planets is itself a free parameter, enabling agnostic searches for additional companions. By casting a methodologically wide net across a controlled sample, we can identify and quantify biases introduced by pipeline choice, activity modelling, and stellar properties, laying the groundwork for unbiased demographic studies. This work constitutes a first step toward building a homogeneous, RV-based catalog of sub-Neptune density measurements.
Order-by-order Modeling of Exoplanet Radial Velocity Data
Zachary Langford
In the era of extremely precise radial velocity (EPRV) spectrographs, we are now in a regime where instrumental precision is below the intrinsic variability of many stars. These EPRV instruments, in principle, can provide sub-1 m/s measurement errors by collapsing the multi-wavelength spectra down to a single RV measurement at each epoch. However, astrophysical variations can be correlated in both time and wavelength, which will contaminate these types of RV measurements. In turn, this can bias the resulting estimation of exoplanet orbital parameters. We explore new methods for measuring exoplanet orbital parameters that take advantage of the fact that RV data sets are fundamentally multi-wavelength. Using simple Bayesian modeling techniques, and publicly available software and EPRV data, we show that we can achieve better Msini uncertainties compared to fitting single-RV-per-epoch time-series.
When Should We Use Gaussian Processes? Structure Function Diagnostics for RV Analysis in the Magellan TESS Survey
Jiayin Li
The Magellan TESS Survey (MTS) is a long-term radial velocity follow-up program using Magellan/PFS to characterize TESS small-planet systems in a statistically uniform framework. We present a homogeneous RV analysis of 25 MTS systems monitored over more than five years, focusing on the connection between inner small planets and outer giant companions. A major challenge is distinguishing long-period planetary signals from correlated stellar variability without introducing modeling biases. Because many hosts are relatively quiet, indiscriminate use of Gaussian Processes (GPs) can absorb genuine planetary signals, particularly non-transiting or long-period companions. We therefore develop a diagnostic pipeline based on Structure Function (SF) analyses of RV residuals after subtracting known transiting planets, together with stellar activity indicators such as SHK. GP components are introduced only when both RV and activity diagnostics support correlated stellar noise, reducing overfitting and enabling a less biased characterization of planetary architectures.
Investigating Systematic Noise in Ground-Based Exoplanet Transmission Spectroscopy with the 2m Himalayan Chandra Telescope
Bestha Manjunath
The detection of weak exoplanet atmospheric signals from ground-based spectroscopic observations is fundamentally limited by time- and wavelength-dependent systematic effects. Understanding, modeling, and mitigating these systematics is becoming increasingly important for next-generation precision spectroscopic surveys, where correlated noise can dominate over the planetary signal. Although nearly 6,000 exoplanets have been discovered to date, atmospheric characterization has been achieved for only a small fraction, highlighting the need to improve the treatment of systematic noise in high-precision spectroscopy.
In this work, we investigate systematic effects in ground-based exoplanet transmission spectroscopy using the 2m Himalayan Chandra Telescope (HCT). We employed the Hanle Faint Object Spectrograph and Camera (HFOSC) and the Hanle Echelle Spectrograph (HESP) to perform both low- and high-resolution spectroscopic observations of transiting exoplanets. Low-resolution observations of WASP-33b and WASP-12b were used to study chromatic and time-correlated systematics in differential spectrophotometry. In parallel, high-resolution observations of HD 209458b and KELT-9b obtained with HESP were analysed to explore systematic effects in transmission spectroscopy and cross-correlation analyses. We will discuss approaches for identifying and mitigating systematic trends across both the time and wavelength domains, including results showing evidence for Fe II absorption in KELT-9b.
LHS 6050b: Cool sub-Neptune around an active mid M-dwarf star
Ylenia Mascolo
We present the newly discovered sub-Neptune LHS 6050b (radius of 2.2±0.2 R⊕, mass of 5.2±2.2 M⊕, equilibrium temperature of 190K). The planet orbits within the outer edge of the habitable zone about an active, rapidly rotating M4V in a 40 day period orbit. We confirmed the bulk characteristics of this planet using both photometric datasets from TESS and ground-based facilities, and spectroscopic observations from ESPRESSO. We collected a total of 65 radial velocity measurements in two campaigns.
Stellar activity dominates the planetary Doppler signal by one order of magnitude in the measured velocities. We implemented a multi-dimensional Gaussian Process with a quasi-periodic kernel, and performed tests to disentangle the activity signals from the Keplerian component, and to ensure the Gaussian Process retained the planetary signal.
LHS 6050b is one of the cooler sub-Neptunes to have its low density constrained, suggesting a thin gaseous envelope around a water or rocky world.
Towards more precise RVs via integrating data-driven machine learning with physical models of telluric absorption
Kristo Ment
Despite advances in radial velocity (RV) instrumentation, sub-meter-per-second RVs have been difficult to achieve in practice due to the presence of time-variable contaminating features in measured spectra, stemming both from telluric absorption as well as intrinsic stellar variability. StellarSpectraObservationFitting.jl (SSOF) is a software package written in Julia that was developed to mitigate this issue via a purely data-driven machine learning approach. Specifically, SSOF is capable of modeling individual time-variable stellar or telluric features at the spectral level, which has already been demonstrated to yield more precise measured RVs in NEID data when compared to a CCF-based pipeline. We present novel results using an augmented version of SSOF that utilizes telluric spectra derived from physical models of oxygen and water vapor absorption. We demonstrate that combining the data-driven approach of SSOF with telluric absorption models can further improve the precision of derived RVs as well as the interpretability of modeled spectral features, especially in cases where the amount or quality of data alone do not allow for an accurate modeling of telluric absorption. We obtain a significantly reduced scatter in the RVs derived from the red orders of 3 stars observed by NEID where telluric water absorption is prevalent.
A Perturbative Approach to Radial Velocity Extraction
Aviv Ofir
Building on ideas from photometric transit searches, we developed a new technique for the extraction of radial velocities from high-resolution spectra based on perturbation theory. The approach treats individual flux residuals from the mean as proportional to the local spectral slope, the proportionality constant being the RV-induced wavelength shift in the stellar spectrum. The technique reveals substantial order-dependent systematics in the ESPRESSO data, which we correct using SysRem. The methodology relies on modern spectrographs having well-sampled spectra, it is conceptually simple, computationally fast, requires no resampling, and produces RV precision exceeding that of previous work. For instance, for WASP 76b after correction, we achieve sub-meter per second RMS of the residuals using archival ESPRESSO data, more than a factor of two better than previous analyses. We verify the performance of the algorithm using measurements of other well-known stars and derive improved accuracy for multiple systems (e.g. Tau Ceti and others).
Machine Learning Approaches to Mitigate Stellar Activity: From Gaussian Processes to Transformers
Manuel Perger
Recent advances in instrumentation have shifted the primary challenge in exoplanet detection from instrumental noise to stellar magnetic activity. Surface inhomogeneities introduce noise 2–3× greater than that of the least active stars, obscuring the signals of smaller exoplanets. To address this, I present StarSim, a simulation tool designed to model the impact of stellar activity on exoplanet observables.
Using StarSim, we 1) Extract and analyze stellar activity signals (e.g., orthonormal CCF activity indicators, autoencoder studies on simulated spectra), 2) develop novel Gaussian Process kernels (e.g., the published QPC kernel and ongoing multi-GP research), and 3) train transformer-based neural networks to mitigate stellar signals in observational datasets - already validated on time-series data, where we achieved significant reductions in stellar contributions for three test stars.
This work bridges the gap between simulation and observation, offering a robust framework to enhance the detection of Earth-like exoplanets in the presence of stellar activity.
Mitigating Convective RV Variability in EPRV: Oscillations, Granulation, and Supergranulation
Brandon Rajkumar
Earth-like planets around Sun-like stars produce radial velocity (RV) signals at the level of tens of cm/s. However, variability generated by stellar convection, including pressure-mode (p-mode) oscillations, granulation and supergranulation, can produce RV signals ranging from tens of cm/s to several m/s, potentially obscuring planetary signals in Extreme Precision Radial Velocity (EPRV) surveys. Firstly, we introduce ExTEMPO, an open-source tool that uses stellar scaling relations and stellar parameters with associated uncertainties to estimate the p-mode and granulation noise budgets of Sun-like stars, which can inform EPRV surveys. ExTEMPO is also being used to optimise the structure of observation strategies. We also present initial work using DISCO (Disc Integrated Stellar Convection) to search for line-profile diagnostics of supergranulation-driven velocity shifts. Together, these projects aim to improve our understanding of convective variability and support the detection of Earth-like planets in upcoming EPRV surveys.
The BiSON Calibration: Physics-Consistent Neural Framework of Multi-Instrument Solar RVs
Federica Rescigno
Data observed with the Birmingham Solar Oscillations Network (BiSON) can be an invaluable asset for the study of stellar variability in the EPRV regime. BiSON's very long temporal baseline, 40s cadence, and near-continuous coverage offer a unique opportunity but also a challenge: its signal is dominated by systematics with no straightforward analytical model.
I present a neural network calibration framework designed for multi-instrument timeseries that enforces solar signal coherence across the different sites. By requiring physical consistency between stations, the neural calibration allows for an unsupervised transition from local systematic correction to global, physics-aligned calibration.
The result is the highest-fidelity, multi-decade solar RV dataset currently available, enabling new analysis of stellar activity signals over decades, including granulation, magnetic activity, and oscillations, providing a unique testbed for next-generation mitigation strategies.
A Template-Free, Line-by-Line Framework for RV Estimation and Stellar Activity Mitigation
Joseph Salzer
Detecting Earth-analogue exoplanets via RV measurements is fundamentally limited by stellar variability, which can mimic or obscure planetary signals. While true Keplerian motion induces a uniform Doppler shift, stellar activity alters the shape of individual spectral lines. We introduce a novel framework that exploits these changes by analyzing the broken transitivity of template-free, pairwise relative velocities. For each line, we employ a GP model to estimate the relative velocity between epoch pairs. In the process, a fully connected velocity matrix is constructed. Without stellar activity, these matrices are perfectly transitive; however, line-shape variations inject measurable non-transitive deviations. By projecting these empirical measurements onto their closest transitive matrix, we isolate the true center-of-mass velocity. The resulting residual matrix provides a Doppler-invariant signature of line-profile asymmetries. Applying singular value decomposition to these residuals yields data-driven activity indicators, naturally separating pure kinematics from thermodynamic variability.
Systematic biases on template-based RV extraction
André M. Silva
In radial velocity (RV) surveys and in the follow-up of transiting exoplanets, observations are carried out over multiple months. This allows to properly sample the orbital period of the orbiting companions and to characterize any stellar signals. However, several science cases—such as atmospheric characterization via transmission or emission spectroscopy, or asteroseismology—require high-cadence observations acquired over much shorter timescales, often limited to a single night or a few consecutive nights.
In this talk, we will present two previously unidentified biases in extracted RVs when using template-based algorithms.
The first effect is linked to the construction of stellar templates from observations collected within a short time-span. The presence of this bias is shown in two template matching pipelines, present in the data of multiple state-of-the-art spectrographs, with varying amplitudes across different stars. We demonstrate that the effect can be recovered on a larger sample of 19 targets, totaling 4124 ESPRESSO observations spread through 38 nights. In this sample, we consistently find a systematic quasi-linear bias affecting the RV extraction with typically negative slopes up to $\sim$ -52 m/s/h. We hypothesise that contamination from microtelluric features or other fixed pattern noise is the likely root cause of this effect, which could have implications for high-precision RV studies, particularly in short-timescale observing campaigns.
The second effect arises from the interpolation of stellar spectra that is common in such methods, with a more pronounced effect on short time-span observations. We show that on ESPRESSO observations taken over a few days, the effect can reach 1 m/s in high signal-to-noise (SNR) datasets, and up to 25 m/s in low SNR cases. When the data is collected over a larger temporal window, over multiple months, we place the upper ceiling of this effect to be 20 cm/s through real ESPRESSO observations.
The interplay between these effects thus translate into a significant challenge to be surpassed, not only for RV analysis, but also for other science cases that rely on such data-driven stellar models.
A multifractal view of stellar noise
Fabio Del Sordo
I will illustrate a method based on multifractal modelling that is aimed at understanding the stellar noise in exoplanetary observations. The method is particulary developed in order to provide insights and unravel those timescales that are not strictly periodic but instead develop as stochastic processes, and therefore are difficult to be understood with analysis based on Fourier decomposition. I will show applications to radial velocities, as well as cases where performing joint application to spectral and photometric observations.
Mitigating the Effect of Spectral Shape Variability on Radial Velocity Measurements Using Distance-Based Methods
Shay Zucker
We present a new, model-independent approach for mitigating the effect of spectral-shape variability on radial velocity (RV) measurements using distance-based methods. The approach compares the structure of measured RV variations with the pairwise similarity structure of spectra after approximate rest-frame alignment. This provides a way to mitigate apparent RV variability associated with spectral-shape changes, without requiring an explicit physical model of stellar activity.
We investigate the performance of the approach on simulated spectroscopic time series containing both orbital and activity-induced variability. Initial demonstrations show promising recovery of the underlying Doppler signal, and we are now exploring applications to real spectroscopic datasets of active planet-hosting stars.
The method is intended as a data-driven tool for stellar-activity mitigation in next-generation RV surveys, and may also have applications to other types of spectroscopic variability, such as pulsating stars.
Leveraging a new community EPRV data standard
Jennifer Burt
The most recent generation of EPRV spectrographs has now accumulated sufficient data volumes and observing baselines to investigate how the specific hardware and software approaches adopted by the individual instrument teams affect final RVs and stellar variability metrics. Our team has defined an EPRV data standard and ‘translator’ tools to facilitate a new era of cross-instrument comparisons and identify previously undetectable, smaller scale instrumental systematics that may be impacting science results. This data standard can also provide a starting point for new instruments and reduce the burden of independently developing a data standard and pipeline. I will share the first release version of the data standard and translator tools, which cover data products from order-by-order spectra to the final derived radial velocities and stellar variability indicators, and seek input from participants on how these could be improved to better support large scale GP analyses of multi-instrument EPRV data sets.
Noise mitigation is way better than noise modeling
David W. Hogg
GPs have had a huge impact on exoplanet discovery and characterization projects, because they provide extremely flexible noise models for noise sources (such as stellar variability) that we don’t understand. These noise models make our inferences more accurate, but not more precise. When we can use data features or housekeeping data to directly mitigate the noise—predict it, even imperfectly—we improve both accuracy and precision. GPs have a role in mitigation too, of course. I demonstrate these points with both toy and real examples.
Learning from the Loudest: What active stars can teach us about detecting Earth 2.0
Louise Nielsen
In the hunt for smaller and cooler exoplanets that have the potential to resemble our own Earth, overcoming stellar activity will be the all-encompassing challenge. Drawing on experience from characterising planets around young, active stars, we are confident that we can robustly detect planetary signals in RV measurements that are 10 times smaller than the amplitude induced by stellar activity. I will discuss how we can test and develop our stellar activity mitigation and modelling techniques on young, active stars, while also highlighting the challenges which are unique to finding Earth-like planets around solar-type stars. I will focus on new ESPRESSO observations that have been obtained with the aim of determining the masses and bulk densities of young planets to directly test theories of early planet formation and evolution. I will show how organising photometric monitoring contemporaneously with RVs can alleviate some of the need for densely sampled spectra.
Stellar Variability in the PLATO Era
Thomas Wilson
The upcoming PLATO mission will conduct photometric observations of ~250,000 bright FGKM stars over at least 4 years supported by ground-based high-spectral resolution RV campaigns of promising exoplanetary systems. These high-precision, long-baseline, and often contemporaneous, datasets will offer the unprecedented ability to detect and characterise small, long-period worlds and to photometrically and spectroscopically study stellar activity processes. Asteroseismologically-derived ages and estimates of stellar rotation periods will be produced by the PLATO Stellar Analysis System from near-continuous light curves. However, beyond the direct mission products much can be learned about stellar variability processes synchronously observed by PLATO and EPRV instruments. In this talk, I will review the PLATO data products and observing strategy, and discuss recent work using multi-dimension GPs to simultaneously model magnetic activity in ESPRESSO and NGTS observations of a five-planet, metal-poor star to detect all worlds in RVs for the first time and accurately measure their masses.
Radial velocity mass measurement of the young ultra-low-density planet HIP 67522 b
Baptiste Klein
HIP67522 b is one of the most intriguing young planets discovered so far. JWST observations reported clear detections of the 17-Myr planet atmosphere, suggesting an extraordinarily-low bulk density (<0.1 g/cm^3). I will present the first radial velocity (RV) measurement of the mass of the planet from archival observations. The star’s rapid rotation (vsini~54 km/s) and intense, fast-evolving stellar activity severely limit the RV precision. Instead, the planet search is performed, jointly with a data-driven stellar activity modelling, directly from the cross-correlation functions of the stellar spectra. We report a fair RV detection of HIP67522 b, with a mass discrepant with the JWST estimates, likely due to degeneracies in atmospheric models with unknown planet mass. We also place upper limits on the mass of planet c, and study the chromospheric emission of the star, which is likely a prime target to search for star-planet magnetic interactions.
A multi-band photometric study of flares on the young, active M-dwarf G227-22
Moshikkeeran Senthilnathan
Stellar flares on M-dwarfs are a critical source of activity noise in radial velocity datasets, yet their chromatic emission properties remain poorly constrained. We present a multi-band photometric study of the young, active M-dwarf G227-22, combining four years of TESS time-series photometry with simultaneous ground-based observations in the B and Rc filters. From 35 TESS sectors, we detect 1,962 flares spanning energies of 10^31-10^35 erg and construct flare frequency distributions characterising the long-term activity statistics of the system. Simultaneous B and Rc photometry of large flares allows us to derive the time-resolved temperature, area, and luminosity evolution of individual events. We find evidence of non-thermal emission at flare peaks, which is inconsistent with standard single-temperature blackbody models widely assumed in stellar activity characterisation. This result has direct implications for the calibration of activity indicators and the accuracy of flare energy estimates in next-generation Extreme Precision Radial Velocity surveys.