arXiv subjects

Eamonn Kerins

Publications and source records attributed to Eamonn Kerins.

At least 19 recordsLinked to original sources

arXiv2026

Investigation of Transit Timing and an Optical Transmission Spectrum of the Hot Jupiter WASP-11 b

WASP-11~b/HAT-P-10~b is an inflated hot Jupiter, which has a low density that makes it a good target for atmospheric studies using the transmission spectroscopy technique. In this work, we present 31 new transit light curves of WASP-11~b/HAT-P-10~b, obtained through the SPEARNET network. These data were analyzed along with previously published ground-based observations and space-based data from \texttt{TESS}. We refine the planetary parameters of WASP-11~b/HAT-P-10~b and perform a transit timing analysis using data spanning 16 years. The updated ($O-C$) diagram shows no significant evidence of orbital decay. The TTV analysis reveals no significant signals indicative of additional planets. Atmospheric analysis using multi-band optical observations indicates a strong Rayleigh scattering slope in the transmission spectra, which may originate from the planetary atmosphere itself or be influenced by contamination such as stellar activity or light from the companion star.

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arXiv2026

The Transit Timing and Transmission Spectrum of Hot Jupiter WASP-43 b from a decade of Multi-band Transit Follow-up Observations

We present a new set of 35 transit light curves of the hot Jupiter WASP-43~b, obtained through the SPEARNET network. These datasets were analyzed together with previously published ground-based observations, as well as space-based data from \emph{TESS}, \emph{HST}, and \emph{JWST}, to refine the planetary parameters of WASP-43~b. A total of 188 mid-transit times, measured with \texttt{TransitFit}, were analyzed for potential timing variations. The transit timing variations do not show any significant evidence of orbital decay. Atmospheric retrievals using \emph{HST}/WFC3 G141 transmission spectra suggest that higher-temperature solutions are associated with higher water abundances. However, when these data are combined with observations from ground-based telescopes, \emph{TESS}, and \emph{JWST}, the increased modeling complexity across the broad wavelength baseline presents significant challenges for atmospheric characterization. These results highlight that high-precision, multi-instrument datasets will be necessary to break existing degeneracies in the atmospheric modeling of this target in the future.

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arXiv2026

An Updated SynthPop Model for Microlensing Simulations I: Model Description & Evaluation

The optimization and interpretation of microlensing surveys depends on having an accurate model of the Milky Way. However, existing population synthesis Galactic modeling tools often perform poorly in replicating the stellar contents of the inner Galactic bulge region and reproducing microlensing survey results. We present an updated Galactic model implementation within the \synthpop framework that has been tuned for simulating the upcoming {\it Nancy Grace Roman Space Telescope}'s Galactic Bulge Time Domain Survey (RGBTDS). We evaluate the model against stellar catalogs and kinematics from optical and infrared surveys toward the Galactic bulge, finding good agreement in much of the bulge, including the RGBTDS' contiguous lower bulge fields. However, within Galactic latitudes of $b\lesssim0.5^\circ$ of the Galactic plane, some inconsistencies arise which may impact projections for the RGBTDS' Galactic center field. The model over-predicts optical microlensing event rate per star measurements by a $\sim20$\%, but detailed comparisons to near-infrared measurements are hampered by their lack of detection efficiencies. {\it Roman}'s GBTDS and Galactic Plane Survey will be instrumental in resolving the remaining model inconsistencies and improving our understanding of the structure of the central few degrees of our Galaxy.

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arXiv2025

Predictions of the Nancy Grace Roman Space Telescope Galactic Exoplanet Survey. V. Detection Rates of Multiplanetary Systems in High Magnification Microlensing Events

The Nancy Grace Roman Space Telescope will expand the reach of gravitational microlensing surveys by increasing the number of events monitored and the precision of their light curves. We investigate Roman's ability to detect triple-lens microlensing systems, cases where a foreground star with two bound exoplanets produces detectable anomalies in a microlensing event, using its planned high-cadence observations toward the Galactic bulge. We simulate a large set of high-magnification microlensing light curves based on Roman's expected survey characteristics. A detection criterion, based on a required $χ^2$ improvement for a two-planet model, is applied to determine whether the second planet can be reliably distinguished from a single-planet (binary-lens) model. Our simulations show that the majority of two-planet microlensing events would be detectable with Roman. Events in which both planets are relatively massive (planet-star mass ratios of order $10^{-3}$), or in which the more massive planet occupies a favorable resonant configuration, produce strong central perturbations, resulting in detection efficiencies of roughly 90\%. By contrast, systems with only low-mass planets ($q \sim 10^{-4}$) or with less favorable alignments generate much weaker signals, which often fall below the detection threshold. In general, the planetary mass ratios and the resulting caustic geometry (e.g., central caustic size in resonant versus wide/close orbits) are the dominant factors governing detectability. Taking into account the expected frequency of planetary systems and the fraction of high-magnification events, we estimate that Roman will detect a high-magnification triple-lens event in approximately 4.5\% of multi-planet microlensing events, corresponding to about 64 events over the course of the full survey.

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arXiv2025

Predictions of the Nancy Grace Roman Space Telescope Galactic Exoplanet Survey. IV. Lens Mass and Distance Measurements

As part of the Galactic Bulge Time Domain Survey (GBTDS), the Nancy Grace Roman Galactic Exoplanet Survey (RGES) will use microlensing to discover cold outer planets and free-floating planets unbound to stars. NASA has established several science requirements for the GBTDS to ensure RGES success. A key advantage of RGES is Roman's high angular resolution, which will allow detection of flux from many host stars. One requirement specifies that Roman must measure the masses and distances of 40% of detected planet hosts with 20% precision or better. To test this, we simulated microlensing events toward the GBTDS fields and used Fisher matrix analysis to estimate light curve parameter uncertainties. Combining these with Roman imaging observables (lens flux, relative lens-source proper motion), we estimated the achievable precision of lens mass and distance measurements. Using pyLIMASS, a publicly available code for estimating lens properties, we applied this analysis to 3,000 simulated events. Assuming the Cassan et al. (2012) exoplanet mass function, we find that >40% of host stars meet the required 20% precision threshold, confirming that the GBTDS can satisfy the mission requirement. We validated our approach by comparing our inferred lens masses and distances to empirical measurements from detailed image-constrained light curve modeling of historical microlensing events with Hubble and Keck follow-up imaging. Our results agree within roughly 1 sigma, demonstrating that both approaches yield consistent and reliable mass and distance estimates, and confirming the robustness of our simulations for Roman-era microlensing science.

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arXiv2025

Technique-agnostic exoplanet demography for the Roman era -- I. Testing a demography retrieval framework using simulated Kepler-like transit datasets

The Nancy Grace Roman Space Telescope (Roman) will unveil for the first time the full architecture of planetary systems across Galactic distances through the discovery of up to 200,000 cool and hot exoplanets using microlensing and transit detection methods. Roman's huge exoplanet haul, and Galactic reach, will require new methods to leverage the full exoplanet demographic content of the combined microlensing and transit samples, given the different sensitivity bias of the techniques to planet and host properties and Galactic location. We present a framework for technique-agnostic exoplanet demography (TAED) that can allow large, multi-technique exoplanet samples distributed over Galactic distance scales to be combined for demographic studies. Our TAED forward modelling and retrieval framework uses parameterised model exoplanet demographic distributions to embed planetary systems within a stellar population synthesis model of the Galaxy, enabling internally consistent forecasts to be made for all detection methods that are based on spatio-kinematic system properties. In this paper, as a first test of the TAED framework, we apply it to simulated transit datasets based on the Kepler Data Release 25 to assess parameter recovery accuracy and method scalability for a single large homogeneous dataset. We find that optimisation using differential evolution provides a computationally scalable framework that gives a good balance between computational efficiency and accuracy of parameter recovery.

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arXiv2025

Predictions of the Nancy Grace Roman Space Telescope Galactic Exoplanet Survey. III. Detectability of Giant Exomoons of Wide Separation Giant Planets

The Nancy Grace Roman Space Telescope (Roman) will conduct a Galactic Exoplanet Survey (RGES) to discover bound and free-floating exoplanets using gravitational microlensing. Roman should be sensitive to lenses with mass down to ~ 0.02 $M_{\oplus}$, or roughly the mass of Ganymede. Thus the detection of moons with masses similar to the giant moons in our Solar System is possible with Roman. Measuring the demographics of exomoons will provide constraints on both moon and planet formation. We conduct simulations of Roman microlensing events to determine the effects of exomoons on microlensing light curves, and whether these effects are detectable with Roman. We focus on giant planets from 30 $M_{\oplus}$ to 10 $M_{Jup}$ on orbits from 0.3 to 30 AU, and assume that each planet is orbited by a moon with moon-planet mass ratio from $10^{-4}$ to $10^{-2}$ and separations from 0.1 to 0.5 planet Hill radii. We find that Roman is sensitive to exomoons, although the number of expected detections is only of order one over the duration of the survey, unless exomoons are more common or massive than we assumed. We argue that changes in the survey strategy, in particular focusing on a few fields with higher cadence, may allow for the detection of more exomoons with Roman. Regardless, the ability to detect exomoons reinforces the need to develop robust methods for modeling triple lens microlensing events to fully utilize the capabilities of Roman.

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arXiv2025

A planet-host ratio relation to synthesize microlensing and transiting exoplanet demography from Roman

The NASA Nancy Grace Roman Space Telescope (Roman) will be the first survey able to detect large numbers of both cold and hot exoplanets across Galactic distances: $\sim$1,400 cold exoplanets via microlensing and $\sim$200,000 hot, transiting planets. Differing sensitivities to planet bulk properties between the microlensing and transit methods require relations like a planet mass--radius relation (MRR) to mediate. We propose using instead a planet--host {\em ratio} relation (PHRR) to couple directly microlensing and transit observables in demographic forward-modelling simulations. Unlike the MRR, a PHRR uses parameters that are always measured and so can potentially leverage the full Roman exoplanet sample. Using 908 confirmed exoplanets from the NASA Exoplanet Archive, we show that transit depth, $\delta$, and planet--host mass ratio, $q$, obey a PHRR that is continuous over all planet scales. The PHRR is improved by including orbital period, $P$, and host effective temperature, $T_{\star}$. We compare several candidate PHRRs of the form $\delta (q,T_\star, P)$, with the Bayesian Information Criterion favouring power-law dependence on $T_\star$ and $P$, and broken power-law dependence on $q$. The break in $q$ itself depends on $T_\star$, as do the power-law slopes in $q$ either side of the break. The favoured PHRR achieves a fairly uniform $50\%$ relative precision in $\delta$ for all $q$. Approximately $5\%$ of the sample has a transit depth that is strongly over-predicted by the PHRR; around half of these are associated with large stars ($R_\star > 2.5 \, R_{\odot}$) potentially subject to Malmquist bias.

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arXiv2024

Transit Timing Variation of K2-237b: Hints Toward Planet Disk Migration

Hot Jupiters should initially form at considerable distances from host stars and subsequently migrate towards inner regions, supported directly by transit timing variation (TTV). We report the TTV of K2-237b, using reproduced timings fitted from \textit{Kepler} K2 and \textit{TESS} data. The timings span from 2016 to 2021, leading to an observational baseline of 5 years. The timing evolution presents a significant bias to a constant period scenario. The model evidence is evaluated utilizing the Bayesian Information Criterion (BIC), which favours the scenario of period decay with a $Δ$BIC of 14.1. The detected TTV induces a period decay rate ($\dot{P}$) of -1.14$\pm$0.28$\times$10$^{-8}$ days per day ($-$0.36 s/year). Fitting the spectral energy distribution, we find infrared excess at the significance level of 1.5 $σ$ for WISE W1 and W2 bands, and 2 $σ$ level for W3 and W4 bands. This potentially reveals the existence of a stellar disk, consisting of hot dust at 800$\pm$300 K, showing a $L_{dust}/L_{\ast}$ of 5$\pm$3$\times$10$^{-3}$. We obtain a stellar age of 1.0$^{+1.4}_{-0.7}$$\times$10$^{9}$ yr from isochrone fitting. The properties of K2-237b potentially serve as a direct observational support to the planet disk migration though more observation are needed.

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arXiv2024

Spatially resolved microlensing timescale distributions across the Galactic bulge with the VVV survey

We analyze 1602 microlensing events found in the VISTA Variables in the Via Lactea (VVV) near-infrared (NIR) survey data. We obtain spatially-resolved, efficiency-corrected timescale distributions across the Galactic bulge ($|\ell|<10^\circ,$ $|b|<5^\circ$), using a Bayesian hierarchical model. Spatially-resolved peaks and means of the timescale distributions, along with their marginal distributions in strips of longitude and latitude, are in agreement at a 1$σ$ level with predictions based on the Besançon model of the Galaxy. We find that the event timescales in the central bulge fields ($|\ell| < 5^\circ$) are on average shorter than the non-central ($|\ell| > 5^\circ$) fields, with the average peak of the lognormal timescale distribution at 23.6 $\pm$ 1.9 days for the central fields and 29.0 $\pm$ 3.0 days for the non-central fields. Our ability to probe the structure of the Bulge with this sample of NIR microlensing events is limited by the VVV survey's sparse cadence and relatively small number of detected microlensing events compared to dedicated optical surveys. Looking forward to future surveys, we investigate the capability of the Roman telescope to detect spatially-resolved asymmetries in the timescale distributions. We propose two pairs of Roman fields, centred on ($\ell = \pm 9,5^\circ$, $b=-0.125^\circ$) and ($\ell = -5^\circ$, $b=\pm 1.375^\circ$) as good targets to measure the asymmetry in longitude and latitude, respectively.

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arXiv2023

Breaking up with the continuous exoplanet mass-radius relation

We use a carefully selected subsample of 1053 confirmed exoplanets from the NASA Exoplanet Archive to construct empirical power-law exoplanet mass-radius-temperature ($M$-$R$-$T$) relations. Using orthogonal distance regression to account for errors in both mass and radius, we allow the data to decide: 1) the number of distinct planetary regimes; 2) whether the boundaries of these regimes are best described by broken power laws joined at mass break points, or by discontinuous power laws motivated by changes in equations of state and temperature. We find strong support from the data for three distinct planetary $M$-$R$ regimes and for those regimes to be discontinuous. Our most successful model involves an $M$-$R$-$T$ relation in which ice/rock (rocky) and ice-giant (neptunian) planets are segregated by a pure-ice equation of state, whilst neptunes and gas giant (jovian) planets are segregated by a mass break at $M_{\rm br} = 115\pm19~M_{\oplus}$. The rocky planet regime is shown to follow $M \propto R^{0.34\pm0.01}$, whilst neptunes have $M\propto R^{0.55\pm0.02}$. Planets in both regimes are seen to extend to similar maximum masses. In the jovian regime, we find that $M \propto R^{0.00\pm0.01}T^{0.35\pm 0.02}$, where $T$ is the planet equilibrium temperature. This implies that, for jovian planets detected so far, equilibrium temperature alone provides a robust estimator of mass.

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arXiv2023

Revisiting the Transit Timing and Atmosphere Characterization of the Neptune-mass Planet HAT-P-26 b

We present the transit timing variation (TTV) and planetary atmosphere analysis of the Neptune-mass planet HAT-P-26~b. We present a new set of 13 transit light curves from optical ground-based observations and combine them with light curves from the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST), Transiting Exoplanet Survey Satellite (TESS), and previously published ground-based data. We refine the planetary parameters of HAT-P-26 b and undertake a TTV analysis using 33 transits obtained over seven years. The TTV analysis shows an amplitude signal of 1.98 $\pm$ 0.05 minutes, which could result from the presence of an additional $0.02 M_{Jup}$ planet at the 1:2 mean-motion resonance orbit. Using a combination of transit depths spanning optical to near-infrared wavelengths, we find that the atmosphere of HAT-P-26 b contains $2.4^{+2.9}_{-1.6}$% of H$_2$O with a derived temperature of $590^{+60}_{-50}$ K.

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arXiv2023

Transiting Exoplanet Yields for the Roman Galactic Bulge Time Domain Survey Predicted from Pixel-Level Simulations

The Nancy Grace Roman Space Telescope (Roman) is NASA's next astrophysics flagship mission, expected to launch in late 2026. As one of Roman's core community science surveys, the Galactic Bulge Time Domain Survey (GBTDS) will collect photometric and astrometric data for over 100 million stars in the Galactic bulge to search for microlensing planets. To assess the potential with which Roman can detect exoplanets via transit, we developed and conducted pixel-level simulations of transiting planets in the GBTDS. From these simulations, we predict that Roman will find between $\sim$60,000 and $\sim$200,000 transiting planets, over an order of magnitude more planets than are currently known. While the majority of these planets will be giants ($R_p>4R_\oplus$) on close-in orbits ($a<0.3$ au), the yield also includes between $\sim$7,000 and $\sim$12,000 small planets ($R_p<4 R_\oplus$). The yield for small planets depends sensitively on the observing cadence and season duration, with variations on the order of $\sim$10-20% for modest changes in either parameter, but is generally insensitive to the trade between surveyed area and cadence given constant slew/settle times. These predictions depend sensitively on the Milky Way's metallicity distribution function, highlighting an opportunity to significantly advance our understanding of exoplanet demographics, particularly across stellar populations and Galactic environments.

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arXiv2023

RoSETZ: Roman Survey of the Earth Transit Zone -- a SETI-optimized survey for habitable-zone exoplanets

In this White Paper for Nancy Grace Roman Space Telescope (Roman) science, we propose the Roman Survey of the Earth Transit Zone (RoSETZ), a transit search for rocky planets within the habitable zones (HZs) of stars located within the Earth Transit Zone (ETZ). The ETZ holds special interest in the search for extra-terrestrial intelligence (SETI) - observers on planets within the ETZ can see Earth as a transiting planet. RoSETZ would augment the Roman Galactic Bulge Time Domain Survey (GBTDS) as an additional field located $\sim 5$~degrees away from other GBTDS fields. Our simulations show that RoSETZ alone can find from 120 to 630 Earth-sized HZ planets around K- and M-type hosts, with the range reflecting different survey design assumptions. These yields are 5-20 times the number currently known. Such a sample will transform our knowledge of ``Eta-Earth'' ($η_{\oplus}$) -- the occurrence of Earth-sized HZ planets -- and would be the first catalogue of exoplanets selected in a manner optimized according to the Mutual Detectability targetted-SETI strategy. If it can be accommodated alongside the existing GBTDS design, we favour a RoSETZ-Max design that is observed for the duration of the GBTDS. If not, we show that a slimmed-down RoSETZ-Lite design, occupying two GBTDS seasons, would not significantly impact overall GBTDS exoplanet yields, even if time allocated to it had to come from time allocations to other fields. We argue that the angular separation of RoSETZ from other GBTDS fields permits self-calibration of systematic uncertainties that would otherwise hamper exoplanet demographic modelling of both microlensing and transit datasets. Other science possible with RoSETZ data include studies of small solar system bodies and high resolution 3D extinction mapping.

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arXiv2023

Magnifying NASA Roman GBTDS exoplanet science with coordinated observations by ESA Euclid

The ESA Euclid mission is scheduled to launch on July 1st 2023. This White Paper discusses how Euclid observations of the Galactic Bulge Time Domain Survey (GBTDS) area could dramatically enhance the exoplanet science output of the Nancy Grace Roman Space Telescope (Roman). An early Euclid pre-imaging survey of the Roman GBTDS fields, conducted soon after launch, can improve proper motion determinations for Roman exoplanet microlenses that can yield a factor of up to $\sim 5$ improvement in exoplanet mass measurements. An extended Euclid mission would also enable the possibility of sustained simultaneous observations of the GBTDS by Euclid and Roman that would achieve large gains in several areas of Roman exoplanet science, including science that is impossible to achieve with Roman alone. These include: a comprehensive demographic survey for free-floating planets that includes precision mass measurements to establish the true nature of individual candidates; detection, confirmation and mass measurements of exomoons; direct exoplanet mass measurements through parallax and finite source size effects for a large sample of bound exoplanets detected jointly by Euclid and Roman; enhanced false-positive discrimination for the large samples of transiting planets that Roman will detect. Our main recommendation to NASA and ESA is to initiate a Joint Study Group as early as possible that can examine how both missions could best conduct a coordinated campaign. We also encourage flexibility in the GBTDS scheduling.

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arXiv2022

An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E~270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462 (hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462 shows a parallactic signature of the effect of the Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 Msun and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic-disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km/s, suggesting that the BH received a 'natal kick' from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray binaries, and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first for an isolated stellar-mass BH using any technique.

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arXiv2022

Euclid-Roman joint microlensing survey: early mass measurement, free floating planets and exomoons

As the Kepler mission has done for hot exoplanets, the ESA Euclid and NASA Roman missions have the potential to create a breakthrough in our understanding of the demographics of cool exoplanets, including unbound, or "free-floating", planets (FFPs). In this study, we demonstrate the complementarity of the two missions and propose two joint-surveys to better constrain the mass and distance of microlensing events. We first demonstrate that an early brief Euclid survey (7 h) of the Roman microlensing fields will allow the measurement of a large fraction of events relative proper motions and lens magnitudes. Then, we study the potential of simultaneous observations by Roman and Euclid to enable the measurement of the microlensing parallax for the shortest microlensing events. Using detailed simulations of the joint detection yield we show that within one year Roman-Euclid observations will be at least an order of magnitude more sensitive than current ground-based measurements. Depending on the exact distribution of FFP, a joint Roman-Euclid campaign should detect around 130 FFP events within a year, including 110 with measured parallax that strongly constrain the FFP mass, and around 30 FFP events with direct mass and distance measurements. The ability of the joint survey to completely break the microlens mass-distance-velocity degeneracy for a significant subset of events provides a unique opportunity to verify unambiguously the FFP hypothesis or else place abundance limits for FFPs between Earth and Jupiter masses that are up to two orders of magnitude stronger than provided by ground-based surveys. Finally, we study the capabilities of the joint survey to enhance the detection and charcterization of exomoons, and found that it could lead to the detection of the first exomoon.

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arXiv2021

Variable stars in the VVV globular clusters. II. NGC6441, NGC6569, NGC6626 (M28), NGC6656 (M22), 2MASS-GC02, and Terzan10

The Galactic globular clusters (GGCs) located in the inner regions of the Milky Way suffer from high extinction that makes their observation challenging. The VVV survey provides a way to explore these GGCs in the near-infrared where extinction effects are highly diminished. We conduct a search for variable stars in several inner GGCs, taking advantage of the unique multi-epoch, wide-field, near-infrared photometry provided by the VVV survey. We are especially interested in detecting classical pulsators that will help us constrain the physical parameters of these GGCs. In this paper, the second of a series, we focus on NGC6656 (M22), NGC6626 (M28), NGC6569, and NGC6441; these four massive GGCs have known variable sources, but quite different metallicities. We also revisit 2MASS-GC02 and Terzan10, the two GGCs studied in the first paper of this series. We present an improved method and a new parameter that efficiently identify variable candidates in the GGCs. We also use the proper motions of those detected variable candidates and their positions in the sky and in the color-magnitude diagrams to assign membership to the GGCs. We identify and parametrize in the near-infrared numerous variable sources in the studied GGCs, cataloging tens of previously undetected variable stars. We recover many known classical pulsators in these clusters, including the vast majority of their fundamental mode RR Lyrae. We use these pulsators to obtain distances and extinctions toward these objects. Recalibrated period-luminosity-metallicity relations for the RR Lyrae bring the distances to these GGCs to a closer agreement with those reported by Gaia, except for NGC6441. Recovered proper motions for these GGCs also agree with those reported by Gaia, except for 2MASS-GC02, the most reddened GGC in our sample, where the VVV near-infrared measurements provide a more accurate determination of its proper motions.

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