Exomoons are predicted to produce transit timing variations (TTVs) upon their host planet. Unfortunately, so are many other astrophysical phenomena - most notably other planets in the system. In this work, an argument of reductio ad absurdum is invoked, by deriving the transit timing effects that are impossible for a single exomoon to produce. Our work derives three key analytic tests. First, one may exploit the fact that a TTV signal from an exomoon should be accompanied by transit duration variations (TDVs), and that one can derive a TDV floor as a minimum expected level of variability. Cases for which the TDV upper limit is below this floor can thus be killed as exomoon candidates. Second, formulae are provided for estimating whether moons are expected to be 'killable' when no TDVs presently exist, thus enabling the community to estimate whether it's even worth deriving TDVs in the first place. Third, a TTV ceiling is derived, above which exomoons should never be able to produce TTV amplitudes. These tools are applied to a catalog of TTVs and TDVs for two and half thousand Kepler Objects Interest, revealing over two hundred cases that cannot be due to a moon. These tests are also applied to the exomoon candidate Kepler-1625b i, which comfortably passes the criteria. These simple analytic results should provide a means of rapidly rejecting putative exomoons and streamlining the search for satellites.
Recently Kipping (2021) identified the so-called "exomoon corridor", a potentially powerful new tool for identifying possible exomoon hosts, enabled by the observation that fully half of all planets hosting an exomoon will exhibit transit timing variation (TTV) periodicities of 2-4 epochs. One key outstanding problem in the search for exomoons, however, is the question of how well the methods we have developed under the single moon assumption extend to systems with multiple moons. In this work we use $N$-body simulations to examine the exomoon corridor effect in the more general case of $N \ge…
The habitability of exoplanets can be strongly influenced by the presence of an exomoon, and in some cases the exomoon itself could be a possible place for life to develop. For moons outside of the habitable zone, significant tidal heating may raise their surface temperature enough to be considered habitable. Tidal heating of a moon depends on numerous factors such as eccentricity, semimajor axis, size of parent planet, and presence of additional moons. In this work, we explore the degree of tidal heating possible for multi-moon systems in resonance using a combination of semi-analytic and num…
If a transiting exoplanet has a moon, that moon could be detected directly from the transit it produces itself, or indirectly via the transit timing variations it produces in its parent planet. There is a range of parameter space where the Kepler Space Telescope is sensitive to the TTVs exomoons might produce, though the moons themselves would be too small to detect photometrically via their own transits. The Earth's Moon, for example, produces TTVs of 2.6 minutes amplitude by causing our planet to move around their mutual centre of mass. This is more than Kepler's short-cadence interval of 1 …
Satellite formation is a natural by-product of planet formation. With the discovery of nu- merous extrasolar planets, it is likely that moons of extrasolar planets (exomoons) will soon be discovered. Some of the most promising techniques can yield both the mass and radius of the moon. Here, I review recent ideas about the formation of moons in our Solar System, and discuss the prospects of extrapolating these theories to predict the sizes of moons that may be discovered around extrasolar planets. It seems likely that planet-planet collisions could create satellites around rocky or icy planets …
We present two methods to determine an exomoon's sense of orbital motion (SOM), one with respect to the planet's circumstellar orbit and one with respect to the planetary rotation. Our simulations show that the required measurements will be possible with the European Extremely Large Telescope (E-ELT). The first method relies on mutual planet-moon events during stellar transits. Eclipses with the moon passing behind (in front of) the planet will be late (early) with regard to the moon's mean orbital period due to the finite speed of light. This "transit timing dichotomy" (TTD) determines an exo…
Gas giant planets in the Solar system host large satellite systems with multiple regular and irregular moons. Regular moons revolve around their host planet in circular, low inclination short period orbits, and are thought to form in-situ through coagulation processes. In contrast, irregular moons have highly inclined (and even retrograde), typically eccentric and long period orbits around their host planet. Irregular moons are therefore often thought to be unbound objects in helio-centric orbits that were later captured to their current orbits around the planet. Here we study the a different …
Despite numerous attempts, no exomoon has firmly been confirmed to date. New missions like CHEOPS aim to characterize previously detected exoplanets, and potentially to discover exomoons. In order to optimize search strategies, we need to determine those planets which are the most likely to host moons. We investigate the tidal evolution of hypothetical moon orbits in systems consisting of a star, one planet and one test moon. We study a few specific cases with ten billion years integration time where the evolution of moon orbits follows one of these three scenarios: (1) "locking", in which the…
The recent announcement of a Neptune-sized exomoon candidate orbiting the Jupiter-sized object Kepler-1625b has forced us to rethink our assumptions regarding both exomoons and their host exoplanets. In this paper I describe calculations of the habitable zone for Earthlike exomoons in orbit of Kepler-1625b under a variety of assumptions. I find that the candidate exomoon, Kepler-1625b-i, does not currently reside within the exomoon habitable zone, but may have done so when Kepler-1625 occupied the main sequence. If it were to possess its own moon (a "moon-moon") that was Earthlike, this could …
We present new ways to identify single and multiple moons around extrasolar planets using planetary transit timing variations (TTVs) and transit duration variations (TDVs). For planets with one moon, measurements from successive transits exhibit a hitherto undescribed pattern in the TTV-TDV diagram, originating from the stroboscopic sampling of the planet's orbit around the planet-moon barycenter. This pattern is fully determined and analytically predictable after three consecutive transits. The more measurements become available, the more the TTV-TDV diagram approaches an ellipse. For planets…
The photometric transit method has been the most effective method to detect and characterize exoplanets as several ground-based as well as space-based survey missions have discovered thousands of exoplanets using this method. With the advent of the upcoming next generation large telescopes, the detection of exomoons in a few of these exoplanetary systems is very plausible. In this paper, we present a comprehensive analytical formalism in order to model the transit light curves for such moon hosting exoplanets. In order to achieve analytical formalism, we have considered circular orbit of the e…
Discoveries of extrasolar planets in the habitable zone (HZ) of their parent star lead to questions about the habitability of massive moons orbiting planets in the HZ. Around low-mass stars, the HZ is much closer to the star than for Sun-like stars. For a planet-moon binary in such a HZ, the proximity of the star forces a close orbit for the moon to remain gravitationally bound to the planet. Under these conditions the effects of tidal heating, distortion torques, and stellar perturbations become important considerations for exomoon habitability. Utilizing a model that considers both dynamical…
In this paper, the detectability of habitable exomoons orbiting around giant planets in M-dwarf systems using Transit Timing Variations (TTVs) and Transit Timing Durations (TDVs) with Kepler-class photometry is investigated. Light curves of systems with various configurations were simulated around M-dwarf hosts of mass 0.5 Msun and radius 0.55 Rsun. Jupiter-like giant planets which offer the best potential for hosting habitable exomoons were considered with rocky super-Earth-mass moons. The detectability is measured by using the phase-correlation between TTV and TDV signals. Since the TDV sign…
Many attempts have already been made for detecting exomoons around transiting exoplanets but the first confirmed discovery is still pending. The experience that have been gathered so far allow us to better optimize future space telescopes for this challenge, already during the development phase. In this paper we focus on the forthcoming CHaraterising ExOPlanet Satellite (CHEOPS),describing an optimized decision algorithm with step-by-step evaluation, and calculating the number of required transits for an exomoon detection for various planet-moon configurations that can be observable by CHEOPS.…
With the detection of extrasolar moons (exomoons) on the horizon, it is important to consider their potential for habitability. If we consider the circumstellar Habitable Zone (HZ, often described in terms of planet semi-major axis and orbital eccentricity), we can ask, "How does the HZ for an Earth-like exomoon differ from the HZ for an Earth-like exoplanet?" For the first time, we use 1D latitudinal energy balance modelling to address this question. The model places an Earth-like exomoon in orbit around a Jupiter mass planet, which in turn orbits a Sun-like star. The exomoon's surface temper…
We investigate the habitability of hypothethical moons orbiting known exoplanets. This study focuses on big, rocky exomoons that are capable of maintaining a significant atmosphere. To determine their habitability, we calculate the incident stellar radiation and the tidal heating flux arising in the moons as the two main contributors to the energy budget. We use the runaway greenhouse and the maximum greenhouse flux limits as a definition of habitability. For each exoplanet we run our calculations for plausible ranges of physical and orbital parameters for the moons and the planet using a Mont…
Aims. Current and upcoming space missions may be able to detect moons of transiting extra-solar planets. In this context it is important to understand if exomoons are expected to exist and what their possible properties are. Methods. Using estimates for the stability of exomoon orbits from numerical studies, a list of 87 known transiting exoplanets is tested for the potential to host large exomoons. Results. For 92% of the sample, moons larger than Luna can be excluded on prograde orbits, unless the parent exoplanet's internal structure is very different from the gas-giants of the solar system…
One of the primary surprises of exoplanet detections has been the discovery of compact planetary systems, whereby numerous planets reside within ~0.5 AU of the host star. Many of these kinds of systems have been discovered in recent years, indicating that they are fairly common orbital architecture. Of particular interest are those systems for which the host star is low-mass, thus potentially enabling one or more of the planets to lie within the Habitable Zone of the host star. One of the contributors to the habitability of the Earth is the presence of a substantial moon whose tidal effects ca…
The formation of satellites is thought to be a natural by-product of planet formation in our Solar System, and thus, moons of extrasolar planets (exomoons) may be abundant in extrasolar planetary systems, as well. Exomoons have yet to be discovered. However, moons larger than 0.1 Earth masses can be detected and characterized using current transit techniques. Here, we show that collisions between rocky planets with masses between a quarter to ten Earth masses can create impact-generated debris disks that could accrete into moons. Collisions between like-sized objects, at oblique impact angles,…
From analytical studies of tidal heating, eclipses and planetary illumination, it is clear that the exomoon habitable zone (EHZ) - the set of moon and host planet orbits that permit liquid water on an Earthlike moon's surface - is a manifold of higher dimension than the planetary HZ. This paper outlines the first attempt to produce climate models of exomoons which possess all the above sources and sinks of energy. We expand on our previous 1D latitudinal energy balance models (LEBMs), which follow the evolution of the temperature on an Earthlike moon orbiting a Jupiterlike planet, by adding pl…
Moons orbiting extrasolar planets are the next class of object to be observed and characterized for possible habitability. Like the host-planets to their host-star, exomoons have a limiting radius at which they may be gravitationally bound, or the Hill radius. In addition, they also have a distance at which they will become tidally locked and therefore in synchronous rotation with the planet. We have examined the flux phase profile of a simulated, hypothetical moon orbiting at a distant radius around the confirmed exoplanets mu Ara b, HD 28185 b, BD +14 4559 b, and HD 73534 b. The irradiated f…
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education（现代天文学和天体物理学教育部重点实验室）；MEAYIN Science Center（MEAYIN科学中心）
Jupiter and Saturn play host to an impressive array of satellites, making it reasonable to suspect that similar systems of moons might exist around giant extrasolar planets. Furthermore, a significant population of such planets is known to reside at distances of several Astronomical Units (AU), leading to speculation that some moons thereof might support liquid water on their surfaces. However, giant planets are thought to undergo inward migration within their natal protoplanetary disks, suggesting that gas giants currently occupying their host star's habitable zone formed further out. Here we…
An exomoon on a non perfectly circular orbit experiences tidal heating that is capable to significantly contribute to the thermal brightness of the moon. Here we argue that the thermal heat is unevenly distributed on the moon's surface, the emission of the tidal heat is limited to a few hot spots on the surface. A well-known example is the tidally heated Io. Due to their significantly increased temperature, the hot spots enhance the energy emission in thermal wavelengths. We made simulations using Monte-Carlo method to examine this contribution, and to predict about the possible detectability …
Planet-planet scattering is the leading mechanism to explain the broad eccentricity distribution of observed giant exoplanets. Here we study the orbital stability of primordial giant planet moons in this scenario. We use N-body simulations including realistic oblateness and evolving spin evolution for the giant planets. We find that the vast majority (80-90% across all our simulations) of orbital parameter space for moons is destabilized. There is a strong radial dependence, as moons past 0.1 Hill radii are systematically removed. Closer-in moons on Galilean-moon-like orbits (< 0.04 Hill radii…
With most planets and planetary candidates detected in the stellar habitable zone (HZ) being super-Earths and gas giants, rather than Earth-like planets, we naturally wonder if their moons could be habitable. The first detection of such an exomoon has now become feasible, and due to observational biases it will be at least twice as massive as Mars. But formation models predict moons can hardly be as massive as Earth. Hence, a giant planet's magnetosphere could be the only possibility for such a moon to be shielded from cosmic and stellar high-energy radiation. Yet, the planetary radiation belt…
Context: Detecting moons around exoplanets is a major goal of current and future observatories. Moons are suspected to influence rocky exoplanet habitability, and gaseous exoplanets in stellar habitable zones could harbour abundant and diverse moons to target in the search for extraterrestrial habitats. Exomoons will contribute to exoplanetary signals but are virtually undetectable with current methods. Aims: We identify and analyse traces of exomoons in the temporal variation of total and polarised fluxes of starlight reflected by an Earth-like exoplanet and its spatially unresolved moon acro…
Compared to the giant planets in the solar system, exoplanets have many remarkable properties such as the prevalence of giant planets on eccentric orbits and the presence of hot Jupiters. Planet-planet scattering (PPS) between giant planets is a possible mechanism in interpreting above and other observed properties. If the observed giant planet architectures are indeed the outcomes of PPS, such drastic dynamical process must affect their primordial moon systems. In this Letter, we discuss the effect of the PPS on the survival of their regular moons. From the viewpoint of observations, some pre…
The search for life outside of the Solar System should not be restricted to exclusively planetary bodies; large moons of extrasolar planets may also be common habitable environments throughout the Galaxy. Extrasolar moons, or exomoons, may be detected through transit timing effects induced onto the host planet as a result of mutual gravitational interaction. In particular, transit timing variations (TTV) and transit duration variations (TDV) are predicted to produce a unique exomoon signature, which is not only easily distinguished from other gravitational perturbations, but also provides both…
The discovery of an exomoon would provide deep insights into planet formation and the habitability of planetary systems, with transiting examples being particularly sought after. Of the hundreds of Kepler planets now discovered, the seven-planet system Kepler-90 is unusual for exhibiting an unidentified transit-like signal in close proximity to one of the transits of the long-period gas-giant Kepler-90g, as noted by Cabrera et. al. (2014). As part of the 'Hunt for Exomoons with Kepler' (HEK) project, we investigate this possible exomoon signal and find it passes all conventional photometric, d…
In the solar system, moons largely exceed planets in number. The Kepler database has been shown to be sensitive to exomoon detection down to the mass of Mars, but the first search has been unsuccessful. Here, we use a particles-in-cell code to predict the transit of the plasma torus produced by a satellite. Despite the small size of a moon, the spatial extent of its plasma torus can be large enough to produce substantial transit absorptions. The model is used for the interpretation of Hubble Space Telescope early ingress absorptions apparently observed during WASP-12b and HD 189733b UV transit…
Occultation light curves of exomoons may give information on their albedo and hence indicate the presence of ice cover on the surface. Icy moons might have subsurface oceans thus these may potentially be habitable. The objective of our paper is to determine whether next generation telescopes will be capable of albedo estimations for icy exomoons using their occultation light curves. The success of the measurements depends on the depth of the moon's occultation in the light curve and on the sensitivity of the used instruments. We applied simple calculations for different stellar masses in the V…
The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2 Jupiter-mass planet in Kepler 1625 puts interesting constraints on the formation of the system. In particular, the relatively wide orbit of the moon around the planet, at ~40 planetary radii, is hard to reconcile with planet formation theories. We demonstrate that the observed characteristics of the system can be explained from the tidal capture of a secondary planet in the young system. After a quick phase of tidal circularization, the lunar orbit, initially much tighter than 40 planetary radii, subsequently gradually…
An exoplanet-exomoon system presents a superposition of phase curves to observers - the dominant component varies according to the planetary period, and the lesser varies according to both the planetary and the lunar period. If the spectra of the two bodies differs significantly, then it is likely there are wavelength regimes where the contrast between the moon and planet is significantly larger. In principle, this effect could be used to isolate periodic oscillations in the combined phase curve. Being able to detect the exomoon component would allow a characterisation of the exomoon radius, a…
Detections of massive extrasolar moons are shown feasible with the Kepler space telescope. Kepler's findings of about 50 exoplanets in the stellar habitable zone naturally make us wonder about the habitability of their hypothetical moons. Illumination from the planet, eclipses, tidal heating, and tidal locking distinguish remote characterization of exomoons from that of exoplanets. We show how evaluation of an exomoon's habitability is possible based on the parameters accessible by current and near-future technology.
While the solar system contains about 20 times more moons than planets, no moon has been confirmed around any of the thousands of extrasolar planets known so far. Tools for an uncomplicated identification of the most promising exomoon candidates could be beneficial to streamline follow-up studies.} Here we study three exomoon indicators that emerge if well-established planet-only models are fitted to a planet-moon transit light curve: transit timing variations (TTVs), transit duration variations (TDVs), and apparent planetary transit radius variations (TRVs). We re-evaluate under realistic con…
The diversity and quantity of moons in the Solar System suggest a manifold population of natural satellites exist around extrasolar planets. Of peculiar interest from an astrobiological perspective, the number of sizable moons in the stellar habitable zones may outnumber planets in these circumstellar regions. With technological and theoretical methods now allowing for the detection of sub-Earth-sized extrasolar planets, the first detection of an extrasolar moon appears feasible. In this review, we summarize formation channels of massive exomoons that are potentially detectable with current or…
The Kepler space telescope has detected transits of objects as small as the Earth's Moon, and moons as small as 0.2 Earth masses can be detected in the Kepler data by transit timing and transit duration variations of their host planets. Such massive moons around giant planets in the stellar habitable zone (HZ) could serve as habitats for extraterrestrial life. We here assess the danger of exomoons to be in a runaway greenhouse (RG) state due to extensive heating from the planet. We apply pre-computed evolution tracks for giant planets to calculate the incident planetary radiation on the moon a…
Detecting massive satellites of extrasolar planets has now become feasible, which led naturally to questions about their habitability. In a previous study we presented constraints on the habitability of moons from stellar and planetary illumination as well as from tidal heating. Here I refine our model by including the effect of eclipses on the orbit-averaged illumination. Moons in low-mass stellar systems must orbit their planet very closely to remain bound, which puts them at risk of strong tidal heating. I first describe the effect of eclipses on stellar illumination of satellites. Then I c…
Roughly 1000 white dwarfs are known to be polluted with planetary material, and the progenitors of this material are typically assumed to be asteroids. The dynamical architectures which perturb asteroids into white dwarfs are still unknown, but may be crucially dependent on moons liberated from parent planets during post-main-sequence gravitational scattering. Here, we trace the fate of these exomoons, and show that they more easily achieve deep radial incursions towards the white dwarf than do scattered planets. Consequently, moons are likely to play a significant role in white dwarf pollutio…
The tidal interactions between a planet and moon can provide insight into the properties of the host planet. The recent exomoon candidates Kepler-1708 b-i and Kepler-1625 b-i are Neptune-sized satellites orbiting Jupiter-like planets and provide an opportunity to apply such methods. We show that if the tidal migration time is roughly equal to the age of these systems, then the tidal dissipation factor Q for the planets Kepler-1708 b and Kepler-1625 b have values of ~$3\times10^5-3\times10^6$ and ~$1.5\times10^5-4\times10^5$, respectively. In each case, these are consistent with estimates for g…
We present a survey of 41 Kepler Objects of Interest (KOIs) for exomoons using Bayesian photodynamics, more than tripling the number of KOIs surveyed with this technique. We find no compelling evidence for exomoons although thirteen KOIs yield spurious detections driven by instrumental artifacts, stellar activity and/or perturbations from unseen bodies. Regarding the latter, we find seven KOIs exhibiting >5 sigma evidence of transit timing variations, including the 'mega-Earth' Kepler-10c, likely indicating an additional planet in that system. We exploit the moderately large sample of 57 uniqu…
Exomoons are expected to produce potentially detectable transit timing variations (TTVs) upon their parent planet. Unfortunately, distinguishing moon-induced TTVs from other sources, in particular planet-planet interactions, has severely impeded its usefulness as a tool for identifying exomoon candidates. A key feature of exomoon TTVs is that they will always be undersampled, due to the simple fact that we can only observe the TTVs once per transit/planetary period. We show that it is possible to analytically express the aliased TTV periodicity as a function of planet and moon period. Further,…
Assuming our Solar System as typical, exomoons may outnumber exoplanets. If their habitability fraction is similar, they would thus constitute the largest portion of habitable real estate in the Universe. Icy moons in our Solar System, such as Europa and Enceladus, have already been shown to possess liquid water, a prerequisite for life on Earth. We intend to investigate under what circumstances small, icy moons may sustain subsurface oceans and thus be "subsurface habitable". We pay specific attention to tidal heating. We made use of a phenomenological approach to tidal heating. We computed t…
The detection of moons orbiting extrasolar planets ("exomoons") has now become feasible. Once they are discovered in the circumstellar habitable zone, questions about their habitability will emerge. Exomoons are likely to be tidally locked to their planet and hence experience days much shorter than their orbital period around the star and have seasons, all of which works in favor of habitability. These satellites can receive more illumination per area than their host planets, as the planet reflects stellar light and emits thermal photons. On the contrary, eclipses can significantly alter local…
In our previous paper, we evaluated the transit duration variation (TDV) effect for a co-aligned planet-moon system at an orbital inclination of i=90 degrees. Here, we will consider the effect for the more general case of i <= 90 degrees and an exomoon inclined from the planet-star plane by Euler rotation angles $α$, $β$ and $γ$. We find that the TDV signal has two major components, one due to the velocity variation effect described in our first paper and one new component due to transit impact parameter variation. By evaluating the dominant terms, we find the two effects are additive for prog…
If the exomoon candidate orbiting Kepler-1625b truly exists, it is much more massive than the moons observed in the Solar system (Teachey et al. 2017; Teachey & Kipping 2018). This exomoon would be sufficiently large to stably host its own satellite. This has sparked discussion of a new category of celestial object - a moon-moon (Forgan 2018) or submoon (Kollmeier & Raymond 2018). In this Note, I describe initial results of climate modelling of a hypothetical moon-moon in the Kepler-1625b system, calculated using the OBERON code, which jointly computes 1D latitudinal energy balance models for …
Recent studies have shown that large exomoons can form in the accretion disks around super-Jovian extrasolar planets. These planets are abundant at about 1 AU from Sun-like stars, which makes their putative moons interesting for studies of habitability. Technological advances could soon make an exomoon discovery with Kepler or the upcoming CHEOPS and PLATO space missions possible. Exomoon climates might be substantially different from exoplanet climates because the day-night cycles on moons are determined by the moon's synchronous rotation with its host planet. Moreover, planetary illumination…
The orbital sampling effect (OSE) appears in phase-folded transit light curves of extrasolar planets with moons. Analytical OSE models have hitherto neglected stellar limb darkening and non-zero transit impact parameters and assumed that the moon is on a circular, co-planar orbit around the planet. Here, we present an analytical OSE model for eccentric moon orbits, which we implement in a numerical simulator with stellar limb darkening that allows for arbitrary transit impact parameters. We also describe and publicly release a fully numerical OSE simulator (PyOSE) that can model arbitrary incl…
Exomoon detections might be feasible with NASA's Kepler or ESA's upcoming PLATO mission or the ground-based E-ELT. To use observational resources most efficiently we need to know where the largest, most easily detected moons can form. We explore the possibility of large exomoons by following the movement of water (H2O) ice lines in the accretion disks around young super-Jovian planets. We want to know how different heating sources in those disks affect the H2O ice lines. We simulate 2D rotationally symmetric accretion disks in hydrostatic equilibrium around super-Jovian exoplanets. The energy …
An intriguing question in the context of dynamics arises: Could a moon possess a moon itself? Such a configuration does not exist in the Solar System, although this may be possible in theory. Kollmeier et al. (2019) determined the critical size of a satellite necessary to host a long-lived sub-satellite, or submoon. However, the orbital constraints for these submoons to exist are still undetermined. Domingos et al. (2006) indicated that moons are stable out to a fraction of the host planet Hill radius $R_{H,p}$, which in turn depends on the eccentricity of its host's orbit. Motivated by this, …
Recently, Teachey, Kipping, and Schmitt (2018) reported the detection of a candidate exomoon, tentatively designated Kepler-1625b I, around a giant planet in the Kepler field. The candidate exomoon would be about the size and mass of Neptune, considerably larger than any moon in our Solar System, and if confirmed, would be the first in a new class of giant moons or binary planets. Motivated by the large mass ratio in the Kepler-1625b planet and satellite system, we investigate the detectability of similarly massive exomoons around directly imaged exoplanets via Doppler spectroscopy. The candid…
