Planet-moon System Research Articles

Exomoons and Exorings with the Habitable Worlds Observatory. I. On the Detection of Earth–Moon Analog Shadows and Eclipses

The highest priority recommendation of the Astro2020 Decadal Survey for space-based astronomy was the construction of an observatory capable of characterizing habitable worlds. In this paper series we explore the detectability of and interference from exomoons and exorings serendipitously observed with the proposed Habitable Worlds Observatory (HWO) as it seeks to characterize exoplanets, starting in this manuscript with Earth–Moon analog mutual events. Unlike transits, which only occur in systems viewed near edge-on, shadow (i.e., solar eclipse) and lunar eclipse mutual events occur in almost every star–planet–moon system. The cadence of these events can vary widely from ∼yearly to multiple events per day, as was the case in our younger Earth–Moon system. Leveraging previous space-based (EPOXI) light curves of a Moon transit and performance predictions from the LUVOIR-B concept, we derive the detectability of Moon analogs with HWO. We determine that Earth–Moon analogs are detectable with observation of ∼2–20 mutual events for systems within 10 pc, and larger moons should remain detectable out to 20 pc. We explore the extent to which exomoon mutual events can mimic planet features and weather. We find that HWO wavelength coverage in the near-infrared, specifically in the 1.4 μm water band where large moons can outshine their host planet, will aid in differentiating exomoon signals from exoplanet variability. Finally, we predict that exomoons formed through collision processes akin to our Moon are more likely to be detected in younger systems, where shorter orbital periods and favorable geometry enhance the probability and frequency of mutual events.

The origin and evolution of wide Jupiter mass binary objects in young stellar clusters

The recently observed population of 540 free-floating Jupiter-mass objects, including 40 dynamically soft pairs, and two triples, in the Trapezium cluster have raised interesting questions on their formation and evolution. We test various scenarios for the origin and survivability of these free floating Jupiter-mass objects and Jupiter-mass Binary Objects (JuMBOs) in the Trapezium cluster. The numerical calculations are performed by direct NN-body integration of the stars and planets in the Trapezium cluster starting with a wide variety of planets in various configurations. We discuss four models: \mathcal{SPP}𝒮𝒫𝒫, in which selected stars have two outer orbiting Jupiter-mass planets; \mathcal{SPM}𝒮𝒫ℳ, where selected stars are orbited by Jupiter-mass planet-moon pairs; \mathcal{ISF}ℐ𝒮ℱ in which JuMBOs form in situ with the stars, and \mathcal{FFC}ℱℱ𝒞, where we introduce a population of free-floating single Jupiter-mass objects, but no initialised binaries. Models \mathcal{FFC}ℱℱ𝒞 and \mathcal{SPP}𝒮𝒫𝒫 fail to produce enough JuMBOs. Models \mathcal{SPM}𝒮𝒫ℳ can produce sufficient free-floaters and JuMBOs, but requires unusually wide orbits for the planet-moon system around the star. The observed JuMBOs and free-floating Jupiter-mass objects in the Trapezium cluster are best reproduced if they formed in pairs and as free-floaters together with the other stars in a smooth (Plummer) density profile with a virial radius of \sim 0.5∼0.5pc. A fractal (with fractal dimension 1.6) stellar density distribution also works, but requires relatively recent formations (⪆ 0.2⪆0.2Myr after the other stars formed) or a high (⪆ 50⪆50%) initial binary fraction. This would make the primordial binary fraction of JuMBOs even higher than the already large observation fraction of \sim 8∼8% (42/540). The fraction of JuMBOs will continue to drop with time, and the lack of JuMBOs in Upper Scorpius could then result in its higher age, causing more JuMBOs to be ionized. We then also predict that the interstellar density of Jupiter-mass objects (mostly singles with some \sim 2∼2% lucky surviving binaries) is \sim 0.05∼0.05 per pc^{-3}−3 (or around 0.24 per star).

Modelling the light curves of transiting exomoons: a zero-order photodynamic agent added to the Transit and Light Curve Modeller

ABSTRACT Despite the ever-growing number of exoplanets discovered and the extensive analyses carried out to find their potential satellites, only two exomoon candidates, Kepler-1625b-i and Kepler-1708 b-i, have been discovered to date. A considerable amount of effort has been invested in the development of algorithms for modelling, searching, and detecting exomoons in exoplanetary light curves. In this work, we incorporate moon handling capabilities into the state of the art and publicly available code, the Transit and Light Curve Modeller (tlcm). The code is designed for the analysis of transiting exoplanet systems with the inclusion of a wavelet-based noise handling algorithm. Here, we present an updated version of tlcm that is capable of modelling a coplanar planet–moon system on an elliptical orbit around its host, accounting for mutual eclipses between the two bodies (and neglecting perturbative effects) – a so-called photodynamic model. The key benefit of this framework is the ability for a joint analysis of multiple planet–moon transits. We demonstrate the necessity of this software on a case study of Kepler-1625b. Similarly to prior works, we conclude that there is no firm evidence of an exomoon in that system, by showing that temporally correlated noise can mimic apparent lunar transits.

Transit Light Curves for Exomoons: Analytical Formalism

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 exomoon around the host planet, which is indeed the case for tidally locked moons. The formalism uses the radius and orbital properties of both the host planet and its moon as model parameters. The coalignment or noncoalignment of the orbits of the planet and the moon are parameterized using two angular parameters and thus can be used to model all the possible orbital alignments for a star–planet–moon system. This formalism also provides unique and direct solutions to every possible star–planet–moon three circular body alignment. Using the formula derived, a few representative light curves are also presented.

Catching a Planet: A Tidal Capture Origin for the Exomoon Candidate Kepler 1625b I

Abstract 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 widened due to tidal synchronization of the spin of the planet with the orbit, resulting in a synchronous planet-moon system. Interestingly, in our scenario the captured object was originally a Neptune-like planet, turned into a moon by its capture.

Revisiting the exomoon candidate signal around Kepler-1625 b

Context. Transit photometry of the Jupiter-sized exoplanet candidate Kepler-1625 b has recently been interpreted as showing hints of a moon. This exomoon, the first of its kind, would be as large as Neptune and unlike any moon we know from the solar system. Aims. We aim to clarify whether the exomoon-like signal is indeed caused by a large object in orbit around Kepler-1625 b, or whether it is caused by stellar or instrumental noise or by the data detrending procedure. Methods. To prepare the transit data for model fitting, we explore several detrending procedures using second-, third-, and fourth-order polynomials and an implementation of the Cosine Filtering with Autocorrelation Minimization (CoFiAM). We then supply a light curve simulator with the co-planar orbital dynamics of the system and fit the resulting planet–moon transit light curves to the Kepler data. We employ the Bayesian information criterion (BIC) to assess whether a single planet or a planet–moon system is a more likely interpretation of the light curve variations. We carry out a blind hare-and-hounds exercise using many noise realizations by injecting simulated transits into different out-of-transit parts of the original Kepler-1625 light curve: (1) 100 sequences with three synthetic transits of a Kepler-1625 b-like Jupiter-size planet and (2) 100 sequences with three synthetic transits of a Kepler-1625 b-like planet with a Neptune-sized moon. Results. The statistical significance and characteristics of the exomoon-like signal strongly depend on the detrending method (polynomials versus cosines), the data chosen for detrending, and the treatment of gaps in the light curve. Our injection-retrieval experiment shows evidence of moons in about 10% of those light curves that do not contain an injected moon. Strikingly, many of these false-positive moons resemble the exomoon candidate, that is, a Neptune-sized moon at about 20 Jupiter radii from the planet. We recover between about one third and one half of the injected moons, depending on the detrending method, with radii and orbital distances broadly corresponding to the injected values. Conclusions. A ΔBIC of − 4.9 for the CoFiAM-based detrending is indicative of an exomoon in the three transits of Kepler-1625 b. This solution, however, is only one out of many and we find very different solutions depending on the details of the detrending method. We find it concerning that the detrending is so clearly key to the exomoon interpretation of the available data of Kepler-1625 b. Further high-accuracy transit observations may overcome the effects of red noise but the required amount of additional data might be large.

DISTINGUISHING A HYPOTHETICAL ABIOTIC PLANET–MOON SYSTEM FROM A SINGLE INHABITED PLANET

ABSTRACT It has recently been suggested that an exomoon with a CH4 atmosphere, orbiting an abiotic Earth-mass planet with an O2-rich atmosphere, can produce a false positive biosignature at a low–moderate spectral resolution (R = λ/Δλ ≤ 2000). If this were true, inferring the presence of life on exoplanets will be beyond our reach in the next several decades. Here we use a line-by-line radiative transfer model to compute the relevant reflection spectrum between 1 and 3.3 μm. We show that it is possible to separate the combined spectra of such planet–moon systems from an inhabited planet by multiple-band NIR observations. We suggest that future observations near the 2.3 μm CH4 absorption band at a resolution of 100 and an SNR of 10 or more may be a good way to distinguish an abiotic planet–moon system from a inhabited single planet.

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.

Possibility of Detection of Exomoons with Inclined Orbits Orbiting Pulsar Planets Using the Time-of-Arrival Analysis

The perturbation caused by planet-moon binarity on the time-of-arrival (TOA) signal of a pulsar with an orbiting planet is derived for the case of the orbit of the planet-moon system inclined of an angleαwith respect to the plane of the orbit of the planet-moon barycenter around the pulsar. We also consider both the orbits of the moon and the planet-moon barycenter as circular. The signal consists of three sinusoids with frequency, respectively, of(2np−3nb),(2np−nb), and(2np−3nb), wherenpandnbare, respectively, the mean motions of the planet and moon around their barycenter and the planet-moon system around the host, respectively. The amplitude of the signal is equal to the fractionsin⁡I[9(Mp/Mm)/16(Mp+Mm)2][r/R]5(5 sin⁡2α/3−2sin⁡α/3−2 cos⁡2α/9)of the system crossing timeR/c, whereMpandMmare, respectively, the mass of the planet and the mass of the moon,ris their orbital separation,Ris the distance between the host pulsar and planet-moon barycenter,Iis the inclination of the orbital plane of the planet, andcis the speed of light.

How to weigh a star using a moon

Abstract We show that for a transiting exoplanet accompanied by a moon which also transits, the absolute masses and radii of the star, planet and moon are determinable. For a planet–star system, it is well known that the density of the star is calculable from the light curve by manipulation of Kepler's Third Law. In an analogous way, the planetary density is calculable for a planet–moon system which transits a star, and thus the ratio-of-densities is known. By combining this ratio with the observed ratio-of-radii and the radial velocity measurements of the system, we show that the absolute dimensions of the star and planet are determinable. This means such systems could be used as calibrators of stellar evolution. The detection of dynamical effects, such as transit timing variations, allows the absolute mass of the moon to be determined as well, which may be combined with the radius to infer the satellite's composition.

Habitable zones of host stars during the post-MS phase

A star will become brighter and brighter with stellar evolution, and the distance of its habitable zone will become larger and larger. Some planets outside the habitable zone of a host star during the main sequence phase may enter the habitable zone of the host star during other evolutionary phases. A terrestrial planet within the habitable zone of its host star is generally thought to be suitable for the existence of life. Furthermore, a rocky moon around a giant planet may be also suitable for life to survive, provided that the planet–moon system is within the habitable zone of its host star. Using Eggleton’s code and the boundary flux of the habitable zone, we calculate the habitable zone of our Solar system after the main sequence phase. It is found that Mars’ orbit and Jupiter’s orbit will enter the habitable zone of the Solar system during the subgiant branch phase and the red giant branch phase, respectively. And the orbit of Saturn will enter the habitable zone of Solar during the He-burning phase for about 137 million years. Life is unlikely at any time on Saturn, as it is a giant gaseous planet. However, Titan, the rocky moon of Saturn, may be suitable for biological evolution and become another Earth during that time. For low-mass stars, there are similar habitable zones during the He-burning phase as our Solar, because there are similar core masses and luminosities for these stars during that phase.

Transit timing effects due to an exomoon - II

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 $\alpha$, $\beta$ and $\gamma$. 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 prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry could allow for future determination of the orbital sense of motion. We re-evaluate the ratio of TDV and TTV effects, $\eta$, in the more general case of an inclined planetary orbit with a circular orbiting moon and find that it is still possible to directly determine the moon's orbital separation from just the ratio of the two amplitudes, as first proposed in our previous paper.

Transit timing effects due to an exomoon

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 $\alpha$, $\beta$ and $\gamma$. 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 prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry could allow for future determination of the orbital sense of motion. We re-evaluate the ratio of TDV and TTV effects, $\eta$, in the more general case of an inclined planetary orbit with a circular orbiting moon and find that it is still possible to directly determine the moon's orbital separation from just the ratio of the two amplitudes, as first proposed in our previous paper.

Possibility of Detecting Moons of Pulsar Planets through Time-of-Arrival Analysis

The perturbation caused by planet-moon binarity on the time-of-arrival signal of a pulsar with an orbiting planet is derived for the case in which the orbits of the moon and the planet-moon barycenter are both circular and coplanar. The signal consists of two sinusoids with frequency ( -->2np − 3nb) and ( -->2np − nb), where -->np and -->nb are the mean motions of the planet and moon around their barycenter, and the planet-moon system around the host, respectively. The amplitude of the signal is the fraction -->sin I [ 9(MpMm)/16(Mp + Mm)2][r/R]5 of the system crossing time -->R/c, where -->Mp and -->Mm are the masses of the planet and moon, r is their orbital separation, R is the distance between the host pulsar and planet-moon barycenter, I is the inclination of the orbital plane of the planet, and c is the speed of light. The analysis is applied to the case of PSR B1620–26b, a pulsar planet, to constrain the orbital separation and mass of any possible moons. We find that a stable moon orbiting this pulsar planet could be detected, if its mass were >5% of its planet's mass, and if the planet-moon distance were ~2% of the planet-pulsar separation.

The Torque at a Lindblad Vertical Resonance

A fairly uniform, rapidly and differentially rotating disk of rarely colliding particles (when the frequency of interparticle collisions is much smaller than the local orbital frequency) in a planet-moon system is considered. A moon causes a number of orbital resonant effects in this continuous, viscous (through ordinary collisions) disk. In the frame of hydrodynamical theory, the gravitational torques exerted by an exterior moon on particles at an inner Lindblad horizontal resonance and corresponding vertical resonance are estimated. It is shown that the torques are negative at these resonances, so gaps in the disk near each resonance may be created. The latter result can be used to provide a viable clue to solving the puzzle of narrow, dense, and widely separated rings of Uranus. The model advocated suggests that the Uranian ring orbits have a close connection with the small moons of the planet that are interior to the orbit of Miranda, from Cordelia to Mab, discovered by Voyager 2 imaging observations in 1986.

Habitable moons around extrasolar giant planets.

Possible planetary objects have now been discovered orbiting nine different main-sequence stars. These companion objects (some of which might actually be brown dwarfs) all have a mass at least half that of Jupiter, and are therefore unlikely to be hospitable to Earth-like life: jovian planets and brown dwarfs support neither a solid nor a liquid surface near which organisms might dwell. Here we argue that rocky moons orbiting these companions could be habitable if the planet-moon system orbits the parent star within the so-called 'habitable zone', where life-supporting liquid water could be present. The companions to the stars 16 Cygni B and 47 Ursae Majoris might satisfy this criterion. Such a moon would, however, need to be large enough (>0.12 Earth masses) to retain a substantial and long-lived atmosphere, and would also need to possess a strong magnetic field in order to prevent its atmosphere from being sputtered away by the constant bombardment of energetic ions from the planet's magnetosphere.