Spin-orbit Angle Research Articles

The spin-orbit alignment of visual binaries

Context. The angle between the stellar spin-axis and the orbital plane of a stellar or planetary companion has important implications for the formation and evolution of such systems. A study by Hale (1994, AJ, 107, 306) found that binaries with separations a ≲ 30 au are preferentially aligned while binaries on wider orbits are frequently misaligned. Aims. We aim to test the robustness of the Hale study results by reanalysing the sample of visual binaries with measured rotation periods using independently derived stellar parameters and a Bayesian formalism. Methods. Our analysis is based on a combination of data from the Hale study and newly obtained spectroscopic data from the Hertzsprung SONG telescope, combined with astrometric data from Gaia DR2 and the Washington Double Star Catalog. We combine measurements of stellar radii and rotation periods to obtain stellar rotational velocities v. Rotational velocities v are combined with measurements of projected rotational velocities v sin i to derive posterior probability distributions of stellar inclination angles i. We determine line-of-sight projected spin-orbit angles by comparing stellar inclination angles with astrometric orbital inclination angles. Results. We find that the precision of the available data is insufficient to make inferences about the spin-orbit alignment of visual binaries. The data are equally compatible with alignment and misalignment at all orbital separations. Conclusions. We conclude that the previously reported trend that binaries with separations a ≲ 30 au are preferentially aligned is spurious. The spin-orbit alignment distribution of visual binaries is unconstrained. Based on simulated observations, we predict that it will be difficult to reach the sufficient precision in v sin i, rotation periods, and orbital inclination required to make robust statistical inferences about the spin-orbit alignment of visual binaries.

Limits on the Spin–Orbit Angle and Atmospheric Escape for the 22 Myr Old Planet AU Mic b*

Abstract We obtained spectra of the pre-main-sequence star AU Microscopii during a transit of its Neptune-sized planet to investigate its orbit and atmosphere. We used the high-dispersion near-infrared spectrograph InfraRed Doppler (IRD) on the Subaru telescope to detect the Doppler “shadow” from the planet and constrain the projected stellar obliquity. Modeling of the observed planetary Doppler shadow suggests a spin–orbit alignment of the system ( deg), but additional observations are needed to confirm this finding. We use both the IRD data and spectra obtained with NIRSPEC on Keck II to search for absorption in the 1083 nm line of metastable triplet He i by the planet’s atmosphere and place an upper limit for the equivalent width of 3.7 mÅ at 99% confidence. With this limit and a Parker wind model we constrain the escape rate from the atmosphere to M ⊕ Gyr−1, comparable to the rates predicted by an X-ray and ultraviolet energy-limited escape calculation and hydrodynamic models, but refinement of the planet mass is needed for rigorous tests.

The EBLM project – VII. Spin–orbit alignment for the circumbinary planet host EBLM J0608-59 A/TOI-1338 A

ABSTRACT A dozen short-period detached binaries are known to host transiting circumbinary planets. In all circumbinary systems so far, the planetary and binary orbits are aligned within a couple of degrees. However, the obliquity of the primary star, which is an important tracer of their formation, evolution, and tidal history, has only been measured in one circumbinary system until now. EBLM J0608-59/TOI-1338 is a low-mass eclipsing binary system with a recently discovered circumbinary planet identified by TESS. Here, we perform high-resolution spectroscopy during primary eclipse to measure the projected stellar obliquity of the primary component. The obliquity is low, and thus the primary star is aligned with the binary and planetary orbits with a projected spin–orbit angle β = 2${_{.}^{\circ}}$8 ± 17${_{.}^{\circ}}$1. The rotation period of 18.1 ± 1.6 d implied by our measurement of vsin i⋆ suggests that the primary has not yet pseudo-synchronized with the binary orbit, but is consistent with gyrochronology and weak tidal interaction with the binary companion. Our result, combined with the known coplanarity of the binary and planet orbits, is suggestive of formation from a single disc. Finally, we considered whether the spectrum of the faint secondary star could affect our measurements. We show through simulations that the effect is negligible for our system, but can lead to strong biases in vsin i⋆ and β for higher flux ratios. We encourage future studies in eclipse spectroscopy test the assumption of a dark secondary for flux ratios ≳1 ppt.

KELT-9 b’s Asymmetric TESS Transit Caused by Rapid Stellar Rotation and Spin–Orbit Misalignment

Abstract KELT-9 b is an ultra-hot Jupiter transiting a rapidly rotating, oblate early-A-type star in a polar orbit. We model the effect of rapid stellar rotation on KELT-9 b’s transit light curve using photometry from the Transiting Exoplanet Survey Satellite to constrain the planet’s true spin–orbit angle and to explore how KELT-9 b may be influenced by stellar gravity darkening. We constrain the host star’s equatorial radius to be 1.089 ± 0.017 times as large as its polar radius and its local surface brightness to vary by ∼38% between its hot poles and cooler equator. We model the stellar oblateness and surface brightness gradient and find that it causes the transit light curve to lack the usual symmetry around the time of minimum light. We take advantage of the light-curve asymmetry to constrain KELT-9 b’s true spin–orbit angle ( ), agreeing with Gaudi et al. that KELT-9 b is in a nearly polar orbit. We also apply a gravity-darkening correction to the spectral energy distribution model from Gaudi et al. and find that accounting for rapid rotation gives a better fit to available spectroscopy and yields a more reliable estimate for the star’s polar effective temperature.

Is there Na I in the atmosphere of HD 209458b?

HD 209458b was the first transiting planet discovered, and the first for which an atmosphere, in particular Na I, was detected. With time, it has become one of the most frequently studied planets, with a large diversity of atmospheric studies using low- and high-resolution spectroscopy. Here, we present transit spectroscopy observations of HD 209458b using the HARPS-N and CARMENES spectrographs. We fit the Rossiter-McLaughlin effect by combining radial velocity data from both instruments (nine transits in total), measuring a projected spin-orbit angle of − 1.6 ± 0.3 deg. We also present the analysis of high-resolution transmission spectroscopy around the Na I region at 590 nm, using a total of five transit observations. In contrast to previous studies where atmospheric Na I absorption is detected, we find that for all of the nights, whether individually or combined, the transmission spectra can be explained by the combination of the centre-to-limb variation and the Rossiter-McLaughlin effect. This is also observed in the time-evolution maps and transmission light curves, but at lower signal-to-noise ratio. Other strong lines such as Hα, Ca II IRT, the Mg I triplet region, and K I D1 are analysed, and are also consistent with the modelled effects, without considering any contribution from the exoplanet atmosphere. Thus, the transmission spectrum reveals no detectable Na I absorption in HD 209458b. We discuss how previous pioneering studies of this benchmark object may have overlooked these effects. While for some star–planet systems these effects are small, for other planetary atmospheres the results reported in the literature may require revision.

Gravity-darkening Analysis of the Misaligned Hot Jupiter MASCARA-4 b

Abstract MASCARA-4 b is a hot Jupiter in a highly misaligned orbit around a rapidly rotating A3V star that was observed for 54 days by the Transiting Exoplanet Survey Satellite (TESS). We perform two analyses of MASCARA-4 b using a stellar gravity-darkened model. First, we measure MASCARA-4 b’s misaligned orbital configuration by modeling its TESS photometric light curve. We take advantage of the asymmetry in MASCARA-4 b’s transit due to its host star’s gravity-darkened surface to measure MASCARA-4 b’s true spin–orbit angle to be 104° . We also detect a ∼4σ secondary eclipse at 0.491 ± 0.007 orbital phase, proving that the orbit is slightly eccentric. Second, we model MASCARA-4 b’s insolation including gravity darkening and find that the planet’s received X-ray and ultraviolet flux varies by 4% throughout its orbit. MASCARA-4 b’s short-period, polar orbit suggests that the planet likely underwent dramatic orbital evolution to end up in its present-day configuration and that it receives a varying stellar irradiance that perpetually forces the planet out of thermal equilibrium. These findings make MASCARA-4 b an excellent target for follow-up characterization to better understand the orbital evolution and present-day environment of planets around high-mass stars.

The GAPS Programme with HARPS-N at TNG

Aims. In the framework of the GAPS project, we observed the planet-hosting star KELT-9 (A-type star, v sin i ~ 110 km s−1) with the HARPS-N spectrograph at the Telescopio Nazionale Galileo. In this work we analyse the spectra and the extracted radial velocities to constrain the physical parameters of the system and to detect the planetary atmosphere of KELT-9b. Methods. We extracted the mean stellar line profiles from the high-resolution optical spectra via an analysis based on the least-squares deconvolution technique. Then we computed the stellar radial velocities with a method optimised for fast rotators by fitting the mean stellar line profile with a purely rotational profile instead of using a Gaussian function. Results. The new spectra and analysis led us to update the orbital and physical parameters of the system, improving in particular the value of the planetary mass to Mp = 2.88 ± 0.35 MJup. We discovered an anomalous in-transit radial velocity deviation from the theoretical Rossiter-McLaughlin effect solution, calculated from the projected spin-orbit angle λ = −85.78 ± 0.46 degrees measured with Doppler tomography. We prove that this deviation is caused by the planetary atmosphere of KELT-9b, thus we call this effect Atmospheric Rossiter-McLaughlin effect. By analysing the magnitude of the radial velocity anomaly, we obtained information on the extension of the planetary atmosphere as weighted by the model used to retrieve the stellar mean line profiles, which is up to 1.22 ± 0.02 Rp. Conclusions. The Atmospheric Rossiter-McLaughlin effect will be observable for other exoplanets whose atmosphere has non-negligible correlation with the stellar mask used to retrieve the radial velocities, in particular ultra-hot Jupiters with iron in their atmospheres. The duration and amplitude of the effect will depend not only on the extension of the atmosphere, but also on the in-transit planetary radial velocities and on the projected rotational velocity of the parent star.

Ultra-short-period Planets from Secular Chaos

Abstract Over 100 rocky planets orbiting Sun-like stars in very short orbital periods (≲1 day) have been discovered by the Kepler mission. The origin of these planets, known as ultra-short-period (USP) planets, remains elusive. Here, we propose that most of these planets, originally at periods of ∼5–10 days, reach their current orbits via high-eccentricity migration. In a scaled-down version of the dynamics that may have been experienced by their high-mass analogs, the hot Jupiters, these planets reach high eccentricities via chaotic secular interactions with their companion planets and then undergo orbital circularization due to dissipation from tides raised on the planet. This proposal is motivated by the following observations: planetary systems observed by Kepler often contain several super-Earths with non-negligible eccentricities and inclinations, possibly extending beyond ∼au distances; by contrast, only a small fraction of USP planets have known transiting companions, which are generally not closely spaced, and we argue that most of them should have companions with periods ≳10 days. The proposed scenario naturally explains the observation that most USP planets have significantly more distant transiting companions compared to their counterparts at slightly longer periods (1–3 days). Our model predicts that USP planets should have: (i) spin–orbit angles, and inclinations relative to outer planets, in the range of ∼10–50°; (ii) several outer planetary companions extending beyond ∼1 au distances. Both of these predictions may be tested by TESS and its follow-up observations.

Creating retrogradely orbiting planets by prograde stellar fly-bys

Several planets have been found that orbit their host star on retrograde orbits (spin–orbit angle φ > 90°). Currently, the largest measured projected angle between the orbital angular momentum axis of a planet and the rotation axis of its host star has been found for HAT-P-14b to be ≈ 171°. One possible mechanism for the formation of such misalignments is through long-term interactions between the planet and other planetary or stellar companions. However, with this process, it has been found to be difficult to achieve retrogradely orbiting planets, especially planets that almost exactly counter-orbit their host star (φ ≈ 180°) such as HAT-P-14b. By contrast, orbital misalignment can be produced efficiently by perturbations of planetary systems that are passed by stars. Here we demonstrate that not only retrograde fly-bys, but surprisingly, even prograde fly-bys can induce retrograde orbits. Our simulations show that depending on the mass ratio of the involved stars, there are significant ranges of planetary pre-encounter parameters for which counter-orbiting planets are the natural consequence. We find that the highest probability to produce counter-orbiting planets (≈20%) is achieved with close prograde, coplanar fly-bys of an equal-mass perturber with a pericentre distance of one-third of the initial orbital radius of the planet. For fly-bys where the pericentre distance equals the initial orbital radius of the planet, we still find a probability to produce retrograde planets of ≈10% for high-mass perturbers on inclined (60° < i < 120°) orbits. As usually more distant fly-bys are more common in star clusters, this means that inclined fly-bys probably lead to more retrograde planets than those with inclinations <60°. Such close fly-bys are in general relatively rare in most types of stellar clusters, and only in very dense clusters will this mechanism play a significant role. The total production rate of retrograde planets depends then on the cluster environment. Finally, we briefly discuss the application of our results to the retrograde minor bodies in the solar system and to the formation of retrograde moons during the planet–planet scattering phase.

Nonlinear tidal flows in short-period planets

I discuss two related nonlinear mechanisms of tidal dissipation that require finite tidal deformations for their operation: the elliptical instability and the precessional instability. Both are likely to be important for the tidal evolution of short-period extrasolar planets. The elliptical instability is a fluid instability of elliptical streamlines, such as in tidally deformed non-synchronously rotating or non-circularly orbiting planets. I summarise the results of local and global simulations that indicate this mechanism to be important for tidal spin synchronisation, planetary spin-orbit alignment and orbital circularisation for the shortest period hot Jupiters. The precessional instability is a fluid instability that occurs in planets undergoing axial precession, such as those with spin-orbit misalignments (non-zero obliquities). I summarise the outcome of local MHD simulations designed to study the turbulent damping of axial precession, which suggest this mechanism to be important in driving tidal evolution of the spin-orbit angle for hot Jupiters. Avenues for future work are also discussed.

Activity induced variation in spin-orbit angles as derived from Rossiter–McLaughlin measurements

One of the most powerful methods used to estimate sky-projected spin-orbit angles of exoplanetary systems is through a spectroscopic transit observation known as the RossiterMcLaughlin (RM) effect. So far mostly single RM observations have been used to estimate the spin-orbit angle, and thus there have been no studies regarding the variation of estimated spin-orbit angle from transit to transit. Stellar activity can alter the shape of photometric transit light curves and in a similar way they can deform the RM signal. In this paper we present several RM observations, obtained using the HARPS spectrograph, of known transiting planets that all transit extremely active stars, and by analyzing them individually we assess the variation in the estimated spin-orbit angle. Our results reveal that the estimated spin-orbit angle can vary significantly (up to ~42°) from transit to transit, due to variation in the configuration of stellar active regions over different nights. This finding is almost two times larger than the expected variation predicted from simulations. We could not identify any meaningful correlation between the variation of estimated spin-orbit angles and the stellar magnetic activity indicators. We also investigated two possible approaches to mitigate the stellar activity influence on RM observations. The first strategy was based on obtaining several RM observations and folding them to reduce the stellar activity noise. Our results demonstrated that this is a feasible and robust way to overcome this issue. The second approach is based on acquiring simultaneous high-precision short-cadence photometric transit light curves using TRAPPIST/SPECULOOS telescopes, which provide more information about the stellar active region’s properties and allow a better RM modeling.

Stellar Obliquities and Planetary Alignments (SOPA). I. Spin–Orbit Measurements of Three Transiting Hot Jupiters: WASP-72b, WASP-100b, and WASP-109b*

Abstract We report measurements of the sky-projected spin–orbit angles for three transiting hot Jupiters, two of which are in nearly polar orbits, WASP-100b and WASP-109b, and a third in a low-obliquity orbit, WASP-72b. We obtained these measurements by observing the Rossiter–McLaughlin effect over the course of the transits from high-resolution spectroscopic observations made with the CYCLOPS2 optical fiber bundle system feeding the UCLES spectrograph on the Anglo-Australian Telescope. The resulting sky-projected spin–orbit angles are , , and for WASP-72b, WASP-100b, and WASP-109b, respectively. These results suggests that WASP-100b and WASP-109b are on highly inclined orbits tilted nearly 90◦ from their host star’s equator, while the orbit of WASP-72b appears to be well-aligned. WASP-72b is a typical hot Jupiter orbiting a mid-late F star (F7 with T eff = 6250 ± 120 K). WASP-100b and WASP-109b are highly irradiated bloated hot Jupiters orbiting hot early-mid F stars (F2 with T eff = 6900 ± 120 K and F4 with T eff = 6520 ± 140 K), making them consistent with the trends observed for the majority of stars hosting planets on high-obliquity orbits.

A-type Stars, the Destroyers of Worlds: The Lives and Deaths of Jupiters in Evolving Stellar Binaries

Abstract Hot Jupiters (HJs), gas giant planets orbiting their host stars with periods on the order of days, commonly occur in the Galaxy, including relatively massive (1.6–2.4 M ⊙, i.e., A-type main-sequence stars) and evolved stars. The majority of A-type main-sequence stars have stellar binary companions, that can strongly affect the dynamical evolution of planets around either star. In this work, we investigate the effects of gravitational perturbations by a far away stellar companion on the orbital evolution of gas giant planets orbiting A-type stars, the so-called Eccentric Kozai–Lidov mechanism, including the effects of general relativity, post-main-sequence stellar evolution, and tides. We find that only 0.15% of A-type stars will host HJs during their main-sequence lifetimes. However, we also find a new class of planets, Temporary Hot Jupiters (THJs), that form during the post-main-sequence lifetime of about 3.7% of former A-type main-sequence stars. These THJs orbit on periods of tens to a hundred days and only exist for a few 100,000 years before they are engulfed, but they reach similar temperatures as “classical” HJs due to the increased stellar luminosities. THJs’ spin–orbit angles will mostly be misaligned. THJ effects on the host stars’ evolution could also be observable for longer than a few 100,000 years. Overall, we find that approximately 70% of all gas giant planets orbiting A-type stars will eventually be destroyed or engulfed by their star, about 25% during the main-sequence lifetime, about 45% during post-main-sequence evolution.

Discovery of WASP-174b: Doppler tomography of a near-grazing transit

We report the discovery and tomographic detection of WASP-174b, a planet with a near-grazing transit on a 4.23-d orbit around a $V$ = 11.9, F6V star with [Fe/H] = 0.09 $\pm$ 0.09. The planet is in a moderately misaligned orbit with a sky-projected spin-orbit angle of $\lambda$ = 31$^{\circ}$ $\pm$ 1$^{\circ}$. This is in agreement with the known tendency for orbits around hotter stars to be misaligned. Owing to the grazing transit the planet's radius is uncertain, with a possible range of 0.8-1.8 R$_{\rm Jup}$. The planet's mass has an upper limit of 1.3 M$_{\rm Jup}$. WASP-174 is the faintest hot-Jupiter system so far confirmed by tomographic means.

Precessional dynamics of black hole triples: binary mergers with near-zero effective spin

ABSTRACT The binary black hole mergers detected by Advanced LIGO/Virgo have shown no evidence of large black hole spins. However, because LIGO/Virgo best measures the effective combination of the two spins along the orbital angular momentum (χeff), it is difficult to distinguish between binaries with slowly spinning black holes and binaries with spins lying in the orbital plane. Here, we study the spin dynamics for binaries with a distant black hole companion. For spins initially aligned with the orbital angular momentum of the binary, we find that χeff ‘freezes’ near zero as the orbit decays through the emission of gravitational waves. Through a population study, we show that this process predominantly leads to merging black hole binaries with near-zero χeff. We conclude that if the detected black hole binaries were formed in triples, then this would explain their low χeff without the need to invoke near-zero spins or initially large spin–orbit angles.

Tracking spin-axis orbital alignment in selected binary systems: the Torun Rossiter–McLaughlin effect survey

We have obtained high-resolution spectra of four eclipsing binary systems (FM Leo, NN Del, V963 Cen and AI Phe) with the view to gaining insight into the relative orientation of their stellar spin axes and orbital axes. The so called Rossiter-McLaughlin (RM) effect, i.e. the fact that the broadening and the amount of blue- or redshift in the spectra during an eclipse depend on the tilt of the spin axis of the background star, has the potential of reconciling observations and theoretical models if such a tilt is found. We analyse the RM effect by disentangling the spectra, removing the front component and measuring the remaining, distorted lines with a broadening function (BF) obtained from single value decomposition (SVD), weighting by the intensity centre of the BF in the eclipse. All but one of our objects show no significant misalignment, suggesting that aligned systems are dominant. We provide stellar as well as orbital parameters for our systems. With five measured spin-orbit angles we significantly increase (from 9 to 14) the number of stars for which it has been measured. The spin-orbit angle $\beta$ calculated for AI Phe's secondary component shows a misalignment of 87$\pm$17 degrees. NN Del, with a large separation of components and a long dynamical timescale for circularisation and synchronisation, is an example of a close to primordial spin-orbit angle measurement.

Reliability of stellar inclination estimated from asteroseismology: analytical criteria, mock simulations and Kepler data analysis

Advances in asteroseismology of solar-like stars, now provide a unique method to estimate the stellar inclination $i_{\star}$. This enables to evaluate the spin-orbit angle of transiting planetary systems, in a complementary fashion to the Rossiter-McLaughlin effect, a well-established method to estimate the projected spin-orbit angle $\lambda$. Although the asteroseismic method has been broadly applied to the Kepler data, its reliability has yet to be assessed intensively. In this work, we evaluate the accuracy of $i_{\star}$ from asteroseismology of solar-like stars using 3000 simulated power spectra. We find that the low signal-to-noise ratio of the power spectra induces a systematic under-estimate (over-estimate) bias for stars with high (low) inclinations. We derive analytical criteria for the reliable asteroseismic estimate, which indicates that reliable measurements are possible in the range of $20^\circ \lesssim i_{\star} \lesssim 80^\circ$ only for stars with high signal-to-noise ratio. We also analyse and measure the stellar inclination of 94 Kepler main-sequence solar-like stars, among which 33 are planetary hosts. According to our reliability criteria, a third of them (9 with planets, 22 without) have accurate stellar inclination. Comparison of our asteroseismic estimate of $v\sin{i_{\star}}$ against spectroscopic measurements indicates that the latter suffers from a large uncertainty possibly due to the modeling of macro-turbulence, especially for stars with projected rotation speed $v\sin{i_{\star}} \lesssim 5$ km/s. This reinforces earlier claims, and the stellar inclination estimated from the combination of measurements from spectroscopy and photometric variation for slowly rotating stars needs to be interpreted with caution.

Stellar Spin–Orbit Alignment for Kepler-9, a Multi-transiting Planetary System with Two Outer Planets Near 2:1 Resonance

Abstract We present spectroscopic measurements of the Rossiter–McLaughlin effect for the planet b of the Kepler-9 multi-transiting planetary system. The resulting sky-projected spin–orbit angle is λ = −13° ± 16°, which favors an aligned system and strongly disfavors highly misaligned, polar, and retrograde orbits. Including Kepler-9, there are now a total of four Rossiter–McLaughlin effect measurements for multiplanet systems, all of which are consistent with spin–orbit alignment.

Transiting Exoplanet Monitoring Project (TEMP). III. On the Relocation of the Kepler-9 b Transit

AbstractThe Kepler-9 system harbors three known transiting planets. The system holds significant interest for several reasons. First, the outer two planets exhibit a period ratio that is close to a 2:1 orbital commensurability, with attendant dynamical consequences. Second, both planets lie in the planetary mass “desert” that is generally associated with the rapid gas agglomeration phase of the core accretion process. Third, there exist attractive prospects for accurately measuring both the sky-projected stellar spin–orbit angles as well as the mutual orbital inclination between the planets in the system. Following the originalKeplerdetection announcement in 2010, the initially reported orbital ephemerides for Kepler-9 b and c have degraded significantly, due to the limited time base-line of observations on which the discovery of the system rested. Here, we report new ground-based photometric observations and extensive dynamical modeling of the system. These efforts allow us to photometrically recover the transit of Kepler-9 b and thereby greatly improve the predictions for upcoming transit mid-times. Accurate ephemerides of this system are important in order to confidently schedule follow-up observations of this system, for both in-transit Doppler measurements as well as for atmospheric transmission spectra taken during transit.

K2-139 b: a low-mass warm Jupiter on a 29-d orbit transiting an active K0 V star

We announce the discovery of K2-139 b (EPIC 218916923 b), a transiting warm-Jupiter ($T_\mathrm{eq}$=547$\pm$25 K) on a 29-day orbit around an active (log $R^\prime_\mathrm{HK}$ = $-$4.46 $\pm$ 0.06) K0 V star in K2 Campaign 7. We derive the system's parameters by combining the K2 photometry with ground-based follow-up observations. With a mass of~$0.387 _{ - 0.075 } ^ {+ 0.083 } M_{\rm J}$ and radius of $0.808 _{ - 0.033 } ^ {+ 0.034 } R_{\rm J}$, K2-139 b is one of the transiting warm Jupiters with the lowest mass known to date. The planetary mean density of $0.91 _{ - 0.20} ^ { + 0.24 }$ $\mathrm{g cm^{-3}}$ can be explained with a core of $\sim$50 $M_\oplus$. Given the brightness of the host star ($V$ = 11.653 mag), the relatively short transit duration ($\sim$5 hours), and the expected amplitude of the Rossiter-McLaughlin effect ($\sim25 {\rm m s^{-1}}$ ), K2-139 is an ideal target to measure the spin-orbit angle of a planetary system hosting a warm Jupiter.