Stellar Spin-down Research Articles

Stellar Spin-down in Post-mass-transfer Binary Systems

Motivated by measurements of the rotation speed of accretor stars in post-mass-transfer (post-MT) systems, we investigate how magnetic braking affects the spin-down of individual stars during binary evolution with the MESAbinary module. Unlike the conventional assumption of tidal synchronization coupled with magnetic braking in binaries, we first calculate whether tides are strong enough to synchronize the orbit. Subsequently, this influences the spin-down of stars and the orbital separation. In this study, we apply four magnetic braking prescriptions to reduce the spin angular momentum of the two stars throughout the entire binary evolution simulation. Our findings reveal that despite magnetic braking causing continuous spin-down of the accretor, when the donor begins to transfer material onto the accretor, the accretor can rapidly spin up to its critical rotation rate. After MT, magnetic braking becomes more important in affecting the angular momentum evolution of the stars. Post-MT accretor stars thus serve as a valuable test bed for observing how the magnetic braking prescriptions operate in spinning down stars from their critical rotation, including the saturation regimes of the magnetic braking. The rotation rate of the accretor star, combined with its mass, could provide age information since the cessation of MT. By comparing the models against observations, the magnetic braking prescription by Garraffo et al. is found to better align with the rotation data of post-MT accretors.

The Mass Dependence of Hα Emission and Stellar Spindown for Fully Convective M Dwarfs

Fully convective M dwarfs typically remain rapidly rotating and magnetically active for billions of years, followed by an abrupt and mass-dependent transition to slow rotation and quiescence. A robust understanding of this process is complicated by difficulties in estimating M dwarf ages and potential dependencies on other variables such as birth environment or metallicity. To isolate the effect of mass, we consider M dwarfs in wide binaries. We identify 67 widely separated, fully convective (0.08–0.35 M ⊙) M dwarf binary systems using Gaia and measure the Hα feature for each component. We classify the pairs into three categories: systems where both components are active, systems where both are inactive, and candidate transition systems, where one component is active and the other inactive. We gather higher-resolution spectra of the candidate transition systems to verify that their behavior does not result from an unresolved third component, yielding one new triple with surprising activity levels. Neglecting this triple, we find 22 active, 36 inactive, and eight transition pairs. Our results are consistent with the epoch of spindown for these binaries being primarily determined by mass, with mild second-order effects; we place a 1σ upper limit of 0.5 Gyr or 25% on the dispersion in the mass-dependent spindown relation. Our findings suggest that the large dispersion in the spindown epoch previously observed for field stars of a given mass may stem from differences in birth environment, in addition to modest intrinsic stochasticity. We also see evidence that the wide binary population is dispersed over time due to dynamical processing.

TESS Stellar Rotation up to 80 Days in the Southern Continuous Viewing Zone

The Transiting Exoplanet Survey Satellite (TESS) mission delivers time-series photometry for millions of stars across the sky, offering a probe into stellar astrophysics, including rotation, on a population scale. However, light-curve systematics related to the satellite’s 13.7 day orbit have prevented stellar rotation searches for periods longer than 13 days, putting the majority of stars beyond reach. Machine-learning methods have the ability to identify systematics and recover robust signals, enabling us to recover rotation periods up to 35 days for GK dwarfs and 80 days for M dwarfs. We present a catalog of 7245 rotation periods for cool dwarfs in the Southern Continuous Viewing Zone, estimated using convolutional neural networks. We find evidence for structure in the period distribution consistent with prior Kepler and K2 results, including a gap in 10–20 day cool-star periods thought to arise from a change in stellar spin-down or activity. Using a combination of spectroscopic and gyrochronologic constraints, we fit stellar evolution models to estimate masses and ages for stars with rotation periods. We find strong correlations between the detectability of rotation in TESS and the effective temperature, age, and metallicity of the stars. Finally, we investigate the relationships between rotation and newly obtained spot filling fractions estimated from Apache Point Observatory Galactic Evolution Experiment spectra. Field starspot filling fractions are elevated in the same temperature and period regime where open clusters’ magnetic braking stalls, lending support to an internal shear mechanism that can produce both phenomena.

Towards a holistic magnetic braking model from the evolution of cataclysmic variables to stellar spin-down – I: the spin-down of fully convective M-dwarfs

ABSTRACT We extend a magnetic braking (MB) model, which has been used earlier to address the evolution of cataclysmic variables, to address the spin period Pspin evolution of fully convective M-dwarf (FCMD) stars. The MB mechanism is an α–Ω dynamo, which leads to stellar winds that carry away angular momentum. We model our MB torque such that the FCMDs experience an MB torque, approximately scaling as $P_\mathrm{spin}^{-1}$ at shorter periods, before transitioning into a Skumanich-type MB torque, scaling as $P_\mathrm{spin}^{-3}$. We also implement a parametrized reduction in the wind mass-loss owing to the entrapment of winds in dead zones. We choose a set of initial conditions and vary the two free parameters in our model to find a good match of our spin trajectories with open clusters containing FCMDs such as NGC2547, Pleiades, NGC2516, and Praesepe. We find that our model can explain the long spin periods of field stars and that a spread in spin distribution persists till over 3 Gyr. An advantage of our model is in relating physically motivated estimations of the magnetic field strength and stellar wind to properties of the stellar dynamo, which other models often remain agnostic about. We track the spin dependence of the wind mass-losses, Alfvén radii, and surface magnetic fields and find good agreement with observations. We discuss the implications of our results on the effect of the host FCMD on any orbiting exoplanets and our plans to extend this model to explain solar-like stars in the future.

The winds of young Solar-type stars in the Pleiades, AB Doradus, Columba, and β Pictoris

ABSTRACT Solar-type stars, which shed angular momentum via magnetized stellar winds, enter the main sequence with a wide range of rotational periods Prot. This initially wide range of rotational periods contracts and has mostly vanished by a stellar age $t\sim {0.6}\, {\rm Gyr}$, after which Solar-type stars spin according to the Skumanich relation $P_\text{rot}\propto \sqrt{t}$. Magnetohydrodynamic stellar wind models can improve our understanding of this convergence of rotation periods. We present wind models of 15 young Solar-type stars aged ∼24 Myr to ∼0.13 Gyr. With our previous wind models of stars aged ∼0.26 and ∼0.6 Gyr we obtain 30 consistent three-dimensional wind models of stars mapped with Zeeman–Doppler imaging – the largest such set to date. The models provide good cover of the pre-Skumanich phase of stellar spin-down in terms of rotation, magnetic field, and age. We find the mass-loss rate $\dot{M}\propto \Phi ^{{0.9\pm 0.1}}$ with a residual spread of ∼150 per cent and the wind angular momentum loss rate $\dot{J}\propto {}P_\text{rot}^{-1} \Phi ^{1.3\pm 0.2}$ with a residual spread of ∼500 per cent where Φ is the unsigned surface magnetic flux. When comparing different magnetic field scalings for each single star we find a gradual reduction in the power-law exponent with increasing magnetic field strength.

The Empirical Limits of Gyrochronology

The promise of gyrochronology is that, given a star’s rotation period and mass, its age can be inferred. The reality of gyrochronology is complicated by effects other than ordinary magnetized braking that alter stellar rotation periods. In this work, we present an interpolation-based gyrochronology framework that reproduces the time- and mass-dependent spin-down rates implied by the latest open cluster data, while also matching the rate at which the dispersion in initial stellar rotation periods decreases as stars age. We validate our technique for stars with temperatures of 3800–6200 K and ages of 0.08–2.6 gigayears (Gyr), and use it to reexamine the empirical limits of gyrochronology. In line with previous work, we find that the uncertainty floor varies strongly with both stellar mass and age. For Sun-like stars (≈5800 K), the statistical age uncertainties improve monotonically from ±38% at 0.2 Gyr to ±12% at 2 Gyr, and are caused by the empirical scatter of the cluster rotation sequences combined with the rate of stellar spin-down. For low-mass K dwarfs (≈4200 K), the posteriors are highly asymmetric due to stalled spin-down, and ±1σ age uncertainties vary non-monotonically between 10% and 50% over the first few gigayears. High-mass K dwarfs (5000 K) older than ≈1.5 Gyr yield the most precise ages, with limiting uncertainties currently set by possible changes in the spin-down rate (12% systematic), the calibration of the absolute age scale (8% systematic), and the width of the slow sequence (4% statistical). An open-source implementation, gyro-interp, is available online at github.com/lgbouma/gyro-interp.

New insights into the rotational evolution of near-solar age stars from the open cluster M 67

Context. Gyrochronology allows the derivation of ages for cool main sequence stars from their observed rotation periods and masses, or a suitable proxy of the latter. It is increasingly well explored for FGK stars, but requires further measurements for older ages and K–M-type stars. Aims. Recent work has shown that the behavior of stellar spindown differs significantly from prior expectations for late-type stars. We study the 4 Gyr-old benchmark open cluster M 67 to explore this behavior further. Methods. We combined a Gaia DR3 sample with the Kepler K2 superstamp of Campaign 5 around M 67 and created new light curves from aperture photometry. The light curves are subjected to an extensive correction process to remove instrumental systematics and trending, followed by period analysis to measure stellar rotation. Results. We identify periodic signals in 136 light curves, 47 of which are from the rotation of effectively single main-sequence stars that span from early-G to mid-M type. These results connect well to prior work on M 67 and extend it to much later spectral types. Conclusions. We find that the rotation periods of single stars of age 4 Gyr define a tight relationship with color, ranging from spectral types F through M. The corresponding surface of rotation period against age and mass is therefore well-defined to an older age than was previously known. However, the deviations from prior expectations of the stellar spindown behavior are even more pronounced at 4 Gyr. The binary cluster members do not follow the single star relationship. The majority are widely scattered below the single star sequence. Consequently, they do not seem to be suitable for gyrochronology at present.

Tidal star–planet interaction and its observed impact on stellar activity in planet-hosting wide binary systems

ABSTRACT Tidal interaction between an exoplanet and its host star is a possible pathway to transfer angular momentum between the planetary orbit and the stellar spin. In cases where the planetary orbital period is shorter than the stellar rotation period, this may lead to angular momentum being transferred into the star’s rotation, possibly counteracting the intrinsic stellar spin-down induced by magnetic braking. Observationally, detecting altered rotational states of single, cool field stars is challenging, as precise ages for such stars are rarely available. Here we present an empirical investigation of the rotation and magnetic activity of a sample of planet-hosting stars that are accompanied by wide stellar companions. Without needing knowledge about the absolute ages of the stars, we test for relative differences in activity and rotation of the planet hosts and their co-eval companions, using X-ray observations to measure the stellar activity levels. Employing three different tidal interaction models, we find that host stars with planets that are expected to tidally interact display elevated activity levels compared to their companion stars. We also find that those activity levels agree with the observed rotational periods for the host stars along the usual rotation–activity relationships, implying that the effect is indeed caused by a tidal interaction and not a purely magnetic interaction that would be expected to affect the stellar activity, but not necessarily the rotation. We conclude that massive, close-in planets have an impact on the stellar rotational evolution, while the smaller, more distant planets do not have a significant influence.

Stellar mid-life crisis: subcritical magnetic dynamos of solar-like stars and the breakdown of gyrochronology

ABSTRACT Recent observations have revealed the surprising breakdown of stellar gyrochronology relations at about the age of the Sun hinting the middle-aged, solar-like stars transition to a magnetically inactive future. We provide a theoretical basis for these intriguing observations inspired by simulations with a mathematical-dynamo model that can explore long-term solar cycle fluctuations. We reproduce the observed bimodal distribution of sunspot numbers, but only for subcritical dynamos. Based on a bifurcation analysis, we argue that the ageing of solar-like stars makes the magnetically weak dynamo regime readily accessible. Weak magnetic field production in this regime compromises wind-driven angular momentum losses, thus disrupting the hegemony of magnetic braking on stellar rotational spin-down. This hypothesis of subcritical magnetic dynamos of solar-like stars provides a self-consistent, unifying physical basis for a diversity of solar-stellar phenomena such as why stars beyond their mid-life do not spin-down as fast as in their youth, the break-down of stellar gyrochronology relations, the observed bimodal distribution of long-term sunspot observations, and recent findings suggesting that the Sun may be transitioning to a magnetically inactive future.

Slingshot prominences: a hidden mass loss mechanism

ABSTRACT Whilst ‘slingshot’ prominences have been observed on M-dwarfs, most if not all theoretical studies have focused on solar-like stars. We present an investigation into stellar prominences around rapidly rotating young M-dwarfs. We have extrapolated the magnetic field in the corona from Zeeman-Doppler maps and determined the sites of mechanical stability where prominences may form. We analyse the prominence mass that could be supported and the latitude range over which this material is distributed. We find that for these maps, much of this prominence mass may be invisible to observation – typically <1 per cent transits the stellar disc. On the rapidly rotating M-dwarf V374 Peg (Prot = 0.45 d) where prominences have been observed, we find the visible prominence mass to be around only 10 per cent of the total mass supported. The mass loss rate per unit area for prominences scales with the X-ray surface flux as $\dot{M}/A \propto \, F_\mathrm{ X}^{1.32}$ that is very close to the observationally derived value for stellar winds. This suggests that prominence ejection may contribute significantly to the overall stellar wind loss and spin-down. A planet in an equatorial orbit in the habitable zone of these stars may experience intermittent enhancements of the stellar wind due to prominence ejections. On some stars, this may occur throughout 20 per cent of the orbit.

Single-hemisphere Dynamos in M-dwarf Stars

Abstract M-dwarf stars below a certain mass are convective from their cores to their photospheres. These fully convective objects are extremely numerous, very magnetically active, and the likely hosts of many exoplanets. Here we study, for the first time, dynamo action in simulations of stratified, rotating, fully convective M-dwarf stars. Importantly, we use new techniques to capture the correct full ball geometry down to the center of the star. We find surprising dynamo states in these systems, with the global-scale mean fields confined strongly to a single hemisphere, in contrast to prior stellar dynamo solutions. These hemispheric-dynamo stars are likely to have profoundly different interactions with their surroundings, with important implications for exoplanet habitability and stellar spindown.

Alfvén-wave-driven Magnetic Rotator Winds from Low-mass Stars. I. Rotation Dependences of Magnetic Braking and Mass-loss Rate

Abstract Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of sunlike stars with a range of rotation rates, covering the fast and slow magneto-rotator regimes, including the transition between the two. We generalize an Alfvén-wave-driven solar wind model that builds on previous works by including the magneto-centrifugal force explicitly. In this model, the surface-averaged open magnetic flux is assumed to scale as , where and Ro are the surface open-flux filling factor and Rossby number, respectively. We find that, (1) the angular-momentum loss rate (torque) of the wind is described as , yielding a spin-down law . (2) The mass-loss rate saturates at , due to the strong reflection and dissipation of Alfvén waves in the chromosphere. This indicates that the chromosphere has a strong impact in connecting the stellar surface and stellar wind. Meanwhile, the wind ram pressure scales as , which is able to explain the lower envelope of the observed stellar winds by Wood et al. (3) The location of the Alfvén radius is shown to scale in a way that is consistent with one-dimensional analytic theory. Additionally, the precise scaling of the Alfvén radius matches previous works, which used thermally driven winds. Our results suggest that the Alfvén-wave-driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main sequence.

The Impact of Metallicity on the Evolution of the Rotation and Magnetic Activity of Sun-like Stars

Abstract The rotation rates and magnetic activity of Sun-like and low-mass (≲1.4M ⊙) main-sequence stars are known to decline with time, and there now exist several models for the evolution of rotation and activity. However, the role that chemical composition plays during stellar spin-down has not yet been explored. In this work, we use a structural evolution code to compute the rotational evolution of stars with three different masses (0.7, 1.0, and 1.3 M ⊙) and six different metallicities, ranging from [Fe/H] = −1.0 to [Fe/H] = +0.5. We also implement three different wind-braking formulations from the literature (two modern and one classical) and compare their predictions for rotational evolution. The effect that metallicity has on stellar structural properties, and in particular the convective turnover timescale, leads the two modern wind-braking formulations to predict a strong dependence of the torque on metallicity. Consequently, they predict that metal-rich stars spin down more effectively at late ages (≳1 Gyr) than metal-poor stars, and the effect is large enough to be detectable with current observing facilities. For example, the formulations predict that a Sun-like (solar-mass and solar-aged) star with [Fe/H] = −0.3 will have a rotation period of less than 20 days. Even though old, metal-poor stars are predicted to rotate more rapidly at a given age, they have larger Rossby numbers and are thus expected to have lower magnetic activity levels. Finally, the different wind-braking formulations predict quantitative differences in the metallicity dependence of stellar rotation, which may be used to test them.

The Revolution Revolution: Magnetic Morphology Driven Spin-down∗

Abstract Observations of young open clusters (OCs) show a bimodal distribution of rotation periods that has been difficult to explain with existing stellar spin-down models. Detailed magnetohydrodynamic (MHD) stellar wind simulations have demonstrated that surface magnetic field morphology has a strong influence on wind-driven angular momentum loss. Observations suggest that faster rotating stars store a larger fraction of their magnetic flux in higher-order multipolar components of the magnetic field. In this work, we present an entirely predictive new model for stellar spin-down that accounts for the stellar surface magnetic field configuration. We show how a magnetic complexity that evolves from complex toward simple configurations as a star spins down can explain the salient features of stellar rotation evolution, including the bimodal distribution of both slow and fast rotators seen in young OCs.

A New Look at an Old Cluster: The Membership, Rotation, and Magnetic Activity of Low-mass Stars in the 1.3 Gyr Old Open Cluster NGC 752

Abstract The nearby open cluster NGC 752 presents a rare opportunity to study stellar properties at ages >1 Gyr. However, constructing a membership catalog for it is challenging; most surveys have been limited to identifying its giants and dwarf members earlier than mid-K. We supplement past membership catalogs with candidates selected with updated photometric and proper-motion criteria, generating a list of 258 members, a >50% increase over previous catalogs. Using a Bayesian framework to fit MESA Isochrones & Stellar Tracks evolutionary models to literature photometry and the Tycho-Gaia Astrometric Solution data available for 59 cluster members, we infer the age of and distance to NGC 752: 1.34 ± 0.06 Gyr and pc. We also report the results of our optical monitoring of the cluster using the Palomar Transient Factory. We obtain rotation periods for 12 K and M cluster members, the first periods measured for such low-mass stars with a well-constrained age >1 Gyr. We compare these new periods to data from the younger clusters Praesepe and NGC 6811, and to a theoretical model for angular momentum loss, to examine stellar spin-down for low-mass stars over their first 1.3 Gyr. While on average NGC 752 stars are rotating more slowly than their younger counterparts, the difference is not significant. Finally, we use our spectroscopic observations to measure Hα for cluster stars, finding that members earlier than ≈M2 are magnetically inactive, as expected at this age. Forthcoming Gaia data should solidify and extend the membership of NGC 752 to lower masses, thereby increasing its importance for studies of low-mass stars.

How supercritical are stellar dynamos, or why do old main-sequence dwarfs not obey gyrochronology?

Asteroseismological determinations of stellar ages have shown that old main-sequence dwarfs do not obey gyrochronology. Their rotation is slow compared to young stars but faster than gyrochronology predicts. This can be explained by the presence of a maximum rotation period beyond which the large-scale dynamo switches off and stops providing global magnetic fields necessary for stellar spindown. Assuming this explanation, the excess of stellar dynamo parameters over their marginal values can be estimated for given spectral type and rotation rate. The estimation gives the dynamo number for the Sun about 10% above its critical value. The corresponding dynamo model provides - though with some further tuning - reasonable results for the Sun. Following the same approach, the differential rotation and marginal dynamo modes are computed for stars between 0.7 and 1.2 solar masses. With increasing stellar mass, the differential rotation and the ratio of toroidal-to-poloidal field are predicted to increase while the field topology changes from dipolar to mixed quadrupolar-dipolar parity.

Rotation-Driven Phase Transitions in the Cores of Pulsars

In this paper, we discuss the impact of rotation on the particle composition of rotating neutron stars (pulsars). Particular emphasis is put on the formation of quark matter during stellar spin-down, driven by continuous gravitational compression. Our study is based on modern models for the nuclear equation of state whose parameters are tightly constrained by nuclear data, neutron star masses, and the latest estimates of neutron star radii.

Studying stellar spin-down with Zeeman–Doppler magnetograms

Magnetic activity and rotation are known to be intimately linked for low-mass stars. Understanding rotation evolution over the stellar lifetime is therefore an important goal within stellar astrophysics. In recent years, there has been increased focus on how the complexity of the stellar magnetic field affects the rate of angular momentum-loss from a star. This is a topic that Zeeman-Doppler imaging (ZDI), a technique that is capable of reconstructing the large-scale magnetic field topology of a star, can uniquely address. Using a potential field source surface model, we estimate the open flux, mass loss-rate and angular momentum-loss rates for a sample of 66 stars that have been mapped with ZDI. We show that the open flux of a star is predominantly determined by the dipolar component of its magnetic field for our choice of source surface radius. We also show that, on the main sequence, the open flux, mass- and angular momentum-loss rates increase with decreasing Rossby number. The exception to this rule is stars less massive than $0.3M_{\odot}$. Previous work suggests that low mass M dwarfs may possess either strong, ordered and dipolar fields or weak and complex fields. This range of field strengths results in a large spread of angular momentum-loss rates for these stars and has important consequences for their spin down behaviour. Additionally, our models do not predict a transition in the mass-loss rates at the so called wind dividing line noted from Ly$\alpha$ studies.

FK COMAE BERENICES, KING OF SPIN: THE COCOA-PUFS PROJECT* †

ABSTRACT COCOA-PUFS is an energy-diverse, time-domain study of the ultra-fast spinning, heavily spotted, yellow giant FK Comae Berenices (FK Com: HD117555; G4 III). This single star is thought to be a recent binary merger, and is exceptionally active by measure of its intense ultraviolet (UV) and X-ray emissions, and proclivity to flare. COCOA-PUFS was carried out with the Hubble Space Telescope in the UV (1200–3000 Å), using mainly its high-performance Cosmic Origins Spectrograph, but also high precision Space Telescope Imaging Spectrograph; Chandra X-ray Observatory in the soft X-rays (0.5–10 keV), utilizing its High-Energy Transmission Grating Spectrometer; together with supporting photometry and spectropolarimetry in the visible from the ground. This is an introductory report on the project. FK Com displayed variability on a wide range of timescales over all wavelengths during the week-long main campaign, including a large X-ray flare; “super-rotational broadening” of the far-ultraviolet “hot lines” (e.g., Si iv 1393 Å; 8 × 104 K) together with chromospheric Mg ii 2800 Å and C ii 1335 Å (1–3 × 104 K); large Doppler swings suggestive of bright regions alternately on advancing and retreating limbs of the star; and substantial redshifts of the epoch-average emission profiles. These behaviors paint a picture of a highly extended, dynamic, hot (∼10 MK) coronal magnetosphere around the star, threaded by cooler structures perhaps analogous to solar prominences and replenished continually by surface activity and flares. Suppression of angular momentum loss by the confining magnetosphere could temporarily postpone the inevitable stellar spindown, thereby lengthening this highly volatile stage of coronal evolution.

Formation and stellar spin-orbit misalignment of hot Jupiters from Lidov–Kozai oscillations in stellar binaries

Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit misalignment angles. The origin of these HJs remains unclear. This paper investigates the inward migration of giant planets due to Lidov-Kozai (LK) oscillations induced by a distant (100-1000 AU) stellar companion. We conduct a large population synthesis study, including the octupole gravitational potential from the stellar companion, mutual precession of the host stellar spin axis and planet orbital axis, tidal dissipation in the planet, and stellar spin-down in the host star due to magnetic braking. We consider a range of planet masses ($0.3-5\,M_J$) and initial semi-major axes ($1-5$AU), different properties for the host star, and varying tidal dissipation strengths. The fraction of systems that result in HJs depends on planet mass and stellar type, with $f_{\rm HJ} = 1-4\%$ (depending on tidal dissipation strength) for $M_p=1\,M_J$, and larger (up to $8\%$) for more massive planets. The production efficiency of "hot Saturns" ($M_p=0.3M_J$) is much lower, because most migrating planets are tidally disrupted. We find that the fraction of systems that result in either HJ formation or tidal disruption, $f_{\rm mig} \simeq 11-14\%$ is roughly constant, having little variation with planet mass, stellar type and tidal dissipation strength. This "universal" migration fraction can be understood qualitatively from analytical migration criteria based on the properties of octupole LK oscillations. The distribution of final HJ stellar obliquities exhibits a complex dependence on the planet mass and stellar type. For $M_p = (1-3)M_J$, the distribution is always bimodal, with peaks around $30^{\circ}$ and $130^{\circ}$. The distribution for $5M_J$ planets depends on host stellar type, with a preference for low obliquities for solar-type stars, and higher obliquities for more massive ($1.4M_{\odot}$) stars.