Sculpting the Sub-Saturn Occurrence Rate via Atmospheric Mass Loss

The sub-Saturn (∼4–8 R ⊕) occurrence rate rises with orbital period out to at least ∼300 days. In this work we adopt and test the hypothesis that the decrease in their occurrence toward the star is a result of atmospheric mass loss, which can transform sub-Saturns into sub-Neptunes (≲4 R ⊕) more efficiently at shorter periods. We show that under the mass-loss hypothesis, the sub-Saturn occurrence rate can be leveraged to infer their underlying core mass function, and, by extension, that of gas giants. We determine that lognormal core mass functions peaked near ∼10–20 M ⊕ are compatible with the sub-Saturn period distribution, the distribution of observationally inferred sub-Saturn cores, and gas-accretion theories. Our theory predicts that close-in sub-Saturns should be ∼50% less common and ∼30% more massive around rapidly rotating stars; this should be directly testable for stars younger than ≲500 Myr. We also predict that the sub-Jovian desert becomes less pronounced and opens up at smaller orbital periods around M stars compared to solar-type stars (∼0.7 days versus ∼3 days). We demonstrate that exceptionally low-density sub-Saturns, “super-puffs,” can survive intense hydrodynamic escape to the present day if they are born with even larger atmospheres than they currently harbor; in this picture, Kepler 223 d began with an envelope ∼1.5× the mass of its core and is currently losing its envelope at a rate of ∼2 × 10−3 M ⊕ Myr−1. If the predictions from our theory are confirmed by observations, the core mass function we predict can also serve to constrain core formation theories of gas-rich planets.

Rossby Waves in Astrophysics

Rossby waves are a pervasive feature of the large-scale motions of the Earth’s atmosphere and oceans. These waves (also known as planetary waves and r-modes) also play an important role in the large-scale dynamics of different astrophysical objects such as the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and exoplanetary atmospheres. This paper provides a review of theoretical and observational aspects of Rossby waves on different spatial and temporal scales in various astrophysical settings. The physical role played by Rossby-type waves and associated instabilities is discussed in the context of solar and stellar magnetic activity, angular momentum transport in astrophysical discs, planet formation, and other astrophysical processes. Possible directions of future research in theoretical and observational aspects of astrophysical Rossby waves are outlined.

Oscillations of 2D ESTER models

Context. Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotating δ Scuti stars that seem to match theoretical expectations. Aims. In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings. Methods. In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra. Results. Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1 dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

Transport of angular momentum by stochastically excited waves as an explanation for the outburst of the rapidly rotating Be star HD49330

Context. HD 49330 is an early Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. Aims. We modelled the results obtained with CoRoT to understand the link between pulsational parameters and the outburst of this Be star. Methods. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne’s expansion and 2D structure computed with ROTORC. We then modelled κ-driven pulsations. We also adapted the formalism of the excitation and amplitude of stochastically excited gravito-inertial modes to rapidly rotating stars, and we modelled those pulsations as well. Results. We find that while pulsation p modes are indeed excited by the κ mechanism, the observed g modes are, rather, a result of stochastic excitation. In contrast, g and r waves are stochastically excited in the convective core and transport angular momentum to the surface, increasing its rotation rate. This destabilises the external layers of the star, which then emits transient stochastically excited g waves. These transient waves produce most of the low-frequency signal detected in the CoRoT data and ignite the outburst. During this unstable phase, p modes disappear at the surface because their cavity is broken. Following the outburst and ejection of the surface layer, relaxation occurs, making the transient g waves disappear and p modes reappear. Conclusions. This work includes the first coherent model of stochastically excited gravito-inertial pulsation modes in a rapidly rotating Be star. It provides an explanation for the correlation between the variation in the amplitude of frequencies detected in the CoRoT data and the occurrence of an outburst. This scenario could apply to other pulsating Be stars, providing an explanation to the long-standing questions surrounding Be outbursts and disks.

Constraining the oblateness of transiting planets with photometry and spectroscopy

ABSTRACT Rapid planetary rotation can cause the equilibrium shape of a planet to be oblate. While planetary oblateness has mostly been probed by examining the subtle ingress and egress features in photometric transit light curves, we investigate the effect of oblateness on the spectroscopic Rossiter–McLaughlin (RM) signals. We found that a giant planet, with planet-to-star radius ratio of 0.15 and Saturn-like oblateness of 0.098, can cause spectroscopic signatures with amplitudes up to 1.1 m s−1 which is detectable by high-precision spectrographs such as ESPRESSO. We also found that the spectroscopic oblateness signals are particularly amplified for transits across rapidly rotating stars and for planets with spin-orbit misalignment thereby making them more prominent than the photometric signals at some transit orientations. We compared the detectability of oblateness in photometry and spectroscopy and found that photometric light curves are more sensitive to detecting oblateness than the spectroscopic RM signals mostly because they can be sampled with higher cadence to better probe the oblateness ingress and egress anomaly. However, joint analyses of the light curve and RM signal of a transiting planet provides more accurate and precise estimate of the planet’s oblateness. Therefore, ESPRESSO alongside ongoing and upcoming photometric instruments such as TESS, CHEOPS, PLATO, and JWST will be extremely useful in measuring planet oblateness.

Simulating the outer layers of rapidly rotating stars

ABSTRACT This paper presents the results of a set of radiative hydrodynamic simulations of convection in the near-surface regions of a rapidly rotating star. The simulations use microphysics consistent with stellar models, and include the effects of realistic convection and radiative transfer. We find that the overall effect of rotation is to reduce the strength of turbulence. The combination of rotation and radiative cooling creates a zonal velocity profile in which the motion of fluid parcels near the surface is independent of rotation. Their motion is controlled by the strong up and down flows generated by radiative cooling. The fluid parcels in the deeper layers, on the other hand, are controlled by rotation.

Period spacings of gravity modes in rapidly rotating magnetic stars

Context. Stellar internal magnetic fields have recently been shown to leave a detectable signature on period spacing patterns of gravity modes. Aims. We aim to investigate the effect of the obliquity of a mixed (poloidal and toroidal) dipolar internal fossil magnetic field with respect to the rotation axis on the frequency of gravity modes in rapidly rotating stars. Methods. We used the traditional approximation of rotation to compute non-magnetic modes, and a perturbative treatment of the magnetic field to compute the corresponding frequency shifts. We applied the new formalism to HD 43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose field has an obliquity angle of about 80°. Results. We find that frequency shifts induced by the magnetic field on high-radial-order gravity modes are larger with increasing obliquity angle, when the magnetic axis is closer to the equatorial region, where these modes are trapped. The maximum value is reached for an obliquity angle of 90°. This trend is observed for all mode geometries. Conclusions. Our results predict that the signature of an internal oblique dipolar magnetic field is detectable using asteroseismology of gravity modes.

Be and Bn stars: Balmer discontinuity and stellar-class relationship

Context. A significant number of Be stars show a second Balmer discontinuity (sBD) attributed to an extended circumstellar envelope (CE). The fast rotational velocity of Be stars undoubtedly plays a significant role in the formation of the CE. However, Bn stars, which are also B-type rapidly rotating stars, do not all present clear evidence of being surrounded by circumstellar material. Aims. We aim to characterize the populations of Be and Bn stars, and discuss the appearance of the sBD as a function of the stellar parameters. We expect to find new indices characterizing the properties of CEs in Be stars and properties relating Be and Bn stars. Methods. We obtained low- and high-resolution spectra of a sample of Be and Bn stars, derived stellar parameters, characterized the sBD, and measured the emission in the Hα line. Results. Correlations of the aspect and intensity of the sBD and the emission in the Hα line with the stellar parameters and the V sin i are presented. Some Bn stars exhibit the sBD in absorption, which may indicate the presence of rather dense CEs. Six Bn stars show emission in the Hα line, so they are reclassified as Be stars. The sBD in emission appears in Be stars with V sin i ≲ 250 km s−1, and in absorption in both Be and Bn stars with V sin i ≳ 50 km s−1. Low-mass Be and Bn stars share the same region in the Hertzsprung-Russell diagram. The distributions of rotational to critical velocity ratios of Be and Bn stars corresponding to the current stellar evolutionary stage are similar, while distributions inferred for the zero-age main sequence have different skewness. Conclusions. We found emission in the Hα line and signs of a CE in some Bn stars, which motivated us to think that Bn and Be stars probably belong to the same population. It should be noted that some of the most massive Bn stars could display the Be phenomenon at any time. The similarities found among Be and Bn stars deserve to be more deeply pursued.