A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied. Our main conclusions are: [...]Comment: Astronomy & Astrophysics, 597, A37, 17 pages, 11 figure

Pebbles versus planetesimals

In the core accretion scenario, a massive core forms first and then accretes an envelope. When discussing how this core forms some divergences appear. First scenarios of planet formation predict the accretion of km-sized bodies, called planetesimals, while more recent works suggest growth by accretion of pebbles, which are cm-sized objects. These two accretion models are often discussed separately and we aim here at comparing the outcomes of the two models with identical initial conditions. We use two distinct codes: one computing planetesimal accretion, the other pebble accretion. Using a population synthesis approach, we compare planet simulations and study the impact of the two solid accretion models, focussing on the formation of single planets. We find that the planetesimal model predicts the formation of more giant planets, while the pebble accretion model forms more super-Earth mass planets. This is due to the pebble isolation mass concept, which prevents planets formed by pebble accretion to accrete gas efficiently before reaching Miso. This translates into a population of planets that are not heavy enough to accrete a consequent envelope but that are in a mass range where type I migration is very efficient. We also find higher gas mass fractions for a given core mass for the pebble model compared to the planetesimal one caused by luminosity differences. This also implies planets with lower densities which could be confirmed observationally. Focusing on giant planets, we conclude that the sensitivity of their formation differs: for the pebble accretion model, the time at which the embryos are formed, as well as the period over which solids are accreted strongly impact the results, while for the planetesimal model it depends on the planetesimal size and on the splitting in the amount of solids available to form planetesimals

Impact of the measured parameters of exoplanets on the inferred internal structure

Exoplanet characterization is one of the main foci of current exoplanetary science. For super-Earths and sub-Neptunes, we mostly rely on mass and radius measurements, which allow to derive the body's mean density and give a rough estimate of the planet's bulk composition. However, the determination of planetary interiors is a very challenging task. In addition to the uncertainty in the observed fundamental parameters, theoretical models are limited due to the degeneracy in determining the planetary composition. We aim to study several aspects that affect internal characterization of super-Earths and sub-Neptunes: observational uncertainties, location on the M-R diagram, impact of additional constraints as bulk abundances or irradiation, and model assumptions. We use a full probabilistic Bayesian inference analysis that accounts for observational and model uncertainties. We employ a Nested Sampling scheme to efficiently produce the posterior probability distributions for all the planetary structural parameter of interest. We include a structural model based on self-consistent thermodynamics of core, mantle, high-pressure ice, liquid water, and H-He envelope. Regarding the effect of mass and radius uncertainties on the determination of the internal structure, we find three different regimes: below the Earth-like composition line and above the pure-water composition line smaller observational uncertainties lead to better determination of the core and atmosphere mass respectively, and between them structure characterization only weakly depends on the observational uncertainties. We show that small variations in the temperature or entropy profiles lead to radius variations that are comparable to the observational uncertainty, suggesting that uncertainties linked to model assumptions can become more relevant to determine the internal structure than observational uncertainties.Comment: 12 pages, 12 figure

Supernova type Ia luminosities, their dependence on second parameters, and the value of H_0

A sample of 35 SNe Ia with good to excellent photometry in B and V, minimum internal absorption, and 1200 < v < \approx 30000 km/s is compiled from the literature. As far as their spectra are known they are all Branch-normal. For 29 of the SNe Ia also peak magnitudes in I are known. The SNe Ia have uniform colors at maximum, i.e. =-0.012 mag (sigma=0.051) and =-0.276 mag (sigma=0.078). In the Hubble diagram they define a Hubble line with a scatter of $\sigma_M$=0.21-0.16 mag, decreasing with wavelength. The scatter is further reduced if the SNe Ia are corrected for differences in decline rate Delta_m_15 or color (B-V). A combined correction reduces the scatter to sigma<=0.13 mag. After the correction no significant dependence remains on Hubble type or galactocentric distance. The Hubble line suggests some curvature which can be differently interpreted. A consistent solution is obtained for a cosmological model with Omega_M=0.3, Omega_Lambda=0.7, which is indicated also by much more distant SNe Ia. Absolute magnitudes are available for eight equally blue (Branch-normal) SNe Ia in spirals, whose Cepheid distances are known. If their well defined mean values of M_B, M_V, and M_I are used to fit the Hubble line to the above sample of SNe Ia one obtains H_0=58.3 km/s/Mpc, or, after adjusting all SNe Ia to the average values of Delta_m_15 and (B-V), H_0=60.9 km/s/Mpc. Various systematic errors are discussed whose elimination tends to decrease H_0. The finally adopted value at the 90-percent level, including random and systematic errors, is H_0=58.5 +/- 6.3 km/s/Mpc. Several higher values of H_0 from SNe Ia, as suggested in the literature, are found to depend on large corrections for variations of the light curve parameter and/or on an unwarranted reduction of the Cepheid distances of the calibrating SNe Ia.Comment: 42 pages, including 9 figures; submitted to Ap

A Cepheid Distance to NGC 4603 in Centaurus

In an attempt to use Cepheid variables to determine the distance to the Centaurus cluster, we have obtained images of NGC 4603 with the Hubble Space Telescope on 9 epochs using WFPC2 and the F555W and F814W filters. This galaxy has been suggested to lie within the ``Cen30'' portion of the cluster and is the most distant object for which this method has been attempted. Previous distance estimates for Cen30 have varied significantly and some have presented disagreements with the peculiar velocity predicted from redshift surveys, motivating this investigation. Using our observations, we have found 61 candidate Cepheid variable stars; however, a significant fraction of these candidates are likely to be nonvariable stars whose magnitude measurement errors happen to fit a Cepheid light curve of significant amplitude for some choice of period and phase. Through a maximum likelihood technique, we determine that we have observed 43 +/- 7 real Cepheids and that NGC 4603 has a distance modulus of 32.61 +0.11/-0.10 (random, 1 sigma) +0.24/-0.25 (systematic, adding in quadrature), corresponding to a distance of 33.3 Mpc. This is consistent with a number of recent estimates of the distance to NGC 4603 or Cen30 and implies a small peculiar velocity consistent with predictions from the IRAS 1.2 Jy redshift survey if the galaxy lies in the foreground of the cluster.Comment: Accepted for publication in the Astrophysical Journal. 17 pages with 17 embedded figures and 3 tables using emulateapj.sty. Additional figures and images may be obtained from http://astro.berkeley.edu/~marc/n4603

The New Generation Planetary Population Synthesis (NGPPS). IV. Planetary systems around low-mass stars

Context. Previous theoretical works on planet formation around low-mass stars have often been limited to large planets and individual systems. As current surveys routinely detect planets down to terrestrial size in these systems, models have shifted toward a more holistic approach that reflects their diverse architectures. Aims. Here, we investigate planet formation around low-mass stars and identify differences in the statistical distribution of modeled planets. We compare the synthetic planet populations to observed exoplanets and we discuss the identified trends. Methods. We used the Generation III Bern global model of planet formation and evolution to calculate synthetic populations, while varying the central star from Solar-like stars to ultra-late M dwarfs. This model includes planetary migration, N-body interactions between embryos, accretion of planetesimals and gas, and the long-term contraction and loss of the gaseous atmospheres. Results. We find that temperate, Earth-sized planets are most frequent around early M dwarfs (0.3 M⊙–0.5 M⊙) and that they are more rare for Solar-type stars and late M dwarfs. The planetary mass distribution does not linearly scale with the disk mass. The reason behind this is attributed to the emergence of giant planets for M⋆ ≥ 0.5 M⊙, which leads to the ejection of smaller planets. Given a linear scaling of the disk mass with stellar mass, the formation of Earth-like planets is limited by the available amount of solids for ultra-late M dwarfs. For M⋆ ≥ 0.3 M⊙, however, there is sufficient mass in the majority of systems, leading to a similar amount of Exo-Earths going from M to G dwarfs. In contrast, the number of super-Earths and larger planets increases monotonically with stellar mass. We further identify a regime of disk parameters that reproduces observed M-dwarf systems such as TRAPPIST-1. However, giant planets around late M dwarfs, such as GJ 3512b, only form when type I migration is substantially reduced. Conclusions. We are able to quantify the stellar mass dependence of multi-planet systems using global simulations of planet formation and evolution. The results fare well in comparison to current observational data and predict trends that can be tested with future observations

The New Generation Planetary Population Synthesis (NGPPS) VI. Introducing KOBE: Kepler Observes Bern Exoplanets

Context. Observations of exoplanets indicate the existence of several correlations in the architecture of planetary systems. Exoplanets within a system tend to be of similar size and mass, evenly spaced, and are often ordered in size and mass. Small planets are frequently packed in tight configurations, while large planets often have wider orbital spacing. Together, these correlations are called the peas in a pod trends in the architecture of planetary systems. Aims. In this paper these trends are investigated in theoretically simulated planetary systems and compared with observations. Whether these correlations emerge from astrophysical processes or the detection biases of the transit method is examined. Methods. Synthetic planetary system were simulated using the Generation III Bern Model. KOBE, a new computer code, simulates the geometrical limitations of the transit method and applies the detection biases and completeness of the Kepler survey. This allows simulated planetary systems to be compared with observations. Results. The architecture of synthetic planetary systems, observed via KOBE, show the peas in a pod trends in good agreement with observations. These correlations are also present in the theoretical underlying population, from the Bern Model, indicating that these trends are probably of astrophysical origin. Conclusions. The physical processes involved in planet formation are responsible for the emergence of evenly spaced planets with similar sizes and masses. The size–mass similarity trends are primordial and originate from the oligarchic growth of protoplanetary embryos and the uniform growth of planets at early times. Later stages in planet formation allows planets within a system to grow at different rates, thereby decreasing these correlations. The spacing and packing correlations are absent at early times and arise from dynamical interactions

A delta Scuti distance to the Large Magellanic Cloud

We present results from a well studied delta Scuti star discovered in the LMC. The absolute magnitude of the variable was determined from the PL relation for Galactic delta Scuti stars and from the theoretical modeling of the observed B,V,I light curves. The two methods give distance moduli for the LMC of 18.46+-0.19 and 18.48+-0.15, respectively, for a consistent value of the stellar reddening of E(B-V)=0.08+-0.02. We have also analyzed 24 delta Scuti candidates discovered in the OGLE II survey of the LMC, and 7 variables identified in the open cluster LW 55 and in the galaxy disk by Kaluzny et al. (2003, 2006). We find that the LMC delta Scuti stars define a PL relation whose slope is very similar to that defined by the Galactic delta Scuti variables, and yield a distance modulus for the LMC of 18.50+-0.22 mag. We compare the results obtained from the delta Scuti variables with those derived from the LMC RR Lyrae stars and Cepheids. Within the observational uncertainties, the three groups of pulsating stars yield very similar distance moduli. These moduli are all consistent with the "long" astronomical distance scale for the Large Magellanic Cloud.Comment: Accepted for publication on A

Classical Cepheid Pulsation Models: IX. New Input Physics

We constructed several sequences of classical Cepheid envelope models at solar chemical composition ($Y=0.28, Z=0.02$) to investigate the dependence of the pulsation properties predicted by linear and nonlinear hydrodynamical models on input physics. To study the dependence on the equation of state (EOS) we performed several numerical experiments by using the simplified analytical EOS originally developed by Stellingwerf and the recent analytical EOS developed by Irwin. Current findings suggest that the pulsation amplitudes as well as the topology of the instability strip marginally depend on the adopted EOS. We also investigated the dependence of observables predicted by theoretical models on the mass-luminosity (ML) relation and on the spatial resolution across the Hydrogen and the Helium partial ionization regions. We found that nonlinear models are marginally affected by these physical and numerical assumptions. In particular, the difference between new and old models in the location as well as in the temperature width of the instability strip is on average smaller than 200 K. However, the spatial resolution somehow affects the pulsation properties. The new fine models predict a period at the center of the Hertzsprung Progression ($P_{HP}=9.65$$-$9.84 days) that reasonably agree with empirical data based on light curves ($P_{HP}=10.0\pm 0.5$ days; \citealt{mbm92}) and on radial velocity curves ($P_{HP}=9.95\pm 0.05$ days; \citealt{mall00}), and improve previous predictions by Bono, Castellani, and Marconi (2000, hereinafter BCM00).Comment: 35 pages, 7 figures. Accepted for publication in the Astrophysical Journa

A water budget dichotomy of rocky protoplanets from 26^{26}Al-heating

In contrast to the water-poor inner solar system planets, stochasticity during planetary formation and order of magnitude deviations in exoplanet volatile contents suggest that rocky worlds engulfed in thick volatile ice layers are the dominant family of terrestrial analogues among the extrasolar planet population. However, the distribution of compositionally Earth-like planets remains insufficiently constrained, and it is not clear whether the solar system is a statistical outlier or can be explained by more general planetary formation processes. Here we employ numerical models of planet formation, evolution, and interior structure, to show that a planet's bulk water fraction and radius are anti-correlated with initial $^{26}$Al levels in the planetesimal-based accretion framework. The heat generated by this short-lived radionuclide rapidly dehydrates planetesimals prior to accretion onto larger protoplanets and yields a system-wide correlation of planet bulk abundances, which, for instance, can explain the lack of a clear orbital trend in the water budgets of the TRAPPIST-1 planets. Qualitatively, our models suggest two main scenarios of planetary systems' formation: high-$^{26}$Al systems, like our solar system, form small, water-depleted planets, whereas those devoid of $^{26}$Al predominantly form ocean worlds, where the mean planet radii between both scenarios deviate by up to about 10%.Comment: Preprint version; free-to-read journal version at https://rdcu.be/bmdlw; blog article at https://t.co/p6SValG1i