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Gamma-ray astronomy has become one of the main experimental ways to test the modified dispersion relations (MDRs) of photons in vacuum, obtained in some attempts to formulate a theory of Quantum Gravity. The MDRs in use imply time delays which depend on the energy, and which increase with distance following some function of redshift. The use of transient, or variable, distant and highly energetic sources, already allows us to set stringent limits on the energy scale related to this phenomenon, usually thought to be of the order of the Planck energy, but robust conclusions on the existence of MDR-related propagation effects still require the analysis of a large population of sources. In order to gather the biggest sample of sources possible for MDR searches at teraelectronvolt energies, the H.E.S.S., MAGIC and VERITAS collaborations enacted a joint task force to combine all their relevant data to constrain the Quantum Gravity energy scale. In the present article, the likelihood method used, to combine the data and provide a common limit, is described in detail and tested through simulations of recorded data sets for a gamma-ray burst, three flaring active galactic nuclei and two pulsars. Statistical and systematic errors are assessed and included in the likelihood as nuisance parameters. In addition, a comparison of two different formalisms for distance dependence of the time lags is performed for the first time. In a second article, to appear later, the method will be applied on all relevant data from the three experiments., Comment: 19 pages, 9 figures, submitted to ApJ. Latest version including first referee's comments

HD 98800 is a young ($\sim10$ Myr old) and nearby ($\sim45$ pc) quadruple system, composed of two spectroscopic binaries orbiting around each other (AaAb and BaBb), with a gas-rich disk in polar configuration around BaBb. While the orbital parameters of BaBb and AB are relatively well constrained, this is not the case for AaAb. A full characterisation of this quadruple system can provide insights on the formation of such a complex system. The goal of this work is to determine the orbit of the AaAb subsystem and refine the orbital solution of BaBb using multi-epoch interferometric observations with the VLTI/PIONIER and radial velocities. The PIONIER observations provide relative astrometric positions and flux ratios for both AaAa and BaBb subsystems. Combining the astrometric points with radial velocity measurements, we determine the orbital parameters of both subsystems. We refined the orbital solution of BaBb and derived, for the first time, the full orbital solution of AaAb. We confirmed the polar configuration of the circumbinary disk around BaBb. From our solutions, we also inferred the dynamical masses of AaAb ($M_{Aa} = 0.93 \pm 0.09$ and $M_{Ab} = 0.29 \pm 0.02$ M$_{\odot}$). We also revisited the parameters of the AB outer orbit. Using the N-body simulation, we show that the system should be dynamically stable over thousands of orbital periods and that it made preliminary predictions for the transit of the disk in front of AaAb which is estimated to start around 2026. We discuss the lack of a disk around AaAb, which can be explained by the larger X-ray luminosity of AaAb, promoting faster photo-evaporation of the disk. High-resolution infrared spectroscopic observations would provide radial velocities of Aa and Ab (blended lines in contemporary observations), which would allow us to calculate the dynamical masses of Aa and Ab independently of the parallax of BaBb., Comment: Accepted for publication in Astronomy \& Astrophysiscs journal (01/09/2021)

A key process in planet formation is the exchange of angular momentum between a growing planet and the protoplanetary disc, which makes the planet migrate through the disc. Several works show that in general low-mass and intermediate-mass planets migrate towards the central star, unless corotation torques become dominant. Recently, a new kind of torque, called the thermal torque, was proposed as a new source that can generate outward migration of low-mass planets. While the Lindblad and corotation torques depend mostly on the properties of the protoplanetary disc and on the planet mass, the thermal torque depends also on the luminosity of the planet, arising mainly from the accretion of solids. Thus, the accretion of solids plays an important role not only in the formation of the planet but also in its migration process. In a previous work, we evaluated the thermal torque effects on planetary growth and migration mainly in the planetesimal accretion paradigm. In this new work, we study the role of the thermal torque within the pebble accretion paradigm. Computations are carried out consistently in the framework of a global model of planet formation that includes disc evolution, dust growth and evolution, and pebble formation. We also incorporate updated prescriptions of the thermal torque derived from high resolution hydrodynamical simulations. Our simulations show that the thermal torque generates extended regions of outward migration in low viscosity discs. This has a significant impact in the formation of the planets., Comment: Accepted for publication in MNRAS

The discovery of a giant planet candidate orbiting the white dwarf WD 1856+534 with an orbital period of 1.4 d poses the questions of how the planet reached its current position. We here reconstruct the evolutionary history of the system assuming common envelope evolution as the main mechanism that brought the planet to its current position. We find that common envelope evolution can explain the present configuration if it was initiated when the host star was on the AGB, the separation of the planet at the onset of mass transfer was in the range 1.69-2.35 au, and if in addition to the orbital energy of the surviving planet either recombination energy stored in the envelope or another source of additional energy contributed to expelling the envelope. We also discuss the evolution of the planet prior to and following common envelope evolution. Finally, we find that if the system formed through common envelope evolution, its total age is in agreement with its membership to the Galactic thin disc. We therefore conclude that common envelope evolution is at least as likely as alternative formation scenarios previously suggested such as planet-planet scattering or Kozai-Lidov oscillations., Comment: 7 pages, 3 figures, 2 tables; accepted for publication in MNRAS

We study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim at computing the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler's size distribution. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection-diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation and sublimation at the water iceline are included. The disc evolution is computed for $\alpha$-discs with photoevaporation from the central star. The planets grow from a moon-mass embryo by silicate pebble accretion and gas accretion. We analyse the effect of a different initial disc mass, $\alpha$-viscosity, disc metallicity and embryo location. Finally, we compute atmospheric mass-loss due to evaporation. We find that inside the ice line, the fragmentation barrier determines the size of pebbles, which leads to different planetary growth patterns for different disc viscosities. Within the iceline the pebble isolation mass typically decays to values below 5 M$_{\oplus}$ within the first million years of disc evolution, limiting the core masses to that value. After computing atmospheric-mass loss, we find that planets with cores below $\sim$4 M$_{\oplus}$ get their atmospheres completely stripped, and a few 4-5 M$_{\oplus}$ cores retain a thin atmosphere that places them in the gap/second peak of the Kepler size distribution. Overall, we find that rocky planets form only in low-viscosity discs ($\alpha \lesssim 10^{-4}$). When $\alpha \geq 10^{-3}$, rocky objects do not grow beyond Mars-mass. The most typical outcome of dry pebble accretion is terrestrial planets with masses spanning from Mars to $\sim$4 M$_{\oplus}$., Comment: Accepted for publication in A&A

The existence of a Radius Valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between that of Earth and Neptune. The goal of this work is to provide insights into the existence of the Radius Valley from, first, a pure formation point of view, and second, a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift and fragmentation; and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We account for gas accretion and type-I/II migration. We perform an extensive parameter study evaluating a wide range in disc properties and embryo's initial location. We account for photoevaporation driven mass-loss after formation. We find that due to the change in dust properties at the water ice line, rocky cores form typically with $\sim$3 M$_{\oplus}$ and have a maximum mass of $\sim$5 M$_{\oplus}$, while icy cores peak at $\sim$10 $M_{\oplus}$, with masses lower than 5 M$_{\oplus}$ being scarce. When neglecting the gaseous envelope, rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes for cores more massive than $\sim$10 M$_{\oplus}$ inflates the radii of those planets above 4 R$_{\oplus}$. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, the second peak can host water-rich planets with thin H-He atmospheres. Some envelope-loss mechanism should operate efficiently at short orbital periods to explain the presence of $\sim$10-40 M$_{\oplus}$ planets falling in the second peak of the size distribution., Comment: Accepted for publication in A&A Letters

The diversity in mass and composition of planetary atmospheres stems from the different building blocks present in protoplanetary discs and from the different physical and chemical processes that these experience during the planetary assembly and evolution. This review aims to summarise, in a nutshell, the key concepts and processes operating during planet formation, with a focus on the delivery of volatiles to the inner regions of the planetary system., Comment: Accepted for publication in Space Science Reviews. 25 pages of text, 19 pages of references. Part of ISSI special collection on Diversity of Atmospheres

Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplanetary disk. We compute, through numerical simulations, the gas and dust evolution, including dust growth, fragmentation, radial drift and particle accumulation at a pressure bump. We also consider the formation of planetesimals by streaming instability and the formation of a moon-size embryo that grows into a giant planet by the hybrid accretion of pebbles and planetesimals. We find that pressure maxima in protoplanetary disks are efficient collectors of dust drifting inwards. The condition of planetesimal formation by streaming instability is fulfilled due to the large amount of dust accumulated at the pressure bump. Then, a massive core is quickly formed (in $\sim 10^4$ yr) by the accretion of pebbles. After the pebble isolation mass is reached, the growth of the core slowly continues by the accretion of planetesimals. The energy released by planetesimal accretion delays the onset of runaway gas accretion, allowing a gas giant to form after $\sim$1 Myr of disk evolution. The pressure maximum also acts as a migration trap. Pressure maxima in protoplanetary disks are preferential locations for dust traps, planetesimal formation by streaming instability and planet migration traps. All these conditions allow the fast formation of a giant planet by the hybrid accretion of pebbles and planetesimals., Comment: Accepted for publication in Astronomy & Astrophysics

Considering corrections produced by modified dispersion relations on the equation of state parameter of radiation, we study the induced black hole metric inspired by Kiselev's ansatz, thus defining a deformed Reissner-Nordstr\"{o}m metric. In particular, we consider thermodynamic properties of such a black hole from the combined viewpoints of the modified equation of state parameter and the phenomenological approach to the quantum gravity problem called rainbow gravity., Comment: 16 pages, 8 figures

As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semi-major axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal discs. Moreover, it was recently shown that if the planet's luminosity due to solid accretion is taken into account, inward migration could be slowed down and even reversed. In this work, we study the planet formation process incorporating, and comparing, updated type I migration rates for non-isothermal discs and the role of planet's luminosity over such rates. We find that the latter can have important effects on planetary evolution, producing a significant outward migration for the growing planets., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society

This work is the second part of a project that attempts to analyze the formation of Solar system analogues (SSAs) from the gaseous to the post-gas phase, in a self-consistently way. In the first paper (PI) we presented our model of planet formation during the gaseous phase which provided us with embryo distributions, planetesimal surface density, eccentricity and inclination profiles of SSAs, considering different planetesimal sizes and type I migration rates at the time the gas dissipates. In this second work we focus on the late accretion stage of SSAs using the results obtained in PI as initial conditions to carry out N-body simulations. One of our interests is to analyze the formation of rocky planets and their final water contents within the habitable zone. Our results show that the formation of potentially habitable planets (PHPs) seems to be a common process in this kind of scenarios. However, the efficiency in forming PHPs is directly related to the size of the planetesimals. The smaller the planetesimals, the greater the efficiency in forming PHPs. We also analyze the sensitivity of our results to scenarios with type I migration rates and gap-opening giants, finding that both phenomena act in a similar way. These effects seem to favor the formation of PHPs for small planetesimal scenarios and to be detrimental for scenarios formed from big planetesimals. Finally, another interesting result is that the formation of water-rich PHPs seems to be more common than the formation of dry PHPs., Comment: 24 pages, 13 figures - Accepted for publication in Monthly Notices of the Royal Astronomical Society

The discovery of giant planets in wide orbits represents a major challenge for planet formation theory. In the standard core accretion paradigm planets are expected to form at radial distances $\lesssim 20$ au in order to form massive cores (with masses $\gtrsim 10~\textrm{M}_{\oplus}$) able to trigger the gaseous runaway growth before the dissipation of the disc. This has encouraged authors to find modifications of the standard scenario as well as alternative theories like the formation of planets by gravitational instabilities in the disc to explain the existence of giant planets in wide orbits. However, there is not yet consensus on how these systems are formed. In this letter, we present a new natural mechanism for the formation of giant planets in wide orbits within the core accretion paradigm. If photoevaporation is considered, after a few Myr of viscous evolution a gap in the gaseous disc is opened. We found that, under particular circumstances planet migration becomes synchronised with the evolution of the gap, which results in an efficient outward planet migration. This mechanism is found to allow the formation of giant planets with masses $M_p\lesssim 1 M_{\rm Jup}$ in wide stable orbits as large as $\sim$130 au from the central star., Comment: Accepted for publication in MNRAS Letters. Comments are welcome

Population synthesis models of planetary systems developed during the last $\sim$15 years could reproduce several of the observables of the exoplanet population, and also allowed to constrain planetary formation models. We present our planet formation model, which calculates the evolution of a planetary system during the gaseous phase. The code incorporates relevant physical phenomena for the formation of a planetary system, like photoevaporation, planet migration, gas accretion, water delivery in embryos and planetesimals, a detailed study of the orbital evolution of the planetesimal population, and the treatment of the fusion between embryos, considering their atmospheres. The main goal of this work, unlike other works of planetary population synthesis, is to find suitable scenarios and physical parameters of the disc to form solar system analogs. We are specially interested in the final planet distributions, and in the final surface density, eccentricity and inclination profiles for the planetesimal population. These final distributions will be used as initial conditions for N-body simulations, to study the post-oligarchic formation in a second work. We then consider different formation scenarios, with different planetesimal sizes and different type I migration rates. We find that solar system analogs are favored in massive discs, with low type I migration rates, and small planetesimal sizes. Besides, those rocky planets within their habitables zones are dry when discs dissipate. At last, the final configurations of solar system analogs include information about the mass and semimajor-axis of the planets, water contents, and the properties of the planetesimal remnants., Comment: 20 pages, 10 figures, Accepted for publication in MNRAS

To study the terrestrial-type planet formation during the post oligarchic growth, the initial distributions of planetary embryos and planetesimals used in N-body simulations play an important role. Most of these studies typically use ad hoc initial distributions based on theoretical and numerical studies. We analyze the formation of planetary systems without gas giants around solar-type stars focusing on the sensitivity of the results to the particular initial distributions of planetesimals and embryos. The formation of terrestrial planets in the habitable zone (HZ) and their final water contents are topics of interest. We developed two different sets of N-body simulations from the same protoplanetary disk. The first set assumes ad hoc initial distributions for embryos and planetesimals and the second set obtains these distributions from the results of a semi-analytical model which simulates the evolution of the gaseous phase of the disk. Both sets form planets in the HZ. Ad hoc initial conditions form planets in the HZ with masses from $0.66M_{\oplus}$ to $2.27M_{\oplus}$. More realistic initial conditions obtained from a semi-analytical model, form planets with masses between $1.18M_{\oplus}$ and $2.21M_{\oplus}$. Both sets form planets in the HZ with water contents between 4.5% and 39.48% by mass. Those planets with the highest water contents respect to those with the lowest, present differences regarding the sources of water supply. We suggest that the number of planets in the HZ is not sensitive to the particular initial distribution of embryos and planetesimals and thus, the results are globally similar between both sets. However, the main differences are associated to the accretion history of the planets in the HZ. These discrepancies have a direct impact in the accretion of water-rich material and in the physical characteristics of the resulting planets., Comment: Accepted for publication in Astronomy and Astrophysics, 13 pages, 9 figures

Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to the Stasheff polytopes. The vector space $\st$ spanned by the faces of permutohedra has a natural structure of tridendriform bialgebra, we prove that it is free as a tridendriform algebra and exhibit a basis. Our result implies that the subspace of primitive elements of the coalgebra $\st$ , equipped with the coboundary map of permutohedra, is a free cacti algebra., Comment: 35 pages

Models of planet formation are mainly focused on the accretion and dynamical processes of the planets, neglecting their chemical composition. In this work, we calculate the condensation sequence of the different chemical elements for a low-mass protoplanetary disk around a solar-type star. We incorporate this sequence of chemical elements (refractory and volatile elements) in our semi-analytical model of planet formation which calculates the formation of a planetary system during its gaseous phase. The results of the semi-analytical model (final distributions of embryos and planetesimals) are used as initial conditions to develope N-body simulations that compute the post-oligarchic formation of terrestrial-type planets. The results of our simulations show that the chemical composition of the planets that remain in the habitable zone has similar characteristics to the chemical composition of the Earth. However, exist differences that can be associated to the dynamical environment in which they were formed., Comment: 3 pages, 4 figures - Accepted for publication in the Bolet\'in de la Asociaci\'on Argentina de Astronom\'ia, vol.57