arXiv subjects

Cristobal Petrovich

Publications and source records attributed to Cristobal Petrovich.

65 records · Page 4Linked to original sources

arXiv2015

The stability and fates of hierarchical two-planet systems

We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector Machine algorithm to search for an empirical boundary that best separates stable systems from systems experiencing either ejections or collisions with the star. We propose the following new criterion for dynamical stability: $a_{\rm out}(1-e_{\rm out})/[a_{\rm in}(1+e_{\rm in})]>2.4\left[\max(μ_{\rm in},μ_{\rm out})\right]^{1/3}(a_{\rm out}/a_{\rm in})^{1/2}+1.15$, which should be applicable to planet-star mass ratios $μ_{\rm in},μ_{\rm out}=10^{-4}-10^{-2}$, integration times up to $10^8$ orbits of the inner planet, and mutual inclinations $\lesssim40^\circ$. Systems that do not satisfy this condition by a margin of $\gtrsim0.5$ are expected to be unstable, mostly leading to planet ejections if $μ_{\rm in}>μ_{\rm out}$, while slightly favoring collisions with the star for $μ_{\rm in}<μ_{\rm out}$. We use our numerical integrations to test other stability criteria that have been proposed in the literature and show that our stability criterion performs significantly better for the range of system parameters that we have explored.

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arXiv2014

Steady-state planet migration by the Kozai-Lidov mechanism in stellar binaries

We study the steady-state orbital distributions of giant planets migrating through the combination of the Kozai-Lidov (KL) mechanism due to a stellar companion and friction due to tides raised on the planet by the host star. We run a large set of Monte Carlo simulations that describe the secular evolution of a star-planet-star triple system including the effects from general relativistic precession, stellar and planetary spin evolution, and tides. Our simulations show that KL migration produces Hot Jupiters (HJs) with semi-major axes that are generally smaller than in the observations and they can only explain the observations if the following are both true: (i) tidal dissipation at high eccentricities is at least $\sim 150$ times more efficient than the upper limit inferred from the Jupiter-Io interaction; (ii) highly eccentric planets get tidally disrupted at distances $\gtrsim 0.015$ AU. Based on the occurrence rate and semi-major axis distribution of HJs, we find that KL migration in stellar binaries can produce at most $\sim 20\%$ of the observed HJs. Almost no intermediate-period (semi-major axis $\sim0.1-2$ AU) planets are formed by this mechanism - migrating planets spend most of their lifetimes undergoing KL oscillations at large orbital separations ($>2$ AU) or as Hot Jupiters.

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arXiv2014

Rotochemical heating of millisecond and classical pulsars with anisotropic and density-dependent superfluid gap models

When a rotating neutron star loses angular momentum, the progressive reduction of the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium, inducing reactions that release heat (rotochemical heating). This effect has previously been studied by Fernández & Reisenegger (2005) for non-superfluid neutron stars and by Petrovich & Reisenegger (2010) for superfluid millisecond pulsars. Both studies found that pulsars reach a quasi-steady state in which the compression driving the matter out of beta equilibrium is balanced by the reactions trying to restore the equilibrium. We extend previous studies by considering the effect of density-dependence and anisotropy of the superfluid energy gaps, for the case in which the dominant reactions are the modified Urca processes, the protons are non-superconducting, and the neutron superfluidity is parametrized by models proposed in the literature. By comparing our predictions with the surface temperature of the millisecond pulsar PSR J0437-4715 and upper limits for twenty-one classical pulsars, we find the millisecond pulsar can be only explained by the models with the effectively largest energy gaps (type B models), the classical pulsars require with the gap models that vanish for some angle (type C) and two different envelope compositions. Thus, no single model for neutron superfluidity can simultaneously account for the thermal emission of all available observations of non-accreting neutron stars, possibly due to our neglect of proton superconductivity.

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arXiv2014

Scattering outcomes of close-in planets: constraints on planet migration

Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($e\lesssim0.1$, $i\lesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on a low-eccentricity, low-inclination orbit. This result is inconsistent with the observations. We conclude that eccentricity and inclination excitation from planet-planet scattering must precede migration of planets into short-period orbits. This result constrains theories of planet migration: the semi-major axis must shrink by 1-2 orders of magnitude without damping the eccentricity and inclination.

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arXiv2012

Planets Near Mean-Motion Resonances

The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for two-planet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both cases the distribution of systems in period ratio develops a characteristic asymmetric peak-trough structure around the resonance, qualitatively similar to that observed in the Kepler sample. We verify this result with numerical integrations of the restricted three-body problem. We show that for the 3:2 resonance, where the observed peak-trough structure is strongest, our simple model is consistent with the observations for a range of mean planet masses 20-100M_{\oplus}. This mass range is higher than expected, by at least a factor of three, from the few Kepler planets with measured masses, but part of this discrepancy could be due to oversimplifications in the dynamical model or uncertainties in the planetary mass-radius relation.

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arXiv2012

Disk-satellite interaction in disks with density gaps

Gravitational coupling between a gaseous disk and an orbiting perturber leads to angular momentum exchange between them which can result in gap opening by planets in protoplanetary disks and clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks. Understanding the co-evolution of the disk and the orbit of the perturber in these circumstances requires knowledge of the spatial distribution of the torque exerted by the latter on a highly nonuniform disk. Here we explore disk-satellite interaction in disks with gaps in linear approximation both in Fourier and in physical space, explicitly incorporating the disk non-uniformity in the fluid equations. Density gradients strongly displace the positions of Lindblad resonances in the disk (which often occur at multiple locations), and the waveforms of modes excited close to the gap edge get modified compared to the uniform disk case. The spatial distribution of the excitation torque density is found to be quite different from the existing prescriptions: most of the torque is exerted in a rather narrow region near the gap edge where Lindblad resonances accumulate, followed by an exponential fall-off with the distance from the perturber. Despite these differences, for a given gap profile the full integrated torque exerted on the disk agrees with the conventional uniform disk theory prediction at the level of ~10%. The nonlinearity of the density wave excited by the perturber is shown to decrease as the wave travels out of the gap, slowing down its nonlinear evolution and damping. Our results suggest that gap opening in protoplanetary disks and gas clearing around SMBH binaries can be more efficient than the existing theories predict. They pave the way for self-consistent calculations of the gap structure and the orbital evolution of the perturber using accurate prescription for the torque density behavior.

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arXiv2011

The origin of the negative torque density in disk-satellite interaction

Tidal interaction between a gaseous disk and a massive orbiting perturber is known to result in angular momentum exchange between them. Understanding astrophysical manifestations of this coupling such as gap opening by planets in protoplanetary disks or clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks requires knowledge of the spatial distribution of the torque exerted on the disk by a perturber. Recent hydrodynamical simulations by Dong et al (2011) have shown evidence for the tidal torque density produced in a uniform disk to change sign at the radial separation of $\approx 3.2$ scale heights from the perturber's orbit, in clear conflict with the previous studies. To clarify this issue we carry out a linear calculation of the disk-satellite interaction putting special emphasis on understanding the behavior of the perturbed fluid variables in physical space. Using analytical as well as numerical methods we confirm the reality of the negative torque density phenomenon and trace its origin to the overlap of Lindblad resonances in the vicinity of the perturber's orbit - an effect not accounted for in previous studies. These results suggest that calculations of the gap and cavity opening in disks by planets and binary SMBHs should rely on more realistic torque density prescriptions than the ones used at present.

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arXiv2011

Density Waves Excited by Low-Mass Planets in Protoplanetary Disks I: Linear Regime

Density waves excited by planets embedded in protoplanetary disks play a central role in planetary migration and gap opening processes. We carry out 2D shearing sheet simulations to study the linear regime of wave evolution with the grid-based code Athena, and provide detailed comparisons with the theoretical predictions. Low mass planets (down to ~0.03 Earth mass at 1 AU) and high spatial resolution (256 grid points per scale height) are chosen to mitigate the effects of wave nonlinearity. To complement the existing numerical studies, we focus on the primary physical variables such as the spatial profile of the wave, torque density, and the angular momentum flux carried by the wave, instead of secondary quantities such as the planetary migration rate. Our results show percent level agreement with theory in both physical and Fourier space. New phenomena such as the change of the toque density sign far from the planet are discovered and discussed. Also, we explore the effect of the numerical algorithms, and find that a high order of accuracy, high resolution, and an accurate planetary potential are crucial to achieve good agreement with the theory. We find that the use of a too large time-step without properly resolving the dynamical time scale around the planet produces incorrect results, and may lead to spurious gap opening. Global simulations of planet migration and gap opening violating this requirement may be affected by spurious effects resulting in e.g. the incorrect planetary migration rate and gap opening mass.

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arXiv2011

Long-period thermal oscillations in superfluid millisecond pulsars

In previous papers, we have shown that, as the rotation of a neutron star slows down, it will be internally heated as a consequence of the progressively changing mix of particles (rotochemical heating). In previously studied cases (non-superfluid neutron stars or superfluid stars with only modified Urca reactions), this leads to a quasi-steady state in which the star radiates thermal photons for a long time, possibly accounting for the ultraviolet radiation observed from the millisecond pulsar J0437-4715. For the first time, we explore the phenomenology of rotochemical heating with direct Urca reactions and uniform and isotropic superfluid energy gaps of different sizes. We first do exploratory work by integrating the thermal and chemical evolution equations numerically for different energy gaps, which uncovers a rich phenomenology of stable and unstable solutions. To understand these, we perform a stability analysis around the quasi-steady state, identifying the characteristic times of growing, decaying, and oscillating solutions. For small gaps, the phenomenology is similar to the previously studied cases, in the sense that the solutions quickly converge to a quasi-steady state. For large gaps ($\gtrsim 0.05$ MeV), these solutions become unstable, leading to a limit-cycle behavior of periodicity $\sim 10^{6-7} yr, in which the star is hot ($T_s\gtrsim 10^5$ K) for a small fraction of the cycle ($\sim 5- 20 %$), and cold for a longer time.

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arXiv2010

Rotochemical heating in millisecond pulsars: modified Urca reactions with uniform Cooper pairing gaps

Context: When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy. This mechanism is named rotochemical heating and has previously been studied for neutron stars of nonsuperfluid matter, finding that they reach a quasi-steady configuration in which the rate at which the spin-down modifies the equilibrium concentrations is the same at which neutrino reactions restore the equilibrium. Aims: We describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons Δ_n and protons Δ_p on the rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed. By this, we may determine the amplitude of the superfluid energy gaps for the neutron and protons needed to produce different thermal evolution of MSPs. Results: We find that the chemical imbalances in the star grow up to the threshold value Δ_{thr}= min(Δ_n+ 3Δ_p, 3Δ_n+Δ_p), which is higher than the quasi-steady state achieved in absence of superfluidity. Therefore, the superfluid MSPs will take longer to reach the quasi-steady state than their nonsuperfluid counterparts, and they will have a higher a luminosity in this state, given by L_γ~ (1-4) 10^{32}Δ_{thr}/MeV \dot{P}_{-20}/P_{ms}^3 erg s^-1. We can explain the UV emission of the PSR J0437-4715 for 0.05 MeV<Δ_{thr}<0.45 MeV.

astro-ph.HE↗

arXiv2010

Rotochemical heating in millisecond pulsars with Cooper pairing

When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy. This mechanism is named rotochemical heating and has previously been studied for neutron stars of non-superfluid matter, finding that they reach a quasi-steady state in which the rate that the spin-down modifies the equilibrium concentrations is the same to that of the neutrino reactions restoring the equilibrium. On the other hand, the neutron star interior is believed to contain superfluid nucleons, which affect the thermal evolution of the star by suppressing the neutrino reactions and the specific heat, and opening new Cooper pairing reactions. In this work we describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons and protons on rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed. We find that the chemical imbalances grow up to a value close to the energy gaps, which is higher than the one of the nonsuperfluid case. Therefore, the surface temperatures predicted with Cooper pairing are higher and explain the recent measurement of MSP J0437-4715.

astro-ph.HE↗