56 research outputs found
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: , which should be applicable to planet-star mass ratios
, integration times up to
orbits of the inner planet, and mutual inclinations . Systems
that do not satisfy this condition by a margin of are expected to
be unstable, mostly leading to planet ejections if , while slightly favoring collisions with the star for . 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.Comment: 15 pages, 9 figures, to be published in the Astrophysical Journa
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 \Delta_n and protons \Delta_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 \Delta_{thr}= min(\Delta_n+ 3\Delta_p, 3\Delta_n+\Delta_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_\gamma ~ (1-4)
10^{32}\Delta_{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<\Delta_{thr}<0.45 MeV.Comment: (accepted version to be published in A&A
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.Comment: VIII Symposium in Nuclear Physics and Applications: Nuclear and
Particle astrophysics. Appearing in the American Institute of Physics (AIP)
conference proceeding
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 (, ) 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.Comment: 11 pages, 3 figures, accepted for publication in Ap
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