130 research outputs found
Eccentricity evolution of spinning binaries
We study the evolution of the eccentricity of an eccentric orbit with
spinning components. We develop a prescription to express the evolving
eccentricity in terms of initial eccentricity and frequency. For that purpose
we considered the spins to be perpendicular to the orbital plane. Using this we
found an analytical result for the contribution of spin in eccentricity
evolution. As a result, we expressed orbital eccentricity in a series of
initial eccentricity and gravitational wave frequency. The prescription
developed here can easily be used to find arbitrarily higher-order
contributions of initial eccentricity. With the eccentricity evolution at hand,
we computed the evolving energy and angular momentum fluxes for eccentric orbit
with spinning components. This result can be used to construct the waveforms of
spinning compact objects in an eccentric orbit.Comment: arXiv admin note: text overlap with arXiv:2305.0377
Horizon fluxes of binary black holes in eccentric orbits
I compute the rate of change of mass and angular momentum of a black hole,
namely tidal heating, in an eccentric orbit. The change is caused due to the
tidal field of the orbiting companion. I compute the result for both the
spinning and non-spinning black holes in the leading order of the mean motion,
namely . I demonstrate that the rates get enhanced significantly for
nonzero eccentricity. Since eccentricity in a binary evolves with time I also
express the results in terms of an initial eccentricity and azimuthal frequency
. In the process, I developed a prescription that can be used to
compute all physical quantities in a series expansion of initial eccentricity,
. This result was only known in the leading order while ignoring the
contribution of the spin on the eccentricity evolution. Although the
eccentricity evolution result still ignores the spin effect in the current
work, the prescription can be used to compute higher-order corrections of
initial eccentricity post-leading order. Using this result I computed the rate
of change of mass and angular momentum of a black hole in terms of initial
eccentricity and azimuthal frequency up to .Comment: arXiv admin note: text overlap with arXiv:1605.00304 by other author
On the Consistency of Maximum Likelihood Estimation of Probabilistic Principal Component Analysis
Probabilistic principal component analysis (PPCA) is currently one of the
most used statistical tools to reduce the ambient dimension of the data. From
multidimensional scaling to the imputation of missing data, PPCA has a broad
spectrum of applications ranging from science and engineering to quantitative
finance.
Despite this wide applicability in various fields, hardly any theoretical
guarantees exist to justify the soundness of the maximal likelihood (ML)
solution for this model. In fact, it is well known that the maximum likelihood
estimation (MLE) can only recover the true model parameters up to a rotation.
The main obstruction is posed by the inherent identifiability nature of the
PPCA model resulting from the rotational symmetry of the parameterization. To
resolve this ambiguity, we propose a novel approach using quotient topological
spaces and in particular, we show that the maximum likelihood solution is
consistent in an appropriate quotient Euclidean space. Furthermore, our
consistency results encompass a more general class of estimators beyond the
MLE. Strong consistency of the ML estimate and consequently strong covariance
estimation of the PPCA model have also been established under a compactness
assumption.Comment: 15 pages, 1 figure, to appear in NeurIPS 2023. Update: included minor
typographical correction
Effect of superfluid matter of neutron star on the tidal deformability
We study the effect of superfluidity on the tidal response of a neutron star
in a general relativistic framework. In this work, we take a dual-layer
approach where the superfluid matter is confined in the core of the star. Then,
the superfluid core is encapsulated with an envelope of ordinary matter fluid
which acts effectively as the low-density crustal region of the star. In the
core, the matter content is described by a two-fluid model where only the
neutrons are taken as superfluid and the other fluid consists of protons and
electrons making it charge neutral. We calculate the values of various tidal
love numbers of a neutron star and discuss how they are affected due to the
presence of entrainment between the two fluids in the core. We also emphasize
that more than one tidal parameter is necessary to probe superfluidity with the
gravitational wave from the binary inspiral
Relativistic tidal properties of superfluid neutron stars
We investigate the tidal deformability of a superfluid neutron star. We
calculate the equilibrium structure in the general relativistic two-fluid
formalism with entrainment effect where we take neutron superfluid as one fluid
and the other fluid is comprised of protons and electrons, making it a charge
neutral fluid. We use a relativistic mean field model for the equation of state
of matter where the interaction between baryons is mediated by the exchange
, and mesons. Then, we study the linear, static
perturbation on the star to compute the electric-type Love number following
Hinderer's prescription.Comment: Accepted for publication in Physical Review
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