12,955 research outputs found
Accuracy in Measuring the Neutron Star Mass in Gravitational Wave Parameter Estimation for Black Hole-Neutron Star Binaries
Recently, two gravitational wave (GW) signals, named as GW150914 and
GW151226, have been detected by the two LIGO detectors. Although both signals
were identified as originating from merging black hole (BH) binaries, GWs from
systems containing neutron stars (NSs) are also expected to be detected in the
near future by the Advanced detector network. In this work, we assess the
accuracy in measuring the NS mass () for the GWs from BH-NS binaries
adopting the Advanced LIGO sensitivity with a signal-to-noise ratio of 10. By
using the Fisher matrix method, we calculate the measurement errors ()
in assuming the NS mass of and low
mass BHs with the range of . We used the
TaylorF2 waveform model where the spins are aligned with the orbital angular
momentum, but here we only consider the BH spins. We find that the fractional
errors () are in the range of in our
mass region for a given dimensionless BH spin as . The errors
tend to increase as the BH spin increases, and this tendency is stronger for
higher NS masses (or higher total masses). In particular, for the highest mass
NSs (), the errors can be larger than the true
value of if the dimensionless BH spin exceeds .Comment: 5 pages, 2 figures, submitted to JKP
Testing the validity of the phenomenological gravitational waveform models for nonspinning binary black hole searches at low masses
The phenomenological gravitational waveform models, which we refer to as
PhenomA, PhenomB and PhenomC, generate full inspiral-merger-ringdown waveforms
of coalescing binary back holes (BBHs). These models are defined in the Fourier
domain, thus can be used for fast matched filtering in the gravitational wave
search. PhenomA has been developed for nonspinning BBH waveforms, while PhenomB
and PhenomC were designed to model the waveforms of BBH systems with
nonprecessing (aligned) spins, but can also be used for nonspinning systems. In
this work, we study the validity of the phenomenological models for nonspinning
BBH searches at low masses, and , with Advanced LIGO. As our complete signal waveform model, we adopt
EOBNRv2 that is a time-domain inspiral-merger-ringdown waveform model. To
investigate the search efficiency of the phenomenological template models, we
calculate fitting factors by exploring overlap surfaces. We find that only
PhenomC is valid to obtain the fitting factors better than 0.97 in the mass
range of . Above , PhenomA is most efficient in symmetric
mass region, PhenomB is most efficient in highly asymmetric mass region, and
PhenomC is most efficient in the intermediate region. Specifically, we propose
an effective phenomenological template family that can be constructed by
employing the phenomenological models in four subregions individually. We find
that fitting factors of the effective templates are better than 0.97 in our
entire mass region and mostly greater than 0.99.Comment: 13 pages, 4 figures, matched to the published version in CQ
Real-space Hamiltonian method for low-dimensional semiconductor heterostructures
We present a new method for calculating electronic states in low-dimensional
semiconductor heterostructures, which is based on the real-space Hamiltonian in
the envelope function approximation. The numerical implementation of the method
is extremely simple; all subband energy levels and envelope functions are
directly obtained by a single evaluation of the heterostructure Hamiltonian
matrix. We test the method in the 6- and 8-band k \cdot p models as well as in
a simple parabolic one-band model and demonstrate its great accuracy. The
method can be straightforwardly generalized to a general n-band k \cdot p
model. We describe three different approaches within the method which make it
possible to investigate the origin and removal of the spurious or unphysical
solutions, which has long been an important issue in the community.Comment: 44 pages, 15 figure
Note on maximal estimates of generalized Schr\"odinger equation
In this study we extend the recent works on the pointwise convergence for the
solutions of Schr\"odinger equations based on Du, Guth, and Li and Du and Zhang
to generalized Schr\"odinger equations. We establish the associated maximal
estimates for a general class of phase functions, which give the pointwise
convergence for whenever .Comment: 30 page
Symmetric bilinear form on a Lie algebra
Let be the finite dimensional simple Lie algebra associated to an
indecomposable and symmetrizable generalized Cartan matrix of finite type and let be a finite dimensional Lie algebra
related to a quantum group obtained by Hodges,
Levasseur and Toro \cite{HoLeT} by deforming the quantum group .
Here we see that is a generalization of and give a -invariant symmetric bilinear form on
Validity of the Effective Fisher matrix for parameter estimation analysis: Comparing to the analytic Fisher matrix
The effective Fisher matrix method recently introduced by Cho et al. is a
semi-analytic approach to the Fisher matrix, in which a local overlap surface
is fitted by using a quadratic fitting function. Mathematically, the effective
Fisher matrix should be consistent with the analytic one at the infinitesimal
fitting scale. In this work, using the frequency-domain waveform (TaylorF2), we
give brief comparison results between the effective and analytic Fisher
matrices for several non-spinning binaries consisting of binary neutron stars
with masses of (1.4, 1.4)M_sun, black hole-neutron star of (1.4, 10)M_sun, and
binary black holes of (5, 5) and (10, 10)M_sun for a fixed signal to noise
ratio (SNR=20) and show a good consistency between two methods. We also give a
comparison result for an aligned-spin black hole-neutron star binary with a
black hole spin of \chi=1, where we define new mass parameters (Mc, \eta^-1,
\chi^7/2) to find good fitting functions to the overlap surface. The effective
Fisher matrix can also be computed by using the time-domain waveforms which are
generally more accurate than frequency-domain waveform. We show comparison
results between the frequency-domain and time-domain waveforms (TaylorT4) for
both the non-spinning aligned-spin binaries.Comment: 8 pages, 3 figure
Application of the effective Fisher matrix to the frequency domain inspiral waveforms
The Fisher matrix (FM) has been generally used to predict the accuracy of the
gravitational wave parameter estimation. Although a limitation of the FM has
been well known, it is still mainly used due to its very low computational cost
compared to the Monte Carlo simulations. Recently, Rodriguez et al. [Phys. Rev.
D 88, 084013 (2013)] performed Markov chain Monte Carlo (MCMC) simulations for
nonspinning binary systems with total masses , they found
systematic differences between the predictions from FM and MCMC for . On the other hand, an effective Fisher matrix (eFM) was recently
introduced by Cho et al. [Phys. Rev. D 87, 24004 (2013)]. The eFM is a
semi-analytic approach to the standard FM, in which the partial derivative is
taken by a quadratic fitting function to the local overlap surface. In this
work, we apply the eFM method to several nonspinning binary systems and find
that the error bounds in eFM are qualitatively in good agreement with the MCMC
results of Rodriguez et al. in all mass regions. In particular, we provide
concrete examples showing an importance of taking into account the
template-dependent frequency cutoff of the inspiral waveforms.Comment: 13 pages, 5figures; final version accepted for publication in CQG;
changed significantly from v
Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra
We observe \cite[Proposition 4.1]{LaLe} that Poisson polynomial extensions
appear as semiclassical limits of a class of Ore extensions. As an application,
a Poisson generalized Weyl algebra considered as a Poisson version of the
quantum generalized Weyl algebra is constructed and its Poisson structures are
studied. In particular, it is obtained a necessary and sufficient condition
such that is Poisson simple and established that the Poisson
endomorphisms of are Poisson analogues of the endomorphisms of the
quantum generalized Weyl algebra.Comment: 10 page
Gravitational Wave Searches for Aligned-Spin Binary Neutron Stars Using Nonspinning Templates
We study gravitational wave searches for merging binary neutron stars (NSs).
We use nonspinning template waveforms towards the signals emitted from
aligned-spin NS-NS binaries, in which the spins of the NSs are aligned with the
orbital angular momentum. We use the TaylorF2 waveform model, which can
generate inspiral waveforms emitted from aligned-spin compact binaries. We
employ the single effective spin parameter to represent the
effect of two component spins () on the wave function. For a
target system, we choose a binary consisting of the same component masses of
and consider the spins up to , We investigate
fitting factors of the nonspinning templates to evaluate their efficiency in
gravitational wave searches for the aligned-spin NS-NS binaries. We find that
the templates can achieve the fitting factors exceeding only for the
signals in the range of . Therefore,
we demonstrate the necessity of using aligned-spin templates not to lose the
signals outside that range. We also show how much the recovered total mass can
be biased from the true value depending on the spin of the signal.Comment: 4 pages, 2 figure
On inhomogeneous Strichartz estimates for fractional Schr\"odinger equations and their applications
In this paper we obtain some new inhomogeneous Strichartz estimates for the
fractional Schr\"odinger equation in the radial case. Then we apply them to the
well-posedness theory for the equation
, , with radial
initial data below and radial potentials under the scaling-critical range .Comment: To appear in Discrete Contin. Dyn. Syst., 22 pages, 2 figure
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