arXiv subjects

Achamveedu Gopakumar

Publications and source records attributed to Achamveedu Gopakumar.

51 records · Page 3Linked to original sources

arXiv2011

PSR J1903+0327 : A Unique Milli-Second Pulsar with a Main-Sequence Companion Star

PSR J1903+0327 is a mili-second pulsar with a mass of 1.67 M_{\odot} in a highly eccentric orbit (e=0.44) around a main-sequence star. This unique system cannot be reconciled with current observations where milli-second pulsars are generally seen to orbit white dwarfs in almost exactly circular orbits. Current theoretical models of binary and stellar formation and evolution cannot explain the high eccentricity of this system either. In this work, we present three new epochs of optical spectroscopy for the companion to PSR J1903+0327, obtained to confirm the association of the main-sequence star with the pulsar. These 3 new epochs together with the 2 previous ones obtained by Freire et al. (2011) firmly establish the high eccentricity of the companion's orbit as predicted by pulsar timing. Using all five epochs of optical data, we have provided an independent estimate of the mass-ratio, R=1.56\pm0.15 as well as the systemic radial velocity of the binary, γ= 42.1\pm2.5 km/s. We constrain the spectral type of the pulsar companion to lie between F5 V -- G0 V (a slightly earlier type than suggested previously) by measuring the equivalent widths of two of the three Ca-triplet lines (8498 Å, 8542 Å) and the Paschen line at 8598 Å(P14); we also broadly constrain the metallicity of the companion. Additionally, we have placed a somewhat better limit on the rotational velocity of the pulsar companion of v_{rot}\sin{i} \leq 66 km/s which is still not sufficient to allow a test of general relativity using this system.

astro-ph.HE↗

arXiv2009

Ruling out Kozai resonance in highly eccentric galactic binary millisecond pulsar PSR J1903+0327

We investigate the observational signatures associated with one of the proposed formation scenario for the recently discovered highly eccentric binary millisecond pulsar (MSP) PSR J1903+0327 in the galactic plane. The scenario requires that the MSP to be part of a hierarchical triple (HT), consisting of inner and outer binaries, experiencing the Kozai resonance. Numerical modeling of a bound point mass HT, while incorporating the effects due to the quadrupolar interactions between the binary orbits and dominant contributions to the general relativistic periastron precession in the inner binary, reveals that, at the present epoch, the orbital eccentricity of the binary MSP should decrease for reasonable ranges in the HT parameters. The estimated decrements in the orbital eccentricity of the inner binary are few parts in $10^{5}$, substantially higher than the reported accuracies in the estimation of the orbital eccentricity of the binary MSP, while employing various general relativistic timing models for isolated binary pulsars. For wide ranges in the allowed orbital parameters, the estimated rate of change in the eccentricity of the inner binary is orders of magnitude higher than the value recently measured by the pulsar timing analysis. Therefore, we rule out the scenario that the MSP is part of a HT undergoing the Kozai oscillations. The origin of this system in a typical globular cluster is also shown to be less likely than inferred in the discovery paper.

astro-ph.SR↗

arXiv2008

Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case

We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $Mω= 0.1$, the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal-mass case to 12% when the black holes' spins are $S_i/M_i^2 = 0.85$. Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.

gr-qc↗

arXiv2008

Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution

Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Schäfer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a transparent Hamiltonian way and in Burke-Thorne gauge structure, the effects of gravitational radiation reaction into the above Skeleton dynamics with the help of 3.5PN accurate angular momentum flux for compact binaries in quasi-circular orbits to obtain a Semi-Analytic Puncture Evolution to model merging black-hole binaries. With the help of the TaylorT4 approximant at 3.5PN order, we perform a {\it first-order} comparison between gravitational wave phase evolutions in Numerical Relativity and our approach for equal-mass binary black holes. This comparison reveals that a modified Skeletonian reactive dynamics that employs flexible parameters will be required to prevent the dephasing between our scheme and Numerical Relativity, similar to what is pursued in the Effective One Body approach. A rough estimate for the gravitational waveform associated with the binary black-hole coalescence in our approach is also provided.

gr-qc↗

arXiv2007

Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case

We compare the phase evolution of equal-mass nonspinning black-hole binaries from numerical relativity (NR) simulations with post-Newtonian (PN) results obtained from three PN approximants: the TaylorT1 and T4 approximants, for which NR-PN comparisons have already been performed in the literature, and the recently proposed approximant TaylorEt. The accumulated phase disagreement between NR and PN results over the frequency range $Mω= 0.0455$ to $Mω= 0.1$ is greater for TaylorEt than either T1 or T4, but has the attractive property of decreasing monotonically as the PN order is increased.

gr-qc↗

arXiv2007

New Class of Gravitational Wave Templates for Inspiralling Compact Binaries

Compact binaries inspiralling along quasi-circular orbits are the most plausible gravitational wave (GW) sources for the operational, planned and proposed laser interferometers. We provide new class of restricted post-Newtonian accurate GW templates for non-spinning compact binaries inspiralling along PN accurate quasi-circular orbits. Arguments based on data analysis, theoretical and astrophysical considerations are invoked to show why these time-domain Taylor approximants should be interesting to various GW data analysis communities.

gr-qc↗

arXiv2006

Accurate and efficient gravitational waveforms for certain galactic compact binaries

Stellar-mass compact binaries in eccentric orbits are almost guaranteed sources of gravitational waves for Laser Interferometer Space Antenna. We present a prescription to compute accurate and efficient gravitational-wave polarizations associated with bound compact binaries of arbitrary eccentricity and mass ratio moving in slowly precessing orbits. We compare our approach with those existing in the literature and present its advantages.

gr-qc↗

arXiv2006

Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach

Using the Effective One Body approach, that includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of non-spinning black holes of comparable masses moving in quasi-circular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a ``burst'' of linear momentum flux emitted slightly before coalescence. When using the most natural expression for the linear momentum flux during the plunge, together with a Taylor-expanded $(v/c)^4$ correction factor, we find that the maximum value of the terminal recoil is $\sim 74$ km/s and occurs for a mass ratio $m_2/m_1 \simeq 0.38$. We comment, however, on the fact that the above `best bet estimate' is subject to strong uncertainties because the location and amplitude of the crucial peak of linear momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the Effective One Body approach are no longer justified. Changing the analytical way of estimating the linear momentum flux, we find maximum recoils that range between 49 and 172 km/s. (Abridged)

gr-qc↗

arXiv2006

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Schäfer, Phys. Rev. D \textbf{70}, 104011 (2004)]. The gravitational-wave (GW) polarizations $h_{+}$ and $h_{\times}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do \emph{astrophysics} with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.

gr-qc↗

arXiv2005

The deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction

We formally show that the conservative second post-Newtonian (PN) accurate dynamics of spinning compact binaries moving in eccentric orbits, when spin effects are restricted to the leading order spin-orbit interaction cannot be chaotic for the following two distinct cases: (i) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin and (ii) the binary consists of equal mass compact objects, having two arbitrary spins. We rest our arguments on the recent determination of PN accurate Keplerian-type parametric solutions to the above cases, indicating that the PN accurate dynamics is integrable in these two situations. We compare predictions of our case (i) with those from a numerical investigation of an equivalent scenario that observed chaos in the associated dynamics. We also present possible reasons for the discrepancies.

gr-qc↗

arXiv2005

Parametric derivation of the observable relativistic periastron advance for binary pulsars

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of \emph{simple precession}, namely, case (i), the binary consists of equal mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737--3039, derived by Damour and Schäfer many years ago, using a different procedure.

gr-qc↗

arXiv2005

Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct `ready to use' reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate `timing formula', that may be useful for the radio observations of relativistic binary pulsars like J0737-3039.

gr-qc↗

arXiv2004

Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits

We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are explicitly given in terms of the 3PN accurate conserved orbital energy and angular momentum in both Arnowitt, Deser, and Misner-type and harmonic coordinates. Our representation will be required to construct post-Newtonian accurate `ready to use' search templates for the detection of gravitational waves from compact binaries in inspiralling eccentric orbits. Due to the presence of certain 3PN accurate gauge invariant orbital elements, the parametrization should be useful to analyze the compatibility of general relativistic numerical simulations involving compact binaries with the corresponding post-Newtonian descriptions. If required, the present parametrization will also be needed to compute post-Newtonian corrections to the currently employed `timing formula' for the radio observations of relativistic binary pulsars.

gr-qc↗

arXiv2004

Phasing of gravitational waves from inspiralling eccentric binaries

We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling {\it circular} orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of {\it inspiralling eccentric} orbits involves {\it three different time scales}: orbital period, periastron precession and radiation-reaction time scales. By using an improved `method of variation of constants', we show how to combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. We explicitly implement our method at the 2.5PN post-Newtonian accuracy. Our final results can be viewed as computing new `post-adiabatic' short period contributions to the orbital phasing, or equivalently, new short-period contributions to the gravitational wave polarizations, $h_{+,\times}$, that should be explicitly added to the `post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects on the orbital phasing of the latter in the usual adiabatic approximation. Our results should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric gravitational wave detectors (especially if Kozai oscillations turn out to be significant in globular cluster triplets), and for the future space-based interferometer LISA.

gr-qc↗

arXiv2003

A minimal no-radiation approximation to Einstein's field equations

An approximation to Einstein's field equations in Arnowitt-Deser-Misner (ADM) canonical formalism is presented which corresponds to the magneto-hydrodynamics (MHD) approximation in electrodynamics. It results in coupled elliptic equations which represent the maximum of elliptic-type structure of Einstein's theory and naturally generalizes previous conformal-flat truncations of the theory. The Hamiltonian, in this approximation, is identical with the non-dissipative part of the Einsteinian one through the third post-Newtonian order. The proposed scheme, where stationary spacetimes are exactly reproduced, should be useful to construct {\em realistic} initial data for general relativistic simulations as well as to model astrophysical scenarios, where gravitational radiation reaction can be neglected.

gr-qc↗