#oscillate osculate orbit

[hellfridge]

jayvik epigraph I

You held to me like a lung to breath We collided head first Our lips never met but merged and though I've never kissed you I have tasted an eternity inside you with no moment wasted just once. (until air came between us)

aaand the song this made me think of, which might fit the longing vibe in these flashbacks? hm

[arxt1]

Post-Newtonian Kozai-Lidov Mechanism and its Effect on Cumulative Shift of Periastron Time of Binary Pulsar. (arXiv:2006.11545v2 [gr-qc] UPDATED)

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

from gr-qc updates on arXiv.org https://ift.tt/2Ypbti9

[arxt1]

Post-Newtonian Kozai-Lidov Mechanism and its Effect on Cumulative Shift of Periastron Time of Binary Pulsar. (arXiv:2006.11545v1 [gr-qc])

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

from gr-qc updates on arXiv.org https://ift.tt/2Ypbti9

[arxt1]

Excitation of f-modes during mergers of spinning binary neutron star. (arXiv:2003.02373v2 [gr-qc] UPDATED)

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

from gr-qc updates on arXiv.org https://ift.tt/38ryx1l

[arxt1]

Excitation of f-modes during mergers of spinning binary neutron star. (arXiv:2003.02373v2 [gr-qc] UPDATED)

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

from astro-ph.HE updates on arXiv.org https://ift.tt/38ryx1l

[arxt1]

Excitation of f-modes during mergers of spinning binary neutron star. (arXiv:2003.02373v1 [gr-qc])

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

from gr-qc updates on arXiv.org https://ift.tt/38ryx1l

[arxt1]

Excitation of f-modes during mergers of spinning binary neutron star. (arXiv:2003.02373v1 [gr-qc])

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

from astro-ph.HE updates on arXiv.org https://ift.tt/38ryx1l

[arxt1]

Compact binary inspiral: Nature is perfectly happy with a circle. (arXiv:1906.08064v2 [gr-qc] UPDATED)

It is standard lore that gravitational radiation reaction circularizes the orbits of inspiralling binary systems. But in recent papers, Loutrel et al. have argued that at late times in such inspirals, one measure of eccentricity actually increases, and that this could have observable consequences. We show that this variable, the magnitude of the Runge-Lenz vector ($e_{\rm RL}$), is not an appropriate measure of orbital eccentricity, when the eccentricity is smaller than the leading non-Keplerian perturbation of the orbit. Following Loutrel et al., we use Newtonian equations of motion plus the leading gravitational radiation-reaction terms, the osculating-orbits approach for characterizing binary orbits, and a two-timescale analysis for separating secular from periodic variations of the orbit elements. We find that $e_{\rm RL}$ does grow at late times, but that the actual orbital variables $r$ and $dr/dt$ show no such growth in oscillations. This is in complete agreement with Loutrel et al. We reconcile this apparent contradiction by pointing out that it is essential to take into account the direction of the Runge-Lenz vector, not just its magnitude. At late times in an inspiral, that direction, which defines the pericenter angle, advances at the same rate as the orbital phase. The correct picture is then of a physically circular orbit whose osculating counterpart is indeed eccentric but that resides permanently at the orbit's latus rectum at $-90^{\rm o}$, therefore exhibiting no oscillations. Including first post-Newtonian effects in the equations of motion, we show that $e_{\rm RL}$ grows even more dramatically. But the phase of the Runge-Lenz vector again rotates with the orbit at late times, but now the osculating orbit resides at "perpetual apocenter", so again the physical orbit circularizes.

from gr-qc updates on arXiv.org https://ift.tt/2nEnSz0

[arxt1]

Compact binary inspiral: Nature is perfectly happy with a circle. (arXiv:1906.08064v1 [gr-qc])

It is standard lore that gravitational radiation reaction circularizes the orbits of inspiralling binary systems. But in recent papers, Loutrel et al. have argued that at late times in such inspirals, one measure of eccentricity actually increases, and that this could have observable consequences. We show that this variable, the magnitude of the Runge-Lenz vector ($e_{\rm RL}$), is not an appropriate measure of orbital eccentricity, when the eccentricity is smaller than the leading non-Keplerian perturbation of the orbit. Following Loutrel et al., we use Newtonian equations of motion plus the leading gravitational radiation-reaction terms, the osculating-orbits approach for characterizing binary orbits, and a two-timescale analysis for separating secular from periodic variations of the orbit elements. We find that $e_{\rm RL}$ does grow at late times, but that the actual orbital variables $r$ and $dr/dt$ show no such growth in oscillations. This is in complete agreement with Loutrel et al. We reconcile this apparent contradiction by pointing out that it is essential to take into account the direction of the Runge-Lenz vector, not just its magnitude. At late times in an inspiral, that direction, which defines the pericenter angle, advances at the same rate as the orbital phase. The correct picture is then of a physically circular orbit whose osculating counterpart is indeed eccentric but that resides permanently at the orbit's latus rectum at $-90^{\rm o}$, therefore exhibiting no oscillations. Including first post-Newtonian effects in the equations of motion, we show that $e_{\rm RL}$ grows even more dramatically. But the phase of the Runge-Lenz vector again rotates with the orbit at late times, but now the osculating orbit resides at "perpetual apocenter", so again the physical orbit circularizes.

from gr-qc updates on arXiv.org http://bit.ly/2N1AXyg

[arxt1]

Cumulative Shift of Periastron Time of Binary Pulsar with Kozai-Lidov Oscillation. (arXiv:1903.00287v2 [gr-qc] UPDATED)

We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 years.

from gr-qc updates on arXiv.org http://bit.ly/2UNIPlA

[arxt1]

Nature Abhors a Circle. (arXiv:1801.09009v4 [gr-qc] UPDATED)

The loss of orbital energy and angular momentum to gravitational waves produced in a binary inspiral forces the orbital eccentricity to adiabatically evolve and oscillate. For comparable-mass binaries, the osculating eccentricity is thought to decrease monotonically in the inspiral. Contrary to this, we here show that, once the osculating eccentricity is small enough, radiation reaction forces it to grow secularly before the binary reaches the last stable orbit. We explore this behavior, its physical interpretation and consequences, and its potential impact on future gravitational wave observations.

from gr-qc updates on arXiv.org http://bit.ly/2E0mjBA

[arxt1]

Nature Abhors a Circle. (arXiv:1801.09009v3 [gr-qc] UPDATED)

The loss of orbital energy and angular momentum to gravitational waves produced in a binary inspiral forces the orbital eccentricity to adiabatically evolve and oscillate. For comparable-mass binaries, the osculating eccentricity is thought to decrease monotonically in the inspiral. Contrary to this, we here show that, once the osculating eccentricity is small enough, radiation reaction forces it to grow secularly before the binary reaches the last stable orbit. We explore this behavior, its physical interpretation and consequences, and its potential impact on future gravitational wave observations.

from gr-qc updates on arXiv.org https://ift.tt/2E0mjBA