Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTwo timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
131
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Inspirals of stellar mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. Detection of these sources and extracting information from the signal relies on accurate theoretical models of the binary dynamics. We cast the equations describing binary inspiral in the extreme mass ratio limit in terms of action angle variables, and derive properties of general solutions using a two-timescale expansion. This provides a rigorous derivation of the prescription for computing the leading order orbital motion. As shown by Mino, this leading order or adiabatic motion requires only knowledge of the orbit-averaged, dissipative piece of the self force. The two timescale method also gives a framework for calculating the post-adiabatic corrections. For circular and for equatorial orbits, the leading order corrections are suppressed by one power of the mass ratio, and give rise to phase errors of order unity over a complete inspiral through the relativistic regime. These post-1-adiabatic corrections are generated by the fluctuating piece of the dissipative, first order self force, by the conservative piece of the first order self force, and by the orbit-averaged, dissipative piece of the second order self force. We also sketch a two-timescale expansion of the Einstein equation, and deduce an analytic formula for the leading order, adiabatic gravitational waveforms generated by an inspiral.
rate research
Read More
We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.
An expected source of gravitational waves for future detectors in space are the inspirals of small compact objects into much more massive black holes. These sources have the potential to provide a wealth of information about astronomy and fundamental physics. On short timescales the orbit of the small object is approximately geodesic. Generic geodesics for a Kerr black hole spacetime have a complete set of integrals and can be characterized by three frequencies of the motion. Over the course of an inspiral, a typical system will pass through resonances where two of these frequencies become commensurate. The effect of the resonance will be to alter significantly the rate of inspiral for the duration of the resonance. Understanding the impact of these resonances on gravitational wave phasing is important to detect and exploit these signals for astrophysics and fundamental physics. Two differential equations that might describe the passage of an inspiral through such a resonance are investigated. These differ depending on whether it is the phase or the frequency components of a Fourier expansion of the motion that are taken to be continuous through the resonance. Asymptotic and hyperasymptotic analysis are used to find the late-time analytic behavior of the solution for a system that has passed through a resonance. Linearly growing (weak resonances) or linearly decaying (strong resonances) solutions are found depending on the strength of the resonance. In the weak-resonance case, frequency resonances leave an imprint (a resonant memory) on the gravitational frequency evolution. The transition between weak and strong resonances is characterized by a square-root singularity, and as one approaches this transition from above, the solutions to the frequency resonance equation bunch up into families exponentially fast.
We describe a new class of resonances for extreme mass-ratio inspirals (EMRIs): tidal resonances, induced by the tidal field of nearby stars or stellar-mass black holes. A tidal resonance can be viewed as a general relativistic extension of the Kozai-Lidov resonances in Newtonian systems, and is distinct from the transient resonance already known for EMRI systems. Tidal resonances will generically occur for EMRIs. By probing their influence on the phase of an EMRI waveform, we can learn about the tidal environmental of the EMRI system, albeit at the cost of a more complicated waveform model. Observations by LISA of EMRI systems therefore have the potential to provide information about the distribution of stellar-mass objects near their host galactic-center black holes.
The inspiral of stellar-mass compact objects, like neutron stars or stellar-mass black holes, into supermassive black holes provides a wealth of information about the strong gravitational-field regime via the emission of gravitational waves. In order to detect and analyse these signals, accurate waveform templates which include the effects of the compact objects gravitational self-force are required. For computational efficiency, adiabatic templates are often used. These accurately reproduce orbit-averaged trajectories arising from the first-order self-force, but neglect other effects, such as transient resonances, where the radial and poloidal fundamental frequencies become commensurate. During such resonances the flux of gravitational waves can be diminished or enhanced, leading to a shift in the compact objects trajectory and the phase of the waveform. We present an evolution scheme for studying the effects of transient resonances and apply this to an astrophysically motivated population. We find that a large proportion of systems encounter a low-order resonance in the later stages of inspiral; however, the resulting effect on signal-to-noise recovery is small as a consequence of the low eccentricity of the inspirals. Neglecting the effects of transient resonances leads to a loss of 4% of detectable signals.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
