Gravitational waves from compact objects inspiralling into massive black holes

Size: px
Start display at page:

Download "Gravitational waves from compact objects inspiralling into massive black holes"

Transcription

1 Gravitational waves from compact objects inspiralling into massive black holes Éanna Flanagan, Cornell University American Physical Society Meeting Tampa, Florida, 16 April 2005

2 Outline Extreme mass-ratio inspirals as sources for LISA: capture mechanism, estimates of detection rates Science payoffs from these systems: physics & astrophysics Theoretical challenge: high accuracy computation of strong-field orbital evolution & waveforms (generic orbits, Kerr) Flux-balancing approach Gravitational self-force approach Recent developments: adiabatic waveforms now computable using result due to Mino, sufficient for signal detection.

3 Orbits about Sgr A* (3 x 10 M ) 6 o Ghez et al 2003

4 Capture of compact objects Stars in stellar cusp kicked into loss cone through multibody scattering, captured into tight elliptical orbit Main sequence stars tidally disrupted, compact objects (white dwarfs, neutron stars, black holes) survive Orbit gradually decays; orbits during last year, inside LISA waveband (Finn & Thorne 2000), in the relativistic regime v/c 1. Orbit gradually circularizes due to gravitational wave emission, but still substantial eccentricity at innermost stable orbit (Cutler, Kennefick & Poisson 1994)

5 Signal seen by LISA 10 c n log h, h , , , , yr r ~ = ~ 3.26 N cyc = 460, / f, Hz.999 m = 2 1 mo , day 2,410 a =.999 r ~ isco = 1.18 Circular, equatorial inspiral of 1 M object into a 10 6 M black hole at 1 Gpc (Finn & Thorne 2000).

6 Event Rates From Gair et. al. (2003), based on estimates of black hole mass density using M σ relation, and using Freitag s (2001) simulation of stellar population/dynamics of Milky Way.

7 Event Rates (cont) (Gair et. al. 2003).

8 Richness of orbital dynamics equatorial plane horizon spin axis r = min pm 1 + e inclination angle (ι) r = pm max 1 e Boyer Lindquist frequencies (Hz) f φ f θ f r M = 10 6 M sun a/m = eccentricity = 1/2 inclination = 45 degrees 10 1 minimum radius, or periholion (M)

9 Science Goals LISA should observe 1000 inspirals of compact objects (µ 1 10M ) into massive black holes (M 10 6 M ) (Gair et al. 2003). Last 1 yr of inspiral will contain M/µ 10 5 cycles of waveform. Many scientific payoffs: 1. Measure BH masses and spins to accuracy 10 4 (Poisson 1994, Barack & Cutler 2004); constrain growth history (mergers versus accretion) of the black holes (Hughes & Blandford 2003). 2. Learn about central parsec of galactic nuclei from measured event rate and distribution of inspiralling objects masses. 3. Precise test of general relativity in the strong field regime. Measure multipole moments of central object (Ryan 1995,1997), unambiguous identification as BH

10 Theoretical Challenge Achieving these science goals will require templates with phase errors 1 over entire signal of 1 yr; fractional phase accuracy Signal detection will require templates with phase errors 1 over 3 weeks (Gair et. al. 2004). Required: (a 1). eccentric, inclined orbits about rapidly spinning black holes We currently lack the theoretical tools to compute such accurate templates. However there has been much progress recently. Foundation for all computational methods: µ/m 1. Gravitational field of compact object treated as linear perturbation of Kerr spacetime.

11 Current methods of computing templates Use of post-newtonian methods: Yields crude waveforms that have been already used to roughly scope out LISA s ability ability to detect inspiral events (Gair et al. 2004) and to measure the waveform s parameters (Barack & Cutler 2004). Use of conservation laws: Use fluxes of energy and z-component of angular momentum to infinity and down the black hole to infer adiabatic evolution of orbit; restricted to equatorial and circular orbits (Cutler, Kennefick & Poisson 1994; Shibata 1994; Glampedakis & Kennefick 2002; Hughes 2000,2001). Direct computation of the self-force: Formal expression known (Mino, Sasaki & Tanaka 1997, Quinn & Wald 1997). Finding a practical computational scheme in Kerr is difficult; much work over last few years. Time-domain numerical simulations: Numerically integrate the Teukolsky equation as a 2+1 PDE in the time domain, regularizing the point particle source. (Krivan et al. 1997, Burko & Khanna 2002, Scheel et al. 2003, Martel 2003, Lopez-Aleman et al. 2003, Pazos-Avalos & Lousto 2004). Accuracy 10% so far.

12 Conservation law method Orbits characterized by energy E, angular momentum L z, Carter constant Q. Use Teukolsky-Sasaki-Nakamura black hole perturbation formalism to compute de/dt and dl z /dt, infer gradual evolution of orbit in special cases where Q evolution not needed. Summary: a > 0 e > 0 ι > 0 evolution Cutler et al. (1994) Shibata (1993) Shibata (1994) Hughes (2001) Glampedakis et al. (2002) Drasco et al. (2005)

13 Gravitational Self Force Analogous to Abraham-Lorentz-Dirac force for charged particles ma = qe + 2q 2 ȧ/c 3. Meaning of self force: consider an isolated body of mass M and size L moving in a vacuum gravitational field characterized by a lengthscale L ext.

14 Gravitational Self Force (cont) Complications arise in curved spacetime:

15 Gravitational Self Force (cont) General result is (Mino, Sasaki and Tanaka, 1997; Quinn and Wald 1997) F α (τ) = 1 2 µ(gαβ + u α β) [ β h tail λσ λh tail βσ ] σh tail βλ, τ(x) ε h tail αβ = µ lim dτ G ret αβ,α ε 0 β [ x, (τ )u z(τ)]uα β (τ ) = h ret αβ hsing αβ. Substantial efforts have been made to turn this into a practical computational scheme using mode decompositions (eg Barack et al 2002). Not yet completely successful. Significant simplifications arise when one makes use of adiabaticity of inspirals (Mino 2003).

16 Adiabatic waveforms Orbital periods M; radiation reaction time M 2 /µ = M/ε, where ε = µ/m. Orbital evolution governed by d 2 x α dτ + dx β dx γ 2 Γα βγ dτ dτ = ε [ a α 0,diss + ] [ aα 0,cons + ε 2 a α 1,diss + ] aα 1,cons + O(ε 3 ), where a 0 = P (h ret h sing ), and a 1 is unknown. Orbital [ phase can be expanded using two-time expansion as Φ(t) = Φ0 (t, εt) + εφ 1 (t, εt) + O(ε 2 ) ]. 1 ε Adiabatic waveforms are those obtained using leading order orbit Φ 0. Instantaneously accurate to O(ε), cumulative phase errors O(1). Orbits characterized by E = ξ α u α, L z = ψ α u α, Q = K αβ u α u β. Sufficient to know Ė, L z, Q. Conservation-law waveforms are adiabatic. Mino (2003) has shown how to obtain adiabatic waveforms for generic orbits: Q = 2ε K αβ u α a β 0 = 2ε K αβu α a β 0 where a 0 = P (h ret h adv )/2.

17 Mino s Argument Generic bound orbits in Kerr have the property that they are arbitrarily close to geodesics for which there exists an isometry of the form t t 0 t, ϕ ϕ 0 ϕ under which the geodesic is invariant. Obtain K αβ u α a β 0 [hret αβ ] = K αβ u α a α 0 [hadv αβ, ] where ξ = /( t) and brackets mean a time average. Now average these two terms using a 0 [h] = P (h h sing ); the singular parts cancel.

18 Accuracy of adiabatic waveforms In slow-motion limit v/c 1, post-adiabatic correction terms can be identified in post-newtonian expressions. Using post-3.5-newtonian waveforms to compute the phase error, minimized over time of arrival and initial phase, for a 10M, 10 6 M inspiral gives: (Finn and Thorne 2000) Adiabatic waveforms are likely good enough for signal detection [phase coherence requirement 3 weeks (Gair et al. 2004)], but not for parameter extraction (phase coherence requirement entire signal).

19 Implementing Mino s prescription Use expansion of Gal tsov (1992) of radiative Greens function in terms of modes. Use radiation gauge (expression for < Q > is gauge invariant). Evaluate time average using integral over torus in phase space, obtain (Drasco, Flanagan & Hughes 2005): Ė = Λ Z H Λ 2 + Z Λ 2 L z = Λ ω mkn m [ Z H Λ 2 + Z Λ 2] Q = Λ ( Z H Λ ) Z H Λ + ( Z Λ ) Z Λ, where Λ = (l, m, k, n). Amplitudes ZΛ H, Z Λ computed by existing Drasco-Hughes code. New amplitudes Z Λ H, Z Λ have to be added to code. Both sets of amplitudes are given by integrals over tori in phase space.

20 Conclusions There are no obstacles remaining to prevent computation of adiabatic inspiral waveforms for generic orbits. These waveforms will likely be accurate enough for signal detection with LISA. Analysis of detected signals and parameter extraction will require going beyond this approximation and using the local self-force. This remains a significant challenge.

How black holes get their kicks! Gravitational radiation recoil from binary inspiral and plunge into a rapidly-rotating black hole.

How black holes get their kicks! Gravitational radiation recoil from binary inspiral and plunge into a rapidly-rotating black hole. How black holes get their kicks! Gravitational radiation recoil from binary inspiral and plunge into a rapidly-rotating black hole. Marc Favata (Cornell) Daniel Holz (U. Chicago) Scott Hughes (MIT) The

More information

When one black hole is not like the other

When one black hole is not like the other When one black hole is not like the other Cal Poly, San Luis Obispo Center for Computational Relativity and Gravitation Rochester Institute of Technology 13 December 2010 Current gravitational-wave searches

More information

4. MiSaTaQuWa force for radiation reaction

4. MiSaTaQuWa force for radiation reaction 4. MiSaTaQuWa force for radiation reaction [ ] g = πgt G 8 g = g ( 0 ) + h M>>μ v/c can be large + h ( ) M + BH μ Energy-momentum of a point particle 4 μ ν δ ( x z( τ)) μ dz T ( x) = μ dτ z z z = -g dτ

More information

Progress on orbiting particles in a Kerr background

Progress on orbiting particles in a Kerr background Progress on orbiting particles in a Kerr background John Friedman Capra 15 Abhay Shah, Toby Keidl I. Intro II. Summary of EMRI results in a Kerr spacetime A. Dissipative ( adiabatic ) approximation (only

More information

Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA

Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LI Lee Samuel Finn Department of Physics, Astronomy & Astrophysics,

More information

arxiv:gr-qc/ v1 31 Aug 2006

arxiv:gr-qc/ v1 31 Aug 2006 (Sort of) Testing relativity with extreme mass ratio inspirals Scott A. Hughes arxiv:gr-qc/0608140v1 31 Aug 2006 Department of Physics and MIT Kavli Institute Massachusetts Institute of Technology, Cambridge,

More information

POST-NEWTONIAN METHODS AND APPLICATIONS. Luc Blanchet. 4 novembre 2009

POST-NEWTONIAN METHODS AND APPLICATIONS. Luc Blanchet. 4 novembre 2009 POST-NEWTONIAN METHODS AND APPLICATIONS Luc Blanchet Gravitation et Cosmologie (GRεCO) Institut d Astrophysique de Paris 4 novembre 2009 Luc Blanchet (GRεCO) Post-Newtonian methods and applications Chevaleret

More information

Test bodies and naked singularities: is the self-force the cosmic censor?

Test bodies and naked singularities: is the self-force the cosmic censor? Test bodies and naked singularities: is the self-force the cosmic censor? Enrico Barausse (University of Guelph) in collaboration with V. Cardoso (CENTRA, Lisbon) & G. Khanna (UMass Darmouth) based on

More information

The Gravitational Radiation Rocket Effect. Marc Favata Cornell University GR17, Dublin, July 2004

The Gravitational Radiation Rocket Effect. Marc Favata Cornell University GR17, Dublin, July 2004 The Gravitational Radiation Rocket Effect recoil Marc Favata Cornell University GR17, Dublin, July 004 Favata, Hughes, & Holz, ApJL 607, L5, astro-ph/040056 Merritt, Milosavljevic, Favata, Hughes, & Holz,

More information

Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes

Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes INSTITUTE OF PHYSICS PUBLISHING Class. Quantum Grav. 8 (200) 3989 3994 CLASSICAL AND QUANTUM GRAVITY PII: S0264-938(0)2650-0 Towards the solution of the relativistic gravitational radiation reaction problem

More information

POST-NEWTONIAN THEORY VERSUS BLACK HOLE PERTURBATIONS

POST-NEWTONIAN THEORY VERSUS BLACK HOLE PERTURBATIONS Rencontres du Vietnam Hot Topics in General Relativity & Gravitation POST-NEWTONIAN THEORY VERSUS BLACK HOLE PERTURBATIONS Luc Blanchet Gravitation et Cosmologie (GRεCO) Institut d Astrophysique de Paris

More information

Ballistic orbits for Gravitational Waves

Ballistic orbits for Gravitational Waves for Gravitational Waves Giuseppe d'ambrosi Jan-Willem van Holten [arxiv:1406.4282] Kyoto 02-07-2015 18th Capra meeting on Radiation Reaction in GR 1 2 3 Giuseppe d'ambrosi for Gravitational Waves 2 Black

More information

Black Holes. Theory & Astrophysics. Kostas Glampedakis

Black Holes. Theory & Astrophysics. Kostas Glampedakis Black Holes Theory & Astrophysics Kostas Glampedakis Contents Part I: Black hole theory. Part II: Celestial mechanics in black hole spacetimes. Part III: Energy extraction from black holes. Part IV: Astrophysical

More information

Sources of Gravitational Waves

Sources of Gravitational Waves 1 Sources of Gravitational Waves Joan Centrella Laboratory for High Energy Astrophysics NASA/GSFC Gravitational Interaction of Compact Objects KITP May 12-14, 2003 A Different Type of Astronomical Messenger

More information

Measuring EMRIs: A reality check

Measuring EMRIs: A reality check Measuring EMRIs: A reality check Image: Steve Drasco, CalPoly What modeling and data analysis work must be done in order to achieve the science that has been promised for extreme mass ratio inspiral measurements?

More information

Astrophysics with LISA

Astrophysics with LISA Astrophysics with LISA Alberto Vecchio University of Birmingham UK 5 th LISA Symposium ESTEC, 12 th 15 th July 2004 LISA: GW telescope LISA is an all-sky monitor: All sky surveys are for free Pointing

More information

Testing the Kerr Black Hole Hypothesis. Cosimo Bambi (Ludwig-Maximilians-Universität München) 5 June 2012, ESAC Madrid, Spain

Testing the Kerr Black Hole Hypothesis. Cosimo Bambi (Ludwig-Maximilians-Universität München) 5 June 2012, ESAC Madrid, Spain Testing the Kerr Black Hole Hypothesis Cosimo Bambi (Ludwig-Maximilians-Universität München) 5 June 2012, ESAC Madrid, Spain Plan of the talk Motivations Theoretical and observational facts How can we

More information

Analytic methods in the age of numerical relativity

Analytic methods in the age of numerical relativity Analytic methods in the age of numerical relativity vs. Marc Favata Kavli Institute for Theoretical Physics University of California, Santa Barbara Motivation: Modeling the emission of gravitational waves

More information

HOMEWORK 10. Applications: special relativity, Newtonian limit, gravitational waves, gravitational lensing, cosmology, 1 black holes

HOMEWORK 10. Applications: special relativity, Newtonian limit, gravitational waves, gravitational lensing, cosmology, 1 black holes General Relativity 8.96 (Petters, spring 003) HOMEWORK 10. Applications: special relativity, Newtonian limit, gravitational waves, gravitational lensing, cosmology, 1 black holes 1. Special Relativity

More information

Black Holes: From Speculations to Observations. Thomas Baumgarte Bowdoin College

Black Holes: From Speculations to Observations. Thomas Baumgarte Bowdoin College Black Holes: From Speculations to Observations Thomas Baumgarte Bowdoin College Mitchell and Laplace (late 1700 s) Escape velocity (G = c = 1) 2M v esc = R independent of mass m of test particle Early

More information

What I did in grad school. Marc Favata

What I did in grad school. Marc Favata What I did in grad school Marc Favata B-exam June 1, 006 Kicking Black Holes Crushing Neutron Stars and the adiabatic approximation in extreme-mass-ratio inspirals How black holes get their kicks: The

More information

Black Hole Physics via Gravitational Waves

Black Hole Physics via Gravitational Waves Black Hole Physics via Gravitational Waves Image: Steve Drasco, California Polytechnic State University and MIT How to use gravitational wave observations to probe astrophysical black holes In my entire

More information

Gravitational Waves & Intermediate Mass Black Holes. Lee Samuel Finn Center for Gravitational Wave Physics

Gravitational Waves & Intermediate Mass Black Holes. Lee Samuel Finn Center for Gravitational Wave Physics Gravitational Waves & Intermediate Mass Black Holes Lee Samuel Finn Center for Gravitational Wave Physics Outline What are gravitational waves? How are they produced? How are they detected? Gravitational

More information

Self-consistent motion of a scalar charge around a Schwarzschild black hole

Self-consistent motion of a scalar charge around a Schwarzschild black hole Self-consistent motion of a scalar charge around a Schwarzschild black hole Ian Vega 1 Peter Diener 2 Barry Wardell 3 Steve Detweiler 4 1 University of Guelph 2 Louisiana State University 3 University

More information

Testing GR with Compact Object Binary Mergers

Testing GR with Compact Object Binary Mergers Testing GR with Compact Object Binary Mergers Frans Pretorius Princeton University The Seventh Harvard-Smithsonian Conference on Theoretical Astrophysics : Testing GR with Astrophysical Systems May 16,

More information

Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits

Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits Wen-Biao Han Shanghai Astronomical Observatory, Chinese Academy of Sciences 80 Nandan Road, Shanghai,

More information

Overview and Innerview of Black Holes

Overview and Innerview of Black Holes Overview and Innerview of Black Holes Kip S. Thorne, Caltech Beyond Einstein: From the Big Bang to Black Holes SLAC, 14 May 2004 1 Black Hole Created by Implosion of a Star Our Focus: quiescent black hole

More information

Binary Sources of Gravitational Radiation

Binary Sources of Gravitational Radiation Binary Sources of Gravitational Radiation We now turn our attention to binary systems. These obviously have a large and varying quadrupole moment, and have the additional advantage that we actually know

More information

Dynamics of star clusters containing stellar mass black holes: 1. Introduction to Gravitational Waves

Dynamics of star clusters containing stellar mass black holes: 1. Introduction to Gravitational Waves Dynamics of star clusters containing stellar mass black holes: 1. Introduction to Gravitational Waves July 25, 2017 Bonn Seoul National University Outline What are the gravitational waves? Generation of

More information

The post-adiabatic correction to the phase of gravitational wave for quasi-circular extreme mass-ratio inspirals.

The post-adiabatic correction to the phase of gravitational wave for quasi-circular extreme mass-ratio inspirals. The post-adiabatic correction to the phase of gravitational wave for quasi-circular extreme mass-ratio inspirals. Based on unpublished, still progressing works Soichiro Isoyama (Yukawa Institute for Theoretical

More information

Waveform modeling for LIGO parameter estimation: status & challenges for LISA Prayush Kumar Cornell University

Waveform modeling for LIGO parameter estimation: status & challenges for LISA Prayush Kumar Cornell University Waveform modeling for LIGO parameter estimation: status & challenges for LISA Prayush Kumar Cornell University The Architecture of LISA Science Analysis: Imagining the Future January 16-19, 2018 1 Outline

More information

2.5.1 Static tides Tidal dissipation Dynamical tides Bibliographical notes Exercises 118

2.5.1 Static tides Tidal dissipation Dynamical tides Bibliographical notes Exercises 118 ii Contents Preface xiii 1 Foundations of Newtonian gravity 1 1.1 Newtonian gravity 2 1.2 Equations of Newtonian gravity 3 1.3 Newtonian field equation 7 1.4 Equations of hydrodynamics 9 1.4.1 Motion of

More information

High-velocity collision of particles around a rapidly rotating black hole

High-velocity collision of particles around a rapidly rotating black hole Journal of Physics: Conference Series OPEN ACCESS High-velocity collision of particles around a rapidly rotating black hole To cite this article: T Harada 2014 J. Phys.: Conf. Ser. 484 012016 Related content

More information

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits Western University Scholarship@Western Physics and Astronomy Publications Physics and Astronomy Department 01 The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar

More information

Indirect (source-free) integration method for EMRIs: waveforms from geodesic generic orbits and self-force consistent radial fall

Indirect (source-free) integration method for EMRIs: waveforms from geodesic generic orbits and self-force consistent radial fall Indirect (source-free) integration method for EMRIs: waveforms from geodesic generic orbits and self-force consistent radial fall Alessandro Spallicci 1 Luca Bonetti 1,Stéphane Cordier 2, Richard Emilion

More information

Gravitational Waves. Masaru Shibata U. Tokyo

Gravitational Waves. Masaru Shibata U. Tokyo Gravitational Waves Masaru Shibata U. Tokyo 1. Gravitational wave theory briefly 2. Sources of gravitational waves 2A: High frequency (f > 10 Hz) 2B: Low frequency (f < 10 Hz) (talk 2B only in the case

More information

Gravitational Waves and Their Sources, Including Compact Binary Coalescences

Gravitational Waves and Their Sources, Including Compact Binary Coalescences 3 Chapter 2 Gravitational Waves and Their Sources, Including Compact Binary Coalescences In this chapter we give a brief introduction to General Relativity, focusing on GW emission. We then focus our attention

More information

Analytic methods in the age of numerical relativity

Analytic methods in the age of numerical relativity Analytic methods in the age of numerical relativity vs. Marc Favata Kavli Institute for Theoretical Physics University of California, Santa Barbara Motivation: Modeling the emission of gravitational waves

More information

Gauge-invariant quantity. Monday, June 23, 2014

Gauge-invariant quantity. Monday, June 23, 2014 Gauge-invariant quantity U Topics that will be covered Gauge-invariant quantity, U, (reciprocal of the red-shift invariant, z), the 1 st order (in mass-ratio) change in u t. For eccentric orbits it can

More information

Pinhole Cam Visualisations of Accretion Disks around Kerr BH

Pinhole Cam Visualisations of Accretion Disks around Kerr BH Pinhole Camera Visualisations of Accretion Disks around Kerr Black Holes March 22nd, 2016 Contents 1 General relativity Einstein equations and equations of motion 2 Tetrads Defining the pinhole camera

More information

Key ideas on how inspiral-merger-ringdown waveforms are built within the effective-one-body formalism

Key ideas on how inspiral-merger-ringdown waveforms are built within the effective-one-body formalism Key ideas on how inspiral-merger-ringdown waveforms are built within the effective-one-body formalism Alessandra Buonanno Maryland Center for Fundamental Physics & Joint Space-Science Institute Department

More information

Non-existence of time-periodic dynamics in general relativity

Non-existence of time-periodic dynamics in general relativity Non-existence of time-periodic dynamics in general relativity Volker Schlue University of Toronto University of Miami, February 2, 2015 Outline 1 General relativity Newtonian mechanics Self-gravitating

More information

Relativistic theory of surficial Love numbers

Relativistic theory of surficial Love numbers Department of Physics, University of Guelph APS April Meeting 2013, Denver Newtonian tides 1 In Newtonian theory, the tidal environment of a body of mass M and radius R is described by the tidal quadrupole

More information

Gravity s Standard Sirens. B.S. Sathyaprakash School of Physics and Astronomy

Gravity s Standard Sirens. B.S. Sathyaprakash School of Physics and Astronomy Gravity s Standard Sirens B.S. Sathyaprakash School of Physics and Astronomy What this talk is about Introduction to Gravitational Waves What are gravitational waves Gravitational wave detectors: Current

More information

Black Hole Astrophysics Chapters 7.5. All figures extracted from online sources of from the textbook.

Black Hole Astrophysics Chapters 7.5. All figures extracted from online sources of from the textbook. Black Hole Astrophysics Chapters 7.5 All figures extracted from online sources of from the textbook. Recap the Schwarzschild metric Sch means that this metric is describing a Schwarzschild Black Hole.

More information

Lecture XIX: Particle motion exterior to a spherical star

Lecture XIX: Particle motion exterior to a spherical star Lecture XIX: Particle motion exterior to a spherical star Christopher M. Hirata Caltech M/C 350-7, Pasadena CA 95, USA Dated: January 8, 0 I. OVERVIEW Our next objective is to consider the motion of test

More information

(Super)massive Black Holes in Galactic Nuclei and LISA

(Super)massive Black Holes in Galactic Nuclei and LISA (Super)massive Black Holes in Galactic Nuclei and LISA 14 July 2004: 5 th LISA symposium Sterl Phinney Caltech LISA sources Cosmological backgrounds (e.g. from electroweak phase transition) Burst sources

More information

Savvas Nesseris. IFT/UAM-CSIC, Madrid, Spain

Savvas Nesseris. IFT/UAM-CSIC, Madrid, Spain Savvas Nesseris IFT/UAM-CSIC, Madrid, Spain What are the GWs (history, description) Formalism in GR (linearization, gauges, emission) Detection techniques (interferometry, LIGO) Recent observations (BH-BH,

More information

Testing astrophysical black holes. Cosimo Bambi Fudan University

Testing astrophysical black holes. Cosimo Bambi Fudan University Testing astrophysical black holes Cosimo Bambi Fudan University http://www.physics.fudan.edu.cn/tps/people/bambi/ 29 October 2015 Interdisciplinary Center for Theoretical Studies (USTC, Hefei) Plan of

More information

Tidal deformation and dynamics of compact bodies

Tidal deformation and dynamics of compact bodies Department of Physics, University of Guelph Capra 17, Pasadena, June 2014 Outline Goal and motivation Newtonian tides Relativistic tides Relativistic tidal dynamics Conclusion Goal and motivation Goal

More information

Black holes as particle accelerators: a brief review

Black holes as particle accelerators: a brief review Black holes as particle accelerators: a brief review Tomohiro Harada Department of Physics, Rikkyo University 15/10/2014, Seminar at Kobe University Based on arxiv:14097502 with Masashi Kimura (Cambridge)

More information

Astrophysics to be learned from observations of intermediate mass black hole in-spiral events. Alberto Vecchio

Astrophysics to be learned from observations of intermediate mass black hole in-spiral events. Alberto Vecchio Astrophysics to be learned from observations of intermediate mass black hole in-spiral events Alberto Vecchio Making Waves with Intermediate Mass Black Holes Three classes of sources IMBH BH(IMBH) IMBH

More information

THIRD-YEAR ASTROPHYSICS

THIRD-YEAR ASTROPHYSICS THIRD-YEAR ASTROPHYSICS Problem Set: Stellar Structure and Evolution (Dr Ph Podsiadlowski, Michaelmas Term 2006) 1 Measuring Stellar Parameters Sirius is a visual binary with a period of 4994 yr Its measured

More information

GRAVITATIONAL WAVES. Eanna E. Flanagan Cornell University. Presentation to CAA, 30 April 2003 [Some slides provided by Kip Thorne]

GRAVITATIONAL WAVES. Eanna E. Flanagan Cornell University. Presentation to CAA, 30 April 2003 [Some slides provided by Kip Thorne] GRAVITATIONAL WAVES Eanna E. Flanagan Cornell University Presentation to CAA, 30 April 2003 [Some slides provided by Kip Thorne] Summary of talk Review of observational upper limits and current and planned

More information

How well can gravitational waves pin down merging black holes?

How well can gravitational waves pin down merging black holes? How well can gravitational waves pin down merging black holes? Using gravitational wave information to point our telescopes and find the merger event on the sky Scott A. Hughes, MIT How do we measure GWs?

More information

The laws of binary black hole mechanics: An update

The laws of binary black hole mechanics: An update The laws of binary black hole mechanics: An update Laboratoire Univers et Théories Observatoire de Paris / CNRS A 1 Ω κ 2 z 2 Ω Ω m 1 κ A z m The laws of black hole mechanics [Hawking 1972, Bardeen, Carter

More information

High-Energy Astrophysics Lecture 6: Black holes in galaxies and the fundamentals of accretion. Overview

High-Energy Astrophysics Lecture 6: Black holes in galaxies and the fundamentals of accretion. Overview High-Energy Astrophysics Lecture 6: Black holes in galaxies and the fundamentals of accretion Robert Laing Overview Evidence for black holes in galaxies and techniques for estimating their mass Simple

More information

Head on Collision of Two Unequal Mass Black Holes

Head on Collision of Two Unequal Mass Black Holes Head on Collision of Two Unequal Mass Black Holes Peter Anninos (1) and Steven Bran (2) (1) National Center for Supercomputing Applications, Beckman Institute, 405 N. Mathews Avenue, Urbana, Illinois,

More information

arxiv: v1 [gr-qc] 17 Dec 2013

arxiv: v1 [gr-qc] 17 Dec 2013 The gravitational two-body problem in the vicinity of the light ring: Insights from the black-hole-ring toy model Shahar Hod The Ruppin Academic Center, Emeq Hefer 40250, Israel and arxiv:32.4969v [gr-qc]

More information

Black Hole-Neutron Star Binaries in General Relativity. Thomas Baumgarte Bowdoin College

Black Hole-Neutron Star Binaries in General Relativity. Thomas Baumgarte Bowdoin College Black Hole-Neutron Star Binaries in General Relativity Thomas Baumgarte Bowdoin College Keisuke Taniguchi, Joshua Faber, Stu Shapiro University of Illinois Numerical Relativity Solve Einstein s equations

More information

Charged particle motion around magnetized black hole

Charged particle motion around magnetized black hole Charged particle motion around magnetized black hole Martin Kološ, Arman Tursunov, Zdeněk Stuchĺık Silesian University in Opava, Czech Republic RAGtime workshop #19, 23-26 October, Opava 2017 Black hole

More information

DYNAMICS OF MIXED BINARIES

DYNAMICS OF MIXED BINARIES DYNAMICS OF MIXED BINARIES Luciano Rezzolla Albert Einstein Institute, Golm, Germany In collaboration with Frank Löffler & Marcus Ansorg [Phys. Rev. D 74 104018 (2006)] SISSA (Trieste, Italy), AEI (Golm,

More information

Classical and Quantum Dynamics in a Black Hole Background. Chris Doran

Classical and Quantum Dynamics in a Black Hole Background. Chris Doran Classical and Quantum Dynamics in a Black Hole Background Chris Doran Thanks etc. Work in collaboration with Anthony Lasenby Steve Gull Jonathan Pritchard Alejandro Caceres Anthony Challinor Ian Hinder

More information

CONTENTS. 1. Introduction. 2. General Relativistic Hydrodynamics. 3. Collapse of Differentially Rotating Stars. 4. Summary

CONTENTS. 1. Introduction. 2. General Relativistic Hydrodynamics. 3. Collapse of Differentially Rotating Stars. 4. Summary Collapse of Differentially Rotating Supermassive Stars: Post Black Hole Formation Stage Motoyuki Saijo (Rikkyo University, Japan) Ian Hawke (University of Southampton, UK) CONTENTS 1. Introduction 2. General

More information

15 Capra Ranch Meeting. Self-force driven inspiral of a scalar point particle into a Schwarzschild black hole: a progress report. Roland Haas Caltech

15 Capra Ranch Meeting. Self-force driven inspiral of a scalar point particle into a Schwarzschild black hole: a progress report. Roland Haas Caltech 15 Capra Ranch Meeting th Self-force driven inspiral of a scalar point particle into a Schwarzschild black hole: a progress report Roland Haas Caltech 1 Extreme Mass Ratio Inspirals Solar-mass, compact

More information

Self-force: foundations and formalism

Self-force: foundations and formalism University of Southampton June 11, 2012 Motivation Extreme-mass-ratio inspirals solar-mass neutron star or black hole orbits supermassive black hole m emits gravitational radiation, loses energy, spirals

More information

Introduction to Numerical Relativity

Introduction to Numerical Relativity APCTP Winter School, January 17-18, 2003 Introduction to Numerical Relativity RIKEN Institute, Computational Science Division, Hisaaki Shinkai 1. Subjects for Numerical Relativity Why Numerical Relativity?

More information

Newtonian instantaneous action at a distance General Relativity information carried by gravitational radiation at the speed of light

Newtonian instantaneous action at a distance General Relativity information carried by gravitational radiation at the speed of light Modern View of Gravitation Newtonian instantaneous action at a distance G µ = 8 µ # General Relativity information carried by gravitational radiation at the speed of light Gravitational Waves GR predicts

More information

Measuring the Whirling of Spacetime

Measuring the Whirling of Spacetime Measuring the Whirling of Spacetime Lecture series on Experimental Gravity (revised version) Kostas Glampedakis Prologue: does spin gravitate? M 1 M 2 System I: F = GM 1M 2 r 2 J 1 J 2 System II: M 1?

More information

Luc Blanchet, JGRG 22(2012) The first law of binary black hole dynamics RESCEU SYMPOSIUM ON GENERAL RELATIVITY AND GRAVITATION JGRG 22

Luc Blanchet, JGRG 22(2012) The first law of binary black hole dynamics RESCEU SYMPOSIUM ON GENERAL RELATIVITY AND GRAVITATION JGRG 22 Luc Blanchet, JGRG 22(2012)111503 The first law of binary black hole dynamics RESCEU SYMPOSIUM ON GENERAL RELATIVITY AND GRAVITATION JGRG 22 November 12-16 2012 Koshiba Hall, The University of Tokyo, Hongo,

More information

Gravity Waves and Black Holes

Gravity Waves and Black Holes Gravity Waves and Black Holes Mike Whybray Orwell Astronomical Society (Ipswich) 14 th March 2016 Overview Introduction to Special and General Relativity The nature of Black Holes What to expect when Black

More information

Spin and mass of the nearest supermassive black hole

Spin and mass of the nearest supermassive black hole Spin and mass of the nearest supermassive black hole Vyacheslav I. Dokuchaev Institute for Nuclear Research, Russian Academy of Sciences Moscow, Russia 16th Lomonosov Conference MSU, 2013 Rotating (a 1)

More information

Covariant Equations of Motion of Extended Bodies with Mass and Spin Multipoles

Covariant Equations of Motion of Extended Bodies with Mass and Spin Multipoles Covariant Equations of Motion of Extended Bodies with Mass and Spin Multipoles Sergei Kopeikin University of Missouri-Columbia 1 Content of lecture: Motivations Statement of the problem Notable issues

More information

FORMATION AND EVOLUTION OF COMPACT BINARY SYSTEMS

FORMATION AND EVOLUTION OF COMPACT BINARY SYSTEMS FORMATION AND EVOLUTION OF COMPACT BINARY SYSTEMS Main Categories of Compact Systems Formation of Compact Objects Mass and Angular Momentum Loss Evolutionary Links to Classes of Binary Systems Future Work

More information

GRAVITATIONAL WAVES FROM BINARY NEUTRON STARS AND TEST PARTICLE INSPIRALS INTO BLACK HOLES

GRAVITATIONAL WAVES FROM BINARY NEUTRON STARS AND TEST PARTICLE INSPIRALS INTO BLACK HOLES GRAVITATIONAL WAVES FROM BINARY NEUTRON STARS AND TEST PARTICLE INSPIRALS INTO BLACK HOLES A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of

More information

Scott A. Hughes, MIT SSI, 28 July The basic concepts and properties of black holes in general relativity

Scott A. Hughes, MIT SSI, 28 July The basic concepts and properties of black holes in general relativity The basic concepts and properties of black holes in general relativity For the duration of this talk ħ=0 Heuristic idea: object with gravity so strong that light cannot escape Key concepts from general

More information

Coalescing binary black holes in the extreme mass ratio limit

Coalescing binary black holes in the extreme mass ratio limit Coalescing binary black holes in the extreme mass ratio limit Alessandro Nagar Relativity and Gravitation Group, Politecnico di Torino and INFN, sez. di Torino www.polito.it/relgrav/ alessandro.nagar@polito.it

More information

Gravitational Wave Memory Revisited:

Gravitational Wave Memory Revisited: Gravitational Wave Memory Revisited: Memories from the merger and recoil Marc Favata Kavli Institute for Theoretical Physics Metals have memory too What is the GW memory? Generally think of GW s as oscillating

More information

The Lazarus Project. Black Hole Mergers: from simulation to observation

The Lazarus Project. Black Hole Mergers: from simulation to observation Built a model for binary black hole mergers which incorporate the best information available Use Lazarus results explore the interface between source modeling, data analysis The Lazarus Project Black Hole

More information

In deriving this we ve used the fact that the specific angular momentum

In deriving this we ve used the fact that the specific angular momentum Equation of Motion and Geodesics So far we ve talked about how to represent curved spacetime using a metric, and what quantities are conserved. Now let s see how test particles move in such a spacetime.

More information

Black Hole Mergers at Galactic. The Final Parsec: Supermassive. Centers. Milos Milosavljevic. California Institute of Technology

Black Hole Mergers at Galactic. The Final Parsec: Supermassive. Centers. Milos Milosavljevic. California Institute of Technology The Final Parsec: Supermassive Black Hole Mergers at Galactic Centers Milos Milosavljevic California Institute of Technology MBH Binaries Form in Galaxy Mergers Borne et al 2000 by transferring binding

More information

An introduction to gravitational waves. Enrico Barausse (Institut d'astrophysique de Paris/CNRS, France)

An introduction to gravitational waves. Enrico Barausse (Institut d'astrophysique de Paris/CNRS, France) An introduction to gravitational waves Enrico Barausse (Institut d'astrophysique de Paris/CNRS, France) Outline of lectures (1/2) The world's shortest introduction to General Relativity The linearized

More information

papers but GWs propagate on a curved background along null geodesics, in the geometrical optics approximation. 1 / 15

papers but GWs propagate on a curved background along null geodesics, in the geometrical optics approximation. 1 / 15 Standard sirens Since one obtains the chirp mass independently of the distance from the phase evolution, one can measure the luminosity) distance to a compact binary coalescence using just the GW observations

More information

Quasars and AGN. What are quasars and how do they differ from galaxies? What powers AGN s. Jets and outflows from QSOs and AGNs

Quasars and AGN. What are quasars and how do they differ from galaxies? What powers AGN s. Jets and outflows from QSOs and AGNs Goals: Quasars and AGN What are quasars and how do they differ from galaxies? What powers AGN s. Jets and outflows from QSOs and AGNs Discovery of Quasars Radio Observations of the Sky Reber (an amateur

More information

Fig. 1. On a sphere, geodesics are simply great circles (minimum distance). From

Fig. 1. On a sphere, geodesics are simply great circles (minimum distance). From Equation of Motion and Geodesics The equation of motion in Newtonian dynamics is F = m a, so for a given mass and force the acceleration is a = F /m. If we generalize to spacetime, we would therefore expect

More information

Gravitational Wave Memory Revisited:

Gravitational Wave Memory Revisited: Gravitational Wave Memory Revisited: Memory from binary black hole mergers Marc Favata Kavli Institute for Theoretical Physics arxiv:0811.3451 [astro-ph] and arxiv:0812.0069 [gr-qc] What is the GW memory?

More information

arxiv:gr-qc/ v1 23 Jan 1995

arxiv:gr-qc/ v1 23 Jan 1995 Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order Luc Blanchet 1, Thibault Damour 2,1, Bala R. Iyer 3, Clifford M. Will 4, and Alan G. Wiseman 5 1 Département d Astrophysique

More information

Gravitational Radiation from Encounters with Compact Binaries in Globular Clusters

Gravitational Radiation from Encounters with Compact Binaries in Globular Clusters Gravitational Radiation from Encounters with Compact Binaries in Globular Clusters Marianna Mao under the direction of Professor Edmund Bertschinger Sarah Vigeland Phillip Zukin Massachusetts Institute

More information

6 th lecture of Compact Object and Accretion, Master Programme at Leiden Observatory

6 th lecture of Compact Object and Accretion, Master Programme at Leiden Observatory 6 th lecture of Compact Object and Accretion, Master Programme at Leiden Observatory Accretion 1st class study material: Chapter 1 & 4, accretion power in astrophysics these slides at http://home.strw.leidenuniv.nl/~emr/coa/

More information

Post-Newtonian Approximation

Post-Newtonian Approximation Post-Newtonian Approximation Piotr Jaranowski Faculty of Physcis, University of Bia lystok, Poland 01.07.2013 1 Post-Newtonian gravity and gravitational-wave astronomy 2 3 4 EOB-improved 3PN-accurate Hamiltonian

More information

Self-force: Numerical Implementations

Self-force: Numerical Implementations Self-force: Numerical Implementations Barry Wardell University College Dublin 15th Capra Meeting On Radiation Reaction In General Relativity, University Of Maryland EMRIs A major goal of the Capra programme

More information

Introduction to General Relativity and Gravitational Waves

Introduction to General Relativity and Gravitational Waves Introduction to General Relativity and Gravitational Waves Patrick J. Sutton Cardiff University International School of Physics Enrico Fermi Varenna, 2017/07/03-04 Suggested reading James B. Hartle, Gravity:

More information

arxiv:astro-ph/ v1 25 Aug 1992

arxiv:astro-ph/ v1 25 Aug 1992 The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries Curt Cutler, (1) Theocharis A. Apostolatos, (1) Lars Bildsten, (1) Lee Samuel Finn, (2) Eanna E. Flanagan,

More information

arxiv:gr-qc/ v2 26 Feb 2007

arxiv:gr-qc/ v2 26 Feb 2007 Gravitational waves from Extreme Mass Ratio Inspirals in non-pure Kerr spacetimes Enrico Barausse 1, Luciano Rezzolla 2,3, David Petroff 4, and Marcus Ansorg 2 1 SISSA, International School for Advanced

More information

the astrophysics of emris

the astrophysics of emris the astrophysics of emris Capture of compact objects by SMBHs Pau Amaro Seoane August 2015, Astro-GR@Brazil 2015, ICTP-SAIFR Max-Planck Institute for Gravitational Physics (Albert Einstein Institute) capture

More information

The effect of f - modes on the gravitational waves during a binary inspiral

The effect of f - modes on the gravitational waves during a binary inspiral The effect of f - modes on the gravitational waves during a binary inspiral Tanja Hinderer (AEI Potsdam) PRL 116, 181101 (2016), arxiv:1602.00599 and arxiv:1608.01907? A. Taracchini F. Foucart K. Hotokezaka

More information

arxiv: v1 [gr-qc] 14 Dec 2007

arxiv: v1 [gr-qc] 14 Dec 2007 High accuracy simulations of Kerr tails: coordinate dependence and higher multipoles Manuel Tiglio, 1,2 Lawrence E. Kidder, 3 and Saul A. Teukolsky 3 1 Department of Physics and Astronomy, and Center for

More information

Centrifugal force in Kerr geometry

Centrifugal force in Kerr geometry Centrifugal force in Kerr geometry Sai Iyer and A R Prasanna Physical Research Laboratory Ahmedabad 380009 INDIA Abstract We have obtained the correct expression for the centrifugal force acting on a particle

More information

Strong gravity and relativistic accretion disks around supermassive black holes

Strong gravity and relativistic accretion disks around supermassive black holes Strong gravity and relativistic accretion disks around supermassive black holes Predrag Jovanović Astronomical Observatory, Volgina 7, 11060 Belgrade 38, SERBIA Abstract Here we used numerical simulations

More information

Searching for Intermediate Mass Black Holes mergers

Searching for Intermediate Mass Black Holes mergers Searching for Intermediate Mass Black Holes mergers G. A. Prodi, Università di Trento and INFN for the LIGO Scientific collaboration and the Virgo collaboration special credits to Giulio Mazzolo and Chris

More information