Are symmetric tidal streams possible with long-range dark-matter forces?

The unique dynamics of the tidal disruption of satellite galaxies is an extremely sensitive probe of long-range interactions between dark-matter particles. Dark-matter forces that are several percent the strength of gravity will lead to order unity changes in the ratio of the number of stars in the leading and trailing tidal streams of a satellite galaxy. The approximate symmetry of the stellar tidal streams of the Sagittarius dwarf galaxy would thus exclude attractive dark-matter forces greater than 10% the strength of gravity which would entirely eliminate the leading stream. However, recent simulations suggest that dark-matter forces 100% the strength of gravity could completely strip the stellar component of Sagittarius of its dark matter, allowing for the subsequent development of symmetric tidal streams. Here we argue that these simulations use inconsistent initial conditions corresponding to separate pure stellar and pure dark-matter satellites moving independently in the host galaxy's halo, rather than a single disrupting composite satellite as had been intended. A new simulation with different initial conditions, in particular a much more massive satellite galaxy, might demonstrate a scenario in which symmetric tidal streams develop in the presence of large dark-matter forces. This scenario must satisfy several highly restrictive criteria described in this paper.Comment: 11 pages, 4 figures, final PRD versio

Galilean Equivalence for Galactic Dark Matter

Satellite galaxies are tidally disrupted as they orbit the Milky Way. If dark matter (DM) experiences a stronger self-attraction than baryons, stars will preferentially gain rather than lose energy during tidal disruption, leading to an enhancement in the trailing compared to the leading tidal stream. The Sgr dwarf galaxy is seen to have roughly equal streams, challenging models in which DM and baryons accelerate differently by more than 10%. Future observations and a better understanding of DM distribution should allow detection of equivalence violation at the percent level

Tidal Tails Test the Equivalence Principle in the Dark Sector

Satellite galaxies currently undergoing tidal disruption offer a unique opportunity to constrain an effective violation of the equivalence principle in the dark sector. Theories in which cold dark matter (CDM) couples to a light scalar field naturally lead to a long-range force between dark matter particles. An inverse-square-law force of this kind would manifest itself as a violation of the equivalence principle in the dynamics of CDM compared to baryons in the form of gas or stars. In a previous paper, we showed that an attractive force would displace stars outwards from the bottom of the satellite's gravitational potential well, leading to a higher fraction of stars being disrupted from the tidal bulge further from the Galactic center. Since stars disrupted from the far (near) side of the satellite go on to form the trailing (leading) tidal stream, an attractive dark-matter force will produce a relative enhancement of the trailing stream compared to the leading stream. This distinctive signature of a dark-matter force might be detected through detailed observations of the tidal tails of a disrupting satellite, such as those recently performed by the Two-Micron All-Sky Survey (2MASS) and Sloan Digital Sky Survey (SDSS) on the Sagittarius (Sgr) dwarf galaxy. Here we show that this signature is robust to changes in our models for both the satellite and Milky Way, suggesting that we might hope to search for a dark-matter force in the tidal features of other recently discovered satellite galaxies in addition to the Sgr dwarf.Comment: 29 pages, 13 figures, final version published in PR

Can binary mergers produce maximally spinning black holes?

Gravitational waves carry away both energy and angular momentum as binary black holes inspiral and merge. The relative efficiency with which they are radiated determines whether the final black hole of mass $M_f$ and spin $S_f$ saturates the Kerr limit ($\chi_f \equiv S_f/M_f^2 \leq 1$). Extrapolating from the test-particle limit, we propose expressions for $S_f$ and $M_f$ for mergers with initial spins aligned or anti-aligned with the orbital angular momentum. We predict the the final spin at plunge for equal-mass non-spinning binaries to better than 1%, and that equal-mass maximally spinning aligned mergers lead to nearly maximally spinning final black holes ($\chi_f \simeq 0.9988$). We also find black holes can always be spun up by aligned mergers provided the mass ratio is small enough.Comment: 4 pages, 6 figues, sublitted to PR

Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $\tau$, during which the orbital angular momentum precesses about the total angular momentum by an angle $\alpha$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $\omega \equiv 2\pi/\tau$ and the precession frequency $\Omega \equiv \alpha/\tau$. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency $\Omega - n\omega$ for integer $n$. As black holes inspiral, they can pass through nutational resonances ($\Omega = n\omega$) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than $10^{-3}$ radians for nutational resonances at binary separations $r > 10M$. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate $n=0$ nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with $n$ providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.Comment: 18 pages, 9 figures, version published in PR

Binary black hole merger: symmetry and the spin expansion

We regard binary black hole (BBH) merger as a map from a simple initial state (two Kerr black holes, with dimensionless spins {\bf a} and {\bf b}) to a simple final state (a Kerr black hole with mass m, dimensionless spin {\bf s}, and kick velocity {\bf k}). By expanding this map around {\bf a} = {\bf b} = 0 and applying symmetry constraints, we obtain a simple formalism that is remarkably successful at explaining existing BBH simulations. It also makes detailed predictions and suggests a more efficient way of mapping the parameter space of binary black hole merger. Since we rely on symmetry rather than dynamics, our expansion complements previous analytical techniques.Comment: 4 pages, 4 figures, matches Phys. Rev. Lett. versio

precession: Dynamics of spinning black-hole binaries with python

This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevD.93.124066We present the numerical code precession, a new open-source python module to study the dynamics of precessing black-hole binaries in the post-Newtonian regime. The code provides a comprehensive toolbox to (i) study the evolution of the black-hole spins along their precession cycles, (ii) perform gravitational-wave-driven binary inspirals using both orbit-averaged and precession-averaged integrations, and (iii) predict the properties of the merger remnant through fitting formulas obtained from numerical-relativity simulations. precession is a ready-to-use tool to add the black-hole spin dynamics to larger-scale numerical studies such as gravitational-wave parameter estimation codes, population synthesis models to predict gravitational-wave event rates, galaxy merger trees and cosmological simulations of structure formation. precession provides fast and reliable integration methods to propagate statistical samples of black-hole binaries from/to large separations where they form to/from small separations where they become detectable, thus linking gravitational-wave observations of spinning black-hole binaries to their astrophysical formation history. The code is also a useful tool to compute initial parameters for numerical-relativity simulations targeting specific precessing systems. precession can be installed from the python Package Index, and it is freely distributed under version control on github, where further documentation is provided.D. G. is supported by the UK STFC and the Isaac Newton Studentship of the University of Cambridge. Partial support is also acknowledged from the Royal Astronomical Society, Darwin College of the University of Cambridge, the Cambridge Philosophical Society, the H2020 ERC Consolidator Grant No. MaGRaTh–646597, the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904, the STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet and TACC Stampede clusters through NSF-XSEDE Award No. PHY-090003, the Cambridge High Performance Computing Service Supercomputer Darwin using Strategic Research Infrastructure Funding from the HEFCE and the STFC, and DiRAC’s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grants No. ST/H008586/1 and No. ST/K00333X/1. M. K. is supported by Alfred P. Sloan Foundation Grant No. FG-2015-65299 and NSF Grant No. PHY-1607031

Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation

We study the influence of astrophysical formation scenarios on the precessional dynamics of spinning black-hole binaries by the time they enter the observational window of second- and third-generation gravitational-wave detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA and the Einstein Telescope. Under the plausible assumption that tidal interactions are efficient at aligning the spins of few-solar mass black-hole progenitors with the orbital angular momentum, we find that black-hole spins should be expected to preferentially lie in a plane when they become detectable by gravitational-wave interferometers. This "resonant plane" is identified by the conditions \Delta\Phi=0{\deg} or \Delta\Phi=+/-180{\deg}, where \Delta\Phi is the angle between the components of the black-hole spins in the plane orthogonal to the orbital angular momentum. If the angles \Delta \Phi can be accurately measured for a large sample of gravitational-wave detections, their distribution will constrain models of compact binary formation. In particular, it will tell us whether tidal interactions are efficient and whether a mechanism such as mass transfer, stellar winds, or supernovae can induce a mass-ratio reversal (so that the heavier black hole is produced by the initially lighter stellar progenitor). Therefore our model offers a concrete observational link between gravitational-wave measurements and astrophysics. We also hope that it will stimulate further studies of precessional dynamics, gravitational-wave template placement and parameter estimation for binaries locked in the resonant plane.Comment: 26 pages, 11 figures, 3 tables, accepted in Physical Review D. 4 movies illustrating resonance locking are available online: for links, see footnote 8 of the pape

Transition from adiabatic inspiral to plunge into a spinning black hole

A test particle of mass mu on a bound geodesic of a Kerr black hole of mass M >> mu will slowly inspiral as gravitational radiation extracts energy and angular momentum from its orbit. This inspiral can be considered adiabatic when the orbital period is much shorter than the timescale on which energy is radiated, and quasi-circular when the radial velocity is much less than the azimuthal velocity. Although the inspiral always remains adiabatic provided mu << M, the quasi-circular approximation breaks down as the particle approaches the innermost stable circular orbit (ISCO). In this paper, we relax the quasi-circular approximation and solve the radial equation of motion explicitly near the ISCO. We use the requirement that the test particle's 4-velocity remain properly normalized to calculate a new contribution to the difference between its energy and angular momentum. This difference determines how a black hole's spin changes following a test-particle merger, and can be extrapolated to help predict the mass and spin of the final black hole produced in finite-mass-ratio black-hole mergers. Our new contribution is particularly important for nearly maximally spinning black holes, as it can affect whether a merger produces a naked singularity.Comment: 9 pages, 6 figures, final version published in PRD with minor change