Extreme Mass Ratio Research Articles

Black (W)hole: An Artscience and Education Collaboration

Black (W)hole is an immersive art installation created collaboratively by artists and scientists utilizing data visualization of an extreme mass ratio inspiral (EMRI) and the sonification of its emitted gravitational waves in an experiential work of “artscience” and science education. The sensory-rich environment of the installation engages mind and body, expanding and enriching the participant’s capacity to imagine and wonder about the beauty and meaning of this highly abstract astronomical object, the black hole. The work investigates both historical and current gravitational wave astronomy, illustrating our 21st-century understanding of the cosmos.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

The Regge–Wheeler–Zerilli (RWZ) wave-equation describes Schwarzschild–Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of $\ell$, and in doing so develop an efficient new method for generating the MST renormalised angular momentum, $\nu$.

FOLLOW-UP PHOTOMETRY OF TWO NEW ECLIPSING PCEBs FROM THE SLOAN DIGITAL SKY SURVEY

In this work, we present the result of our follow-up observations of SDSS J092741.73+332959.1 and SDSS J130733.49+215636.7 using the 2.35 m Thai National Telescope and ULTRASPEC instrument. Both systems are listed among the recently found white dwarf main sequence binaries from the Sloan Digital Sky Survey. SDSS J092741.73+332959.1 is a new PCEB with a period of 2.3 days, the longest orbital period known to date for white dwarf binaries. SDSS J130733.49+215636.7 is confirmed to be an eclipsing system with a period of 0.21 days from the Catalina Survey's light curve, however the parameters for the white dwarf are still uncertain. Our goal is to determine precise parameters for both systems using the Binary Maker 3 software. The observation for SDSS J0927+3329 was done on 9 January 2014 in the SDSS r' filter while the data for SDSS J1307+2156 were taken in the z' filter on 27 April 2014. Our models show that the red dwarf companions in both systems are well constrained inside their Roche Lobes. We find that the binary M2/M1 ratio in SDSS J0927+3329 is close to 0.5, with white dwarf and M-dwarf temperatures of 12000 K and 3300 K, respectively. Our preliminary result for SDSS J1307+2156 show that this system has an extreme mass ratio of 0.3. The white dwarf in this system has a temperature of 7500 K and the companion star has an effective temperature of 3150 K.

Measuring Intermediate-Mass Black-Hole Binaries with Advanced Gravitational Wave Detectors.

We perform a systematic study to explore the accuracy with which the parameters of intermediate-mass black-hole binary systems can be measured from their gravitational wave (GW) signatures using second-generation GW detectors. We make use of the most recent reduced-order models containing inspiral, merger, and ringdown signals of aligned-spin effective-one-body waveforms to significantly speed up the calculations. We explore the phenomenology of the measurement accuracies for binaries with total masses between 50M(⊙) and 500M(⊙) and mass ratios between 0.1 and 1. We find that (i) at total masses below ∼200M(⊙), where the signal-to-noise ratio is dominated by the inspiral portion of the signal, the chirp mass parameter can be accurately measured; (ii) at higher masses, the information content is dominated by the ringdown, and total mass is measured more accurately; (iii) the mass of the lower-mass companion is poorly estimated, especially at high total mass and more extreme mass ratios; and (iv) spin cannot be accurately measured for our injection set with nonspinning components. Most importantly, we find that for binaries with nonspinning components at all values of the mass ratio in the considered range and at a network signal-to-noise ratio of 15, analyzed with spin-aligned templates, the presence of an intermediate-mass black hole with mass >100M(⊙) can be confirmed with 95% confidence in any binary that includes a component with a mass of 130M(⊙) or greater.

DISCOVERY OF A LOW-MASS COMPANION AROUND HR 3549

We report the discovery of a low-mass companion to HR3549, an A0V star surrounded by a debris disk with a warm excess detected by WISE at 22 $\mu$m ($10\sigma$ significance). We imaged HR3549 B in the L-band with NAOS-CONICA, the adaptive optics infrared camera of the Very Large Telescope, in January 2013 and confirmed its common proper motion in January 2015. The companion is at a projected separation of $\simeq 80$ AU and position angle of $\simeq 157^\circ$, so it is orbiting well beyond the warm disk inner edge of $r > 10$ AU. Our age estimate for this system corresponds to a companion mass in the range 15-80 $M_J$, spanning the brown dwarf regime, and so HR3549 B is another recent addition to the growing list of brown dwarf desert objects with extreme mass ratios. The simultaneous presence of a warm disk and a brown dwarf around HR3549 provides interesting empirical constraints on models of the formation of substellar companions.

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'\^{e}tre}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.

A SIMPLE ANALYTICAL MODEL FOR GAPS IN PROTOPLANETARY DISKS

An analytical model is presented for calculating the surface density as a function of radius in protoplanetary disks in which a planet has opened a gap. This model is also applicable to circumbinary disks with extreme binary mass ratios. The gap profile can be solved for algebraically, without performing any numerical integrals. In contrast with previous one-dimensional gap models, this model correctly predicts that low-mass (sub-Jupiter) planets can open gaps in sufficiently low-viscosity disks, and it correctly recovers the power-law dependence of gap depth on planet-to-star mass ratio q, disk aspect ratio , and dimensionless viscosity ? found in previous numerical studies. Analytical gap profiles are compared with numerical calculations over a range of parameter space in q, , and ?, demonstrating accurate reproduction of the ?partial gap? regime, and general agreement over a wide range of parameter space.

An ignored high fill-out, extreme mass ratio contact binary V1222 Tauri

Abstract Two color light curves of V1222 Tau were analyzed by using the latest version of the W–D code. The results show that V1222 Tau is an extreme mass ratio (q = 8.884 ± 0.149), high fill-out (f = 53.2% ± 1.9%) contact binary system. The period of V1222 Tau might have a parabolic variation according to a preliminary (O − C) analysis, with a possibly large long-term increase rate, dP/dt = +8.19 × 10−6 d yr−1.

Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III. Spin-orbit coupling revisited

The first- and second-order dissipative self force and the first order conservative self force are applied together with spin-orbit coupling to the quasi-circular motion of a test mass in the spacetime of a Schwarzschild black hole, for extreme or intermediate mass ratios. The partial dephasing of the gravitational waveform (at the order that is independent of the system's mass ratio) due to the self force is compared with that of spin-orbit coupling. We find that accurate waveforms for parameter estimation need to include both effects. Specifically, we find a particular value for the spin parameter such that the spin-orbit effect cancels out the self-force effect on the waveform. Exclusion of dephasing effects that are independent of the mass ratio therefore might lead to a non-perturbative error in the estimation of the system's parameters.

FIRST PRECISION LIGHT CURVE ANALYSIS OF THE NEGLECTED EXTREME MASS RATIO SOLAR-TYPE BINARY HR BOOTIS

HR Bootis is a neglected binary that is found to be a solar-type (G2V) extreme mass ratio binary (EMRB). It was discovered by Hanley & Shapley in 1940. Surprisingly, little has been published in the intervening years. In 1999 it was characterized by a 0.31587 day orbital period. Since that time it has been observed by various observers who have determined ?20 timings of minimum light over the past ?15,000 orbits. Our observations in 2012 represent the first precision curves in the BVRcIc Johnson?Cousins wavelength bands. The light curves have rather low amplitudes, averaging some 0.5 magnitudes, yet they exhibit total eclipses, which is typical of the rare group of solar-type EMRBs. An improved linear ephemeris was computed along with a quadratic ephemeris showing a decaying orbit, which indicates magnetic breaking may be occurring. The light curve solution reveals that HR Boo is a contact system with a somewhat low 21% Roche-lobe fill-out but a mass ratio of q = 4.09 (0.2444), which defines it as an EMRB. Two spots, both hot, were allowed to iterate to fit the light curve asymmetries. Their radii are 32? and 16?. Both are high-latitude polar spots indicative of strong magnetic activity. The shallow contact yet nearly equal component temperatures makes it an unusual addition to this group.

Orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period

ASTROD-GW (ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (EMRIs) and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The 3 spacecrafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD-GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry (TDI) for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precession-period. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° (no inclination), 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.

A NEW CLASS OF NASCENT ECLIPSING BINARIES WITH EXTREME MASS RATIOS

Early B-type main-sequence (MS) stars (M$_1$ = 5-16 M$_{\odot}$) with closely orbiting low-mass stellar companions (q = M$_2$/M$_1$ < 0.25) can evolve to produce Type Ia supernovae, low-mass X-ray binaries, and millisecond pulsars. However, the formation mechanism and intrinsic frequency of such close extreme mass-ratio binaries have been debated, especially considering none have hitherto been detected. Utilizing observations of the Large Magellanic Cloud galaxy conducted by the Optical Gravitational Lensing Experiment, we have discovered a new class of eclipsing binaries in which a luminous B-type MS star irradiates a closely orbiting low-mass pre-MS companion that has not yet fully formed. The primordial pre-MS companions have large radii and discernibly reflect much of the light they intercept from the B-type MS primaries ($\Delta$I$_{\rm refl}$ = 0.02-0.14 mag). For the 18 definitive MS + pre-MS eclipsing binaries in our sample with good model fits to the observed light curves, we measure short orbital periods P = 3.0-8.5 days, young ages $\tau$ = 0.6-8 Myr, and small secondary masses M$_2$ = 0.8-2.4 M$_{\odot}$ (q = 0.07-0.36). The majority of these nascent eclipsing binaries are still associated with stellar nurseries, e.g. the system with the deepest eclipse $\Delta$I$_1$ = 2.8 mag and youngest age $\tau$ = 0.6$\pm$0.4 Myr is embedded in the bright H II region 30 Doradus. After correcting for selection effects, we find that (2.0$\pm$0.6)% of B-type MS stars have companions with short orbital periods P = 3.0-8.5 days and extreme mass ratios q = 0.06-0.25. This is $\approx$10 times greater than that observed for solar-type MS primaries. We discuss how these new eclipsing binaries provide invaluable insights, diagnostics, and challenges for the formation and evolution of stars, binaries, and H II regions.

CVs Around the Minimum Orbital Period

We discussed features of Cataclysmic Variables at the period minimum. In general, most of them must be WZ Sge-type objects. Main characteristics of the prototype star (WZ Sge) are discussed. A part of WZ Sge-type objects has evolved past the period limit and formed the bounce back systems. We also explore conditions and structure of accretion disks in such systems. We show that the accretion disk in a system with extreme mass ratio grows in size reaching a 2:1 resonance radius and are relatively cool. They also become largely optically thin in the continuum, contributing to the total flux less than the stellar components of the system. In contrast, the viscosity and the temperature in spiral arms formed at the outer edge of the disk are higher and their contribution in continuum plays an increasingly important role. We model such disks and generate light curves which successfully simulate the observed double-humped light curves in the quiescence.

UBVRIANALYSIS OF THE TOTALLY ECLIPSING EXTREME MASS RATIO W UMa BINARY, GSC 3208 1986

GSC 3208 1986 is an NSVS and TYCHO binary, first observed from 1999 to 2000. It is a W UMa binary with a period of 0.405 days. The present observations were taken in 2012 September and are of high precision, averaging a standard deviation of better than 5 mmag. The amplitude of the light curve is very nearly 0.5 mag yet it undergoes total eclipses. Dominion Astrophysical Observatory spectra give an F3V type ( K) for the system, the earliest of the extreme mass ratio W UMa binaries. The linear period determination of 0.4045672 days was calculated with the two sets of epochs available. An early NSVS light curve reveals that the period has been smoothly decreasing over its past 12,000 orbits. The binary may be undergoing sinusoidal oscillations due to the presence of a third body, possibly with a period of years. The high inclination of 85° results in a long duration secondary total eclipse, lasting some 49.5 minutes. Findings indicate that GSC 3208 1986 is an immaculate extreme mass ratio, q(m2/m1) = 0.24, A-type W UMa binary.

Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits

Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-motion binary orbits. We use black hole perturbation theory, so our results assume extreme mass ratios. We develop tools to compute the distortion to a black hole's curvature for any spin parameter, and for tidal fields arising from any bound orbit, in the frequency domain. We also develop tools to visualize the horizon's distortion for black hole spin $a/M\ensuremath{\le}\sqrt{3}/2$ (leaving the more complicated $a/Mg\sqrt{3}/2$ case to a future analysis). We then study how a Kerr black hole's event horizon is distorted by a small body in a circular, equatorial orbit. We find that the connection between the geometry of tidal distortion and the orbit's evolution is not as simple as in the Newtonian limit.

Ballistic orbits in Schwarzschild space-time and gravitational waves from EMR binary mergers

We describe a special class of ballistic geodesics in Schwarzschild space-time, extending to the horizon in the infinite past and future of observer time, which are characterized by the property that they are in 1–1 correspondence, and completely degenerate in energy and angular momentum, with stable circular orbits. We derive analytic expressions for the source terms in the Regge–Wheeler and Zerilli–Moncrief equations for a point-particle moving on such a ballistic orbit, and compute the gravitational waves emitted during the infall in an extreme mass ratio black-hole binary coalescence. In this way a geodesic approximation to the plunge phase of compact binaries is obtained.

The VAST Survey – IV. A wide brown dwarf companion to the A3V star ζ Delphini★

We report the discovery of a wide co-moving substellar companion to the nearby ($D=67.5\pm1.1$ pc) A3V star $\zeta$ Delphini based on imaging and follow-up spectroscopic observations obtained during the course of our Volume-limited A-Star (VAST) multiplicity survey. $\zeta$ Del was observed over a five-year baseline with adaptive optics, revealing the presence of a previously-unresolved companion with a proper motion consistent with that of the A-type primary. The age of the $\zeta$ Del system was estimated as $525\pm125$ Myr based on the position of the primary on the colour-magnitude and temperature-luminosity diagrams. Using intermediate-resolution near-infrared spectroscopy, the spectrum of $\zeta$ Del B is shown to be consistent with a mid-L dwarf (L$5\pm2$), at a temperature of $1650\pm200$ K. Combining the measured near-infrared magnitude of $\zeta$ Del B with the estimated temperature leads to a model-dependent mass estimate of $50\pm15$ M$_{\rm Jup}$, corresponding to a mass ratio of $q=0.019\pm0.006$. At a projected separation of $910\pm14$ au, $\zeta$ Del B is among the most widely-separated and extreme-mass ratio substellar companions to a main-sequence star resolved to-date, providing a rare empirical constraint of the formation of low-mass ratio companions at extremely wide separations.

HELIOSEISMOLOGY AND ASTEROSEISMOLOGY: LOOKING FOR GRAVITATIONAL WAVES IN ACOUSTIC OSCILLATIONS

Current helioseismology observations allow the determination of the frequencies and surface velocity amplitudes of solar acoustic modes with exceptionally high precision. In some cases, the frequency accuracy is better than one part in a million. We show that there is a distinct possibility that the quadrupole acoustic modes of low order could be excited by gravitational waves (GWs), if the GWs have a strain amplitude in the range $10^{-20}h_{-20}$ with $h_{-20}\sim 1$ or $h_{-20}\sim 10^{3}$, as predicted by several types of GW sources, such as galactic ultracompact binaries or extreme mass ratio inspirals and coalescence of black holes. If the damping rate at low order is $ 10^{-3}\eta_N$ $\mu{\rm Hz}$, with $\eta_N\sim 10^{-3} $ - $1,$ as inferred from the theory of stellar pulsations, then GW radiation will lead to a maximum rms surface velocity amplitude of quadrupole modes of the order of $h_{-20}\eta_N^{-1}\sim$ $10^{-9}$ - $10^{-3}$ ${\rm cm\; s^{-1}}$, on the verge of what is currently detectable via helioseismology. The frequency and sensitivity range probed by helioseismological acoustic modes overlap with, and complement, the capabilities of eLISA for the brightest resolved ultracompact galactic binaries.

Simultaneous optical and near-IR photometry of 4U1957+115 - a missing secondary star

We report the results of quasi-simultaneous optical and NIR photometry of the low-mass X-ray binary, 4U 1957+115. Our observations cover B, V, R, I, J, H and K-bands and additional time-series NIR photometry. We measure a spectral energy distribution, which can be modelled using a standard multi-temperature accretion disc, where the disc temperature and radius follow a power-law relation. Standard accretion disc theory predicts the power law exponent to be -3/4, and this yields, perhaps surprisingly, acceptable fits to our SED. Given that the source is a persistent X-ray source, it is however likely that the accretion disc temperature distribution is produced by X-ray heating, regardless of its radial dependence. Furthermore, we find no evidence for any emission from the secondary star at any wavelength. However, adding a secondary component to our model allows us to derive a 99\% lower limit of 14 or 15 kpc based on Monte Carlo simulations and using either an evolved K2 or G2V secondary star respectively. In $>$60\% of cases the distance is $>$80kpc. Such large distances favor models with a massive ($>$15 M$_{\odot}$) black hole primary. Our quasi-simultaneous J and V-band time-series photometry, together with the SED, reveals that the optical/NIR emission must originate in the same region i.e. the accretion disc. The likely extreme mass ratio supports suggestions that the accretion disc must be precessing which, depending on the length of the precession period, could play a major part in explaining the variety of optical light curve shapes obtained over the last two decades.