Dimensionless Spin Parameter Research Articles

Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars

In our previous work (Paper I) we applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central compact object in three Galactic microquasars assuming the possibility that the central compact body is a super-spinning object (or a naked singularity) with external spacetime described by Kerr geometry with a dimensionless spin parameter $a\equiv cJ/GM^2>1$. Here we extend our consideration, and in a consistent way investigate implications of a set of ten resonance models so far discussed only in the context of $a<1$. The same physical arguments as in Paper I are applied to these models, i.e. only a small deviation of the spin estimate from $a=1$, $a\gtrsim 1$, is assumed for a favoured model. For five of these models that involve Keplerian and radial epicyclic oscillations we find the existence of a unique specific QPO excitation radius. Consequently, there is a simple behaviour of dimensionless frequency $M\times\nu_{U}(a)$ represented by a single continuous function having solely one maximum close to $a\gtrsim1$. Only one of these models is compatible with the expectation of $a\gtrsim 1$. The other five models that involve the radial and vertical epicyclic oscillations imply the existence of multiple resonant radii. This signifies a more complicated behaviour of $M\times\nu_{U}(a)$ that cannot be represented by single functions. Each of these five models is compatible with the expectation of $a\gtrsim 1$.

Constraint on the black hole spin of M87 from the accretion-jet model

Abstract The millimetre bump, as found in high-resolution multiwaveband observations of M87 by Prieto et al., most possibly comes from the synchrotron emission of thermal electrons in advection-dominated accretion flow (ADAF). It is possible to constrain the accretion rate near the horizon if both the nuclear millimetre emission and its polarization are produced by the hot plasma in the accretion flow. The jet power of M87 has been extensively explored, which is around $8_{\rm -3}^{+7}\times 10^{42}$ erg s−1 based on the analysis of the X-ray cavity. The black hole (BH) spin can be estimated if the jet power and the accretion rate near the horizon are known. We model the multiwavelength spectral energy distribution (SED) of M87 with a coupled ADAF–jet model surrounding a Kerr BH, where the full set of relativistic hydrodynamical equations of the ADAF are solved. The hybrid jet formation model, as a variant of the Blandford–Znajek model, is used to model the jet power. We find that the SMBH should be fast rotating with a dimensionless spin parameter $a_{*}\simeq 0.98_{\rm -0.02}^{+0.012}$.

A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with NuStar

Abstract We present NuSTAR observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, , of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K α line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be ISCO (innermost stable circular orbit), assuming a dimensionless spin parameter , and ISCO for (errors quoted at 1σ). This value proves to be model independent. For and , for example, 1.08 ± 0.06 ISCO translates to a physical radius of km, and the NS would have to be smaller than this radius (other outcomes are possible for allowed spin parameters and masses). For GX 17+2, ISCO for and ISCO for . For and , ISCO translates to km. The inner accretion disk in 4U 1705-44 may be truncated just above the stellar surface, perhaps by a boundary layer or magnetosphere; reflection models give a radius of 1.46–1.64 ISCO for and 1.69–1.93 ISCO for . We discuss the implications our results may have on the equation of state of ultradense, cold matter and our understanding of the innermost accretion flow onto NSs with low surface magnetic fields, and systematic errors related to the reflection models and spacetime metric around less idealized NSs.

Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence

We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, accounting for all the spin-weighted quadrupolar modes, and separately accounting for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported in LVC_PE[1] (at 90% confidence), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Followup simulations performed using previously-estimated binary parameters most resemble the data. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz \in [64 - 82M_\odot], mass ratio q = m2/m1 \in [0.6,1], and effective aligned spin \chi_eff \in [-0.3, 0.2], where \chi_{eff} = (S1/m1 + S2/m2) \cdot\hat{L} /M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and \chi_{eff} are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z between 64.0 - 73.5M_\odot and the final black hole's dimensionless spin parameter is consistent with af = 0.62 - 0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to LVC_PE[1].

THE SPIN OF THE BLACK HOLE IN THE X-RAY BINARY NOVA MUSCAE 1991

ABSTRACT The bright soft X-ray transient Nova Muscae 1991 was intensively observed during its entire eight-month outburst using the Large Area Counter on board the Ginga satellite. Recently, we obtained accurate estimates of the mass of the black hole primary, the orbital inclination angle of the system, and the distance. Using these crucial input data and Ginga X-ray spectra, we have measured the spin of the black hole using the continuum-fitting method. For four X-ray spectra of extraordinary quality we have determined the dimensionless spin parameter of the black hole to be (1σ confidence level), a result that we confirm using 11 additional spectra of lower quality. Our spin estimate challenges two published results: it is somewhat higher than the value predicted by a proposed relationship between jet power and spin; and we find that the spin of the black hole is decidedly prograde, not retrograde as has been claimed.

A key factor to the spin parameter of uniformly rotating compact stars: crust structure

We study the dimensionless spin parameter j ≡ cJ/(GM2) of different kinds of uniformly rotating compact stars, including traditional neutron stars, hyperonic neutron stars and hybrid stars, based on relativistic mean field theory and the MIT bag model. It is found that jmax ∼ 0.7, which had been suggested in traditional neutron stars, is sustained for hyperonic neutron stars and hybrid stars with M > 0.5 M⊙. Not the interior but rather the crust structure of the stars is a key factor to determine jmax for three kinds of selected compact stars. Furthermore, a universal formula j = 0.63(f/fK) − 0.42(f/fK)2 + 0.48(f/fK)3 is suggested to determine the spin parameter at any rotational frequency f smaller than the Keplerian frequency fK.

Hyperon Effects on the Spin Parameter of Rotating Neutron Stars**Supported by the National Natural Science Foundation of China under Grant Nos 11175108, U1432119, 1146114100, 11205075, 11375076 and 11475104, the Shandong Natural Science Foundation under Grant No ZR2014AQ012, and the Foundation of Shandong University under Grant No 2015WHWLJH01.

Based on the equations of state from the relativistic mean field theory without and with the inclusion of strangeness-bearing hyperons, we study the dimensionless spin parameter j = cJ/(GM2) of uniformly rotating neutron stars. It is shown that the maximum value of the spin parameter jmax of a neutron star rotating at the Keplerian frequency fK is jmax ∼ 0.7 when the star mass M > 0.5M⊙, which is sustained for various versions of equations of state without and with hyperons. The relationship between j and the scaled rotation frequency f/fK is found to be insensitive to the star mass or the adopted equation of state in the models without hyperons. However, the emergence of hyperons in neutron stars will lead to an uncertainty of the spin parameter j, which in turn could generate a complexity in the theoretical study of the quasi-periodic oscillations observed in disk-accreting compact-star systems.

Shadow of noncommutative geometry inspired black hole

In this paper, the shadow casted by the rotating black hole inspired by noncommutative geometry is investigated. In addition to the dimensionless spin parameter a/M0 with M0 black hole mass and inclination angle i, the dimensionless noncommutative parameter √ϑ/M0 is also found to affect the shape of the black hole shadow. The result shows that the size of the shadow slightly decreases with the parameter √ϑ/M0, while the distortion increases with it. Compared to the Kerr black hole, the parameter √ϑ/M0 increases the deformation of the shadow. This may offer a way to distinguish noncommutative geometry inspired black hole from Kerr one via astronomical instruments in the near future.

Black hole-neutron star binary merger: Dependence on black hole spin orientation and equation of state

We systematically performed numerical-relativity simulations for black hole (BH) - neutron star (NS) binary mergers with a variety of the BH spin orientation and equations of state (EOS) of the NS. The initial misalignment angles of the BH spin are chosen in the range of i_tilt,0 = 30--90[deg.]. We employed four models of NS EOS with which the compactness of the NS is in the range of C = M_NS/R_NS = 0.138--0.180, where M_NS and R_NS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q = M_BH/M_NS, and the dimensionless spin parameter of the BH, chi, are chosen to be Q = 5 and chi = 0.75, together with M_NS = 1.35 M_sun. We obtain the following results: (i) The inclination angle of i_tilt,0 < 70[deg.] and i_tilt,0 < 50[deg.] are required for the formation of a remnant disk with its mass larger than 0.1 M_sun for the case C = 0.140 and C = 0.160, respectively, while the disk mass is always smaller than 0.1M_sun for C = 0.175. The ejecta with its mass larger than 0.01 M_sun is obtained for i_tilt,0 < 85[deg.] with C = 0.140, for i_tilt,0 < 65[deg.] with C = 0.160, and for i_tilt,0 < 30[deg.] with C = 0.175. (ii) The rotational axis of the dense part of the remnant disk is approximately aligned with the remnant BH spin for i_tilt,0 = 30[deg.]. On the other hand, the disk axis is misaligned initially with ~ 30[deg.] for i_tilt,0 = 60[deg.], and the alignment with the remnant BH spin is achieved at ~ 50--60 ms after the onset of merger. The accretion time scale of the remnant disk is typically ~ 100 ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically ~ 0.2--0.3c and depends only weakly on i_tilt,0 and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for i_tilt,0 < 60[deg.].

Gravitational waves from a particle in circular orbits around a rotating black hole to the 11th post-Newtonian order

We compute the energy flux of the gravitational waves radiated by a particle of mass |$\mu$| in circular orbits around a rotating black hole of mass |$M$| up to the 11th post-Newtonian order (11PN), i.e. |$v^{22}$| beyond the leading Newtonian approximation where |$v$| is the orbital velocity of the particle [L. Blanchet, Living Rev. Relativity 5, 3 (2002)]. By comparing the PN results for the energy flux with high-precision numerical results in black hole perturbation theory, we find the region of validity in the PN approximation becomes larger with increasing PN order. If one requires the relative error of the energy flux in the PN approximation to be less than |$10^{-5}$|⁠, the energy flux at 11PN (4PN) can be used for |$v\lessapprox 0.33$| (⁠|$v \lessapprox 0.13$|⁠). The region of validity can be further extended to |$v\lessapprox 0.4$| if one applies a resummation method to the energy flux at 11PN. We then compare the orbital phase during a two-year inspiral from the PN results with the high-precision numerical results. We find that, for late (early) inspirals when |$q\le 0.3$| (⁠|$q\le 0.9$|⁠), where |$q$| is the dimensionless spin parameter of the black hole, the difference in the phase is less than 1 (⁠|$10^{-4}$|⁠) rad and hence these inspirals may be detected in the data analysis for space detectors such as eLISA|$/$|New Gravitational wave Observatory by the PN templates. We also compute the energy flux radiated into the event horizon for a particle in circular orbits around a non-rotating black hole at 22.5PN, i.e. |$v^{45}$| beyond the leading Newtonian approximation, which is comparable to the PN order derived in our previous work for the energy flux to infinity at 22PN.

Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars

We have previously applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central Kerr black hole in the three Galactic microquasars, GRS 1915+105, GRO J1655-40, and XTE J1550-564. Here we explore the alternative possibility that the central compact body is a super-spinning object (or a naked singularity) with the external space-time described by Kerr geometry with a dimensionless spin parameter a = cJ/GM2 > 1.We calculate the relevant spin intervals for a subset of HF QPO models considered in the previous study. Our analysis indicates that for all but one of the considered models there exists at least one interval of a > 1 that is compatible with constraints given by the ranges of the central compact object mass independently estimated for the three sources. For most of the models, the inferred values of a are several times higher than the extreme Kerr black hole value a = 1. These values may be too high since the spin of superspinars is often assumed to rapidly decrease due to accretion when a >> 1. In this context, we conclude that only the epicyclic and the Keplerian resonance model provides estimates that are compatible with the expectation of just a small deviation from a = 1.

A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime

We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the Teukode code are presented. The code can efficiently deliver waveforms at future null infinity. The accuracy and convergence of the waveforms’ phase and amplitude is demonstrated. As a first application of the method, we compute the gravitational waveforms from inspiraling and coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass black hole is modeled as a point particle whose dynamics is driven by an effective-one-body-resummed analytical radiation reaction force. We compare the analytical, mechanical angular momentum loss (computed using two different prescriptions) to the gravitational wave angular momentum flux. We find that higher-order post-Newtonian corrections are needed to improve the consistency for rapidly spinning binaries. We characterize the multipolar waveform as a function of the black-hole spin. Close to merger, the subdominant multipolar amplitudes (notably the m = 0 ones) are enhanced for retrograde orbits with respect to prograde ones. We argue that this effect mirrors nonnegligible deviations from the circularity of the dynamics during the late-plunge and merger phase. For the first time, we compute the gravitational wave energy flux flowing into the black hole during the inspiral using a time-domain formalism proposed by Poisson. Finally, a self-consistent, iterative method to compute the gravitational wave fluxes at leading-order in the mass of the particle is developed. The method can be used alternatively to the analytical radiation reaction in cases where the analytical information is poor or not sufficient. Specifically, we apply it to compute dynamics and waveforms for a rapidly rotating black hole with dimensionless spin parameter . For this case, the simulation with the consistent flux differs from the one with the analytical flux by gravitational wave cycles over a total of about 250 cycles. In this simulation the horizon absorption accounts for about gravitational wave cycles.

THE SPIN OF THE BLACK HOLE 4U 1543-47

We present a new analysis of Rossi X-ray Timing Explorer observations of the 2002 outburst of the transient X-ray nova 4U 1543-47. We focus on observations in the High/Soft state, and attempt to measure the spin of the black hole by simultaneously fitting the thermal disk continuum and by modeling the broadened iron k-shell emission lines and additional blurred reflection features. Previous works have found that use of these methods individually returns contradictory values for the dimensionless spin parameter a* =cJ/GM^2. We find that when used in conjunction with each other, a moderate spin is obtained (a*=0.43 +0.22 -0.31) that is actually consistent with both other values within errors. We discuss limitations of our analysis, systematic uncertainties, and implications of this measurement, and compare our result to those previously claimed for 4U 1543-47.

Stochastic angular momentum slews and flips and their effect on discs in galaxy formation models

The angular momentum of galactic discs in semi-analytic models of galaxy formation is usually updated in time as material is accreted to the disc by adopting a constant dimensionless spin parameter and little attention is paid to the effects of accretion with misaligned angular momenta. These effects are the subject of this paper, where we adopt a Monte-Carlo simulation for the changes in the direction of the angular momentum of a galaxy disc as it accretes matter based on accurate measurements from dark-matter haloes in the Millennium II simulation. In our semi-analytic model implementation, the flips seen the dark matter haloes are assumed to be the same for the cold baryons; however, we also assume that in the latter the flip also entails a difficulty for the disc to increase its angular momentum which causes the disc to become smaller relative to a no-flip case. This makes star formation to occur faster, specially in low mass galaxies at all redshifts allowing galaxies to reach higher stellar masses faster. We adopt a new condition for the triggering of starbursts during mergers. As these produce the largest flips it is natural to adopt the disc instability criterion to evaluate the triggering of bursts in mergers instead of one based on mass ratios as in the original model. The new implementation reduces the average lifetimes of discs by a factor of 2, while still allowing old ages for the present-day discs of large spiral galaxies. It also provides a faster decline of star formation in massive galaxies and a better fit to the bright end of the luminosity function at z = 0.

The Angular Momentum Dichotomy

AbstractIn the context of the formation of spiral galaxies the evolution and distribution of the angular momentum of dark matter halos have been discussed for more than 20 years, especially the idea that the specific angular momentum of the halo can be estimated from the specific angular momentum of its disk (e.g. Fall &amp; Efstathiou (1980), Fall (1983) and Mo et al. (1998)). We use a new set of hydrodynamic cosmological simulations called Magneticum Pathfinder which allow us to split the galaxies into spheroidal and disk galaxies via the circularity parameter ϵ, as commonly used (e.g. Scannapieco et al. (2008)). Here, we focus on the dimensionless spin parameter λ = J |E|1/2 / (G M5/2) (Peebles 1969, 1971), which is a measure of the rotation of the total halo and can be fitted by a lognormal distribution, e.g. Mo et al. (1998). The spin parameter allows one to compare the relative angular momentum of halos across different masses and different times. Fig. 1 reveals a dichotomy in the distribution of λ at all redshifts when the galaxies are split into spheroids (dashed) and disk galaxies (dash-dotted). The disk galaxies preferentially live in halos with slightly larger spin parameter compared to spheroidal galaxies. Thus, we see that the λ of the whole halo reflects the morphology of its central galaxy. For more details and a larger study of the angular momentum properties of disk and spheroidal galaxies, see Teklu et al. (in prep.).

Statistical properties of dark matter mini-haloes at z ≥ 15

Understanding the formation of the first objects in the universe critically depends on knowing whether the properties of small dark matter structures at high-redshift (z > 15) are different from their more massive lower-redshift counterparts. To clarify this point, we performed a high-resolution N-body simulation of a cosmological volume 1 Mpc/h comoving on a side, reaching the highest mass resolution to date in this regime. We make precision measurements of various physical properties that characterize dark matter haloes (such as the virial ratio, spin parameter, shape, and formation times, etc.) for the high-redshift (z > 15) dark matter mini-haloes we find in our simulation, and compare them to literature results and a moderate-resolution comparison run within a cube of side-length 100 Mpc/h. We find that dark matter haloes at high-redshift have a log-normal distribution of the dimensionless spin parameter centered around {\lambda} $\sim$ 0.03, similar to their more massive counterparts. They tend to have a small ratio of the length of the shortest axis to the longest axis (sphericity), and are highly prolate. In fact, haloes of given mass that formed recently are the least spherical, have the highest virial ratios, and have the highest spins. Interestingly, the formation times of our mini-halos depend only very weakly on mass, in contrast to more massive objects. This is expected from the slope of the linear power spectrum of density perturbations at this scale, but despite this difference, dark matter structures at high-redshift share many properties with their much more massive counterparts observed at later times.

Search for gravitational radiation from intermediate mass black hole binaries in data from the second LIGO-Virgo joint science run

This paper reports on an unmodeled, all-sky search for gravitational waves from merging intermediate mass black hole binaries (IMBHB). The search was performed on data from the second joint science run of the LIGO and Virgo detectors (July 2009 - October 2010) and was sensitive to IMBHBs with a range up to $\sim 200$ Mpc, averaged over the possible sky positions and inclinations of the binaries with respect to the line of sight. No significant candidate was found. Upper limits on the coalescence-rate density of nonspinning IMBHBs with total masses between 100 and $450 \ \mbox{M}_{\odot}$ and mass ratios between $0.25$ and $1\,$ were placed by combining this analysis with an analogous search performed on data from the first LIGO-Virgo joint science run (November 2005 - October 2007). The most stringent limit was set for systems consisting of two $88 \ \mbox{M}_{\odot}$ black holes and is equal to $0.12 \ \mbox{Mpc}^{-3} \ \mbox{Myr}^{-1}$ at the $90\%$ confidence level. This paper also presents the first estimate, for the case of an unmodeled analysis, of the impact on the search range of IMBHB spin configurations: the visible volume for IMBHBs with nonspinning components is roughly doubled for a population of IMBHBs with spins aligned with the binary's orbital angular momentum and uniformly distributed in the dimensionless spin parameter up to 0.8, whereas an analogous population with antialigned spins decreases the visible volume by $\sim 20\%\,$.

NuSTARANDXMM-NEWTONOBSERVATIONS OF NGC 1365: EXTREME ABSORPTION VARIABILITY AND A CONSTANT INNER ACCRETION DISK

We present a spectral analysis of four coordinated NuSTAR+XMM-Newton observations of the Seyfert galaxy NGC 1365. These exhibit an extreme level of spectral variability, which is primarily due to variable line-of-sight absorption, revealing relatively unobscured states in this source for the first time. Despite the diverse range of absorption states, each of the observations displays the same characteristic signatures of relativistic reflection from the inner accretion disk. Through time-resolved spectroscopy we find that the strength of the relativistic iron line and the Compton reflection hump relative to the intrinsic continuum are well correlated, as expected if they are two aspects of the same broadband reflection spectrum. We apply self-consistent disk reflection models to these time-resolved spectra in order to constrain the inner disk parameters, allowing for variable, partially covering absorption to account for the vastly different absorption states observed. Each of the four observations is treated independently to test the consistency of the results obtained for the black hole spin and the disk inclination, which should not vary on observable timescales. We find both the spin and the inclination determined from the reflection spectrum to be consistent, confirming NGC 1365 hosts a rapidly rotating black hole; in all cases the dimensionless spin parameter is constrained to be a* > 0.97 (at 90% statistical confidence or better).

HALO SPIN PARAMETER IN COSMOLOGICAL SIMULATIONS

Using a cosmological ΛCDM simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter λ proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock’s spin parameter λ′ avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between λ and λ′ depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter, λ′′, which is simply designed to roughly recover the value of λ but to use the same halo quantities as used in λ′. If the Plummer potential is adopted, the λ′′ is related to the Bullock’s definition as λ′′ = 0.80 × (1 + z)? 1/12 λ′. Hence, the new spin parameter λ′′ distribution becomes consistent with a log-normal distribution frequently seen for the λ′ while its mean value is much closer to that of λ. On the other hand, in case of the Newtonian potential model, we obtain the relation of λ′′ = (1 + z)? 1/8 λ′; there is no significant difference at z = 0 as found by others but λ′ becomes more overestimated than λ or λ′′ at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the λ′ for small-mass halos with Mh 12 M ⊙ seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.

THE SPIN OF THE BLACK HOLE GS 1124–683: OBSERVATION OF A RETROGRADE ACCRETION DISK?

We re-examine archival Ginga data for the black hole binary system GS 1124-683, obtained when the system was undergoing its 1991 outburst. Our analysis estimates the dimensionless spin parameter a=cJ/GM^2 by fitting the X-ray continuum spectra obtained while the system was in the "Thermal Dominant" state. For likely values of mass and distance, we find the spin to be a=-0.25 (-0.64, +0.05) (90% confidence), implying that the disk is retrograde (i.e. rotating antiparallel to the spin axis of the black hole). We note that this measurement would be better constrained if the distance to the binary and the mass of the black hole were more accurately determined. This result is unaffected by the model used to fit the hard component of the spectrum. In order to be able to recover a prograde spin, the mass of the black hole would need to be at least 15.25 Msun, or the distance would need to be less than 4.5 kpc, both of which disagree with previous determinations of the black hole mass and distance. If we allow f_col to be free, we obtain no useful spin constraint. We discuss our results in the context of recent spin measurements and implications for jet production.