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At least 1,387 records · Page 77
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DOE OSTI2016

Kinematically identified recoiling supermassive black hole candidates in SDSS QSOs with z < 0.25

We have performed a spectral decomposition to search for recoiling supermassive black holes (rSMBHs) in Sloan Digital Sky Survey (SDSS) quasi-stellar objects (QSOs) with z < 0.25. Out of 1271 QSOs, we have identified 26 rSMBH candidates that are recoiling toward us. The projected recoil velocities range from −76 to −307 km s{sup −1} with a mean of −149 ± 58 km s{sup −1}. Most of the rSMBH candidates are hosted by gas-rich luminous infrared galaxies (LIRGs)/ultra-luminous infrared galaxies (ULIRGs), but only 23% of them show signs of tidal features, which suggests that a majority of them are advanced mergers. We find that the black hole masses M {sub BH} of the rSMBH candidates are on average ∼5 times smaller than those of their stationary counterparts and cause a scatter in the M{sub BH}−σ{sub ∗} relation. The Eddington ratios of all of the rSMBH candidates are larger than 0.1, with a mean of 0.52 ± 0.27, suggesting that they are actively accreting mass. Velocity shifts in high-excitation coronal lines suggest that the rSMBH candidates are recoiling with an average velocity of about −265 km s{sup −1}. The electron density in the narrow line region of the H ii rSMBH candidates is about 1/10 of that in active galactic nucleus (AGN) rSMBH candidates, probably because the AGN in the former was more spatially offset than that in the latter. The estimated spatial offsets between the rSMBH candidate and the center of the host galaxy range from 0.″21 to 1.″97 and need to be confirmed spatially with high-resolution adaptive optics imaging observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The first low-mass black hole X-ray binary identified in quiescence outside of a globular cluster

The observed relation between the X-ray and radio properties of low-luminosity accreting black holes (BHs) has enabled the identification of multiple candidate black hole X-ray binaries (BHXBs) in globular clusters (GCs). Here, we report an identification of the radio source VLA J213002.08+120904 (aka M15 S2), recently reported in Kirsten et al., as a BHXB candidate. They showed that the parallax of this flat-spectrum variable radio source indicates a 2.2{sub −0.3}{sup +0.5} kpc distance, which identifies it as lying in the foreground of the GC M15. We determine the radio characteristics of this source and place a deep limit on the X-ray luminosity of ∼4 × 10{sup 29} erg s{sup −1}. Furthermore, we astrometrically identify a faint red stellar counterpart in archival Hubble images with colors consistent with a foreground star; at 2.2 kpc, its inferred mass is 0.1–0.2 M {sub ⊙}. We rule out that this object is a pulsar, neutron star X-ray binary, cataclysmic variable, or planetary nebula, concluding that VLA J213002.08+120904 is the first accreting BHXB candidate discovered in quiescence outside of a GC. Given the relatively small area over which parallax studies of radio sources have been performed, this discovery suggests a much larger population of quiescent BHXBs in our Galaxy, 2.6 × 10{sup 4}–1.7 × 10{sup 8} BHXBs at 3σ confidence, than has been previously estimated (∼10{sup 2}–10{sup 4}) through population synthesis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Controversy of the GRO J1655-40 black hole mass and spin estimates and its possible solutions

Estimates of the black hole mass M and the dimensionless spin a in the microquasar GRO J1655-40 implied by strong gravity effects related to the timing and spectral measurements are controversial, if the mass restriction determined by the dynamics related to independent optical measurements, M {sub opt} = (5.4 ± 0.3) M {sub ⊙}, is applied. The timing measurements of twin high-frequency (HF) quasiperiodic oscillations (QPOs) with the frequency ratio 3:2 and the simultaneously observed low-frequency (LF) QPO imply spin in the range a∈(0.27--0.29) if models based on the frequencies of geodesic epicyclic motion are used to fit the timing measurements, and the correlated creation of the twin HF QPOs and the LF QPO at a common radius is assumed. On the other hand, the spectral continuum method implies a∈(0.65--0.75), and the Fe-line-profile method implies a∈(0.94--0.98). This controversy can be cured if we abandon the assumption of the occurrence of the twin HF QPOs and the simultaneously observed LF QPO at a common radius. We demonstrate that the epicyclic resonance model of the twin HF QPOs is able to predict the spin in agreement with the Fe-profile method, but no model based on the geodesic epicyclic frequencies can be in agreement with the spectral continuum method. We also show that the non-geodesic string loop oscillation model of twin HF QPOs predicts spin a > 0.3 under the optical measurement limit on the black hole mass, which is in agreement with both the spectral continuum and Fe-profile methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Constraints on black hole/host galaxy co-evolution and binary stalling using pulsar timing arrays

Pulsar timing arrays are now setting increasingly tight limits on the gravitational wave background from binary supermassive black holes (SMBHs). But as upper limits grow more constraining, what can be implied about galaxy evolution? We investigate which astrophysical parameters have the largest impact on predictions of the strain spectrum and provide a simple framework to directly translate between measured values for the parameters of galaxy evolution and pulsar timing array (PTA) limits on the gravitational wave background of binary SMBHs. We find that the most influential observable is the relation between a host galaxy's central bulge and its central black hole, M{sub ∙}--M{sub bulge}, which has the largest effect on the mean value of the characteristic strain amplitude. However, the variance of each prediction is dominated by uncertainties in galaxy stellar mass functions. Using this framework with the best published PTA limit, we can set limits on the shape and scatter of the M{sub ∙}--M{sub bulge} relation. We find our limits to be in contention with strain predictions using two leading measurements of this relation. We investigate several possible reasons for this disagreement. If we take the M{sub ∙}--M{sub bulge} relations to be correct within a simple power-law model for the gravitational wave background, then the inconsistency is reconcilable by allowing for an additional “stalling” time between a galaxy merger and evolution of a binary SMBH to sub-parsec scales, with lower limits on this timescale of ∼1–2 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SDSS J0159+0105: a radio-quiet quasar with a centi-parsec supermassive black hole binary candidate

We report a candidate centi-parsec supermassive black hole binary (SMBHB) in the radio-quiet quasar SDSS J0159+0105 at z = 0.217. With a modified Lomb–Scargle code (GLSdeDRW) and auto-correlation analysis, we detect two significant (at P > 99%) periodic signals at ∼741 day and ∼1500 day from the 8.1 yr Catalina V-band light curve of this quasar. The period ratio, which is close to 1:2, is typical of a black hole binary system with a mass ratio of 0.05 < q < 0.8 according to recent numerical simulations. SDSS J0159+0105 has two SDSS spectroscopic observations separated by ∼10 yr. There is a significant change in the broad Hβ profile between the two epochs, which can be explained by a single broad-line region (BLR) around the binary system illuminated by the aforementioned mini-disks, or a stream of gas flowing from the circumbinary disk to one of the SMBHs. From the single BLR assumption and the orbital period t {sub orb} ∼ 1500 day, we estimate the total virial masses of M {sub SMBHB} ∼ 1.3 × 10{sup 8} M {sub ⊙}, the average distances of BLR of ∼0.04 pc (∼50 lt-day, with ±0.3 dex uncertainty), and an SMBHB separation of d = (0.01 pc)M{sub 8,tot}{sup 1/3} (T {sub rest}/3.3 yr){sup 2/3} ∼ 0.013 pc (15 lt-day). Based on analytical work, the postulated circumbinary disk has an inner radius of 2d = 0.026 pc (30 lt-day). SDSS J0159+0105 also displays unusual spectral energy distribution. The unique properties of SDSS J0159+0105 are consistent with it being a centi-parsec SMBHB.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE PROPERTIES OF HYPERVELOCITY STARS AND S-STARS ORIGINATING FROM AN ECCENTRIC DISK AROUND A SUPERMASSIVE BLACK HOLE

Hypervelocity stars (HVSs), which are observed in the Galactic halo, are believed to be accelerated to large velocities by a process of tidal disruption of binary stars passing close to the supermassive black hole (SMBH) which resides in the center of the Galaxy. It is, however, still unclear where these relatively young stars were born and what dynamical process pushed them to nearly radial orbits around the SMBH. In this paper we investigate the possibility that the young binaries originated from a thin eccentric disk, similar to the one currently observed in the Galactic center. By means of direct N -body simulations, we follow the dynamical evolution of an initially thin and eccentric disk of stars with a 100% binary fraction orbiting around the SMBH. Such a configuration leads to Kozai–Lidov oscillations of orbital elements, bringing a considerable number of binaries to the close vicinity of the black hole. Subsequent tidal disruption of these binaries accelerates one of their components to velocities well above the escape velocity from the SMBH, while the second component becomes tightly bound to the SMBH. We describe the main kinematic properties of the escaping and tightly bound stars within our model, and compare them qualitatively to the properties of the observed HVSs and S-stars, respectively. The most prominent feature is strong anisotropy in the directions of the escaping stars, which is observed for Galactic HVSs but has not yet been explained.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

EMISSION SIGNATURES FROM SUB-PARSEC BINARY SUPERMASSIVE BLACK HOLES. I. DIAGNOSTIC POWER OF BROAD EMISSION LINES

Motivated by advances in observational searches for sub-parsec supermassive black hole binaries (SBHBs) made in the past few years, we develop a semi-analytic model to describe spectral emission-line signatures of these systems. The goal of this study is to aid the interpretation of spectroscopic searches for binaries and to help test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this work, we present the methodology and a comparison of the preliminary model with the data. We model SBHB accretion flows as a set of three accretion disks: two mini-disks that are gravitationally bound to the individual black holes and a circumbinary disk. Given a physically motivated parameter space occupied by sub-parsec SBHBs, we calculate a synthetic database of nearly 15 million broad optical emission-line profiles and explore the dependence of the profile shapes on characteristic properties of SBHBs. We find that the modeled profiles show distinct statistical properties as a function of the semimajor axis, mass ratio, eccentricity of the binary, and the degree of alignment of the triple disk system. This suggests that the broad emission-line profiles from SBHB systems can in principle be used to infer the distribution of these parameters and as such merit further investigation. Calculated profiles are more morphologically heterogeneous than the broad emission lines in observed SBHB candidates and we discuss improved treatment of radiative transfer effects, which will allow a direct statistical comparison of the two groups.

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DOE OSTI2016

The local black hole mass function derived from the M{sub BH}–P and the M{sub BH}–n relations

We present a determination of the supermassive black hole (SMBH) mass function for early- and late-type galaxies in the nearby universe (z < 0.0057), established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern hemisphere. The sample is defined by limiting luminosity (redshift-independent) distance, D {sub L} = 25.4 Mpc, and a limiting absolute B-band magnitude, M{sub B}=−19.12. These limits define a sample of 140 spiral, 30 elliptical (E), and 38 lenticular (S0) galaxies. We established the Sérsic index distribution for early-type (E/S0) galaxies in our sample. Davis et al. established the pitch angle distribution for their sample, which is identical to our late-type (spiral) galaxy sample. We then used the pitch angle and the Sérsic index distributions in order to estimate the SMBH mass function for our volume-limited sample. The observational simplicity of our approach relies on the empirical relation between the mass of the central SMBH and the Sérsic index for an early-type galaxy or the logarithmic spiral-arm pitch angle for a spiral galaxy. Our SMBH mass function agrees well at the high-mass end with previous values in the literature. At the low-mass end, although inconsistencies exist in previous works that still need to be resolved, our work is more in line with expectations based on modeling of black hole evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A REVERBERATION-BASED BLACK HOLE MASS FOR MCG-06-30-15

We present the results of a reverberation campaign targeting MGC-06-30-15. Spectrophotometric monitoring and broad-band photometric monitoring over the course of four months in spring 2012 allowed a determination of a time delay in the broad H β emission line of τ = 5.3 ± 1.8 days in the rest frame of the active galactic nucleus (AGN). Combined with the width of the variable portion of the emission line, we determine a black hole mass of M {sub BH} = (1.6 ± 0.4) × 10{sup 6} M {sub ⊙}. Both the H β time delay and the black hole mass are in good agreement with expectations from the R {sub BLR}– L and M {sub BH}– σ {sub ⋆} relationships for other reverberation-mapped AGNs. The H β time delay is also in good agreement with the relationship between H β and broad-band near-IR delays, in which the effective size of the broad-line region is ∼4–5 times smaller than the inner edge of the dust torus. Additionally, the reverberation-based mass is in good agreement with estimates from the scaling relationship of the break in the X-ray power spectral density, and with constraints based on stellar kinematics derived from integral field spectroscopy of the inner ∼0.5 kpc of the galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Do the most massive black holes at z = 2 grow via major mergers?

The most frequently proposed model for the origin of quasars holds that the high accretion rates seen in luminous active galactic nuclei (AGN) are primarily triggered during major mergers between gas-rich galaxies. While plausible for decades, this model has only begun to be tested with statistical rigor in the past few years. Here, we report on a Hubble Space Telescope study to test this hypothesis for z = 2 quasars with high supermassive black hole masses (M{sub BH}=10{sup 9}--10{sup 10} M{sub ⊙} ), which dominate cosmic black hole growth at this redshift. We compare Wide Field Camera 3 F160W (rest-frame V-band) imaging of 19 point source-subtracted quasar hosts to a matched sample of 84 inactive galaxies, testing whether the quasar hosts have greater evidence for strong gravitational interactions. Using an expert ranking procedure, we find that the quasar hosts are uniformly distributed within the merger sequence of inactive galaxies, with no preference for quasars in high-distortion hosts. Using a merger/non-merger cutoff approach, we recover distortion fractions of f{sub m,qso}=0.39±0.11 for quasar hosts and f{sub m,gal}=0.30±0.05 for inactive galaxies (distribution modes, 68% confidence intervals), with both measurements subjected to the same observational conditions and limitations. The slight enhancement in distorted fraction for quasar hosts over inactive galaxies is not significant, with a probability that the quasar fraction is higher P(f{sub m,qso}>f{sub m,gal})=0.78 (0.78σ), in line with results for lower mass and lower z AGN. We find no evidence that major mergers are the primary triggering mechanism for the massive quasars that dominate accretion at the peak of cosmic quasar activity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Cosmological simulations of early black hole formation: halo mergers, tidal disruption, and the conditions for direct collapse

Gravitational collapse of a massive primordial gas cloud is thought to be a promising path for the formation of supermassive black holes in the early universe. We study conditions for the so-called direct collapse (DC) black hole formation in a fully cosmological context. We combine a semianalytic model of early galaxy formation with halo merger trees constructed from dark matter N-body simulations. We locate a total of 68 possible DC sites in a volume of 20 h{sup −1} Mpc on a side. We then perform hydrodynamics simulations for 42 selected halos to study in detail the evolution of the massive clouds within them. We find only two successful cases where the gas clouds rapidly collapse to form stars. In the other cases, gravitational collapse is prevented by the tidal force exerted by a nearby massive halo, which otherwise should serve as a radiation source necessary for DC. Ram pressure stripping disturbs the cloud approaching the source. In many cases, a DC halo and its nearby light source halo merge before the onset of cloud collapse. When the DC halo is assembled through major mergers, the gas density increases rapidly to trigger gravitational instability. Based on our cosmological simulations, we conclude that the event rate of DC is an order of magnitude smaller than reported in previous studies, although the absolute rate is still poorly constrained. It is necessary to follow the dynamical evolution of a DC cloud and its nearby halo(s) in order to determine the critical radiation flux for DC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY

The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least action. The coupling between the spin of elementary particles and torsion in the Einstein–Cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin fluid, and thus avoids the formation of singularities in black holes. The collapsing matter in a black hole should therefore bounce at a finite density and then expand into a new region of space on the other side of the event horizon, which may be regarded as a nonsingular, closed universe. We show that quantum particle production caused by an extremely high curvature near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) of this universe. This scenario can thus explain inflation without a scalar field and reheating. We show that, depending on the particle production rate, such a universe may undergo several nonsingular bounces until it has enough matter to reach a size at which the cosmological constant starts cosmic acceleration. The last bounce can be regarded as the big bang of this universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Electrically charged matter in permanent rotation around magnetized black holes: A toy model for self-gravitating fluid tori

We present an analytical approach for the equilibrium of a self-gravitating charged fluid embedded in a spherical gravitational and dipolar magnetic fields produced by a central mass. Our scheme is proposed, as a toy model, in the context of gaseous/dusty tori surrounding supermassive black holes in galactic nuclei. While the central black hole dominates the gravitational field and remains electrically neutral, the surrounding material has a non-negligible self-gravitational effect on the torus structure. By charging mechanisms it also acquires non-zero electric charge density, so the two influences need to be taken into account to achieve a self-consistent picture. Using our approach we discuss the impact of self-gravity, represented by the term d{sub t} (ratio of the torus total mass to the mass of the central body), on the conditions for existence of the equilibrium and the morphology and typology of the tori. By comparison with a previous work without self-gravity, we show that the conditions can be different. Although the main aim of the present paper is to discuss a framework for the classification of electrically charged, magnetized, self-gravitating tori, we also mention potential astrophysical applications to vertically stratified fluid configurations.

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DOE OSTI2016

INDICATION OF THE BLACK HOLE POWERED JET IN M87 BY VSOP OBSERVATIONS

In order to study the collimation and acceleration mechanism of relativistic jets, the jet streamline of M87 at milliarcsecond scale is extensively investigated with images from VSOP observations at 1.6 and 5 GHz. Thanks to the higher angular resolution of VSOP, especially in the direction transverse to the jet, we resolved the jet streamline into three ridgelines at the scale of milli arcseconds. While the properties of the outer two ridgelines are in good agreement with those measured in previous observations and can be expressed by one power-law line with a power law index of 1.7, an inner ridgeline is clearly observed for the first time. We compared the measured size with the outermost streamline expected by Blandford and Znajek's parabolic solutions, which are anchored at the event horizon, with different black hole spin parameters. We revealed that the observed inner ridgeline is narrower than the prediction, suggesting the origin of the inner ridgeline to be part of a spine originating from the spinning black hole. The inner ridgeline becomes very dim at large distances from the central engine at 5 GHz. We considered two possible cases for this; Doppler beaming and/or radiative cooling. Either case seems to be reasonable for its explanation, and future multi-frequency observations will discriminate those two possibilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The universal “heartbeat” oscillations in black hole systems across the mass-scale

The hyperluminous X-ray source (HLX-1, peak X-ray luminosity ∼10{sup 42} erg s{sup −1}) near the spiral galaxy ESO 243-49, which underwent recurrent outbursts within a period of ∼400 days, is possibly the best candidate for an intermediate mass black hole (IMBH). The physical reason for this quasiperiodic variability is still unclear. We explore the possibility of radiation-pressure instability in the accretion disk by modeling the light curve of HLX-1, and find that it can roughly reproduce the duration, period, and amplitude of the recurrent outbursts in HLX-1 with an IMBH of ∼10{sup 5} M{sub ⊙}. Our result provides a possible mechanism to explain the recurrent outbursts in HLX-1. We further find a universal correlation between the outburst duration and the bolometric luminosity for the black hole (BH) sources with a very broad mass range (e.g., X-ray binaries, HLX-1, and active galactic nuclei), which is roughly consistent with the prediction of radiation-pressure instability of the accretion disk. These results imply that “heartbeat” oscillations triggered by radiation-pressure instability may appear in different-scale BH systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

THE MEGAMASER COSMOLOGY PROJECT. IX. BLACK HOLE MASSES FOR THREE MASER GALAXIES

As part of the Megamaser Cosmology Project, we present VLBI maps of nuclear water masers toward five galaxies. The masers originate in sub-parsec circumnuclear disks. For three of the galaxies, we fit Keplerian rotation curves to estimate their supermassive black hole (SMBH) masses, and determine (2.9 ± 0.3) × 10{sup 6} M {sub ⊙} for J0437+2456, (1.7 ± 0.1) × 10{sup 7} M {sub ⊙} for ESO 558–G009, and (1.1 ± 0.2) × 10{sup 7} M {sub ⊙} for NGC 5495. In the other two galaxies, Mrk 1029 and NGC 1320, the geometry and dynamics are more complicated and preclude robust black hole mass estimates. Including our new results, we compiled a list of 15 VLBI-confirmed disk maser galaxies with robust SMBH mass measurements. With this sample, we confirm the empirical relation of R {sub out} ∝ 0.3 M {sub SMBH} reported in Wardle and Yusef-Zadeh. We also find a tentative correlation between maser disk outer radii and Wide-Field Infrared Survey Explorer luminosity. We find no correlations of maser disk size with X-ray 2–10 keV luminosity or [O iii] luminosity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Application of the Nonballistic Model to the Black Hole Candidate XTE J1752-223 and the Quasar NRAO 150

Optical and radio observations of the black hole candidate XTE J1752-223 have exhibited a slightly curved motion of the jet components, which is associated with its radio light curve. In addition, observations of the quasar NRAO 150 have revealed a core–jet structure wobbling with a high angular speed. In this paper, the phenomena displayed in these two different sources are interpreted as the precession of a bent jet. In such a scenario, hot spots reproduced at different separations from the core precess on the same precession cone, in which different components correspond to different propagation times to the observer. By fitting the kinematics of the components of XTE J1752-223 and its light curve with a curved pattern of precession period 314 days, we find that the propagation time can make an earlier event appear later, and the jet axis can oscillate during its precession. Simulating the quasar NRAO 150 with the same scenario reveals that the knots at larger separation from the core precess at a slower speed than those closer in. A possible mechanism relating to the cooling time of a component is proposed. These three new results are of importance in understanding the physics underlying the curved jet as well as the activity of the central engine of different black hole systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Relation Between Globular Cluster Systems and Supermassive Black Holes in Spiral Galaxies: The Case Study of NGC 4258

We aim to explore the relationship between globular cluster total number, N{sub GC}, and central black hole mass, M {sub •}, in spiral galaxies, and compare it with that recently reported for ellipticals. We present results for the Sbc galaxy NGC 4258, from Canada–France–Hawaii Telescope data. Thanks to water masers with Keplerian rotation in a circumnuclear disk, NGC 4258 has the most precisely measured extragalactic distance and supermassive black hole mass to date. The globular cluster (GC) candidate selection is based on the (u{sup ∗}−i{sup ′}) versus (i{sup ′}−K{sub s}) diagram, which is a superb tool to distinguish GCs from foreground stars, background galaxies, and young stellar clusters, and hence can provide the best number counts of GCs from photometry alone, virtually free of contamination, even if the galaxy is not completely edge-on. The mean optical and optical-near-infrared colors of the clusters are consistent with those of the Milky Way and M 31, after extinction is taken into account. We directly identify 39 GC candidates; after completeness correction, GC luminosity function extrapolation, and correction for spatial coverage, we calculate a total N{sub GC}=144±31{sub −36}{sup +38} (random and systematic uncertainties, respectively). We have thus increased to six the sample of spiral galaxies with measurements of both M {sub •} and N{sub GC}. NGC 4258 has a specific frequency S{sub N}=0.4±0.1 (random uncertainty), and is consistent within 2σ with the N{sub GC} versus M {sub •} correlation followed by elliptical galaxies. The Milky Way continues to be the only spiral that deviates significantly from the relation.

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