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We extend the classical Kadec 1/4 theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation.

This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form $F=h+\eta$, where $\eta$ is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources $h(t)=\sum\limits_{j=0}^M h_je^{-\rho_j(t-t_j)}\chi_{[t_j,\infty)}(t)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield.

We present an efficient algorithm for solving fractional programming problems whose objective functions are the ratio of a low-rank quadratic to a positive definite quadratic with convex constraints. The proposed algorithm for these convex-convex problems is based on the Shen-Yu Quadratic Transform which finds stationary points of concave-convex sum-of-ratios problems. We further use elements of the algorithm proposed in [arXiv:1802.10192] and the classic Dinkelbach approach to ensure convergence. We show that our algorithm performs better than previous algorithms for low-rank problems.

Reinforcement learning in a multi agent system is difficult because these systems are inherently non-stationary in nature. In such a case, identifying the type of the opposite agent is crucial and can help us address this non-stationary environment. We have investigated if we can employ some probing policies which help us better identify the type of the other agent in the environment. We've made a simplifying assumption that the other agent has a stationary policy that our probing policy is trying to approximate. Our work extends Environmental Probing Interaction Policy framework to handle multi agent environments.

We characterize the incidence and intensity of low-level super-massive black hole activity within the Fornax cluster, through X-ray observations of the nuclei of 29 quiescent early-type galaxies. Using the \textit{Chandra X-ray Telescope}, we target 17 galaxies from the HST Fornax Cluster Survey, down to a uniform (3$\sigma$) limiting X-ray luminosity threshold of $5\cdot10^{38}$ergs$^{-1}$, which we combine with deeper, archival observations for an additional 12 galaxies. A nuclear X-ray point-source is detected in 11 out of 29 targets. After accounting for the low mass X-ray binary contamination to the nuclear X-ray signal, the X-ray active fraction is measured at $26.6\% \pm 9.6\%$. The results from this analysis are compared to similar investigations targeting quiescent early types in the Virgo cluster, as well as the field. After correcting for the different mass distributions, the measured Fornax active fraction is less than the field fraction, at more than 3$\sigma$, confirming that the funneling of gas to the nuclear regions of cluster members is inhibited compared to those galaxies in the field. At the same time, we find no statistically significant difference between Fornax and Virgo galaxies, with only marginal evidence for a lower active fraction in Fornax (1 $\sigma$); if real, owing to Fornax's higher galaxy number density, this could indicate that galaxy-galaxy interactions are more effective at gas removal than galaxy-gas effects., Comment: Accepted by ApJ

The magnetic activity levels of planet host stars may differ from that of stars not known to host planets in several ways. Hot Jupiters may induce activity in their hosts through magnetic interactions, or through tidal interactions by affecting their host's rotation or convection. Measurements of photospheric, chromospheric, or coronal activity might then be abnormally high or low compared to control stars that do not host hot Jupiters, or might be modulated at the planet's orbital period. Such detections are complicated by the small amplitude of the expected signal, by the fact that the signals may be transient, and by the difficulty of constructing control samples due to exoplanet detection biases and the uncertainty of field star ages. We review these issues, and discuss avenues for future progress in the field., Comment: 10 pp, 4 figures. From "Chapter 9: Flares and star-planet interaction"; Solar and Stellar Flares and Their Effects on Planets, Proceedings IAU Symposium No. 320, 2015, A.G. Kosovichev, S.L. Hawley & P. Heinzel, eds., From the 2015 IAU General Assembly in Honolulu, HI, USA, Focus Meeting 13: Brightness Variations of the Sun and Sun-like Stars, 5-6 August 2015

Motivated by theoretical expectations that Nuclear Star Clusters (NSCs) in galactic centers may provide a favorable environment for super-massive black holes to form and/or efficiently grow, we set out to measure the fraction of nearby nucleated galaxies that also host an Active Galactic Nucleus (AGN). We targeted a distance-limited sample of 98 objects with the Chandra X-ray Telescope, down to a uniform X-ray luminosity threshold of $\sim$10$^{38}$ erg s$^{-1}$. The sample is composed of 47 late-types and 51 early-types, enabling us to further investigate the active fraction as a function of galactic morphology. After correcting for contamination to the nuclear X-ray signal from bright X-ray binaries, we measure an active fraction $f$=11.2$\%^{+7.4}_{-4.9}$ (1$\sigma$ C.L.) across the whole sample, in agreement with previous estimates based on an heterogeneous combination of optical, X-ray and radio diagnostics, by Seth et al. (2008). After accounting for the different stellar mass distributions in our samples, we find no statistically significant difference in the active fraction of early- vs. late-type nucleated galaxies, with $f$=10.6$\%^{+11.9}_{-4.9}$ and 10.8$\%^{+11.3}_{-6.3}$, respectively. For the early-type nucleated galaxies, we are able to carry out a controlled comparison with a parent sample of non-nucleated galaxies covering the same stellar mass range, finding again no statistically significant difference in the active fraction. Taken at face value, our findings suggest that the presence of a NSC does not facilitate nor enhance accretion-powered emission from a nuclear super-massive black hole. This is true even for late-type nucleated galaxies, home to bluer NSCs and arguably larger gas reservoirs., Comment: ApJ accepted, 12 pages, 8 Figures, 4 Tables

The nature of the relationship between low-level supermassive black hole (SMBH) activity and galactic cold gas, if any, is currently unclear. Here, we test whether central black holes may feed at higher rates in gas-rich galaxies, probing SMBH activity well below the active regime down to Eddington ratios of ~1e-7. We use a combination of radio data from the ALFALFA survey and from the literature, along with archival X-ray flux measurements from the Chandra X-ray observatory, to investigate this potential relationship. We construct a sample of 129 late-type galaxies, with MB<-18 out to 50 Mpc, that have both HI masses and sensitive X-ray coverage. Of these, 75 host a nuclear X-ray source, a 58% detection fraction. There is a highly significant correlation between nuclear X-ray luminosity LX and galaxy stellar mass Mstar with a slope of 1.7+/-0.3, and a tentative correlation (significant at the 2.8 sigma level) between LX and HI gas mass MHI. However, a joint fit to LX as a function of both Mstar and MHI finds no significant dependence on MHI (slope 0.1+/00.3), and similarly the residuals of LX-LX(Mstar) show no trend with MHI; the apparent correlation between LX and MHI seems to be entirely driven by Mstar. We demonstrate quantitatively that these results are robust against X-ray binary contamination. We conclude that the galaxy-wide cold gas content in these spirals does not strongly correlate with their low-level supermassive black hole activity, and suggest fueling is a localized process., Comment: Resubmitted to ApJ after addressing referee report. Comments welcome

We present new Chandra X-ray observations of seven low-mass black holes (~1e6 Msun) accreting at low Eddington ratios between -2.0

We present a sample of accreting supermassive black holes (SMBHs) in dwarf galaxies at $z<1$. We identify dwarf galaxies in the NEWFIRM Medium Band Survey with stellar masses $M_{\star}<3\times 10^{9} M_{\odot}$ that have spectroscopic redshifts from the DEEP2 survey and lie within the region covered by deep (flux limit of $\sim 5\times 10^{-17} - 6\times 10^{-16} \rm{erg \ cm}^{-2} \ \rm{s}^{-1}$) archival Chandra X-ray data. From our sample of $605$ dwarf galaxies, $10$ exhibit X-ray emission consistent with that arising from AGN activity. If black hole mass scales roughly with stellar mass, then we expect that these AGN are powered by SMBHs with masses of $\sim 10^5-10^6 \ M_{\odot}$ and typical Eddington ratios $\sim 5\%$. Furthermore, we find an AGN fraction consistent with extrapolations of other searches of $\sim 0.6-3\%$ for $10^9 \ M_{\odot} \leq M_{\star} \leq 3\times 10^{9} \ M_{\odot}$ and $0.1

We investigate whether magnetic interaction between close-in giant planets and their host stars produce observable statistical enhancements in stellar coronal or chromospheric activity. New Chandra observations of 12 nearby (d<60 pc) planet-hosting solar analogs are combined with archival Chandra, XMM-Newton, and ROSAT coverage of 11 similar stars to construct a sample inoculated against inherent stellar class and planet-detection biases. Survival analysis and Bayesian regression methods (incorporating both measurements errors and X-ray upper limits; 13/23 stars have secure detections) are used to test whether "hot Jupiter" hosts are systematically more X-ray luminous than comparable stars with more distant or smaller planets. No significant correlations are present between common proxies for interaction strength (Mp/a^2 or 1/a) versus coronal activity (Lx or Lx/Lbol). In contrast, a sample of 198 FGK main-sequence stars does show a significant (~99% confidence) increase in X-ray luminosity with Mp/a^2. While selection biases are incontrovertibly present within the main-sequence sample, we demonstrate that the effect is primarily driven by a handful of extreme hot-Jupiter systems with Mp/a^2 >450 Mjup/AU^2, which here are all X-ray luminous but to a degree commensurate with their Ca II H and K activity, in contrast to presented magnetic star-planet interaction scenarios that predict enhancements relatively larger in Lx. We discuss these results in the context of cumulative tidal spin-up of stars hosting close-in gas giants (potentially followed by planetary infall and destruction). We also test our main-sequence sample for correlations between planetary properties and UV luminosity or Ca II H and K emission, and find no significant dependence., Comment: 16 pages, 2 tables, 10 figures, accepted to ApJ

The optical light profiles of nearby early type galaxies are known to exhibit a smooth transition from nuclear light deficits to nuclear light excesses with decreasing galaxy mass, with as much as 80 per cent of the galaxies with stellar masses below 10^10 Msun hosting a massive nuclear star cluster. At the same time, while all massive galaxies are thought to harbor nuclear super-massive black holes (SMBHs), observational evidence for SMBHs is slim at the low end of the mass function. Here, we explore the environmental dependence of the nucleation fraction by comparing two homogeneous samples of nearby field vs. cluster early type galaxies with uniform Hubble Space Telescope (HST) coverage. Existing Chandra X-ray Telescope data for both samples yield complementary information on low-level accretion onto nuclear SMBHs. Specifically, we report on dual-band (F475W & F850LP) Advanced Camera for Surveys (ACS) imaging data for 28 out of the 103 field early type galaxies that compose the AMUSE-Field Chandra survey, and compare our results against the companion HST and Chandra surveys for a sample of 100 Virgo cluster early types (ACS Virgo Cluster and AMUSE-Virgo surveys, respectively). We model the two-dimensional light profiles of the field targets to identify and characterize NSCs, and find a field nucleation fraction of 26% (+17%, -11%; at the 1-sigma level), consistent with the measured Virgo nucleation fraction of 30% (+17%, -12%), across a comparable mass distribution. Coupled with the Chandra result that SMBH activity is higher for the field, our findings indicate that, since the last epoch of star formation, the funneling of gas to the nuclear regions has been inhibited more effectively for Virgo galaxies, arguably via ram pressure stripping., Comment: 13 pages, 9 figures. Accepted for publication in ApJ

Distinct seed formation mechanisms are imprinted upon the fraction of dwarf galaxies currently containing a central supermassive black hole. Seeding by Pop III remnants is expected to produce a higher occupation fraction than is generated with direct gas collapse precursors. Chandra observations of nearby early-type galaxies can directly detect even low-level supermassive black hole activity, and the active fraction immediately provides a firm lower limit to the occupation fraction. Here, we use the volume-limited AMUSE surveys of ~200 optically-selected early-type galaxies to characterize simultaneously, for the first time, the occupation fraction and the scaling of nuclear X-ray luminosity with stellar mass, accounting for intrinsic scatter, measurement uncertainties, and X-ray limits. For early-type galaxies with log(M_star/M_sun)<10, we obtain a lower limit to the occupation fraction of >20% (at 95% confidence), but full occupation cannot be excluded. The preferred dependence of log(L_X) upon log(M_star) has a slope of about 0.7-0.8, consistent with the "downsizing" trend previously identified from the AMUSE dataset, and a uniform Eddington efficiency is disfavored at ~2 sigma. We provide guidelines for the future precision with which these parameters may be refined with larger or more sensitive samples., Comment: Changes from v1: slightly improved galaxy distances (analysis rerun with nearly identical results), added table with sample properties, expanded discussion of methodology, updated references. Resubmitted to ApJ

Ultraluminous X-ray sources (ULXs) are some of the brightest phenomena found outside of a galaxy's nucleus, and their explanation typically invokes accretion of material onto a black hole. Here, we perform the largest population study to date of ULXs in early-type galaxies, focusing on whether a galaxy's large scale environment can affect its ULX content. Using the AMUSE survey, which includes homogeneous X-ray coverage of 100 elliptical galaxies in the Virgo cluster and a similar number of elliptical galaxies in the field (spanning stellar masses of 1e8-1e12 M_sun), we identify 37.9 +/- 10.1 ULXs in Virgo and 28.1 +/- 8.7 ULXs in the field. Across both samples, we constrain the number of ULXs per unit stellar mass, i.e., the ULX specific frequency, to be 0.062 +/- 0.013 ULXs per 10^10 M_sun (or about 1 ULX per 1.6e11 M_sun of galaxy stellar mass). We find that the number of ULXs, the specific frequency of ULXs, and the average ULX spectral properties are all similar in both cluster and field environments. Contrary to late-type galaxies, we do not see any trend between specific ULX frequency and host galaxy stellar mass, and we show that dwarf ellipticals host fewer ULXs than later-type dwarf galaxies at a statistically meaningful level. Our results are consistent with ULXs in early-type galaxies probing the luminous tail of the low-mass X-ray binary population, and are briefly discussed in context of the influence of gravitational interactions on the long-term evolution of a galaxy's (older) stellar population., Comment: 17 pages, 3 figures, 4 tables. Accepted for publication in ApJ

We present a spectroscopic and photometric determination of the distance to the young Galactic open cluster Westerlund 2 using WFPC2 imaging from the Hubble Space Telescope and ground-based optical spectroscopy. HST imaging in the F336W, F439W, F555W, and F814W filters resolved many sources previously undetected in ground-based observations and yielded photometry for 1136 stars. We identified fifteen new O-type stars, along with two probable binary systems, including MSP 188 (O3 + O5.5). We fit reddened SEDs based on the Padova isochrones to the photometric data to determine individual reddening parameters $R_{V}$ and $A_{V}$ for O-type stars in Wd2. We find average values $\langle R_{V} \rangle = 3.77 \pm 0.09$ and $\langle A_{V} \rangle = 6.51 \pm 0.38$ mag, which result in a smaller distance than most other spectroscopic and photometric studies. After a statistical distance correction accounting for close unresolved binaries (factor of 1.08), our spectroscopic and photometric data on 29 O-type stars yield that Westerlund 2 has a distance $\langle d \rangle = 4.16 \pm 0.07$ (random) $+0.26$ (systematic) kpc. The cluster's age remains poorly constrained, with an upper limit of 3 Myr. Finally, we report evidence of a faint mid-IR PAH ring surrounding the well-known binary candidate MSP~18, which appears to lie at the center of a secondary stellar grouping within Westerlund 2., Comment: 58 pages, 20 figures

(Abridged) We present a systematic study of the X-ray and multiwavelength properties of a sample of 17 highly radio-loud quasars (HRLQs) at z > 4 with sensitive X-ray coverage from new Chandra and archival Chandra, XMM-Newton, and Swift observations. Eight of the new and archival observations are reported in this work for the first time. New Chandra observations of two moderately radio-loud and highly optically luminous quasars at z > 4 are also reported. Our HRLQ sample represents the top ~5% of radio-loud quasars in terms of radio loudness. We found that our HRLQs have an X-ray emission enhancement over HRLQs at lower redshifts (by a typical factor of ~3), and this effect, after controlling for several factors which may introduce biases, has been solidly estimated to be significant at the 3-4 sigma level. HRLQs at z=3-4 are also found to have a similar X-ray emission enhancement over z < 3 HRLQs, which supports further the robustness of our results. We discuss models for the X-ray enhancement's origin including a fractional contribution from inverse Compton scattering of cosmic microwave background photons. No strong correlations are found between the relative X-ray brightness and optical/UV emission-line rest-frame equivalent widths (REWs) for radio-loud quasars. However, the line REWs are positively correlated with radio loudness, which suggests that relativistic jets make a negligible contribution to the optical/UV continua of these HRLQs (contrary to the case where the emission lines are diluted by the relativistically boosted continuum). Our HRLQs are generally consistent with the known anti-correlation between radio loudness and X-ray power-law photon index. We also found that the two moderately radio-loud quasars appear to have the hardest X-ray spectra among our objects, suggesting that intrinsic X-ray absorption (N_H~10^23 cm^-2) may be present., Comment: ApJ in press; 9 figures, 13 tables

AU Mon is a long-period (11.113 d) Algol-type binary system with a persistent accretion disk that is apparent as double-peaked H-alpha emission. We present previously unpublished optical spectra of AU Mon which were obtained over several years with dense orbital phase coverage. We utilize these data, along with archival UV spectra, to model the temperature and structure of the accretion disk and the gas stream. Synthetic spectral profiles for lines including H-alpha, H-beta, and the Al III and Si IV doublets were computed with the Shellspec program. The best match between the model spectra and the observations is obtained for an accretion disk of inner/outer radius 5.1/23 R_sun, thickness of 5.2 R_sun, density of 1.0e-13 g/cm^3, and maximum temperature of 14000 K, along with a gas stream at a temperature of ~8000 K transferring ~2.4e-9 M_sun/yr. We show H-alpha Doppler tomograms of the velocity structure of the gas, constructed from difference profiles calculated through sequentially subtracting contributions from the stars and accretion structures. The tomograms provide independent support for the Shellspec modeling, while also illustrating that residual emission at sub-Keplerian velocities persists even after subtracting the disk and stream emission. Spectral variability in the H-alpha profile beyond that expected from either the orbital or the long-period cycle is present on both multi-week and multi-year timescales, and may reflect quasi-random changes in the mass transfer rate or the disk structure. Finally, a transient UV spectral absorption feature may be modeled as an occasional outflow launched from the vicinity of the disk-stream interaction region., Comment: 16 pages, 12 figures, 3 tables, emulateapj. Accepted to ApJ

Magnetic (or tidal) interactions between "hot Jupiters" and their host stars can potentially enhance chromospheric and coronal activity. An ideal testbed for investigating this effect is provided by the extreme WASP-18 system, which features a massive (~10 times Jupiter) close-in (~1 day period) transiting planet orbiting a young F6 star. Optical and X-ray observations of WASP-18 were conducted in November 2011. The high-resolution echelle spectrograph MIKE was used on the 6.5m Magellan Clay telescope to obtain 13 spectra spanning planetary orbital phases of 0.7-1.4, while the X-ray Telescope on Swift provided contemporaneous monitoring with a stacked exposure of ~50 ks. The cores of the Ca II H and K lines do not show significant variability over multiple orbits spanning ~8 d, in contrast to the expectation of phase-dependent chromospheric activity enhancements for efficient star-planet interaction. The star is also X-ray faint, with log Lx < 27.6 erg/s (0.3-2 keV), indicating that coronal activity is likewise low. The lack of detectable star-planet interaction in this extreme system requires that any such effect must here be transient, if indeed present. We demonstrate that searches for Ca II H and K variability can potentially mistake a stellar hotspot, if observed over a short segment of the rotation period, for planet-induced activity. Taken together, these results suggest that the utility of star-planet interaction as a robust method of estimating exoplanet magnetic field strengths may be limited., Comment: Accepted to ApJ; 9 pages emulateapj, 5 figures, 1 table (v2: corrected fn15, typos, refs)

[abridged] The radio:X-ray correlation for hard and quiescent state black hole X-ray binaries is critically investigated in this paper. New observations of known sources, along with newly discovered ones, have resulted in an increasingly large number of outliers lying well outside the scatter about the quoted best-fit relation. Here, we employ and compare state of the art data clustering techniques in order to identify and characterize different data groupings within the radio:X-ray luminosity plane for 18 hard and quiescent state black hole X-ray binaries with nearly simultaneous multi-wavelength coverage. Linear regression is then carried out on the clustered data to infer the parameters of a relationship of the form {ell}_{r}=alpha+beta {ell}_x through a Bayesian approach (where {ell} denotes log lum). We conclude that the two cluster model, with independent linear fits, is a significant improvement over fitting all points as a single cluster. While the upper track slope (0.63\pm0.03) is consistent, within the errors, with the fitted slope for the 2003 relation (0.7\pm0.1), the lower track slope (0.98\pm0.08) is not consistent with the upper track, nor it is with the widely adopted value of ~1.4 for the neutron stars. The two luminosity tracks do not reflect systematic differences in black hole spins as estimated either from reflection, or continuum fitting method. These results are insensitive to the selection of sub-samples, accuracy in the distances, and to the treatment of upper limits. Besides introducing a further level of complexity in understanding the interplay between synchrotron and Comptonised emission from black hole X-ray binaries, the existence of two tracks in the radio:X-ray domain underscores that a high level of caution must be exercised when employing black hole luminosity relations for the purpose of estimating a third parameter, such as distance or mass., Comment: MNRAS, in press (10 pages, 7 figures)

We use the AMUSE-Virgo and AMUSE-Field surveys for nuclear X-ray emission in early-type galaxies to conduct a controlled comparison of low-level supermassive black hole activity within cluster and field spheroids. While both the Virgo and the Field samples feature highly sub-Eddington X-ray luminosities (log L_x/L_Edd between -8 and -4), we find that after accounting for the influence of host galaxy stellar mass, the field early-type galaxies tend toward marginally greater (0.38+/-0.14 dex) nuclear X-ray luminosities, at a given black hole mass, than their cluster counterparts. This trend is qualitatively consistent with the field black holes having access to a greater reservoir of fuel, plausibly in the form of cold gas located near the nucleus. We are able to rule out at high confidence the alternative of enhanced X-ray activity within clusters. Presuming nuclear X-ray emission correlates with the total energy and momentum output of these weakly accreting black holes, this indicates that low-level active galactic nucleus feedback is not generally stronger within typical cluster galaxies than in the field. These results confirm that for most cluster early-type galaxies (i.e., excluding brightest cluster galaxies) direct environmental effects, such as gas stripping, are more relevant in quenching star formation., Comment: Corrected typos and references; 6 pages emulateapj, 2 tables, 3 figures. Published in ApJ Letters

We present the first results from AMUSE-Field, a Chandra survey designed to characterize the occurrence and intensity of low-level accretion onto supermassive black holes (SMBHs) at the center of local early-type field galaxies. This is accomplished by means of a Large Program targeting a distance-limited (<30 Mpc) sample of 103 early types spanning a wide range in stellar masses. We acquired new ACIS-S observations for 61 objects down to a limiting (0.3-10 keV) luminosity of 2.5x10^38 erg/s, and we include an additional 42 objects with archival (typically deeper) coverage. A nuclear X-ray source is detected in 52 out of the 103 galaxies. After accounting for potential contamination from low-mass X-ray binaries, we estimate that the fraction of accreting SMBHs within the sample is 45+/-7 percent, which sets a firm lower limit on the occupation fraction within the field. The measured nuclear X-ray luminosities are invariably highly sub-Eddington, with -8

We complete our census of low-level nuclear activity in Virgo Cluster early-type galaxies by searching for obscured emission using Spitzer Space Telescope mid-infrared (MIR) imaging at 24mu. Of a total sample of 95 early-type galaxies, 53 objects are detected, including 16 showing kiloparsec-scale dust in optical images. One dimensional and two dimensional surface photometry of the 37 detections without extended dust features reveals that the MIR light is more centrally concentrated than the optical light as traced by Hubble Space Telescope F850LP-band images. No such modeling was performed for the sources with dust detected in the optical images. We explore several possible sources of the MIR excess emission, including obscured nuclear emission. We find that radial metallicity gradients in the stellar population appear to be a natural and most likely explanation for the observed behavior in a majority of the sources. Alternatively, if the concentrated MIR emission were due to nuclear activity, it would imply a MIR-to-X luminosity ratio ~5-10 for the low luminosity AGN detected in X-rays by our survey. This ratio is an order of magnitude larger than that of typical low-luminosity AGN and would imply an unusual spectral energy distribution. We conclude that the black holes found by our survey in quiescent early-type galaxies in Virgo have low bolometric Eddington ratios arising from low accretion rates and/or highly radiatively inefficient accretion., Comment: 17 pages, 8 figures; accepted for publication in ApJ