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AMUSE-Field I: Nuclear X-ray Properties of Local Field and Group Spheroids across the Stellar Mass Scale

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<log(L_X/L_Edd)<-4. As also found in a companion survey targeting Virgo early types, the active fraction increases with increasing host galaxy stellar mass, reflective of"Eddington incompleteness"within the lower-mass objects. For the Field sample, the average nuclear X-ray luminosity scales with the host stellar mass as M_star^(0.71+/-0.10), with an intrinsic scatter of 0.73+/-0.09 dex. A majority of the AMUSE-Field galaxies (78%) inhabits groups, enabling us to investigate the influence of group richness upon nuclear activity. We see no evidence for a positive correlation between nuclear X-ray luminosity, normalized to host properties, and galaxy density. Rather, while the scatter is substantial, it appears that the Eddington-scaled X-ray luminosity of group members may be slightly lower than for isolated galaxies, and that this trend continues to cluster early-types.

The peak of the quasar space density around z ∼ 2 (e.g., Brown et al. 2006;Hopkins et al. 2007; Kelly et al. 2010) 4 and the ∼10 8 yr quasar lifetime (e.g., Yu & Tremaine 2002) suggest (e.g., Soltan 1982) that "inactive" galactic nuclei typically also host SMBHs accreting at low levels and/or radiating inefficiently in a postquasar stage which may result after much of the available fuel has been consumed or expelled (e.g., Hopkins et al. 2005). The distinctions between active galactic nuclei (AGNs), low-luminosity AGNs (Ho 1999(Ho , 2008, and formally inactive galaxies are somewhat arbitrary, but as a general guideline (which we will adhere to in this work) AGNs display bolometric, Eddington-scaled luminosities in excess of a few percent, low-luminosity AGNs are in the range 10 −4 < L/L Edd < 10 −2 , and inactive nuclei are highly sub-Eddington, with L/L Edd < ∼ 10 −4 . The Milky Way is one example of a formally inactive galaxy. It is known to host a quiescent central SMBH with mass of 3.6 × 10 6 M ⊙ (e.g., Schödel et al. 2009) from which low-level, persistent accretion-powered X-ray emission has been detected (L X /L Edd ≃ 10 −11 ; Baganoff et al. 2001). Even low levels of SMBH accretion-powered activity in nearby galaxies may be detected efficiently in sensitive, high spatial resolution X-ray observations, although contamination from bright X-ray binaries must be properly accounted for when dealing with nuclear X-ray luminosities comparable to the Eddington limit for a few solar masses (e.g., Zhang et al. 2009;Gallo et al. 2010). This problem can be substantially alleviated by restricting the search for highly sub-Eddington nuclei to early-type galaxies, as they conveniently avoid the brighter high-mass X-ray binaries produced concurrently with star formation (e.g., King et al. 2001;Ghosh et al. 2009).
From X-ray and other observations as well as numerical simulations, a coherent scenario for the history and observed characteristics of quiescent or weakly accreting SMBHs in early-type galaxies is emerging. Although hot halo gas or stellar winds provide readily available fuel and gas infall may proceed at near the Bondi rate, outflows can drive off a substantial fraction of the accreting mass and the radiative efficiency is inferred from observed spectral energy distributions to be highly sub-Eddington (e.g., Di Matteo et al. 2000;Pellegrini 2005;Soria et al. 2006b).
The growth of SMBHs is believed to be closely tied to the evolution of their hosts (as evidenced by, for example, the correlations between SMBH mass and bulge luminosity or central stellar velocity dispersion; see, e.g., overview by Ferrarese & Ford 2005). Radiative and mechanical AGN feedback act to regulate SMBH accretion and quench star formation (e.g., Ciotti et al. 2009Ciotti et al. , 2010Pellegrini et al. 2012), and mechanical feedback continues to play an important role in low-activity "radio-mode" systems (e.g., Croton et al. 2006;Merloni & Heinz 2007;Marulli et al. 2008). The assembly of early-type galaxies apparently proceeds hierarchically, despite the older ages and shorter star-formation timescales of massive ellipticals (e.g., De Lucia et al. 2006;Eliche-Moral et al. 2010), with cold-gas-rich/poor ("wet"/"dry") mergers tending to produce discy/boxy types (e.g., Kang et al. 2007;Hopkins & Quataert 2011).
Naturally the properties of higher-mass SMBHs (in more massive galaxies) may be more easily constrained; the dominance of compact stellar nuclei at lower luminosities (e.g., Ferrarese et al. 2006a) presented initial observational challenges to establishing whether lower-mass early-type galaxies necessarily even contained a SMBH. The presence of "missing light" or cores within luminous ellipticals may be explained by binary black holes disrupting the interior region in the process of merging (e.g., Kormendy et al. 2009 and references therein), and so preserved nuclear star clusters could potentially indicate a lack of a SMBH binary phase (e.g., Kang et al. 2007). However, it is now clear that SMBHs may coexist with nuclear star clusters (e.g., Seth et al. 2008;Graham & Spitler 2009;Kormendy et al. 2009).
To quantify the rate of low-level SMBH activity over a well defined sample of nearby early-type galaxies, our group carried out the AGN MUltiwavelength Survey of Early-Type Galaxies in the Virgo cluster. AMUSE-Virgo (ID 8900784, Chandra Cycle 8, PI: Treu, 454 ks) targeted the 100 spheroidal galaxies which compose the Hubble ACS Virgo Cluster Survey (VCS; Côté et al. 2004) with Chandra ACIS-S and Spitzer MIPS (Gallo et al. 2008(Gallo et al. , 2010Leipski et al. 2012). The VCS sample was selected based solely on optical properties and spans a wide range in stellar mass, from 10 8 −10 12 M ⊙ . At the average Virgo distance of 16.5 Mpc (Mei et al. 2007), the AMUSE-Virgo Chandra snapshot observations (about 5 ks each) reached a 2σ limiting 0.5-7 keV luminosity of 1.3 × 10 38 erg s −1 (i.e., close to the Eddington limit for 1 M ⊙ ). A nuclear X-ray source was detected by G10 in 32/100 objects, which, after taking into consideration the minor but non-negligible effects of low-mass X-ray binary (LMXB) contamination, sets a lower limit of 24-34% (at the 95% confidence level) to the occupation fraction of SMBHs in the nuclei of cluster early-type galaxies. Within the AMUSE-Virgo survey the fraction of X-ray-active SMBHs is seen to increase with host stellar mass, 5 but in a manner consistent with arising from "Eddington incompleteness", i.e., the intrinsic inability of any luminosity-limited survey to reach the same Eddington-scaled luminosity level across a wide range of inferred black hole masses. Despite this effect, which obviously penalizes lower mass black holes, the average Eddington-scaled X-ray luminosity of the AMUSE-Virgo galaxies is found to scale inversely with black hole mass as L X /L Edd ∝ M −0.62 BH , so that nearby lower-mass SMBHs are relatively more X-ray-active (a trend G10 refer to as "downsizing in black hole accretion"). In all cases the X-ray luminosity is highly sub-Eddington, with 10 −8 < ∼ L X /L Edd < ∼ 10 −5 . While this and other studies (e.g., Pellegrini 2005;Zhang et al. 2009;Boroson et al. 2011) have provided useful and detailed census of low-level SMBH activity within the local universe, including as a function of the host galaxy properties (Pellegrini 2010), the impact of environment upon the occurrence and intensity of SMBH activity remains unclear. The properties of early-type galaxies in more sparsely populated regions are distinct from their counterparts in clusters: relative to cluster sources, field early-type galaxies face reduced ram pressure stripping (e.g., Acreman et al. 2003;Gavazzi et al. 2010;Shin et al. 2012) and on average contain more cold gas and tend to have younger stellar populations (e.g., Thomas et al. 2005;Oosterloo et al. 2010). Within clusters, tidal interactions play an important role (e.g., Gnedin 2003), for example as harassment from highspeed encounters (e.g., Treu et al. 2003); such effects are only infrequently relevant to isolated field galaxies, although within groups the lower galaxy velocity dispersions can help facilitate mergers. Early work with ROSAT links the environment with X-ray emission, but to a debated degree; for example, Brown & Bregman (2000) found that cluster early-type galaxies tend to be more X-ray luminous than their field counterparts, and hypothesized that this results from environmental suppression of outflows or the availability for accretion of hot intergalactic gas within clusters, whereas O'Sullivan et al. (2001) found similar L X (L B ) relations for cluster, group, and field galaxies. While such results are intriguing, their utility is necessarily restricted by the limited angular resolution of ROSAT , which makes it difficult to disentangle diffuse thermal X-ray or off-nuclear X-ray binary emission from that linked to the SMBH.
The goal of this work is to investigate low-level SMBH activity within a well defined sample of nearby field spheroidal galaxies (E and E-S0 galaxies), and to characterize the dependence (if any) of such activity upon environmental effects, such as living in isolation versus belonging to a group of galaxies, or belonging to a poor versus a rich group. Toward this end, we were awarded a Large Chandra program building upon and extending AMUSE-Virgo to non-cluster environments: AMUSE-Field (ID 11620915, Chandra Cycle 11, 479 ks, PI Gallo) carried out new observations of 61 field early-type galaxies located within 30 Mpc and spanning a wide range of stellar and black hole masses. The new observations are supplemented with an additional 42 objects with archival coverage, for a total of 103 objects. This paper is structured as follows: §2 describes the sample selection and Chandra data reduction; §3 provides the X-ray results; §4 investigates the dependence of nuclear X-ray luminosity on stellar mass; §5 discusses environmental influences upon SMBH accretion; §6 summarizes and concludes. L X , M star , and M BH are the nuclear 0.3-10 keV X-ray luminosity, galaxy stellar mass, and black hole mass, respectively, and are given in units of erg s −1 , M ⊙ , and M ⊙ throughout. Errors are 1σ unless otherwise noted.

REDUCTION
The AMUSE-Field sample was selected based only on optical galaxy properties, in the following manner. We first searched the HyperLeda 6 catalog (Paturel et al. 2003) for spheroidal galaxies, conservatively defined as having type E or E-S0, with inferred heliocentric velocities less than 1800 km s −1 and distances less than 30 Mpc. 7 Objects near the Galactic plane (|b| < 30 • ) were excluded, to avoid absorption effects. Objects near the Virgo cluster (within ≃ 6 • of 12.44h, 12.72 • ) or the Fornax cluster (within ≃ 0.2 • of 3.64h, −35.45 • ) were likewise excluded, to avoid contamination by cluster galaxies; these are the only clusters lying within the considered volume. Finally, objects were required to have absolute B magnitudes more luminous than M B = −13. This results in a list of 204 objects. Of these 204 objects, 42 already possessed high-quality archival Chandra ACIS-S3 imaging observations, which we define here as exposure > 3 ks and off-axis angle < 5 ′ . 61 additional targets were selected such that the full AMUSE-Field sample, made up of 103 early-type galaxies, provides representative coverage of a wide range in absolute B magnitude. Chandra exposures for the 61 new targets (which we shall generally refer to as "snapshots") vary between ∼ 2 − 12 ks, and were chosen to achieve a common sensitivity threshold of 2.5 × 10 38 erg s −1 (0.3-10 keV). Optical properties of the individual galaxies 8 are listed in Table 1, along with their derived stellar and black hole masses ( §4.1) and their group membership ( §5).
The Chandra ACIS-S X-ray data were reduced in a 6 http://leda.univ-lyon1.fr/ 7 For significantly larger distances, the total stellar mass enclosed by the Chandra point spread function becomes sufficiently large that the possibility of cumulative LMXB contamination is nonnegligible; see discussion in G10. 8 The full AMUSE-Field sample includes four objects for which we had X-ray data in hand but that do not technically meet all selection criteria. NGC 5077 has a distance of 40.2 Mpc but is otherwise suitable. PGC 132768, 042737, and 042596 (all X-ray nondetections) do not have a morphological type listed in HyperLeda; digital sky images suggest their morphologies, while spheroidal, are somewhat irregular. uniform fashion following the general procedure applied to the AMUSE-Virgo sample (G08, G10). Here we describe the astrometry correction, event reprocessing, lightcurve filtering, source detection, and aperture photometry. The calculation of X-ray luminosities from net count rates is described in §3.1.
The default Chandra astrometry is generally accurate to < ∼ 0.3 ′′ (1σ; e.g., §3 of Eckart et al. 2005), which is sufficient to identify uniquely which X-ray source, if any, is located nearest the galactic nucleus. For cases in which the pointing fell within the SDSS footprint, we improve the X-ray astrometry through cross-matching X-ray sources to their optical counterparts. A first-pass X-ray source list was created by running wavdetect on a 0.3-7 keV image generated from the pipeline level 2 event file. For each non-nuclear (> 10 ′′ ) ACIS-S3 X-ray source, the nearest primary SDSS object with r-band magnitude m r < 23 (hence highly accurate optical position) was sought, to within a radius dependent upon the wavdetect estimated net counts as well as the X-ray off-axis angle (this X-ray positional uncertainty is based on §2.3 of Hong et al. 2005). The average offset in right ascension and declination was calculated using weighting by the inverse uncertainties; any 3σ outliers were discarded and this process was repeated. The resulting offsets were converted to pixel shifts and used to generate a new aspect solution file. The number of "clean" matches to SDSS objects used to calculate the shifts ranged from 2 to 10, and in no cases were the shifts in x or y greater than one pixel (i.e., 0.5 ′′ ). Astrometry for pointings outside the SDSS footprint, or for observations lacking sufficient high-confidence cross matches, was not adjusted.
A background lightcurve of the S3 chip (with point sources excluded), binned to 200 s, was screened for flaring using the deflare script. Periods of anomalously high or low background were identified as any > 3σ deviations from the mean count rate for most observations, and as any > 2.5σ or > 2σ deviations in a few instances where strong flaring was present, and confirmed through manual inspection. Such periods were then excluded through application of the deflare-generated good-time intervals as a filter to the level 2 event file.
An updated point source list was then compiled through running wavdetect on a clean 0.3-7 keV image with scales of 1, 1.4, 2, 2.8, and 4 pixels, using a 1.5 keV exposure map and a threshold significance of 10 −6 (which corresponds to approximately one false detection expected per chip). Net count rates were calculated for each source from aperture photometry conducted within 95% encircled energy radii (at 1.5 keV), with local background estimated from the median of eight nearby regions. For Field galaxies lacking a nuclear X-ray detection, the 95% confidence upper limit is estimated from the local background. Where the number of background counts is less than 10 we use the Bayesian formalism of Kraft et al. (1991) to determine the limit; elsewhere, we use Equation 9 from Gehrels (1986).
As they are the brightest galaxies within our volumelimited sample, the archival sources are generally more luminous, more massive, and thus able to retain more hot gas. For those objects, it is advantageous to determine the nuclear SMBH X-ray luminosity from the hard-band counts, so as to minimize contamination from the diffuse soft emission. The diffuse emission may be  Table 2) with detected nuclear Xray emission, smoothed with a Gaussian kernel of five pixels (2.5 ′′ ) and plotted with common squareroot intensity scaling. Images are centered at the catalog optical coordinates of the host galaxy, and the position of the X-ray source associated with the nucleus is marked with a black cross. The rightmost panel in the bottom row shows the stacked image of snapshot targets that individually lack a nuclear X-ray detection (scaling does not match other frames); the central region is detected, with an average X-ray luminosity consistent with arising from a population of enclosed LMXBs.
modeled as thermal (hot gas) and power-law (unresolved LMXBs) components (e.g., G10; Boroson et al. 2011). For these galaxies, the contribution from hot gas generally drops below ∼5% of the nuclear X-ray flux at energies < ∼ 2 keV. Therefore, for archival galaxies with sufficiently high signal-to-noise data, defined as ≥ 50 counts in the 0.3-7 keV band (29/42 objects), we calculate X-ray flux from the 2-7 keV count rate. 9 In a few instances for which strong diffuse emission overlapped the nucleus even in the hard band, the local background was manually adjusted.

RESULTS
3.1. Nuclear X-ray census X-ray properties of the AMUSE-Field sample are listed in Table 2, and notes on selected archival objects are given in Appendix A. From the 103 field galaxies, a nuclear X-ray source is detected in 52 cases, for a detection fraction of 50%. The detection fraction is naturally higher for the archival objects (33/42, or 79%), due to their generally deeper exposures 10 References for previously published analysis of the archival objects are also listed in Table 2. 9 There are two exceptions: one snapshot object, ESO 540-014, has sufficient counts to permit use of the 2-7 keV rate, and one archival object, NGC 1052, has a sufficiently hard observed spectrum that we use the 0.3-7 keV rate to avoid overestimating the X-ray flux.
10 Of the nine archival upper limits, five have effective exposure times less than 10 ks, two are small galaxies serendipitously observed off-axis (θ > ∼ 2.5 ′ ), and two (NGC 5846 and NGC 3923; see Appendix A) do not show a cleanly resolved central point source.
The detection fraction for the snapshot objects is 19/61, or 31%. Cutout images of all snapshot targets with detected nuclear X-ray emission are shown in Figure 1, smoothed with a Gaussian kernel of five pixels. Count rates (either 0.3-7 keV or 2-7 keV, as discussed in §2) were converted to 0.3-10 keV fluxes with PIMMS, 11 assuming a power-law spectrum with Γ = 2 and Galactic absorption. For each galaxy the radial-velocity distance modulus in HyperLeda was used to calculate the nuclear 0.3-10 keV X-ray luminosity, L X . For most of these objects, non-redshift distances are not available in HyperLeda or NED; from the remainder, the non-redshift distance modulus from HyperLeda is an average of 0.16 lower, corresponding to a distance ∼ 1.5 Mpc closer at d ∼ 20 Mpc. For the low redshift of these objects, the k-correction is insignificant and is therefore neglected.
Nine field galaxies have logL X > ∼ 39.8: NGC 1052, 2768, 4036, 4203, 4278, 4494, 5077, IC 1459, and ESO 540−014. All but the last of these are from the archival sample. Each one of these nine galaxies has radio and/or optical properties consistent with the presence of lowlevel AGN activity.  (2006) as Seyfert 1, LINER b, LINER b, and Seyfert 2 galaxies, respectively. In comparison, the AMUSE-Virgo sample contains only two objects (M87 and NGC 4564) with log L X > 39.8 (from Table 1 of G10).

Origins of the nuclear X-ray emission
The correspondence between higher values of X-ray luminosity and optical or radio indicators of activity ( §3.1) already supports that, for at least these objects, the nuclear X-ray emission is linked to the central SMBH. Indeed, prior studies of early-type galaxies (G08, G10, and references in §1) have overwhelmingly associated nuclear point-source L X measurements with low-level SMBH activity. While our observations are not designed to determine the precise X-ray emission mechanism, various proposed inefficient accretion flow models (see, e.g., discussion and references in Soria et al. 2006b) may apply to the objects in the AMUSE samples. We here also consider alternative origins for the nuclear X-ray emission, and find that they likely explain at most a small fraction of the observed detections.
The probability of finding an unrelated background source of equal or greater flux within the Chandra PSF for any given nuclear X-ray detection is negligible, based on the N (S) relation provided by Moretti et al. (2003), which Bauer et al. (2004) find matches the source count distribution within the Chandra Deep Fields. Contamination from LMXBs, while still unlikely, must be considered as a potential source of nuclear X-ray emission ( §3.2.1). Tidal disruption of stars may provide an alternative method of fueling SMBHs ( §3.2.2).

Low mass X-ray binary contamination
Where a nuclear star cluster is not present, the total number of LMXBs and their cumulative X-ray luminos-ity scale approximately with the stellar mass (Gilfanov 2004;Kim & Fabbiano 2004;Humphrey & Buote 2006), and so the number of LMXBs per unit stellar mass above a particular luminosity threshold may be estimated from the X-ray luminosity function for LMXBs (e.g., Gilfanov 2004). We estimate the projected stellar mass enclosed by the Chandra PSF based on the fractional luminosity within 2 ′′ ; as most of the Field galaxies currently lack high-resolution HST imaging, we use as a comparative template similarly-distant Virgo early-type galaxies with −17 < M B < −16 (i.e., log (M star /M ⊙ ) ∼ 9 − 10) which tend to have effective radii 10-20 ′′ with Sersic indices of 1.0-2.5 (Ferrarese et al. 2006b). The total X-ray luminosity from LMXBs within the nucleus of a typical such galaxy is L X = 1.0×10 37 erg s −1 , which is 4% of the Field detection limit. The expected nuclear contribution from LMXBs can be several times greater in large ellipticals, where the total stellar mass can be log (M star /M ⊙ ) ∼ 11 (here the smaller fraction of the effective radius enclosed by the PSF is partially offset by a higher Sersic index, for simple models, but see, e.g., Ferrarese et al. 2006b for discussion of surface brightness profiles), but for such galaxies in the Field sample the nuclear X-ray luminosities are generally substantially above the detection limit. In summary, due to the steepness of the LMXB luminosity function above a few 10 38 erg s −1 , for most of the Field galaxies it is highly unlikely that the PSF-enclosed stellar mass would generate significant LMXB contribution to the measured L X values. Figure 2 shows the log L X number density for the Field sample, which may be satisfactorily modeled as dN/dlogL X = 100 × (L X /10 38 ) −0.6 . As for the Virgo sample (see Figure 6 of G10), this is much shallower than would be expected if most of the X-ray detections were actually LMXB-dominated.
Massive nuclear star clusters, with inferred radii around a few tens of pc, become increasingly prominent down the mass function (e.g., Bekki & Graham 2010;Graham et al. 2011; and references therein). The enhanced stellar encounter rates within a nuclear star cluster implies a larger possibility of chance LMXB contamination. To account for this effect, for nucleated galaxies G10 conservatively adopted the higher X-ray luminosity function of LMXBs in globular clusters, as estimated by Sivakoff et al. (2007). Unfortunately, most of the field galaxies discussed here currently lack the two-color highresolution optical imaging (i.e., carried out with HST ACS) necessary to confirm the presence of a nuclear star cluster and to infer its mass.
To estimate the degree of LMXB contamination within the field sample detections, we note that the AMUSE-Virgo sample contained 6/32 objects with both a nuclear star cluster and an X-ray detection. All six of these objects had log (M star /M ⊙ ) < 10.5 (and in total there are 16 Virgo X-ray detections with log (M star /M ⊙ ) < 10.5). The influence of nuclear star clusters at higher stellar masses, even if present, is of decreasing relevance; Graham & Spitler (2009) find that in mixed nuclei the SMBH mass dominates that of the nuclear star cluster for spheroid masses above ∼ 10 10 M ⊙ . In 4/6 of the Virgo objects with both a nuclear star cluster and an X-ray detection (i.e., in 4/16 of Virgo X-ray detected objects with log (M star /M ⊙ ) < 10.5), G10 calculate that the X-ray emission was likely due to LMXB rather than Figure 2. The log LX number density for the AMUSE-Field sample (solid blue line) may be modeled as dN/dlogLX = 100 × (LX/10 38 ) −0.6 (dotted black line). For comparison, the result for the AMUSE-Virgo sample (dashed red line) is plotted along with the Field number density rescaled by 0.5 (dotted cyan line). The luminosity function for LMXBs is much steeper (see, e.g., Figure 6 of G10), confirming that in almost all cases the X-ray detections are linked to low-level SMBH activity.
SMBH activity. Applying a similar rate 12 of 4/16=0.25 to the 22 Field galaxies with log (M star /M ⊙ ) < 10.5 and X-ray detections suggests that in < ∼ 6 cases the X-ray emission might be contaminated by a bright LMXB; Figure 4 shows one plausible distribution of intrinsic SMBH detections in the Field sample (here the galaxies with presumed nuclear star cluster LMXB contamination all have L X < 5 × 10 38 erg s −1 ). The detected intrinsic fraction of accreting SMBHs within the Field sample is then ∼46/103 (rather than the observed 52/103 rate of X-raydetected nuclei), or 45 ± 7%, which sets a lower limit to the occupation fraction of SMBHs within these galaxies.
Off-nuclear X-ray sources from many of the archival observations are discussed elsewhere (e.g., . Within the snapshot observations, several offnuclear X-ray sources are detected within three times the effective radius (this limit is sometimes used to construct catalogs of ultraluminous X-ray sources (ULXs) or LMXBs; e.g., Irwin et al. 2003). Based on the cosmic N (S) relation previously discussed, the majority of these are unlikely to be unrelated background sources. Presuming the off-nuclear X-ray sources have distances as for the corresponding galaxy, we do not find any ULXs with L X > ∼ 10 40 erg s −1 . A complete catalog of ULXs for the Field snapshot galaxies will be presented in a later work, in which their properties will be placed in context with our upcoming HST observations and will be compared to ULXs found within the AMUSE-Virgo snapshot sample.

X-ray emission from stellar tidal disruption
One interesting possibility for fueling SMBHs is through tidal disruption of stars (e.g., Rees 1988). Simulations indicate that such events could result in temporary super-Eddington infall, followed by thin-disk accretion, likely transitioning to a radiatively-inefficient flow (Strubbe & Quataert 2009). The predicted spectrum includes soft X-ray blackbody emission, plausibly with an additional power-law tail (Strubbe & Quataert 2011). A handful of individual cases of potential tidal disruption events have been identified (e.g., Lin et al. 2011 and references therein), including most recently the spectacular Swift J164449.3+573451 (Burrows et al. 2011;Levan et al. 2011); in this rare case L X significantly exceeds L Edd for the inferred modest black hole mass (log M BH /M ⊙ = 5.5 ± 1.1; Miller & Gültekin 2011), suggesting the observed emission comes predominantly from a beamed relativistic jet (Bloom et al. 2011;Burrows et al. 2011;Cannizzo et al. 2011). Deep surveys generally provide only loose upper limits on the typical rate (e.g., < 10 −4 yr −1 per galaxy; Luo et al. 2008), but numerical simulations carried out by Brockamp et al. (2011) suggest that approximately 3.0 ± 1.4 events per 10 5 yr are typical for a SMBH of 10 6 M ⊙ . We use this rate to estimate the fraction of time for which a 10 6 M ⊙ black hole would display L X,tidal > 2.5×10 38 erg s −1 (the AMUSE-Field detection limit).
The timescale until the accretion rate drops below Eddington, following the canonical t −5/3 scaling (Rees 1988), is < ∼ 0.3-1 yr (Strubbe & Quataert 2009). Subsequent evolution of the disk-dominated emission as t −1.2 (Cannizzo et al. 1990) is likely curtailed afteṙ m < ∼ 10 −2ṁ Edd (Strubbe & Quataert 2009), around ∼100 yr, after which material likely accretes through a thick disk. Presuming isotropic emission for simplicity, and taking L X,tidal ≃10 42 erg s −1 during the initial flare (motivated by Strubbe & Quataert 2011), then L X,tidal ≃4×10 39 erg s −1 after ∼100 yr, dropping below our detectability threshold by < ∼ 1000 yr (or sooner for an abrupt transition to radiatively inefficient accretion). The fraction of time for which a tidal disruption event could dominate the X-ray emission observed in a similar AMUSE-Field galaxy is then < ∼ 3%. (These estimates are for a solar-mass main-sequence star; see, e.g., Li et al. 2002 andLodato et al. 2009 for alternatives). For reference, the AMUSE-Field sample contains 31 galaxies with M BH < 10 6 M ⊙ , so we might anticipate detecting X-ray emission associated with stellar disruption in about one object.
For SMBHs with M BH > 10 7 M ⊙ , tidal disruption is expected to be less significant, as the distance at which a stellar trajectory can dynamically enter the loss cone exceeds the radius of influence (Brockamp et al. 2011), and in addition the refill timescale is quite long in large ellipticals, particularly core galaxies (Merritt & Wang 2005). Most (42/52) of the AMUSE-Field galaxies with X-ray detections have M BH > 10 7 M ⊙ . In view of the above, we conclude that the nuclear X-ray emission in the AMUSE-Field galaxies is not related to tidal disruption events, although without multi-epoch observations we cannot rule it out for any specific object. Instead, the SMBHs in these galaxies are more likely currently fed through quasi-continuous but highly sub-Eddington accretion, as arising from, for example, mass loss from evolved stars (Soria et al. 2006b;Volonteri et al. 2011).

Stacking non-detection
The 42 snapshot observations lacking a nuclear X-ray detection were stacked to check for a joint detection and assess their average X-ray luminosity. After excising all off-nuclear X-ray point sources (occupying areas here defined by their wavdetect ellipses), the 0.3-7 keV images were stacked at the optical position of each target. The combined image (Figure 1, lower right) has an effective exposure of 307 ks. There is a significant excess of counts near the center, with 42.2 net counts (87.1 total, 44.9 background) present within a 10 pixel (4.9 ′′ ) extraction radius. (Stacking random positions does not produce a significant detection.) For an average N H of 2 × 10 20 cm −2 and taking Γ = 2, the rate of (1.4 ± 0.4) × 10 −4 counts s −1 corresponds to an average (unabsorbed) 0.3-10 keV flux of 1.1×10 −15 erg s cm −2 . The mean distance modulus for these 42 objects is 31.5 (20.0 Mpc), which gives an average X-ray luminosity of log L X = 37.7 erg s −1 . Given the total enclosed stellar mass, this is broadly consistent with arising from a population of individually undetectable LMXBs.
The excess X-ray emission within the stacked image is centrally concentrated but not pointlike, and extends to > ∼ 20 ′′ . The net rates within apertures of 4, 6, 10, 20, 40, and 60 pixels are 3.6, 6.3, 13.7, 23.0, 35.3, and 37.6 × 10 −5 counts s −1 , respectively. This indicates that the excess X-ray emission is not exclusively nuclear, and likely includes contributions from off-nuclear LMXBs as well as hot gas.
These results further confirm that the nuclear X-ray luminosities calculated for snapshot targets with X-ray detections do not suffer significantly from LMXB or hot gas contamination. With the caveat that the presence or absence of a nuclear star cluster has not been established for specific sources, the average overall contribution to L X from an underlying ensemble of LMXBs within a 2-3 ′′ aperture based on the above measurement is <5-9% of the minimum snapshot detected nuclear X-ray emission (log L X = 38.4 erg s −1 ), and the contribution from hot gas is negligible.

GLOBAL PROPERTIES OF THE AMUSE-FIELD SAMPLE
Here we determine and discuss the global properties of the AMUSE-Field sample, including stellar and black hole masses as well as Eddington-scaled X-ray luminosities. We then proceed to investigate the scaling between the measured nuclear X-ray luminosity and the host galaxy stellar mass, and we calculate the residual X-ray luminosity after accounting for this dependence. Finally, we test against the full Field sample the properties of the snapshot targets (which comprise a uniformsensitivity subset) and of elliptical galaxies (to check for possible systematic morphological effects). Table 3 contains the derived properties of the full AMUSE-Field sample as well as three subsets thereof, composed of: 1) snapshot targets; 2) elliptical galaxies, and 3) group members. (The influence of group richness is discussed in more detail in §5.) For each of the above subsets, along with the full sample, the mean and 25th, 50th, and 75th percentiles are calculated for the following quantities: log (M star /M ⊙ ), log (M BH /M ⊙ ), log (M BH /M star ), M B , and log L X for both detections and for all objects. The Kaplan-Meier distribution, which handles censored data (Kaplan & Meier 1968), was determined for X-ray luminosities including upper limits using the survival analysis package ASURV 13 (e.g., Lavalley et al. 1992). 14 To reduce any potential bias from archival observations, we conservatively impose a luminosity limit of log L X > 38.2 when examining the distribution of log L X (or quantities derived therefrom) with limits included, and when carrying out fitting of L X (M star ); six objects (two detected) from the full Field sample do not meet this screening criteria. The adopted methodology and calculation of these quantities is described in detail in the following sub-sections.

Stellar and black hole masses
The host galaxy stellar mass is calculated from the absolute B magnitude and from optical/IR color. Absolute B magnitudes for the total galaxy (for these sources, essentially equivalent to the spheroidal luminosities) are taken from the HyperLeda catalog. These are based on total B magnitudes reduced to the RC3 system and corrected for Galactic absorption, and calculated for distances identical to those used to determine L X . We calibrate our procedure against the stellar masses established for the galaxies in the AMUSE-Virgo survey, which were determined based on F457W and F850LP HST/ACS imaging (G08 §3.3); these filters roughly correspond to SDSS g and z bands (Fukugita et al. 1996) and provide nearly equivalent colors. The primary relation used to calculate stellar mass is Table 7 of Bell et al. 2003); Figure 3 illustrates that using SDSS g − z model-magnitude colors (corrected for Galactic extinction) gives results consistent with those obtained from the higher-resolution HST/ACS data, with a mean difference of −0.01 ± 0.36. Where SDSS coverage is not available, we use instead corrected B − V colors (taken from HyperLeda) as Table 7 of Bell et al. 2003), but here we also add 0.07 which is the empirical median offset between M star derived from g − z versus B − V colors. No physical meaning is ascribed to this adjustment, which may merely arise from inconsistent effective apertures; similar median offsets are found for AMUSE-Virgo galaxies. The agreement between these methods is good (Figure 3; mean difference 0.03 ± 0.12). Where neither SDSS coverage nor HyperLeda B − V magnitudes are available, we use B − K colors (with total K magnitudes taken from the 2MASS catalog of extended sources) as Table 1 of Bell & de Jong 2001), but here we also add 0.18 which is the empirical median offset between M star derived from g − z versus B − K colors. The agreement between the g − z and B − K methods is also good (Figure 3; mean difference 0.03 ± 0.13). Finally, in the four cases (PGC 132768, PGC 064718, PGC 740586, and 6dF J2049400−324154) where neither SDSS coverage, nor HyperLeda B − V colors, nor 2MASS extended-source K magnitudes, were available, the median g − z = 1.16 is used to estimate M star . The X-ray detection fraction for the Field sample is illustrated versus M star in Figure 4.
Black hole masses (M BH ) are estimated from the massstellar velocity dispersion (M BH − σ) or else from the mass-bulge luminosity (M BH − L B ) correlations (e.g., see overview by Ferrarese & Ford 2005). These have been calibrated with independent measures of M BH , such as yielded by reverberation mapping , enabling straight-forward estimation of M BH . We use the updated relations presented in Gültekin et al. (2009), specifically those derived for early-type galaxies. As they find the scatter in the M BH − σ relation to be slightly lower than in the M BH − L relation for early-type galaxies, we use the former where high-quality measurements of σ are available in the literature. We note that caution is warranted when applying this correlation to a heterogeneous sample, as it is not clear that the M BH − σ relation holds in identical form to low masses (Greene et al. 2010) or high luminosities (Lauer et al. 2007) or for barred galaxies (Graham 2008) or to higher redshifts (Treu et al. 2007;Woo et al. 2008). Only the first of these The red histogram shows nuclear X-ray detections, while the shaded histogram incorporates a statistical correction for potential LMXB contamination from nuclear star clusters. The bottom panel shows the X-ray detection fraction (solid crosses) within bins of low, moderate, and high stellar mass. The increased detection fraction with increasing stellar mass (e.g., Ho et al. 1997) results here primarily from an ability to detect X-ray emission to a lower Eddington fraction in higher-mass objects. A qualitatively similar effect was found for the Virgo sample (dashed crosses in bottom panel).
points is potentially relevant for this sample, and in practice there is only one Field galaxy with σ < 25 km s −1 , a measurement we discard due to concerns as to systematic errors.
Eddington luminosities are calculated from the abovedetermined black hole mass as L Edd = 1.3 × 10 38 (M BH /M ⊙ ) erg s −1 , and Eddington-scaled X-ray luminosities, log (L X /L Edd ), for the AMUSE-Field sample are plotted in Figure 5 versus both M BH and M star . Values from the AMUSE-Virgo sample are also shown for comparison. The distributions of M BH and M star are formally inconsistent (KS-test p = 0.01 and p < 0.001, respectively) between the Field and Virgo samples, but qualitatively similar general trends with Eddingtonscaled X-ray luminosities are observed.
It appears that a fixed L X /L Edd value (or range) across 5 < log (M BH /M ⊙ ) < 9 does not provide an adequate match to the observed data, which show a scarcity of large L X /L Edd values at large M BH . All objects are highly sub-Eddington, with Eddington-scaled nuclear X-ray luminosities ranging from < 10 −8 to 10 −4 . Clearly, the limiting sensitivity of the survey (∼ 2.5 × 10 38 erg s −1 for snapshot targets) acts to restrict the observable Eddington ratio for detected sources: due to the correlation between black hole mass and host stellar mass (linked to the underlying dependence of stellar mass on bulge optical luminosity), nuclear X-ray sources may be detected down to lower Eddington-scaled luminosities within higher M star galaxies, and this Eddingtonincompleteness effect can explain the increase in the Xray detection fraction with increasing stellar mass seen in Figure 4. This effect was noted by G10 for the Virgo sample. Despite these observational complications, the relative weakness of SMBH activity associated with the highest black hole masses in the Field sample is a qualitatively similar trend to the "downsizing" tendency noted by G10.

4.2.
Nuclear X-ray luminosity as a function of host stellar mass In the following we assess the relationship between nuclear X-ray luminosity and stellar mass within the AMUSE-Field sample, to investigate how activity in the nucleus is linked to the large-scale properties of the host galaxy. As M star is calculated from M B as well as color, this analysis is similar to examining a luminosityluminosity correlation and is grounded in observed quantities. It is reasonable to expect that some factor of the observed correlation between nuclear X-ray luminosity and stellar mass is merely reflective of a correlation between nuclear X-ray luminosity and black hole mass; because M star and M BH are correlated and, for many of these objects, both based on M B , it is difficult to disentangle their relative influence upon nuclear X-ray luminosities. Here we restrict out analysis to nuclear X-ray luminosity considered as a function of host stellar mass; we defer study of the L X (M BH ) relation to a later work , in which we compare the functional form of this relation within the AMUSE-Field sample to that found for the AMUSE-Virgo cluster early-types (G10), while fully accounting for the multiple methods of determining M BH and for the inconsistency in M star distributions between the Field and Virgo samples.
Fitting is carried out using the Bayesian IDL code of Kelly (2007), which incorporates both uncertainties and censoring, to determine the best-fit parameters. The functional form investigated is (log L X − 38.4) = A + B × (log M star − 9.8), where the variables are centered on approximately the median values. Points with log L X < 38.2 are excluded to avoid any potential bias from archival observations, but this has only a minimal effect on the result (e.g., the slope is insignificantly flattened by 0.07±0.14). Errors are taken to be 0.1 on log L X and 0.1 on log (M star /M ⊙ ), in both cases associated with the uncertainty in the distance rather than measurement error of the X-ray counts or the bulge luminosity. Several alternative forms of errors were investigated, including errors increasing with decreasing luminosities; in general, larger errors produce a slightly steeper slope but do not appreciably affect any of the below conclusions. Three Gaussians are used in the independent variable mixture modeling, and a minimum of 5000 iterations are performed with Gibbs sampling. The most likely parameter values are estimated as the median of 10000 draws from the posterior distribution, with credible intervals corresponding to 1σ errors calculated as the 16th and 84th percentiles. For completeness, we verified that using instead ASURV with either the expectation-maximization or Buckley-James method (Buckley & James 1979) identifies similar trends, with slightly flatter slopes.
Results are illustrated in Figure 6, with best-fit co- The Field sample is plotted with circles (snapshot/archival sources are blue/purple) and the Virgo sample is also plotted, with red diamonds, for comparison. X-ray detections/limits are shown as filled/open symbols. The solid black line in the left panel indicates the sensitivity limit of the Virgo survey, corresponding to the Eddington limit for a one solar mass black hole. While the distributions of black hole and stellar mass are formally inconsistent between the field and Virgo samples, qualitatively similar trends with Eddington-scaled X-ray luminosity are observed. Table 4. For the full AMUSE-Field sample, with all objects included, the best fit relation is (log L X − 38.4) = (−0.04 ± 0.12) + (0.71 ± 0.10) × (log M star − 9.8), with a rather large intrinsic scatter of σ = 0.73 ± 0.09. Consistent results are obtained for the subsets of snapshot targets, ellipticals, and group members. If only X-ray detected points are considered, the slope is considerably flatter, B = 0.35 ± 0.12 for the full sample. Residual X-ray luminosities may now be calculated as ∆L X,M * = log L X − log L X (log M star ), where log L X (log M star ) is the best-fit linear relation for the full Field sample as defined above. ∆L X,M * thus provides a measure of relative X-ray brightness after accounting for the typical influence of stellar mass. As M star is derived from absolute B luminosity, the correlation we find for L X as a function of M star is qualitatively similar to the tendency noted by Pellegrini (2010) for L X to increase with L B . The slope for the full AMUSE-Field sample of B = 0.71 ± 0.10 is incompatible with zero dependence, but also appears to be less than unity (at the 2.9σ level), indicating that nuclear X-ray luminosity may increase less rapidly than M star : this would imply lower-mass galaxies are more X-ray luminous per unit stellar mass. While the general trend in Figure 6 is clear, the observed dispersion in both L X and ∆L X,M * is larger for log M star > 10.5M ⊙ , and so it is possible that a more complex model could provide an improved representation of L X across the full range of stellar masses.

Uniform-sensitivity and morphologically distinct
sub-samples While the AMUSE-Field sample is by design fairly homogeneous, it does include both snapshot and archival objects, and both type E and type E-S0 galaxies. The snapshot sample possesses an approximately constant X-ray luminosity sensitivity threshold due to the deliberate choice of exposure times, which is not the case for the archival sample. Elliptical galaxies are completely spheroidal, whereas transition objects may include small disk components. It is thus useful to check the characteristics of these subsets.
Snapshot targets: The archival Chandra coverage available prior to selection of the snapshot sample understandably favored brighter galaxies expected to provide a high X-ray count rate. Within our volume-limited sample, the snapshot targets therefore tend to be galaxies of lower optical luminosity, and lower stellar mass. The ratios of black hole to stellar mass [i.e., log (M BH /M star )] are consistent with each other (KS p = 0.29) between the snapshot targets and the full Field sample, as log M BH is also lower for the snapshot targets. (Note that for a majority of the snapshot targets the M BH − L relation is used to calculate M BH and so black hole mass is directly dependent on optical luminosity. The M BH − L relation predicts slightly higher M BH values at low luminosities; see, e.g., discussion in G08.) The snapshot targets tend toward modestly lower X-ray luminosities where detected, and the difference is enhanced when upper limits are included (due to the lower detection fraction for the snapshot targets; §3.1); the snapshot targets have lower mean and Kaplan-Meier quartile log L x values, and two-sample tests conducted within ASURV indicate that the snapshot distribution of log L X is inconsistent with that of the full Field sample (logrank p = 0.006, Peto & Prentice p = 0.003; Latta 1981). However, the best-fit log L X (log M star ) relation for snapshot targets has an intercept and slope consistent with that for the full Field Figure 6. X-ray luminosity as a function of host galaxy stellar mass. Symbols are as in Figure 5. The solid line is the best-fit linear relation (to logarithmic quantities, for objects with log LX > 38.2) for the full Field sample, while the dotdashed, dotted, and dashed lines are for the snapshot, elliptical, and group member subsets; see §4.2 for details. For reference, the triple-dot-dashed line is the fit to X-ray detections only. All fit coefficients are provided in Table 4. sample. Further, the distribution of residual X-ray luminosities for the snapshot targets matches that of the full Field sample; the ∆L X,M * Kaplan-Meier quartiles are −0.29, 0.07, 0.37 for the snapshot targets and −0.36, 0.05, 0.38 for the Field sample, and two-sample tests also support consistency (logrank and Peto & Prentice p > 0.5). This confirms that after accounting for the dependence of L X upon M star , the snapshot targets have X-ray properties in line with those of the full Field sample. As the snapshot observations are sensitive to a uniform limiting luminosity ( §2), we further conclude that the full Field sample is not biased by the wide variety in exposure times of the archival objects.
Elliptical galaxies: Most (93/103) of the galaxies in the Field sample are ellipticals, and so it is not surprising that the properties of these ellipticals are virtually identical to those of the full Field sample. The detection fraction for ellipticals is 46/93 or 49%, whereas for nonellipticals (including three somewhat irregular spheroids unclassified in HyperLeda) it is 6/10 or 60% (for E-S0 galaxies in particular it is 6/7). While the mean or median L X values for objects are ∼ 0.5 dex greater for the 6 X-ray detected type E-S0 galaxies than for the 46 X-ray detected type E galaxies, the same holds true for M star values, and so the mean or median ∆L X,M * agree to within 0.1. In any event the scatter is sufficiently large that both the log L X and ∆L X,M * distributions for detected objects are consistent (KS p > 0.5) between field type E or type E-S0 galaxies; more quantitative assessment of any minor differences in nuclear X-ray properties would require a much larger sample of type E-S0 galaxies. It would also be interesting to examine a companion sample of S0 galaxies, for which we might expect the active fraction and the typical nuclear X-ray luminosity to be somewhat higher than for ellipticals, based on the increasing AGN fraction toward later morphological types and bluer galaxies found by Choi et al. (2009) and attributed by them to a relatively greater gas supply.

INFLUENCE OF GROUP RICHNESS ON NUCLEAR ACTIVITY
Although by construction the galaxies in the AMUSE-Field sample do not reside in clusters (recall from §2 that the coordinate selection excluded objects in the direction of Fornax and Virgo), some of them are members of groups, inhabiting regions characterized by galaxy over-densities intermediate between isolated and cluster environments. Groups provide a suitable environment for strong interactions and mergers, since the number density is higher than for the field but the dispersion in radial velocities of galaxies in groups is smaller than that found in clusters (recall the dynamical friction in a close encounter between two galaxies scales inversely with the square of their relative velocities). Tidal and ram-pressure stripping become increasingly important effects in richer groups (and clusters). As a consequence, membership in a group, and the richness of that group, could have an impact on the interaction history of a galaxy and on its gas content, both of which may be potentially relevant to the fueling of the SMBH. Here we investigate whether group membership or group properties influence nuclear X-ray activity.
We use the newly available catalog by Makarov & Karachentsev (2011) to determine group membership, if any, for each target. There are 8 AMUSE-Field objects not present in this catalog, and so the following analysis is limited to 95 objects. Following their approach, groups consist of four or more associated galaxies present within the zero-velocity surface; 74 (78%) AMUSE-Field galaxies satisfy this criteria. The largest group included here is that centered on NGC 5846, which contains 74 members; the Field sample includes 18 of these, of which 3 have X-ray detections (the nucleus of NGC 5846 itself is not significantly detected above the diffuse emission; see Appendix A). Overall, the detection fraction for group members is 40/74 or 54%, while for objects with n group < 4 (we will refer to these as "non-group" members but it is understood that they are also obviously not cluster members) it is 11/21 or 52%; these rates are consistent with being identical. There are 12 "isolated" galaxies (with n group = 1, although these may not be true void galaxies as in, e.g., Kreckel et al. 2011), of which 5 have X-ray detections, or 42%.
Restricting consideration to X-ray detected objects, the mean or median L X values for non-group members are consistent with those for group members (difference < 0.1 dex), but as the M star values of the non-group members tend to be lower by ≃0.6 dex, their mean and median ∆L X,M * values are higher (by ≃0.4 and ≃0.3, respectively). The scatter is large enough that the distributions of log L X and ∆L X,M * are consistent (KS p > 0.2) between group members or non-members. The 5 X-ray detected isolated 15 galaxies have even lower M star values than other non-group members, and consequent higher ∆L X,M * values (overcoming marginally lower L X values); here again the distributions of log L X and ∆L X,M * are not formally inconsistent at the α = 0.05 level (KS p = 0.38 and p = 0.06, respectively; the latter case is perhaps borderline).
When upper limits are incorporated, similar conclusions hold. Comparing non-group to group members, the distributions in log L X or ∆L X,M * are consistent (logrank and Peto & Prentice p > 0.4), despite slightly lower log L X and slightly higher ∆L X,M * values (by ∼0.2 dex) in non-group members. The Kaplan-Meier quartiles are systematically somewhat lower in log L X for isolated galaxies compared to group members (0.54, 1.08, 1.61 versus 0.70, 1.62, 2.11), but somewhat greater in ∆L X,M * (0.06, 0.32, 0.47 versus −0.40, 0.03, 0.30). The distributions are not formally inconsistent (logrank and Peto & Prentice p > 0.1). Eddington-scaled X-ray luminosities also display an apparent progression from lower to higher values moving from group to non-group to isolated galaxies, but again the significance is borderline. 16 We conclude that there is suggestive but inconclusive evidence that non-group members, particularly isolated galaxies, tend toward slightly enhanced values of log L X /L Edd or ∆L X,M * as compared to group members. If these results are confirmed, a possible interpretation is that interactions with the intra-group medium and other group members act to remove gas that could otherwise become available for SMBH accretion. This may be a secondary effect; for example, if star formation near the galaxy center were reduced by environmental interactions, less mass would be provided to the SMBH from stellar winds.
The nuclear X-ray luminosity, Eddington-scaled X-ray luminosity, and residual X-ray luminosity are plotted versus group size and group radial velocity dispersion in Figure 7. We also include the 100 cluster spheroids from the AMUSE-Virgo sample (G08, G10), with artificial random scatter added to their abscissa coordinates for improved visual clarity. The stellar mass of each galaxy is indicated by the size of the associated marker. While no strong trends are present and the scatter in X-ray properties is large, there appears to be a progression from generally higher to generally lower values of Eddington-scaled and residual X-ray luminosity moving from isolated to group to cluster environments. As groups are more hospitable to strong galaxy-galaxy interactions than are clusters (due to lower galaxy velocity dispersions), a continuous progression implies that merger history may not be the dominant factor controlling current nuclear X-ray activity. Instead, interactions with the intra-group or intra-cluster medium, which increase in importance as the galaxy velocity dispersions and the density of the medium increase, may influence low-level SMBH fueling. (A more quantitative and statistically-robust comparison 16 Including upper limits, the mean log L X /L Edd values for group members, non-group members, and isolated galaxies are −7.06 ± 0.11, −6.62 ± 0.20, and −6.26 ± 0.19, with median values of −7.22, −6.98, −6.63; removing ESO 540−014 from the isolated subset gives instead a mean of −6.41 ± 0.14 and median of −6.69. Two-sample tests for group members versus non-group members, isolated galaxies, or isolated galaxies excluding ESO 540−014 give logrank p = 0.10, 0.01, 0.05 and Peto & Prentice p = 0.10, 0.03, 0.12. Figure 7. Nuclear X-ray luminosity (top), Eddington-scaled X-ray luminosity (middle), and residual X-ray luminosity (bottom) plotted as a function of group size (left) and group velocity dispersion (right; note plots truncate lower values of σ 2 group ). Symbols are as in Figure 5 except that symbol size is here indicative of stellar mass. Artificial x-axis scatter has been added to the Virgo points to improve visual clarity. of X-ray luminosities in field versus cluster environments is provided in Miller et al. 2012.) Previous works examining the role of environment on X-ray emission in early-type galaxies found a trend opposite to that discussed above. A study using ROSAT data carried out by Brown & Bregman (2000) concluded that early-types in richer environments tended to be more X-ray luminous, with a positive correlation between L X /L B and galaxy density (but see also O'Sullivan et al. 2001). They speculated that this could reflect the influence of the hot intergalactic gas, either through acting to stifle galactic winds or more directly as an accretion source. We see no evidence for such a trend in the AMUSE-Field nuclear X-ray luminosities. This discrepancy is almost certainly due to the much finer spatial resolution of Chandra, which enables us to disentangle nuclear, accretion powered X-ray emission from soft diffuse X-ray emission from gas. In support of this conclusion, we note that the above ROSAT sample included several galaxies that are also members of our archival sample (NGC 0720, 1407, 4125, 4278, 4494, 4636, 4697, 5322, 5846) and that the X-ray luminosities measured by ROSAT are generally 1-2 orders of magnitude larger than those measured by Chandra.

SUMMARY
This work presents first results from the AMUSE-Field survey, a Large Chandra program designed to characterize low-level SMBH activity within nearby field spheroids. The Field sample contains 103 early-type noncluster galaxies within 30 Mpc, selected entirely based on their optical properties and spanning a wide range in absolute magnitude and stellar mass. For 61 objects we obtained new ACIS-S observations to a uniform limiting luminosity of 2.5 × 10 38 erg s −1 , and for the remaining 42 objects we make use of high-quality archival coverage. The primary results of this paper are as follows: 1. The detection fraction of nuclear X-ray sources is 52/103. A handful of these may be contaminated by LMXBs; we estimate the fraction of accreting SMBHs is 45 ± 7%. This provides a firm lower limit on the SMBH occupation fraction within field spheroids.
2. The ratio of X-ray to Eddington luminosities within the Field sample is in all cases low, from ∼ 10 −4 − 10 −8 . This range is similar to that found in the AMUSE-Virgo study of cluster early-types (G10). Independent of environment, SMBH accretion within local early-types is generally highly sub-Eddington.
3. We quantify the correlation between nuclear X-ray luminosity and host stellar mass, finding a best-fit relation of (log L X − 38.4) = (−0.04 ± 0.12) + (0.71 ± 0.10) × (log M star − 9.8). The calculated slope is incompatible with zero dependence and marginally indicative (2.9σ) of greater L X per unit M star in lower-mass galaxies. 4. After scaling by black hole mass or accounting for the influence of stellar mass, typical values of log L X /L Edd or ∆L X,M * of group members may be slightly lower than for isolated galaxies, and this newlyidentified trend appears to continue to cluster earlytypes. If confirmed, a progressive decrease in relative X-ray luminosity with increasing richness mandates an environmental modulation of SMBH fueling.
Several complementary projects that build on this dataset are underway. A direct comparison of the nuclear X-ray luminosity as a function of black hole mass within field and cluster galaxies, controlling for stellar mass, is discussed in Miller et al. (2012). An additional later work will present the catalog of off-nuclear X-ray sources within the field sample, and compare the distribution of ULXs to that found for Virgo. We are also currently obtaining high-resolution HST /ACS imaging of Field galaxies with X-ray detections, to check for and characterize any nuclear star clusters.
We thank Kayhan Gültekin for sharing his Chandra data in advance of publication, we thank him and Marta Volonteri for useful conversations, and we thank an anonymous referee for constructive suggestions that improved this paper. T. T. acknowledges support from the NSF through CAREER award NSF-0642621, and from the Packard Foundation through a Packard Research Fellowship. J. H. W. acknowledges support by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2010-0021558). Support for this work was provided by NASA through Chandra Awards Number 11620915 (AMUSE-Field) and 08900784 (AMUSE-Virgo) issued by the Chandra X-ray Observatory Center. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. We acknowledge the usage of the HyperLeda database.  Note. -The columns Name, Type, RA, Dec, d, B T , M B , and σ are taken directly or indirectly from the HyperLeda database. Stellar and black hole masses Mstar and M BH are given here as logarithm quantities and calculated as described in §4.1. Group size and velocity dispersions are from Makarov & Karachentsev (2011). Rows are ordered by absolute B magnitude.   Note. -Percentiles are given as the value for the nearest object in the sorted list for detected quantities, and calculated within ASURV (Kaplan-Meier) for log (LX/10 37 ) with upper limits included; note the 25th percentile values here are dominated by censored points and should be taken as indications only. The X-ray luminosities are restricted to log LX > 38.2 to avoid any potential bias from archival observations. a Values are biased because the ASURV changed the first upper limit to a detection for the Kaplan-Meier computation. Note.
-Fits are to the function (log Lx − 38.4) = A + B×(log Mstar − 9.8), where σ is the intrinsic scatter. Fitting is carried out using the IDL code of Kelly (2007); see §4.2 for details.