THE HOST GALAXIES OF LOW-MASS BLACK HOLES^*

The galaxies presented here are drawn from the sample described in Greene & Ho (2007b). This sample is selected from all broad-line active galaxies in the Fourth Data Release (DR4; Adelman-McCarthy et al. 2006) of the SDSS (e.g., York et al. 2000; Greene & Ho 2007a) with z < 0.35. First, the DR4 spectra are continuum-subtracted using a principal component analysis developed by Hao et al. (2005). Then objects with high rms deviations above the continuum in the broad Hα region are selected, and a more detailed profile fitting is applied to isolate those objects with Hα profiles that are broad compared to the narrow [S ii] and [N ii] lines.

Virial BH masses are estimated for all targets, using the broad-line region (BLR) gas as the dynamical tracer. The virial mass is simply M_BH = fR(Δv)²/G, where R is the size of the BLR, Δv is a measure of the broad-line width, such as FWHM, and f is a dimensionless factor that accounts for the unknown geometry and kinematics of the BLR. A few dozen AGNs have direct measurements of their BLR sizes from reverberation mapping, a measurement of the lag between continuum and line variations (e.g., Peterson et al. 2004; Bentz et al. 2009b; Denney et al. 2010). An empirical correlation between BLR radius and AGN luminosity (the radius–luminosity relation) is then used to infer the BLR sizes for other AGNs (e.g., Bentz et al. 2006, 2009b). In this work, we use the luminosity of Hα to infer the BLR radius (Greene & Ho 2005b). The virial mass is then estimated from the luminosity and FWHM of Hα as (e.g., Greene & Ho 2007b; Woo et al. 2010)

$$\begin{equation} M_{\rm {BH}}=3.0\times 10^6\left(\frac{L_{\rm {H}\alpha }}{10^{42}\ \rm{erg}\ \rm{s}^{-1}}\right)^{0.45} \left(\frac{\rm{FWHM}_{\rm{H}\alpha }}{10^3\ \rm{km}\ \rm {s}^{-1}}\right)^{2.06}\,M_\odot. \end{equation} \tag{ 1 }$$

Since we cannot yet determine the value of f for each AGN appropriately, we use a single value of f = 0.75 (e.g., Kaspi et al. 2000) that is intended to represent an ensemble average over our sample. The virial masses we use in this paper are calculated according to the above formula with the Hα luminosity and FWHM based either on the SDSS spectrum or a higher-resolution spectrum from the Echelle Spectrograph and Imager (ESI) on Keck (Sheinis et al. 2002) or the Magellan Echellette Spectrograph (MagE; Marshall et al. 2008). The spectra are presented in Xiao et al. (2011).

From this parent sample, the final 174 BHs were selected to have virial masses smaller⁵ than 2 × 10⁶ M_☉ (Greene & Ho 2007b). An additional 55 galaxies were presented with far-less-certain broad-line masses (called "c"). The HST snapshot pool was taken from these 229 galaxies. These galaxies have a median g-band magnitude of M_g = −19.3 and a median color of 〈g − r〉 = 0.7 mag. The median redshift is 〈z〉 = 0.085, with a maximum redshift of z = 0.35. They have BHs with virial masses ranging from M_BH = 6.2 × 10⁴ M_☉ to 3.8 × 10⁷ M_☉ with a median value 1.2 × 10⁶ M_☉. The BHs are radiating at high fractions of their Eddington limits and most are radio quiet. More properties of these galaxies are described in Greene & Ho (2007b).

In order to study the detailed structure of the host galaxies, we were awarded a snapshot survey with WFPC2 on HST in cycle 16. A total of 147 galaxies from Greene & Ho (2007b) were observed during this program, including some from the "c" sample. Each galaxy was placed at the center of the Planetary Camera CCD. The WFPC2 field of view is divided into four cameras by a four-faceted pyramid mirror near the HST focal plane.⁶ Each camera contains an 800 × 800 pixel detector. Three identical cameras, with a plate scale of 01 pixel⁻¹, form an "L" shape. The fourth camera, the Planetary Camera, is located at the upper right corner of the "L" and has a finer plate scale of 0046 pixel⁻¹. The total effective field of view is ∼322 × 322. The typical FWHM of the point-spread function (PSF) for the Planetary Camera is ∼1.7 pixels in the F814W filter.

Details of the observations are summarized in Table 1. For each object we obtained a short (30 s) exposure in the case of saturation, followed by two dithered ∼600 s exposures with the F814W filter. The mean wavelength of this filter is 8269 Å and the central wavelength is 8012 Å, which is a little different from the Johnson I-band filter. As discussed in Greene et al. (2008), independent of galaxy color the difference in magnitude between F814W and I is so small (<0.05 mag) that throughout we will refer to the HST observations as I-band images.

The raw HST data must be processed before they can be used for scientific analysis. Since the short exposure is only used in two cases (described at the end of this section), we focus here on the long exposures.

The first step is to remove cosmic rays (CRs) using the identification script LACosmic (van Dokkum 2001), which can detect cosmic-ray hits of arbitrary shape and size. Second, we shift the second exposure by 11 × 11 pixels to undo the dither made during the observations. Due to charge-transfer inefficiencies in the WFPC2 CCDs and accumulated radiation damage to the WFPC2 CCDs, the PC images now contain cosmic-ray trails or "ghost CRs" that are not removed by LACosmic. The ghosts are removed as follows. For each pixel in one image, we check whether it deviates by more than 2σ from the median in an 11 × 11 pixel box in the other image. If so, it is likely a ghost CR and it is replaced by the median from the other image. After the two long exposures are combined properly, the final image is ready for analysis.

One exception to the general procedures above occurs when the image core is saturated. The PC chip becomes nonlinear when the counts reach ∼3000 and saturates at ∼4000 counts. Here, we flag a pixel as saturated when the counts exceed 3000.

In our sample, there are only two galaxies with saturated cores, SDSS J030417.78+002827.3 and SDSS J115341.77+461242.2. For these galaxies we replace the saturated pixels with the scaled pixels from the 30 s exposure image. We have also checked the radial profiles for the corrected images to make sure that the radial profiles are smooth and that the correction is applied appropriately. The saturated core of the stellar PSF is replaced in a similar fashion.

An accurate knowledge of the PSF is required for image decomposition, but it is particularly important in our case because the AGN is a bright, unresolved central source. Based on the fitting described below, the fraction of light contributed by the AGN relative to the host galaxy varies over a large range across the sample, from 0% to 80%, with a median of 5%. The effective radii of the bulge components vary from 005 to 6''. Since our primary goal is to study the galaxy bulges, it is important to have an accurate PSF model, especially for the faint bulges.

The PC chip of WFPC2 has a small field of view and so we do not have many bright stars in these images that can be used as a PSF model. Here, we use the Tiny Tim software (Krist 1995) to generate a PSF image for each object. Given the filter and the location of the AGN in the camera, Tiny Tim can model both the spatial and spectral variations in the PSF and account for the effect of charge diffusion. For each galaxy, we generate a PSF model with Tiny Tim at the location of the AGN. We analyze the image based on this PSF.

Any bright stars near the center of an image can also serve as an alternative PSF star. Of the 147 images, only one contains a bright star near the center of the image that is significantly brighter than the AGNs and thus can be used as a PSF model. This star is in the field of SDSS J084234.50+031930.6 and is only 96 pixels away from the center of the galaxy. The core is saturated, but we replace the core using the short exposure. This star is used as an alternative PSF for all the galaxies so that we can estimate the uncertainty due to the PSF model.

There are 14 galaxies for which the fitting fails with this alternate stellar PSF. In these cases, we select another from the PSF archive of WFPC2 with the same observational parameters (such as filter) as our images. This PSF is also used as an alternate PSF to estimate the uncertainty due to the PSF model, but is only used when the stellar PSF model fails. In Figure 1, we compare the radial profiles of the three PSF models arbitrarily normalized at 002. As shown in this plot, the three PSF models are very similar, although they differ somewhat around 01–03. The difference is due to small spatial variations as shown in the left-hand panel of Figure 2 in Kim et al. (2008). The spatial variations for the three PSF models are smaller than 100 pixels so that the cores (∼2 pixels) are very similar. Thus, there are small variations between these and the Tiny Tim PSF model that can be used to quantify the impact of an imperfect PSF model.

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The sizes of the images are 800 × 800 pixels and most galaxies extend to a radius of ∼100–200 pixels or ∼5''–10''. To determine the sky level we start with a circular region with a radius of 350 pixels located at the center of the galaxies. In this way, on the one hand, we can exclude the noise near the edges of the images, while on the other hand we can make use of a large number of pixels. Then we use the command ellipse within IRAF, which follows the methods described in Jedrzejewski (1987), to derive the one-dimensional radial profile of the galaxy. Obvious contaminating features such as bright stars and small galaxies are masked. Typically, the radial profile will converge to an almost constant value at the outer radii. We take the average value of the two to four outermost radial bins in the profile to be the sky value, which will be used in our fitting. We also measure the fluctuations in values at each radius in these outermost bins to estimate the random error, which is typically ∼1% of the sky value. When there are contaminants nearby, the standard deviation can reach 5% of the sky value.

In cases where the primary galaxy is compact and there are multiple stars or galaxies in the field, we use a smaller region for the sky determination. In cases where the galaxy is very extended (e.g., SDSS J110501.97+594103.6), we use observations in the three WF chips to determine the sky value. Finally, there are some galaxies with inclined disks that almost fill part of the image while leaving other parts almost empty. In these cases we put rectangular regions along the galaxy minor axis and use these regions to measure the sky counts and standard deviation.

As the measured galaxy sizes are very sensitive to the adopted sky value, we check the sky values in a few ways. For the 17 most extended galaxies, we create a radial profile extending beyond the PC chip, and calculate the average sky value where the profile becomes constant. In addition, we calculate the average counts in a few randomly chosen blank regions. Results from these different methods agree with the adopted values within 2σ, which means the sky values and uncertainties we adopt are well defined. There is another way to measure the sky value using the mode, or most common pixel value. This determination should be less affected by contamination. The sky values determined from the mode agree with our adopted value within one standard deviation. Another consistency check is described in the Appendix.

Following Greene et al. (2008), we use the GALFIT routine to perform full two-dimensional profile decompositions (e.g., Peng et al. 2002, 2010) with the following goals. First, we want to determine what fraction of the galaxies contain various components, such as bulges, disks, and bars. Second, we wish to measure the bulge properties (luminosity and size) to study the bulge scaling relations (e.g., the fundamental plane) for these galaxies. Third, we will quantify the morphology of the galaxies based primarily on the bulge-to-total (B/T) light ratio (e.g., Simien & de Vaucouleurs 1986). Two-dimensional fitting has the benefit that different components can be modeled with different position angles (P.A.s). PSF convolution is included in a straightforward way. Also, complex components such as nuclear disks and bars can be included. GALFIT models the galaxy components as axisymmetric ellipsoids. Lopsided components can also be modeled with the most recent version, GALFIT 3.0 (Peng et al. 2010), which we use here.⁷

In general, we proceed as follows. First, we look at the image and the one-dimensional radial profile to determine what components to include in our model. Sometimes there is an obvious bar or disk in the galaxy, which is included in the fitting. Most of the time, there are no distinguishing structures and we perform an initial fit with a central PSF for the AGN and a generalized Sérsic model:

$$\begin{equation} \Sigma (r)=\Sigma _e\ {\rm exp}\left\lbrace -b_n\left[\left(\frac{r}{r_e}\right)^{1/n}-1\right]\right\rbrace, \end{equation} \tag{ 2 }$$

where r_e is the effective (half-light) radius, Σ_e is the surface brightness at r_e, n is the Sérsic index, and b_n is chosen so that the region within r_e contains half of the light in the profile integrated to infinity.

For n = 1, the Sérsic model is reduced to an exponential profile. Exponential profiles are usually used to describe disks. The exponential profile is written in another form:

$$\begin{equation} \Sigma (r)=\Sigma _0{\rm exp}\left(\frac{r}{r_s}\right), \end{equation} \tag{ 3 }$$

where Σ₀ is the central surface brightness and r_s is the radius at which the surface brightness drops to 1/e of the central surface brightness. In this paper, the disk size is reported with r_s while for other components we report r_e. For n = 1, there is a simple relation r_e = 1.678r_s.

For n = 4, the Sérsic profile is equivalent to a de Vaucouleurs (1948) profile, which is often used to describe the light profile of elliptical galaxies. In GALFIT, if we let the Sérsic index n float freely, GALFIT will sometimes adopt an unacceptably large n to reduce the χ². As shown in Blanton & Moustakas (2009), most nearby galaxies have a Sérsic index smaller than 5. During our fitting, we fix n = 1, 2, 3, 4, respectively, for the bulge component and see which gives the best fit. Other groups (e.g., Benson et al. 2007; Simmons & Urry 2008) adopt a similar strategy of fixing the Sérsic index to discrete values. If different n values give almost the same parameters and the same reduced χ², then we cannot distinguish between the different Sérsic models. For the bar component, we model the intensity distribution with n = 0.5 (e.g., Freeman 1966; Greene et al. 2008), which is a Gaussian profile.

In order to determine whether a galaxy has bar structure, we visually check the images one by one, since a weak bar may exist even when the outer parts of the galaxy are well fit by a single n = 1 component. For the ambiguous cases when we cannot distinguish between a bar or edge-on disk visually, we check the ellipticity profile and the P.A. profile as described in Menéndez-Delmestre et al. (2007). We use the ellipse command in IRAF to plot ellipticity and P.A. at each radius. For the galaxies with a round bulge at the center, we should see a monotonic increase in ellipticity and a constant P.A. across the bar. Because the bar and the disk usually have different P.A.s, we should also see the ellipticity drop abruptly while the P.A. changes sharply at the end of bar. If we see those signatures simultaneously, we conclude that there is a bar. If either signature is missing and we do not see a bar clearly by eye, we do not classify the galaxy as barred. In Figure 2, we show two examples of this procedure. For galaxy 0823 + 0606, we see both a sharp drop of the ellipticity profile and an almost constant P.A. profile indicative of a bar. For galaxy 0833 + 0620, although there is a change in the ellipticity profile at ∼50 pixels, the P.A. changes with radius and we also do not see a bar-like structure in the image. This galaxy has no large-scale bar.

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After we find the best fit with the AGN component and one Sérsic model, we compare the radial profile of the model and the image and decide whether we need to add a new component. We continue in this way until the model fits the image. Our criteria are that there be no large features in the one-dimensional residuals and that the reduced χ² has a minimum of ∼1.

Note that we are not fitting the spiral arms or knots of star formation and other nonaxisymmetric features, which are apparent in some of the residual images. However, we do fit additional compact components in the central region if necessary, which means any component with an effective radius smaller than the r_e of bulge. In some cases, without this nuclear component there is also extra light in the residuals regardless of the value of n. A similar nuclear component with size ∼100 pc is also found in the nearby low-mass AGN host POX 52 (e.g., Barth et al. 2004; Thornton et al. 2008). This is different from nuclear star clusters in late-type galaxies, which have typical radii ∼2–5 pc (e.g., Böker et al. 2004). As the median redshift of our sample is 0.085, a nuclear star cluster will fall within a single WFPC2 pixel. The bright nuclear point source only makes the situation worse. Therefore, unfortunately, we do not have sufficient angular resolution to search for nuclear star clusters in our sample.

With our image decompositions we only fit the main components of the galaxies, including bulges, extended disks, bars, and nuclear structures. Spiral and irregular structures, such as nuclear spirals or rings, are not fitted and those structures can be seen in the residual images. In Figure 3, we show some example HST images, including the model image, the residual image, and a radial profile.⁸ The models generally match the data well.

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View figure set (147 panels)

Tarball of figure set images

In our sample of 147 galaxies, 136 (93%) have extended disks. Of the disk galaxies, 53 of them (39%) have bars. The bar properties are shown in Table 3. Of the galaxies with disks, only seven are consistent with having no bulge component at all. The remaining 11 diskless systems are smooth and featureless galaxies. Based on their position in the fundamental plane (Section 6.1), we will argue that these galaxies are spheroidal, rather than elliptical, galaxies. Half of the diskless galaxies have a Sérsic index n > 2, which is larger than the average Sérsic index of the whole sample but similar to POX 52 (e.g., Thornton et al. 2008). However, in general their luminosities and sizes are larger than POX 52. The average absolute bulge luminosity and bulge size of these 11 galaxies are both larger than the average values of the whole sample. As listed in Table 4, four of those galaxies have an additional compact component with a size that is smaller than the effective radius of the bulge. Finally, there are seven galaxies consistent with having no bulge component at all. Details are given below.

Mergers are believed to be an efficient way to trigger AGN activity and feed gas to the central supermassive BH (e.g., Hopkins & Quataert 2010; Mayer et al. 2010). Mergers are also thought to trigger star formation in galaxies (e.g., Barton et al. 2000, 2007; Blanton & Moustakas 2009). Observations have found examples of mergers in AGNs with more massive BHs. (e.g., Liu et al. 2010). For our sample of low-mass BHs, we can check whether or not mergers are a common and important phenomenon.

In our sample, 13 of the galaxies (9%) are detected with close companions that are likely physically interacting. Some of them show obvious long tails, which are clear signatures of tidal interaction. In Figure 4, we show six example interacting galaxies. Although the fraction of interacting galaxies in our sample is only ∼9%, it is already larger than the 1%–2% reported for luminous galaxies (e.g., Blanton & Moustakas 2009). However, we caution that we identify the companions only visually based on our HST images. We do not use well-defined criteria, nor do we have a well-defined control sample to compare it with (e.g., Woods & Geller 2007; Darg et al. 2010) as this is not our main focus.

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The ratio between the bulge and total light (B/T; the AGN is excluded) varies from 0 (no bulge detected) to 1 (for spheroidal galaxies). The mean value is 〈B/T〉 = 0.28 with a median of 0.18. In most cases B/T is either less than 0.5 or greater than 0.9, with only 15 galaxies in between. If we restrict our sample to those galaxies with a detected disk component, then the mean becomes 〈B/T〉 = 0.23 with a median value of 0.16. In this case, the ratio is always <0.85.

Based on B/T, we can assign a Hubble type to each galaxy following the Third Reference Catalogue (RC3; Simien & de Vaucouleurs 1986; de Vaucouleurs et al. 1991). For the 129 galaxies with a detected disk and bulge component, we find: 2% are Hubble-type E; 15% are Hubble-type S0; 18% are Hubble-type Sa; 28% are Hubble-type Sb; 30% are Hubble-type Sc; and the remaining 7% are Hubble-type Sd. A histogram for the Hubble-type distribution is given in the bottom panel of Figure 5, which shows that our sample peaks at Hubble-type Sbc to Scd.

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In the top panel of Figure 5, we also show the relationship between the bulge magnitude and B/T. This plot clearly shows that B/T is larger when the bulge luminosity is larger. In other words, when the bulge becomes more luminous, the disk component becomes relatively faint. It is clear that some of the bulge magnitudes are very uncertain, particularly at low values of B/T. The uncertainty in the bulge magnitude is dominated by uncertainties in the PSF model, but the sky level also plays a role.

There are 27 galaxies (18% of the total sample) with B/T <5%. As the extension of these very faint galaxies, there are even some galaxies with no detected bulge component, which are described below.

As discussed in the Introduction, we are interested in how many bulgeless galaxies contain AGNs. In our sample, we find seven galaxies (5% of the sample) that are best fitted by pure disks. They are 0916+3834, 0942+4800, 0953+3650, 1102+4638, 1116+4236, 1437+5458, and 1534+0408. These galaxies are either fitted by a pure exponential disk (three) or a bar plus an exponential disk (four). The bulge magnitude limits range from <20.6 to <18.4 mag. However, because there is a bright AGN component at the center and four of them are at redshift z ≈ 0.2, a small bulge could escape detection in the HST images. Deeper and higher-resolution observations are needed to confirm their bulgeless nature. Such a small number of bulgeless galaxies with AGN activity even in such a large sample suggests that these systems are truly rare, although the SDSS selection does introduce a bias against faint galaxies and AGNs (Greene & Ho 2007a).

In our sample, there are 53 galaxies with detected bars and 4 with compact nuclear components (i.e., components smaller than the bulge effective radius that require an additional Sérsic profile). Looking only at galaxies with extended disks, the bar fraction is 39%. Excluding the disk galaxies with an inclination angle larger than 60°, where it is difficult to detect a bar (e.g., Hao et al. 2009), the bar fraction drops to 37%. It is interesting to compare our sample with narrow-line Seyfert 1 (NLS1) galaxies. Like our galaxies, NLS1s are thought to have BHs with relatively modest BH masses (⩽10⁷ M_☉) and high Eddington ratios (e.g., Pounds et al. 1995; Crenshaw et al. 2003). Crenshaw et al. (2003) find that >60% of the NLS1s in their sample have a bar. The bar fraction in our sample is much smaller than that of Crenshaw et al. (2003). Actually, the bar fraction here is also smaller than that of luminous AGNs and star-forming galaxies. Based on the classification and structure information for ∼2000 galaxies from the SDSS, Hao et al. (2009) claim that the AGN optical bar fraction is 47% and that the optical bar fraction in star-forming galaxies is 50%. In inactive galaxies, the bar fraction is only 29%, which is close to that in our sample.

A relation between bar fraction and B/T is also claimed. People find that the bar fraction increases with decreasing B/T, meaning that the bar fraction is larger in disk-dominated galaxies (e.g., Marinova et al. 2009). This conclusion is also confirmed in our sample. We divide our sample into three equal bins in B/T: 0–0.33, 0.33–0.66, and 0.66–1. The bar fraction (with highly inclined "bars" excluded) in the three bins is 45%, 11%, and 0%, respectively. Histograms of the barred galaxy fractions for each Hubble type (Figure 5) shows that the bar fraction is largest in Sbc–Scd galaxies and is very small for early-type galaxies.

Some theoretical models have proposed that bar driving can be an efficient mechanism to funnel gas down to small scales where it can be accreted by the BH (e.g., Shlosman et al. 1990; Hopkins & Quataert 2010). However, observations do not find a definite connection between bars and AGN activity. For example, some groups (e.g., Ho et al. 1997; Mulchaey & Regan 1997) do not find an excess of bars in Seyfert galaxies, while other groups (e.g., Knapen et al. 2000; Laurikainen et al. 2004) claim a higher fraction of bars in Seyfert galaxies. We have also compared the AGN magnitudes for the galaxies with and without bars. The galaxies with bars do not show significantly larger AGN luminosities. We see no evidence that bars are the dominant feeding mechanism for the AGNs in our sample. Instead, the bar fraction is roughly consistent with what we expect from inactive galaxies.

In Figure 6, we show three different projections of the fundamental plane. The open blue circles are our sample. All the others are comparison samples taken in the V band from Kormendy et al. (2009), Ferrarese et al. (2006), and Gavazzi et al. (2005). We choose the Virgo galaxies as a comparison here because they have very deep and uniform photometry and analysis. They constitute a clean representative sample of local red galaxies. The sample is not complete, but nicely demarcates the region occupied by elliptical and spheroidal galaxies in the fundamental plane.

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In order to properly compare the samples, we calculate the magnitude difference between the HST filters F814W and F555W⁹ based on a template elliptical galaxy spectrum from the Kinney–Calzetti atlas (Kinney et al. 1996) using calcphot in IRAF. The result is V − I = 1.34 mag, which is also the value used in Greene et al. (2008). We shift the comparison elliptical and S0 galaxies from the V band to the I band with this conversion factor. Spheroidal galaxies are typically bluer than elliptical galaxies. For the spheroidal galaxies, we adopt V − I = 1.09 mag, the color of Sbc galaxies listed in Table 3 of Fukugita et al. (1995), because spheroidal galaxies are redder than Scd galaxies but bluer than Sa galaxies based on the B − I color (Gavazzi et al. 2005; Greene et al. 2008).

We fit log–linear or linear relations to the fundamental plane for our galaxies with disk components, following the same fitting method as described in Greene & Ho (2006). The fitting method is based on a Levenberg–Marquardt algorithm. The intrinsic scatter is an additional error term that is chosen such that the minimum χ² is one. Upper limits are not included in the fits. The fitting results are shown in Table 5. In the μ_e − r_e plane (the top left panel of Figure 6), our sample galaxies have a steeper scaling than that of elliptical galaxies and classical bulges. The difference is even more significant in the μ_e − M_I plane. The fundamental plane of these pseudobulges has a different slope and normalization than the elliptical or the spheroidal galaxies, such that the faint end is closer to faint elliptical galaxies while the bright end is closer to bright spheroidal galaxies.

Table 5. Fit Results

	Our Sample					Ellipticals and S0
Relation	α	β	0	Median Value		α	β	0	Median Value
log (re)–μe	4.88 ± 029	18.53 ± 0.09	0.16	−0.26		2.43 ± 0.16	19.53 ± 0.13	0.67	0.097
MI–μe	0.53 ± 0.12	18.82 ± 0.13	0.54	−19.42		−0.68 ± 0.10	19.93 ± 0.23	1.31	−20.97
MI–re	−0.17 ± 0.02	−0.23 ± 0.02	0.22	−19.42		−0.33 ± 0.02	0.24 ± 0.05	0.26	−20.97
	Our Sample + Gültekin et al.					Gültekin et al.
Relation	α	β	0	Median Value		α	β	0	Median Value
MI–log (σ)	−0.13 ± 0.01	2.00 ± 0.02	0.07	−20.37		−0.10 ± 0.01	2.32 ± 0.02	0.06	−22.52

Notes. We fit y = α × (x − x₀) + β, where x (the independent variable) is listed first in Column 1 and y (the dependent variable) is listed second. x₀ is the median value of x and is kept fixed. ₀ is the intrinsic scatter. All the fits are done on the original data before corrections for stellar age are applied.

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Previous results have also found that the photometric scaling relations of pseudobulges diverge from those of classical bulges. Carollo (1999) finds that their "exponential" (or pseudo) bulges span a much wider range of effective surface brightnesses than do classical bulges and elliptical galaxies. Fisher & Drory (2010) present a similar result. They see almost no dependence of effective surface brightness on effective radius. Our findings are similar over the range of effective radius that we share. Thus, the observed scaling relations also support our assertion that our disk sample is dominated by pseudobulges.

There are 11 galaxies without extended disks. These systems are more challenging to interpret. On the one hand, they are typically 2 mag more luminous than luminous spheroidal galaxies (green squares in Figure 7). However, they are larger and have lower surface brightnesses than faint ellipticals of their luminosity. The difference is most significant in the μ_e − r_e plane (the top panel of Figure 7). Thus, as in Greene et al. (2008), we conclude that the sample is made up predominantly of spheroidal systems whose luminosities are boosted by ongoing star formation. As we will see in the next section, their scaling in the Faber–Jackson relation strengthens our conclusion here (Section 6.2).

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6.1.1. Stellar Population Effects

It is important to note that our sample galaxies likely contain younger stars on average than Virgo cluster galaxies. Unfortunately we do not have direct measurements of the bulge colors. However, inactive spiral galaxies at these masses are all bluer than more massive galaxies (e.g., Roberts & Haynes 1994). This is also true for bulges (e.g., Bender et al. 1992). Furthermore, it is likely that some of the nuclear structures represent ongoing or recent star formation. One way to compensate for this difference is to estimate the mass-to-light ratio (M/L) for the bulges. We can estimate their dynamical M/L using σ_* observations. The bulge virial mass can be estimated as ∼6.5 r_eσ²/G (e.g., Taylor et al. 2010), where G is the gravitational constant. We find an average M/L in our sample of ∼1.8 (in units of M_☉/L_☉). For a typical elliptical galaxy in the I band, the M/L is ∼4–6 (e.g., Cappellari et al. 2006). If we keep the stellar mass fixed but imagine that the stars evolve to the same age as those in elliptical galaxies, the luminosity would be decreased by a factor of 2.2–3.3, corresponding to an increase of 0.8–1.3 mag. Although we do not know the bulge M/L for individual galaxies, we can take the average impact of fading the stellar populations to be ∼1 mag.

Applying a shift of 1 mag to our sample, the fundamental plane would then appear as shown in Figure 8. This average accounting for stellar population effects only strengthens our conclusions. Our galaxies occupy a different region of the fundamental plane from elliptical/S0 galaxies. At the bright/large end, the galaxies clearly deviate from the fundamental plane of massive elliptical galaxies. However, at the faint/compact end, the galaxies are more consistent with the fundamental plane of small elliptical galaxies like M32 than they are with spheroidals of the same size or luminosity. In addition, the locus of the diskless galaxies moves closer to that of the spheroidal galaxies.

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We have considered photometric projections of the fundamental plane. For a subset of galaxies, we can also examine the Faber & Jackson (1976) relation between stellar velocity dispersion (σ_*) and bulge luminosity. Previous results suggest that pseudobulges demonstrate considerably larger scatter in the Faber–Jackson relation, with a tendency to have a lower σ_* at a given luminosity (e.g., Kormendy & Illingworth 1983; Dressler & Sandage 1983; Kormendy & Kennicutt 2004; Greene et al. 2008). We examine the situation for our sample.

We have σ_* measurements for 34 galaxies in the sample. The data were taken at Keck with ESI and at Magellan with MagE. The measurements are based on direct-pixel fitting of broadened stellar templates to the galaxy spectra (Barth et al. 2005; Xiao et al. 2011). For the remaining objects, we do not have direct stellar velocity dispersion measurements. Instead, we use the widths of forbidden lines from the narrow-line region as an approximate indicator of the stellar velocity dispersion. In most AGNs, the widths of low-ionization emission lines, such as [O ii] and [S ii], are a good proxy for σ_*, as shown in Nelson & Whittle (1996) and Greene & Ho (2005a), and then discussed in detail in Ho (2009). In this paper, we refer to dispersions based on [S ii] as σ_gas, which are used whenever we have no σ_* measurement.

6.2.1. Restricted Sample

6.2.2. Results

In Figure 9, we show the relation between I-band bulge magnitude and bulge velocity dispersion σ_* in the host galaxy. The clean restricted sample is labeled with open blue circles filled with a black dot. We compare our results to the inactive early-type galaxies in Gültekin et al. (2009). We choose this sample because it is a well-studied representative sample of elliptical galaxies with very good measurements of luminosity and velocity dispersion. Our goal is simply to demarcate the region occupied by elliptical galaxies in this plane, so that we can compare with our sample distribution. The V-band magnitudes reported in Gültekin et al. are shifted to the I band assuming V − I = 1.34 mag as above. On average, our sample has smaller σ_* at a fixed bulge magnitude than the early-type galaxies. The best-fit relations for Gültekin et al.'s sample alone and the results with the clean sample included are shown in Table 5. Our galaxies clearly have a different Faber–Jackson slope. One way to quantify the difference between our sample and classical bulges is to calculate the average difference between the observed value σ_* and the predicted value σ_predict, as defined in Section 6.2.1. For the clean sample, we find 〈σ_predict − σ_*〉 = 36 ± 8 km s⁻¹, where the latter represents the error in the mean.

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We can also quantify the difference in terms of bulge magnitude. At a fixed velocity dispersion σ_*, our sample galaxies have larger luminosities on average than do early-type galaxies. We can calculate the average difference 〈M_predict − M_I〉, where M_predict is calculated based on the observed velocity dispersion and the extrapolated Faber–Jackson relation given by Gültekin et al. (2009). For the clean sample, we get 〈M_predict − M_I〉 = 1.8 mag with the error for the mean value to be 0.4 mag.

Not only is σ_* for our sample significantly smaller at a given bulge magnitude, but the scatter in the relation is also significantly larger. In order to quantify the scatter, we fit the log–linear relation log σ = α + βM_I to the data. Following the fitting method used in Tremaine et al. (2002) and Greene & Ho (2006), we include an intrinsic scatter such that the reduced χ² (Equation (1) of Greene & Ho 2006) has a best-fit value of one. The sample from Gültekin et al. (2009) alone has an intrinsic scatter of 0.064 dex. When we include our sample with σ_* from ESI/MagE spectra, the intrinsic scatter is increased to 0.071 dex. As shown in Figure 9, the slope also gets steeper when our sample is included. We find effectively the same results if we include the galaxies with σ_gas.

By comparing the Faber–Jackson relation for our sample and early-type galaxies as shown in Figure 9, we find that our sample has systematically smaller σ_* than the predicted value σ_predict. This offset, like those seen in the photometric scalings above, is in the same sense as has been observed for inactive pseudobulge samples (Kormendy & Illingworth 1983). Thus, in sum, the scaling relations are consistent with the fact that >70% of our galaxies contain pseudobulges.

It is also interesting to compare the Faber–Jackson relation of our sample with inactive spheroidal galaxies. Matković & Guzmán (2005) and Cody et al. (2009) study the Faber–Jackson relation for what they refer to as "dwarf early-type" galaxies in the Coma cluster with R-band magnitudes ranging from −22.0 to −17.5 mag and −20.7 to −15.6 mag or I-band magnitudes of ∼ − 23.2 to −16.8 mag (Fukugita et al. 1995). According to their positions in the fundamental plane (e.g., Graham & Guzmán 2003), these galaxies obey our definition of spheroidal galaxies. They are found to have a relation L∝σ², which is much flatter than the relation L∝σ⁴ for more luminous galaxies. As shown in Table 5, when we fit our sample (galaxies with σ_* measurements) combined with that of Gültekin et al., we find L∝σ³. Specifically, the 11 diskless galaxies lie very close to the spheroidal galaxies from Matković & Guzmán (2005), and are systematically offset from the best-fit relation of elliptical galaxies. This is true even after we shift our sample to account for different stellar populations, and confirms our conclusion from Figure 7 that the diskless galaxies are actually bright spheroidal galaxies.

6.2.3. Uncertainties in the Faber–Jackson Analysis