HOST GALAXIES OF LUMINOUS QUASARS: STRUCTURAL PROPERTIES AND THE FUNDAMENTAL PLANE

Our full sample is primarily drawn from the 20 nearby luminous quasars of Bahcall et al. (1997), with the addition of a few objects from Dunlop et al. (2003) and Guyon et al. (2006). The analyses presented here include ten QSOs from this larger sample of 28 whose spectra show sufficient signal-to-noise ratio (S/N) to allow measurement of the velocity dispersion via the techniques described below. These ten objects are PG 0052+251, PHL 909, PKS 0736+017, 3C 273, PKS 1302-102, PG 1309+355, PG 1444+407, PKS 2135-147, 4C 31.63, and PKS 2349-014.

The full sample from Bahcall et al. (1997) was selected solely on the basis of luminosity (M_V < −22.9), redshift (z ⩽ 0.20), and galactic latitude (|b|> 35°). All the quasars in the Véron-Cetty & Véron (1991) catalog that satisfied the redshift, luminosity, and galactic latitude criteria were included, amounting to 14 objects.

These 14 quasars with z⩽ 0.20 have an average (median) absolute magnitude 〈M_V〉 = −23.4 (23.2) and an average redshift 〈z〉 = 0.17. Only three radio-loud (RL) quasars are present in the original sample of 14 objects. By combining the time available from GTO and GO programs, Bahcall et al. (1997) added an additional six quasars with redshifts in the range 0.20 <z< 0.30; these additional objects satisfied the same luminosity and galactic latitude constraints as the original sample. The additional objects contained three RL quasars, bringing the total number of RL objects in the sample to 6 of 20 quasars.

Bahcall's final sample of 20 objects shows an average (median) absolute magnitude of −23.6 (−23.2) and an average redshift of z = 0.19. For nearly all (18) of the quasars, 15.1 <V< 16.7, but two are much brighter in the optical band: 3C 273 (V = 12.8) and HE 1029–140 (V = 13.9).

Off-nuclear spectra of seven of the host galaxies presented here were obtained with the Low Resolution Imaging Spectrograph (Oke et al. 1994) on the Keck telescope during 1996–1997. Typical offsets for the long-slit observations were 2–4''. Observed wavelength ranges covered ∼ 4500–7000 Å at a spectral resolution of Δλ∼ 11 Å (300 km s⁻¹). The average S/N Å⁻¹ for the galaxies in this study ranges from 1.8 to 13.9, with a mean of 5.3, over the wavelength range of 3850–4200 Å. Further observation details for these Keck data can be found in Sheinis (2002) and Miller & Sheinis (2003).

We are currently obtaining spectra of additional host galaxies using an integral field unit (IFU), Sparsepak (Bershady et al. 2004, 2005), which feeds the Bench Spectrograph on the 3.5-m WIYN Telescope. ¹ The central core of Sparsepak fibers are 47 in diameter on 56 spacings. Though not optimally sized for the host galaxies in this study that have typical effective radii of 1.3–65, we are finding this IFU and the excellent image quality of WIYN to be quite effective in isolating host galaxy light from the central quasar light. We use a configuration of the Bench Spectrograph that provides an observed wavelength coverage of ∼4270–7130 Å at a resolution of Δλ∼ 5 Å (110 km s⁻¹). In the work presented here, PG 1309+355 was observed on WIYN in 2007 June; PHL 909 and PKS 0736+017 were observed in 2007 December. These spectra have S/N spanning of 2.4–8.9 Å⁻¹, with an average of 5.7 Å⁻¹, for exposure times of 2–4 hr.

These objects all have Hubble Space Telescope (HST) or ground-based adaptive optics (AO) images in the archive for analysis of host galaxy properties. We take galaxy magnitudes and effective radii from the Bahcall et al. (1997) two-dimensional de Vaucouleurs profile fits for eight of the objects. These data for 4C 31.63 are provided by Hamilton et al. (2002) and Guyon et al. (2006) and for PKS 0736+017 by Dunlop et al. (2003). We use color corrections from Fukugita et al. (1995) and Poggianti (1997) to convert all to r-band and adopt a cosmology of Ω_M = 0.3, Ω_Λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹. Relevant object data are given in Table 1.

To aid in the interpretation of the nature of our QSO host galaxies, we will compare their structural properties to other types of galaxies. This comparison sample includes SDSS early-type galaxies from Bernardi et al. (2003a, 2003b, 2006). The Bernardi et al. (2003a) sample consists of nearly 9000 early-type galaxies that are placed on the FP in Bernardi et al. (2003b). Bernardi et al. (2006) search for the most massive galaxies by selecting SDSS objects with high stellar velocity dispersions, σ_* > 350 km s⁻¹, resulting in approximately 70 galaxies massive enough to be considered giant ellipticals. They find that these galaxies lie on the FP, but at its outer extreme.

For further comparison, we add the host galaxies of PG QSOs from Dasyra et al. (2007) who investigated the possibility that these QSOs were triggered during mergers of galaxies that contain gas, as are ultraluminous infrared galaxies (ULIRGs). They conclude that some, but not all, ULIRGs may undergo a QSO phase as the merger evolves and that the progenitors of both PG QSOs and ULIRGs are likely to be similar. Dasyra et al. (2007) compare their QSOs to a sample of galaxy merger remnants from Rothberg & Joseph (2006) that we add to our comparison as well. These objects were selected to be late-stage mergers in which the cores have coalesced into single nuclei.

The redshift distributions of our QSO host galaxies and the comparison samples are shown in Figure 1.

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Host galaxy magnitudes in Bahcall et al. (1997) are given for the F606W HST filter. We convert these to r-band using their F606-V colors for individual galaxies, and using the average colors for early-type galaxies from Faber et al. (1989) and Gebhardt et al. (2003), B − V = 0.95, and B − r = 1.25. We take the magnitudes of 4C 31.63 from Hamilton et al. (2002) in the F702W HST filter and of PKS 0736+017 from Dunlop et al. (2003) in the R-band, both of which we convert to r-band using average colors for E and S0 galaxies from Fukugita et al. (1995). With m_r we calculate host galaxy surface brightness from

$$\begin{equation} \mu _{e}(r) = m_{r} + 2.5 {\rm log}\big(2\pi R_{e}^{2}\big) - K(z) - 10\, {\rm log}(1+z), \end{equation} \tag{ 1 }$$

as in Bernardi et al. (2003a), where R_e is in arcsec. K-corrections are given in Bernardi et al. (2003a) for the large sample of early-type galaxies and we use their values. To derive K(z) for the other galaxies, we linearly fit the Bernardi et al. (2003a) K-corrections that are derived from a combination of Bruzual & Charlot (2003) models and early-type galaxy templates from Coleman et al. (1980), and apply them as K(z) = 1.25z to the Bernardi et al. (2006) comparison galaxies and the QSO host galaxies (Figure 2). Below z = 0.28 this fit gives a median difference for the Bernardi et al. (2003a) galaxies of ΔK(z) = 0.0040 with a standard deviation of σ_K(z) = 0.0038. Above z = 0.28, affecting 16 of the Bernardi et al. (2006) galaxies, these values change to ΔK(z) = −0.0080 and σ_K(z) = 0.0028. Our K(z) relation is extrapolated to redshifts higher than the fitted range for five of the Bernardi et al. (2006) galaxies.

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The light from the quasars in this study is as much as 3.5 mag brighter than the entire host galaxy. The regions of the host galaxies that we observed were typically 5–8 mag fainter than the quasar. As a result of the blurring produced by the Earth's atmosphere, plus a small contribution from the intrinsic optical point-spread function (PSF) and diffraction produced by the telescope, some light from the quasar entered the spectrograph in the off-nucleus observations, either long slit or fiber.

To spectrally remove the scattered light, we must both determine the fraction of light in the extracted spectrum that is from the quasar and also account for wavelength-dependent scattering efficiency due to atmospheric seeing (in the sense that as seeing gets worse, more scattering into a fixed offset distance from the quasar occurs with a shorter wavelength). We approximate these two factors by deriving a scattering efficiency curve of the form, $\psi = A_1 + A_{2} \lambda ^{-A_{3}}$. We subtract the product of the scattering efficiency curve and the observed central quasar spectrum from the off-nuclear spectrum and iteratively fit that result by two-population stellar synthesis galaxy model spectra from Bruzual & Charlot (2003). Examples of this approach are shown for 4C 31.63 and PG 1444+407 in Figure 3, where the upper solid black lines are the observed off-nuclear spectra, the dotted blue lines are the product of the nuclear quasar spectrum and the derived scattering efficiency curve, and the lower solid red lines are the resulting scatter-subtracted host galaxy spectra. For this work we are concerned only with a small spectral region around the 4000 Å break to measure stellar velocity dispersion. This scatter-subtraction approximation is sufficient for such a small region. However, in future work, to accurately determine constituent stellar populations of the host galaxies using the entire observed spectrum, we plan to implement a more rigorous scattering model based on the geometry of the slit/fiber, its distance from the central quasar, approximate seeing conditions, and selective weighting of more important spectral features, such as QSO broad-line regions.

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The basic model spectra fitting techniques used here are a modified version of Wolf et al. (2007) and Liu et al. (2007). We use six fitting parameters: old age, young age, luminosity-weighed fraction of the young age, and the scattering efficiency coefficients A₁, A₂, and A₃. Given the relatively low S/N of the spectra, we are not able to distinguish metallicity, so only [Fe/H] = 0 models are used. Age ranges for the old stellar population run from 10 Myr up to the age of the universe at the redshift of the quasar. Young ages are allowed to be any in the model grid that are younger than the current old age. χ² is calculated at each wavelength and weighted by the observed spectrum's noise at that point, $\chi _{i}^{2} = \big[\big(F_{{\rm gal}_{i}} - \alpha F_{{\rm model}_{i}}\big)\big/\sigma _{i}\big]^{2}$, where F_gal is the flux of the scatter-subtracted galaxy spectrum, F_model is the flux of the model galaxy spectrum, α is a model spectrum normalization parameter, σ is the observed spectral noise, and the index i refers to each wavelength point. For the Keck data, noise spectra are generated by measuring the rms of the rest-frame spectrum at three locations devoid of prominent spectral features: ∼3600 Å, ∼5400 Å, and ∼6100 Å. We fit a polynomial to the measured rms values and extrapolate across the entire wavelength range to generate the galaxy's noise spectrum. For the WIYN data, noise spectra are calculated directly using the observed sky spectra. In both data, spectral features not included in the model spectra, such as sky residuals or galaxy emission lines, are masked and do not affect the χ² calculation. The best-fitting combination of parameters is selected as the one that provides the minimum χ² value when summed over wavelength.

We measure velocity dispersions from stellar absorption lines in the host galaxies by fitting a stellar template that has been convolved with a Gaussian profile to the off-nuclear, scatter-subtracted galaxy spectrum. The continuum is normalized on both galaxy and template spectra and a direct fit is done in pixel space using the code of Karl Gebhardt (Gebhardt et al. 2000b, 2003). The template is compiled from 21 weighted stellar spectra from the Coudé Feed Spectral Library at KPNO (Valdes et al. 2004), that were selected to provide a good representation of main sequence A stars through K giants. We use the same group of stars as Gebhardt et al. (2003), which are listed with their parameters in Table 2. We are able to use this library of stellar spectra taken with a different instrument because the spectral resolution (Δλ = 1.8 Å) is much higher than our host galaxy data. Fitting parameters include the weights of the individual stellar spectra and the Gaussian width to which the combined template is convolved. We select the best fit as the combination that provides the lowest rms differences from the galaxy spectrum.

Velocity dispersion uncertainties are calculated through Monte Carlo simulations by adding Gaussian noise to each pixel in the final template, which has a very high S/N, at a level such that the mean matches the noise in the initial galaxy spectrum and the standard deviation is given by the rms of the initial fit. The velocity dispersion is measured for 100 noise realizations and the mean and standard deviation of these results provide the measured velocity dispersion and its 1σ uncertainty. The distribution of measured values is also used to determine the sigma bias of the measurement. As long as the bias is much less than the uncertainty, the measurement is considered valid (see the Appendix).

We use the approximate wavelength range of 3850–4200 Å for our velocity dispersion fits, which contains the Ca ii H&K (3968, 3934 Å) absorption lines. Even though these lines were historically avoided because of their intrinsic broadening, they have been shown to work very well in the presence of mixed stellar populations in galaxies (Kobulnicky & Gebhardt 2000; Gebhardt et al. 2003), as long as the mix of stellar spectra in the fitting template is individually determined for each galaxy. Greene & Ho (2006) also point out that the Ca H&K lines should be good for measuring σ_* in powerful AGNs because they may be the only stellar absorption lines with sufficient equivalent width to persist in high-luminosity AGNs. We mask a few features in the region including Hδ since Balmer line widths may be dominated by rotation and pressure broadening of A stars; the H8 line just blueward of Ca K; and the Ca H line in some cases that show contamination. We also tested the Mg ib triplet (5167, 5173, 5184 Å) region and found that it did not produce reliable results in these data (see the Appendix).

The velocity dispersion fits for our ten host galaxies are shown in Figure 4. The black solid lines are the galaxy spectra and the dashed red overlays are the best-fitting templates. The yellow shaded regions mark features that were masked and disregarded during the fit. PKS 2135-147 contained particularly strong broad QSO emission at the Ca H line. 3C 273 and PKS 2349-014 also show contamination from narrow emission near this line. Our measured dispersions are given in Table 3, along with the radii at which the galaxies were observed, the relative fractions of stars in the best-fitting template (A V, F-G V, G-K III), the spectral S/N over the fitted region, and the amount of scattered quasar light that was removed from the spectrum. The measured velocity dispersions range from 150 to 346 km s⁻¹ with a mean of 272 km s⁻¹. We tested the possibility of the A stars in the template inflating the velocity dispersions measured from the Ca ii lines by removing them from the available stellar templates and got the same results within the uncertainties. In fact, the measured σ's with the A stars in the mix were systematically lower by ∼7%.

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Note that three velocity dispersions are marked as upper limits. Tests on velocity dispersion standard galaxies of McElroy (1995) show that we should be able to measure down to about 20% below the instrumental resolution of 300 km s⁻¹, or 240 km s⁻¹ (see the Appendix). We mark any measurements <250 km s⁻¹ as upper limits. For PG 0052+251, even though its fit looks reasonable in Figure 4, the measured σ_* exhibits higher sigma bias than the rest of our objects over the range of input σs relevant for our spectral resolution (see the Appendix). The data seem to indicate that the true σ_* is below our resolution. Therefore, we can only give an upper limit on the velocity dispersion of PG 0052+251. On close inspection of its spectrum, this measurement may be affected by insufficient scatter subtraction of an Ne iii emission line at 3969 Å in the quasar spectrum (Hewitt & Burbidge 1993) that falls in the vicinity of the Ca H&K lines, causing a strange shape to the lines (Figure 4). Despite the fact that this galaxy has a relatively high S/N, the amount of scattered quasar light and location of this feature prevent accurate scatter subtraction around these lines. Figure 5 shows our scatter subtraction of PG 0052+251 with the Ca H&K lines marked and the stellar population model fit for this galaxy. Although the continuum and many other features of the host galaxy are fit very well by the model, the line depths between 3800 and 4100 Å, which is riddled with quasar emission, are very discrepant, signaling that the galaxy absorption lines may be contaminated. It is possible that this could contribute to the problematic sigma bias in the velocity dispersion measurements on this galaxy. A further discussion of tests of σ_* measurement on galaxy spectra diluted by residual scattered quasar light can be found in the Appendix.

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2.7.1. Aperture Correction

Because velocity dispersion varies with galaxy radius, to match the comparison data we aperture-correct all host galaxy velocity dispersions from the radius at which σ_* was measured to the radius of R_e/8, as in Bernardi et al. (2003a) (see Jørgensen et al. 1995),

$$\begin{equation} \sigma _{\rm cor} = \sigma _{\rm meas} \left(\frac{R_{\rm obs}}{R_{e}/8} \right)^{0.04}. \end{equation} \tag{ 2 }$$

In the Keck data, the host galaxy spectra are off-nuclear long-slit observations for which the extracted spectra are summed along the slit; therefore, the weighted average radius along the summed portion of the slit is used as the effective observed radius. For the WIYN data, the approximate radius at which the fiber was centered is used. Effective observed radii are given in Table 3. Aperture-corrected velocity dispersions of the host galaxies are used in the following FP analysis. Average aperture corrections are 9% for these galaxies.

Previous work has shown that host galaxies of AGN lie on the FP occupied by quiescent early-type galaxies (e.g., Woo et al. 2004; Treu et al. 2007; Dasyra et al. 2007). Here we explore the properties of the host galaxies of higher-luminosity quasars. We place the QSO host galaxies on the FP in Figure 6, using the r-band projection against effective radius, R_e from Bernardi et al. (2006),

$$\begin{equation} {\rm log}\, \sigma _{*} + 0.2 \left[ \mu _{e}(r) - 19.64 \right], \end{equation} \tag{ 3 }$$

with R_e in kpc, the stellar velocity dispersion, σ_*, in km s⁻¹, and the surface brightness, μ_e(r), in mag arcsec⁻². Our QSO host galaxies are shown as large circles (green are RL and yellow are radio-quiet (RQ), using the division defined in Kellermann et al. 1994 at L_5 GHz∼ 10²⁶ W Hz⁻¹). The numbers inside these symbols correspond to object numbers in the tables. The PG QSO host galaxies of Dasyra et al. (2007) are shown as triangles. These objects are all RQ and some have known morphologies (Guyon et al. 2006): the large filled triangles are ellipticals, the crosses on triangles denote ellipticals with signs of interaction, the large open triangles are early types, the large open triangles with asterisks are spirals, and the small filled triangles are unknown. Comparison of SDSS early-type galaxies are the small cyan points (Bernardi et al. 2003a) and early types with σ_* > 350 km s⁻¹ (Bernardi et al. 2006) are the open diamonds. Merger remnant galaxies from Rothberg & Joseph (2006) are denoted as squares: normal mergers are shown as filled red squares, luminous infrared galaxies (LIRG)/ULIRGs as filled black squares, and shell ellipticals as open squares.

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The QSO hosts occupy both regions covered by the Bernardi et al. (2003a, 2006) early-type galaxy samples, while the merger remnants lie within or below the main early-type galaxy distribution. All of our RL QSO hosts lie near the upper envelope of the FP, while the RQ objects (both ours and those of Dasyra et al. 2007) mostly lie within the main locus. The implications of a location in the upper envelope of the FP are higher stellar velocity dispersion, lower surface brightness, or larger effective radius than normal for typical early-type galaxies. The Bernardi et al. (2006) galaxies occupy this region as well. Bernardi et al. concluded that these massive galaxies were not outliers, but merely at the outer extreme of the FP distribution. Figure 7 plots the fundamental galaxy parameters against each other. It is clear from these plots that our host galaxies at the upper extreme of the FP have systematically higher velocity dispersions, lower surface brightnesses, and larger effective radii than the normal early-type galaxies.

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A caveat to keep in mind is that we have used surface brightnesses and effective radii derived from two-dimensional de Vaucouleurs profile fits to all galaxies, regardless of morphology. This was an attempt to analyze all objects in the same way for comparison; however, some objects have obvious morphological disturbances atypical of early-type galaxies. Three host galaxies of RQ QSOs show obvious spiral structure. The consequences of fitting disk galaxies with an r^1/4 model, which is more characteristic of their bulges, is discussed in Section 4.1.

Now we explore the behavior of the mass-to-light ratios (M/L) of the galaxies. For this analysis we calculate the galaxy mass from

$$\begin{equation} M_{*} = \frac{5 \sigma _{*}^{2} R_{e}}{G} [M_{\odot }], \end{equation} \tag{ 4 }$$

where 5 is a structural constant corresponding to R_tidal/R_core ≈ 100, where R_core is the radius at which surface brightness has dropped to half its central value, for King surface brightness models of giant to intermediate-mass ellipticals (Bender et al. 1992). The luminosity is calculated from

$$\begin{equation} L = 2\pi \langle I_{e} \rangle R_{e}^{2} [L_{\odot }], \end{equation} \tag{ 5 }$$

with 〈I_e〉, the mean surface brightness within R_e, calculated from

$$\begin{equation} \mathrm{log} \langle I_{e} \rangle = -0.4(\langle \mu _{e} \rangle -c_{1} - c_{2}(z)) [L_{\odot } \mathrm{pc}^{-2}], \end{equation} \tag{ 6 }$$

where c₁ = 26.4 for the Gunn r-band (Jørgensen et al. 1996), c₂(z) is a redshift-dependent correction to our cosmology, and μ_e is the surface brightness in units of mag arcsec⁻².

Table 4 gives the values of M/L and stellar mass for our host galaxies and the lower-right panel of Figure 7 shows the calculated M/L as a function of velocity dispersion for our hosts and the comparison objects. As noted in Bernardi et al. (2003b), the slope of the (M/L)–σ_* relation can be quite different when the M/L calculated from observables is compared with that predicted from the FP. Therefore, we use the M/L calculated from observables. The host galaxies of RL quasars show a systematically higher M/L than that of the RQ objects.

We now compile all information on our individual QSOs and their host galaxies. The magnitudes quoted in this section are from Bahcall et al. (1997) except for 4C 31.63, which is from Hamilton et al. (2002), and PKS 0736+017, which is from Dunlop et al. (2003). All quoted velocity dispersions are aperture-corrected values. Stellar populations are qualitatively mentioned, based on the model fitting performed during our scatter subtraction process. More accurate stellar populations will be analyzed in future work. Where relevant, implied star-formation rates from the [O ii] line emission in the entire host galaxies are taken from Ho (2005). For reference, mean galaxy parameters for the different types of objects are given in Table 5.

3.3.1. PG 0052+251

3.3.2. PHL 909 (0054+144)

3.3.3. PKS 0736+017

3.3.4. 3C 273 (PG 1226+023)

3.3.5. PKS 1302-102

3.3.6. PG 1309+355

3.3.7. PG 1444+407

3.3.8. PKS 2135-147

3.3.9. 4C 31.63 (2201+315)

3.3.10. PKS 2349-014

Although we have thus far utilized the parameters of our QSO host galaxies that were derived from two-dimensional r^1/4 profile fits, Bahcall et al. (1997) actually found that four galaxies were better fitted by an exponential disk model: PG 0052+251, PG 1444+407, PG 1309+355, and PKS 1302-102. The first three of these show obvious spiral structure and the fourth one is described as a disturbed elliptical. We now analyze the properties derived from exponential disk fits to these four galaxies. Placement of disk galaxies on the FP is not technically correct since this relation holds only for early-type galaxies and bulges. Nonetheless, we do it here to investigate the range in which these galaxies should fall, given that they are likely to have a bulge component and that our velocity dispersion measurements may have contained light from both the disk and the bulge. Therefore, these galaxies should exist somewhere between the positions of pure bulge and pure disk.

Table 6 gives the exponential disk parameters derived by Bahcall et al. (1997) and our galaxy properties calculated from them. We convert Bahcall's disk scale lengths, R_s, to effective radii, R_e, using R_e = 1.6785 R_s (de Vaucouleurs & Pence 1978). The new galaxy positions (for objects 1, 5, 6, and 7) are shown on the FP in Figure 8 and on galaxy parameter plots in Figure 9. The lines connected to the new points illustrate the range between the new exponential disk model locations and the previous r^1/4 model locations for these galaxies. It can be seen in Figure 8 that all four host galaxies move up on the FP. Interestingly, PKS 1302-102, the RL QSO, now resides among the loci of the RL objects, rather than appearing to exist in a transition region between the RL and RQ groups. The RQ QSOs have also moved up into the region occupied by massive early-type galaxies. Their masses derived from the new radii, also given in Table 6, are indeed all well above 10¹¹ M_☉. Regardless of assumed morphology, these are massive galaxies. It can be seen in Figure 9 that these four RQ galaxies now lie among the largest, lowest surface brightness, and highest M/L QSO hosts from Dasyra et al. (2007). However, it is expected that disk galaxies in that sample would move similarly if exponential disk models were used to derive their parameters.

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Of the six RL objects in our sample, all are morphologically classified (Table 1) as elliptical galaxies except for PKS 2349-014 and PKS 0736+017, which are complex and interacting with clear tidal tails, nevertheless well fit by a r^1/4 light distribution. Bahcall et al. (1997) and Schweizer (1996) suggest that PKS 2349-014 may be a proto-elliptical galaxy resulting from a merger of two spirals. PKS 1302-102, PKS 2135-147, PKS 2349-014, and 4C 31.63 all have companions within 5'' of the QSO. Of the four RQ objects, PG 0052+251 is classified as an Sb galaxy and shows HII regions; PG 1444+407 is classified as an E1 by Bahcall et al. (1997), as a spiral by Hamilton et al. (2002), and may contain a bar (Hutchings & Neff 1992; Bahcall et al. 1997); PG 1309+355 is an Sab with tightly wound spiral arms; and PHL 909 is clearly an elliptical galaxy. PHL 909 is our only RQ host with a nearby companion.

Our QSO hosts at the upper envelope of the FP are either elliptical or interacting galaxies. Three RQ spiral galaxies and one elliptical lie on the FP. If we also consider the Dasyra et al. (2007) QSO hosts, ellipticals, interacting ellipticals, early-types, and spirals all lie on the FP close to our four RQ hosts. An early-type and spiral also lie well below the FP among the merger remnants. This lack of morphological consistency suggests that host galaxy morphology alone is not the driver of the position on the FP or in the galaxy property plots of Figure 7 for this small sample.

If we look at the different groups of objects in the plots of Figures 6 and 7, we see trends suggesting different classes of galaxies. First we address the general trends. All objects—quiescent early-type galaxies, massive early-type galaxies, quasar host galaxies, and galaxy merger remnants—lie nearly on the FP (or are expected to lie there once faded, in the case of the merger remnants). Of course, we expect the early-type galaxies, including QSO hosts of that morphology, to be there. The RL hosts lie among the massive early-type galaxies at the upper edge of the plane. The merger remnants were morphologically chosen to be near the end of the merger sequence with the stipulation that the cores have already coalesced into a single nucleus. Since we believe that early-type galaxies form from mergers, it is not surprising that these also occupy the FP. The LIRG/ULIRGs have a slight offset below the plane due to their currently high luminosity, but are expected to fade up to the FP after the starbursts end. The RL quasar hosts are morphologically either early-type or interacting and on their way to forming early types, and, therefore, they would be expected on the FP. Perhaps the hardest to explain are the RQ QSO hosts that show definite signs of spiral structure (three of our RQ objects and two of the Dasyra et al. 2007 sample).

The upper-left plot of Figure 7 shows surface brightness and effective radius. The merger remnants tend to be small and bright, suggesting that nuclear starbursts are in progress. The massive early-type galaxies from SDSS are bright and mostly large, though a few stretch down to small radii. The Dasyra et al. (2007) QSO hosts tend to have lower surface brightness for a given radius than either the massive galaxies or the merger remnants, residing near the center of the distribution of normal early-type galaxies from SDSS. Our three RQ hosts that are spirals lie in the transition region between normal and massive early-type quiescent galaxies, while the elliptical host resides up among the normal quiescent early types.

In the upper-right plot of Figure 7, the stellar velocity dispersions of the merger remnants and the lower-luminosity RQ QSO hosts overlap and fall well within the distribution of normal early-type galaxies, as concluded by Dasyra et al. (2007). It has been suggested that LIRG/ULIRGs form intermediate-sized elliptical galaxies from the merger of two gas-rich spiral galaxies and will not evolve into the brightest QSOs (Genzel et al. 2001; Tacconi et al. 2002; Rothberg & Joseph 2006; Dasyra et al. 2006). This idea is supported by the similar velocity dispersions of these two classes of objects, and by their mass-to-light ratios (the lower-right plot of Figure 7; note that most of our RQ QSO hosts are on the high end of the other PG QSO hosts in σ_* and M_*). The merger remnants have a lower M/L due to their currently high luminosities, but after fading should reside among the lower-luminosity RQ QSO hosts in Figures 6 and 7. There is a clear distinction between these objects and our massive RL QSO hosts in σ_* and R_e (and thus stellar mass). The separation occurs at σ_*∼ 300 km s⁻¹, R_e∼ 6 kpc, and corresponding M_* ∼ 7 × 10¹¹ M_☉. Such a distinction between RL and RQ QSOs has been observed as a function of estimated black hole mass (Dunlop et al. 2003), however, here we have deduced it using directly measured host galaxy stellar velocity dispersions.

Because our method of calculating galaxy mass assumes that the velocity anisotropies are small and that the system is dynamically hot (Bender et al. 1992), the masses calculated in this way for spiral galaxies or those with strong interactions will be systematically incorrect. We now consider only the galaxies that are known to have elliptical morphologies. The RQ elliptical QSO host sample consists of PHL 909, PG 0007+106, PG 1617+175, and PG 2214+139 (the last three are from Dasyra et al. 2007), while the RL sample includes 3C 273, PKS 2135-147, and 4C 31.63. Our calculated masses for the RQ group of ellipticals are 1.3–2.4 × 10¹¹ M_☉ with an average of 1.9 × 10¹¹ M_☉. The RL group has calculated masses of 9.4–29.8 × 10¹¹ M_☉ with an average of 17.4 × 10¹¹ M_☉. This gives an RL/RQ division somewhere between 2.4–9.4 × 10¹¹ M_☉, or M_*∼ 5.9 ± 3.5 × 10¹¹ M_☉, for the elliptical QSO host galaxies.

Mean galaxy parameters are given in Table 5 for the different groups of galaxies. Overall, our RQ hosts show properties similar to normal early-type galaxies, though slightly larger and more massive. A comparison of properties of our RQ hosts and normal early-type galaxies show R_e = 5.7, 4.9 kpc, respectively, M/L = 5.3, 7.0, σ_* = 241, 190 km s⁻¹, and M_* = 4.4, 2.1 × 10¹¹ M_☉. However, our RL hosts are more analogous to the massive early-type galaxies. They are larger (11.4, 8.0 kpc, respectively) with lower surface brightness (20.8, 19.8 mag arcsec⁻¹), lower σ_* (321, 403 km s⁻¹) and M/L (12.4, 14.7), but higher M_* (14.8, 12.2 × 10¹¹ M_☉). It appears that we have two classes of objects, regardless of the surface brightness model used for the disk galaxies (refer also to Figures 8 and 9): very massive galaxies with RL quasars and intermediate-mass galaxies with RQ quasars. This supports the conclusions of Malkan (1984) who found in an imaging study that RQ quasars have the color, size, surface brightness, and scale length of normal early-to-intermediate-type spiral galaxies, while RL quasars appear to reside in moderate to bright ellipticals.

We see in Figures 6 and 7 that all RL QSO hosts reside among the massive early-type galaxies. A more detailed look at the radio properties of these objects reveals a correlation between radio luminosity and σ_*, shown in Figure 10 with 5 GHz radio fluxes taken from Kellermann et al. (1994) and the NASA/IPAC Extragalactic Database (modified to our adopted cosmology of Ω_M = 0.3, Ω_Λ = 0.7, H₀ = 70 km s⁻¹ Mpc⁻¹). A similar correlation was found by Nelson & Whittle (1996) for RQ Seyfert galaxies, which extended to higher luminosity radio galaxies when considering the core radio emission. They interpreted this correlation as a dependence of radio emission on galaxy bulge mass.

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Subsequent studies (Franceschini et al. 1998; McLure et al. 1999; Nelson 2000; Laor 2000; Lacy et al. 2001; Ho 2002; Dunlop et al. 2003; Snellen et al. 2003; McLure & Jarvis 2004; Woo et al. 2005) have looked at the dependence of radio luminosity on black hole mass (M_BH), which we now know is related to σ_* and galaxy bulge mass (Gebhardt et al. 2000a; Ferrarese & Merritt 2000). Franceschini et al. (1998) found a tight dependence of L_5 GHz ∝ M^2.66_BH for a sample of 13 nearby early-type galaxies with M_BH estimated from stellar or gas kinematics. There has been some disagreement on this correlation as different types of objects were analyzed (McLure et al. 1999; Lacy et al. 2001; Ho 2002; Snellen et al. 2003; Woo et al. 2005; McLure & Jarvis 2004) and scatter about the relation grew to several orders of magnitude when AGNs of different activity levels were added. For these larger samples, a wide range of radio luminosity is possible for a given M_BH and it is likely more dependent on BH accretion rate than on the mass (Ho 2002). Ho (2002) suggested that the L_radio–M_BH relation arises indirectly through more fundamental correlations between radio luminosity and bulge mass and between bulge mass and black hole mass, similar to the original interpretation of Nelson & Whittle (1996). For strongly active quasars, we find a tighter correlation of radio luminosity with host galaxy bulge mass (calculated from directly measured host galaxy parameters) than with black hole mass (inferred from the Tremaine et al. 2002 M_BH–σ relation). This relationship is shown in Figure 11. Our best linear regression fit to the data gives the relation L_radio ∼ M^3.56_bulge with an rms scatter of 1.09 dex.

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One consensus that has arisen from all of these studies is that RL AGNs almost exclusively have M_BH⩾ 10⁸ M_☉. Indeed all of our RL quasars in Figure 10 have M_BH > 10⁸ M_☉. The best-fit line to the QSO hosts of this work and of Dasyra et al. (2007) suggests a steeper slope of L_5 GHz ∝ M^3.8_BH with an rms scatter of 1.36 dex; however, given our limited sample size, the small M_BH range covered by the data, the large scatter associated with this relation, and possible differences in black hole mass estimation techniques (the black hole masses of the QSOs in this study and their place on M_BH–σ relation will be discussed in future work), the QSOs in this study are consistent with the previously determined L_5 GHz–M_BH correlation. Like the host galaxy parameters in Section 4.3, radio emission has a dependence on the mass of either the host galaxy and/or the central black hole. Our data on active quasars show a stronger dependence on the host galaxy mass.