BULGES OF NEARBY GALAXIES WITH SPITZER: SCALING RELATIONS IN PSEUDOBULGES AND CLASSICAL BULGES

Many studies have found that bulges are never smaller than a few hundred parsecs (e.g., Graham 2001; Balcells et al. 2007; Fisher et al. 2009). Thus, we set a distance limit of 20 Mpc such that all bulges in our sample will be resolved to r ≲ 150 pc with IRAC on Spitzer.

We cross reference the RC3 (de Vaucouleurs et al. 1991) with the Spitzer archive. We select all galaxies between Hubble types S0 and Sd (as given in RC3) available in the Spitzer archive within our distance limit (20 Mpc). We do not analyze bulges later type than Sd because bulges are extremely rare in Sdm-Irr galaxies

We restrict our sample to exclude significantly inclined galaxies. We only keep galaxies that satisfy R25 < 0.5. (R25 is the mean decimal logarithm of the ratio of the major isophotal diameter at isophotal diameter, D25, to that of the minor axis.) This corresponds to an inclination of about 75° for an Sc spiral. This cut yields 331 galaxies. We visually identify nine galaxies that are highly inclined, but not excluded by the R25 criterion because of a very large bulge-to-total ratio. These galaxies are removed from the sample.

We only select galaxies that are free of tidal tails, warps, and asymmetries in IRAC1 images. This is done to attempt to reduce the number of galaxies significantly affected by interactions or mergers with other galaxies. For each galaxy, we also consider comments in the Carnegie Atlas of Galaxies (Sandage & Bedke 1994); galaxies described as "amorphous" and/or "peculiar" are scrutinized for evidence of recent or ongoing interactions. We remove 34 galaxies due to peculiar morphology or tidal tails.

The total list that meets all of the above selection criteria is 297 galaxies. Of these 297 galaxies, 146 have adequate data in the Spitzer archive. Note that a handful of galaxies have over-exposed centers, or the galaxy is not well covered in the Spitzer image. Those galaxies are not included in the 146 disk galaxy sample.

We also wish to compare the location of pseudobulges and classical bulges in parameter space to that of elliptical galaxies. We therefore include a set of elliptical galaxies as a control sample. A problem for calculating Sérsic fits to elliptical galaxies is that resulting parameters are highly dependent on both spatial resolution (for low luminosity elliptical galaxies) and field of view (for high luminosity ellipticals). Yet, near-IR HST archival data are not necessarily available, and typical data in the Spitzer archive do not always cover the entire galaxy. Furthermore, to assure an unbiased comparison, we wish to have a complete set of elliptical galaxies.

We use the elliptical galaxy sample and data from Kormendy et al. (2009). Kormendy et al. (2009) determine surface photometry for all elliptical galaxies in the Virgo cluster. They construct V-band surface brightness profiles of composite data sets of HST and ground-based data. To reduce the effects of sky subtraction errors and smearing due to point-spread functions (PSFs), Kormendy et al. (2009) capitalized on the wealth of published data available on Virgo ellipticals. Therefore, galaxies in their sample tend to have many different data sources which are averaged together. Also, they add extremely deep new observations from the McDonald 0.8 m telescope, frequently reaching 30 V mag arcsec⁻².

We use the half-light radius, r_e, and Sérsic index, n, directly from the fits in Kormendy et al. (2009). For luminosity and surface brightness we shift the measurement in Kormendy et al. (2009) to account for the V − L color, L designating the magnitude in IRAC channel 1. This carries an implicit assumption that color gradients in elliptical galaxies average to zero. Though not exactly true, this assumption is supported by relatively flat g − z profiles in Kormendy et al. (2009). If a galaxy has 3.6 μm data in the Spitzer archive, we calculate the luminosity at 3.6 μm, and we integrate the V-band profile to the maximum isophotal radius observed in the 3.6 μm profile; this yields V − L for that galaxy. For those elliptical galaxies that do not have data in the Spitzer archive, we use the average V − L of the rest of the elliptical galaxies in the sample. The root-mean-squared deviation of V − L about the mean is 0.5 mag. Therefore, differences of less than half a magnitude will be considered less significant in our analysis. It is well known that fainter elliptical galaxies are bluer; however, Bower et al. (1992) find that the correction is roughly ±0.2 mag, which is small enough to be negligible for our purposes. The elliptical galaxy sample consists of 27 galaxies; therefore, the total sample in this paper is increased to 173 galaxies.

Table 1 lists the properties of our sample galaxies. In Figure 1, we compare our sample properties to those of the complete RC3. (Note that at our distance limit the RC3 is complete to M_B ≲ −16.5 B-mag.) From top to bottom, the properties shown are distance, RC3 T-type, absolute B_T magnitude, and the physical radius in parsecs of the isophote at 25 B-mag arcsec⁻².

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Our sample is complete within 9 Mpc, and 75% complete within 13 Mpc. Beyond 13 Mpc the Spitzer coverage becomes very incomplete. Overall, the available data in the Spitzer archive yield the inclusion of half the galaxies that meet our selection criteria in the RC3.

Hubble type correlates with B/T (Simien & de Vaucouleurs 1986), and thus provides an important tool for identifying biases among bulge samples. The second panel from the top in Figure 1 shows the distribution of T-types in our sample. Our sample distribution appears very similar to that of the complete RC3. Our selection is fairly independent of Hubble type, with a dip at S0/a (T = 0). There is a slight bias in the sense that more galaxies are missing at later Hubble types Sbc–Scd (T = 4–6).

We are missing more galaxies that are smaller. Comparing our sample to the RC3 we find that our sample includes 66% of galaxies larger than one standard deviation from the mean D25, 52% of those within one standard deviation, and only 29% of galaxies below one standard deviation. However, our sample includes galaxies in the extremes of the distribution. For the purpose of this paper, our sample adequately covers the properties of the complete RC3 distribution.

Including the entire Spitzer archive of bulge–disk galaxies out to 20 Mpc means that our data come from a variety of campaigns, each with separate goals and often differing observational strategies. A few notable surveys comprise of the vast majority of galaxies in our sample: the SINGS survey (Kennicutt et al. 2003), the nearby bulge survey (Fisher et al. 2009), and the local volume survey (Dale et al. 2009).

For the analysis in subsequent sections, we define a subset of our sample of higher-quality data. We do this so that we can make sure that bulges with low signal-to-noise or bright Seyfert nuclei do not cause us to miss correlations that would be seen with better data. The criteria we use for creating the high-quality data sample are as follows.

• 1.  
  Availability of optical images from HST for morphological classification, as described below. Of the complete sample, 24 galaxies do not have optical HST images.
• 2.  
  B/T ⩾ 1% and radius at which the Sérsic bulge and the exponential disk equal in surface brightness, r_b=d, be greater than twice the PSF of the surface brightness profile. In this cut, 19 galaxies are removed.
• 3.  
  Finally, we remove any galaxies with a prominent active galactic nucleus (AGN); this is to ensure that the mid-IR color is not skewed by non-thermal emission. Most of these galaxies do not make it into the sample to begin with because the AGN typically results in overexposed IRAC images. To identify the remaining AGNs, we use the same method used by Fisher et al. (2009). We measure the cuspiness of the 8 μm profile by measuring the ratio of the flux within 2'' (200 pc at 20 Mpc) to that of the entire galaxy. We only include those galaxies with flux ratio less than 15%. Of the remaining sample, 10 have L₈(r < 2'')/L₈(total) < 15%, leaving the clean sample at 94 galaxies. We note that this criterion may bias our sample against extremely cuspy and compact bulges. However, galactic nuclei contain less than 1% of galaxy stellar light (Phillips et al. 1996). An object containing more than 15% of the stellar light within 200 pc lies outside any known parameter correlation of galactic components.

We use post basic calibrated data images taken on the Spitzer with IRAC channel 1, centered at 3.6 μm, to measure the light profiles of galaxies in our sample. When available, we also use HST NICMOS data, typically in the F160W filter.

We calculate sky values by fitting a second-order surface to the areas of the image not covered by galaxy light. Then we subtract the surface from the image. In some cases, there is not enough area on the image that is not affected by galaxy light to constrain the surface fit. In these cases, we take a mean value in an unaffected region of the image, and then we compare the resulting profile from the 3.6 μm with one calculated on 2MASS (Skrutskie et al. 2006) H-band images, which allow for more accurate sky subtraction. If the 3.6 μm profile is significantly different, we determine the sky again using a different region of the image. At 3.6 μm the sky values are very near zero, and typically of not much concern. For the 8.0 μm channel, "sky" (which is most likely diffuse emission from the Milky Way) is more important. Typical uncertainties from sky subtraction are 0.3 mag for the IRAC CH1 and 0.1 mag for IRAC CH4.

We use the isophote fitting routine of Bender & Moellenhoff (1987) to generate ellipse fits. First, interfering foreground objects are identified in each image and masked manually. Then, isophotes are sampled by 256 points equally spaced in an angle θ relating to polar angle by tan θ = a/b tan ϕ, where ϕ is the polar angle and b/a is the axial ratio. An ellipse is then fitted to each isophote by least squares. The software determines six parameters for each ellipse: relative surface brightness, center position, major and minor axis lengths, and position angle along the major axis. We combine HST and Spitzer data by shifting the zeropoint of the NICMOS data to match the IRAC profile. The two profiles are then averaged, to construct a composite HST+Spitzer IR profile.

We determine bulge and disk parameters by fitting each surface brightness profile with a one-dimensional Sérsic function plus an exponential outer disk,

$$\begin{equation} I(r)=I_0\exp [-(r/r_0)^{1/n_b}] + I_d\exp \left[-(r/h) \right]\,, \end{equation} \tag{ 1 }$$

where I₀ and r₀ represent the central surface brightness and scale length of the bulge, I_d and h represent the central surface brightness and scale length of the outer disk, and n_b represents the bulge Sérsic index. The half-light radius, r_e, of the bulge is obtained by converting r₀,

$$\begin{equation} r_e=(b_n)^nr_0, \end{equation} \tag{ 2 }$$

where the value of b_n is a proportionality constant defined such that Γ(2n) = 2γ(2n, b_n). Γ and γ are the complete and incomplete gamma functions, respectively. We use the approximation b_n ≈ 2.17n_b − 0.355. We restrict our range in possible Sérsic indices to n_b>0.33 to ensure that the approximation is accurate. A more precise expansion is given in MacArthur et al. (2003). The average surface brightness within the half-light radius, 〈μ_e〉, is given by

$$\begin{equation} \langle \mu _e\rangle =m_{3.6} + 2.5\log \big(\pi r_e^2\big), \end{equation} \tag{ 3 }$$

where m_3.6 is the magnitude in 3.6 μm. We adjust all luminosities by the average ellipticity in the region in which that parameter dominates the light. (Also, see Graham & Driver 2005 for a review of the properties of the Sérsic function.)

Despite its successes, the Sérsic bulge plus outer exponential disk model of bulge–disk galaxies does not account for many features of galaxy surface brightness profiles. Disks of intermediate-type galaxies commonly have features such as bars, rings, and lenses (see Kormendy 1982 for a description of these). Further, Carollo et al. (2002) show that many bulges of early- and intermediate-type galaxies contain nuclei. Bars, rings, lenses, and similar features do not conform to the smooth nature of Equation (1); hence, we carefully exclude regions of the profile perturbed by such structures from the fit. This is a subjective procedure, as it requires selectively removing data from a galaxy's profile, and undoubtedly has an effect on the resulting parameters. We are often helped to identify bars by the structure of the ellipticity profile, as described in Jogee et al. (2004) and also Marinova & Jogee (2007). For a detailed description of this procedure, and analysis of its effects see the Appendix of Fisher & Drory (2008). They find that not accounting for bars can have the affect of increasing n_b by at most 0.5. For those galaxies in which a bar is present, it is our assumption that removing the bar from the fit provides the best estimation of the properties of the underlying bulge and disk. All of our fits are given in tabular form in Table 2 and also shown as figures in Appendix B.

In addition to Sérsic fitting, we determine the bulge luminosity by a non-parametric method to obtain a second estimate of bulge luminosity and surface density. To isolate the light from the bulge, we must subtract underlying disk light. For this purpose, we fit an exponential profile I_exp(r) = I₀exp(−r/h) to the major-axis surface brightness profile of the outer part of the galaxy. The range included in the exponential fit is determined iteratively. Typically, this exponential fit is determined on isophotes with radii larger than the radius which includes 20% of the light. Bars are masked as usual. Note this fit is independent of the fit described in Equation (1). To account for the variable ellipticity profiles of these disk galaxies we take the mean ellipticity for each component and adjust the luminosity accordingly: $L_{\rm disk}=(1-\bar{\epsilon })L_{\mathrm{exp}}$. We then calculate the inward extrapolation of the fit to the central (or bulge) region; thus, L_bulge = L(r < R_XS) − L_disk(r < R_XS) where R_XS is the radius containing the light that is in excess of the inward extrapolation of the outer exponential.

We include HST/NICMOS F160W images in the analysis for all galaxies with available archival data. This is done because it increases dynamic fitting range on the bulge. The composite profile is NICMOS data for r < 122, and IRAC 3.6 μm data at larger radii. Inclusion of the NICMOS data may affect the results in two ways.

First, this procedure assumes a color gradient of zero from L band to H band in our bulges. This assumption introduces a source of uncertainty, yet allows for a more complete description of the stellar light profile. To quantify this uncertainty we calculate the entire radial surface brightness profile in H band using NICMOS and 2MASS data. We then shift that profile to have the same zero point as the IRAC 3.6 μm profile, and then calculate the bulge luminosity, which we call L_3.6(H). The error in luminosity due to the stitching is the difference L_3.6 − L_3.6(H) scaled by the fraction of light that comes from the shifted NICMOS F160W data:

$$\begin{equation} \delta L_{\rm stitch} \equiv L_{3.6}-L_{3.6(H)} \times L_{3.6}(r<1\farcs 22)/L_{3.6}. \end{equation} \tag{ 4 }$$

This error is typically less than 5% and rarely larger than errors from other sources, such as fitting uncertainty. We use NICMOS data because it is our experience that the high-resolution data increase accuracy, even if precision is compromised slightly.

Second, Balcells et al. (2003) find that supplementing ground-based profiles with HST data systematically affects Sérsic index, making it smaller. This effect is certainly distance dependent. Our distance limit is 20 Mpc, closer than most galaxies in Balcells et al. (2003), and likely is nearby enough to prevent this from affecting our profiles. Nonetheless, we carry out a test to determine if any such bias is present.

We re-fit all galaxies that have both HST and Spitzer images. In this second fit, we do not include isophotes that have smaller major axis than the half width of the PSF of IRAC 3.6 μm, which is 15. In most galaxies, we keep all other input parameters exactly the same. However, the χ² space of bulge–disk decomposition that includes a Sérsic bulge can be very complicated and highly degenerate, in some cases reduction of the fit range resulted in independent minima in parameter space. In those cases, we are forced to reduce the allowable parameter range accordingly.

Figure 2 shows the comparison of parameters from decomposition of IRAC-only isophotes to those derived combining NICMOS and IRAC data. The top panel shows Sérsic index, the middle panel half-light radius, and the bottom panel bulge-to-total light ratio. In each panel, a solid line representing the line of equality is plotted. Bulges in which the inner cut in the fitting range is larger than the resolution of IRAC are denoted as open circles, all other bulges are denoted as closed circles. We do not include galaxies with B/T < 0.01, as there parameters are too poorly constrained to be meaningful.

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In all properties there is good agreement between both methods of decomposition. The bulge-to-total ratio appears to be the most robust quantity. This is likely due to the degeneracy between surface brightness, radius, and Sérsic index with respect to bulge magnitude. Also, we do not expect the inner truncation radius of the fit to greatly alter fit parameters of outer disk properties in nearby galaxies. Half-light radius also shows good agreement. The most scatter appears to be in Sérsic index, which also shows a slight trend. In bulges with Sérsic index higher than about n_b ∼ 3.5–4, the Sérsic index determined from IRAC-only profiles is slightly smaller than that determined with composite Spitzer+HST data. The average of the absolute value of the difference between the lower resolution and higher resolution data is in all cases less than 10%.

In Figure 3, we redraw a figure from Fisher et al. (2009) which shows examples of bulges with E-type morphology (top two panels) and bulges with D-type morphology (bottom four panels). The striking contrast between the exemplary D-type and E-type bulges is evident. When the outer disk is not seen, the bulges with E-type morphology appear morphologically indistinguishable from elliptical galaxies. On the other hand, the bottom four bulges show pronounced disk phenomena including: nuclear spirals that extend all the way to the center of the galaxy (e.g., NGC 4030 and NGC 4736), small bars that are not much larger than a few hundred parsec across (e.g., NGC 4736), nuclear rings (e.g., NGC3351), and somewhat chaotic nuclear patchiness that is reminiscent of late-type disk galaxies (e.g., NGC 2903). We do not show images of all of our bulges, rather we direct interested readers to the Hubble Legacy Archive.³

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In Figure 4, we show the images of the bulges with D-type morphology from Figure 3 taken with NICMOS F160W. In all of these near-IR images, the same features that motivated D-type (hence pseudobulge) classification in the optical bands are still present. Yet, the nuclear spiral in NGC 4736 is much weaker, although the nuclear bar in this bulge is still visible. The features found in the optical are not merely small perturbations caused by dust inside a smooth light distribution, but likely features of the stellar mass distribution.

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Emission in the 8 μm channel on Spitzer is dominated by dust, mostly re-radiated light from polycyclic aromatic hydrocarbons (Leger & Puget 1984). Also, Helou et al. (2004) show that the 8 μm emission in the nearby disk galaxy NGC 300 traces the edges of H ii. Thus, it is correlated with the number of ionizing photons from young stars, and therefore with local star formation rate.

In Figure 5, we show the correlation between mid-IR bulge color (from this data set) with specific star formation rate (from overlapping galaxies in Fisher et al. 2009). A linear regression to the data is plotted as a black line. There is an important distinction between the two data sets, Fisher et al. (2009) subtract an inward extrapolation of the exponential disk for the stellar mass, we do not for this calculation. We find a correlation, with Pearson correlation coefficient r² = 0.65, between mid-IR color, M_3.6 − M_8.0, and specific star formation rate.

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Calzetti et al. (2007) show that differences in interstellar medium metallicity, and likely stellar populations of the galaxy, can strongly affect the correlation between 8 μm emission and luminosity of ionizing photons. Given that we are specifically looking at bulges that may have widely varying stellar populations and metallicities, this is an important caveat. However, when studying a large number of bulges, that may be difficult to resolve. The increased resolution of IRAC data over MIPS data is very important. Thus, we limit the interpretation of 8 μm emission to an on/off metric of star formation. That is to say, we use the 8 μm emission to determine if the bulge is active, and we refrain from using 8 μm emission as a means to quantify the star formation rate. In this paper, it is sufficient to merely know if the bulge is active or inactive, and Figure 5 indicates that mid-IR color is a good estimate in 90% of the bulges. For a detailed discussion of the properties of star formation rates in pseudobulges the interested reader should see Fisher et al. (2009).

Andredakis et al. (1995) showed that bulges in early-type galaxies have larger Sérsic index than those in late-type galaxies. This motivated many authors (e.g., Kormendy & Kennicutt 2004) to assume that Sérsic index of a bulge is correlated with bulge type. Fisher & Drory (2008) directly test this hypothesis and find that in decomposition in the V-band pseudobulges (bulges with D-type morphology) have n_b ≲ 2 and classical bulges (with E-type morphology) have n>2. In this paper, we will also consider the possibility that Sérsic index can be used to identify bulge types. Also we will re-test the connection between bulge Sérsic index and optical bulge morphology with near-IR decompositions that more robustly reflect the stellar light density.

For the comparison of HST morphology to other bulge diagnostics we use the higher quality data set. This is done to ensure that poorly constrained Sérsic fits or phenomena such as AGNs do not artificially generate ambiguity in bulge diagnostics.

In Figure 6, we show the distribution of mid-IR color (top) and Sérsic index (bottom) of bulges. In both panels, those bulges with D-type morphology (that is pseudobulges) are represented by blue histograms filled with forward slanting lines, and bulges with E-type morphology are represented by red histograms filled with backward slanting lines.

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In the top panel of Figure 6, we show that no bulge with E-type morphology has mid-IR color redder than M_3.6 − M_8.0>0.3, and very few (2 of 22) have M_3.6 − M_8.0>0.0. However, as found in Fisher et al. (2009), there is a broad distribution of star formation activity in pseudobulges. Pseudobulges can be both active and inactive. When a bulge is active, in almost every case (96%) that bulge has D-type morphology. Also the majority of bulges with D-type morphology (64%) have mid-IR colors that are redder than any classical bulge. Therefore, use of mid-IR color alone to identify pseudobulges merely finds one type of pseudobulge: active pseudobulges.

In the bottom panel of Figure 6, we find the same result as found in the V band by Fisher & Drory (2008): the vast majority (93%) of bulges with D-type morphology have Sérsic index less than n_b ⩽ 2. Conversely, all bulges with E-type morphology have Sérsic index greater than 2. Only one bulge with E-type morphology has Sérsic index n_b ∼ 2 (NGC 1617 has n_b = 2.1). This confirms that the correlation between Sérsic index and bulges morphology is independent of wavelength.

In the high-quality sample, there are 53 galaxies with positive mid-IR color (based on visual inspection of Figure 5 this translates very roughly to SFR/M ≳ 40 Gyr⁻¹) and only six of those galaxies have a bulge with Sérsic index greater than 2; two of those six active high-n_b bulges have E-type morphology. In the high-quality sample, we find 18 bulges with low Sérsic index and low specific SFR. The eight pseudobulges with the lowest specific SFR are all S0 galaxies.

If a bulge has a positive value of M_3.6 − M_8.0, then that bulge is 96% likely to have low-Sérsic index and D-type nuclear morphology (hence be a pseudobulge). However, if the bulge is inactive then there is little we can say about the type of bulge from mid-IR color alone. As found by both Drory & Fisher (2007) and Fisher et al. (2009), some pseudobulges are inactive and also reside in inactive galaxies. The take away is that bulges with E-type morphology are always inactive and always have n_b>2. Bulges with D-type morphology almost always have n_b < 2 and usually are active. We will investigate the nature of those bulges that have disk-like nuclear morphology, low Sérsic index but are non-star forming in subsequent sections.

Here we turn our attention to the correlations of Sérsic index with other photometric parameters. Fisher & Drory (2008) find with V-band decompositions that it is not only the value of the Sérsic index that is different between pseudobulges and classical bulges, but the way that Sérsic index scales with other parameters. However, their sample did not contain a significant number of galaxies with low B/T or small n_b. Using our more representative sample, we observe the same result at 3.6 μm where light better traces the stellar mass and is less affected by dust.

In Figure 7, we show the correlations of the bulge Sérsic index with half-light radius of the bulge, surface brightness at the half-light radius, and magnitude of the bulge at 3.6 μm (from bottom to top). In all panels, we represent elliptical galaxies as black squares. In each panel, we also show a black line representing a fit to the elliptical galaxies only. Filled symbols represent high-quality data and open symbols represent data that does not fulfill the requirements of the high-quality data set. In the left panels, we identify bulges based on nuclear morphology; bulges with D-type morphology are represented by blue circles, and those bulges with E-type morphology are represented by red squares. If no optical HST images are available, we plot the bulge as an open black circle. Note that all galaxies in the high-quality sample have optical HST data. In the right panels, we identify bulges based on activity. Those bulges with mid-IR color M_3.6 − M_8.0>0, indicating higher specific star formation rate, are represented by blue circles. Those bulges with mid-IR color M_3.6 − M_8.0 < 0 indicating low specific star formation rates are represented by red squares.

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First, we note the similarity in these scaling relations between bulges with E-type morphology and elliptical galaxies. In each panel, bulges with E-type morphology follow the correlations established by elliptical galaxies. There is slightly more scatter in the bulges with E-type morphology than in the elliptical galaxies alone; however, this is not at all surprising since the presence of an outer disk means that Sérsic function fits to bulges are less well constrained than those in elliptical galaxies.

Also, Kormendy et al. (2009) find that the distribution of Sérsic indices in elliptical galaxies is bimodal and that elliptical galaxies with Sérsic index higher than n = 4 are almost exclusively giant ellipticals with core profiles in their central region and that show no signs of rotation. Conversely, they find that elliptical galaxies with lower Sérsic index have cuspy centers, are lower in luminosity, and have dynamics indicative of an oblate spheroid that is flattened by rotation. In the bottom panel of Figure 7, it is clear that bulges with E-type morphology are like low-luminosity ellipticals with Sérsic index less than n_b ∼ 4. This restriction is important for interpreting parameter correlations; the set of classical bulges alone may not always reflect the distribution of all elliptical galaxies.

In Figure 7, for those bulges with D-type morphology it is clear that no correlation exists between the Sérsic index and half-light radius, surface-brightness, or bulge magnitude. In magnitude and surface brightness, the bulges with D-type morphology appear to be scattered with no regularity. However, the half-light radius of bulges with D-type morphology is limited to a very narrow range in parameter space. We will discuss the half-light radii of bulge types in more detail in Section 7.2.

In the right panels of Figure 7, we select bulges based on mid-IR color. Because the correlation between Sérsic index and morphology (described in the last section) is so strong, it is not surprising that we see similar behavior here. Bulges with active star formation (M_3.6 − M_8.0>0) show no correlation between Sérsic index and any other bulge structural property shown here. Also, selecting for bulges that are inactive (M_3.6 − M_8.0 < 0) does not uniquely select for bulges that correlate like elliptical galaxies in parameter space shown in Figure 7.

These results provide confirmation that the differences in Sérsic index correlations of pseudobulges found in Fisher & Drory (2008) are due to real differences in the distribution of stellar mass. They are not simply due to differences in internal extinction or mass-to-light ratios.

How different should we expect pseudobulges and classical bulges to be in photometric parameter space? First, pseudobulges and classical bulges do not differ dramatically in the bulge-to-total ratio, many of which are in the range B/T ∼ 0.1–0.4—and in Sa to Sc galaxies, disk size and mass do not follow a strong trend (Roberts & Haynes 1994) with Hubble type. Therefore, it follows that bulges will be similar in size and luminosity, and thus surface brightness as well. At least some overlap ought to exist between pseudobulges and classical bulges in luminosity, size, and surface brightness.

Carollo (1999) shows that pseudobulges deviate toward lower density in the photometric projections of the fundamental plane. Gadotti (2009) uses the Kormendy (1977) relation between 〈μ_e〉–r_e to define pseudobulges. They select pseudobulges as those bulges that are more than 1σ lower in surface density than the correlation for elliptical galaxies. However, they also find that many of the bulges on the Kormendy (1977) relation have low Sérsic index and also have young stellar populations. It is not clear that using only projections of the fundamental plane can uniquely identify a class of bulges.

In Figure 8, we show the Kormendy (1977) relation between 〈μ_e〉–r_e (bottom panels (a) and (d)) and the correlation between surface brightness and bulge magnitude (top panels (b) and (c)). The left panels show the correlations using morphology as the method of identifying pseudobulges and the right panels show these correlations using Sérsic index as a method of diagnosing bulge types. In each panel, we also plot a line that represents the corresponding scaling relation fit to the elliptical galaxies only.

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Those bulges with E-type morphology and those with n_b>2 are similar to low-luminosity elliptical galaxies in both 〈μ_e〉–r_e and the 〈μ_e〉–M^Sersic_3.6 parameter correlation. Kormendy (1977) shows that elliptical galaxies follow a tight positive correlation between size and surface density. Also, in elliptical galaxies more luminous systems are less dense (Kormendy 1985; Lauer 1985). We observe similar behavior for classical bulges (identified both through morphology and Sérsic index) in our sample.

A few of the bulges with D-type morphology that also have high Sérsic index appear as red squares in the right two panels ((c) and (d)) in Figure 8, and blue circles in the left two panels ((a) and (b)). Two are clearly evident in the 〈mu_e〉–M_3.6 parameter space as low-luminosity outliers with respect to the correlation established by elliptical galaxies. For at least these cases the difference in morphology appears to indicate that a physical difference in structure exists, despite the high Sérsic index.

Bulges with D-type morphology and/or those bulges with n_b < 2 show little-to-no correlation in the 〈μ_e〉–r_e parameter space. Though this is evident by simple inspection, we calculate Pearson's correlation coefficient for the pseudobulges and find r² = 0.08, this is in comparison to r² = 0.87 for the correlation of ellipticals and classical bulges in the same parameters. (For this calculation, we identify any bulge with disk-like nuclear morphology and/or n_b < 2 as a pseudobulge, and all other bulges are classical bulges.)

In Figures 8(b) and 8(c), it is clear that bulges with low Sérsic index and those with D-type nuclear morphology establish a correlation that is opposite to the traditional correlation for elliptical galaxies in the 〈μ_e〉–M_3.6 plane. As pseudobulges (identified by morphology or Sérsic index) become more luminous they become more dense.

In Figure 9, we show the same two photometric projections of the fundamental plane; however, in this figure bulges are distinguished by the mid-IR color. Those bulges with M_3.6 − M_8.0>0 indicating active star formation are represented by blue circles, and those bulges with M_3.6 − M_8.0 < 0 indicating low specific star formation rate are represented by red squares. As with Sérsic index and morphology the absence of star formation in a bulge does not select for a unique type of bulge. Therefore, little can be said of a bulge's position with respect to the fundamental plane based solely on specific star formation rate.

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In Figure 10, we re-plot the 〈μ_e〉–M_3.6 parameter space of pseudobulges only. Here pseudobulges are selected as bulges with either D-type morphology or n_b < 2. The black line in each panel represents a fit to all bulges with B/T>0.01. Bulges with D-type morphology often have non-Sérsic components (e.g., nuclear rings and nuclear star clusters), and thus Sérsic fits to pseudobulges may be poorly constrained. We therefore measure bulge magnitude and mean surface brightness within the half-light radius non-parametrically, as described in Section 3.3. The left panel shows parameters derived from the Sérsic decompositions and the right panel shows parameters derived non-parametrically.

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Interestingly, the non-parametric 〈μ_e〉–M_3.6 correlation shows lower scatter than that of the parametric fits; the Pearson coefficients are r² = 0.69 for non-parametric and r² = 0.44 for the Sérsic derived quantities. The scaling relations for non-parametric quantities are

$$\begin{equation} M_{3.6}=0.84\pm 0.01\times \langle \mu _e\rangle - 32.43\pm 0.08, \end{equation} \tag{ 5 }$$

and for the Sérsic derived parameters

$$\begin{equation} M_{3.6}=0.71\pm 0.01\times \langle \mu _e\rangle - 30.66\pm 0.11. \end{equation} \tag{ 6 }$$

Both relations have a positive slope that is slightly more shallow than a linear relationship. The difference between these is quite possibly a result of the non-Sérsic components (e.g., nuclear rings and nuclear star clusters) which may contain higher fractions of the light in lower-luminosity bulges. We note that the lowest magnitude bulges are not on the correlation at all. This may be because they are so low in S/N that the parameters are somewhat meaningless, or perhaps it is not accurate to treat these galaxies as having a bulge at all. We include them on the plot for completeness.

In the top panel of Figure 11, we compare the magnitude of bulges at 8 μm, dominated by dust emission, to the magnitude at 3.6 μm, which is almost completely stellar light. We calculate M_8,dust using the relation from Helou et al. (2004), where M_8,dust = −2.5 × log₁₀(L₈ − 0.232 × L_3.6). For both pseudobulges and classical bulges (diagnosed in this section by the union of nuclear morphology and Sérsic index) there is a positive correlation between the bulge luminosity of the stars at 3.6 μm and that of the dust at 8 μm. All bulges with 8 μm dust emission brighter than M_8,dust = −20.3 are indeed pseudobulges.

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It is clear from Figures 6 and 11 that in those bulges with n_b>2 and E-type nuclear morphology (classical bulges), the 8 μm dust emission is lower than the emission at 3.6 μm. The average classical bulge is 1.7 ± 1 mag fainter in 8 μm dust flux than in the 3.6 μm band. In most bulges with low Sérsic index or D-type nuclear morphology (pseudobulges), the 8 μm dust luminosity is typically as bright and often brighter than the stellar luminosity at 3.6 μm.

However, a significant minority (16%) of bulges with D-type nuclear morphology or n_b < 2 in our sample are bright at 3.6 μm but have low dust luminosity. Fisher et al. (2009) note the existence of bulges with disk-like morphology and low Sérsic index that have low specific star formation rates, using the more precise UV+24 μm star formation rate indicator; however, their sample was much smaller, and they did not have as accurate bulge structural parameters. They call these objects "inactive pseudobulges." Figure 4 shows NGC 4736 which turns out to be such a case. It is worth noting that, unlike in the three other examples which are active pseudobulges, the nuclear spiral that prompted classification of this galaxy as a pseudobulge is much weaker in the near-IR image. However, a nuclear bar (which is a disk feature) is visible, and also the Sérsic index of this bulge is below 2.

In the bottom panel of Figure 11, we show the comparison of bulge magnitude at 3.6 μm to bulge light at 8 μm without subtracting the stellar contribution. We overplot a line showing the region in the M_3.6 versus M₈ plane which contains 90% of the classical bulges (identified by having both high Sérsic index and E-type nuclear morphology). This yields the boundaries M_3.6 − M_8.0 < 0 and M^sersic_3.6 < −18. We will refer to those bulges with low Sérsic index or disk-like optical morphology, in this region of Figure 11 as inactive pseudobulges.

In Figure 12, we show the location of inactive pseudobulges on the 〈μ_e〉–M_3.6 and 〈μ_e〉–r_e planes. Inactive pseudobulges are represented by magenta circles, all other symbols are the same as in Figure 7. Inactive pseudobulges occupy a region of parameter space where both classical bulges and bright active pseudobulges are found.

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Classical bulges and inactive pseudobulges are slightly higher in surface density at a given half-light radius than elliptical galaxies. In fact, we are unable to fit a correlation that simultaneously includes giant ellipticals and inactive pseudobulges. This may be a real feature; however, it could also be an effect of how we calculate the 3.6 μm zero points for elliptical galaxies. As discussed earlier, we use the Sérsic fits from Kormendy et al. (2009) for elliptical galaxy parameters because this provides a volume-limited sample of very well-determined Sérsic fits. When the galaxy has Spitzer data we shift the magnitude by the observed V − L when the galaxy is covered with Spitzer, when the galaxy does not we use the mean V − L correction. The elliptical galaxies observed with Spitzer are preferentially brighter, and the deviation we see is in low-luminosity ellipticals. Given that the difference between classical bulges and elliptical galaxies is so small, we cannot know with our data alone if the difference in 3.6 μm luminosity between classical bulges and elliptical galaxies is a real effect.

In Figure 13, we show that inactive pseudobulges almost always have n_b < 2 (aside from NGC 4371 which has n_b = 3.9 ± 0.6). Therefore, in Sérsic index inactive pseudobulges are similar to active pseudobulges and unlike classical bulges. On average, inactive pseudobulges have slightly higher Sérsic index than active pseudobulges. The mean Sérsic index is 〈n_b〉 = 1.6 ±  0.3 for inactive pseudobulges and 〈n_b〉 = 1.3 ±  0.6 for active pseudobulges. Note that to calculate the average of the inactive pseudobulges we remove the value for NGC 4371, including the value changes the average to 〈n_b〉 = 1.7 ± 0.6. Also inactive pseudobulges have similar half-light radii as active pseudobulges (〈r_e〉 = 461 pc and 〈r_e〉 = 380 pc, respectively).

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In Figures 14 and 15, we show the distribution of absolute magnitude of the bulge in 3.6 μm (Figure 14, left), bulge Sérsic index (Figure 14, right), half-light radius of the bulge (Figure 15, left), and Hubble type (Figure 15, right). We have divided the sample of pseudobulges (both high-quality and non-high-quality galaxies) into three groups, of equal numbers, based on mid-IR color of the bulge. The ranges of the groups from top to bottom are as follows: M_3.6 − M_8.0 is less than 0.66 mag, from 0.67 mag to 1.40 mag, and greater than 1.40 mag.

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The least active group preferentially contains more luminous pseudobulges. However, this is somewhat by design because at the same 8 μm luminosity a bulge that is brighter in 3.6 μm will have lower mid-IR color. However, from the mid to high range of mid-IR color there appears to be little-to-no trend with bulge luminosity. There appears to be some change in the distribution of Sérsic indices for active and inactive bulges. In the least active group, there is a strong pile up of pseudobulges with n_b ∼ 1.6 and very few pseudobulges with low values of n_b. The high and intermediate activity groups have a large fraction with very low values of Sérsic index. There is only one bulge with n_b ≲ 0.8 in the lowest specific star formation bin. It appears that Sérsic index of the bulge is linked somehow to specific star formation rate, however, that link is not so simple as a one-to-one correlation.

We find little-to-no correlation between mid-IR color and bulge half-light radius. The median r_e of inactive pseudobulges is not very different than the median r_e of the most active group. In Hubble type, there is minimal evolution that is as one expects: most of the earlier-type galaxies have low specific star formation rate.

Morphological identification of pseudobulges is straightforward and simple. However, it is also subjective and is limited to those bulges with HST images. Therefore, we need to move to more objective methods of pseudobulge identification that are based on quantifiable properties. The Sérsic index has been shown here, and in Fisher & Drory (2008), to be a very good tool for identifying bulges. However, because inactive pseudobulges are so similar to classical bulges in both specific star formation rate and location in photometric projections of the fundamental plane, using Sérsic index alone with no information about stellar populations or star formation appears too simplistic.

We find three important groups of bulges in our sample. Thus, we propose the following criteria for diagnosing bulges: pseudobulges have Sérsic index n_b < 2 or nuclear morphology that is similar to a disk galaxy, as described by Kormendy & Kennicutt (2004). Furthermore, Sérsic index and nuclear morphology are tightly correlated. Also, these bulges follow very different structural parameter correlations than elliptical galaxies do. There is not such a clear distinction in mid-IR color (and hence in specific star formation rate). If the bulge is active (M_3.6 − M_8.0>0 which very roughly corresponds to SFR/M ∼ 40 Gyr⁻¹) it almost always has low Sérsic index or disk-like optical morphology. If the bulge is not active then it does not necessarily have a large Sérsic index nor E-type nuclear morphology. We refer to the bulges with low Sérsic index or disk-like nuclear morphology, but are not actively forming stars (M_3.6 − M_8.0 < 0) as inactive pseudobulges. We suggest that classical bulges are those bulges with both E-type nuclear morphology and n_b>2. These bulges coincide in parameter space with photometric projections of the fundamental plane and are inactive.

Recently, progress has been made simulating the formation of bulge–disk galaxies in hierarchical clustering scenarios through additional channels such as "clump" instabilities that form in high redshift disks and also secular evolution. The question remains what type of bulges result in these simulations. Robertson et al. (2006) show that rotationally supported disks can be formed in very gas-rich mergers which are more likely at high redshift. However, in their suite of simulations the most common result was the formation of bulge-dominated galaxies. The formation of a disk galaxy in a late merger by Governato et al. (2009) is indeed remarkable; however, the resulting bulge-to-total ratio of the simulated galaxy of 0.65 is far greater than any pseudobulge in our sample. Likewise, Brook et al. (2007) simulate a major merger which produces a kinematic profile indicative of two nested disks; however, the smaller disk is still larger than the typical pseudobulge in our sample. Indeed, the spatial resolution limit in Brook et al. (2007) is barely small enough to resolve the typical pseudobulge in our sample. Elmegreen et al. (2008) find that clump instabilities in high redshift disk galaxies, as simulated by Noguchi (1999) and more recently Ceverino et al. (2009), are most likely to form bulges that resemble classical bulges. Debattista et al. (2004) simulate bulge formation via internal disk evolution with collisionless N-body simulations. They find that simulated bulges built via secular evolution are able to maintain a low Sérsic index. However, Fisher et al. (2009) show that present-day star formation leads to a significant addition of stellar mass to pseudobulges, and therefore star formation and gas physics cannot be neglected. Eliche-Moral et al. (2006) simulate the growth of bulges in minor mergers using collisionless N-body simulations, and find that merging increases the Sérsic index of bulges from n ∼ 1.5 to roughly n ∼ 2. Though by neglecting star formation and dissipative processes it becomes difficult to interpret their results. Unfortunately, simulating galaxies with stars, gas, and star formation is a difficult and computing-time-intensive process. It is therefore rare that a simulation has a fine enough spatial resolution to resolve the bulge for accurate Sérsic decomposition. However, it is fairly well accepted that elliptical galaxies are the result of mergers (recently Kormendy et al. 2009). Thus, if bulges have different scaling relations than elliptical galaxies, we can thus stipulate that either they did not form in mergers, or something was significantly different about the mergers (e.g., gas fraction or mass ratio) to generate the different scaling relations.

Pseudobulges in our sample show little-to-no correlation between half-light radius and any other bulge parameter. In Figure 16, we re-illustrate the correlations of half-light radius with bulge magnitude (bottom), mean surface brightness (middle), and Sérsic index (top). For clarity, in this figure we plot classical bulges and elliptical galaxies (left) separate from pseudobulges and inactive pseudobulges (right). In each panel, we also show a black line representing the regression fit to the elliptical galaxies and classical bulges for the associated parameters. Over a 9 mag difference in bulge magnitude, pseudobulges remain roughly constant in size. There is no change with surface brightness nor with Sérsic index. Due to inherent parameter correlations in hot, virialized systems (like the fundamental plane) it would be essentially impossible for two pseudobulges to have roughly the same half-light radius, and be 9 mag different in luminosity.

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In Figures 8, 10, and 12, we show that pseudobulges have a positive correlation in 〈μ〉 − M_3.6. We show this with luminosity and surface brightness derived from Sérsic fits and from non-parametric measurements of bulge luminosity and density, thus it is not likely a relic of correlated errors in Sérsic fits.

How might a pseudobulge grow its mass without increasing size? Fisher et al. (2009) find that the star formation rate surface density of pseudobulges correlates with stellar bulge mass and surface density of stellar mass in such a way that more massive bulges have higher star formation rate densities. If pseudobulges begin with very low mass, but a variety of star formation rate densities, then after a period of time those bulges with higher star formation rate density will have higher stellar mass density. In this scenario the total mass of the bulge has not changed, but rather a mass element has changed state from cold gas to stars. Therefore, a star in orbit within the bulge remains unaffected by the increase in stellar mass. Thus as stellar bulge mass increases, but the size of the bulge does not. Furthermore, this means that the surface brightness and bulge luminosity of the star light should be positively correlated, which indeed is what we observe.

Both Drory & Fisher (2007) and Fisher et al. (2009) find pseudobulges that are either residing in non-star-forming galaxies or non-star forming themselves. They are identified as pseudobulges by nuclear morphology and Sérsic index. It is worth noting that this finding illustrates the necessity of combining information about the ISM or stellar populations with other pseudobulge indicators, such as Sérsic index and morphology. In Section 6.1, we show that non-star-forming pseudobulges indeed exist in our sample as well.

In Figure 12, we show that inactive pseudobulges are not inconsistent with the parameter correlations set by classical bulges and elliptical galaxies. However, it is not obvious that they would establish those correlations themselves. We have shown that inactive pseudobulges are like active pseudobulges in two ways (morphology and Sérsic index) and like classical bulges in two ways (parameter correlations and specific star formation rate), though there similarity to classical bulges in activity is by definition. Therefore, observationally speaking they are ambiguous objects.

Fisher et al. (2009) find that in all bulges there is measurable star formation in progress. However, in classical bulges that star formation is unimportant when compared to the stellar mass of the bulge. Furthermore, correlations between star formation rate density and the stellar mass of the bulge and disk only exist for pseudobulges, and the star formation is capable of doubling the pseudobulge stellar mass in relatively short times. They conclude that internal bulge growth is a nearly ubiquitous phenomenon. It is simply not important in classical-bulge galaxies. Also, in later-type galaxies many studies (e.g., Carollo et al. 2007; MacArthur et al. 2009) show that pseudobulges can have large populations of old stars within a young bulge. Therefore, there is room in the stellar population budget for a low-luminosity classical bulge. If these are both true then it would make sense that there be some cases where the pseudobulge and classical bulge are similar mass.

What we wish to estimate is what would we observe if a low Sérsic pseudobulge were to exist in the same location as a classical bulge. To study this we select two classical bulge galaxies, NGC 3521 and NGC 2841, and add a model pseudobulge to the profile. We then decompose the resulting using Equation (1). Both galaxies are chosen because the original decomposition unaffected by non-Sérsic components (e.g., bars and/or rings), and the Sérsic index is well determined. The original Sérsic indices of the real bulges are n_b = 2.6 and 3.6, respectively. We choose the model pseudobulge in all cases to have n_b = 1.5 and we fix the size according to the scaling relation between pseudobulge size and disk scale length (Courteau et al. 1996; MacArthur et al. 2003; Fisher & Drory 2008), we choose r_e = 0.2*h. We then scale the pseudobulge luminosity to 0.5×, 1×, 2×, and 3× that of the classical bulge. Note that these relative weights are for the pseudobulges (and classical bulge) 3.6 μm luminosity only. If these two different bulge components have different mass-to-light ratios stemming from having very different star formation histories, then a more sophisticated method would need to be applied. Yet for our purposes, a description of the luminosity is most important. We decompose the resulting profile as usual, using Equation (1), with a single Sérsic function for the bulge and an exponential outer disk. The resulting profile of the composite bulge galaxy is well fit by a Sérsic function bulge and exponential outer disk. In the two cases with a high classical bulge Sérsic index, and the L_pseudo/L_classical ≧ 2 we observe a small cusp in the profile that looks similar to a nucleus. No other peculiarities are visible in the constructed surface brightness profiles.

In Figure 17, we investigate the location of the composite pseudo+classical bulge models we describe above. The black lines are from fits to classical bulges and elliptical galaxies. The magenta circles represent the inactive pseudobulges from our survey, and the black circles represent the composite model systems. The composites are in exactly the same location as the inactive pseudobulges. In every case, addition of a pseudobulge component to the classical bulge galaxy results in lowering the Sérsic index. In the case in which the classical bulge has n_b = 2.6 when L_pseudo ≧ L_classical the resulting Sérsic index of the composite system is less than 2. For the case in which the classical bulge has a larger Sérsic index (n_b = 3.6) the Sérsic index of the composite bulge only falls below n_b = 2 for the most extreme case in which L_pseudo = 3 × L_classical. Given that the mean Sérsic index of inactive pseudobulges is 〈n_b〉 ∼ 1.6, if this is indeed what is occurring in inactive pseudobulges then the underlying classical bulges in inactive pseudobulges would need to have smaller Sérsic index.

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Fisher et al. (2009) find that in all bulge types there is bulge growth via internal star formation. However, in classical bulges the specific star formation is very low, unlike in pseudobulges where specific star formation rates are higher. The results of Fisher et al. (2009) and the results of this experiment suggest that almost every bulge has a component of new stars. In classical bulges the light of the new stars is unimportant. In pseudobulges the new stars dominant the light of the bulge component. The inactive pseudobulges may be systems in which the two components (old and young) have similar luminosity and the classical component has a low Sérsic index. The questions remain: is there a low-luminosity cut off below which old components no longer exists? Also, is the old component of stars in pseudobulges (both active and inactive) compatible with the properties of a typical classical bulge?