THE ORIGIN OF DUST IN EARLY-TYPE GALAXIES AND IMPLICATIONS FOR ACCRETION ONTO SUPERMASSIVE BLACK HOLES

One of the most striking characteristics of elliptical and lenticular galaxies is their apparent uniformity. Much more than their later-type cousins, early-type galaxies appear to have quite smooth and symmetric surface brightness profiles. Their morphological self-similarity is largely because most early-type galaxies, and in particular ellipticals, are expected to be the result of nearly equal mass mergers that have produced symmetric stellar distributions via dynamical relaxation. This assembly process, combined with the generally large halos that host early-type galaxies, has also substantially heated the gas in their interstellar medium (ISM) such that cooling and subsequent star formation are quite inefficient. As a result, their stellar populations tend to be mostly old and well mixed, which reinforces their similar and smooth appearance.

Against the backdrop of these similarities, and the simplicity of this general picture, the differences between nominally similar early-type galaxies are cast into sharper relief than for the more highly structured late-type disk galaxy population. One striking difference is that some, but not all, early-type galaxies clearly contain cold, interstellar dust. This was revealed in IRAS observations that detected a number of elliptical galaxies at 100 μm (Jura et al. 1987; Knapp et al. 1989; Goudfrooij & de Jong 1995; Bregman et al. 1998). A study by Knapp et al. (1992) also demonstrated that ellipticals had emission at 10–12 μm in excess of what was expected from stellar photospheres alone. This excess could be explained by circumstellar dust emission from evolved stars and proved to be a strong observational confirmation of expectations for mass loss from old stellar populations.

The presence of dust in early-type galaxies is interesting because it may provide additional information about their formation histories, the properties of dust when embedded within a substantially greater fraction of hot gas than is present in typical spirals, and the evolution of the ISM, in addition to stellar mass loss from evolved stars. Yet the presence of dust is also in apparent conflict with the expectation that the dust destruction timescale should be relatively short (τ_dust ∼ 2 × 10⁴ yr), largely due to sputtering of small grains in their hot ISM (Draine & Salpeter 1979b).

Observations with the Hubble Space Telescope (HST) revealed that dust lanes were common and probably present in the majority of early-type galaxies. These observations showed dust lanes in absorption within hundreds of parsecs to a kpc of the nucleus (van Dokkum & Franx 1995). This study also noted that the incidence of dust is higher is radio galaxies than in radio-quiet galaxies, estimated that the mass of dust ranged from 10³ to 10⁷ M_☉, and that the distribution of the dust lanes suggests external accretion. Subsequent studies of atomic (Morganti et al. 2006) and molecular gas kinematics (Young et al. 2011; Davis et al. 2011) supported external accretion because the gas kinematics are often decoupled from the stellar kinematics.

While there is good, anecdotal evidence for external accretion, the evolved stars in early-type galaxies are also a potential source for the dust (Knapp et al. 1992). Athey et al. (2002) showed that the mid-infrared emission from early-type galaxies is consistent with stellar mass loss of order 0.1–1 M_☉ yr⁻¹ for a typical L* galaxy. For a dust-to-gas ratio of _dg = 0.005 and a dust lifetime of 10⁷–10⁸ yr characteristic of the Milky Way, this would lead to a typical reservoir of 5 × 10³ to 5 × 10⁵M_☉ (or 10–100 M_☉ for τ_dust = 2 × 10⁴ yr). While this dust would initially match the spatial and kinematic distribution of the evolved stellar population, Mathews & Brighenti (2003) suggest that cooling in dust-rich gas could lead to clumping and settling into the central kiloparsec on a timescale of 10⁸–10⁹ yr. While this substantially exceeds the expected lifetime of individual dust grains, the clumpiness may sufficiently shield the dust to produce a steady-state dust mass that is consistent with the observations. However, the internal origin hypothesis does not explain the dramatic variation in dust mass between otherwise quite similar galaxies. Temi et al. (2004) showed that there is no correlation between the far-infrared luminosity of early-type galaxies and their visible-wavelength luminosities, even though visible-wavelength light should correlate reasonably well with the number of mass-losing stars. This absence of a correlation can be more readily explained by the external accretion hypothesis.

Another important aspect of these studies was the observation that the majority of the early-type galaxies with dust also have emission-line nuclei that often indicate the presence of a LINER or Seyfert galaxy (van Dokkum & Franx 1995; Ravindranath et al. 2001; Lauer et al. 2005). In order to investigate this correlation with a well-selected sample of early-type galaxies, in Simões Lopes et al. (2007) we studied archival HST images of a carefully matched sample of active and inactive early-type hosts and determined that all active early-type galaxies also have dust within hundreds of parsecs of their nuclei, while only ∼25% of inactive galaxies had evidence for dust. This study showed that ∼60% of the early-type galaxy population has interstellar dust. As we noted in Simões Lopes et al. (2007), the high incidence of dust in early-type galaxies presents a key challenge to the external origin hypothesis, namely that ∼60% of the early-type galaxy population must have accreted a gas and dust-rich dwarf within a time period comparable to the dust destruction time. For a dust destruction timescale of 10⁷–10⁸ yr, this implies a very high rate of gas-rich mergers.

A missing ingredient in the Simões Lopes et al. (2007) study is that there was no constraint on the dust mass distribution in the early-type galaxies, which would provide a useful constraint on the mass range and consequently mass ratio of the satellite galaxies required to provide the observed mass of dust. Simões Lopes et al. (2007) also employed the structure map technique of Pogge & Martini (2002) to identify dust lanes. As this is a contrast enhancement technique, it is insensitive to uniform or diffusely distributed dust. Uniformly distributed dust in the galaxies without dust lanes in the central kpc would provide strong support for the internal origin hypothesis.

Over the last few years, several studies with Spitzer and Herschel have assembled far-infrared measurements and estimated dust masses and basic dust properties for many early-type galaxies. One result of this work is that the dust in early-type galaxies is warmer than in spiral galaxies (Bendo et al. 2003; Skibba et al. 2011; Smith et al. 2012; Auld et al. 2013), which may be due to more intense radiation fields or different dust grain properties. The Herschel KINGFISH survey showed that early-type galaxies exhibit a strong correlation between the dust to stellar flux ratio and the specific star formation rate, which could be due to low levels of ongoing star formation (Skibba et al. 2011). The Herschel Reference Survey (Smith et al. 2012) and the Herschel Virgo Cluster Survey (Auld et al. 2013) detect many early-type galaxies and measure dust masses in the range of ∼10⁵–10⁷ M_☉. The Smith et al. (2012) study concluded that much of this dust was acquired from interactions due to the wide range in dust to stellar mass ratio. A similar conclusion was reached by Rowlands et al. (2012), who detected 5.5% of luminous early-type galaxies in the Herschel-ATLAS/GAMA study. While only sensitive to quite high dust masses (their mean detected dust mass was 5.5 × 10⁷ M_☉), they conclude that these high dust masses could not be produced internally.

In this paper, we present a Spitzer archival study of the origin of the dust in early-type galaxies. Our sample is composed of galaxies in the Simões Lopes et al. (2007) early-type galaxy sample that have both IRAC and MIPS observations. We describe this sample in Section 2 and our data processing and photometry in Section 3. All of the galaxies in this sample are detected in the IRAC bands, which are dominated by stellar emission, as well as in the 24 μm MIPS band. Many are also detected in the longer-wavelength MIPS bands. The 24 μm emission from galaxies not detected at longer wavelengths appears to be dominated by circumstellar dust. We describe how we account for this emission in Section 4. To derive the dust masses and properties of the dust, we fit these galaxies with the dust models of Draine & Li (2007). These fits and the derived properties are described in Section 5. We use these data to develop a new hypothesis for the origin of the dust in early-type galaxies in Section 6 and summarize our results in Section 7.

Our sample is composed of 38 bright, nearby, early-type galaxies (types E, E/S0, and S0). They constitute all of the early-type galaxies from the HST study of Simões Lopes et al. (2007) that have observations in at least two MIPS bands. The goal of the Simões Lopes et al. (2007) study was to compare dust structure in the central hundreds of parsecs between active and inactive galaxies and that sample contained equal numbers of well-matched active and inactive galaxies from the Palomar survey of Ho et al. (1995). The Palomar survey is very well suited for this purpose because it consists of very high signal-to-noise ratio (S/N) spectroscopy of all bright galaxies in a fixed region of the sky. Furthermore, all of the nuclear spectra have been classified as either absorption-line nuclei, H ii galaxies, LINERs, transition objects, or Seyfert galaxies (Ho et al. 1997b). The Palomar survey sample is thus both unbiased with respect to nuclear activity and has homogeneous and sensitive nuclear classifications. A further advantage is that there are a large number of ancillary data products, which are described in Ho (2008).

The Simões Lopes et al. (2007) study began with all of the LINERs and Seyfert galaxies (hereafter simply active galaxies) in the Palomar sample with HST observations and, for each active galaxy, identified a control (inactive) galaxy with the same morphology, distance, luminosity, and axis ratio. They identified 26 early-type pairs with relatively strict matching criteria (morphological T type within 1 unit, absolute B magnitude within 1 mag, distance within 50%) and eight additional pairs of early-type galaxies that were not as well matched. These 34 pairs of active and inactive early-type galaxies had very similar distributions of distances, luminosities, and morphological types and are consequently very well suited to compare the differences between active and inactive early-type galaxies. As noted in the Introduction, that HST study found that all active, early-type galaxies possess some form of dust structure within several 100 pc of their nuclei, whereas only 26% (nine) of the inactive galaxies exhibited evidence for such dust. These data thus show there is a strong dichotomy between dusty and active early-type galaxies and typically dust-free and inactive early-type galaxies. Furthermore, as Ho et al. (1997b) found that 50% of all early-type galaxies are classified as LINERs or Seyferts (active), this result also indicates that about 60% of all early-type galaxies have dust.

We constructed our sample from all of the early-type galaxies in the Simões Lopes et al. (2007) study that have observations in at least two MIPS bands, and in most cases all three are available. All of the galaxies also have IRAC observations, in addition to the HST observations. This sample has approximately equal numbers of active and inactive galaxies and should be an unbiased subset of the Simões Lopes et al. (2007) sample because these galaxies were targeted for MIPS observations by a multitude of small programs. Because of this selection, and a desire not to decrease the sample size further, we did not attempt to create a pair-matched sample from this subset. We did confirm that there are no obvious trends between the active and inactive subsets as a function of distance and morphological type. Figure 1 shows the distance distribution for galaxies classified as type E, E/S0, and S0. While the true ellipticals extend out to larger distances than the two other types, the distribution of active and inactive galaxies are similar. The morphological classification, activity type, and distance for all of the galaxies are presented in Table 1, along with whether or not they were observed to have dust structures in the study of Simões Lopes et al. (2007). Figure 2 presents HST images from that study, as well as Spitzer IRAC and MIPS images, for galaxies in this sample.

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We obtained all available IRAC and MIPS data for these galaxies from the Spitzer archive. The IRAC data correspond to images in bandpasses centered at approximately 3.6 μm, 4.5 μm, 5.7 μm, and 8 μm. For most galaxies, the first three bands are dominated by stellar emission, while the fourth is dominated by emission from polycyclic aromatic hydrocarbons (PAHs). For most early-type galaxies, the fourth band is also dominated by stellar emission, rather than PAHs, as we discuss further below. The MIPS data correspond to images in bandpasses with nominal centers at 24 μm, 70 μm, and 160 μm. Emission at 24 μm is typically dominated by hot dust, which is either interstellar or circumstellar, while emission at longer wavelengths is dominated by cooler, diffuse, interstellar dust. We typically started our analysis with the basic calibrated data (BCD) for the MIPS observations and the post-BCD (PBCD) products for the IRAC observations. In the subsections below we describe any additional processing, photometric measurements, and how we determined upper limits.

3.1. IRAC Data

The PBCD data for these galaxies are sufficiently robust that no additional processing was necessary in most cases. The few exceptions were galaxies that had relatively few IRAC observations. In these cases we obtained the BCD data from the archive and processed them into mosaics with the MOPEX software package from the Spitzer Science Center.

We measured aperture photometry in all four IRAC bands with the phot task in IRAF. We typically adopted an aperture radius of 1' because this includes nearly all of the observed dust emission at longer wavelengths. In some cases we used an 05 radius due to either nearby, bright objects or the extent of the imaging data in one or more bands. In several cases bright, foreground stars were in the aperture and we masked them out by replacing those pixel values with the median of nearby pixels. The aperture size and photometry for each galaxy is listed in Table 2. These measurements include the extended source aperture correction.

Table 2. Spitzer Photometry

Name	Aperture	3.55 μm	4.49 μm	5.73 μm	7.87 μm	23.68 μm	71.42 μm	155.9 μm
NGC 0315	1'	88.0	55.0	39.6	30.8	98.8 (4.0)	320.3 (33.4)	475 (58)
NGC 0821	05	100.9	60.6	40.2	25.1	8.8 (0.7)	<25.9	<87.4
NGC 1023	1'	330.0	197.8	135.9	82.7	52.3 (2.1)	<31.5	<29.7
NGC 2300	1'	122.6	73.0	49.4	30.2	19 (0.8)	<16.9	<66.6
NGC 2768	1'	136.1	83.8	58.4	39.6	32.4 (1.3)	513.2 (51.5)	486 (61)
NGC 2787	1'	178.4	107.8	78.6	60.8	40.5 (1.6)	962.9 (96.6)	833 (103)
NGC 3226	05	59.6	36.0	29.1	26.9	28 (1.2)	270.2 (28.0)p	...
NGC 3377	1'	141.1	87.4	58.5	36.1	17.2 (0.7)	55.3 (12.3)	160 (22)
NGC 3414	05	98.8	59.9	42.1	30.5	26.2 (1.1)	272 (28.5)	...
NGC 3607	1'	0.0	123.5	0.0	105.4	89 (3.6)	1620.1 (162.3)	2314 (278)
NGC 3640	05	138.0	84.3	56.7	35.3	19.5 (0.8)	<25.6	<49.8
NGC 3945	1'	133.6	83.0	57.4	34.8	34.4 (1.4)	268.1 (27.4)	...
NGC 3998	1'	199.4	127.0	96.8	74.9	149.5 (6.0)	521.5 (52.5)	615 (74)
NGC 4026	1'	151.2	97.9	67.0	40.8	20.3 (0.8)	156 (16.2)	288 (35)
NGC 4138	1'	94.1	62.1	64.6	102.8	173.9 (7.0)	2121.2 (212.2)	3555 (427)
NGC 4278	1'	201.9	122.6	86.4	62.3	46.3 (1.9)	709.1 (71.4)	741 (90)
NGC 4291	1'	84.3	51.9	34.4	20.6	21.4 (0.9)	<32.9	<39.1
NGC 4293	1'	78.9	61.5	72.5	114.0	528.9 (21.2)	5193 (519.3)	6890 (827)
NGC 4365	1'	191.7	116.0	81.0	49.6	31.2 (1.3)	<16.0	<35.3
NGC 4371	1'	107.0	63.8	43.1	27.3	15.1 (0.6)	30.5 (6.3)	<29.7
NGC 4382	1'	206.8	131.2	94.9	58.8	54 (2.2)	<29.0	<34.4
NGC 4406	1'	206.3	122.5	83.8	51.2	40.1 (1.6)	<27.3	<31.6
NGC 4526	1'	310.6	191.7	170.0	224.2	284.8 (11.4)	7599.6 (760.0)	7049 (846)
NGC 4550	05	71.9	45.0	30.2	21.4	9.6 (0.5)	166.8 (18.3)	...
NGC 4570	1'	150.7	90.5	60.0	36.9	14.5 (0.6)	<25.0	<29.7
NGC 4578	1'	57.1	34.9	23.3	14.3	6.9 (0.4)	<29.0	<29.7
NGC 4589	05	103.9	64.4	44.8	29.9	14 (0.6)	204.8 (20.9)	326 (40)
NGC 4612	1'	62.3	38.7	25.8	16.4	9.6 (0.5)	<17.8	<33.4
NGC 4621	1'	224.6	132.1	89.8	55.5	33.2 (1.3)	<16.4	<29.7
NGC 4636	1'	167.2	99.4	68.2	42.4	24 (1.0)	112.8 (16.0)	...
NGC 4649	05	399.7	234.7	161.6	99.1	59.4 (2.4)	<18.7	<29.7
NGC 4694	1'	43.1	28.2	37.4	73.2	117.5 (4.7)	1391.9 (139.3)	2170 (262)
NGC 5077	1'	93.1	56.5	38.8	25.3	20.3 (0.8)	171.8 (19.2)	192 (26)
NGC 5273	1'	39.2	27.0	24.2	27.7	95.5 (3.8)	685 (68.8)	610 (74)
NGC 5308	1'	88.5	54.1	36.7	21.9	7.6 (0.3)	<26.3	...
NGC 5557	1'	94.6	57.3	39.2	23.7	14.8 (0.6)	<13.5	<33.4
NGC 5576	1'	119.0	74.2	51.8	31.3	16.1 (0.7)	<19.4	<32.5
NGC 7619	1'	96.9	59.5	40.7	24.6	13.3 (0.5)	<18.2	<29.7

Notes. Photometry of the galaxies in the sample. Columns: (1) galaxy name; (2) aperture radius in arcmin for the 3.6–70 μm measurements (a PSF model was used for the 160 μm photometry, as well as the 70 μm photometry of NGC 3226, which is marked with a p superscript); (3–6) flux in IRAC channels 1–4 in mJy; (7–9) flux in MIPS channels 1–3 in mJy. Uncertainties include statistical and calibration uncertainties. All upper limits are 3σ upper limits. While NGC 4636 is clearly detected at 160 μm, we were unable to obtain a good photometric measurement.

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The apertures are smaller than the full extent of the visible emission of these galaxies (e.g., D₂₅). While these smaller apertures have less noise, in some cases they may lead to underestimates of the total emission.

3.2. MIPS Data

Most of the dust in galaxies is in the ISM. This dust is likely composed of a mix of amorphous silicate and graphitic grains, as well as small PAH particles. Both stars and PAH particles contribute emission to the 8 μm IRAC band, so it is important to accurately determine the stellar contribution to the 8 μm band in order to measure the PAH component. Similarly, both hot, circumstellar dust around evolved stars and hot, interstellar dust contribute emission to the 24 μm MIPS band, so it is important to determine the circumstellar contribution to the 24 μm band in order to quantify the warm component of the diffuse ISM. In the next two subsections, we describe how we used our sample of galaxies with no evidence for interstellar dust to obtain an empirical measurement of the stellar and circumstellar emission in the 8 μm and 24 μm bands.

4.1. Stellar Contribution

IRAC 8 μm observations of most galaxies include contributions from both stellar photospheres and PAH molecules. In order to study the total flux and spatial distribution of PAHs, the conventional practice is to remove the stellar contribution by subtraction of a scaled version of the 3.6 μm flux, where this scale factor is calculated from models of stellar photospheres. Helou et al. (2004) estimated that this value is 0.232 based on stellar population models from Starburst 99 (Leitherer et al. 1999) and noted this factor is not very sensitive to star formation history or metallicity. They do note that the 3.6 μm emission may include a hot dust component, based on earlier work (Bernard et al. 1994; Hunt et al. 2002), but estimate that this is a small contribution. Draine et al. (2007) obtained a similar value of 0.260 with the assumption that the emission is described by a 5000 K blackbody.

The stellar contribution at 8 μm is a small fraction of the total emission from the late-type spiral NGC 300 studied by Helou et al. (2004). This is also true for most of the galaxies in the SINGS sample studied by Draine et al. (2007). While approximately half of the galaxies in our sample are similarly expected to have substantial dust emission at 8 μm, others may have little to no dust emission in this band. For these galaxies, an accurate estimate of the scale factor specific to early-type galaxy stellar populations is necessary to correctly identify and measure PAH emission at 8 μm.

We have empirically estimated the appropriate scale factor for early-type galaxies with the nominally dust-free galaxies in our sample. Figure 3 shows the ratios of f₈/f_3.6 and f₈/f_4.5 for the subset of the sample with the smallest values of these ratios as a function of 4.5 μm luminosity. In both cases, all of the dust-free galaxies have similar values of these ratios, which correspond to f₈/f_3.6 = 0.25 ± 0.01 and f₈/f_4.5 = 0.42 ± 0.01. The uncertainty quoted for both ratios represents the rms variation of the dust-free galaxies. The average photometric uncertainty for the ratio measurement is also shown in each panel, although because it includes (correlated) absolute calibration uncertainties it is an overestimate of the true uncertainty in the individual points. The measured value for f₈/f_3.6 is consistent at 1σ with the value of 0.260 chosen by Draine et al. (2007) and is 2σ from the value of 0.232 calculated by Helou et al. (2004).

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We have compared these values to the predicted flux ratios from stellar population models by Maraston (2005) and Conroy et al. (2009) to judge how well the models fit these flux ratios, examine the expected variation due to stellar population differences, and estimate the significance of the 24 μm detections of apparently dust-free galaxies (in Section 4.2). As early-type galaxies are primarily composed of old stellar populations, and this component is expected to dominate the stellar emission in the infrared, we only examine models with single stellar population ages, but consider metallicities from solar to supersolar. From Maraston (2005) we calculate the f₈/f_3.6 and f₈/f_4.5 ratios for metallicities of Z = 0.02, Z = 0.04, and Z = 0.07, a Kroupa initial mass function (IMF), and their red horizontal-branch prescription. From Conroy et al. (2009) we calculate these ratios for Z = 0.019 and Z = 0.035, a Kroupa IMF, the Padova isochrones, and the Basel library.

The flux ratios for these models as a function of population age are shown in Figure 4. The f₈/f_3.6 and f₈/f_4.5 ratios from the models agree well with the empirical data shown in Figure 3. The Maraston (2005) models indicate a trend of larger f₈/f_3.6 ratio at larger metallicities. The Conroy et al. (2009) models appear relatively insensitive to metallicity, but do show some increase at larger ages. The f₈/f_4.5 ratios for both sets of models agree well with each other and the data, and also appear essentially independent of age and metallicity. Models with different IMF prescriptions lead to essentially identical results and are not shown.

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4.2. Circumstellar Dust

While the galaxies without evidence for dust in HST images were also undetected at 70 μm and 160 μm, all are detected at 24 μm. Figure 5 displays a similar plot to Figure 3, but for 24 μm rather than 8 μm. This figure indicates that the 24 μm emission is relatively constant for the apparently dust-free galaxies, although the scatter is larger than for the 8 μm emission. The larger scatter may be due to stellar population differences, such as age or metallicity. This was indicated by the work of Athey et al. (2002), who measured significant intrinsic scatter between the mid-infrared and B-band luminosities of nine early-type galaxies. The ratios and the rms variation we measure are f₂₄/f_4.5 = 0.253 ± 0.074 and f₂₄/f_3.6 = 0.154 ± 0.047. While some of the dusty galaxies also have consistent values of these ratios, the ratios for many are much larger and some are not shown on the figure.

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These ratios for all galaxies, including the apparently dust-free galaxies, are several times larger than expected from stellar photospheric emission alone. The right panels of Figure 4 show the empirical f₂₄/f_3.6 and f₂₄/f_4.5 ratios compared to the same Maraston (2005) and Conroy et al. (2009) models described in the previous section. In both cases the empirical values are approximately a factor of three higher than all of the models. The models are also in good agreement with each other and show little evidence for significant variation as a function of stellar population age or metallicity. We therefore conclude that the 24 μm emission is clearly in excess of stellar photospheric emission, yet it does scale with the flux of the stellar population.

The most likely origin of this excess 24 μm flux is emission from hot dust in the circumstellar envelopes of evolved stars. For a population of galaxies with relatively uniform and old stellar populations, the fraction of evolved stars with circumstellar dust should be an approximately fixed fraction of the stellar mass, which in turn is reasonably well represented by the flux at 3.6 μm and 4.5 μm. Models of infrared emission from dust shells around asymptotic giant branch (AGB) stars by Piovan et al. (2003) include substantial circumstellar emission from 10 to 40 μm from old stars. This emission includes a local maximum that approximately falls within the 24 μm band and has been identified with silicate emission in oxygen-rich AGB stars (Suh 2002). Bressan et al. (2007) studied Spitzer IRS spectroscopy of many early-type galaxies, including a number of the inactive galaxies in our sample (NGC 4365, NGC 4371, NGC 4382, NGC 4570, NGC 4621), and these data show clear evidence for dust emission beyond 8 μm that is well fit by a dusty silicate circumstellar envelope model (Bressan et al. 1998). This emission spectrum is also well fit by a scaled version of Spitzer IRS data for stars in the globular cluster 47 Tuc studied by Lebzelter et al. (2006).

For galaxies with a substantial amount of cold, interstellar dust (⩾10⁶ M_☉), such as late-type galaxies, the circumstellar dust emission at 24 μm is relatively negligible. However, most of the galaxies in our sample are substantially more dust poor for their stellar mass. It is consequently important to estimate and subtract the circumstellar contribution to the 24 μm MIPS photometry to obtain an accurate estimate, or upper limit, for the cold dust component. In the next section, we describe our dust model fits and how we incorporate the circumstellar dust emission into the interstellar dust mass estimates and upper limits.

Approximately half of these early-type galaxies are detected in the MIPS 70 μm and 160 μm bands, which indicates the presence of cold, interstellar dust. In this section, we describe how we fit our IRAC and MIPS photometry for these galaxies with the dust models of Draine & Li (2007), estimate the total dust mass, and compare the properties of the dust in early-type galaxies to dust in other morphological types. We also derive upper limits to the cold dust mass for galaxies that we do not detect at 70 μm and 160 μm. The SEDs and our best fits are shown in Figure 6.

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All of the galaxies with dust lanes in the HST structure maps are also detected at 8 μm. We use the empirical scale factor derived in Section 4.1 to measure the PAH emission in this bandpass and examine the spatial distribution of the PAHs. We also estimate the fraction of the dust in PAHs with the Draine & Li (2007) models for the galaxies with suitable data and compare them to other studies.

5.1. Fit to Draine & Li Models

Most of the dust in galaxies is in the ISM. This dust absorbs energy from starlight, which then re-emits this radiation at mid- and far-infrared wavelengths. The emission spectrum of this dust can be used to estimate the total mass in dust, as well as other properties, given a model for the typical grain size distribution and composition. These models are used to characterize the absorption and re-emission of the interstellar radiation field (ISRF) as a function of wavelength and may consequently be used to derive the dust mass from the observed luminosity.

We employ the models of Draine & Li (2007) to characterize the properties of the dust in these galaxies and derive dust masses. These models assume that dust is comprised of a mixture of carbonaceous and silicate grains, and varying amounts of PAH particles. The main observational constraints on the grain size distribution, relative mixture and opacities of carbonaceous and silicate grains, and the properties of the PAH particles are the wavelength-dependent extinction observed in the Milky Way (Mathis et al. 1983), long-wavelength observations of the Milky Way (Finkbeiner et al. 1999), and studies of the properties of PAH emission from the Milky Way and nearby galaxies (e.g., Smith et al. 2007).

The mid- to far-infrared emission from dust grains depends on the incident ISRF, and thus a characterization of the distribution of starlight intensities is also necessary to infer the properties of the dust. Integrated measurements of entire galaxies will typically include emission from dust that has been heated by a wide range of different values of the local ISRF. While some studies perform detailed radiative transfer calculations to estimate the local value of the ISRF for individual dust grains (e.g., Popescu et al. 2000; Gordon et al. 2001; Piovan et al. 2006), this approach typically relies on many assumptions and may not be necessary to obtain reasonable estimates of the dust mass and other dust properties. Draine & Li (2007) propose a simple parameterization of the ISRF where a fraction γ of the dust mass is exposed to high-intensity radiation, such as may occur near the sites of star formation, and the remainder is exposed to the average ISRF. The dust exposed to a wide range of ISRF intensities, which Draine & Li (2007) refer to as dust associated with photodissociation regions (or simply PDR dust) is exposed to a power-law distribution of intensities from U_min to U_max, where U is a dimensionless scale factor such that U = 1 for the local ISRF derived by Mathis et al. (1983), U_min is the minimum value of the ISRF, U_max is the maximum value, and the power-law index is α. The dust exposed to the average ISRF is exposed to a radiation field of intensity U_min and is referred to as diffuse dust. The diffuse dust is expected to be relatively cold and dominate the emission in the 70 μm and 160 μm bands, while if present the PDR dust may be important at shorter wavelengths, most notably the 24 μm MIPS band. Draine et al. (2007) find that the spectral energy distributions (SEDs) of galaxies in the SINGS sample are satisfactorily reproduced with U_max = 10⁶ and a power-law index of α = 2. We fix these two model parameters at those values for this study as well. The ISRF for the dust models is consequently just characterized by U_min and γ. As early-type galaxies have relatively little star formation, we do not expect large values of γ; however, γ may not be completely negligible as some early-type galaxies have modest amounts of star formation. The PDR component may also represent dust near the active nucleus in the small number of moderate-luminosity active galactic nuclei (AGNs) in this sample.

Very small dust grains and PAHs are subject to single-photon heating to high temperatures and thus emit at much shorter wavelengths than larger grains (Sellgren 1984). PAHs are also very likely to be the cause of the emission features observed at 3.3, 6.2, 7.7, 8.6, and 11.3 μm in the Milky Way and most galaxies, and in particular the 7.7 μm feature dominates the nonstellar emission in the IRAC 8 μm band. This emission has been identified with C–C stretch and C–H bending modes, primarily from ionized PAHs. The Draine & Li (2007) models include PAHs as small as 20 carbon atoms and note that PAHs with <1000 carbon atoms dominate the emission at wavelengths λ < 20 μm. They present seven different Milky Way dust models that have different size distributions of very small grains and different PAH fractions q_PAH of 0.5%–4.6%, where q_PAH = 4.6% is a reasonable match to the Milky Way. Because each of these seven dust models has a different PAH fraction, q_PAH uniquely describes the dust model. The dust emission from a given galaxy is consequently characterized by q_PAH, U_min, γ, and the total dust mass M_dust. In the next subsection, we describe how we derive these four parameters.

5.1.1. Flux Ratios

The 8 μm, 24 μm, 70 μm, and 160 μm bands may be dominated by dust emission. We use the data from these four bands to determine the four parameters of the Draine & Li (2007) model: q_PAH, U_min, γ, and M_dust. Our approach uses the graphical procedure described in Draine & Li (2007) to estimate the best-fit dust model. This procedure employs three flux ratios to determine the model that is the best fit to the spectral shape. The total luminosity is used to estimate the dust mass in the context of the best-fit model. The ratios defined in that paper are

$$\begin{equation} P_{7.9} = \frac{\left\langle \nu f_\nu ^{{\rm ns}} \right\rangle _{7.9}}{\langle \nu f_\nu \rangle _{71} + \langle \nu f_\nu \rangle _{160}} \end{equation} \tag{ 1 }$$

$$\begin{equation} P_{24} = \frac{\left\langle \nu f_\nu ^{{\rm ns}} \right\rangle _{24}}{\langle \nu f_\nu \rangle _{71} + \langle \nu f_\nu \rangle _{160}} \end{equation} \tag{ 2 }$$

$$\begin{equation} R_{71} = \frac{\langle \nu f_\nu \rangle _{71}}{\langle \nu f_\nu \rangle _{160}}. \end{equation} \tag{ 3 }$$

The superscript "ns" refers to the nonstellar contribution to that bandpass. For the 8 μm band, this is the value after subtraction of the empirical stellar contribution with the procedure described in Section 4.1. For the 24 μm band, this is the value after the subtraction of the empirical stellar and circumstellar dust contribution to the 24 μm band as described in Section 4.2. The measured values of these ratios are listed in Table 3.

Table 3. Dust Model Fits

Name	P7.9	P24	R71	qPAH	Umin	γ	log Mdust
				(%)
NGC 0315	0.13	0.48	1.47	2.50	2.0	0.2	6.7
NGC 0821	...	...	...	2.50	7.0	0.0	<4.7
NGC 1023	...	...	...	2.50	7.0	0.0	<3.9
NGC 2300	...	...	...	2.50	7.0	0.0	<4.9
NGC 2768	0.06	...	2.31	1.12	15.0	0.0	5.5
NGC 2787	0.11	...	2.52	1.77	15.0	0.0	5.2
NGC 3226	...	...	...	2.50	7.0	0.0	5.5
NGC 3377	...	...	0.75	2.50	2.0	0.0	4.7
NGC 3414	...	...	...	2.50	5.0	0.0	5.6
NGC 3607	0.18	0.07	1.53	3.19	7.0	0.0	6.3
NGC 3640	...	...	...	2.50	7.0	0.0	<4.6
NGC 3945	...	...	...	2.50	7.0	0.0	5.4
NGC 3998	0.25	0.44	1.85	3.90	7.0	0.15	5.7
NGC 4026	...	...	1.18	2.50	5.0	0.0	5.3
NGC 4138	0.19	0.13	1.30	3.19	5.0	0.02	6.3
NGC 4278	0.10	...	2.09	1.77	5.0	0.0	5.4
NGC 4291	...	...	...	2.50	7.0	0.0	<5.0
NGC 4293	0.10	0.19	1.65	1.77	7.0	0.04	6.5
NGC 4365	...	...	...	2.50	7.0	0.0	<4.2
NGC 4371	...	...	...	2.50	7.0	0.0	<4.3
NGC 4382	...	...	...	2.50	7.0	0.0	<4.7
NGC 4406	...	...	...	2.50	7.0	0.0	<4.5
NGC 4526	0.12	0.07	2.35	2.50	15.0	0.0	6.4
NGC 4550	...	...	...	2.50	7.0	0.0	4.9
NGC 4570	...	...	...	2.50	7.0	0.0	<4.2
NGC 4578	...	...	...	2.50	7.0	0.0	<4.3
NGC 4589	0.08	...	1.37	1.12	3.0	0.0	6.1
NGC 4612	...	...	...	2.50	7.0	0.0	<4.2
NGC 4621	...	...	...	2.50	7.0	0.0	<4.1
NGC 4636	...	...	...	2.50	7.0	0.0	4.7
NGC 4649	...	...	...	2.50	7.0	0.0	<4.2
NGC 4694	0.23	0.14	1.40	3.90	5.0	0.02	6.1
NGC 5077	...	...	1.95	2.50	12.0	0.0	5.7
NGC 5273	0.15	0.28	2.45	3.19	15.0	0.06	5.4
NGC 5308	...	...	...	2.50	7.0	0.0	<4.6
NGC 5557	...	...	...	2.50	7.0	0.0	<4.9
NGC 5576	...	...	...	2.50	7.0	0.0	<4.6
NGC 7619	...	...	...	2.50	7.0	0.0	<5.1

Notes. Dust model results of the galaxies in the sample. Columns: (1) galaxy name; (2) P7.9; (3) P24; (4) R71; (5) q_PAH; (6) U_min; (7) γ; (8) log of M_dust in solar masses. Galaxies with measurements of P7.9, P24, and/or R71 were fit with the Draine & Li (2007) models. The remaining galaxies were fit with a fixed set of parameters: (q_PAH, U_min, γ) = (2.50%, 7.0, 0.0). Dust mass upper limits are for this fixed model and the 3σ upper limits at 70 μm and 160 μm. More details are provided in Section 5.1.

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Not all of the galaxies with detections at 8 μm, 70 μm, and 160 μm have a value for P_7.9 in Table 3 because in three cases (NGC 3377, NGC 4026, and NGC 5077) the flux of the nonstellar component at 8 μm is consistent with the uncertainty in the empirical scale factor and our aperture measurements, even though weak PAH emission is apparent in Figure 2. For a similar reason, no P₂₄ value is quoted for seven galaxies (the previous three cases, as well as NGC 2768, NGC 2787, NGC 4278, and NGC 4589) because there is more substantial variation in the empirical scale factor that corrects for the contribution from (mostly) hot, circumstellar dust in this passband.

The ratio P_7.9 is effectively a measure of the fraction of the dust emission that is radiated by PAHs, and thus provides the strongest constraint on the dust model and the q_PAH parameter. Draine & Li (2007) note that because the 8 μm emission is almost exclusively due to single-photon heating, P_7.9 is not very sensitive to the starlight intensity. The exception is that if the PAH fraction is very small, exposure to a more intense ISRF (larger γ) will lead to enhanced PAH emission that may produce values of P_7.9 that are comparable to models with larger q_PAH and smaller values of γ. P_7.9 is less sensitive to γ for larger values of q_PAH because these galaxies exhibit substantial PAH emission even when γ = 0.

The value of γ is mostly determined by the ratio P₂₄. This ratio is sensitive to the fraction of the dust emission near 24 μm and is dominated by hot, PDR dust (γ > 0) if a hot component is present. According to Draine & Li (2007), when larger grains are heated by starlight intensities above U ∼ 20, they will contribute to the 24 μm emission. In contrast, dust that is heated by starlight intensities of U ∼ 0.1–10 is sufficiently cold that it emits most of its luminosity at longer wavelengths, such as the 70 μm and 160 μm bands.

The coldest dust component is diffusely distributed in the ISM and heated by the average ISRF of the galaxy, U_min. The ratio R₇₁ is sensitive to U_min because the intensity of the ISRF is correlated with the characteristic temperature of the cold component, and this affects the ratio of the flux in the 70 μm and 160 μm bands. For small values of γ (on order a few percent or less), the ratio R₇₁ is very sensitive to U_min because the 70 μm flux has a negligible contribution from PDR dust. For larger values of γ, the PDR dust contribution to the 70 μm emission is more important. In galaxies with substantial star formation, the values of both R₇₁ and P₂₄ are larger and R₇₁ is less sensitive to U_min.

5.1.2. Dust Model Parameters

There are eight galaxies in our sample with sufficient data to constrain all three Draine & Li (2007) model parameters. For these galaxies, we follow the graphical procedure recommended by Draine & Li (2007) and first estimate q_PAH from the values of P_7.9 and R₇₁, and then use the values of P₂₄ and R₇₁ to estimate γ and U_min. Four additional galaxies have just P_7.9 and R₇₁, which is sufficient to constrain the dust model. A histogram of q_PAH for these 11 galaxies is shown in the first panel of Figure 7. The median value of q_PAH is 2.50% for these galaxies. The second panel shows the distribution of γ for the subset of eight galaxies with sufficient coverage of the diffuse emission. The median value of γ for these eight is 0.03. Finally, there are three galaxies with just R₇₁. For these galaxies we assume q_PAH = 2.50% and γ = 0 (to provide a more conservative constraint on the dust mass than γ = 0.03) and then estimate U_min. The median value of U_min is 7.0.

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With the dust model fixed, the dust mass is

$$\begin{equation} M_{{\rm dust}} = \frac{\Psi }{\langle U \rangle } (\langle \nu f\nu \rangle _{24} + \langle \nu f \nu \rangle _{71} + \langle \nu f\nu \rangle _{160}) D^2. \end{equation} \tag{ 4 }$$

The quantity Ψ is uniquely determined by the three parameters q_PAH, γ, and U_min that describe the dust model, the quantity 〈U〉 accounts for starlight heating in both PDRs and the diffuse ISM, and D is the distance. Dust mass histograms are shown for different morphological types in Figure 8 and for active and inactive galaxies in Figure 9.

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The distributions of q_PAH, γ, and U_min are generally different from the distributions found by Draine et al. (2007) for the SINGS sample. The q_PAH values are generally lower, with the median of q_PAH = 2.5% below the median value of 3.4% found by Draine et al. (2007) for the 61 galaxies in the SINGS sample with similar IRAC and MIPS data. The 8 μm PAH feature is mostly due to ionized PAHs (Joblin et al. 1994), so the weakness of this feature may indicate a greater fraction of neutral PAHs, rather than a smaller PAH fraction. Kaneda et al. (2005) proposed this explanation based on their study of IRS spectra for four elliptical galaxies, which showed the short-wavelength PAH features were weak or absent, but the longer-wavelength features at 11.3 μm and 12.7 μm were prominent. Their sample includes NGC 4589, for which our best model fit yields q_PAH = 1.12%, yet the longer-wavelength PAH features are clearly present in the IRS spectrum. Kaneda et al. (2005) suggest the relative absence of UV radiation in ellipticals could produce physical conditions amenable to primarily neutral PAHs. Such conditions are also indicated by the SED of the bulge of M31 by Groves et al. (2012).

Other potential explanations include the preferential destruction of small particles, such as due to sputtering in hot gas or an AGN, and low gas-phase metallicities. The dominance of larger PAHs over smaller ones, which could be a consequence of sputtering (Schutte et al. 1993; Tsai & Mathews 1995; Micelotta et al. 2010), would weaken the 8 μm feature. The q_PAH value is also observed to decline in galaxies with low gas-phase oxygen abundance. Draine et al. (2007) find that the median PAH fraction is 1.0% for galaxies with gas-phase oxygen abundances below 12 + log₁₀O/H < 8.1 (it is also low for a small fraction of higher metallicity galaxies). Even though our sample is expected to possess solar to supersolar stellar abundances, the cold gas abundance may be quite low if it is the remnant of an accreted, low-mass satellite. Finally, relatively luminous AGNs have also been implicated in the destruction of PAHs (Lutz et al. 2008) and all but three of the galaxies with detections in all seven bands are AGNs, although they are low-luminosity AGNs. Smith et al. (2007) found that AGNs may modify the relative distribution of intensities of various PAH features, and in particular suppress those from 5–8 μm. However, low-luminosity AGNs do not appear to negatively affect the PAH abundance, as Draine et al. (2007) found that the median q_PAH fraction was actually slightly higher (3.8%) for AGNs than the median of their full sample, as well the median of 28 galaxies with H ii nuclei (3.1%).

Nearly all of the galaxies have γ < 0.1 and the median value is γ = 0.03. This is consistent with the near-absence of star formation in these galaxies. The small values of γ also mean that the model fits and dust masses are more reliable, as in this regime the parameter R₇₁ provides a better estimate of U_min. The median U_min value for this sample is 7.0, which is several times higher than the SINGS sample median of 1.5. The median for the subsample of SINGS galaxies with SCUBA data is in better agreement with our data. In the case of SINGS galaxies with SCUBA observations, the cold and PDR dust components are better separated, and thus U_min is better measured for those galaxies. We may be able to measure larger values of U_min without longer-wavelength submillimeter observations because our galaxies have lower values of γ. Early-type galaxies may also have more intense ISRFs than spiral galaxies due to the presence of hot, evolved stars and higher stellar densities. This is also suggested by their higher dust temperatures relative to spirals (Bendo et al. 2003; Skibba et al. 2011; Smith et al. 2012; Auld et al. 2013). Emission from hot, evolved stars contributes to and may dominate the LINER emission spectra from some galaxies (Sarzi et al. 2010). Longer-wavelength observations would help further constrain the value of U_min, while far-infrared line ratios would help to constrain the spectral shape of the ionizing photons (e.g., Malhotra et al. 2000).

An important caveat that affects the interpretation of the dust model parameters is that uncertainties, or intrinsic variations, in the empirical scale factors derived in Section 4.1 increase the uncertainties in the dust model parameters. As noted previously, the data shown in Figures 3 and 5 exhibit evidence for intrinsic variation in these quantities, and some variation is expected due to stellar population differences. This is particularly relevant for P_7.9 and P₂₄, which largely determine q_PAH and γ, and so these parameters are not as well constrained as U_min. In practice, as γ is expected to be small due to the general absence of star formation in these galaxies, the biggest potential uncertainty lies with q_PAH.

The measured dust masses for our sample are M_dust ∼ 10⁵–10^6.5 M_☉, which are two or three orders of magnitude lower than the dust masses for spiral galaxies of comparable size, but similar to other early-type galaxies (Goudfrooij & de Jong 1995; Draine et al. 2007; Smith et al. 2012). The dust masses that result from this procedure are fairly robust, even though they are only based on measurements out to 160 μm. This is true even if the model parameters q_PAH, γ, and U_min are not well constrained by the data because q_PAH has a negligible impact on the dust mass estimate and γ = 0 is a good approximation for most galaxies. For the full range of models presented in Draine & Li (2007), we also note that the value of Ψ that is set by the best-fit model only varies from ∼0.044 to 0.066 g (erg s⁻¹)⁻¹. This indicates that even if the dust model were not constrained at all by the data and one simply adopted the average of this range, there would only be a ∼20% uncertainty in the dust mass within the context of these models. An additional uncertainty is the ISRF because the absence of flux measurements at wavelengths longer than 160 μm do not constrain a potentially substantial mass of cold dust. However, the available data can constrain the ISRF quite well because these galaxies have little star formation. Another estimate of the uncertainties comes from the overlap between several galaxies in our study and previous investigations with Infrared Space Observatory (Xilouris et al. 2004), Spitzer (Temi et al. 2007), and longer-wavelength Herschel data (Smith et al. 2012; Auld et al. 2013). The dust masses derived by those previous studies assumed a modified blackbody and mostly agree with our estimates to within a factor of two. The noteworthy exception is NGC 3945, for which Smith et al. (2012) derive over an order of magnitude larger dust mass. The difference could be ascribed to the fact that we use a smaller aperture, although our 70 μm flux is within 5% of the IRAS 60 μm value. However, due to the large uncertainty in this IRAS measurement it is still possible that we are missing extended emission from dust in this object. We may be able to put tighter constraints on the dust mass for this object with future analysis of Herschel photometry. We also note we were unable to obtain a good measurement of NGC 3945 at 160 μm. We do retain NGC 3945 in our sample. Another comparison was performed by Gordon et al. (2010), who found that dust masses estimated from ⩽160 μm data can differ by 10%–36% relative to dust mass estimates that include Herschel measurements at 250 μm and 350 μm, although this study was based only on observations of the Large Magellanic Cloud and therefore does not include uncertainties due to differences in grain size and ISRF intensity distributions. Nevertheless, this study and a recent one by Aniano et al. (2012) of two nearby spirals that also compared Spitzer and Herschel provide good evidence against substantial masses of cold dust.

A final uncertainty is that the physical dust model that works so well for the Milky Way may not be appropriate for early-type galaxies, that is, the size and composition are different because of different formation and processing histories. For example, sputtering can reduce the fraction of small grains relative to the initial grain size distribution. The generally smaller values of q_PAH in early-type galaxies relative to spirals may indicate that this is the case, although there is also allowance for this difference in the Draine & Li (2007) models. The study of four ellipticals by Kaneda et al. (2005) also provides some evidence that the shape of the radiation field is softer in ellipticals than in the Milky Way, which may not be adequately compensated by an adjustment in U_min. Provided all early-type galaxies are different in the same manner, then the relative dust masses we have derived here should nevertheless be robust. The true uncertainties in the dust masses are likely dominated by these model details and are difficult to quantify. Under the assumption that the dust model is a reasonably good match to early-type galaxies, we estimate that the uncertainties in the dust masses are on order a factor of two or three due to a combination of aperture differences, calibration uncertainties, and differences (or uncertainties) in the dust models.

5.1.3. Upper Limits

Approximately half of the galaxies in our sample are not detected at 70 μm and 160 μm. These non-detections nevertheless provide very useful constraints on the total dust mass in these galaxies because of the extraordinary sensitivity of the Spitzer MIPS instrument. To calculate upper limits on the dust masses in these galaxies, we employ a dust model with q_PAH = 2.50%, γ = 0, and U_min = 7.0. The values of q_PAH and U_min are representative of the galaxies with the best data (see Figure 7). We chose to use γ = 0, rather than the median value of γ = 0.03, because this leads to a more conservative constraint on the dust mass.

We use this dust model to calculate the largest value of the dust mass that is consistent with the 3σ upper limits at 70 μm and 160 μm. These upper limits are listed in Table 3 and shown in Figures 8 and 9. The figures clearly show that the upper limits on the dust masses are approximately an order of magnitude lower than the measured dust masses.

All of these upper limits are for galaxies that show no evidence of dust lanes within hundreds of parsecs of their nuclei based on our earlier HST study (Simões Lopes et al. 2007, and also shown in the leftmost panels of Figure 2). While the structure map technique is insensitive to uniformly distributed or very diffuse dust, the Spitzer data place very strong upper limits on the mass of such dust. The PAH images are also valuable in this respect, as we describe in the next subsection.

5.2. PAHs

5.3. Distribution of Dust Masses

The dust mass distribution shown in Figure 8 shows that most detections have 10⁵–10⁶ M_☉ of dust. There are only three detections below 10⁵ M_☉ (NGC 3377, NGC 4550, and NGC 4626), while there are many upper limits that extend an order of magnitude lower and suggest a relative absence of galaxies with <10⁵ M_☉ of dust. For example, if there were as many galaxies with dust masses in the range 10⁴–10⁵ M_☉ as in the range 10⁵–10⁶, we would expect ten galaxies in this lower range and that we would detect half of them, yet only one is detected. This apparent dichotomy is also supported by the similar dichotomy in the detection of dust lanes in HST images of these galaxies (see Table 1), as we do not expect the Spitzer and HST images to have comparable dust mass sensitivity.

One possible explanation is a difference in morphological type. Figure 8 splits the detections and upper limits by morphology into ellipticals, S0s, and E/S0s. We see no evidence that true ellipticals or true S0 galaxies are more or less likely to have interstellar dust. The sensitivity of the data sets for each morphological type are also comparable. The upper limits on the dust mass in undetected ellipticals and lenticulars both span the full range of upper limits from approximately 10⁴–10⁵ M_☉. We used the Astronomical Survival Analysis (ASURV) programs from Feigelson & Nelson (1985), as implemented in the IRAF STSDAS STATISTICS package, to compare the elliptical and lenticular subsamples. We ran five different tests through the twosampt task and these indicated that the distributions are consistent. These similar distributions are in contrast to the results of Smith et al. (2012) with the Herschel Reference Survey, who detected dust in 24% of ellipticals and 62% of S0s with SPIRE. This difference in detection rate between the two morphological types could be due to their larger sample of 62 early-type galaxies. Another potential explanation is that Cortese et al. (2012) found that the dust to stellar mass ratio is lower for ellipticals than lenticulars. If our ellipticals were more massive than our lenticulars, this would also explain their similar dust masses.

We investigated if there is a correlation between dust detections or upper limits and cluster membership. Environment may correlate with the absence of dust because the hot atmospheres of clusters may lead to an increase in the rate of dust destruction, although many cluster early-type galaxies do maintain their own atmospheres (e.g., Sun et al. 2005). With regard to environment, clusters of galaxies have substantially fewer gas-rich dwarf galaxies and sufficiently high relative velocities that mergers are more rare. We searched for differences as a function of environment, and whether or not environment could explain the dust dichotomy, with the 14 Virgo members and 27 nonmembers in our sample and detect dust in 18/27 (66.6%) nonmembers, compared to 5/14 (45.4%) Virgo members. This difference suggests a slightly larger incidence of dust in galaxies outside of Virgo, although it is not statistically significant. Smith et al. (2012) performed a similar analysis for the early-type galaxies in the Herschel Reference Survey and found a similar trend, but that it was also not statistically significant. We also investigated whether or not membership influenced the detection of dust in the inactive sample. We detect dust in 2 of the 11 inactive Virgo members, compared to three out of 11 of the inactive galaxies outside of Virgo. There is thus no evidence that membership in the Virgo Cluster is correlated with a lower incidence of dust in inactive galaxies.

We also compared the dust detection rate with stellar luminosity, which correlates well with stellar mass. More massive galaxies generally have higher ISM temperatures, which will lead to faster dust destruction rates. This naively suggests an anticorrelation between dust mass and stellar luminosity, although no such anticorrelation is present in our data. In Figure 10, we show the dust masses and upper limits as a function of L_4.5, a proxy for stellar mass. While the minimum detected dust mass is a function of stellar luminosity, this is because more luminous galaxies are more rare and thus at larger distances.

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The dichotomy between the dust mass estimates and upper limits thus suggests that there are distinct populations of dusty and non-dusty early-type galaxies, rather than a continuum of dust masses. To explore this possibility further, we resampled our data many times in order to determine if the apparent dichotomy is due to the sensitivity distribution of our data, rather than an intrinsically nonuniform distribution of dust masses. To perform these calculations, we estimated the minimum flux sensitivity of the 160 μm data for each galaxy. We then generated a uniform distribution in log M_dust, randomly assigned dust masses from this distribution to galaxies in our sample, calculated the flux at 160 μm based on a randomly selected galaxy's distance for the dust model used to estimate upper limits, and determined if this flux would correspond to a detection or upper limit based on the sensitivity of the same galaxy's data set. We generated 1000 realizations of our data set and found that the sensitivity and distance distribution of our data set does not produce the observed dichotomy between detections and upper limits for an intrinsically uniform distribution in log M_dust approximately ∼95% of the time.

While this is formally marginally significant, an important caveat to this statistical analysis is that it does not include variations due to the best-fit dust model, which may add a factor of two uncertainty to the dust mass, with the possibility that we may systematically underestimate the dust mass by tens of percent in some cases, particularly for nearby galaxies with extended emission, and potential correlations with morphology, stellar mass, and environment. We plan to re-examine this potential dichotomy with a larger sample.

5.4. Correlation with AGNs

The main motivation for this study was to use dust mass estimates for early-type galaxies to constrain the origin of their dust. Our estimates demonstrate that dusty early-type galaxies have 10⁵–10^6.5 M_☉ of dust, while the remainder have at least one order of magnitude less. Our sample is representative of the early-type galaxy population as a whole because the original selection of the sample was from the magnitude-limited Palomar Survey of Ho et al. (1995). In Simões Lopes et al. (2007), we selected an equal number of active and inactive galaxies from all of the early-type galaxies in the Palomar survey that had visible-wavelength HST images. Half of this sample were active galaxies and half were not, which is equivalent to the relative frequency of active and inactive galaxies in the early-type galaxy population. Simões Lopes et al. (2007) then found that all of the galaxies classified as active had dust lanes within the central kpc, whereas only 25% of the inactive galaxies had them. While we have more inactive galaxies than active galaxies in this sample, we still find that all active galaxies have interstellar dust and find a similarly small fraction (5/22 or 23%) of the inactive galaxies have dust. We therefore conclude that ∼60% of all early-type galaxies have dust, including all of those classified as active, and ∼40% do not.

The presence of dust in any early-type galaxy has long been a puzzle because thermal sputtering of dust grains in the hot (T > 10⁶ K) gas that comprises the bulk of their ISM should destroy dust on the timescale τ_dust ∼ 2 × 10⁴ yr (Draine & Salpeter 1979b). These galaxies clearly do have evolved stars that produce dust, as indicated by the strong evidence for hot, circumstellar dust, and this dust must be ejected into the ISM at an approximately constant rate due to the age of their stellar populations. The expected rate of mass loss, the dust-to-gas ratio of this material, and the dust destruction timescale, can be used to estimate the steady-state dust mass of these galaxies. As noted in the Introduction, for reasonable estimates of the mass-loss rate, dust-to-gas ratio, and dust destruction time in hot gas, the steady-state dust mass should be 10 − 100(τ_dust/2 × 10⁴ yr) M_☉, that is, none of the galaxies should have been detected.

The dust destruction timescale could be longer if the temperature of the hot phase is closer to 10⁵ K, or if some of the gas and dust cools rapidly and settles into a cooler phase (Mathews & Brighenti 2003), although the dust destruction timescale needs to be many orders of magnitude longer to produce dust masses of 10⁵ M_☉ and above. A further complication is that this calculation predicts the expected steady-state dust mass for all early-type galaxies. As early-type galaxies form a fairly homogeneous population, all early-type galaxies should have similar dust production rates and destruction timescales. The internal origin model is consequently inconsistent with the order-of-magnitude differences in dust mass for similar galaxies, such as is illustrated by Figure 10.

The many galaxies with upper limits on the dust mass provide an upper limit on the typical dust destruction timescale in the hot ISM through an inversion of the argument presented above. For typical early-type galaxies, the most stringent upper limits on the dust mass are approximately M_dust < 10⁴–10^4.5. For a continual dust production rate of (0.1–1) × 0.005 = (5–50) × 10⁻⁴ M_☉ yr⁻¹, the upper limit on the dust destruction timescale is

$$\begin{equation} \tau _{{\rm dust}} < 2 \times 10^7 \left(\frac{M_{{\rm dust,lim}}}{10^4}\right) \left(\frac{0.1}{\dot{M}_{{\rm gas}}}\right) \left(\frac{0.005}{\epsilon _{{\rm dg}}}\right)\ {\rm yr}, \end{equation} \tag{ 5 }$$

where M_{dust, lim} is the upper limit on the dust mass, $\dot{M}_{{\rm gas}}$ is the gas mass-loss rate of the evolved stellar population, and _dg is the dust-to-gas ratio. This upper limit is comparable to the value of τ_dust < 46 ± 25 Myr derived by Clemens et al. (2010) with a similar argument, as well as more recent work by Smith et al. (2012). Both values are consistent with, although several orders of magnitude greater than, the calculations of Draine & Salpeter (1979b), and inconsistent with an internal origin for the one to two orders of magnitude more dust present in approximately half of the sample. As noted in the Introduction, a number of previous studies have also pointed out the difficulties with a purely internal origin (Simões Lopes et al. 2007; Rowlands et al. 2012). In particular, the recent study by Smith et al. (2012) reached a similar conclusion with a similar analysis of 62 early-type galaxies observed by Herschel.

The alternative, and favored, hypothesis for the origin of the dust is the accretion of gas-rich satellites (e.g., Tran et al. 2001; Verdoes Kleijn & de Zeeuw 2005). The morphology of the dust lanes observed in HST images indicates that many of them are chaotic and clumpy and this appears inconsistent with steady accumulation from stellar mass loss (van Dokkum & Franx 1995; Simões Lopes et al. 2007). Furthermore, when smooth dust disks are present, they do not always share the major axis of the host galaxy. Kinematic observations of atomic (e.g., Bertola et al. 1984, 1992; Sarzi et al. 2006; Morganti et al. 2006) and molecular (Combes et al. 2007; Davis et al. 2011) gas in early-type galaxies also indicate that the gas kinematics are often not aligned with the kinematics of the stars, which further suggests an external origin.

The key challenges to the external origin hypothesis are that the merger rate of gas-rich satellites is low and the dust destruction timescale is short, yet dust is present in slightly more than half of all early-type galaxies. That is, the external origin model must satisfy the constraint

$$\begin{equation} f_{{\rm dust}} = \Re _{{\rm merg}} \tau _{{\rm dust}}, \end{equation} \tag{ 6 }$$

where f_dust = 0.6 is the fraction of the population with dust above some minimum mass, ℜ_merg is the merger rate of gas-rich satellites that could supply sufficient dust, and τ_dust is the dust destruction time. Dwarf galaxies with 10⁵–10⁶ M_☉ of dust (comparable in size to the Magellanic clouds) would correspond to 1: 300–1: 100 mass-ratio mergers for the galaxies in this sample. Based on the equations provided by Stewart et al. (2009), we calculate that the cumulative merger rate for mass ratios from equal-mass mergers to 1: 300 mergers is ℜ_merg = 0.07–0.2 Gyr⁻¹, which is more than two orders of magnitude higher than our upper limit of τ_dust < 0.02 Gyr and more than four orders of magnitude greater than the theoretical estimate (Draine & Salpeter 1979b). These values predict f_dust < 0.0014–0.004, or a discrepancy of 150–430.

To evaluate the significance of this discrepancy, we estimate the uncertainty in both quantities. First, the merger rate we have adopted may be an overestimate because the theoretical calculations predict the merger rates for all galaxies as a function of stellar mass, yet not all satellite galaxies may have sufficient cold gas. It is also possible that the theoretical estimates underestimate the true merger rates. Observational evidence for an underestimate was presented by Lotz et al. (2011), who found that the observed merger rates are approximately a factor of five higher than the predictions of Stewart et al. (2009) and other recent, theoretical analyses. Lotz et al. (2011) posit that the disagreement between theory and observation could be because the visibility timescale for the mergers has been overestimated, or the theoretical rate has been underestimated. While the merger visibility timescale is arguably more uncertain that the merger rates from simulations, this comparison indicates the merger rates are unlikely more than a factor of a few larger than the theoretical estimates. There is consequently insufficient uncertainty in the merger rates to resolve this discrepancy.

The other potential resolution is that the dust destruction timescale is actually substantially higher than both the theoretical estimate of Draine & Salpeter (1979b) and our empirical upper limit. While this requires an increase of about two orders of magnitude relative to the upper limit, the dust destruction timescale is much more uncertain than the merger rate. One reference value is the dust destruction timescale for the Milky Way τ_{dust, MW} = 0.4 Gyr, which is dominated by the impact of supernova shocks on the cold, neutral medium (Barlow & Silk 1977; Draine & Salpeter 1979a; Dwek & Scalo 1980; Jones et al. 1994). As the supernova rate in early-type galaxies is several times lower than in the Milky Way (e.g., Li et al. 2011), the dust destruction timescale may be several times larger in their cold ISM and plausibly on the order of a Gyr, provided the accreted dust does not mix with the hot ISM. This may be the case if a much larger dust destruction timescale, combined with the highest estimated merger rates, predicts a dusty fraction that is only a factor of a few below what is needed to reproduce the observations. This is plausibly within the uncertainties of these order-of-magnitude estimates, particularly if dust destruction is very inefficient in the cold ISM of early-type galaxies and the cold ISM does not mix efficiently with the hot phase. However, it is also plausible that the lifetime will be less because there is less cold ISM. A more precise estimate could be obtained with an analysis of the fraction of the supernova energy that impacts the cold ISM.

While it may be possible for purely external accretion to work, we instead propose that the solution is a hybrid of internal production and external accretion. When early-type galaxies accrete a gas-rich satellite, they accrete substantial amounts of both cold gas and dust. While dust will be destroyed by a combination of supernova shocks and sputtering, this destruction could be balanced by continued dust grain growth in the accreted cold ISM. While this process is not constrained by observations of early-type galaxies, many studies of the Milky Way have concluded that >90% of dust formation by mass occurs in the cold ISM (Draine & Salpeter 1979a; Dwek & Scalo 1980; McKee 1989; Draine 2009), rather than from stellar sources such as mass loss and supernova alone (Barlow et al. 2010; Matsuura et al. 2011; Dunne et al. 2011). The Milky Way has M_gas = 5 × 10⁹ M_☉ of cold gas that produces M_dust = 2.5 × 10⁷M_☉ per dust destruction timescale, which corresponds to a steady-state dust mass of _dgM_gas. While the dust destruction timescale is likely different from the Milky Way value, the steady-state dust mass is likely to be within an order of magnitude of that predicted by the product of the Milky Way dust-to-gas ratio and the observed cold gas supply.

Continued dust production in the accreted cold gas removes the main weakness of the internal origin hypothesis because the mass of neutral gas in early-type galaxies varies by orders of magnitude (e.g., Welch et al. 2010), even though their stellar populations are quite similar. The hybrid solution also removes the main weakness of the external origin hypothesis because dust destruction is at least partially balanced by growth in the cold gas. As a result, the timescale that is important to explain the demographics of dust is the cold gas depletion timescale, rather than the destruction timescale of individual grains. As the depletion timescale for the cold gas appears to be on the order of Gyr, largely due to star formation, it is sufficient to maintain substantial quantities of dust in approximately half of all early-type galaxies.

This hybrid solution leads to several testable predictions. First, the cold gas in early-type galaxies should be lower metallicity than the old stellar population, which may be accessible with gas-phase abundance measurements. Second, the dusty early-type galaxies should have cold gas to dust ratios comparable to the accreted satellite population, unless the cold gas and dust are destroyed at different rates. Finally, there should be more evidence of mergers within the last few Gyr in the dusty early-type galaxies than those that appear dust free.

Both external accretion and our hybrid solution also constrain the lifetime of the low-luminosity AGN in the dusty early-type galaxies. If the only source of the cold gas and dust that fuels the supermassive black hole is external accretion, and these accretion events only occur every few Gyr, the high incidence of AGNs implies that these galaxies remain (weakly) active for several Gyr as well, while the inactive galaxies remain inactive for comparable timescales. The mass of dust, and the two orders of magnitude more cold gas in the ISM, is more than sufficient to maintain accretion rates of ⩽0.01 M_☉ yr⁻¹ for this time, as well as fuel the modest circumnuclear star formation necessary to produce the nuclear stellar disks seen in many dust-free early-type galaxies (e.g., Simões Lopes et al. 2007).

We have analyzed the dust in a representative sample of 38 early-type galaxies and used these data to constrain the origin of their dust. This analysis is largely based on archival Spitzer IRAC and MIPS observations, although these galaxies also have HST observations that reveal the presence or absence of dust lanes in the central kpc, as well as high S/N, visible-wavelength spectroscopy that provides uniform classifications of nuclear activity.

The IRAC and MIPS observations detect emission from dust from every galaxy that exhibits dust lanes seen in absorption in HST observations. This dust emission is clearly due to both PAH particles, as detected with IRAC 8 μm observations, and cold interstellar dust, as detected by MIPS observations at 70 μm and 160 μm. Conversely, galaxies that show no evidence for dust lanes in HST observations also do not exhibit dust emission at longer wavelengths. The absence of dust emission indicates that galaxies without clumpy dust lanes within hundreds of parsecs of their centers do not have a substantial quantity of uniform, diffusely distributed dust that would have been difficult to detect with contrast enhancement techniques.

The galaxies with no evidence for interstellar dust are a valuable sample to estimate the stellar SED for old stellar populations. We use these data to estimate the ratio of the stellar emission at 8 μm to that at 3.6 μm and 4.5 μm. We then use these flux ratios to scale and subtract the stellar contribution from the 8 μm band for the galaxies with interstellar dust and obtain a good estimate of the emission from PAHs in this bandpass. These flux ratios are in reasonable agreement with spectral synthesis models of old stellar populations.

We also used the galaxies without interstellar dust to estimate the ratio of the flux in the 24 μm MIPS band to the shorter-wavelength, photospheric emission at 3.6 μm and 4.5 μm. The ratio of the 24 μm emission to these two shorter-wavelength bands is fairly constant across galaxies of a wide range of luminosity, yet the ratio exceeds that expected from photospheric emission by approximately a constant factor of four. We conclude that the discrepancy is because emission from hot dust in the circumstellar envelopes of evolved stars makes a substantial contribution to the 24 μm band. We use this ratio to remove the circumstellar dust contribution from the early-type galaxies that have dust in order to study the dust properties of the ISM.

A number of these galaxies have sufficient diffuse dust emission that we can determine one or more of the dust model parameters introduced by Draine & Li (2007). These are the PAH fraction q_PAH, the fraction of the dust heated by a strong radiation field γ, and the minimum starlight intensity U_min. The best-fit model and the far-infrared luminosity then determine the dust mass. This analysis indicates that early-type galaxies are usually well fit by the same dust models that work well for spiral galaxies. We do find evidence that early-type galaxies have slightly lower values of q_PAH, which may be due to the presence of primarily neutral PAHs and/or reflect low ISM metallicity. These galaxies also have lower values of γ and higher values of U_min than typical spirals.

The dust masses of these early-type galaxies are at least several orders of magnitude lower than the dust masses of spirals. The dust mass of a typical early-type galaxy detected in the far-infrared is 10⁵–10^6.5 M_☉; however, many galaxies are undetected in the long-wavelength MIPS bands and the upper limits on the dust masses in these galaxies range up to an order of magnitude lower, or 10⁴–10⁵. As our sample was designed to be representative of the entire early-type galaxy population, our results indicate that approximately 60% of typical early-type galaxies have ⩾10⁵ M_☉ of interstellar dust.

There is no correlation between the presence of dust and galaxy morphology. Our sample contains approximately equal numbers of ellipticals and lenticular galaxies and the same fraction of each morphological type has interstellar dust. We also see no strong evidence for a correlation between the presence of dust and environment. There is a strong correlation between the detection of dust and the presence of visible-wavelength emission lines, which are usually consistent with some form of nuclear activity. We detect dust emission from all of the galaxies with nuclear activity, while only approximately 25% of the galaxies classified as inactive have detectable dust emission. Based on the relatively weak nuclear emission in these galaxies, we conclude that the dust, and the larger reservoir of cold gas associated with it, is a necessary but not sufficient condition for accretion onto the central, supermassive black hole.

We use our dust mass measurements and the demographics of dust in early-type galaxies to demonstrate that most of the dust mass cannot originate from evolved stars. The main argument is that there are order-of-magnitude variations in the dust mass between galaxies with the same morphological type and stellar mass. We also use these data to rule out an exclusively external origin for the dust. An external origin requires that the product of the merger rate of gas-rich galaxies and the dust destruction timescale equals the fraction of dusty early-type galaxies. While many observations of dust lane morphology and gas kinematics provide strong evidence for an external origin, the observed dust masses require mergers of gas-rich galaxies that are at least an order of magnitude too rare to explain the presence of dust in the majority of early-type galaxies. The dust destruction timescale would need to be nearly an order of magnitude greater than the Milky Way value of 4 × 10⁸ yr, rather than the expectation that it is 10⁴–10⁵ yr due to sputtering in hot gas, in order for purely external accretion to be viable.

We propose instead that the external accretion of cold gas provides an environment for the continual growth of dust for much longer than the nominal destruction timescale of individual grains. If dust grains continue to grow in mass in the externally accreted cold medium, the reduction in the steady-state dust mass should scale with the much longer depletion timescale of the cold gas, rather than the typical destruction timescale for individual grains. In fact, continual dust grain growth in this cold gas seems inevitable, provided the conditions are similar to those that lead to dust grain growth in the Milky Way. The longer gas depletion timescale of several gigayears is consistent with the merger rates of gas-rich satellites, the morphology and kinematics of the cold dust and gas, and the distribution of dust masses. In this scenario, the lifetime for the low-luminosity AGNs present in most dusty, early-type galaxies is also comparable to this several gigayear timescale.

We thank Ramiro Simões Lopes for his assistance with the early stages of this project. We are grateful to Karin Sandstrom and the referee for many comments on the manuscript, as well as to Alison Crocker, Adam Leroy, and Craig Sarazin for helpful discussions. P.M. is grateful for support from the sabbatical visitor program at the North American ALMA Science Center (NAASC) at NRAO and the hospitality of both the NAASC and the University of Virginia while this work was completed. This work is based on archival data obtained with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Support for this work was provided by an award issued by JPL/Caltech.

Facilities: HST - Hubble Space Telescope satellite, Spitzer - Spitzer Space Telescope satellite