IRS Spectra of Solar-Type Stars

# Explorations Beyond the Snow Line: Spitzer/IRS Spectra of Debris Disks Around Solar-Type Stars

S. M. Lawler, C. A. Beichman, G. Bryden, D. R. Ciardi, A. M. Tanner, K. Y. L. Su, K. R. Stapelfeldt, C. M. Lisse, D. E. Harker 1) Astronomy Department, Wesleyan University, Middletown, CT 06459 2) NASA Exoplanet Science Institute, California Institute of Technology, Pasadena, CA 91125 3) present address: University of British Columbia, Department of Physics and Astronomy, 6244 Agricultural Road, Vancouver, BC V6T 1Z1 Canada 4) Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109 5) Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 6) Johns Hopkins University - Applied Physics Laboratory, SD/SRE, MP3-W155, 7707 Montpelier Road, Laurel, MD 20723 7) Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0424
###### Abstract

We have observed 152 nearby solar-type stars with the Infrared Spectrometer (IRS) on the Spitzer Space Telescope. Including stars that met our criteria but were observed in other surveys, we get an overall success rate for finding excesses in the long wavelength IRS band (30–34 m) of 11.8. The success rate for excesses in the short wavelength band (8.5–12 ) is 1 including sources from other surveys. For stars with no excess at 8.5–12 m, the IRS data set limits of around 1,000 times the level of zodiacal emission present in our solar system, while at 30–34 m set limits of around 100 times the level of our solar system. Two stars (HD 40136 and HD 10647) show weak evidence for spectral features; the excess emission in the other systems is featureless. If the emitting material consists of large (10 m) grains as implied by the lack of spectral features, we find that these grains are typically located at or beyond the snow line, 1–35 AU from the host stars, with an average distance of 14 6 AU; however smaller grains could be located at significantly greater distances from the host stars. These distances correspond to dust temperatures in the range 50–450 K. Several of the disks are well modeled by a single dust temperature, possibly indicative of a ring-like structure. However, a single dust temperature does not match the data for other disks in the sample, implying a distribution of temperatures within these disks. For most stars with excesses, we detect an excess at both IRS and MIPS wavelengths. Only three stars in this sample show a MIPS 70 excess with no IRS excess, implying that very cold dust is rare around solar-type stars.

infrared: stars — circumstellar matter — planetary systems — Kuiper Belt

## 1 Introduction

Mid-infrared spectroscopic observations of some young debris stars such as Pictoris (Telesco & Knacke, 1991), 51 Oph (Fajardo-Acosta et al., 1993), and BD+20 307 (HIP 8920; Song et al., 2005) have revealed warm dust composed, at least in part, of small (sub-micron) grains of crystalline silicates such as forsterite and enstatite. The similarity of these spectral features to those seen in comet C/1995 O1 (Hale-Bopp; e.g., Wooden et al., 2000) suggests that this circumstellar material may represent debris from either cometary or asteroidal material located within the habitable zones of the stars. Dramatically, observations with the Infrared Spectrometer on the Spitzer Space Telescope (IRS; Houck et al., 2004) revealed a bright spectrum of features due to hot (400 K) silicate grains around the nearby (12.6 pc), mature (2 Gyr) K0 V star, HD 69830 (Beichman et al., 2005b). This star, with a level of exo-zodiacal emission 1,400 times that of our own solar system, is also accompanied by a trio of Neptune-mass planets which may be trapping material in an exterior 2:1 resonance at 1 AU (Lisse et al., 2007). However, these spectral features are not present in all stars with debris disks. More than a dozen classic debris disks, around mostly mature stars (including Fomalhaut), examined by Spitzer (Jura et al., 2004; Stapelfeldt et al., 2004) show little or no spectral structure while showing clear excess at these wavelengths. Similarly, most of the other stars with excesses in other surveys with IRS show no evidence for small grains, suggesting that the grains in these systems are larger than 10 m (Beichman et al., 2006a; Chen et al., 2006). These grains may be similar to those in our own zodiacal cloud which are predominantly larger than 10-100 m with some smaller silicate grains, yielding only a weak 10 m emission feature (e.g., Reach et al., 2003).

We have used IRS on Spitzer to observe a sample of FGKM stars within 25 pc of the Sun to assess the frequency, amount, and properties of the warm dust located within the habitable zones around solar-like stars. Some stars also have data from the Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al., 2004), providing additional information about cool dust located in the Kuiper belts of these systems. This information can shed light on the formation and evolution of circumstellar material located relatively close to the host star.

This study addresses the nature of asteroidal and cometary material, which as the techniques of planet detection improve, may prove to be tracers for gas giant and rocky planets. This is highlighted by the discovery of three planets orbiting in the immediate vicinity of the HD 69830 debris disk (Lovis et al., 2006), as well as by the recent images of an exoplanet within the annulus of Fomalhaut’s debris disk (Kalas et al., 2008), and three exoplanets around HR 8799 (Marois et al., 2008), which was previously known to have an IR excess (Rhee et al., 2007). Together with planets, this circumstellar material forms complete planetary systems (Beichman et al., 2007). In this paper we discuss our sample selection ( 2); review our reduction procedure and present our spectra ( 3); discuss measured IR excesses ( 4); present our models and discuss the nature of the debris disks around 19 stars with detected IRS and/or MIPS 70 excesses ( 5); and review implications of our results for debris disks around solar-type stars ( 6).

## 2 The Sample

The primary goal of our IRS survey is to perform a uniform census of nearby FGKM stars to determine the frequency and amount of warm dust located within the habitable zones of these stars. The survey complements our more complete understanding of the frequency and amount of the cold dust located near the Kuiper Belts of solar-type stars (e.g., Bryden et al., 2006). We have chosen a sample of solar-like stars (spectral types F, G, K and early M) from the Hipparcos dataset based upon the following criteria: a) effective temperature in the range 7300 T 3800 K corresponding to F0–M0 spectral types; b) luminosity class V; c) distance within 25 pc of the Sun; d) no nearby stellar companions; e) not variable as identified by Hipparcos or other catalogs; f) predicted m) flux density of at least 30 mJy; g) not observed previously by Spitzer with IRS as of 2004 when this sample was defined. This last criterion eliminated 51 stars of which 8 have IRS excesses; these numbers have been taken into account in the statistics of detections discussed in 4.1. This sample does not include every star that meets these criteria, but stars in the sample have been chosen somewhat randomly, so this should represent an unbiased sample of stars meeting these criteria.

There are 152 stars in the sample, distributed fairly evenly in spectral type. The ends of the distribution are not as well populated, mostly as a result of the distance criterion at the bright end, and the minimum flux density criterion at the faint end. Figures 13 show the distribution of stars in spectral type, age, and metallicity, which are listed for each star in Table 1.

The most uncertain stellar parameter is, of course, age, for these mature, main sequence stars. While the values given in Table 1 (and shown in Figure 2) are derived from many heterogeneous sources, we gave priority to spectroscopic determinations from Wright et al. (2004) or Valenti & Fischer (2005). If not from these two sources, quoted values are an average of a wide variety of values taken from the literature. Thus, the age of any given star must be regarded with caution, i.e., not more accurate than a factor of two. Of the sample overall, it is safe to say that the vast majority are older than 1 Gyr, well beyond the age when infrared excesses are known to be common among A–G stars (Su et al., 2006; Siegler et al., 2007). HD 10647 highlights the problems with determining ages. Chen et al. (2006) suggest 300 Myr, and the common space motion of this star with the Tucanae-Horlogium association lends credence to a young age estimate (Zuckerman & Song, 2004). However, Valenti & Fischer (2005) suggest an age around 2–4 Gyr. We use the younger value of 300 Myr.

Of the 152 stars selected, we have MIPS data at 24 m and 70 m for 78 stars from a variety of programs (noted in Table 4). These data permit us to cross-correlate the longer wavelength detections of cooler, Kuiper Belt dust with our shorter wavelength detections of hotter dust, yielding a more complete understanding of the dust distribution and mass within exo-zodiacal clouds.

## 3 Observations and Data Reduction

We observed each star with all four wavelength modules of the IRS: Short-Low Order 2 and 3 (SL2; 5.1–7.5 , SL3; 7.1–8.4 ), Short-Low Order 1 (SL1; 7.5–14.0 ), Long-Low Order 2 (LL2; 14.0–20.5 ), and Long-Low Order 1 (LL1; 20–34 ), as part of the Spitzer GO program 20463 (D. Ciardi, P.I.). The basic observing sequence and associated data reduction have been described in Beichman et al. (2005a) and Beichman et al. (2006a). In summary, we have used the fact that the vast majority of the sample (85%) shows no excess in an initial examination of the IRS data or in longer wavelength MIPS data to derive a “superflat” to improve the relative calibration of all the spectra and thus to make small deviations from expected photospheric levels detectable with the greatest possible sensitivity.

The data reduction procedure started with the Spitzer Science Center (SSC)-calibrated spectrum, obtained either from images resulting from the subtraction of the two Nod positions and extracted using the SSC program Spice, or from the default Nod1 - Nod2 difference spectra provided by the SSC. The error bars are calculated by combining the errors provided by the SSC with 2 of the photospheric flux at each wavelength. A superflat was created for groups of 15–20 stars in nearby IRS campaigns (Table 2), grouping stars by the date their data were taken. Each superflat was derived by taking the ratio of the SSC-spectra to Kurucz models (Kurucz, 1992) appropriate for the effective temperature and metallicity of each star fitted to near-IR and visible photometry as described in Bryden et al. (2006) and Beichman et al. (2006a). Stars with obvious excesses in the IRS data or with excesses in the MIPS data (when available) were excluded from the superflat. A few objects with problems in the IRS spectra, e.g., another star near the slit or obvious pointing problems, were also rejected. To increase the sample size in making superflats, we used IRS data from this sample and two closely related surveys that were taken at around the same time: the SIM/TPF sample (Beichman et al., 2006b), and the FGK sample (Beichman et al., 2006a). Each module was normalized to the photospheric model using a single constant whose value differed from unity by less than 25% with a dispersion of 8%. The spectral data for each star in a group were then divided by the group’s superflat at each wavelength, thereby eliminating any of the residual flat-field errors missed by the standard Spitzer pipeline reduction, including the “droop” at 12 which was a significant source of error in some of our brightest stars. As shown in Figure 4, this process produces very uniform spectra, with the average fractional excesses ObservedPhotospherePhotosphere of all the stars used to make the superflats deviating from zero by less than 0.5.

The defining characteristic of the dozens of debris disks we (and others) have examined is an excess that first becomes detectable at some minimum wavelength (typically longward of 20 m, in the IRS LL1 or LL2 modules) and then deviates more and more from the photosphere, rising to longer wavelengths. To look for weak excesses we calculated a multiplicative calibration factor for each star and each IRS module using the first 10 data points in each module to “pin” the short wavelength end of each module to the photospheric model. While the origin of these residual gain errors is unknown (errors in the photospheric extrapolation, stellar variability, or residual calibration errors are all possible), the values of this calibration factor are small and uniformly distributed around unity: .

Three stars, HD 10360, HD 162004, and HD 185144, had calibration factors significantly outside this range. Examination of 2MASS images with the IRS slit superimposed showed that HD 10360 and HD 162004 had close companions that were in or close to the IRS slit when data were taken. The AOR for HD 185144 was improperly aligned with the slit, passing over the edge of the star rather than the center, causing the flux to be improperly measured in the SL1 module. There was no evidence of an excess for any of these three stars, albeit at a reduced level of precision (5–10).

The technique of calibrating each module to the star’s photosphere produced smaller residuals and showed no significant deviation from zero over the entire IRS wavelength range for the vast majority of the sample. Defining, for convenience, two “photometric bands” useful for isolating either the silicate features (8.5–12 ) or a long-wavelength excess (30–34 ), we see that the dispersion in the deviation from a smooth photosphere was reduced from 8 to 1 (8.5–12 ) and 2 (30–34 ) when examining non-excess stars. We found no deviation between the stellar photosphere and the IRS data for the majority of the sample, nor did we see any strong evidence of silicate features in any of the stars (8.5–12 ). We did, however, find clear evidence of excesses longward of 15–25 for 16 stars and hints of a feature at 20 m for HD 10647 and HD 40136.

In applying our technique we were very careful not to artificially suppress any excess by our method of pinning the short wavelength end of a module to the photospheric model. For example, for any stars showing even a small excess in LL2 (14–21 m), we adjusted the short end of LL2 to fit the photosphere, and then adjusted the LL1 spectrum (21–34 m) to fit the LL2 spectrum in their region of overlap with a single gain term. If the SL1 spectrum (7–14 m) showed any hint of excess emission (this was only the case for one star: HD 219623), we tied LL1 LL2 SL1, and anchored the short wavelength end of SL1 to the photosphere. In this way, we proceeded from longer to shorter wavelengths ensuring that no potential excess was lost.

Splicing the modules together in this way does not necessarily produce results consistent with other methods of combining the modules. HD 10647, which has the largest fractional excess of any of our sample stars, has its LL1 module spliced to the end of the LL2 module, which gives an excess of mJy in the 30–34 band. Chen et al. (2006) found an excess of mJy in the same band for this star, implying that these error bars should be inflated when comparing excesses between surveys.

We should note, however, that any excess from very hot dust, with roughly a Rayleigh-Jeans spectrum at IRS wavelengths, would be lost in this procedure. This very hot dust has been invoked to account for a spatially resolved excess at 2.2 observed by the Palomar Testbed Interferometer (PTI) and Center for High Angular Resolution Astronomy (CHARA) interferometer (Ciardi et al., 2001; Absil et al., 2006). Thus, we cannot rule out the existence of material much hotter than 1000 K around any of these stars.

Seven stars in the sample had an additional IRS measurement from either the FGK or SIM/TPF samples (Table 3). For each of these stars we co-added the measured flux at each wavelength, which reduced the noise and allowed us to remove bad pixels. Three of these stars (HD 185144, HD 190406, and HD 222237) have no excess and this was confirmed by comparing the two separate datasets. Interestingly, HD 185144, which was tagged as a bad measurement because of low SL1 values due to improper slit alignment, also had low SL1 values in its redundant measurement. Out of the remaining four stars, three (HD 115617, HD 158633, and HD 199260) have excesses that were confirmed in the separate datasets, and one star (HD 117043) has a weak excess after coadding.

### 3.1 SL2 and SL3 Analysis

We examined the shortest wavelength data (SL2 and the “bonus” order, SL3) using the same technique as described above. We adjusted the SL3 data to fit SL2 and then tied the short wavelength end of SL2 to the photospheric model. The dispersion () around fits to the photospheric models is 1% in a photometric band defined between 6 and 6.5 m and 2% in a photometric band defined between 7.5 and 8 m. There was no evidence of any excess shortward of 8 m above the 3 level.

In performing the fitting we found that there was a systematic offset between the Kurucz models and Spitzer spectra for stars later than K5. Figure 5 shows the fractional excess in the SL2/SL3 wavelength band relative to the Kurucz models pinned to the stellar emission at 5 , for four groups of spectral types: F, G, K0–K4, and K5 and later. F and G stars reproduce the Kurucz photospheres very clearly, while early K show small deviations (1%) and late K and early M stars show greater deviations (3%). As reported by Bertone et al. (2004), both of the commonly used stellar atmosphere models, Kurucz and NextGen (Hauschildt et al., 1999a, b), fail to accurately match later spectral type stars. From our analysis here and from previous investigations which used MIPS 24 m observations of nearby K and M stars (Beichman et al., 2006b; Gautier et al., 2007) and found redder colors than predicted by theory for both Kurucz and NextGen, it appears that this deviation between model and actual spectra is most severe closer to the near infrared. Examination of the longer wavelength emission for these later type stars (IRS modules SL1 and LL1/2, and MIPS data when available) revealed no evidence for longer wavelength excess emission. Thus, we attribute this disagreement, resulting in a 5–10% apparent excess, as due to problems with the photospheric models in the 2–10 m portion of the spectrum, and not as real excess due to dust emission.

### 3.2 MIPS photometry

While the focus of this paper is IRS spectra, for many of our sample stars there is corresponding MIPS photometry at both 24 and 70 . Most of this data has already been published, for consistency we have re-reduced all of it with a uniform set of analysis parameters. Our analysis is similar to that previously described in Beichman et al. (2005a), Bryden et al. (2006), and Beichman et al. (2006b). At 24 , images are created from the raw data using software developed by the MIPS instrument team (Gordon et al., 2005), with image flats chosen as a function of scan mirror position to correct for dust spots and with individual frames normalized to remove large scale gradients (Engelbracht et al., 2007). At 70 , images are also processed with the MIPS instrument team pipeline which includes corrections for time-dependent transients (Gordon et al., 2007). Aperture photometry is performed as in Beichman et al. (2005a) with aperture radii of 153 and 148, background annuli of 306-434 and 394-788, and aperture corrections of 1.15 and 1.79 at 24 and 70 respectively. For three systems that are marginally resolved at 70 (HD 10647, HD 38858, and HD 115617; see 5.2.3), the small aperture fails to capture all of the extended emission; for these three cases the MIPS fluxes listed in Table 5 are based on model fits to each disk (Bryden et al., in prep). While our procedure has changed little since Bryden et al. (2006) was published, note that improvements in the instrument calibration since then have increased the overall 70 flux conversion by 4%, from 15.8 to 16.5 mJy/arcsec/MIPS_70_unit (MIPS_70_unit is an internally defined standard based on the ratio of the measured signal to that from the stimulator flash signal; Gordon et al., 2007). Overall, we find no qualitative disagreement between our results and those from earlier publications.

## 4 Results

After flattening and normalizing the IRS spectra as described above, we estimate the fractional excess ObservedPhotospherePhotosphere. We will continue to use the two photometric bands previously defined to isolate either the silicate features (8.5–12 ) or a long-wavelength excess (30–34 ). Figures 6 and 7 show histograms of the fractional excess measured in these photometric bands. In assessing the significance of an excess we looked at the internal uncertainty in the flux density measurement of a given star and the fractional excess relative to the 2% dispersion in the entire sample (Table 4). The amplitude of the fractional excess relative to the entire population is more important in assessing the reality of an excess than the internal signal to noise ratio (S/N) in an individual spectrum. There are a number of stars that appear to have a significant excess when looking only at the internal uncertainties, but which are not so impressive when compared to the dispersion in the overall population. To assess the significance of any possible excess we define 10 and 32 as ObservedPhotosphereNoise for the two photometric bands, where Noise is a combination of the dispersion in the fractional excess of the individual spectrum and the population-averaged dispersion: 1 (8.5–12 ) and 2 (30–34 ). For a star to have an excess, we require for an IRS-only detection or if the star also has a MIPS 70 excess. Based on the data presented in Table 4 we can claim statistically significant 30–34 excesses for 16 stars (Table 5). By this same criterion, no stars in the sample have a significant 8.5–12 m excess.

Complete IRS data for all 16 stars with excesses in these wavelengths are presented in the Appendix. Figure 8 shows the IRS spectra for four representative stars without excesses, while Figure 9 shows the IRS spectra for all stars that do have significant excesses in the IRS wavelengths. The dotted lines in the right hand panels of Figures 8 and 9 show an estimate of the 2 dispersion in the deviations from the photospheric models based on the entire sample; deviations between these lines should be regarded with skepticism.

### 4.1 Statistics of Detections

We detected IRS excess emission toward 16 stars. These excesses begin longward of 25 for 10 stars, and between 15–25 for the other 6 stars. Two of the excess detections are of borderline significance and are included because of the additional information of a MIPS 70 excess (see 4.2): HD 110897 and HD 117043, both with 32 = 2.8. Out of the sample of 152 stars, these 16 stars correspond to a 30–34 excess detection rate of , which is consistent with the fraction of stars with excesses found in a previous IRS survey: (Beichman et al., 2006a). We must however, correct these statistics for the sources that were not observed as part of this sample because they were claimed as part of other, earlier Spitzer programs. Comparing our initial selection of sources meeting our astrophysical criteria with early Guaranteed Time or Legacy programs yields 51 additional stars, which we list in Table 6. With this correction, the success rate for long-wavelength IRS excesses is not , but , essentially the same as found in our earlier determination (Beichman et al., 2006a), but with much lower uncertainty.

HD 72905, from the FGK survey (Beichman et al., 2006a), presents an interesting example of the challenges in identifying a weak infrared excess, particularly around 8-14 m where the stellar photosphere is bright. Using IRAC data from the FEPS program (Carpenter et al., 2008) we use our standard technique to fit Hipparcos visible photometry, partially saturated 2MASS observations at JHK, and IRAC 3.6 and 4.8 m data to a Kurucz model for a 6,000 K G0V star with [Fe/H] = -0.08. The resultant fit has a reduced of 0.97. Pinning the SL2 data to a Kurucz photosphere using the 20 shortest wavelength SL2 points requires a 2% adjustment to the SSC pipeline data and reveals no fractional excess from 5-8 m greater than 2%. A similar conclusion applies if we fit a solar photosphere (Rieke et al., 2008) to the IRAC 3.6 and 4.8 m data. Extending the Kurucz photosphere to longer wavelengths yields a marginal excess of about 5% at IRAC 7.8 m that carries through to IRS SL1 and MIPS 24 µm. The fractional excess has a significance at the 2 level relative to the 2% uncertainties in the photospheric models. However, changing photospheric models makes the excess all but vanish. Fitting the Rieke et al. (2008) solar photosphere instead of the Kurucz model reduces the level of excess to 2% or less out to 25 m (including MIPS 24). We conclude that we cannot claim any statistically significant excess at 25 m. At longer wavelengths, the difference between photospheric models becomes less important and the existence of a weak excess starting at m becomes evident.

None of our sample stars showed excesses in the short wavelength 8.5–12 portion of the spectrum, giving a fractional incidence of 0.7% for these mature stars. Adding in stars with previous Spitzer observations, we find an overall excess detection rate of 2 stars (HD 69830 and HD 109085) out of 203 = for the 8.5–12 band. This confirms the rarity of detectable short-wavelength excesses compared with ones at longer wavelengths, as seen in Beichman et al. (2006a) and noted in earlier studies using the Infrared Astronomical Satellite (IRAS) and the Infrared Space Observatory (ISO).

The FEPS survey (Carpenter et al., 2008; Hillenbrand et al., 2008) used Spitzer to observe nearby sun-like stars with ages between 3 Myr and 3 Gyr. Using our criteria of 3 above the photosphere (or 2 with a known 70 excess), Hillenbrand et al. (2008) find excesses in the 30–34 band for 22 out of the sample of 328 stars, although not all stars in the sample have reported IRS spectra. Carpenter et al. (2008) measure excesses using colors rather than comparison with Kurucz models, and find 71 out of 314 stars () with excesses in the long wavelength IRS band, and 2 out of 314 () in the short wavelength IRS band. As these stars are on average younger than the stars in our sample, it is not surprising that there is a higher incidence of IRS-detected excesses.

Five stars in the sample were known to have planets as of May 2009: HD 4308 (Udry et al., 2006), HD 10647 (Mayor et al., 2003), HD 40307 (Mayor et al., 2009), HD 154345 (Wright et al., 2008), and HD 164922 (Butler et al., 2006). Of these five stars, only HD 10647 shows an excess at both 70 and IRS wavelengths. The other four planet-bearing systems have no detected excesses.

### 4.2 Discussion of MIPS Results

We have MIPS data from other programs for about half (78) of the sample stars, as noted in Table 4. Table 5 lists all of the stars in our sample with IRS and/or MIPS 70 excesses. Of the 16 stars with IRS excesses, 14 have excesses in both the 30–34 IRS band and the MIPS photometry at 70 ; only HD 154577 has an IRS excess with no detectable MIPS excess (HD 190470 is in a particularly noisy field close to the galactic plane, so the error bars on the 70 flux are so large that nothing can be said about whether or not there is an excess). Including the stars with previous IRS observations (Table 6) gives 22 stars with IRS excesses, 20 of which also have strong or weak MIPS 70 excesses. HD 110897 was not originally considered to have an IRS excess because of a marginal 32 value (2.8), but this can be considered a weak excess because of the additional information of a strong MIPS 70 excess. HD 117043 has a marginally significant IRS excess (32 = 2.8) and a marginally significant MIPS 70 excess (70 = 1.9), but because 32 is close to 3, this star was also included as a weak excess detection at both wavelengths.

Out of the 73 stars with both MIPS 70 and IRS data, only three stars (HD 90089, HD 132254, and HD 160032) have excess MIPS 70 emission with no significant IRS excess. Hillenbrand et al. (2008) finds a similar trend, with 80 of their stars with MIPS 70 excesses also possessing IRS 33 excesses, and no reported stars possessing an IRS excess with no corresponding MIPS 70 excess. This implies that there may be a lower limit to debris disk temperatures, with a corresponding upper limit on disk sizes. Kuiper belt analogs appear to happen preferentially in regions with temperatures around 50 K, and not at lower temperatures.

All of the stars with MIPS 70 data also have MIPS 24 measurements. Only two stars have greater than 2 24 fractional excesses: HD 10647 has a 24 excess that agrees with its large IRS excess. HD 38392 has a large apparent 24 excess with no IRS excess. However, examination of the 2MASS and MIPS 24 image for this star shows a bright companion star, HD 38393 ( 2.5 mag), about 15 away. Although the IRS slit does not cross the companion star, and therefore should not effect the spectrum, the uncertainty in the 24 photometry is inflated by the companion. Further, this star appears to be variable at the 5% level in a number of visible compilations (Hipparcos time series photometry and Nitschelm et al., 2000). An alternate explanation is the presence of an M dwarf companion. Such a companion could produce a 20 excess at 24 , and would be too faint to notice if the system’s spectral type was measured using optical observations. Follow-up imaging using adaptive optics would be needed to test this hypothesis. Reinforcing the peculiarity of the MIPS 24 datapoint, the MIPS data do not show any 70 excess for HD 38392.

### 4.3 Limits on the Fractional Disk Luminosity

A useful metric for the limits on dust surrounding these stars is , which is related to the fractional flux limit of an excess relative to the Rayleigh Jeans tail of the star’s photosphere  (Bryden et al., 2006; Beichman et al., 2006a):

 LdustL∗=FdustF∗exd−1xd(TdT∗)3 (1)

where ObservedPhotosphere. At the peak of the blackbody curve has a constant value of 3.91, corresponding to K at 10 . At this wavelength . At 30–34 the corresponding equation is , assuming K. (For comparison, the typical dust temperatures traced by the MIPS 24 and 70 data are 154 and 53 K, respectively.) In Table 4 and Figure 10 we evaluate for each star using the appropriate effective temperature (listed in Table 1), luminosity (from our stellar photosphere models), and its measured fractional excess in each band, , or, in the case of an upper limit, where is the dispersion in fractional excess averaged over the whole sample (0.010 at 8.5–12 ; 0.028 at 30–34 ). This definition of assumes that the emitting material is all at the location where the peak of the blackbody matches the wavelength of observation such that for stars with excesses the given value of is actually a minimum. More dust emission, and higher values of , would be required for material located substantially interior or exterior to this point.

The 3 limits on at 8.5–12 and 30–34 have 2 clipped average values of and respectively (Table 4). In comparison with our solar system, which has 10 (Backman & Paresce, 1993; Dermott et al., 2002), the IRS results set limits (3) on warm (360 K) dust peaking at 10 of 1,000 times the level of dust emission in our solar system. For cooler dust (115 K) peaking at 30–34 , the 3 limit corresponds to 100 times the nominal of our zodiacal cloud. For objects with excesses in the IRS bands, we determine explicitly by integrating over the data between 10–34 and using the models discussed below ( 5.2.1) to extrapolate out to and beyond the MIPS 70 datapoint.

### 4.4 Comparing IRS and MIPS Statistics

Figure 11 summarizes the rates of IR excess detection in IRS spectral surveys and compares them with MIPS photometric results. For two wavelengths in each instrument, the distribution of detection rates is shown as a function of the fractional dust flux (). Note that can be easily translated to a fractional disk luminosity using Equation 1. It is clear from this figure that the dominant dust around solar-type stars tends to be colder than is optimal for detection at IRS wavelengths and generally exhibits higher at longer wavelengths. Nevertheless, because we can detect excesses down to much smaller levels of within the IRS spectra, the overall detection rate of IR excess for IRS at 32  is similar to that for MIPS at 70 . By comparison, IRS at 10  and MIPS at 24  have relatively few detections, but are both consistent with the overall trend from the other wavelengths. While it is difficult to extrapolate these distributions down to fainter values, the curves can be fit by log-normal distributions with median values of 0.06 at 70  and 0.003 at 32 . These fractional fluxes correspond to for a solar temperature star, consistent with estimates for our Kuiper Belt’s emission (Stern, 1996).

While the individual spectra provide the best measure of the range of dust temperatures in each system ( 5.1), Figure 11 provides a sense of the generalized disk characteristics. The separation between the 32 and 70 distributions in Figure 11, for example, can be translated to a representative dust temperature of 65 K. In reality a range of temperatures are present and, as is found in 5.2.1, the dust in each system is often not well fit by a single emission temperature, but rather by a distribution. This is also apparent from the overall statistics, as evidenced by the inability of a single blackbody to fit the trends seen in Figure 11; the separation between the 24 and 70 curves is consistent with 75 K dust, while the separation between the 10 and 70 curves corresponds to dust temperatures 100 K. A similar trend is found by Hillenbrand et al. (2008), who find that 1/3 of their surveyed debris disks have evidence for multiple dust temperatures based on their colors at MIPS and IRS wavelengths.

## 5 Discussion

### 5.1 Characteristics of the Spectra

The excesses found in this survey are in most cases weak and relatively featureless beyond a simple rise to longer wavelengths. A few objects are exceptional: HD 10647 stands out for having a very strong excess, rising up to 70 and continuing out to 160 (Tanner et al., 2009); this source also appears to be extended at 70 (Bryden et al., in prep). HD 40136 and possibly HD 10647 show a bump around 20 which might be attributable to small grains. In addition to HD 10647, HD 38858 and HD 115617 also both show evidence for extended MIPS emission (Bryden et al., in prep).

### 5.2 Models for the Dust Excesses

The IRS and MIPS excesses detected toward some of the 152 stars discussed here can be used to characterize the properties and spatial location of the emitting material. Unfortunately, even the simplest characterization cannot be unique given the wide variety of grain sizes and compositions as well as possible locations for these different species. The complexity of debris disks is evident as one attempts to model the most prominent debris disks for which high-quality IRS spectra and fully resolved maps are available (e.g. Vega; Su et al., 2005). In this section we first apply a simple, single-component model that fits the majority of sources; we assume uniform, large-grained (10 ) dust is located in an annulus centered on the star. We then examine somewhat more sophisticated models for disks where additional complexity seems warranted.

#### 5.2.1 Simple Dust Models

As a first step in analyzing these data we fitted the IRS spectra and MIPS 70 photometry using a simple model of optically thin dust located within a single dust annulus centered around the star. As described in Beichman et al. (2006a) we calculated the power-law temperature profiles, , for grains in radiative equilibrium with the central star. We use dust emissivities for 10 silicate grains (Draine & Lee, 1984; Weingartner & Draine, 2001), the minimal size suggested by the lack of significant features in most of the spectra. For the 10 silicate grains we obtained the following numerical relationship: . These calculated coefficients and power-law constants closely follow analytical results (Backman & Paresce, 1993). We then calculated the dust excess by integrating over the surface brightness of a disk between and , with . The disk surface density distribution expected for grains dominated by Poynting-Robertson drag is roughly uniform with radius, i.e.,  (Burns et al., 1979; Buitrago & Mediavilla, 1985; Backman, 2004). We examined a number of other cases with that would reflect different dust dynamics, but did not find results that were substantially different from those for .

We fitted the excess emission from a single annulus to 83 data points longward of 21  (just longward of the last point used for flux normalization of the LL1 IRS module) for 10 stars, and to 160 data points longward of 14  (just longward of the last point used for the flux normalization of the LL2 IRS module) for 9 stars, depending on whether there was any hint of an excess shortward of 21 . We included the MIPS 70 data, which was available for all 19 of the stars modeled. By varying , and we were able to minimize the reduced to values between 0.6–1.2, except for HD 10647, which has a fit with a reduced of 5.7, indicating a simple 10 dust grain model does not satisfactorily fit the infrared excess observed for this star (see 5.2.2 and 5.2.3). Results of the model fitting are shown in Figure 12 and Table 7 and are discussed below.

Mass estimates are notoriously tricky to derive given uncertainties in grain sizes. Assuming a silicate grain density of 3.3 g cm, we calculate dust masses of 4 –2.4 . Extrapolating this estimate using the index power-law appropriate for a distribution of sizes from a collisional cascade (Dohnanyi, 1969) up to a maximum size of 10 km yields total mass estimates as shown in Table 7. Submillimeter observations of all these sources would further constrain the dust size and distribution and thus the total mass of the emitting material.

values were obained by integrating the excess over frequency, including a power law interpolation between 35 and 70 (if available). We used a simple blackbody curve to extrapolate beyond 70 , based on the middle of the temperature range found by the model and quoted in Table 7. For stars with a 70 excess only, we used Equation 1 at 70 .

The models match the spectra quite well (Figure 12), yielding dust temperatures between 50–450 K (Figure 13) and dust locations between 1–35 AU (Figure 14). The majority of disks are located between 10 and 30 AU from their stars with several (7/19) showing a single temperature fit perhaps indicative of a ring-like structure that may be found with higher resolution data. Since the IRS data place only a limit on the emission shortward of 34 for HD 90089, HD 132254, and HD 160032, the single grain model can be used to show that the inner edge of the disk seen at 70 must start beyond 15 AU corresponding to material cooler than 70K. The mean value of the disk sizes shown in Figure 14 is 14 6 AU.

It is important to note, however, that these disk sizes are crucially dependent on the assumed grain size and that, as discussed below, smaller grains could dramatically increase the distance at which the emitting grains are actually located (e.g., Bryden et al., in prep).

#### 5.2.2 More Complex Dust Models

While models using single population of 10 m dust grains reproduce the weak, featureless spectra of most of our stars with excesses, we tried to model some of the excesses using a more realistic mixture of grains of different sizes and material compositions. The compositional model applied to HD 69830 (Lisse et al., 2007) and HD 113766 (Lisse et al., 2008) utilizes a combination of water ice, amorphous and crystalline olivine, and amorphous and crystalline pyroxene. The mix used here contains roughly 50:50 rocky dust and water ice, similar to the abundances seen in the small icy bodies of the Kuiper Belt. But of the 152 program stars, only two (HD 10647 and HD 40136) show hints for spectral features around 20 m and neither of these stars has a statistically significant IRS excess shortward of 18 m, severely hampering the fitting due to the lack of emission features available to constrain the models. The remainder of the stars did not offer enough statistically significant data to merit more sophisticated modeling than the simple characterization described in §5.2.1.

Applying the compositional model to HD 40136, we were able to derive good, although relatively unconstrained fits to the 18–35 m IRS data, finding evidence for crystalline olivine (50:50 Fe/Mg rich), crystalline pyroxene, FeS and some water ice, with a reduced   0.8 (Figure 15). Removing silicates worsened the fit to a reduced   1.6, mostly due to a failure to fit the data around the 18–20  silicate feature. However, the signal to noise ratio is poor shortward of 20  due to the bright stellar photosphere, making these identifications preliminary.

The model for HD 10647 yields a similar mix of ices and silicates, with a reduced   0.8 (Figure 15). Removing silicates from the fit gives a significantly worse reduced   56, strongly supporting the inclusion of silicates in the model spectrum. This model is discussed further in Tanner et al. (2009).

Because of the low signal to noise ratio shortward of 18 for both of these stars, identification of minerals will have to await future observations. The Herschel Space Observatory could prove especially useful to check for the evidence of a water ice feature near 62  (Figure 15).

#### 5.2.3 Stars with Observed Extended Emission

HD 10647, HD 38858, and HD 115617 are all marginally extended in their MIPS 70 images. When dust rings are fit to this extended emission, Bryden et al. (in prep) find much larger radii (100 AU) than indicated by our models. This can be explained by either different grain emissivities, or by two populations of dust grains: larger, 10 dust grains in a closer annulus (10–30 AU), and smaller dust grains at larger radii (100 AU)

HD 10647 and HD 115617 are also detected in MIPS 160 images (Tanner et al., 2009), further supporting the hypothesis of two dust populations. At 160 , emission from the stellar photosphere is negligible, so the detected emission is attributed to cold (30 K) dust at large distances (100 AU) from the star, much farther out than our model based on the warm dust predicts.

The case of the planet-bearing star HD 10647 is particularly interesting since not only is it detected at 160 m and resolved at 70 m, its disk is also resolved in coronagraphic images from the Advanced Camera for Surveys on the Hubble Space Telescope (Stapelfeldt et al., 2007). Its very high and young age make this the most likely star in our sample to have small grains due to a recent collisional event. A compositional model (as used in  5.2.2) incorporating an additional population of very cold, small grains composed primarily of water ice fits the combined data sets very well. The data and the relevant model are discussed in depth in Tanner et al. (2009).

### 5.3 Characteristics of the Dust

Only 3 stars have convincing evidence for warm dust: HD 40136, HD 190470, and HD 219623. One star, HD 117043, has hints of warm excess but is too weak at both IRS and MIPS for further consideration. HD 40136 and HD 219623 have MIPS excesses as well, while HD 190470 has significant cirrus contamination so the MIPS limit is poor. The simple model ( 5.2.1) for HD 40136 and HD 219623 show material extending to within 1 AU (Figure 14), suggestive of disks with active reprocessing of material, given the short grain lifetimes at these small orbital radii (Wyatt, 2008).

All of the remaining stars with excesses have their emitting material located in regions analogous to the Kuiper Belt in our solar system, typically beyond 10 AU, out to a maximum value of 30 AU (Figure 14). In the two cases where the signal-to-noise ratio is (barely) adequate for mineralogical analysis, HD 10647 ( 5.2.2 and Tanner et al., 2009) and HD 40136 ( 5.2.2), the suggestion of significant amounts of water ice is intriguing and is to be expected for regions that lie well beyond the snow line, where volatiles are predicted to be abundant (Pollack et al., 1996). Figure 14 shows the location of the snow line for 1 Myr old stars (using stellar models from Siess et al., 2000), an age when stellar luminosity and the volatile content of the outer disk should be stabilizing. The majority of our sample have material located at or well beyond the snow line.

The total quantity of material responsible for the observed excesses is poorly constrained by our data, because of uncertainties in grain properties and in the extrapolation up to maximum particle size. Table 7 lists total masses extrapolating a population of bodies with 3.3 g cm and a size distribution up to 10 km. The median value for 13 stars with strong IRS and MIPS excesses is 0.34 . The average and standard deviation, 1.0  2.1 , are dominated by a few outliers with more massive disks: HD 1461, HD 38858, and HD 45184 all around 1–2 , and especially HD 10647 with an extrapolated total mass of 7.7 . These mass estimates can be compared to various estimates for the mass of our own Kuiper belt or to models of the primitive solar nebula. In the Nice model of the protosolar nebula, for example, the outer disk is predicted to contain roughly 10-150  of material in bodies with densities of 1 g cm in sizes up to 300 km (Alessandro et al., 2009). It is difficult to compare these values directly to ours, since we assumed a smaller maximum size, 10 km, vs. 300 km for Alessandro et al. (2009). However, this is offset by our different density assumptions: we assumed 3.3 g cm, while Alessandro et al. (2009) used 1 g cm. More importantly, our 18–70  data are probably missing significant emission from other populations of dust: more distant and/or larger grains would emit at longer wavelengths. On the other hand, the order of magnitude agreement between our measurements and nominal solar system values is encouraging.

It should be noted however, that the stars with strong excesses are in the minority of our sample (12%) and that the vast majority of the mature stars in our study (and other Spitzer studies) have Kuiper Belt disk masses less than 0.1 . This relatively strict upper limit must eventually be reconciled with the presence or absence of gas giant or icy giants in the outer reaches of planetary systems.

## 6 Conclusion

We have used the IRS instrument on the Spitzer Space Telescope to look for excesses around nearby, solar-type stars. We find that none of our 152 sample stars have significant excesses in the 8.5–12 portion of the spectrum, while 16 have excesses beginning at 15–25 and rising to longer wavelengths. Including stars that meet our sample criteria and were previously observed with the IRS instrument, we find that of nearby, solar-type stars have excesses at 30–34 , while only have excesses at 8.5–12 . The rarity of short wavelength excesses is consistent with models (Wyatt et al., 2007); for ages older than 1 Gyr, disks should fall below our sensitivity threshold. Bright emission such as that seen toward HD 69830 must be intrinsically rare, have a duty cycle less than 1 of the typical 2 Gyr age of these stars, or an occurrence less than once per 20 million years. This could mean the habitable zones of nearby solar-type stars have a very low incidence of massive collisions, providing opportunity for stable, catastrophe-free terrestrial planets.

This publication makes use of data products from the Two-Micron All Sky Survey (2MASS), as well as from IPAC/IRSKY/IBIS, SIMBAD, VizieR, the ROE Debris Disks Database website, and the Extrasolar Planets Encyclopaedia website. The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407. Development of MIPS was funded by NASA through the Jet Propulsion Laboratory, subcontract 960785. Some of the research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. S. M. L. would like to thank Seth Redfield and Roy Kilgard for very helpful comments and advice regarding this paper.

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