A&A 387, 285-293 (2002)
DOI: 10.1051/0004-6361:20020366

A 25 micron search for Vega-like disks around main-sequence stars with ISO[*]

R. J. Laureijs1,[*] - M. Jourdain de Muizon2,3,[*] - K. Leech1,[*] - R. Siebenmorgen4 - C. Dominik5 - H. J. Habing6 - N. Trams7 - M. F. Kessler1,[*]


1 - ISO Data Centre, ESA Astrophysics Division, Villafranca del Castillo, PO Box 50727, 28080 Madrid, Spain
2 - LAEFF-INTA, ESA VILSPA, PO Box 50727, 28080 Madrid, Spain
3 - DESPA, Observatoire de Paris, 92190 Meudon, France
4 - ESO, K. Schwarzschildstr. 2, 85748 Garching bei München, Germany
5 - Astr. Inst. Anton Pannekoek, Univ. Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands
6 - Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands
7 - Integral Science Operations, ESA ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

Received 10 August 2001 / Accepted 8 March 2002

Abstract
We present an ISO 25 $\mu $m photometric survey of a sample of 81 nearby main-sequence stars in order to determine the incidence of "warm'' dust disks. All stars were detected by ISO. We used an empirical relation to estimate the photospheric flux of the stars at 25 $\mu $m. We find 5 stars (6%) with excess above the photospheric flux which we attribute to a Vega-like disk. These stars show disk temperatures not warmer than 120 K. Our study indicates that warm disks are relatively rare. Not a single star in our sample older than 400 Myr has a warm disk. We find an upper limit of $M_{\rm disk}~=~2\times 10^{-5}~M_{\oplus}$ for the mass of the disks which we did not detect.

Key words: stars: planetary systems - stars: general - infrared: stars


  
1 Introduction

After the initial discoveries by IRAS, the search and analysis of Vega-like disks in the infrared has received a substantial boost with the availability of data from the Infrared Space Observatory (ISO, Kessler et al. 1996). ISO has improved on IRAS in several important ways. Firstly, the number of bands has been increased and the infrared wavelength coverage has been extended to 200 $\mu $m; secondly, the detection limits have been lowered; and, thirdly, imaging and spectroscopy have been made possible on arcsec scales. One major ISO finding, based on a statistical study, is that the detection of a debris dust disk depends strongly on the age of a star: the probability of detecting a Vega-like disk comes close to unity for main-sequence dwarfs of less than 400 Myr (Habing et al. 1999; Habing et al. 2001, hereafter Paper I). Disks around older main-sequence stars are much less frequent, but they still exist. The precise mechanism that prevents these older disks from dissipating is still an open question (Jourdain de Muizon et al. 2001).

The search for new Vega-like stars has been based either on the analysis of the infrared colours using the IRAS database (Fajardo-Acosta et al. 2000; Mannings & Barlow 1998, and references therein for previous IRAS surveys), or by comparing the far-infrared flux with a prediction based on a photospheric model or extrapolation from optical photometry. In most cases the surveys rely on the measurements at 60 $\mu $m, because the excess emission is high compared to the photospheric flux and the background confusion is low compared to observations at longer wavelengths.

A significant excess at shorter wavelengths is a signature of warm debris material, presumably closer to the star than the particles emitting at the longer wavelengths. Detecting such an excess generally requires a high photometric accuracy due to the relatively large contribution of the photospheric emission.

In this paper we analyse photometric data at 25 $\mu $m of a sample of 81 main-sequence stars in order to determine the fraction of the stars which have significant infrared excess at 25 $\mu $m.

In Sect. 2 we describe the sample, the different data sets and the processing of the ISOPHOT data. In order to achieve the highest possible photometric accuracy we merged the ISO and IRAS data taking into account the systematic differences in calibration between the two data sets. The merging of the data sets and the extraction of the stars with 25 $\mu $m excess are described in Sect. 3. The results are analysed in Sect. 4. In Sect. 5 we discuss the properties of the excess stars. The conclusions are stated in Sect. 6.

  
2 Observations and data processing

2.1 Presentation of the sample

For a full description and discussion of the sample we refer to Paper I; here we briefly describe the properties of the 25 $\mu $m sample. The stars were selected on the following selection criteria: (1) all stars are within 25 pc of the Sun; (2) a spectral type later than B9 but earlier than M, and only dwarfs of type IV-V or V; (3) a predicted photospheric flux at 60 $\mu $m of at least 30 mJy; (4) no (optical) binaries within the aperture; (5) no known variables.

The third selection criterion implies that the minimum photospheric flux at 25 $\mu $m is of the order of 90 mJy. During the mission, some stars were added but these have not biased the statistics (cf. Paper I, Sect. 5.4).

In Table 1 we have listed the properties of the stars of the sample observed at 25 $\mu $m. Columns 1 to 3 describe the catalogue names of the stars, including the ISO observation identifier. Columns 4 to 6 list the optical stellar parameters from the Hipparcos Catalogue (Perryman et al. 1997), the spectral types in Col. 6 come from the machine-readable version of the Hipparcos Catalogue. Column 7 gives the age of the star from Lachaume et al. (1999). Columns 8 and 9 give the predicted flux density from Eq. (1) (below) and IRAS flux density, respectively. Columns 10 and 11 list flux density plus uncertainty obtained from the ISO data. Columns 12 and 13 give the adopted flux density plus uncertainty as described in Sect. 3.1. Finally, Col. 14 lists possible flags - "E'' indicating a significant excess, and "N'' indicating that the star was not included in the 60 $\mu $m list of Paper I due to instrumental reasons and visibility constraints during the ISO mission.


   
Table 1: The stars of the sample at 25 $\mu $m.
HD HIP ISO_id V B-V Spect. age $F_{\nu}^{\rm pred}$ $F_{\nu}^{\rm IRAS}$ $F_{\nu}^{\rm ISO}$ $\Delta F_{\nu}^{\rm ISO}$ $F_{\nu}^{\rm ad}$ $\Delta F_{\nu}^{\rm ad}$ Excess
      mag mag   Gyr Jy Jy Jy Jy Jy Jy Flag
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
693 910 37500901 4.89 0.487 F5V 5.13 0.231 0.174 0.254 0.013 0.214 0.040  
1581 1599 85900104 4.23 0.576 F9V 6.46 0.511 0.496 0.491 0.011 0.494 0.008  
4628 3765 39502507 5.74 0.890 K2V 7.94 0.241   0.209 0.016 0.209 0.016  
4813 3909 38701510 5.17 0.514 F7IV-V 1.38 0.189 0.221 0.220 0.030 0.220 0.021  
7570 5862 38603613 4.97 0.571 F8V 3.16 0.256 0.246 0.232 0.029 0.239 0.020  
9826 7513 42301519 4.10 0.536 F8V 2.88 0.530 0.519 0.532 0.021 0.526 0.015  
10700 8102 39301216 3.49 0.727 G8V 7.24 1.373 1.542 1.096 0.023 1.319 0.223  
10780 8362 45701319 5.63 0.804 K0V 2.82 0.223 0.149 0.176 0.003 0.163 0.013  
12311 9236 17902322 2.86 0.290 F0V 0.81 0.972 0.999 1.108 0.048 1.053 0.055  
13445 10138 81301125 6.12 0.812 K0V 5.37 0.145 0.131 0.161 0.032 0.146 0.022  
13709 10320 40101128 5.27 -0.01 A0V 0.34 0.049 0.112 0.076 0.026 0.094 0.018 N
14412 10798 40101731 6.33 0.724 G8V 7.24 0.100 0.107 0.151 0.016 0.129 0.022  
14802 11072 40301534 5.19 0.608 G2V 5.37 0.225 0.244 0.266 0.039 0.255 0.028  
15008 11001 15700537 4.08 0.034 A3V 0.45 0.168 0.174 0.138 0.001 0.156 0.018  
17051 12653 41102840 5.40 0.561 G3IV 3.09 0.169 0.163 0.223 0.048 0.193 0.034  
17925 13402 28302143 6.05 0.862 K1V 0.08 0.171 0.189 0.202 0.023 0.196 0.016  
19373 14632 81001846 4.05 0.595 G0V 3.39 0.627 0.600 0.674 0.018 0.637 0.037  
20630 15457 79201552 4.84 0.681 G5Vvar 0.30 0.361 0.334 0.433 0.031 0.383 0.050  
20766 15330 27506149 5.53 0.641 G2V 4.79 0.176 0.202 0.077 0.018 0.139 0.063  
20807 15371 57801755 5.24 0.600 G1V 7.24 0.212 0.209 0.242 0.017 0.225 0.016  
22001 16245 69100658 4.71 0.410 F5IV-V 2.04 0.231 0.242 0.251 0.012 0.247 0.008  
22484 16852 79501561 4.29 0.575 F9V 5.25 0.482 0.486 0.536 0.036 0.511 0.025  
26965 19849 84801864 4.43 0.820 K1V 7.24 0.697 0.816 0.711 0.022 0.763 0.053  
30495 22263 83901667 5.49 0.632 G3V 0.21 0.179 0.160 0.161 0.010 0.160 0.007  
33262 23693 58900870 4.71 0.526 F7V 2.95 0.296 0.314 0.236 0.020 0.275 0.039  
34411 24813 83801473 4.69 0.630 G0V 6.76 0.373 0.343 0.269 0.016 0.306 0.037  
37394 26779 83801976 6.21 0.840 K1V 0.34 0.141 0.146 0.156 0.006 0.151 0.005  
38392   70201401 6.15 0.940 K2V 0.87 0.183 0.153 0.207 0.027 0.180 0.027  
38393 27072 70201304 3.59 0.481 F7V 1.66 0.755 0.701 0.849 0.031 0.775 0.074  
38678 27288 69202307 3.55 0.104 A2Vann 0.37 0.328 0.826 0.748 0.040 0.787 0.039 E
39060 27321 70201079 3.85 0.171 A3V 0.28 0.294 6.294 5.810 0.205 6.052 0.242 E
43834 29271 19000682 5.08 0.714 G5V 7.24 0.309 0.286 0.334 0.039 0.310 0.027  
48915 32349 72301710 -1.4 0.009 A0m...   25.28 24.264 20.222 0.625 22.243 2.021  
50281 32984 71802113 6.58 1.071 K3V 2.63 0.162   0.185 0.029 0.185 0.029  
74576 42808 15600188 6.58 0.917 K2V 0.81 0.117 0.284 0.140 0.018 0.212 0.072 N
84737 48113 14300497 5.08 0.619 G2V 5.37 0.255 0.234 0.261 0.004 0.247 0.014 N
88230 49908 14500801 6.60 1.326 K8V 7.59 0.285 0.418 0.407 0.007 0.412 0.005 E, N
90839 51459 13100204 4.82 0.541 F8V 1.18 0.276 0.279 0.392 0.094 0.335 0.067 N
95128 53721 18000207 5.03 0.624 G0V 6.31 0.270 0.222 0.236 0.023 0.229 0.016 N
97603 54872 16900610 2.56 0.128 A4V 0.68 0.868   0.894 0.021 0.894 0.021 N


   
Table 1: continued.
HD HIP ISO_id V B-V Spect. age $F_{\nu}^{\rm pred}$ $F_{\nu}^{\rm IRAS}$ $F_{\nu}^{\rm ISO}$ $\Delta F_{\nu}^{\rm ISO}$ $F_{\nu}^{\rm ad}$ $\Delta F_{\nu}^{\rm ad}$ Excess
      mag mag   Gyr Jy Jy Jy Jy Jy Jy Flag
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
101501 56997 17200316 5.31 0.723 G8Vvar 1.55 0.255   0.308 0.027 0.308 0.027 N
102365 57443 25400519 4.89 0.664 G3/G5V 7.24 0.333 0.351 0.374 0.016 0.362 0.011 N
102647 57632 18401422 2.14 0.090 A3Vvar 0.24 1.160 1.659 1.467 0.055 1.563 0.096 E
106591 59774 14301528 3.32 0.077 A3Vvar 0.48 0.378 0.386 0.422 0.016 0.404 0.018  
110833 62145 60000525 7.01 0.936 K3V 12.60 0.082   0.090 0.022 0.090 0.022  
112758 63366 40100128 7.54 0.769 K0V 5.89 0.036   0.075 0.036 0.075 0.036 N
114710 64394 21501031 4.23 0.572 G0V 3.63 0.507 0.461 0.436 0.041 0.449 0.029  
114762 64426 39000531 7.30 0.525 F9V 11.22 0.027   0.030 0.021 0.030 0.021 N
115383 64792 24101534 5.19 0.585 G0Vs 3.80 0.215 0.191 0.208 0.021 0.199 0.015 N
117176 65721 39600734 4.97 0.714 G5V 7.59 0.342 0.384 0.315 0.006 0.349 0.034 N
120136 67275 39400137 4.50 0.508 F7V 1.38 0.346 0.346 0.322 0.007 0.334 0.012 N
126660 70497 19501343 4.04 0.497 F7V 2.95 0.516 0.517 0.558 0.039 0.537 0.027  
128167 71284 26900346 4.47 0.364 F3Vwvar 1.70 0.261 0.295 0.314 0.043 0.305 0.030  
134083 73996 08901049 4.93 0.429 F5V 1.82 0.197 0.176 0.217 0.009 0.197 0.020  
139664 76829 09000155 4.64 0.413 F5IV-V 1.12 0.248 0.493 0.253 0.032 0.373 0.120  
142373 77760 28100658 4.60 0.563 F9V 8.51 0.354 0.408 0.388 0.035 0.398 0.025  
142860 78072 08901261 3.85 0.478 F6V 3.24 0.591 0.630 0.763 0.031 0.697 0.067  
149661 81300 80700364 5.77 0.827 K2V 2.09 0.206 0.224 0.173 0.014 0.198 0.026  
154088 83541 45801567 6.59 0.814 K1V 7.24 0.094   0.089 0.009 0.089 0.009  
156026 84478 09401670 6.33 1.144 K5V 0.63 0.239   0.266 0.017 0.266 0.017  
157214 84862 09101273 5.38 0.619 G0V 7.24 0.193 0.196 0.182 0.023 0.189 0.016  
157881 85295 09202576 7.54 1.359 K7V 5.25 0.130 0.112 0.185 0.022 0.148 0.036  
160691 86796 45800282 5.12 0.694 G5V 6.17 0.286 0.321 0.244 0.036 0.282 0.038  
166620 88972 36901485 6.38 0.876 K2V 7.24 0.130 0.133 0.136 0.011 0.135 0.007  
172167 91262 08900788 0.03 -0.00 A0Vvar 0.35 6.351 8.079 8.234 0.305 8.156 0.215 E
173667 92043 10600291 4.19 0.483 F6V 2.40 0.436 0.430 0.445 0.011 0.437 0.008  
185144 96100 28801094 4.67 0.786 K0V 5.50 0.522 0.553 0.554 0.017 0.553 0.012  
185395 96441 54801897 4.49 0.395 F4V 1.29 0.274 0.221 0.236 0.029 0.229 0.021  
187642 97649 13001001 0.76 0.221 A7IV-V 1.23 5.723 5.757 5.166 0.179 5.462 0.296  
191408 99461 34301404 5.32 0.868 K2V 7.24 0.339 0.450 0.474 0.027 0.462 0.019 E
192310 99825 18300407 5.73 0.878 K3V   0.237 0.289 0.311 0.025 0.300 0.018  
197692 102485 13501110 4.13 0.426 F5V 2.00 0.408 0.367 0.387 0.034 0.377 0.024  
203280 105199 08900313 2.45 0.257 A7IV-V 0.89 1.314 1.220 1.262 0.029 1.241 0.021  
203608 105858 10902816 4.21 0.494 F6V 10.47 0.439 0.459 0.459 0.017 0.459 0.012  
207129 107649 13500819 5.57 0.601 G2V 6.03 0.156 0.143 0.269 0.030 0.206 0.063  
209100 108870 18300322 4.69 1.056 K5V 1.29 0.894 0.980 1.155 0.048 1.067 0.087  
215789 112623 14401525 3.49 0.083 A3V 0.54 0.328 0.354 0.384 0.032 0.369 0.023  
216956 113368 35300828 1.17 0.145 A3V 0.22 3.259 3.419 3.414 0.057 3.417 0.041 E
217014 113357 37401640 5.45 0.666 G5V 5.13 0.200 0.175 0.179 0.031 0.177 0.022  
219134 114622 09102431 5.57 1.000 K3Vvar   0.353 0.387 0.349 0.028 0.368 0.020  
222368 116771 37800834 4.13 0.507 F7V 3.80 0.485 0.526 0.524 0.039 0.525 0.028   

  Notes:  HD106591 was observed twice, the ISO flux density is the weighted average; the second ISO_id is 33700128.

		      HD110833 is not in the list of Lachaume et al. (1999), the age is estimated by us according to Lachaume et al. (1999)

2.2 IRAS data

The IRAS data were obtained from the IRAS faint source catalog (IFSC, Moshir et al. 1989). When no IFSC data are available we have taken data from the IRAS point source catalog.

2.3 Predicted photospheric fluxes

In order to decide whether a star has any excess emission at 25 $\mu $m we have used the relation derived by Plets (1997):

 
V-[25] = -0.03 + 2.99 (B-V) - 1.06  (B-V)2 + 0.47  (B-V)3,     (1)

which is based on the analysis of photometric data obtained in the optical and with IRAS of a very large sample of stars. The relation is valid for B-V as high as 1.6 mag. However, investigation of the V-[25] versus B-Vdiagrams by Mathioudakis & Doyle (1993) showed that K dwarfs may have higher infrared fluxes than predicted by Eq. (1) in case B-V > 1.2 mag. We will take these findings into consideration when assessing stars with significant infrared excess.

Equation (1) is tied to the IRAS calibration. We adopted a flux density of 6.73 Jy for [25]=0 mag, this value is consistent with the IRAS photometric calibration (IRAS Explanatory Supplement).

For the analysis of likely excess stars we needed to estimate the photospheric flux at 12 $\mu $m. We used the relationship similar to Eq. (1) derived by Waters et al. (1987). The photospheric flux densities in the far-infrared ( $\lambda~\geq~60$ $\mu $m) were estimated by assuming that for a given star the magnitude longward of 60 $\mu $m is identical to the 60 $\mu $m magnitude as given in Paper I.

The values of V and B-V were taken from the Hipparcos Catalogue (Perryman et al. 1997). At the low flux end with $F_{\nu}(25~{\rm {\mu}m})<$ 300 mJy, an uncertainty of mV= 0.01 corresponds to about 2 mJy and B-V= 0.01 corresponds to about 5 mJy. Consequently, the statistical uncertainty in the "predicted'' flux density according to Eq. (1) is estimated to be of the order of 2-3%.

2.4 ISO data processing

The ISOPHOT data at 25 $\mu $m (Lemke et al. 1996) were collected throughout the ISO mission (Leech & Pollock 2000) with observation template AOT PHT03 in triangular chopped mode (Klaas et al. 1994). The chopper throw was 60'' and the aperture used was 52''. The on-target exposure time was 128 s and an equal amount of time was spent on the two background positions.

The data were processed using ISOPHOT interactive analysis PIA Version 8.1 (Gabriel et al. 1997). All standard signal corrections were applied. A generic chopper pattern of two plateaux of 4 "source plus background'' and 4 "background'' signals were derived. For the signal difference we have taken the average of the last two signals of each plateau. The signals were converted to flux densities under the assumption that the responsivity of the detector has the same value at the beginning of each ISO revolution, and changes with orbital phase due to ionising radiation according to an empirical function tabulated in the "Cal G'' table PPRESP (Laureijs et al. 2001).

To check the ISO results we have correlated the ISO fluxes with the predicted fluxes and found a tight correlation. However, the correlation is not along the line of unit slope but along a power law where the high fluxes ( $F_{\nu}>~1$ Jy) are systematically underestimated and the lower fluxes ( $F_{\nu}<~300$ mJy) are systematically overestimated with respect to the model predictions, see Fig. 1.


  \begin{figure} \par\resizebox{\hsize}{!}{\includegraphics{RJL1808f1.eps}} \end{figure} Figure 1: Comparison between the photometric data of ISO and IRAS. Left panel: the correlation between ISO and IRAS. For the ISOPHOT data at 25 $\mu $m we assumed a default detector responsivity and standard calibrations. Right panel: the same correlation after correction of the ISO fluxes to obtain an overall match with the predicted fluxes. The solid lines represent the lines of unit slope.
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Assuming that the majority of the stars in our sample have no significant excess emission at 25 $\mu $m we recalibrated the ISO fluxes to the predicted fluxes so that the correlation between subsamples of the two data sets scatters around the line of unit slope. The method is illustrated in Fig. 1 where the correlations are given between the ISO and IRAS fluxes before and after the correction. A detailed description of the recalibration is given elsewhere (Laureijs & Jourdain de Muizon 2000). It should be stressed that the recalibration systematically changes the fluxes in the ISO sample as a whole and does not affect the relative scatter amoung the individual observations. Also, the Plets (1997) predictions are based on the IRAS calibration, whereas the ISOPHOT calibration is based on a different photometric system. The recalibration ensures that the fluxes of the ISO observations are consistent with the IRAS calibration.

  
3 Results

  
3.1 Extraction of 25 $\mu $m excess stars

The predicted, IRAS, and recalibrated ISO fluxes are listed in Table 1. The IRAS and ISO fluxes have been colour corrected assuming a stellar photosphere, the colour correction factors are 1.40 and 1.28 for IRAS and ISO, respectively. The table includes the adopted flux $F_{\nu}^{\rm ad}$ at 25 $\mu $m, determined in the following way:

 
$\displaystyle F_{\nu}^{\rm ad} = (F_{\nu}^{\rm ISO}+F_{\nu}^{\rm IRAS})/2,$     (2)


\begin{displaymath}{\Delta}F_{\nu}^{\rm ad} = {\rm max}({\Delta}F_{\nu}^{\rm ISO}/\sqrt{2},~ (F_{\nu}^{\rm ISO}-F_{\nu}^{\rm IRAS})/2). \end{displaymath}

We make the conservative assumption that for most of the individual measurements the uncertainty in the IRAS flux is as large as that of ISO. We checked the validity of this assumption by analysing the distribution of residual fluxes $F_{\nu}-F_{\nu}^{\rm pred}$ for the IRAS and ISO measurements separately (cf. Fig. 3). We found that both distributions have similar FWHM, of about 80 mJy, which suggests similar uncertainties for the IRAS and ISO data. In case no IRAS flux is available the ISO flux and uncertainty were adopted.


  \begin{figure} \par\resizebox{\hsize}{!}{\includegraphics{RJL1808f2.eps}} \end{figure} Figure 2: V-[25] versus B-V colour for all stars in the sample. The solid line is the photospheric emission as predicted by Eq. (1). The dashed line is the relationship for K and M dwarfs with B-V > 0.8 derived by Mathioudakis & Doyle (1993).
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The visual-infrared colour-colour diagram for the stars in the sample is presented in Fig. 2. The predicted photospheric flux follows closely the distribution of points in the sample indicating that Eq. (1) is applicable. The good match also indicates that most of the 25 $\mu $m flux densities are predominantly photospheric. The sample contains 5 stars with B-V >1.0 (Table 1), these stars are all K dwarfs and have V-[25] above the prediction. On the other hand, the relation derived by Mathioudakis & Doyle (1993) for K and M dwarfs predicts values of V-[25] which are too high for the three stars with highest V-[25].

To assess the photometric quality of the sample we present a histogram of the difference $F_{\nu}^{\rm ad}-F_{\nu}^{\rm pred}$ in Fig. 3. The distribution is strongly peaked and suggests a normal distribution close to zero for the majority of stars in the sample.


  \begin{figure} \par\resizebox{\hsize}{!}{\includegraphics{RJL1808f3.eps}} \end{figure} Figure 3: Distribution of deviations from the predicted fluxes. The dashed bins give the number of stars below and above the given flux limits. The solid line is a normal distribution based on $\sigma~=$ 35 mJy, mean = 8 mJy.
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The parameters of the normal distribution have been derived as follows. Initially, an intermediate mean and standard deviation was derived of the stars in the interval $\vert F_{\nu}^{\rm ad}-F_{\nu}^{\rm pred}\vert <~100$ mJy. Judging from the histogram we decided that the stars falling outside this interval must be outliers. Subsequently, all stars were rejected which are more than 2.6 standard deviations away from the mean (i.e. $\leq$1% probability of occurrence). This yields an interval of $-81~{\rm mJy}< F_{\nu}^{\rm ad}-F_{\nu}^{\rm pred} <~97$ mJy. The mean of the remaining stars is 8 mJy with a dispersion of 35 mJy. The normal distribution has been included in Fig. 3. Application of a Kolmogorov-Smirnov test showed that the distribution in the given interval is normal with a significance level of 5%.

This analysis indicates that for the majority of the stars in the sample, the 25 $\mu $m fluxes are consistent with the expected photospheric fluxes. The overall scatter between the observations and expectations is 35 mJy. Judging from the individual uncertainties of the 25 $\mu $m fluxes, we conclude that most of the scatter must come from the infrared measurements and that the predicted fluxes which are only based on optical data are very accurate, within 8 mJy for the sample average. In addition, there is no indication that the distribution is non-normal, suggesting that there is no statistical evidence for a surplus of positive excesses in the distribution for $F_{\nu}^{\rm ad}-F_{\nu}^{\rm pred} <~97$ mJy.


  \begin{figure} \par\resizebox{\hsize}{!}{\includegraphics{RJL1808f4.eps}} \end{figure} Figure 4: The properties of the stars more than 3 $\sigma $ away from the peak of the distribution presented in Fig. 3. The error bars present ${\pm }3{\times }{\Delta }F_{\nu }^{\rm ad}$. The star HD 39060 ($\beta $ Pic) is not included due to its off-scale positive excess of a lot.
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A total of 11 (=14%) targets fall outside the ${\pm}3~\sigma$ interval, and 2 out of these 11 targets are below the expected flux. For these outlying stars we have plotted in Fig. 4 the ratio $F_{\nu}^{\rm ad}/F_{\nu}^{\rm pred}$. In order to indicate the significance of the deviation we have included ${\pm}3~{\Delta}F_{\nu}^{\rm ad}$ error bars, highlighting the uncertainties in the individual measurements.

Figure 4 indicates that 7 stars (6 stars plus $\beta $ Pic) with $F_{\nu}^{\rm ad}/F_{\nu}^{\rm pred}~>~0$ have fluxes which are more than $3{\Delta}F_{\nu}^{\rm ad}$ above the predicted values. These stars have been flagged in Table 1.

3.2 Infrared excess from K dwarfs

Two of the 7 excess stars are classified as K dwarfs (Table 1). It is likely that Eq. (1) does not apply for these type of stars but rather the relation derived by Mathioudakis & Doyle (1993), see also Fig. 2. Indeed, for HD 88230 Mathioudakis & Doyle (1993) predict a photospheric flux of 513 mJy which is above $F_{\nu}^{\rm ad}=412$ mJy observed by us. For HD 191408 the value for B-V is low, in the regime where the difference between Eq. (1) and the relation by Mathioudakis & Doyle is small. The measured 25 $\mu $m flux of 462 mJy for HD 191408 is still more than $3{\Delta}F_{\nu}^{\rm ad}$ above the flux of 383 mJy expected for K dwarfs. In conclusion, we reject the detection of an excess in HD 88230.

3.3 List of excess stars in the sample

We have listed resulting the excess stars in Table 2. The excess emission at 25 $\mu $m depends on the shape of the spectral energy distribution and the response of the filterband. We only determined the in-band excess emission for the ISO observations.


 

 
Table 2: Stars showing significant deviations from the predicted photospheric flux at 25 $\mu $m. The dust temperatures $T_{\rm d}$ are derived from the 25/60 flux ratio (Sect. 4.1).
HD name ${F_{\nu}^{\rm star}}$ Excess $T_{\rm d}$
    Jy Jy K
38678 $\zeta$ Lep 0.33 $0.54\pm0.05$ $122\pm6$
39060 $\beta $ Pic 0.29 $7.06\pm0.26$ $82\pm1$
102647 $\beta $ Leo 1.16 $0.39\pm0.07$ $83\pm5$
172167 $\alpha$ Lyr 6.35 $2.41\pm0.39$ $81\pm4$
191408*   0.34 $0.17\pm0.03$ (-)
216956 $\alpha$ PsA 3.26 $0.20\pm0.07$ $49\pm1$
* Not a Vega-like excess star, see Sect. 4.1


If the excess emission is not point-like but comes from a region which is a significant fraction of the beam profile, then the averaging of the two flux measurements is not valid. In all positive excess cases except for HD 191408, the IRAS excess at 25 $\mu $m is larger than the ISO excess. This might indicate that the excess emission is extended and has partly been resolved by ISO (cf. Fig. 5).

  
4 Analysis

  
4.1 Spectral energy distributions

Using IRAS and published ISO observations obtained at other wavelengths we have determined the far-infrared spectral energy distributions of the excess stars. The spectral energy distributions after subtraction of the photospheric emission component have been plotted in Fig. 5. When the observed emission in the IRAS 12 $\mu $m band is within 5% of the estimated photospheric emission, an upper limit of 5% photospheric emission is presented.

The 12/25 flux ratio for HD 191408 yields a colour temperature of about 600 K assuming a $\lambda ^{-1}$ dust emissivity. In combination with the ISO upper limit at 60 $\mu $m we consider it more likely that the excess emission is due to coronal free-free emission. Also $F_{\nu}\propto{\lambda}^{-1.7}$ at 12-25 $\mu $m, a typical power law for free-free emission ( $F_{\nu}\propto{\lambda}^{-2}{-}{\lambda}^{0}$). We therefore exclude this star in the subsequent analysis.


  \begin{figure} \par\resizebox{\hsize}{!}{\includegraphics{RJL1808f5.eps}} \end{figure} Figure 5: The far-infrared spectral energy distributions of the 25 $\mu $m excess stars (cf. Table 2) after subtraction of the photospheric emission; open squares: the excess emission derived from IRAS data, filled squares: ISO data. The ISO data at 60 and 170 $\mu $m were taken from Paper I, for $\beta $ Leo we added 60 and 90 $\mu $m data from the ISO archive. The solid lines are $\lambda ^{-1}$ modified blackbody curves fitted to the 25/60 colour of the ISO excess emission. Except for the upper limits and HD 191408, all data points were colour corrected according to the corresponding modified blackbody.
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Of the five remaining stars we have derived the 25/60 colour temperatures to analyse the temperature of the dust causing the 25 $\mu $m excess emission. Assuming a $\lambda ^{-1}$ dust emissivity, we find temperatures between 49 and 122 K. The inferred temperatures are included in Table 2. HD 38678 has the highest temperature (122 K) and is the only star for which the 25 $\mu $m excess flux density is higher than that at 60 $\mu $m.

4.2 Properties of the 25 $\mu $m excess stars

The fraction of Vega-like stars in our sample with a significant excess at 25 $\mu $m is 5 out of 81 or 6%. Did we overlook genuine 25 $\mu $m excess stars? There are two stars for which IRAS shows a significant excess which cannot be confirmed by ISO. The IRAS measurement of g Lup (HD 139664) at 25 $\mu $m (493 mJy) would indicate a strong excess above the photosphere. We find, however, an ISO flux ($253\pm32$ mJy) which is close to the predicted photospheric flux. This star shows one of the largest discrepancies between ISO and IRAS. HD74576 (see Table 1) is the other star where IRAS would indicate an excess higher than 120 mJy but is rejected because of an inconsistent ISO measurement. Based on these two cases we conclude that from our 25 $\mu $m sample, the uncertainty in the number of excess stars is at most two, giving a most probable fraction of Vega-like stars with 25 $\mu $m excess of 6% and a maximum possible fraction of 9%. This is smaller than the fraction found at 60 $\mu $m (18%) in Paper I.

4.3 Properties of the Vega-like disks

The non-detection of significant 25 $\mu $m excess emission for all other stars in the sample shows that the Vega-like disks are generally cool: the largest fraction of the dust in the disk must be colder than 120 K. The median 25 $\mu $m flux in our sample is $F^{\rm median}_{\nu}=310$ mJy ([25]=3.3 mag). To be detectable in our sample the typical contrast C25 between emission from a presumed disk and the stellar photosphere must be greater than ${C_{25}~>3{\sigma}/F^{\rm median}_{\nu}}$, i.e. C25> 0.3. Assuming a disk temperature of 120 K, the minimum detectable dust mass of the disk is estimated to be ${M_{\rm d}=2\times10^{-5}}$ ${M_{\oplus}}$for an A0 dwarf ( ${T_{\rm eff}=}$ 9600 K) and $2\times10^{-6}$ ${M_{\oplus}}$ for a G0 dwarf ( ${T_{\rm eff}=}$ 6000 K). See Appendix A for a description of the calculation. These masses increase for lower dust temperatures. For comparison, the minimum detectable mass in the survey at 60 $\mu $m is ${M_{\rm d}>1\times10^{-5}}$ ${M_{\scriptstyle\oplus}}$(Paper I). Our Vega-like candidates are all included in the list of Paper I. Since all Vega candidates in Paper I have inferred masses larger than ${1\times10^{-5}~M_{\scriptstyle\oplus}}$ we conclude that we have detected essentially the warmest disks at 25 $\mu $m.

Three stars in our sample ($\beta $ Leo, $\alpha$ Lyr, and $\beta $ Pic) show significantly more far-infrared emission at $\lambda>60~\mu$m than the modified black body energy distributions would predict, see Fig. 5. This could be an indication of the presence of colder dust material in the disk, presumably at larger radii from the stars.

The minimum detectable mass of ${\rm 2\times10^{-6}}$ ${M_{\oplus}}$ for a G0 dwarf assumes an arbitrarily chosen fixed distance between the disk and the star. The detection of only A stars suggests that only stars of this stellar type are sufficiently bright to heat the dust at a minimum distance of the star. For example, a 1 $\mu $m size silicate particle must be at $\sim$35 AU from an A0 star to be at a temperature of 120 K. At this distance, the temperature of a similar dust particle around a G0 star would be $\sim$86 K, yielding a minimum mass of ${M_{\rm d}=2\times10^{-5}}$  ${M_{\oplus}}$. It is therefore more likely that the minimum detectable mass in our sample is ${M_{\rm d}=2\times10^{-5}}$  ${M_{\oplus}}$.

  
5 Discussion

The low fraction of 6% of main-sequence dwarfs exhibiting Vega-like excess emission at 25 $\mu $m gives force to the result by Aumann & Probst (1991) who carried out a similar survey at 12 $\mu $m. They found only 2 statistically significant excess candidates out of 548 nearby stars. These two stars ($\beta $ Pic and $\zeta$ Lep) are also found in our sample of excess candidates. Apparently, warm debris disks are rare.

A similar study by Fajardo-Acosta et al. (2000), where 2MASS data were combined with IRAS data for a sample of 296 main-sequence stars, yielded 8 systems which have a significant excess at 12 $\mu $m. None of their 8 stars is in our initial sample. This low fraction (<3%) is not inconsistent with our result at 25 $\mu $m. Only one of these 12 $\mu $m excess stars is detected at longer wavelengths, and the spectral energy distributions of the 8 stars indicate dust temperatures in excess of 200 K. The temperatures suggest that the systems detected by Fajardo-Acosta et al. (2000) are distinct from the systems we have detected at 25 $\mu $m which all have been detected at 60 $\mu $m (see Fig. 5).

From a survey of 38 main-sequence stars using IRAS and ISOPHOT data Fajardo-Acosta et al. (1999) found no star with a significant excess at 12 $\mu $m, and a fraction of $\sim$14% excess stars at 20 $\mu $m. It is difficult to interpret this fraction since the ISOPHOT data used in their study were inconclusive, and the 20 $\mu $m detections needed confirmation. In any case, the absence of 12 $\mu $m detections indicates that these disks are not warmer than 200 K.

The temperatures and the inferred upper limits for the dust emission at 25 $\mu $m put strong requirements to possible ground based photometric surveys of debris disks at 20 $\mu $m. In order to be able to detect disks below our detection limit of $2\times10^{-5}$  ${M_{\oplus}}$, the contrast between disk emission and photospheric emission is <0.3 (equivalent to larger than 1.3 mag). On the other hand, the accuracy of predicting the infrared photospheric flux is generally not better than 5% which limits the maximum contrast to 3.3 mag. Significant improvement can only be made by imaging the disk.

All five Vega-like candidates in our sample are young, less than 400 Myr (cf. Table 1) with spectral type A0-A3, confirming the finding by Habing et al. (1999) that debris disks are mostly found around stars that just entered the main-sequence. In fact, of the 8 stars in our sample younger than 400 Myr, 5 have a detectable dust disk at 25 $\mu $m, whereas none of the older stars show a significant excess.

The lower limits on the mass have been derived assuming that the size of the disk particles is much smaller than the wavelength. At 25 $\mu $m this corresponds to $a\la3~\mu$m, where a is the radius of a grain. Larger grain sizes yield relatively lower absorption cross sections which increase our minimum mass estimate. Detailed modelling by Krügel & Siebenmorgen (1994) and Dent et al. (2000) which includes the (observed) spatial distribution in the disk, suggests much larger grain sizes of the order of a few tens of $\mu $m. Such sizes could increase our lower limit of the disk mass by one order of magnitude or more.

The dust model calculations by Li & Greenberg (1998) for $\beta $ Pic assuming that the particles are made out of cometary material show that for a given temperature, the grains can span a whole range of distances from the star depending on the composition and mass. For $T_{\rm d}=120$ K they find D=20 AU for the biggest porous silicate aggregates (of 10-4 g) to D=200 AU for the smallest ones (of 10-14 g).

  
6 Conclusions

A 25 $\mu $m survey of 81 late type main-sequence dwarfs using ISO and IRAS data showed that 5 (or 6%) of all stars in the sample exhibit significant infrared excess which can be attributed to a Vega-like dust disk. The low fraction and the fact that the disks have already been identified at 60 $\mu $m indicates that the bulk emission from Vega-like disks is from cool dust ( $T_{\rm d}< 120$ K).

From the detection limit of Vega-like disks we estimate a lower mass limit of ${M_{\rm dust}=~2\times10^{-5}}~M_{\oplus}$ for the disks not detected by us. The survey confirms that there seems to be an absence of detectable amounts of dust at close distances ${D~\loa}$ 20 AU from the stars.

Acknowledgements
The ISOPHOT data presented in this paper were reduced using PIA, which is a joint development by the ESA Astrophysics Division and the ISOPHOT Consortium. We thank the referee, Dr. R. Liseau, for helpful comments leading to improvement of the manuscript.

Appendix A: Derivation of mass upper limit of debris disk

Following the treatment of Paper I, we define $C_{\nu}$, the contrast between the dust emission and the photospheric emission in the infrared:

\begin{displaymath}C_{\nu} = \frac{F_{\rm\nu,dust}}{F_{\rm\nu,star}} = \frac{L_{\rm\nu,dust}}{L_{\rm\nu,star}}\cdot \end{displaymath} (A.1)

Assuming a single sized spherical particle, the dust emission is given by:

\begin{displaymath}L_{\rm\nu,dust} = 4{\pi}^2a^2Q_{\nu}B_{\nu}(T_{\rm d})N, \end{displaymath} (A.2)

where a is the radius, $T_{\rm d}$ the temperature, and ${Q_{\nu}}$ the absorption coefficient of a dust particle. N is the total number of such particles in the disk. The mass of the disk is readily computed from ${M_{\rm dust} = \frac{4}{3}{\pi}a^3 N\rho_{\rm dust}}$where ${\rho_{\rm dust}}$ is the specific mass of the grain material. For dust particles smaller than the wavelength ( ${a<0.1{\lambda}}$) one can write (e.g. Draine & Lee 1984):

\begin{displaymath}Q = \frac{a~q_{\rm o}}{\lambda^2}\cdot \end{displaymath} (A.3)

Approximating ${L_{\rm star}\approx A~T_{\rm eff}^{8.2}}$ for main-sequence dwarfs, and assuming that the Rayleigh approximation is valid in the infrared, we obtain for the star:

\begin{displaymath}L_{\rm\nu,star} = A\frac{2{\pi}k}{{\sigma_{\rm SB}}c^2}\nu^2T_{\rm eff}^{5.2}, \end{displaymath} (A.4)

where ${\sigma_{\rm SB}}$ is the Stefan-Bolzmann constant. The constant A can be derived from the temperature and luminosity of known stars like the Sun or Vega, we adopt ${A=1.33\times10^{-31}}~L_{\odot}$K-8.2. Combining the above equations:

\begin{displaymath}M_{\rm dust} = A\frac{2k}{3{\sigma}}\frac{\rho_{\rm dust}T_{\rm eff}^{5.2}} {q_{\rm o}B_{\nu}(T_{\rm d})} C_{\nu}. \end{displaymath} (A.5)

To estimate ${M_{\rm dust}}$ we assume astronomical silicate (Draine & Lee 1984) with ${q_{\rm o}~=~1.3\times10^{-4}}$ m and ${\rho_{\rm dust}~=~}$3.3 g cm-3. Note that this relationship is independent of the grain size a as long as a is significantly smaller than the infrared wavelength.

References

 

Copyright ESO 2002