Search for Cold Debris Disks around M-dwarfs. II
J.-F. Lestrade, M. C. Wyatt, F. Bertoldi, K. M. Menten, G. Labaigt
aa r X i v : . [ a s t r o - ph . GA ] J u l Astronomy&Astrophysicsmanuscript no. survey07˙rev2 November 5, 2018(DOI: will be inserted by hand later)
Search for Cold Debris Disks around M-dwarfs. II
J.-F. Lestrade , M. C. Wyatt , F. Bertoldi , K. M. Menten , and G. Labaigt Observatoire de Paris - CNRS, 77 av. Denfert Rochereau, F75014, Paris, Francee-mail: [email protected] Institute of Astronomy, University of Cambridge, Cambridge, CB3 OHA, UKe-mail: [email protected] Argelander Institute for Astronomy, University of Bonn, Auf dem H¨ugel 71, Bonn, D-53121, Germanye-mail: [email protected] Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, Bonn D-53121, Germanye-mail: [email protected] Ecole Normale Sup´erieure de Cachan, 61 avenue du Pr´esident Wilson, F94235 - Cachan - Francee-mail: [email protected]
Received 22nd April 2009 ; accepted 6th July 2009
Abstract.
Although 70% of the stars in the Galaxy are M-dwarfs, thermal emission searches for cold debris disks have beenconducted mostly for A-type and solar-type stars. We report on new λ = . . + . − . %, compared to 15 + . − . % for FGK-stars and 22 + − % for A-stars. Hence, for this age group,there is an apparent trend of fewer cold disks for later stellar types, i.e. , lower star masses. Although its statistical significanceis marginal, this trend is strengthened by the deeper sensitivity of observations in the M-dwarf sample. We derive a cold diskfraction of <
10 % for the older (likely a few Gyr) M-dwarfs in our sample. Finally, although inconclusively related to a debrisdisk, we present the complex millimeter structure found around the position of the M1.5 dwarf GJ526 in our sample.
Key words.
Stars : circumstellar matter ; surveys ; stars: low-mass ; planetary systems : formation
1. Introduction
Cold debris disks around main sequence stars are left-overplanetesimals (comets) that could not agglomerate into largerplanets during the initial phase of planet formation. They areassembled as a belt in the periphery of the system in a man-ner analogous to the Kuiper Belt. The study of debris disks,including warm disks such as the asteroid belt in our SolarSystem, advances our knowledge of the origin and evolutionof planetary systems around other stars, similarly to the studyof the Kuiper Belt. It is well recognised that its present-daystructure and dynamics retain important information on the for-mation and evolution of the Solar System. For example, thelow mass and expanded size of the present-day Kuiper Belt canbe traced back to the outward migrations of the giant planets,which exchanged orbital energy with an initially more compactand more massive disk (Hahn & Malhotra 1999, Tsiganis et al.2005, Morbidelli et al., 2005, and Gomes et al. 2005).
Send o ff print requests to : J.-F. Lestrade, e-mail : [email protected] Our current understanding of debris disks has been recentlyreviewed by Wyatt (2008). Mutual collisions between planetes-imals in debris disks produce second-generation dust grainsthat are observable through their thermal emission or scatteredlight. Since the discovery of a first debris disk around the A0main sequence star Vega by IRAS (Aumann et al. 1984), debrisdisks have been searched for photometrically with the infrared(IR) satellites IRAS, ISO and Spitzer. In such observations, anyflux excess above the photospheric level is interpreted as emis-sion from warm (50 −
100 K) circumstellar dust.Through Spitzer observations it was found that 32 ± µ m excess (Su et al. 2006), whileonly 16 + . − . % of 225 observed FG-dwarfs show excess emis-sion (Bryden et al. 2006; Trilling et al. 2008). Submillimeterphotometry has shown that some A-to-G type stars with no de-tectable IRAS excess do however show cold (10 −
50 K) dustemission (Wyatt et al 2003; Najita & Williams 2005). Imagingof scattered light with the HST and of thermal continuum emis-sion with SCUBA has measured disk radii between 50 and150 AU (Smith & Terrile 1984; Kalas, Graham & Clampin
Lestrade et al.: Debris Disks around M-dwarfs . Azimuthal structures havebeen detected in a few of these disks and are thought to becaused by dust associated with planetesimals trapped in meanmotion resonance with an orbiting planet (Wyatt 2003, 2006,Reche et al. 2008), or by dynamical perturbations from a distantstellar companion or passing stars (HD141569A: Augereau &Paploizou 2004).Although low-mass M-dwarfs are the most populous (70%)stars in the Galaxy, they have so far received little attention,mostly because their low luminosity makes the thermal emis-sion and scattered light from their disks more di ffi cult to detect.In a SCUBA survey of young stars of the β Pic moving groupand of the Local Association, Liu et al. (2004) detected the firsttwo debris disks around M-dwarfs, AU Mic and GJ182. UsingSCUBA and MAMBO-2, Lestrade et al. (2006) surveyed 32relatively young M-dwarfs of moving groups and newly de-tected one disk around the M0.5 dwarf GJ842.2. Using Spitzer,Gautier et al. (2007) surveyed 62 nearby M-dwarfs at 24 µ m,and subsamples of 41 at 70 µ m and of 20 at 160 µ m, and foundno firm detection. AU Mic was also imaged in scattered light,revealing an edge-on, structured disk (Liu, 2004 and Krist etal., 2005).Here we present new MAMBO-2 observations of nearbyM-dwarfs, and combined them with our previous survey to an-alyze a total sample of 50 M-dwarfs (Table 1) in terms of theircold debris disks abundance.We present the new M-dwarfs surveyed in §
2, we describethe observations in §
3, and results for debris disks but also forbackground sources in the fields of some of the M-dwarfs in § − mass and luminosity lower than solar − impact theformation of debris disks around them or their detectability.
2. Sample of newly observed M-type dwarfs
To complement our first survey of M-dwarfs, which are inmoving groups of ages <
600 Myr (Lestrade et al 2006), weobserved the most nearby M-dwarfs, irrespective of age. Weselected single M-dwarfs at a distance less than 6 pc and at δ > − ◦ , and added five M-dwarfs binaries and six singleM-dwarfs between 6 and 10 pc that are in common with theSpitzer survey by Gautier et al. (2007). The five binaries in oursample are: GJ725 (M3 and M3.5) separated by 15 ′′ (53 AU ),GJ234 (M4.5 and M8), separated by 1 ′′ (5 AU ), GJ412 (M2and M6), separated by 32 ′′ (160 AU ), GJ569 (M2.5 and M8.5),separated by 1 ′′ (10 AU ), and GJ65 (M5.5 and M5.5), sepa-rated by 2 ′′ (5 . AU ). These angular separations are so smallthat a single MAMBO-2 map can cover both components. Theages of the targeted near-by M-dwarfs are presently unknown.
3. Observations
The diameter usually adopted for debris disks is 120 AU, whichfor near-by stars is larger than the IRAM 30-meter telescope http: // astro.berkeley.edu / kalas / disksite / pages / gallery.html beam of 10 . ′′ FWHM at λ = . ff ective fre-quency centered at 250 GHz (1.20 mm) for thermal emissionspectra. The e ff ective FWHM beam is 10 . ′′ , and the under-sampled field of view of the array is 4 ′ . We used the standardon-the-fly mapping technique, where one map is made of 41azimuthal subscans of 60 sec each, with a scanning velocity of4 ′′ / sec and an elevation incremental step of 4 ′′ , while choppingthe secondary mirror at 2 Hz by 60 ′′ in azimuth. The bolome-ters are arranged in a hexagonal pattern with a beam separationof 22 ′′ . This scanning pattern produces time streams of datathat are converted to a fully sampled spatial map with 3 . ′′ pixels. Our observations were done within pooled observingruns spread over the winter and summer periods from 2005to 2007. Atmospheric conditions were generally good duringthe observations, with typical zenith opacities between 0.1 and0.3 at 250 GHz and low sky noise. The telescope pointing waschecked before and after each map by using the same nearestbright point source, and was found to be stable to better than3 ′′ , except in a few occasions for which we discarded the data.The absolute flux calibration is based on observations of sev-eral standard calibration sources, including planets, and on atipping curve (sky dip) measurement of the atmospheric opac-ity once every few hours. The resulting absolute flux calibrationuncertainty is estimated to be about 10% (rms).The data were analyzed using the mopsic software pack-age written by R. Zylka at IRAM. The double-beam mapswere combined to a single map using the shift-and-add pro-cedure. Compared to a proper image restoration this producesmaps with about a factor 2 better sensitivity, at the expenseof no sensitivity to emission structures in scan direction thatare larger that the wobbler throw of 60 ′′ . In our sample, theshortest integration time per field is 30 minutes, yielding anrms noise level of ∼ . / ′′ beam in the central part ofthe map ( r < ′′ ), steadily rising to ∼ / ′′ beam atits edge ( r ∼ ′′ ). This non-uniform noise across the mapsresults from the fact that the scanned field is about twice aslarge as the bolometer array size, so that more data is takenin the central part of the map than near the edges. Due to thisnon-uniformity, it is judicious to present Signal-to-Noise mapsrather than intensity maps. The longest observation, by far, had20 hour duration and was on GJ628, yielding an rms noise levelof ∼ . / ′′ beam in the central part of the map and ∼ . / ′′ beam at r ∼ ′′ . The sky area covered byeach map corresponds to ∼ σ detection in our maps is statistically significant.Below, we describe the procedure we used to extract discretesources and to search for extended emission.
4. Results
Although initially intended, our complete survey of 50 M-dwarfs turns out not to be flux-limited, which makes its sta-tistical interpretation not straightforward. First we present the estrade et al.: Debris Disks around M-dwarfs 3
Table 1.
The 50 M-dwarfs of our two (sub)mm surveys. Survey I was already presented by Lestrade et al. (2006) but its datawere included in the statistical analysis of this paper. New data were acquired in survey II with MAMBO-2. Selection criteria areages <
600 Myr for survey I and the nearest M-dwarfs but of undetermined ages for survey II. Ages are based on Moving Groups(Local Association (20 −
150 Myr), IC2391 (35 −
55 Myr), AB Dor (100-125 Myr), Castor (200 Myr), Ursa Maj (500 Myr) andHyades (600 Myr)) identified by Montes et al. (2001) and Zuckerman & Inseok Song (2004a,b). Some stars were observed inboth surveys.
Name Spectral Binarity Selection Observed in Bolometer Publicationcriterium survey −
150 Myr I SCUBA Lestrade et al. (2006)GJ212 M0.5 ” ” I ” ”GJ507.1 M1.5 ” ” I ” ”GJ696 M0 ” ” I ” ”GJ876 M4 ” ” I MAMBO ”GJ628 M3.5 ” ” I ” ”GJ402 M4 ” ” I ” ”GJ234 M4.5 + M8 Binary ” I & II ” Lestrade et al. (2006) and this workGJ285 M4.5 Single ” I SCUBA & MAMBO Lestrade et al. (2006)GJ393 M2 ” ” I ” ”GJ9809 M0 ” ” I ” ”GJ875.1 M3 ” 35 −
55 Myr I SCUBA ”GJ856A M3 ” 100-125 Myr I MAMBO ”GJ277B M3.5 ” 200 Myr I SCUBA ”GJ842.2 M0.5 ” ” I ” ”GJ890 M2 ” ” I ” ”GJ1111 M6.5 ” ” I & II MAMBO Lestrade et al. (2006) and this workGJ408 M2.5 ” ” I & II ” ”GJ4247 M4 ” ” I & II SCUBA & MAMBO ”GJ447 M4.0 ” 500 Myr I & II MAMBO ”GJ625 M1.5 ” ” I & II ” ”GJ569 M2.5 + M8.5 Binary ” I & II ” ”GJ873 M3.5 Single ” I ” Lestrade et al. (2006)GJ65 M5.5 + M5.5 Binary 600 Myr I ” ”GJ3379 M4 Single ” I ” ”GJ849 M3.5 ” ” I ” ”GJ791.2 M4.5 ” ” I ” ”GJ109 M3.5 ” ” I & II ” Lestrade et al. (2006) and this workGJ699 M4.0 Single 1.82 pc II MAMBO this workGJ406 M6.0 ” 2.38 pc II ” ”GJ411 M2.0 ” 2.54 pc II ” ”GJ905 M5.5 ” 3.16 pc II ” ”GJ725 M3 + M3.5 Binary 3.57 pc II ” ”GJ54.1 M4.5 Single 3.72 pc II ” ”GJ273 M3.5 ” 3.79 pc II ” ”GJ83.1 M4.5 ” 4.44 pc II ” ”GJ687 M3.0 ” 4.53 pc II ” ”LHS292 M6.5 ” 4.54 pc II ” ”GJ1002 M5.5 ” 4.69 pc II ” ”GJ412 M2 + M6 Binary 4.83 pc II ” ”GJ388 M3.0 Single 4.89 pc II ” ”GJ445 M3.5 ” 5.38 pc II ” ”LHS1723 M4.5 ” 5.43 pc II ” ”GJ526 M1.5 ” 5.43 pc II ” ”GJ251 M3.0 ” 5.57 pc II ” ”GJ205 M1.5 ” 5.71 pc II ” ”GJ213 M4.0 ” 5.87 pc II ” ”GJ908 M1.0 ” 5.93 pc II ” ”GJ581 M3 ” 6.27 pc II ” ”GJ102 M4 ” 7.75 pc II ” ” Lestrade et al.: Debris Disks around M-dwarfs discrete millimeter sources detected in four MAMBO-2 maps(Figs 1, 2 and 3, and Table 2), and we discuss the nature of theintriguing cluster of sources around GJ526. Second, we presentthe deep search for faint debris disks made by averaging inten-sities over an e ff ective area in the 42 MAMBO-2 maps of ourcomplete survey (Tables 3 and 4). The 8 other M-dwarfs wereobserved in wide photometry with SCUBA (Table 5) and werealready discussed by Lestrade et al. (2006). We use the com-plete sample of 50 M-dwarfs to estimate the fraction of cold de-bris disks around M-dwarfs and upper limits of their fractionaldust luminosities. Three stars (GJ285, GJ393 and GJ4247) arein common between Tables 3, 4 and 5. In Table 2, we summarize the characteristics of the discretesources detected with S / N > ∼ ′′ × ′′ in size and centered onthe position of an M-dwarf. The source extraction was done bysearching each map for any pixel with S / N > × χ betweenthe 2-D Gaussian F × exp (cid:16) − . × h ( x − x ) + ( y − y ) i /σ (cid:17) and the measured intensities over this block by varying the peakflux F , the parameter σ (FWHM = . σ ) and the peak posi-tion ( x , y ) by less than a pixel from the S / N > × ′′ − ′′ ) forour sources. This correction amounted to between 5% and 20%of the integrated flux density. The integrated flux densities ofsources in Table 2 are S int = πσ F . We have extracted 13 dis-crete sources with S / N > F in 4 fields out of the 42MAMBO-2 maps ; 8 sources are newly found in the fields ofGJ526, GJ725 and GJ569. They are shown in Fig. 1, 2, and3. The 5 others sources are in the field of GJ628 as alreadyreported in Lestrade et al. (2006) ; typographic errors in theircoordinates in this first publication are corrected in Table 2. Inthis Table, the lowest integrated flux density is 3 . ± . ′′ (2 σ MAMBO-2 position error) to any of thesesources in the USNO-B1 catalogue (Monet et al. 2003), exceptfor MM163007-123942 (GJ628W) at the 1 σ level in position(object I mag = = ′′ from MM134540 + ∼ / deg as measured over the 4 ′ × ′ area centered on the star position.In the field of GJ569 ( ∼ / deg ), there aretwo SDSS objets (mag u = = ′′ fromMM145428 + σ MAMBO-2 position un-certainty (10 . ′′ ) in the NVSS catalogue (Condon et al., 1998)to the flux density limit of 2.5 mJy at 1.4 GHz, except forMM163007 − . σ level in position(object flux density = . ± . σ MAMBO-2 position uncertainty in the 2MASSAll-Sky Catalog of Point Sources (Skrutskie et al., 2006).
The source MM184222 + ff erent atmospheric correlation lengths inthe skynoise reduction within the mopsic data reduction pack-age, yielding similar detections of S / N ∼
7. Systematics a ff ectsthe accuracy of the flux measurement for this source, which isnear the edge of the map. This source is possibly resolved witha source FWHM between 12 ′′ and 15 ′′ depending on the re-duction parameter used. Although this is rare, it has recentlybeen shown that submm galaxies can have multiple compo-nents (Tacconi et al., 2008). We shall discuss this source to-gether with complementary observations in a forthcoming pa-per. The map of GJ526 is shown in Fig. 1. Five sources are de-tected with S / N > S / N > S / N < − < S / N < ′′ × ′′ map ( ∼ | S / N | > ∼ σ source to the West closeto the ellipse but this source is not robust to data selection. Sowe have disregarded it.The ellipse is o ff set by two pixels in right-ascension fromthe position of the star, its semi-major and semi-minor axesare a = ′′ and b = ′′ , and its orientation is PA = − ◦ .This structure might be the projected ring of a clumpy debrisdisk, its inclination being 81 ◦ from the plane of the sky. Theo ff set between the star and the center of the ellipse is only 2pixels and might be caused by position uncertainties or / and byreal source structure. The 5 connected sources appear not tobe embedded in any extended emission as expected for a de- estrade et al.: Debris Disks around M-dwarfs 5 Table 2.
Sources found in our MAMBO-2 survey ( S / N > ′′ at λ = . + Source name Star Field α (J2000) a δ (J2000) a Integrated flux density b S / N Sourceat 1.2 mm (mJy) FWHMMM145428 + . ± . ′′ MM184222 + −
63 6 . − . ′′ − ′′ MM184253 + . ± . ′′ MM134539 + . ± . ′′ MM134540 + . ± . ′′ MM134541 + . ± . ′′ MM134543 + . ± . ′′ MM134546 + . ± . ′′ MM163007-123942 GJ628 c
16 30 07.6 −
12 39 42 7 . ± . ± ′′ MM163022-123925 GJ628 d
16 30 22.3 −
12 39 25 3 . ± . ± ′′ MM163019-123830 GJ628 e
16 30 19.7 −
12 38 30 4 . ± . ′′ MM163015-123911 GJ628 f
16 30 15.6 −
12 39 11 4 . ± . ′′ MM163013-124057 GJ628 g
16 30 13.7 −
12 40 57 4 . ± . ′′ a The MAMBO coordinate uncertainties are ∼ . ′′ . b Flux density (mJy) is integrated under the fitted 2D-Gaussian. c , d , e , f , g : these sources were found in survey I ; ( c ) is GJ628-W, ( d ) is GJ628-E, ( e ) is GJ628-NE, ( f ) is GJ628-NW, and ( g ) is GJ628-SW in Fig 2 and Table 3 of Lestrade et al.(2006). Note that there are typographic errors in the minute column of declinations in Table 3 of Lestrade et al. (2006). The positions of the GJ628 sources given now are correct andsupersede this first publication. Also, the flux densities in this first publication were peak flux densities while they are integrated flux densities now. bris disk though. The mean brightness over a rectangular box220 ′′ × ′′ (92 beams) oriented at PA = − ◦ and centered onthe star is 0 . ± .
073 mJy / ′′ beam, i.e. ∼ σ . Actually, thismean brightness matches the mean of the 5 flux densities of theconnected sources within the box, indicating that any extendedemission must have a brightness < × . / ′′ beam at1.2 mm.We now test whether or not such a source cluster can arisefrom the distribution of background sources. We carry out afirst test to estimate the probability that the connected sourcesaround GJ526 can cluster as tightly as they do in Fig 1 if theywere background sources. For this test, we use the statisticalanalysis of spatial point patterns developed by Diggle (2003).This analysis is based on the nearest neighbour distance, de-fined as the distance between a point (a source for us) and itsnearest neighbour. For GJ526, all the nearest neighbour dis-tances for the 5 sources connected by the ellipse are < ′′ . Theprobability that k distances x be < ′′ among N distances if themean frequence of occurence for x < ′′ over the whole sky is f , is given by the binomial distribution B k = (cid:16) Nk (cid:17) f k (1 − f ) N − k .We can derive the mean frequence of occurence f from thethree empty fields (ELAIS N2, Lockman Hole and COSMOS)mapped by MAMBO-2 (Greves et al., 2004 and Bertoldi et al.,2007). We found there are 9 distances < ′′ between the 71sources of these three fields, and so f = / (71 − = . < ′′ as already mentioned, so k = N = B k that background sources can produce such anumber of small distances is as low as 0.1%.As a second test, we use the elliptical pattern connecting6 submm sources recognisable in the North-West part of theCOSMOS field mapped by MAMBO-2 and displayed in Fig 2of Bertoldi et al. (2007). This field is 20 x
20 arcmin in sizeand the mean occurence of ellipse of major-axis 200 ′′ , as in thefield of GJ526, is 1 / x
20 arcmin − . We compute the Poissonprobability to find a similar ellipse in a field that we take assmall as 200 x
200 arcsec to account for the fact that the ellipsearound GJ526 is found in an area restricted to the central part ofthe map, i.e. centered on the position of GJ525. This probabilityis 2.7%. This test is only indicative because the COSMOS fieldhas been mapped at the level of 1 mJy / beam rms while our mapis twice as deep for the field around GJ526.In summary, the five sources in Fig 1 that are symmetriclylocated around GJ526 are connected by an ellipse almost cen-tered on the star. The two tests carried out above provide indica-tions that this structure is statistically unconsistent with knownspatial distributions of background submm galaxies. Hence, atthis stage, we cannot rule out the hypothesis that the sources areassociated with the star. In this case, the 5 connected sourcescould be indicative of azimuthal structures in an inclined de-bris disk around GJ526 whose extended emission is not seenbecause the map is not deep enough. Complementary obser-vations at 850 µ m, and at shorter wavelengths with Herschelshould attempt to detect the extended emission of the disk. Lestrade et al.: Debris Disks around M-dwarfs
Table 3.
New MAMBO-2 observations at 1.2 mm for nearby M-dwarfs. The table includes mean brightness determined byaveraging map intensities over an e ff ective area to search for faint debris disks that are not readily apparent. Not shown in thistable are the five emission clumps symmetricly located around GJ526 that might be an inclined debris disk (see subsection 4.1.3) Name Spectral D Gal. l. Integration Map rms Mean brightness µ/σ µ σ flux densitytype (pc) ( ◦ ) time (mJy / ′′ beam) µ ± σ µ (2) upper limit (1.2 mm)(hours) (mJy / ′′ beam) (mJy)(1) (2) (3)GJ699 M4.0 1.82 14 1.5 1.22 -0.03 ± < ± < ± < ± < ± < + M3.5 3.57 24 1.0 1.44 0.29 ± < ± < ± < ± < + M8 4.12 -6 2.5 1.03 0.30 ± < ± < ± < ± < ± < + M6 4.83 63 0.5 2.26 -0.21 ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < + M8.5 9.81 59 2.0 1.09 -0.46 ± < (1) rms estimated for r < ′′ in the map ; (2) mean brightness and uncertainty of mean computed by averaging intensities over an e ff ective disk of radius 60 AU ; (3) the 3 σ flux density upper limit is computed also over the same e ff ective area (radius = (*) : background sources in map (see Table 2) ; (**) : possibly a large debris disk (see Fig 1 and subsection 4.1.3). Eventually, astrometry should detect the same prope motionfor the 5 connected sources as for the star GJ526 (2 . ′′ / yr inthe SE direction) if indeed they are part of a debris disk. Themid-epoch of our MAMBO-2 data is early 2007, so that the5 sources should have moved in concert with the star by a fullIRAM-30m beam by 2011, providing definitive proof of a disk.Such a debris disk would have a radius as large as ∼
500 AUat the distance of GJ526. We examine whether or not thisis conceivable. First, we note that exceptionally large debrisdisks, 520 AU and 600 AU in extent, have recently been foundaround the 184 Myr old A0-type dwarf γ Oph at 70 µ m (Su etal. 2008) and around the main sequence F8V q Eri at 870 µ m(Liseau et al. 2008). Second, protoplanetary disks where plan- etesimals and planets form extend to almost 1000 AU as ob-served for example around the young close binary GG Tau(Dutrey, Guilloteau & Simon, 1994). In the model proposed byKenyon and Bromley (2004a), icy-planets successively form inwaves outward in the disk producing larger and larger dustyrings from collisional cascades. In their model, the planet for-mation timescale is 15 − × ( Σ / Σ MMS N ) − ( a /
30 AU) Myrin a quiet disk (their eq (4)). Assuming for Σ as much as 15times the surface density of the minimum-mass solar nebula Σ MMS N as required for the formation of Jupiter in the solar sys-tem (Lissauer 1987), the timescale for planet formation to reach500 AU in the GJ526 system is ∼ estrade et al.: Debris Disks around M-dwarfs 7 Table 4.
M-dwarfs associated with moving groups observed at 1.2 mm in survey I with the MAMBO-2 facility and alreadypresented in Lestrade et al. (2006) but reanalyzed here in a consistent fashion with the new data of Table 3.
Name Spectral D Gal. l. Integration Map rms Mean brightness µ/σ µ σ flux densitytype (pc) ( ◦ ) time (mJy / ′′ beam) µ ± σ µ (2) upper limit (1.2 mm)(hours) (mJy / ′′ beam) (mJy)(1) (2) (3)GJ65 M5.5 2.6 -76 1.0 2.30 -0.15 ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < ± < (1) rms estimated for r < ′′ in the map ; (2) mean brightness and uncertainty of mean computed by averaging intensities over an e ff ective disk of radius 60 AU ; (3) the 3 σ flux density upper limit is computed also over the same e ff ective area (radius = (Berger et al., 2006) is about 2 σ larger than the ZAMS diam-eter predicted by Chabrier & Bara ff e (1997) and Siess et al.(2000). If such a deviation of only 2 σ is real, it is an indica-tion of youth instead for GJ526, and this would pose a problemfor the Kenyon and Bromley model applied to the hypotheticaldebris disk around GJ526. Note that, with the dust surface den-sity profile 15 Σ MMS N × ( r / r ) − / , the mass of solids in a ringat r =
500 AU and 0 . r in width is 1 M ⊕ which is enough toform planetesimals. Finally, the dust mass corresponding to theemission of the 5 sources is between ∼ ∼
10 lunar massesas derived in the Appendix for dust grains with a Dohnanyi sizedistribution and heated both by the stellar luminosity and theinterstellar radiation field. The dust mass is ∼
22 lunar massesif derived conventionally for grey body dust with a mass opac-ity of 1 . g − at 850 µ m and ∝ λ − for λ > µ m, andwith the single dust temperature 4.9K at large radius from thestar ( r =
500 AU) where the interstellar radiation field domi-nates the heating process of grains (see Appendix).
We searched for faint debris disks in each MAMBO-2 map byaveraging intensities over a disk of increasing radius till 30 ′′ to see whether or not the mean brigthness peaks at some an-gular radius θ . The radius limit of 30 ′′ comes from the shift-and-add reduction method and the wobbler throw used of 60 ′′ for the observations. The intention with this averaging was tofind a disk whose structure is not directly apparent in the mapbut whose mean brightness is statistically significant. Naturally,no information on its structure can be recovered with this pro- Table 5.
M-dwarfs observed at 850 µ m with JCMT / SCUBAand already presented in Lestrade et al. (2006) but reanalyzedhere in a consistent fashion with the new data of Tables 3 and4.
Star Sp. Dist. Integration Flux density a Size b type (pc) time 850 µ m (AU)(hrs) (mJy)GJ82 M4 12.0 2 2.0 ± ± c M4.5 5.9 1 -0.7 ± c M2 7.2 1 1.9 ± ± ± c M0 24.9 1 -5.2 ± c M4 9.0 1 1.1 ± ± ± ± ± a Flux density from wide photometry. b Size is the radius of a debris disk as large as the telescope beam (14 ′′ ). c Stars also observed by MAMBO-2 in Tables 3 and 4. cedure. The optimum sensitivity of this method is for face-on disks while highly inclined disks might escape detections.This method is similar to the one used to determine extensionlimits of debris disks in the mid-IR surveys of Sun-like starsconducted by Smith, Wyatt & Dent (2008), although, we do
Lestrade et al.: Debris Disks around M-dwarfs
Fig. 1.
MAMBO-2 Signal-to-Noise ratio map of the fieldaround the M1.5 dwarf GJ526 at λ = . . ′′ × . ′′ . The noise rms is σ = .
58 mJy / ′′ beamin the central region ( r < ′′ ) and increases towards theedges of the map, ∼ . / ′′ beam at r ∼ ′′ .The contours are − σ, − σ, − σ, − σ (dotted lines), and1 σ, σ, σ, σ, σ, σ, σ, σ . The ellipse ( a = ′′ , b = ′′ and PA = − ◦ ) is almost centered on the star position and con-nects five sources that might be clumps of a debris disk inclinedto the plane of the sky by 81 ◦ (see subsection 4.1.3). The field iscentered on the position of GJ526 of early 2006 : α ( J =
13h 45m 44.52s and δ ( J = ◦ ′ . ′′ (red star). SeeTable 2 for integrated flux densities and coordinates of sources.not have the complication of having to accurately substract thephotosphere at λ = . θ foreach star of Tables 3 and 4. All the curves were inspected andfound to wander around zero mean with excursions ≤ σ for θ comprised between 11 ′′ / ′′ , indicating that no new diskwas found by this method.In Fig 4, we provide the distribution of the mean bright-ness µ / uncertainty of mean σ µ listed in Tables 3 and 4 andcomputed for θ corresponding specificly to the adopted diskradius 60 AU at the distances of the stars. The correspondingGaussian probability density function is also plotted in Fig. 4.Comparison between the two distributions indicates there aremore high positive and negative ratios µ/σ µ than expected al-though they stay within ± σ . It means that there are still somesystematic errors in the maps but at a low level, likely causedby remaining atmospheric fluctuations. Fig. 2.
MAMBO-2 Signal-to-Noise ratio map of the fieldaround the binary GJ725 (M3 + M3.5 dwarfs) at λ = . . ′′ × . ′′ . The noise rms is σ = . / ′′ beam in the central region ( r < ′′ ) and increasestowards the edges of the map, ∼ . / ′′ beam at r ∼ ′′ . The contours are − σ, − σ, − σ, − σ (dotted lines), and1 σ, σ, σ, σ, σ, σ, σ . The source MM184222 + S / N ∼ + S / N of 5.1. The field is cen-tered on the position of GJ725A of early 2006 : α ( J = δ ( J = ◦ ′ . ′′ (red star). See Table 2for integrated flux densities and coordinates of the sources. The fractional dust luminosity is the fraction of the stellar radi-ation absorbed and reprocessed to the infrared and (sub)mm bythe dust grains ; it is proportional to the fraction of the sky cov-ered by dust as seen from the star (Dominik and Decin 2003).We used the Stefan-Boltzmann law − black body emission − toestimate dust luminosity, and modified it by emissivity 1 / X λ ,with X λ = λ < µ m and X λ = λ/
210 for λ > µ m(Wyatt 2008). In these conditions, fractional dust luminosityis : L dust L ∗ = × c π h ν ( e h ν/ kT d − S θ d T d R ∗ T ∗ × X λ (1)the normalization coe ffi cient is such that the measured flux den-sity S θ is in Jy , the star distance d in pc , the stellar radius R ∗ in m , the dust and stellar e ff ective temperatures T d and T ∗ in K ,the Planck and Boltzmann constants h and k in J × s and J / K ,the speed of light c in m / s , and the frequency of observation ν in Hz .The standard argument used to fix dust temperature T d inmid-IR surveys of debris disks is that observations are mostsensitive to the dust emission peak, and T d is derived from theWien law. In the (sub)mm range, this law is not appropriate for estrade et al.: Debris Disks around M-dwarfs 9 Fig. 3.
MAMBO-2 Signal-to-Noise ratio map of the fieldaround the binary GJ569 (M2.5 + M8.5 dwarfs) at λ = . . ′′ × . ′′ . The noise rms is σ = . / ′′ beam in the central region ( r < ′′ ) and in-creases towards the edges of the map, ∼ . / ′′ beamat r ∼ ′′ . The contours are − σ, − σ, − σ, − σ (dottedlines), and 1 σ, σ, σ, σ . The source MM145428 + S / N of 4 .
9. Thefield is centered on the position of GJ569A of early 2006 : α ( J =
14h 54m 29.35s and δ ( J = ◦ ′ . ′′ (redstar). See Table 2 for integrated flux density and coordinates ofthe source. T d since we observe in the Rayleigh-Jeans limit. To keep fullgenerality, we avoid choosing a dust temperature T d at some ar-bitrary radius but plot in Figs 5 and 6 fractional dust luminosi-ties and dust masses as functions of disk radius r comprisedbetween 1 and 1000 AU following the approach by Bryden etal. (2006) and Wyatt (2008). At disk radius r , we use the dusttemperature : T d = × ( L . ∗ ) × ( r − . ) (2)from black body equilibrium where L ∗ is the stellar luminos-ity in L ⊙ and r is in AU (Backman & Paresce 1993). Note thatby combining eqs (1) and (2), one gets the expression for frac-tional dust luminosity given by eq (8) of Wyatt (2008) wherethe stellar luminosity L ∗ cancels out.We adopt the 3 σ flux density limit for S θ in eq (1) by in-tegrating brightness over a face-on disk of radius r , or θ at thedistance of the star. If 2 θ > ′′ ( i.e. > IRAM 30m beam) : S θ = × rms × (2 θ ′′ / ′′ ) (mJy)This formula takes into account that the mean brightness un-certainty σ µ improves as rms / p number o f beams while theintegrated flux density increases as number o f beams of thedisk area. Now if 2 θ < ′′ : S θ = × rms (mJy) Fig. 4.
Distribution of the ratios meanbrightness µ / uncertaintyof mean σ µ for the 42 M-dwarfs observed with MAMBO-2, i.e. µ/σ µ listed in Tables 3 and 4. Here, the mean brightness µ is computed over a disk of radius 60 AU adopted for eachstar. The Gaussian probability density function superimposedis scaled so that its integral is 42. Comparison between the twodistributions indicates there are more high positive and nega-tive ratios µ/σ µ than expected although they stay within ± σ .It means that there are still some systematic errors in the mapsbut at a low level, likely caused by remaining atmospheric fluc-tuations. No mean brightness is retained as statistically signifi-cant in the sample.We have used the rms of Tables 3 and 4 that correspond to thecentral part of the maps, thus underestimating slightly the upperlimits computed.In Fig. 5, we show the resulting fractional dust luminosityupper limits for r comprised between 1 and 1000 AU. Thesefunctions first show a steep negative slope as long as 2 θ < ′′ making S θ constant in eq (1), then these functions level o ff when S θ linearly increases with θ , finally they increase whenthe dust temperature saturates at 4.9K because the interstel-lar radiation field becomes dominant over the stellar field (seeAppendix). In this figure, we have added the upper limits ofthe fractional dust luminosities for the 41 M-dwarfs observedat 70 µ m by Spitzer (Gautier et al. 2007), computed in a simi-lar fashion from their 3 σ flux densities. The figure shows thatthe two sets of data are complementary, and lead to a uniformfractional dust luminosity over a large extent of disk radii forthe dozen of M-dwarfs common to the two data sets. In Fig. 6,we present the corresponding dust masses as a function of r for both samples computed with the optically thin emissionmodel ( e.g. Zuckerman 2001) and the mass opacity κ λ ∝ λ − for λ > µ m and κ µ m = . g − .
5. Discussion
The single cold debris disk found in our surveys (GJ842.2, seedetails in Lestrade et al. (2006), and excluding GJ526 at thisstage) makes the detection fraction to amount to 2 + . − . % in oursample of 50 M-dwarfs. The limits are based on the Binomial Fig. 5.
Constraints for the dust luminosity fraction versus diskradius. Note that the x-axis shows the single radius correspond-ing to the single temperature of a disk (ring) assumed infinitelynarrow in our model. We consider the wide range of radii from1 to 1000 AU as plausible for rings of debris. Upper limits areshown as dashed lines, detections as solid lines. Blue lines cor-respond to the (sub)millimeter observations ; i.e. our sample of50 M-dwarfs for which dark blue is used for ”young” M-dwarfs(ages <
200 Myr) and light blue for ”old” M-dwarfs (likely afew Gyr) ; the two submm disk detected around AU Mic andresolved (Liu et al., 2004, Liu 2004) marked by a single bluedot ; the submm disks detected but not clearly resolved aroundGJ182 (Liu et al. 2004) and around GJ842.2 (Lestrade et al.2006) ; the submm transition disk detected around the pre-mainsequence M1 dwarf TWA7 (Matthews, Kalas, & Wyatt, 2007)was also included. Orange lines correspond to Spitzer 70 µ mobservations ; i.e. the sample of 41 M-dwarfs of Gautier et al.(2007) and the detection of the M0 dwarf HD95650 (Smith etal. 2006). There are 16 M-dwarfs in common between the twosamples. These two sets of data are complementary to constrainthe existence of warm dust around M-dwarfs at moderate radii( <
20 AU) and cold dust at large radii ( >
20 AU). Disk diame-ters probed by the observations are limited by the angular sizeof 60 ′′ for the MAMBO-2 maps, of 28 ′′ for SCUBA wide pho-tometry and of 38 . ′′ for Spitzer aperture photometry (Gautieret al. 2007). Some curves are terminated at less than 1000 AUbecause of these angular limits. The calculation of the frac-tional dust luminosity is described in the text. (This figure isavailable in color in electronic form).distribution for a small number sample and are such that 68%of the probability is between the lower and upper uncertaintiesand the peak probablity is the observed fraction 1 /
50, followingBurgasser et al. (2003). We recall that Gautier et al. (2007) hadno detection in a sample of 62 nearby M-dwarfs at 24 µ m and nodetection in a subsample of 41 of them at 70 µ m, i.e. rate < ff erently, Forbrich et al. (2008) have detected photometricexcesses at 24 µ m tracing warm dust around 11 M-dwarfs inthe young open cluster NGC2457 (20-40 Myr) that represent4 . + . − . % of the 225 highly probable member M-stars identifiedin it. Fig. 6.
Constraints for the dust mass versus disk radius. Notethat the x-axis shows the single radius corresponding to thesingle temperature of a disk (ring) assumed infinitely narrow inour model. We consider the wide range of radii from 1 to 1000AU as plausible for rings of debris. Upper limits are shown asdashed lines, detections as solid lines. Blue lines correspond tothe (sub)millimeter observations and orange lines to the Spitzer70 µ m observations as detailed in the legend of Fig.5. The massopacity used to convert flux density to dust mass with the stan-dard optically thin emission model is κ = . g − at 850 µ mand ∝ λ − for λ > µ m. Additional information are in thetext. (This figure is available in color in electronic form). Fig. 7.
Detection rates of cold debris disks versus stellarmasses (stellar types) for stars younger than 200 Myr. Theserates and uncertainties are for disks having dust fractional lu-minosities larger than the limits shown in Fig. 8 of the (sub)mmsurveys used.To discuss how detectability of cold debris disks dependson the mass of the central star, we have compared our re-sult with the observed fractions of cold debris disks aroundstars more massive than M-dwarfs. In the literature, we find ∼
30 cold debris disks around A-to-K type stars detected bysubmm observations (see Fig 3 and caption of Wyatt 2008).But most of these detections come from JCMT / SCUBA sur- estrade et al.: Debris Disks around M-dwarfs 11
Fig. 8.
Dust luminosity versus disk radius limits of the three(sub)mm surveys used to determine the cold disk fractions of”young” M-, FGK- and A-type stars. Shown are the dust lu-minosity fractions of the 19 youngest M-dwarfs of our sam-ple (blue), of the 9 young A-stars (green) and of the 26 youngFGK-stars (red) in the two 850 µ m surveys of Wyatt, Dent &Greaves (2003) and of Najita & Williams (2005). All thesestars are less than 200 Myr old. Most of the curves are upperlimits (dashed lines). The 7 detections are marked by full lines.This plot emphasizes that for stars of lower masses (later stellartypes), even though the surveys are more sensitive, fewer disksare detected. Note that the x-axis shows the single radius cor-responding to the single temperature of a disk (ring) assumedinfinitely narrow in our model. We consider the wide range ofradii from 1 to 1000 AU as plausible for rings of debris. (Thisfigure is available in color in electronic form).veys of IRAS biased samples, i.e. targets with prior IRAS ex-cess detections, unlike our M-dwarfs, for which no such priorknowledge was used in the selection of the sample. There areonly two submm surveys of A-to-K type stars that are unbiasedin this respect and that have depths of ∼ µ m,comparable to our sensitivity at 1.2 mm : the JCMT survey byNajita & Williams (2005) of thirteen F5-to-K3 stars (10 Myr < ages <
180 Myr, 10 < d <
78 pc, 3 detections) and theJCMT survey by Wyatt, Dent & Greaves (2003) of nine B7-to-A0 stars (86 < d <
938 pc, 2 detections) and of thirteenF3-to-K5 stars (27 < d <
250 pc, 1 detection) that are all partof Lindroos binaries (14 Myr < ages <
170 Myr). Combiningthese two submm surveys, we determine the cold disk fractionsof 22 + − % for young A stars (2 detections /
9) and of 15 + . − . %for young FGK stars (4 / . + . − . %.Therefore, for this age range, there is an apparent trend in thesethree fractions, indicative of fewer cold disks detected for laterstellar types − lower star masses − although at a low statisticalsignificance (Fig 7). Nonetheless this trend is notable becausethe surveys are deeper for later stellar types as shown in Fig 8,for disk radii <
100 AU. Interestingly, this trend has recently been found also at 70 µ m in a sample of A to M stars with agesbetween 8 Myr and 1 Gyr by Plavchan et al (2009).We also determine the cold disk fraction of <
10 % forthe ”old” M-dwarfs of our sample having undetermined agesand likely being as old as the average Galactic disk stars(8 . ± . < M d > ∝ < M ∗ > . ± . , where disk mass < M d > andstar mass < M ∗ > are time-averaged over the star accretionperiod (0.5 to 2.5 Myr). Consequently, less primordial materi-als could limit planet formation around M-dwarfs. Collectingmasses of protoplanetary disks determined by (sub)mm ob-servations in the nearest star forming regions, Natta, Grinin,& Mannings, (2000) found M d ∝ M . ± . ∗ , but Andrews& Williams (2005, 2007) show that M d versus M ∗ in Taurus-Auriga is so widely scattered between 0.001 and 0.2 M ⊙ thatit precludes any meaningful correlation fit. Also, compari-son of disk masses of 6 members of the nearby young TWHydrae Association (TWA) suggests no correlation betweendisk masses and stellar types for these reasonably coeval disks(Matthews, Kalas & Wyatt 2007).Removal of circumstellar dust by the Poynting-Robertsone ff ect and radiation pressure processes are diminished aroundM-dwarfs because they are less luminous than solar-type stars,and so dust generated by collisions in any remnant planetesi-mal belt should remain there longer, giving rise to detectableemission. However, the opposite conclusion has been reachedby Plavchan, Jura & Lipscy, (2005) that highlight the fact thatdust removal around M-dwarfs could be dominated by the dragcaused by strong winds associated with their high coronal andchromospheric activities.Theformationofplanetesimalsandplanets depends on thetime scales between the competing processes of coagulationand evaporation in the early period of accumulation. Theorypredicts that t coag increases and t evap decreases with the centralstar mass and with the strength of the FUV and EUV radia-tion field (eqs 47 and 48 in Adams et al. 2004, respectively).From their Fig 10, it can be seen that more than 10 Myr areneeded to evaporate a protoplanetary disk around a solar-massstar, whereas only a few Myr are required to evaporate the samedisk around a low-mass M-dwarf in a stellar cluster with a mod-erate UV flux of ∼ G . This might quench planet forma-tion around M-dwarfs.Early stripping of planetesimals by passing stars is likelysince most stars are born in clusters where stellar encountersas close as 160 AU are likely in the first 100Myr (Kenyon andBromley 2004b). The disruption of planetesimal disks by close stellar encounters has been studied for the A6 star β Pic byLarwood and Kalas (2001). They found that, depending on thepassing star’s trajectory and on the relative star masses, 1% to48% of the planetesimals are lost after encounters. Related is-sues for planetary systems were also discussed by Malmberg etal. (2007).A Lack of gaseous giant planets around M-dwarfs is pre-dicted by Laughlin, Bodenheimer & Adams (2004), caused bythe longer duration required to build a core of 15 M ⊕ . This lackof giant planets might reduce the production of second gen-eration dust in M-dwarf debris disks because of weaker grav-itationnal stirring (Wilner et al. 2002), diminishing their de-tectability.This series of arguments leads to the expectation that de-bris disks around M-dwarfs might be intrinsically less dustyand therefore more di ffi cult to detect than those around moremassive stars of the same age. However, most of these argu-ments assume that the initial protoplanetary disk mass scaleswith the central star mass, which may be plausible but is obser-vationally not well established.
6. Conclusion
To search for emission from cold debris disks, we have used theMAMBO-2 bolometer camera at the IRAM 30m telescope tomap 42 nearby M-dwarfs at 1.2 mm wavelength to a noise levelof 0.6 to 2.8 mJy per 11” beam. We also reanalyzed our earlierMAMBO-2 and SCUBA data to form a coherent sample of 50M-dwarfs. Only one cold debris disk was detected, surround-ing the M0.5 dwarf GJ842.2. In an attempt to discuss how de-tectability of cold debris disks depends on the mass of the cen-tral star, we have compared this result to the observed fractionsof cold disks for more massive stars in the two submm surveysof Wyatt et al. (2003) and Najita & Williams (2005), who re-port detection rates of 22 + − % for A-stars and 15 + . − . % forFGK-stars with stellar ages between 10 and 180 Myr. For the19 youngest M-dwarfs ( ≤
200 Myr) of our sample, we found adetection rate of 5 . + . − . %. Hence, for this age range, there isa mild trend in these three detections rates, indicative of fewercold debris disks detected for later stellar types − lower starmasses − although at a low statistical significance. Nonethlessthis trend is notable because the sensitivities of these surveysare deeper for later stellar types. We also determine the colddisk fraction of <
10 % for the ”old” M-dwarfs (likely a fewGyr) of our sample, indicative that the cold disk fraction maydecrease with stellar age, as is also seen for warm disks. Futureobservations of a larger and better controlled sample of starsof all stellar types with Herschel in the far-IR and deeper ob-servations in the (sub)mm will be able to better clarify theseissues.
7. Appendix : computation of the dust temperatureand mass for the possible large debris diskaround GJ526
The source that heats dust in debris disks is usually the stel-lar radiation field, but in a large debris disk, as possibly foundaround GJ526, the interstellar radiation field dominates at some
Fig A1 : Variation of the temperature of a grain 100 µ m in diameterexposed to the radiation of the stellar field and of the isotropic inter-stellar radiation field. This latter field dominates at some disk radius R that depends on the stellar luminosity. The saturation temperation of4.9K due to the interstellar field is consistent with the computation ofKr¨ugel (2003, p. 249). For M6 only, the dashed line indicates the graintemperature when the interstellar radiation field is not included. (Thisfigure is available in color in electronic form). radius from the star. We compute this transition radius for sev-eral stellar spectral types by solving numerically the integralequation for a grain at thermal equilibrium absorbing both thestellar and interstellar incident fields : Z + ∞ Q abs ( λ, a ) . (cid:16) π a J ∗ ( λ, r ) + π a J IS RF ( λ ) (cid:17) d λ = Z + ∞ π a Q abs ( λ, a ) π B ( λ, T g ) d λ ( A Q abs ( λ, a ) = λ < λ and Q abs ( λ, a ) = λ /λ with λ = π a for λ > λ , which approximate the absorption ef-ficiency computed for carbon by Laor & Draine (1993). Theparameter a is the radius of a spherical grain. The expression B ( λ, T g ) is the Planck function at grain temperature T g that de-pends on a . The intensity of the stellar radiation field J ∗ ( λ, r ) is π B ( T ∗ , λ ) × (4 π R ∗ / π r ) at disk radius r with the star character-ized by its e ff ective temperature T ∗ and its radius R ∗ . Intensityof the Interstellar Radiation Field J IS RF ( λ ) in the solar neigh-bourhood is : J IS RF ( λ ) = i = X i = C i π B ( λ, T i )with components C = , T = . K , C = × − , T = K , C = − , T = K , C = − , T = K , C = × − , T = K , C = . × − , T = K , C = . × − , T = K , at galactocentric distance10kpc (Mathis, Mezger & Panagia 1983). In Fig A1, we solvednumerically eq (A1) to determine dust temperature T g ( r ) asa function of disk radius in modelling grains with the singlesize 2 a = µ m, typical for submm observations, and forseveral stellar spectral types. For GJ526 (M1.5), this figureshows that the interstellar radiation field becomes dominant at estrade et al.: Debris Disks around M-dwarfs 13 Fig A2 : Variation of temperature as a function of grain radius at500 AU from the M1.5 dwarf GJ526. Similar results are reported byKr¨ugel (2003, p. 249). The discontinuity in the silicate curve arisesfrom the piecewise-defined funtion Q abs ( λ, a ) adopted from Laor &Draine (1993). (This figure is available in color in electronic form). r > dN = N a − . da (Dohnanyi 1969) to compute temperature T g ( a ) as a functionof grain size at r =
500 AU with eq (A1) but modified toinclude the grain size distribution. Temperature increases sig-nificantly for a < µ m which is relevant for M-dwarfs be-cause the grain blow-out size is small. For GJ526 (0.031 L ⊙ ),it is as small as 0.04 µ m for carboneous grains, ignoring thee ff ect of stellar wind drag for this star which has a low coro-nal / chromospheric activity (Log L x = − W ], Schmitt &Liefke, 2004). Finally, we use this temperature function T g ( a )at r =
500 AU to determine the dust mass around GJ526 bymatching the total flux density of the 5 clumps ( S . = . ± d is the dis-tance to the star, the predicted flux density is : S ν = N π d Z a max a min π a Q abs ( ν, a ) . π B ( ν, T g ( a )) . a − . da ( A a min is set by the blow-out size ( a min = . µ mfor GJ526). The limit a max is related to the total dust mass M d = πρ N √ a max for the size distribution above and spheri-cal grains of density ρ . M d is the dust mass probed by the mea-sured flux density at the observing λ . Practically, the grain sizelimit a max is the value that makes convergent the computationof the power emitted by M d over a band 2 b centered on theobserved wavelength (1.2 mm). We adopted the convergencecriterium of 5% to match the relative accuracy of the measuredflux density. In other words, a max is increased until the integralbelow converges to within 5% : Z + . mm + b + . mm − b Z a max a min π a Q abs ( λ, a ) . π B ( λ, T g ( a )) . a − . da d λ ( A Fig A3
SED of carboneous dust around GJ526 based on our model fit-ted to the 1.2 mm flux density. Our model includes the collisional dustsize distribution dN = a − . da and the resulting non-uniform temper-ature for grains of various sizes computed in Fig A2. Superimposed isthe corresponding grey-body model computed with the single graintemperature 4.9 K and standard mass opacity 1 . g − at λ = µ m scaled with the e ffi ciency 210 µ m /λ (see text). (This figureis available in color in electronic form). only if the flux density were measured more accurately. Wefound that a max is ∼ ∼ . b = , , × . r toaccount for spatial distribution of the dust in a ring. They foundthat 95% of the flux density comes from grains and pebbles lessthan 100mm in radius. This is comparable to our determinationof a max and the di ff erence must come from di ff erent functionfor T g ( a ) and their hypothesis of dust spatially distributed.Figs A3 and A4 show the SED of the dust around GJ526based on our model for both carboneous and silicate grainsadjusted to the flux density measured at 1.2 mm. The dustmass determined by our model is between ∼ ∼
10 lu-nar masses. We have added in these figures, the SED based onthe standard grey-body model of optically thin dust emission(Hildebrand 1983 and Zuckerman 2001) : S ν = M d × B ( ν, T g ) × κ abs / d ( A κ abs is conventionally taken to be1 . g − at 850 µ m and is scaled by 210 µ m /λ for λ > µ m. This grey dust mass is about 2 to 4 times larger thanthe one determined by our model. This level of accuracy is typ-ical of dust mass estimates for debris disks, presently.The SED of our model is significantly more extended to theFar-IR and to the radio than the grey-body model when bothmodels match the flux density at λ = . ff erences and thus will probe, inessence, the collisional dust size distribution adopted and thenon-uniform grain temperature. Fig A4
SED of silicate dust around GJ526 based on our model andfitted to the 1.2 mm flux density. Same comments as in Fig A3. (Thisfigure is available in color in electronic form).
Acknowledgements.
We are grateful to the sta ff of the IRAM 30-mtelescope, especially Dr S. Leon, for his dedication in managing theMAMBO-2 pool during the transistion period with the new contralsystem and for his unfailing determination to optimize the science re-turn of the telescope despite harsh conditions. We would like to thankan anonymous referee for his careful reading of the manuscript andconstructive remarks. This research has made use of the SIMBADdatabase and of the VizieR catalog access tool, opera ted at theCentre de Donn´ees Stellaires (CDS), Strasbourg,France. This pub-lication makes use of data products from the Two Micron All SkySurvey, which is a joint project of the University of Massachusettsand the Infrared Processing and Analysis Center / California Instituteof Technology, funded by the National Aeronautics and SpaceAdministration and the National Science Foundation. This publicationhas made use of data products from the SDSS and SDSS-II fundedby the Alfred P. Sloan Foundation, the Participating Institutions,the National Science Foundation, the U.S. Department of Energy,the National Aeronautics and Space Administration, the JapaneseMonbukagakusho, the Max Planck Society, and the Higher EducationFunding Council for England. This work is based in part on observa-tions made with the Spitzer Space Telescope, which is operated by theJet Propulsion Laboratory, California Institute of Technology under acontract with NASA.
ReferencesAdams, F.C., Hollenbach, D., Laughlin, G., Gorti, U., 2004,ApJ, 611, 360.Allard, F., Hauschildt, P. H., Alexander, D. R., Tamanai, A., &Schweitzer, A., 2001, ApJ, 556, 357Andrews, S.M., & Williams, J.P., 2005, ApJ, 631, 1134-1160Andrews, S.M., & Williams, J.P., 2007, ApJ, 671, 1800-1812Augereau, J.-C., & Paploizou, J.C.B., 2004, A & A, 414, 1153Aumann, H. H., Beichman, C. A., Gillett, F. C., de Jong, T.,Houck, J. R., Low, F. J., Neugebauer, G., Walker, R. G.,Wesselius, P. R., 1984, ApJ, 278, 23Backman D.E., Paresce, F., 1993, in Protostars and Planets III,ed. E.H. Levy and J.I. Lumine (Tucson : Univ. Press), 1253Berger D.H., et al., 2006, ApJ, 644, 475Bertoldi, F., et al., 2007, ApJ Suppl., 172, 132 Bryden, G. C., et al., 2006, ApJ, 636, 1098Burgasser, A.J., et al., 2003, ApJ, 586, 512.Chabrier, G. & Bara ff e, I., 1997, A&A, 327, 1039Condon, J.J., et al., 1998, AJ, 115, 1693del Peloso, E.F., et al, 2005, A&A, 440, 1153Diggle, P.J., 2003, in Statistical Analysis of Spatial PointPatterns , Publisher : Hodder Arnold.Dohnanyi, J.S., 1969, J. Geophys. Res., 74, 2531Dominik, C., Decin, G., 2003, ApJ, 583, 626.Dutrey, A., Guilloteau, S., Simon, M., 1994, A&A, 286, 149.Forbrich, J., Lada, C. J., Muench, A. A., Teixeira, P. S., 2008,ApJ, 687, 1107Gautier, T. N., Rieke, G. H., Stansberry, J., Bryden, G. C.,Stapelfeldt, K. R., Werner, M. W., Beichman, C. A. et al.,2007, ApJ, 667, 527Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005,Nature, 435, 466.Greaves, J. S., Holland, W. S., Wyatt, M. C., Dent, W. R. F., etal, 2005, ApJ, 619, 187Greve, T.R., et al, 2004, MNRAS, 354,779Hahn, J.M., Malhotra, R., 1999, AJ, 117, 3041.Hildebrand, R.H., 1983, QJLR astr. Soc., 24, 267Holland, W.S., Greaves, J. S., Zuckerman, B., Webb, R. A.,McCarthy, C., Coulson, I. M., Walther, D. M., Dent, W. R.F., Gear, Walter, K., Robson, I., 1998, Nat., 392, 788-791Kalas, P., Graham, J., Clampin, M., 2005, Nature, 435, 1067Kenyon, S.J., Bromley, B.C., 2004a, AJ, 127, 513-530Kenyon, S.J., Bromley, B.C., 2004b, Nature, 432, 598-602Kreysa, E., Gemnd, H. P., Gromke, J., et al. 1998, in AdvancedTechnology MMW, Radio, and Terahertz Telescopes, ed. T.G. Phillips, SPIE, 3357, 319Krist, J.E., et al., 2005, AJ, 129, 1008Kr¨ugel, E., 2003, in
The Physics of Interstellar Dust , Instituteof Physics Publishing : Series Astronomy & AstrophysicsLarwood, J.D., Kalas, P.G., 2001, MNRAS, 323, 402-416.Laughlin, G., Bodenheimer, P., Adams, F., 2004, ApJ, 612,L73-L76Lestrade, J.-F., Wyatt, M. C., Bertoldi, F., Dent, W. R. F.,Menten, K. M., 2006, A&A, 460, 733Liseau, R. et al., 2008, A&A, 480, 47LLissauer, J.J., 1987, Icarus, 69, 249.Liu, M. C., Matthews, B.C., Williams, J.P., Kalas, P.G., 2004,ApJ, 608, 526Liu, M.C. 2004, Sci, 305, 1442Laor, A. & Draine, B.T., 1993, ApJ, 402, 441Malmberg, D. et al., 2007, MNRAS, 378, 1207Mathis, J.S., Mezger, P.G. & Panagia, N., 1983, A&A, 128, 212Matthews, B.C., Kalas, P.G., Wyatt, M.C., 2007, ApJ, 663,1103Monet, D.G., et al., 2003, AJ, 125, 984.Montes, D., et al., 2001, MNRAS, 328, 45Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005,Nature, 435, 462.Najita, J. and Williams, J.P., 2005, ApJ, 635, 625Natta, A., Grinin, V., Mannings, V., 2000, Protostars andPlanets IV (Book-Tucson : University of Arizona Press), p.559 estrade et al.: Debris Disks around M-dwarfs 15
Plavchan, P., Jura, M., & Lipscy, S.J., 2005, ApJ, 631, 1161Plavchan, P., Werner, M.W., Chen, C.H., Stapelfeldt, K.R., Su,K.Y.L., Stau ffff