From our data,we can also investigate the frequency of I-band polarized dwarfs per intervals of spectral type.Three intervals have been chosen:from M4.5V to M9.5V,from L0V to L3V,which corresponds to T e?～2500–1900K,and from L3.5V to L8V,corresponding to T e?～1900–1300K.Table5summarizes our results(note that CFHT-BD-Tau4and J1610?00are excluded from the statistics).For the early L-types, there are3positive detections out of20investigated dwarfs(15±9%),while the rate of linear polarization increases notably for the late types(6detections out of14dwarfs,i.e.43±17%).Similar statistics are obtained from the results of M′e nard et al.(2002),although the number of studied objects in their work is relatively small.We note that in our analysis,exposure times were set for each target to approximately compensate for di?erent brightness.Hence,the minimum detection level of polarization and the mean polarimetric errors of both spectral intervals are alike.Despite this,the incidence of high I-band linear polarization appears to be a factor of2–3larger in the coolest L spectral types than in the early L classes. However,we caution that this result may be biased by the uncertainty of the measurements and the fact that very cool atmospheres may be more polarized:to detect low to moderate degrees of polarization, extremely good signal-to-noise ratios are needed.This is,for example,the case of J1707+43,for which we have measured a polarization degree well below0.4%.
We also caution that there are other biases in our sample possibly in?uencing our statistical analysis. Young objects are signi?cantly brighter and easier to detect.This also applies to unresolved multiple systems, particularly those comprised of nearly equal mass components.We have selected our targets to be amongst the brightest sources for their spectral classes.The tidal e?ects of very close binaries suggest nonspherical shapes,which contributes to increase the net polarization.The binary frequency of?eld ultracool dwarfs is recently determined to be about15%in the separation range1.6–16AU(Gizis et al.(2003)).Very little is known for closer orbits,although Gizis et al.(2003)have suggested that the binary fraction is～5%for separations less than1.6AU.We note that we have resolved one double L dwarf in our sample,J1705?05 (L4),for which we do not detect I-band polarization(P≤0.2%).The separation is estimated at less than 1.3arcsec(i.e.less than about14AU at the distance of10.7pc,Kendall et al.(2004)).Further data(e.g. proper motions)are needed to con?rm the physical link of J1705?05.On the other hand,some of the L dwarfs in our sample might have young ages.As very low-mass stars do at early stages of evolution, very young brown dwarfs also happen to harbor disks from which they can accrete(e.g.Natta&Testi (2001);Jayawardhana et al.(2002)).Disks e?ciently polarize the photons from the central object.We cannot provide precise age estimates for each object in our sample because many lack astrometric parallaxes.
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However,warm disks around low-mass stars and brown dwarfs are typically observed at ages below10Myr (e.g.Brandner et al.(2000);Barrado y Navascu′e s&Mart′?n(2003)).The frequency of such young objects among K-and M-type stars in the solar neighborhood(d≤50pc)is very low(～10%).Hence,we do not expect that the biases due to binarity and extreme youth are critical in our analysis.We will address these topics again in Section5.4,where we discuss each polarized dwarf separately.
In general,and on the assumption that our targets have similar ages(with very few exceptions),our polarimetric observations of late-M and L-type dwarfs are qualitatively in agreement with the theoretical assumption that a plethora of dust grain formation and condensation takes place in the outer atmospheric layers of objects with spectral type later than M7(Tsuji et al.(1996)).As clouds form in progressively cooler objects,they become optically thicker and form deeper within the atmosphere.In addition,as T e?decreases,more grain species are formed.Hence,dust and condensates must play a role in the output energy distributions(absorption,scattering,polarization,chemistry,thermal structure).The tropospheric weather pattern predicted for brown dwarfs(Schubert&Zhang(2000))can more easily produce inhomogeneities in the distribution of the clouds by creating local clearings since the turbulent motions are greater.This would make polarization more likely.On the other hand,optical and near-infrared spectra of the coolest dwarfs (T e?<1300K,the T domain)indicate that,for such low temperatures,dust remains in the form of a thin cloud very deep in the photosphere,i.e.dust grains are segregated and precipitated(e.g.Allard et al.(2001); Burrows et al.(2002);Tsuji et al.(2004)).In this way,dust particles are neither a?ecting the atmospheric thermal structure nor blocking nor polarizing the emergent radiation.There are no T-dwarfs in our sample. Furthermore,the coolest objects in our study lie close to the L–T transition,for which models predict the largest dusty coverage of the photosphere.It would be stimulating to extend the polarimetric studies toward cooler types.There is evidence in early T dwarfs(T0–T3)of e?ects of clouds on the emergent spectra(see Marley et al.(2002);Burrows et al.(2002);Burgasser et al.(2002b);Tsuji et al.(2004)).No polarization from scattering is expected for later types.
5.2.Linear polarization and metallicity
We note that the atmospheric chemical abundance,which may play a critical role in polarization,is not well determined for any of the objects in our sample.
Nevertheless,we have included in our study a suspected low-metallicity L-type dwarf,J1610?00(L′e pine et al.(2003)),which was found in a proper motion survey.The near-infrared colors of this object are bluer than expected for solar metallicity L dwarfs(Zapatero Osorio et al.(2004)).This photometric property is consistent with the predictions of theoretical models for metal-depleted ultracool objects.The low-resolution spectrum shown in L′e pine et al.(2003)also indicates that J1610?00has a low metal content.In our sample, there is another dwarf,J1721+33(L3V),displaying bluer near-infrared colors than average by about0.2mag (Cruz et al.(2003)).In addition,J1721+33has signi?cant proper motion,suggesting that it is part of a low-metallicity population.Our polarimetric measurements for this object and J1610?00are consistent with zero polarization.The low number of suspected metal-depleted ultracool dwarfs in our sample does not allow us to discuss the dependence of polarization on metallicity.However,it is expected that the photons of metal-depleted dwarfs are less polarized than those of metal-rich dwarfs because grain formation is far reduced under low metallicity conditions(Allard et al.(2001)).
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5.3.Linear polarization and photometric variability,activity and rotation
A total of18dwarfs in our sample have been photometrically monitored by other groups to investigate I-,J-or K-band variability.Table6presents a summary.The fourth column of the Table indicates whether broad-band photometric variability has been detected(the?lter is also indicated),and the last column provides the bibliographic references.Seven dwarfs have strong variability detections,four display weak variability,and a few show periodic modulations.We note that the photometric data gathered from the literature are not simultaneous to our polarimetry.The amplitudes of the I-band light curves obtained from the literature and from Goldman(2004,062cfb8171fe910ef12df84dmunication)are depicted as a function of linear polarization in Fig.3.Detections and non-detections are plotted with di?erent symbols.Weak photometric variabilities are considered non-detections in the?gure and in the following discussion.
Whether the formation,distribution and evolution of photospheric dust clouds(“meteorology”)is caus-ing the reported photometric variability is not unequivocally con?rmed.Yet,as discussed by the various authors,there are reasons to believe in a connection between photometric variability and dust clouds(see discussions by Mart′?n et al.(2001a);Bailer-Jones(2002);Bailer-Jones&Lamm(2003)).We would also expect some correlation between polarization and variability in ultracool atmospheres.Four likely polar-ized dwarfs have been photometrically monitored(see Table6).They are labeled in Fig.3.Two of them (Kelu1and J1507?16)are reported to be variable,and the other two(J0036+18and J1412+16)have upper limits on the amplitude of their photometric variations.It is worth mentioning that Kelu1,J1507?16and J0036+18show the smallest I-band amplitudes(≤10mmag)in the sample,which contrasts with their high linear polarizations.On the other hand,the?ve dwarfs with larger photometric amplitudes(≥10mmag) and con?rmed variability(open circles without arrows in Fig.3)do not display signi?cant polarization (P≤0.2%).S.Sengupta(2004,062cfb8171fe910ef12df84dmunication)has suggested that?ux variability,if due to dust activity,needs su?ciently optically thick dust clouds.In this medium,polarization would arise by means of multiple scattering processes,which in turn would reduce the degree of polarization as compared to single scattering of photons in optically thin clouds(see Sengupta(2003)).Thus,dwarfs with strong photometric variability may have less polarization because of multiple scattering.On the other hand,dwarfs with weak or no photometric variability(static dust clouds or optically thin cloud layer)may give rise to higher polar-ization.Nevertheless,we strongly remark that more data are needed before we can con?rm(or discard)any relation between polarization and broad-band photometric variability.At best,polarimetric observations and photometric monitoring should be carried out simultaneously.Furthermore,because ultracool dwarfs rotate very rapidly and because of fast tropospheric motions(Schubert&Zhang(2000)),the patterns of clouds are expected to change in a few rotational periods,producing modi?cations in the amplitudes and directions of the polarization.Hence,the detection of variations in both polarimetry and photometric monitoring will provide a strong case for the evolution of dust clouds(“weather”)in ultracool atmospheres.
