Optical Linear Polarization of Late M- and L-Type Dwarfs(3)

To select the likely polarized sources amongst our targets,we have applied the following criterion: the derived degree of polarization must exceed three times the associated uncertainty(P/σP≥3).On the assumption of a Gaussian distribution of the measurements within their error bars,such a criterion sets the con?dence of positive detections at the level of99%.If U/I is lacking,we have used Q/I as an indicator for the presence of some polarization.In our sample,eleven objects appear to show signi?cant polarization in either the R-band or the I-band or both;they are presented in Table4and are clearly marked in all the Figures of this paper.Along with their spectral types,polarization degrees,position angles of the plane of vibration,and their associated uncertainties,Table4also lists the quantity P/σP,the equivalent widths (if detected spectroscopically)of Hαemission and Li iλ670.8nm absorption,projected rotational velocities and evidence for infrared or near-infrared?ux excesses.The spectroscopic information has been gathered from the literature(Ruiz et al.(1997);Mart′?n et al.(1998),(2001b);Kirkpatrick et al.(1999),(2000); Basri et al.(2000);Schweitzer et al.(2001);Liebert et al.(2003);Jayawardhana et al.(2003);Cruz et al.(2003);Bailer-Jones(2004)),while the evidence for infrared excesses is based on the recent L′and M′photometric measurements by Liu et al.(2003)and Golimowski et al.(2004).We will relate the photometric and spectroscopic properties of each object to its measured polarization in Section5.4.

Our Q/I and U/I measurements are plotted in Fig.1.This plot provides a graphical summary of Tables2and3and illustrates our criterion for polarization.It also shows the symmetrical distribution of the null polarimetric measurements around(0,0),i.e.there is no obvious instrumental bias in our data. The I-band polarization degree is depicted against spectral type in Fig.2.Note that we have labeled the T e?–spectral class calibrations of Dahn et al.(2002)and Vrba et al.(2004)in Fig.2.Three of our targets (J0036+18,J2057?02,and J2224?01)are in common with the previous work of M′e nard et al.(2002). Except for J0036+18,which is polarized according to these authors,our values of I-band linear polarization are in full agreement with their measurements within1σthe error bars.We note,however,that the central wavelength and the passband of the I Bessel?lter used by M′e nard et al.is bluer than those of the I Johnson ?lter used by us.Actually,the passband of the I Bessel?lter appears somewhat intermediate between the Johnson R-and I-bands.

5.Discussion

There are several possible mechanisms that could account for the observed linear polarization of ultra-cool dwarfs:(i)interstellar polarization,(ii)polarization due to strong magnetic?elds(Zeeman splitting, synchrotron emission),(iii)scattering by photospheric particulates of dust,and(iv)scattering by the grains of cool shells or disks around the central dwarf.In Sect.2,we have argued that an interstellar origin for the linear polarization of our objects is unlikely because of their very short distances.M′e nard et al.(2002) discussed widely the three former possible origins(they did not mention the fourth possibility),concluding that,pending de?nitive measurements of the magnetic?elds of ultracool dwarfs,scattering by photospheric

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dust grains remains the most likely origin for the polarization.We also agree with their discussion(and will not repeat it here),coupled with the fact that the presence of circum(sub)stellar disks plays a role in the polarization of the photospheric radiation in very young ultracool dwarfs,as in T Tauri stars.

5.1.Linear polarization and spectral type

Of the total of45targets with spectral types ranging from～M5V to L7.5V,eleven appear to show some degree of polarization(Table4).For these,we have measured I-band polarimetric amplitudes in the interval0.2–2.5%.These values are in agreement with the predictions of Sengupta&Krishan(2001), which were calculated for the case of dust scattering in oblate dwarfs.One of our likely polarized targets is CFHT-BD-Tau4,the young brown dwarf of the Taurus star-forming region(Mart′?n et al.(2001b)).As will be discussed below,a photospheric origin for its observed linear polarization is unlikely,and we rule this object out from the following statistical analysis.We will also remove J1610?00because the metallicity of this dwarf is considerably below solar(L′e pine et al.(2003)).

The rate of intrinsically polarized ultracool dwarfs in our sample with spectral types in the interval L0V–L7.5V turns out to be29±9%,which is below the50%estimated by M′e nard et al.(2002).The larger error bars of our measurements have prevented us from easily detecting polarization dregrees smaller than about0.4%,which is at least4times higher than what M′e nard et al.can measure from their FORS1/VLT data.Observations with better accuracy may con?rm polarization of dwarfs that show marginal detection in our study.Hence,the frequency of29%has to be understood as a lower limit on the ocurrence of linear polarization amongst solar metallicity,?eld L-type dwarfs.This fraction is remarkably high when compared to the frequencies of polarized stars of warmer spectral types,which are typically below10%(see Leroy (1999)).Very recently,M′e nard&Delfosse(2004)have analized20nearby?eld dwarfs spanning spectral classes M1to M6,and have found that all their measurements are compatible with a null polarization. Furthermore,in our sample there are9?eld dwarfs with types ranging from mid-M to very late-M(M9.5V). If the I-band polarization rate of29%were valid for M dwarfs,we would expect to?nd2–3M-type polarized stars in our sample.However,we do not detect signi?cant polarization in any of the M-type?eld targets, which suggests that,at95%con?dence,less than28%of M dwarfs are polarized.Hence,at far-red optical wavelengths,the frequency of highly polarized L-type dwarfs is clearly larger than that of M dwarfs.

This is an evidence for the existence of e?cient dust scattering processes in L-type atmospheres.As will be mentioned in Section5.3,L dwarfs are on average less active than M stars(Gizis et al.(2000)). In addition,L-type atmospheres are more neutral and present higher resistivities because of their lower temperatures;hence,we do not expect the magnetic?elds of L dwarfs to be stronger than those of M stars (see Mohanty et al.(2002)).Furthermore,the weakening of oxides(TiO,VO)in late-M and early-L types and of hydrides(FeH,CrH)at cooler types indicates that the metals like Ti,V and Fe gradually vanish from the gas phase(Mart′?n et al.(1999a);Kirkpatrick et al.(1999)).This occurs at temperatures for which models predict the formation of condensates(Tsuji et al.(1996);Allard et al.(2001)).These phenomena coupled with our polarimetric detections and those of M′e nard et al.(2002)support the presence of signi?cant amounts of dust in ultracool atmospheres.

Also relevant is the study of the degree of linear polarization as a function of the L subtypes(or T e?between2500and1400K).Figure2depicts our results.We shall now focus on the dwarfs with detected polarization according to our criterion.There is a hint for cooler dwarfs displaying larger linear polarization degrees,i.e.the polarization of the I-band radiation seems to be more powerful at low temperatures.The

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dwarfs J2244+20(L6.5V)and J1507?16(L5V),two of the latest objects in our sample,show the largest measured linear polarizations,P=2.5±0.5%and1.36±0.30%,respectively.These values contrast with the moderate polarization observed in the much warmer dwarf J1707+43(L0.5V,P=0.23±0.06%).Interme-diate objects display polarizations between those of the L0.5V and L6.5V dwarfs.Such a trend was also mentioned by M′e nard et al.(2002).Either di?erent sources or mechanisms are inducing the polarization or the trend is possibly related to the rate of grain formation and the vertical distribution of the clouds. As pointed out by Sengupta(2003),there are several possibilities to polarize the radiation via scattering (spherical and nonspherical grains in spherical and oblate photospheres,random distribution of condensates, and presence of dust bands).The more possibilities working at the same time,the larger the polarization. The trend might also be associated to a faster rotation of the coolest dwarfs.However,Mohanty&Basri (2003)and Bailer-Jones(2004)noted that the projected rotational velocities of L0–L8?eld dwarfs show no obvious trend with spectral type.Nevertheless,more polarimetric observations and higher accuracies are required to con?rm this dependency.Theoretically,the metal content is also a key parameter in the rate of grain formation(Allard et al.(2001));hence,changes in the metallicity of ultracool dwarfs may also account for possible scatter in the polarization amplitudes of Fig.2.

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