All the late-M and L-type targets were selected to be amongst the brightest sources for their classes, and have masses very likely in the interval0.03–0.15M⊙,i.e.very low-mass stars and brown dwarfs.They are located at very nearby distances.The astrometric parallaxes of nine dwarfs in our sample(BRI0021,
–4–
J0036+18,Kelu1,J1439+19,J1507?16,J1658+70,LHS3406,GJ4281,and J2224?01)place them between 7and19pc(Dahn et al.(2002)).On the assumption that the rest of the program dwarfs have similar ages and after comparison of their apparent magnitudes with the mean absolute magnitudes for each spectral type,we deduce that all the targets very likely lie within35pc from the Sun,except for CFHT-BD-Tau4. This M7-type dwarf is a very young brown dwarf member of the Taurus star-forming region(Mart′?n et al. (2001b)),and is presumably located at a distance of140pc.L′e pine et al.(2003)reported an upper limit of 30pc on the distance to the metal-depleted dwarf J1610?00,being the most likely value around16pc.The stellar polarizations(mostly interstellar in origin)recently found by Weitenbeck(2004)correspond to?eld stars that are beyond200pc.Moreover,the optical study of Tamburini et al.(2002),based on more than1000 stars,indicates that the contribution to the polarization by the interstellar medium becomes e?ective only after～70pc.Except for CFHT-BD-Tau4,none of our program dwarfs lies at such long distances.Because of their marked proximity,we do not expect signi?cant polarization induced by the interstellar medium,and we will not attempt to remove the interstellar contribution from our polarimetric measurements.
3.Observations
Polarimetric data were collected with the Calar Alto Faint Object Spectrograph(CAFOS)instrument attached to the2.2-m telescope at the Calar Alto Observatory(Spain).In its imaging polarimetric mode, CAFOS,which is mounted at the Cassegrain focus,is equipped with a Wollaston prism with an e?ective beam separation of18.5arcsec,plus a rotable half-wave retarder plate and a stripe mask.This combination provides the capability to measure linear polarization by means of dual beam imaging polarimetry.CAFOS is also equipped with a SITe2048×2048pixels CCD detector(image scale of0.53arcsec/pixel),which was windowed to the central1024×1024pixels providing a?eld of view of9×9arcmin2.The observations were obtained in the following Universal Time(UT)dates corresponding to three di?erent runs:2003Aug28–31 and Sep02,2004May16–21,and2004Aug12–19.Except for2003Sep02,the remaining2003nights and the2004Aug nights were photometric;the2004May run was hampered by thin cirrus and high relative humidity.
Images were obtained in the Johnson R-and I-band?lters centred on641and850nm,respectively. The passband of these?lters is158(R)and150nm(I).All program objects were observed in the I-band because they are relatively brighter at these wavelengths than at shorter wavelengths,and only two of the targets were observed in the R-band(CFHT-BD-Tau4and J0036+18).Raw data were bias subtracted and ?at-?elded using twilight?at frames,which were taken through each of the broad-band?lters and without the polarizing optics.The complete set of calibration images,i.e.bias and twilight?at frames,were collected every night.We did not detect any systematic variation of these images from night to night.Both program sources and standard stars were observed at the same spot within the detector(around pixel512,512of the windowed frames),which is very close to the optical axis of the telescope/instrument system.For linear polarimetry,we collected images at four di?erent angles of the half-wave retarder plate:0,45,22.5and 67.5deg.We provide in Table1the UT date of the observations,the exposure time and number of images obtained per position of the retarder plate,and the full-width-half-maximum(FWHM)and air mass at the time of the observations.The FWHM as measured on the reduced images ranged from1.0to2.9arcsec.
For the calibration of the polarimetric measurements we observed four high-polarization standard stars, namely Hiltner960,BD+64106(Schmidt,Elston,&Lupie(1992)),Cyg OB27and Cyg OB217(Whittet et al.(1992)),on30di?erent occasions.These stars show linear polarization degrees between3.0%and5.2%in
–5–
the R-and I-bands.The two Cyg OB2standards were observed only in I in the2004May campaing,while Hiltner960and BD+64106were observed in the two?lters on many occasions during the three campaings. This has allowed us to check for the e?ciency and stability of the instrument from night to night and from run to run.Our linear polarization measurements of the reference stars have typical standard deviations of σP=0.03–0.10%(depending on the brightness of the source),and appear to be systematically smaller than the catalog values by a factor of1.071±0.004(I-band).This indicates that an e?ciency correction might be needed.However,the great majority of our program objects does not show signi?cant linear polarization.If some polarization is detected,it is below P=2.5%,and the recti?cation for the instrumental e?ciency loss is of the order of(or even smaller than)the error bar of the measurement.Thus,we have not applied any correction to our data.Regarding the position angle of the polarization vibration,θ,we have determined that there is a zero-point correction,which is?3.2±1.1deg.The instrumental polarization was also checked by measuring two unpolarized standard stars,GD319and BD+284211(Turnshek et al.(1990)),on11 di?erent occasions during the three campaings.All the measurements are compatible with zero polarization within1-σthe error bars,suggesting that the position within the detector at which all sources were observed is free of instrumental polarization.
4.Linear polarimetric results
We have obtained the linear polarization degrees and the polarization angles by calculating the nor-malized Stokes parameters,Q/I and U/I,from the recorded images.These quantities depend on ratios of ?uxes at one?lter;the Q/I parameter is derived from the pair of exposures with the half-wave plate at0deg and45deg,and U/I is computed from the images with the half-wave plate at22.5deg and67.5deg.The mathematical expressions used are as follows:
R2Q=o(0?)/e(0?)
R Q+1
(1)
R2U=o(22.5?)/e(22.5?)
R U+1
(2) P=
Q/I (4)
where o(ordinary)and e(extraordinary)refer to the?uxes of the dual images of the program source on a single frame,and P andθare the linear polarization and the polarization angle,respectively.The quantities R Q and R U,used to evaluate the normalized Stokes parameters,correct for possible?at?aws.Fluxes have been derived using di?erent apertures around the targets:0.5,0.8,1.0,1.2and1.5times the average FWHM of each 062cfb8171fe910ef12df84drger apertures have not been considered to avoid contamination from nearby sources and variable sky contributions.We have?nally chosen the1.0×FWHM aperture because it both minimized the photon contribution of nearby contaminants and maximized the signal-to-noise ratio of the measurements.In case of very good seeing(FWHM≤1.3arcsec),the best aperture was1.2×FWHM.We provide our results in Table2,where the names of the program objects have been abreviated conveniently. The measured Stokes parameters and the degree of linear polarization are listed together with the?lter and Modi?ed Julian Date(MJD)of the observations.Error bars are determined from the standard deviation of the multiple measurements(the great majority of the targets were observed more than once in each position of the half-wave retarder).If only one measure is available,the uncertainty is estimated from the
–6–
various apertures.Whenever there are more than one epoch of observations,e.g.CFHT-BD-Tau4,which was observed on four di?erent nights,we provide the average of all the inpidual measurements together with the error of the mean in Table3.Uncertainties in position angle are not well-de?ned for the unpolarized targets,and thus are not listed in Tables2and3.Note that in Tables2–4all values of Q/I,U/I and P are quoted as measured,i.e.without any correction for instrumental e?ciency loss or correction for the statistical bias which a?ects polarimetry at small values of polarimetric signal-to-noise ratio(e.g.Simmons &Stewart(1985)).
