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to provide accurate observational constraints for pre - main sequence evolutionary models , and thereby improve our understanding of star - formation , it is crucial to measure as accurately as possible the properties ( age , mass , luminosity , etc . ) of individual young stars .
the determination of most of these parameters , however , depends critically on the often poorly known distance to the object under consideration . while the average distance to nearby low - mass star - forming regions ( e.g.  taurus or @xmath0ophiuchus ) has been estimated to about 20% precision using indirect methods ( elias 1978a , b ; kenyon et al .
1994 ; knude & hog 1998 ; bertout & genova 2006 ) , the line - of - sight depth of these regions is largely unknown , and accurate distances to individual objects are still missing .
even the highly successful hipparchos mission ( perryman et al .  1997 ) did little to improve the situation ( bertout et al .
1999 ) because young stars are still heavily embedded in their parental clouds and are , therefore , faint in the optical bands observed by hipparchos .
low - mass young stars often generate non - thermal continuum emission produced by the interaction of free electrons with the intense magnetic fields that tend to exist near their surfaces ( e.g.feigelson & montmerle 1999 ) .
if the magnetic field intensity and the electron energy are sufficient , the resulting compact radio emission can be detected with very long baseline interferometers ( vlbi e.g.andr et al .
the relatively recent possibility of accurately calibrating the phase of vlbi observations of faint , compact radio sources using nearby quasars makes it possible to measure the absolute position of these objects ( or , more precisely , the angular offset between them and the calibrating quasar ) to better than a tenth of a milli - arcsecond ( brisken et al .
2000 , 2002 ; loinard et al .  2005 , 2007 ; torres et al .  2007 ; xu et al .
2006 ; hachisuka et al .
2006 ; hirota et al .
2007 ; sandstrom et al .  2007 ) .
this level of precision is sufficient to constrain the trigonometric parallax of sources within a few hundred parsecs of the sun ( in particular of nearby young stars ) with a precision better than a few percents using multi - epoch vlbi observations . with this goal in mind
, we have initiated a large project aimed at accurately measuring the trigonometric parallax of a sample of magnetically active young stars in the most prominent and often - studied northern star - forming regions within 1 kpc of the sun ( taurus , @xmath0ophiuchus , perseus , serpens , etc . ) using the 10-element very long baseline array ( vlba ) of the national radio astronomy observatory ( nrao ) . here
, we will summarize the results obtained so far in taurus and ophiuchus .
all the observations used here were obtained in the continuum at 3.6 cm ( 8.42 ghz ) with the _ very long baseline array _ ( vlba ) of the _ national radio astronomy observatory _ ( nrao ) .
a total of 7 sources were studied so far : three in taurus ( t tau , hubble 4 , and hde  283572 ) , and four in ophiuchus ( s1 , doar21 , vssg14 , and wl5 ) . in all cases ,
between 6 and 12 observations spread over 1.5 to 2 years were obtained .
the data were edited and calibrated following the standard vlba procedures for phase - referenced observations ( see loinard et al .
2007 , and torres et al .
2007 for details ) .
the displacement of the sources on the celestial sphere is the combination of their trigonometric parallax ( @xmath1 ) and their proper motions ( @xmath2 ) . for isolated sources ( such as hubble 4 , and hde  283572 in our case ) , it is common to consider linear and uniform proper motions , so the right ascension and the declination vary as a function of time @xmath3 as :    @xmath4    where @xmath5 and @xmath6 are the coordinates of the source at a given reference epoch , @xmath7 and @xmath8 are the components of the proper motion , and @xmath9 and @xmath10 are the projections over @xmath11 and @xmath12 , respectively , of the parallactic ellipse .    for sources in multiple systems , however , the proper motions are affected by the gravitational influence of the other members of the system . as a consequence ,
the motions are curved and accelerated , rather than linear and uniform . if the orbital period is long compared with the timespan covered by the observations ( as will be the case for t tau see loinard et al .
2003 ) , it is sufficient to include a uniform acceleration in the fit .
this leads to functions of the form :    .distances to the sources in taurus and ophiuchus [ cols="<,^,^,^,^,^,^,^",options="header " , ]     @xmath13    where @xmath14 and @xmath15 are the proper motions at a reference epoch , and @xmath16 and @xmath17 are the projections of the uniform acceleration ( see fig
.  1 for a comparison between fits with and without acceleration terms ) .
finally , if a source is a member of a multiple system whose orbital period is shorter than , or comparable with the timespan covered by the observations ( as will be the case for all ophiuchus sources ) , then a full keplerian fit is needed , but additionnal observations are required to properly constrain that fit .
these observations are currently being obtained for all ophiuchus sources , but are not yet analyzed . as a consequence ,
the fits presented bellow for the ophiuchus sources are based on eqs .
[ uni1 ] and [ uni2 ] .
the resulting uncertainties will be much larger than for the sources in taurus because the orbital motions generate an unmodelled scatter around the mean positions of the sources .
these increased errors should disappear once we include the new observations , and perform a full keplerian fit .
the distance to the seven sources studied here are given in tab .  1 .
for the taurus sources , hipparchos parralaxes ( bertout et al .
1999 ) , and/or estimates based on a modified convergent point method ( bertout & genova 2006 ) are available .
our measurements are always consistent with these values , but are one to two orders of magnitude more accurate . only one other source in taurus ( v773 tau ; lestrade et al.1999 )
has a vlbi - based parallax determination . taking the mean of that and our 3 measurements
, we estimate the mean distance to the taurus cluster to be @xmath18 = 137 pc .
the dispersion about that mean leads to a full width at half maximum depth of about 20 pc , comparable to the linear extent of taurus on the plane of the sky .
traditionnaly assumed to be at a distance of 165 pc ( chini 1981 ) , ophiuchus has recently been proposed to be somewhat nearer , at 120 pc ( knude & hog 1998 ) .
interestingly , two of our sources are consistent with the traditionnal value , but the other two are consistent with a distance of 120 pc . since ophiuchus is only a few parsecs across on the plane of the sky , it is very unlikely to be 40 pc deep .
it is noteworthy that the two sources at about 120 pc ( s1 and doar21 ) are associated with the sub - condensation oph a , whereas the two sources at @xmath19 165 pc ( vssg14 and wl5 ) are associated with the condensation oph b ( see motte et al .
1998 for an overview of the ophiuchus complex ) .
thus , a plausible explanation of our results is that two physically unrelated star - forming regions are located along the line - of - sight toward ophiuchus .
interestingly , knude & hog ( 1998 ) noticed an effect that would be consistent with this possibility in their analysis of extinction towards ophiuchus . while a clear extinction step was clearly visible at 120 pc
, extinction was apparently extending up to about 160 pc .
additional vlbi observations will be needed to confirm the existence of two regions of star - formation towards ophiuchus , and to investigate at which distance the other condensations in ophiuchus are located .
the present results show that vlba observations of non - thermal sources associated with young stars have the potential to improve very significantly our knowledge of the space distribution of star - forming regions in the solar neighborod .
indeed , the precision obtained by these measurements is even sufficient to probe the 3d structure of star - forming regions . coupled with pre - main sequence evolutionnary models , such information could be used to reconstruct the history of star - formation with individual regions .
using phase - referenced multi - epoch _ very long baseline array _ observations , we have measured the trigonometric parallax of several young stars in the taurus and ophiuchus star - forming regions with unprecedented accuracy . the mean distance to the taurus complex 
 was found to be about 140 pc , and its depth around 20 pc , comparable to the linear extent of taurus on the plane of the sky . in ophiuchus , 
 4 sources were observed so far . 
 two of them were found to be at about 160 pc ( the distance traditionally attributed to ophiuchus ) , while the other 2 are at about 120 pc . 
 since the entire ophiuchus complex is only a few parsecs across , this difference is unlikely to reflect the depth of the region . 
 instead , we argue that two physically unrelated sites of star - formation are located along the line of sight toward ophiuchus .