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because essentially all known protostellar or pre - main sequence objects show evidence of winds , jets , or outflows , the current thinking is concentrated on a picture of simultaneous infall and outflow , in which infall and accretion occur towards the protostellar equatorial regions , and a wind breaks out along the poles ( e.g. @xcite ) .
yet early thinking on the stages of young stellar evolution identified a phase in which infall directly strikes the protostellar surface , with no outflow present @xcite .
no clear examples are known of such protostars . in this contribution
i consider limits on the timescale for purely - accreting objects in the context of the standard model of inside - out collapse from a molecular cloud core .
the mathematical formulation is a generalization of @xcite , dropping the assumptions of normal force balance and quasi - stationarity to permit full time - dependence and dynamical expansion ( or collapse ) .
the inside - out collapse of a singular , isothermal sphere yields a mass accretion rate @xmath4 at the center @xcite . here
@xmath2 is the isothermal sound speed in the cloud core . at the origin
is a protostar whose mass grows linearly in time @xmath5 , where @xmath6 is the time since the start of collapse . in the presence of initial , solid - body rotation ,
the infall is distorted , and accretion occurs preferentially onto the circumstellar disk @xcite .
the natural length scale of the distortion is the centrifugal radius @xmath7 , which grows as @xmath8 .
i turn on a wind at the stellar surface , of radius @xmath9 , and numerically determine whether it can halt infall and escape . at early times ,
@xmath10 and the accretion is nearly isotropic , making breakout of the wind difficult . at late times ,
when @xmath11 , escape becomes easy along the poles .    for simplicity , the wind is assumed isotropic and of constant speed @xmath1 , and mass - loss rate @xmath0 .
the wind and infall collide supersonically , and a shocked shell forms .
low speeds imply rapid cooling and a geometrically thin shell .
the dynamics of such time - dependent , thin shells has been discussed in detail by @xcite .
i include the inputs of mass and momentum from infall , the wind , and the gravitational force due to the protostar .
for a given evolutionary time and ratio @xmath12 , i determine the minimum wind speed necessary to break out of the infalling flow .
figure  [ fig : riseandfall ] shows an example calculation of a shell that fails to escape and falls back to the star . in this case , a modest increase in wind speed dramatically changes the outcome , permitting breakout of the shell from the infall region .
i solved the problem in dimensionless form , which reduces the parameter space from six ( @xmath13 ) to three dimensions ( nondimensional time @xmath14 , wind speed @xmath15 , and @xmath16 ) . as a result
, the parameter space has been fully explored .
figure  [ fig : nofit ] shows the critical wind speed for breakout . when the wind ram pressure exceeds the infall ram pressure at the stellar surface , the wind may initially push the shell upwards .
but if the wind speed is less than the critical speed , the shell stalls and falls back .
this is the trapped wind stage . in figure
[ fig : nonsteady ] , its duration is the time between the dashed ( ram pressure balance ) curve and the solid one ( critical wind speed ) for a given ratio @xmath17 .
the results of figures  [ fig : nofit ] and  [ fig : nonsteady ] may be easily scaled to apply to _ anisotropic _ winds , by comparing to an equivalent , isotropic wind having the same mass and momentum loss rates along the z - axis .
indeed , at early times , the evolution is primarily determined by the momentum loss rate of the wind in this direction . at late times , it is the wind speed rather than momentum loss rate that determines breakout .
it is hoped that these semi - analytic results will inspire more detailed exploration of this problem with fully radiative hydrodynamic simulations .
the existing literature ( e.g.  @xcite ) on this is not immediately comparable because they have used a different density law which is self - similar , unlike that of cassen & moosman .
moreover , i argue that initial conditions with wind velocity much greater than the critical velocity are unphysical , as such a strong wind would have broken out at an earlier time , unless the wind itself evolves strongly with time .
strong collimation of wind by anisotropic infall is not seen in the current calculations , although further exploration of this issue is forthcoming .
i note that numerical simulations demonstrating strong collimation due to the circumstellar density asymmetry ( e.g.  @xcite ) have assumed a much more asymmetric density field than that used here .
i am grateful to the observatoire de la cte dazur for a henri poincar fellowship and to the dpartement fresnel , umrs 5528 for hosting my postdoctoral stay in france .
i also thank conacyt / mxico for financial support and s.stahler for encouragement in this work .
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the time of protostellar wind breakout may be determined by the evolution of the infalling flow , rather than any sudden change in the central engine . 
 i examine the transition from pure infall to outflow , in the context of the inside - out collapse of a rotating molecular cloud core . 
 i have followed numerically the motion of the shocked shell created by the impact of a stellar wind and infalling gas . 
 these fully time - dependent calculations include cases both where the shell falls back to the stellar surface , and where it breaks out as a true outflow . assuming a wind launched from the protostellar surface , the breakout time is determined in terms of the parameters describing the wind ( @xmath0 , @xmath1 ) and collapsing cloud core ( @xmath2 , @xmath3 ) . 
 the trapped wind phase consists of a wind sufficiently strong to push material back from the stellar surface , but too weak to carry the heavy , shocked infall out of the star s gravitational potential . to produce a large - scale outflow 
 , the shocked material must be able to climb out of the star s gravitational potential well , carrying with it the dense , swept - up infall .