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understanding stellar convection and accurately representing it in stellar models remains a formidable challenge .
one of the commonly used treatments for convection is the mixing length theory ( mlt ; * ? ? ?
* ) ,  which represents convection with a characteristic length scale .
the mixing length parameter ( which is the ratio of the mixing length to the pressure scale height , @xmath3 ) sets the specific entropy of the convection zone , which in turn adjusts the stellar radius .
this provides a means of determining the mixing length parameter for the sun , since we have precise constraints on the solar radius .
this solar - calibrated value for the mixing length parameter is usually used to model all other stars , but there is evidence suggesting that this is not the case in reality .    even when properly calibrated to the stellar radius , mlt - like treatments of stellar convection fail to accurately represent inefficient convection .
this failure severely limits the accuracy of the convective envelope boundaries within stellar models .
one such boundary is the superadiabatic layer ( sal ) , which is a region near the surface of stars with convective envelopes .
this layer spans several scale heights and encompasses the transition from efficient convective energy transport to radiative .
radiation hydrodynamic ( rhd ) simulations of the sal have proven to be a useful tool for studying realistic stellar convection .
simulations self - consistently couple the convective envelope to the radiative atmosphere , while including important physical processes such as turbulent pressure .
established by as a feasible technique for studying realistic stellar convection in the sal , rhd simulations have been carried by a number of groups .
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efforts to methodically simulate convection in the @xmath4-@xmath5 plane reveal a significant and systematic variation in convective properties over a broad range in stellar properties .
in addition to stellar properties , the convective dynamics near the stellar surface are affected by the chemical composition of the convective envelope .
the recent observational study by @xcite and theoretical work by @xcite both suggest that the stellar surface convection depends on the chemical composition of the convective envelope .
similar results are obtained by @xcite .
@xcite examined helium abundance in 2d simulations , and found that the helium - free case was characterized by larger velocities and flow structures .
the abundance of helium and its effect on stellar convection , however , has not yet been examined systematically . in this study
we build upon our previous work by adding helium abundance to the parameter space of our simulation grid , and isolate its effect on convection by fixing the other dimensions of parameter space .
it is difficult to measure spectroscopically the helium mass fraction present in stars that are cool enough to have convective envelopes .
asteroseismology permits constraints on the helium abundance through measurements of low degree acoustic modes @xcite , however helium abundance in stars remains largely unconstrained .
the common practice is to use a chemical evolution formula , such as that of @xcite . quite separately from chemical evolution , the helium content may be enriched or depleted in stellar envelopes through processes such as rotationally induced mixing and meridional circulation .
for example , the multiple stellar populations present in @xmath6 centauri can be modeled if rather extreme helium abundances are used .
a recent study by @xcite finds that helium mass fractions in excess of @xmath7 yield the best models for certain ehb stars .
conversely , helium could be depleted in the outer layers of stars as a result of diffusion from the gravitational settling ( * ? ? ?
* etc ) .    in sections [ sec : code ] and [ sec : grid ]
describe the 3d rhd code and the grid of simulations used in this work .
section [ sec : microphysics ] outlines the changes to the microphysics induced by altering the hydrogen mass fraction , and the expected effect that these changes will have on convective dynamics .
we then examine in detail the consequences of hydrogen abundance on various properties extracted from the simulations in sections [ sec : salstructure ] through [ sec : spectral ] .
our code simulates convection by solving the compressible navier - stokes equations with radiative transfer , and has been described in detail in @xcite .
the code is originally based on that of @xcite and @xcite but has updated physics and numerical schemes .
the simulation code uses microphysics that are fully consistent with that of the stellar evolution code yrec .
the equation of state and opacity are taken from the opal tables @xcite and the @xcite opacity tables at low temperatures using the heavy element mixture of @xcite .
for the simulations in this work , radiative transfer was computed using the 3d eddington approximation @xcite in the optically thin layers , and the diffusion approximation in the deeper optically thick layers , however , as @xcite showed , using a different radiative transfer scheme ( rays with long - characteristics ) does not make a substantial difference in the sal below the photosphere .
the computational domain is a cartesian box with periodic boundary conditions on the vertical walls , and the top and bottom surfaces are closed .
spatial curvature and the radial variation of gravity are both negligible .
the domain spans the sal so the bottom surface is well below the superadiabatic peak , and the top surface is in the optically thin radiative layers of the atmosphere .
thus , the space between the two surfaces encompasses the transition from fully convective to fully radiative energy transport .
the strategy for exploring the effect of helium on convection closely mirrors the approach described in @xcite , which dealt only with changes to the mass fraction of metal elements . in this study
, we construct a grid of simulations that covers a range in helium mass fractions .
because the effect of helium may differ between metal - rich and metal - poor stars , we compute our simulations with different hydrogen mass fractions ( @xmath8 , @xmath9 , @xmath10 ) for two different metallicities ( @xmath11 , @xmath12 ) .
the grid of simulations comprises six sets , each with a different chemical composition .
the grid is divided into two groups ( each with three sets ) , corresponding to low and high metallicity .
the sets within a group have fixed metallicity , but different helium abundances .
the range in helium and metallicity is quite large , covering a factor of three in @xmath13 and a factor of @xmath14 in @xmath15 . while large , the range in helium mass fraction is less extreme than what has been used to model some stellar populations , including that of @xmath6 centauri , which @xcite recently modeled with helium enrichments of up to @xmath7 .
the grid of 24 simulations is summarized in table [ tab : grid ] .
the two metallicity groups are denoted with ` a ' and ` b ' for the low- and high - metallicity , respectively .
surface gravity is held fixed at @xmath16 for the entire grid .
the effective temperature for each simulation is an output property , and can not be precisely controlled . as such
, simulations typically can not be directly compared , but each set overlaps in the effective temperature range , allowing for comparisons as a function of radiative flux .    [ cols="^,^,^,^,^,^,^,^",options="header " , ]
the signature of helium abundance on stellar convection is smaller than that of metallicity , but is nonetheless significant .
changes to convective properties are primarily caused by opacity .
the sensitivity of convective properties to helium abundance is because of similar reasons as metallicity described in @xcite , namely , for a given , an increase in opacity in the sal is accompanied by a corresponding decrease in density so that the constant radiative energy flux is maintained .
our simulations show systematically larger convective velocities and overshoot with hotter , larger @xmath15 and smaller @xmath13 .    while similar , the effect of helium is distinct from that of metallicity because of the way in which it changes the equation of state .
the mean molecular weight is more sensitive to helium abundance , particularly in the optically thin layers above the maximum superadiabaticity .
the signature of helium might manifest itself separately from that of metallicity in the details of the velocity field , such as the velocity distribution presented in fig .
[ fig : velocity ] .
the key to isolating the effect of helium may be in comparing the hot upflows and cool downdrafts .
[ fig : velocity ] shows variation in the ` upflow ' peak with @xmath15 , and variation in the extreme edge of the ` downflow ' peak with @xmath13 .
radiation accounts for most of the energy flux from the hot upflowing granules
. consequently , the structure and dynamics of the granules are more sensitive to radiative cooling rates , which vary more strongly with metallicity than helium .
conversely , the downflows are less sensitive to radiative cooling rates , but will be affected by the mean molecular weight .
it is possible that the signature of helium abundance is observable through its effect on the convective overshoot in the atmosphere .
in particular , the curvature of spectral line shapes and the absolute shift of the line cores are sensitive to helium abundance .
provided that the metallicity are well constrained , it might be possible to isolate the effect of helium on the velocity field .
old metal - poor stellar populations often exhibit signs of @xmath0-element enrichment . using a set of simulations
separate from our grid , we have carried out tests to measure the magnitude of the effect of changing the heavy element mixture .
details of the heavy element mixture alter the opacity because of changes in the number of ionized electrons , which affects h@xmath17 opacity .
our simulations show that the effect is quite small ; considerably smaller than the effect of changing @xmath15 or @xmath13 . while @xmath0-element enrichment may have a more substantial effect in the deep interior of the star
, we do not measure a significant dependence on the structure of the sal .
our @xmath0-enhancement tests also verify that the effect of helium could not be accounted for by adjusting the heavy element mixture .
jt is supported by nasa atfp grant #
nnx09aj53 g to sb , and acknowledges a pgs - d scholarship from the natural sciences and engineering research council of canada .
this work was supported in part by the facilities and staff of the yale university faculty of arts and sciences high performance computing center .                                                  ,
b. , ludwig , h .- g .
, & steffen , m. 1999 , in astronomical society of the pacific conference series , vol .
173 , stellar structure : theory and test of connective energy transport , ed .
a.  gimenez , e.  f. guinan , & b.  montesinos , 225
we investigate the effect of helium abundance and @xmath0-element enhancement on the properties of convection in envelopes of solar - like main - sequence stars stars using a grid of 3d radiation hydrodynamic simulations . 
 helium abundance increases the mean molecular weight of the gas , and alters opacity by displacing hydrogen . 
 since the scale of the effect of helium may depend on the metallicity , the grid consists of simulations with three helium abundances ( @xmath1 ) , each with two metallicities ( @xmath2 . 
 we find that changing the helium mass fraction generally affects structure and convective dynamics in a way opposite to that of metallicity . 
 furthermore , the effect is considerably smaller than that of metallicity . 
 the signature of helium differs from that of metallicity in the manner in which the photospheric velocity distribution is affected . . 
 a simple model for spectral line formation suggests that the bisectors and absolute doppler shifts of spectral lines depends on the helium abundance . 
 we look at the effect of @xmath0-element enhancement and find that it has a considerably smaller effect on the convective dynamics in the sal compared to that of helium abundance .