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in our universe , dark matter halos evolve in the hierarchical fashion . smallest microhalos form first , and they merge with each other to form larger halos . the size of the smallest microhalos is determined by the scale of collisional damping and free streaming of dark matter particles . analytical studies @xcite predicted their mass to be @xmath3 , though uncertainty in theory of supersymmetry enlarges the interval further . early studies @xcite suggested that a significant fraction of microhalos born in early universe have survived up to present time , and they might be observed as the dominant sources of the annihilation signal . these microhalos could enhance the annihilation signal by a factor of 2 to 5 @xcite , whose signature might have already been observed as electron and positron excess [ pamela @xcite , atic @xcite , ppb - bets @xcite , and fermi @xcite ] . @xcite simulated the formation of microhalos using @xmath4-body simulations . they argued that the density profiles were well fitted by a single power law , @xmath5 , with slope @xmath6 in the range of 1.5 to 2 down to the radius of @xmath7 pc and that most of microhalos will survive against galactic tidal field and encounters with stars .    on the other hand , @xcite argued that the fraction of the mass in subhalos in the solar neighborhood was significantly lower than that averaged over the entire halo . they assumed that the spatial distribution of the microhalos is the same as that of subhalos with mass @xmath8 , and concluded that the microhalos have a negligible impact on detectability . however , it is not clear whether their result for subhalos with a mass @xmath8 can be used to estimate the distribution of halos of @xmath9 . since earth - mass subhalos contain no substructures by definition , their central structures can be completely different from that of more massive halos which contain many substructures . however , there is no simulation of earth - mass halos with sufficient resolution to study the their central structure , so far . @xcite used mass resolution of @xmath10 , which was too low to determine the central structures of microhalos .    in this letter , we report the result of cosmological @xmath4-body simulations with 100 times better mass resolution and 20 times better spatial resolution compared to that used in the previous work @xcite . we performed two high resolution cosmological @xmath4-body simulations . the number of particles is @xmath11 . the size of the simulation box is 30 comoving parsecs with periodic boundary condition . the mass of particles is @xmath12 . for the time integration , we used the greem code @xcite . we used a leapfrog integrator with shared and adaptive time steps . the step size was determined as @xmath13 ( minimum of these two values for all particles ) . we simulated them from @xmath14 to @xmath15 . the ( plummer ) softening length @xmath16 was constant in the comoving coordinate from @xmath14 to @xmath17 , and constant in the physical coordinate ( @xmath18 pc ) from @xmath17 to @xmath19 . to generate the initial particle distribution , we used the mpgrafic package @xcite . we considered two models with different initial matter power spectra .    the matter power spectrum in model a includes the sharp cutoff corresponding to dark matter particle with a mass of 100gev @xcite . the power spectrum of model b is without cutoff . the cosmological parameters adopted are based on the concordance cosmological model [ wmap1 @xcite , @xmath20 . however , we used @xmath21 to be close to recent observational ones @xcite . we did not put any thermal velocities in initial setup of model a to avoid unphysical density fluctuations in small scales @xcite . figure [ fig : snapshot ] shows the snapshots of our simulated universe at @xmath19 . we can see that there are no substructures in one halo of model a , except for caustics generated by non - linear growth of long - wavelength fluctuations . this structure is quite similar to what we see in warm dark matter simulation ( e.g. * ? ? ? * ; * ? ? ? * ) , and different from that of galaxy - sized or larger dark - matter halos @xcite . the difference comes simply from the initial condition . our microhalos do not contain smaller fluctuations inside .     for our standard model ( a ) and model without free - streaming cutoff ( b ) . the width of the images correspond to 12 comoving pc . images in the squares are enlargements of single halos . the size of the squares is 0.6 comoving pc ( 4900aus in physical units ) . , width=491 ]    . four panels show the density , velocity dispersion , phase - space density , and accumulated mass . circles show profiles of a low resolution simulation ( a512 : @xmath22 particles , @xmath23 pc softening length ) . two out of three profiles ( middle and bottom ) are vertically shifted downward by 1 and 2 dex . in the panel of phase - space density profiles , the two profiles ( middle and bottom ) are shifted by 2 and 4 dex . , title="fig:",width=302 ] . four panels show the density , velocity dispersion , phase - space density , and accumulated mass . circles show profiles of a low resolution simulation ( a512 : @xmath22 particles , @xmath23 pc softening length ) . two out of three profiles ( middle and bottom ) are vertically shifted downward by 1 and 2 dex . in the panel of phase - space density profiles , the two profiles ( middle and bottom ) are shifted by 2 and 4 dex . , title="fig:",width=302 ] . four panels show the density , velocity dispersion , phase - space density , and accumulated mass . circles show profiles of a low resolution simulation ( a512 : @xmath22 particles , @xmath23 pc softening length ) . two out of three profiles ( middle and bottom ) are vertically shifted downward by 1 and 2 dex . in the panel of phase - space density profiles , the two profiles ( middle and bottom ) are shifted by 2 and 4 dex . , title="fig:",width=302 ] . four panels show the density , velocity dispersion , phase - space density , and accumulated mass . circles show profiles of a low resolution simulation ( a512 : @xmath22 particles , @xmath23 pc softening length ) . two out of three profiles ( middle and bottom ) are vertically shifted downward by 1 and 2 dex . in the panel of phase - space density profiles , the two profiles ( middle and bottom ) are shifted by 2 and 4 dex . , title="fig:",width=302 ] figure [ fig : profile ] shows the spherically - averaged structures of three most massive halos . we also performed a low resolution simulation of model a for convergence check ( the number of particles was @xmath22 and the softening length was @xmath24 pc ) . two results are identical outside the softening radius . the central density slope for model a is considerably steeper than that for model b. the result of model b is similar to that of large - scale cosmological simulations @xcite . the result of model a is consistent with being a single power law of @xmath1 , for quite a wide range in the radius . our result is reliable down to @xmath25 pc , where the density reaches more than @xmath26 . the left - lower panel of figure [ fig : profile ] shows the rough estimate of the phase - space density given by @xmath27 , where @xmath28 is the velocity dispersion . the slope is close to @xmath29 for @xmath30 pc . because of liouville s theorem , this phase space density can not exceed the initial value at the time of decoupling , which is @xmath31 . thus , the gravitational collapse of the cusp stops at the radius at which the phase space density reaches this limit . this radius and density there are @xmath32 and @xmath33 . we , therefore , can safely conclude the density profile of microhalos is @xmath34 and @xmath35 for @xmath36 . this profile is consistent with the results of early studies of the collapse of self - gravitating gaseous spheres @xcite and recent high resolution simulations of cold collapse @xcite and warm dark matter @xcite . the average density of these earth - mass halos is affected by density fluctuations of larger scales . however , our simulations do not contain large scale fluctuations . as seen in figure [ fig : psfunc ] , press - schechter @xcite theory predicts that the average formation epoch of microhalos is earlier if we take into account larger scale fluctuations . since the average density of a microhalo should be proportional to the cube of its formation redshift , most microhalos should have higher average density than these in our calculation . for simplicity , we use the profile of equation ( [ eq : profile ] ) to estimate the chance of survival of these halos . the tidal cutoff radius of microhalo with the density profile of equation ( [ eq : profile ] ) due to galactic tide is expressed as @xmath37 , where @xmath38 is the distance from the galactic center , if we assume an isothermal halo with the rotation velocity of 220 km / s . we can see that these halos can easily survive at the distance 1kpc , and even at the distance 0.1kpc , the central @xmath25 pc of the halo would still survive .    can encounters with stars destroy the internal cusps of microhalos @xcite ? since the surface number density of disk stars is about 100 @xmath39 at the solar neighborhood , the closest distance a halo with the orbital period of the order of 100 myrs can approach to a star in the hubble time is @xmath40 pc . figure [ fig : encounter ] shows the result of encounter with a @xmath41 star moving at @xmath42 . we selected the most massive microhalo at @xmath19 from the simulation of model a ( the cutoff radius is two times virial value ) , and added velocities on each particle according to the impulsive approximation . then , we simulated the evolution of the microhalo for 27myr after the encounter . we can see that the regions of radius @xmath7 pc survives after encounters with the impact parameters of @xmath43 pcs . theoretically , the cutoff radius due to encounter for the power - law cusp with slope @xmath44 is given by @xmath45 , where @xmath46 is the impact parameter . therefore , the complete disruption requires an encounter with @xmath47 . such close encounters are expected only at the very central regions of the galaxy ( 20pc or less from the center ) . . only particles within the radius of 0.037 pc from the center of the halo are shown . panel b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ] . only particles within the radius of 0.037 pc from the center of the halo are shown . panel b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ] . only particles within the radius of 0.037 pc from the center of the halo are shown . panel b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ] . only particles within the radius of 0.037 pc from the center of the halo are shown . panel b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ] . only particles within the radius of 0.037 pc from the center of the halo are shown . panel b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ] . only particles within the radius of 0.037 pc from the center of the halo are shown . b ( top - middle ) , c ( top - right ) , d ( bottom - left ) , and e ( bottom - middle ) show the distribution of particles at 27 myrs after the encounter with a solar - mass star with the impact parameters @xmath48pc , @xmath49pc , @xmath50pc , and @xmath51pc . the black regions in the center are caused by the initial outer cutoff of the particle distribution and are not real . the upper right box in each panel shows the central region of the microhalo . the central regions are located at the center ( panel a and b ) , and the positions indicated by arrows ( panel c and d ) . in panel e , the central region is destroyed completely . panel f ( bottom - right ) shows the density profiles after the encounter . , title="fig:",width=204 ]    if we extrapolate the subhalo mass function @xmath52 @xcite to the mass of microhalos , the number of microhalos in our galaxy is @xmath53 ( we assumed the mass function @xmath54 ) . the number density of the microhalos near the solar neighborhood is @xmath55 , if the distribution of the microhalos is the same as that of the background dark matter . this extrapolation is justified by the fact that the microhalos survive under tides from our milky way galaxy . note that the above estimate takes into account the effect of merging between small halos and accretion to somewhat larger halo since we extrapolated the mass function obtained by @xmath4-body simulation . the gamma - ray flux of a microhalo is given by @xmath56 where @xmath57 is the number of emitted photon per annihilation , @xmath58 is the mass of dark matter particle , @xmath59 is the interaction cross section of dark matter , and @xmath60 is the outer cutoff radius of a microhalo at which the slope of the density becomes steeper than @xmath44 . mass loss due to the galactic tide or encounters with stars changes @xmath60 of microhalos , but does not affect @xmath61 or @xmath62 except in the cases of extremely close encounters , as we can see in figure 3 . therefore , they have relatively minor effect on the gamma - ray luminosity . after 99% of the mass is lost from a microhalo , it still retains nearly 50% of the luminosity . thus , we can assume that the tidal stripping has practically no effect on the gamma - ray luminosity of our earth - mass halos . these results supports the predictions of early analytical studies @xcite . here , we consider how the gamma - ray flux of the microhalo depends on its formation epoch . the average density of a halo @xmath63 reflects the cosmic density at its formation time @xcite . since the cosmic density is proportional to @xmath64 , @xmath65 , where @xmath66 and @xmath67 is the formation redshift and the typical formation redshift of microhalos in our simulations . from the conservation of the mass , we can derive @xmath68 . we can rewrite @xmath69 in equation ( [ eq : gammarayflux2 ] ) as @xmath70 using equation ( [ eq : profile ] ) . therefore , @xmath71 here , we drop the dependency of the formation redshift in the logarithmic term in equation ( [ eq : gammarayflux2 ] ) , since it is rather weak ( @xmath72 ) . the average boost factor due to the formation epoch is determined as @xmath73 where @xmath74 is the distribution function of the formation epoch . for the ps function in figure [ fig : psfunc ] , its value is @xmath0 1.6 . we apply this boost factor to estimate the gamma - ray luminosity . there are many works on whether or not subhalos and microhalos can be observed via annihilation gamma - ray ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we made the all sky map of the gamma - ray annihilation signal in our galaxy based on the new profile of the microhalo . the observer locates at 8.5 kpc from the center of the halo along its long axis . we consider the emissions from microhalos only . we assume the spatial distribution of microhalos follows the mass distribution of a galaxy sized lcdm halo selected from our previous simulation @xcite . thus , our all - sky map naturally include all subhalos with the mass larger than numerical limit ( @xmath75 ) . in addition , destruction due to encounters with stars are taken into account . we assumed a exponential disk with the surface density , @xmath76 , where @xmath77 is the distance from the galactic center . from the position of an ensemble of microhalos , the impact parameter @xmath46 of encounters with stars are calculated . then , we use the cutoff radius @xmath78 and reduce the gamma - ray luminosity .    in order to include the luminosities of nearby microhalos , we placed randomly 2000 microhalos less than 1pc from the observer . the distribution of formation redshift and the gamma - ray flux of microhalos are given by figure [ fig : psfunc ] and equation ( [ eq : gammarayflux3 ] ) . figure [ fig : gamma - ray ] shows the all sky map . many nearby microhalos are observed as pointlike sources , since their angular size is around 1. therefore , the nearby microhalos are promising sources of gamma - ray signal of the annihilation of dark matter particles . their distance is around @xmath79 and velocity is of the order of @xmath80 . the proper motion is as large as 0.2 deg / year . they might be too dim to be observed by fermi . sommerfeld effect could boost the interaction cross section of dark matter , and enhance by orders of magnitude the gamma - ray luminosity @xcite . these microhalos might be good targets of next generation cherenkov telescope , such as cta . bright microhalos enhance luminosities of all subhalos ( including known milky way satellite ) since subhalos contain a number of microhalos . the brightest gamma - ray source is the integrated emission of microhalos in the galactic center , but it is much more extended compared to the result of previous studies @xcite . these sources may be also good targets for observation . however , baryons would have significant effect on the distribution of dark matter at the center of the galaxy . if baryons disrupt the central cusp of the main halo @xcite , gamma - ray flux from the galactic center might be much smaller . observational data suggests that dwarf galaxies have constant density cores ( e.g. * ? ? ? pulsar timing measurements might be used to detect microhalos . since many of known millisecond pulsars ( msps ) are in the direction of the galactic center , the number density of microhalos around msps is higher than that of solar neighbourhood .    here , we estimate the residual of the time of arrival of a msp due to the gravitational attraction from its nearest neighbor , following @xcite . the residual due to the constant acceleration @xmath81 in the period of @xmath82 is given by @xmath83 where @xmath84 is the speed of light , and @xmath81 is given by @xmath85 where @xmath86 , @xmath87 and @xmath38 are the gravitational constant , the mass of the microhalo , and the distance between the microhalo and the msp . so we have @xmath88 if we assume that a microhalo lost 90% of mass by encounters with stars , the residual is about @xmath89 in twenty years . the change of the distance in ten years is around 400au . since the change in the acceleration is proportional to the third power of the distance , one in ten msps would show the change in the acceleration ten times larger than that of a typical msp , which should be detectable with ppta @xcite after modest improvement in the timing accuracy . note that the mass loss of two weak encounters can be larger than that of a strong encounter @xcite . for simplicity , we used the mass loss due to a strong encounter as estimated in subsection [ sec : encounter ] . however , the mass loss of microhalos in the opossite direction to the galactic center is less than that near sun . msps in the direction should show larger timing residual . we found that earth - mass microhalos have steep central density cusps . their central regions is not disrupted by tidal forces from the parent galaxies or stars and they survive to the present time . our result is different from the recent claims that small - scale structure have a negligible impact on dark matter detectability @xcite . they considerably underestimate annihilation signals because they assumed the density profile for the smallest microhalos was shallower than that we found with high resolution simulations . we are grateful to veniamin berezinsky for helpful discussions . numerical computations were carried out on cray xt4 at center for computational astrophysics , cfca , of national astronomical observatory of japan . is financially supported by research fellowship of the japan society for the promotion of science ( jsps ) for young scientists . this research is partially supported by the special coordination fund for promoting science and technology ( grape - dr project ) , ministry of education , culture , sports , science and technology , japan .
earth - mass dark matter microhalos with size of @xmath0 100 aus are the first structures formed in the universe , if the dark matter of the universe are made of neutralino . here , we report the results of ultra - high - resolution simulations of the formation and evolution of these microhalos . 
 we found that microhalos have the central density cusps of the form @xmath1 , much steeper than the cusps of larger dark halos . 
 the central regions of these microhalos survive the encounters with stars except in very inner region of the galaxy down to the radius of a few hundreds pcs from the galactic center . the annihilation signals from nearest microhalos are observed as gamma - ray point - sources ( radius less than 1 ) , with unusually large proper motions of @xmath2 degree per year . 
 their surface brightnesses are @xmath010% of that of the galactic center . their s / n ratios might be better if they are far from the galactic plane . 
 luminosities of subhalos are determined only by their mass , and they are more than one order of magnitude luminous than the estimation by @xcite : a boost factor can be larger than 1000 . 
 perturbations to the millisecond pulsars by gravitational attractions of nearby earth - mass microhalos can be detected by the observations of parkes pulsar timing array ( ppta ) .