Recently, constraints on bosonic asymmetric dark matter have been imposed based on the existence of old neutron stars excluding the dark matter masses in the range from ∼ 2 keV up to several GeV. The constraints are based on the star destruction scenario where the dark matter particles captured by the star collapse forming a black hole that eventually consumes the host star. In addition, there were claims in the literature that similar constraints can be obtained for dark matter masses heavier than a few TeV. Here we argue that it is not possible to extend to these constraints. We show that in the case of heavy dark matter, instead of forming a single large black hole that consumes the star, the collapsing dark matter particles form a series of small black holes that evaporate fast without leading to the destruction of the star. Thus, no constraints arise for bosonic asymmetric dark matter particles with masses of a few TeV or higher.Preprint: CP 3 - Origins-2012-034 & DIAS-2012 The last few years stellar observations have been used in order to constrain specific dark matter candidates or predict interesting phenomena related to dark matter [1][2][3][4][5][6][7][8][9][10][11][12][13]. Specifically, compact stars such as white dwarfs and neutron stars have been found to impose severe constraints on some dark matter models [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In principle, there are two types of effects that can take place in compact stars and can give rise to constraints on dark matter. The first type is related to the thermal evolution of compact stars [15,16,19,20]. In this case, annihilation of trapped weakly interacting massive particles (WIMPs) inside a compact star can produce significant amount of heat that can change the thermal evolution of the star at later times. As a result, stars old enough to be quite cold might maintain higher temperature due to the released heat.The second type of constraints is related to asymmetric dark matter [14,21,[23][24][25][26][27]. In this case WIMPs carry a conserved quantum number and there is an asymmetry between the populations of WIMPs and anti-WIMPs, so that the annihilation is impossible in the present-day universe where only the WIMPs remain. Such kind of WIMPs can accumulate in a compact star quite efficiently as long as the WIMP-nucleon cross section exceeds a certain critical value which in the case of a neutron star is quite small (σ ∼ 10 −46 cm 2 ) [15], several orders of magnitude smaller than current limits from direct searches. Under certain circumstances, the amount of WIMPs accumulated during the lifetime of the star is sufficient to result in a gravitational collapse of the the WIMPs into a black hole. In the case of fermionic * Electronic address: kouvaris@cp3.sdu.dk † Electronic address: Petr.Tiniakov@ulb.ac.be . (1) This amount of WIMPs can be easily accumulated even by nearby known old neutron stars with the standard assumption about dark matter density near the Earth. As it was pointed out in [23], once ∼ 10 36 WIMPs have been ...