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gamma ray bursts ( grbs ) are interesting highly energetic phenomena for which there is still no definitive explanation on the originating mechanism ( see e.g. * ? ? ? * ; * ? ? ? * ) . regarding the initial event that triggers a grb , the combination of the observed short variability timescales and huge radiated energies points towards cataclysmic events leading to the formation of a stellar compact object with mass @xmath0 and radius @xmath1 releasing a gravitational energy @xmath2 erg . specifically , according to their time duration , grbs can be classified as @xmath3 ( lgrbs ) if the duration of the gamma - ray signal is larger than 2 s and short ( sgrbs ) in other cases @xcite , although the boundary is not sharply delimited ( see e.g. * ? ? ? * ; * ? ? ? there are several pieces of evidence in favour of an association of lgrbs with massive stars , especially the facts that they occur in star - forming regions @xcite and that supernovae have been found in association with a few of them ( see e.g. * ? ? ? this leads to the _ collapsar _ model @xcite where a lgrb is associated with the gravitational collapse of a massive , wolf - rayet , star leading to the formation of an accreting stellar - mass black hole ( bh ) . an alternative scenario where the central engine formed after the gravitational collapse is a young , rapidly rotating ( ms period ) neutron star ( ns ) has also been considered by @xcite , @xcite and @xcite . on the other hand , the identification of the progenitors of sgrbs is more uncertain @xcite . this is partially due to the fact that the detection of sgrb afterglows is technically more difficult , and therefore rarer , than for lgrbs . so far there is only a handful of detected afterglows , since the first detection in 2005 @xcite . sgrbs can occur in all types of galaxies , either of a star - forming type or not @xcite . this is consistent with the most popular scenario , that is the merger of a ns+ns or ns+bh binary system .    as a main motivation for the present contribution and due to the current uncertainties on the origin of ( especially short ) grbs , it is worth investigating other possible classes of cataclysmic events where astrophysical stellar compact objects are involved . we will focus on nss . a ns can be partially characterized by a set of static observables , namely mass , @xmath4 , and radius , @xmath5 . the structure of a ns has been discussed thoroughly in the past ( for a review see e.g. * ? ? ? it can be briefly described by a dense _ core _ , where matter is in the form of a liquid of nucleons ( or additional particles including strangeness ) , and a _ crust _ where matter undergoes a liquid - solid transition into a clusterized myriad of nuclei @xcite . in more detail , the so - called neutron drip ( nd ) line signals the boundary between the outer and inner crust where neutrons start to leak out from nuclei . the mass in the crust is small ( up to a few percent ) as compared to the whole ns and therefore it could be accelerated , if ejected by large energies , to large velocities or even high lorentz factors . the equation of state ( eos ) that governs the description of matter in the inside of nss is currently poorly known . whether matter remains in the form of baryons or deconfined quarks is a matter of debate . the problem of the internal constituents in a ns has been thoroughly and periodically revisited from the early 1930 s when landau predicted the existence of such objects @xcite from the basis of the existence of neutral hadronic particles . from the discovery of the neutron by chadwick in 1932 to 1984 when it was hypothesized @xcite that a more stable type of matter could be possible ( formed by roughly equal quantities of @xmath6 quarks , arising from weak decay of regular @xmath7 matter present in nucleonic matter made of protons and neutrons ) a wide variety of possible nuclear configurations has been proposed . in this latter quark system case , for example , recent attention has been devoted to lattice calculations showing the possibility of the existence of the @xmath8dibaryon , with @xmath9 quark content @xcite and experimental input from the lhc is expected on the formation of a quark - gluon plasma . a stable type of extended strange matter would allow the existence of stars even more compact than nss , i.e. hybrid or pure quark stars ( qss ) @xcite . the transition from a nucleonic type of matter to a quark phase is presently not well understood . from the theoretical point of view , some work has been done @xcite on the possibility of quark bubble nucleation in a cold system , where the temperature is well approximated by @xmath10 . as this mechanism is not efficient enough , this process may seem unlikely to occur . another series of works have been developed by ouyed and collaborators which propose the quark - nova model in which a massive ns converts explosively to a quark star @xcite . the transition is obtained mostly via a central density increase due to spin - down or accretion forming a conversion front that propagates toward the surface . the outcome is ejection of the ns s outermost layers at relativistic speeds . alternatively , as we explain in this work , additional _ external _ agents may be able to produce thermal excitations in these dense degenerate matter systems .    from indications concerning astrophysical and cosmological backgrounds we know that dark matter ( dm ) is distributed inhomogeneously in the universe and , additionally , could be gravitationally accreted onto individual massive astrophysical objects . one of the most popular dark matter candidates is considered to be a majorana - type weakly interacting particle ( wimp ) , although other asymmetric dark matter candidates could exist as well @xcite . from the experimental point of view , current direct and indirect detection experiments try to constrain its properties . for example , direct detection earth - based experiments dama @xcite , cogent @xcite , cresst and lately coupp @xcite seem to point towards a light particle in the @xmath11 @xmath12 mass range ( although this is in tension with other null searches ) while there has been a lot of interest in indirect detection of new excesses of extra photon components from the galactic center that could be due to annihilation of a @xmath13 @xmath12 particle @xcite , albeit so far at only the @xmath14 level of significance . dm passing through astrophysical massive objects is expected to scatter off their constituent nuclei , lose energy , and become trapped by their gravitational field . multiple scatterings cause dm to sink towards the center and afterwards , assuming that it may self - annihilate , a series of end products are available . based on the previous arguments , a set of current experiments try to find evidence for this process in the sun , earth @xcite or even more compact - sized objects such as nss @xcite . recently , new ideas on the possibility that quark bubbles may be formed by spark seeding in the inner cores of dense nss have been proposed by @xcite . sparks would be generated in a sort of _ trojan horse _ mechanism by self - annihilation of dark matter particles gravitationally accreted by nss gathering in their internal cores . as estimated , this would allow release energies of up to about one order of magnitude higher than the quark binding energies in the present baryons @xcite . this mechanism then could lead to the conversion of nss into qss if the transition to quark matter phase is macroscopic . in this way the matter component in the form of dm would not only influence cosmological observables , but even ns dynamics @xcite . similar arguments have been claimed in the solar seismology observables @xcite . we investigate in the present paper whether this type of _ non - repeating _ cataclysmic event could produce sgrbs and what could be a possible specific signature . after a short summary of the scenario in  [ sect : scenario ] , in  [ sect : energetics ] we compare the energy released by sgrbs with the energetics of the progenitor model that we propose and in [ sect : rate ] we discuss the short grb event rate in light of this scenario as compared to observed rates , as well as the natural delay time between the regular ns phase and qs formation and how this mechanism may affect the properties of the host galaxies of short grbs . in  [ sect : engine ] we present and analyze the ejecta and crust masses that could be expelled due to the ns@xmath15qs conversion and we present the details of the resulting central engine model . in  [ sect : grb ] we attempt to discuss the expected temporal (  [ sect : duration ] ) and spectral (  [ sect : spectrum ] ) properties of the prompt gamma - ray emission and the afterglow . in [ sect : gw ] we discuss our results and possible genuine additional signals and gravitational wave emission that could finally lead to a clear identification as compared with the short grb scenario involving binary mergers . finally in [ sect : conclusions ] we give a brief summary of our conclusions and suggestions on how to proceed in further work . there has been some previous work where dm accretion in astrophysical objects has been considered @xcite . as a summary , we start in this section by motivating the scenario where the emission of a sgrb may occur .    in our previous work @xcite the possibility of spark seeding in ns as a result of dm accretion was proposed . we found a relationship between the mass of the dm particle , @xmath16 , and the binding energy of the lump of quark matter or strangelet formed , @xmath17 as calculated from the mit bag model @xcite . @xmath18 where @xmath19 is the baryonic number density and @xmath20 and @xmath21 are the chemical potential and mass of the quark of @xmath22type in the light sector , @xmath23 . @xmath24 is the bag constant . the channels available to the @xmath25 annihilation are , so far , not known and this uncertainty is phenomenologically parametrized into the fraction @xmath26 . inside the ns , it is believed that dm scatters one or more times and thermalizes according to a boltzmann distribution . the thermal radius is given by @xmath27 this radius is , in general , time - dependent since evolution proceeds for central temperatures @xmath28 and baryonic mass densities @xmath29 . dm at high density may self - annihilate to channels involving photons , leptons and light @xmath30 pairs @xcite . due to the fact that either a light or heavy self - annihilating particle in the @xmath31 mass - range may release a spark of energy able to liberate the constituent quark content of the baryons forming the very dense matter in the core of these objects , a pure nucleonic ns could then be considered a metastable state of compact stars . note that a self - annihilating @xmath32 @xmath12 particle as recently suggested in the context of direct detection experiments would , in particular , fit into this scenario . the annihilation power is then given as @xmath33 where @xmath34 is the dm mass density and @xmath35 is the thermally averaged annihilation cross section .    if the spark seeding is able to form quark lumps or strangelets , most likely off - center , inside a volume @xmath36 they could individually grow or coalesce from a stable minimum mass number , so far poorly known , @xmath37 , according to previous estimates @xcite . in this way a _ burning front _ may proceed if particular thermodynamical conditions are fulfilled . if the burning is partial , the final configuration object would be hybrid , constitued by an inner quark matter phase and an outer nucleonic phase . however , if the burning is complete the resultant object would be formed by a pure quark phase . in both cases the final configuration in the mass - radius phase space @xmath38 , as computed from different eos using a variety of many - body effective theories @xcite , is a smaller , slightly lighter , more compact object than the initial one characterized by @xmath39 .    in figure  [ fig : mr ] we show a qualitative scheme , inspired from the work by @xcite , of how the transition would produce a more compact object . the transition point , and therefore the initial configuration mass , would be influenced by the presence of spark seeding by self - annihilating dm in this model . in such a ns @xmath15 qs transition , part of the outer crust of the initial ns can be expelled , and possibly accelerated to relativistic speed , which may lead to a transient episode of high - energy emission . in the following , we discuss a possible association of some grbs with such events . we focus on sgrbs for several reasons :    * the energetics of bright long grbs may be a challenge for this scenario , whereas typical energies of short grbs are in a much better agreement ( see  [ sect : energetics ] ) ; * a delay of at least @xmath40 yr is expected between the formation of a ns and the transition to a qs , which is too long for long grbs as supernovae within a few days have been found in association with some of these events . on the other hand , the scenario naturally leads to a broad distribution of the delay @xmath41 , allowing long delays that are necessary to explain the properties of the afterglows and host galaxies of short grbs ( see  [ sect : rate ] ) ; * the scenario naturally leads to short ( or very short ) timescales for the gamma - ray emission , pointing towards short or ultra - short grbs ( see  [ sect : duration ] ) . since 2005 and the first accurate localization of a sgrb @xcite , the redshift of an increasing number of short grbs has been measured , confirming their cosmological origin and leading to a large dispersion in the isotropic equivalent energy released in gamma - rays , @xmath42 erg @xcite . this energy is emitted by a relativistic outflow which is probably beamed within an opening angle @xmath43 so that the true energy release is @xmath44 , where the beaming factor is defined as @xmath45 unfortunately , the opening angle @xmath43 can not be easily measured in grbs . it can be estimated if a _ jet break _ is identified in the late afterglow @xcite . it is only in very rare cases that a precise constraint on @xmath43 is obtained , such as @xmath46 in grb 051221a @xcite , and even in such cases , it remains partially model - dependent . the distribution of @xmath47 for sgrbs is therefore unknown @xcite . highly beamed sgrbs with @xmath48 would lead to @xmath49 whereas larger opening angles of about @xmath50 give @xmath51 . this will remain as a major source of uncertainty in what follows . in sgrbs , the isotropic equivalent energy @xmath52 is released in gamma - rays on a very short time scale ( @xmath53 s ) and observed well above 1 mev ( see e.g. * ? ? ? then , the gamma - ray emission must be produced from relativistic ejecta to avoid the _ compactness problem _ : this provides a constrain on the minimum value of the lorentz factor for the emission region to be optically thin for @xmath54 annihilation @xcite . the analysis of a few pre-_fermi _ short bursts @xcite leads to @xmath55 from this @xmath54 opacity constraint @xcite . when a sgrb is detected up to the gev range by _ fermi_-lat , stricter constraints are obtained , such as @xmath56 in grb 090510 @xcite . + let us compare these constraints on the energetics and the relativistic nature of the emitting material in sgrbs with the predictions of the scenario described in the previous section . if there is a transition triggered from the inside @xcite , namely due to dm self - annihilation in the central core of a ns ( @xmath4 , @xmath5 ) then the final configuration may lead to a more compact object with partially deconfined quark content . the energy gap to this new configuration ( @xmath57 , @xmath58 ) will release approximately ( here we assume @xmath59 for the sake of comparison ) , @xmath60 note that the internal energy due to the matter equation of state has been estimated to be of the order of @xmath61 @xcite , therefore this estimate is correct up to a numerical factor that somewhat depends on the eos . the energy @xmath62 liberated in a ns@xmath15qs transition can be compared with the energy @xmath63 released in the gravitational collapse leading to the formation of a ns ( standard core - collapse supernova ) . we define this ratio ( in the approximation @xmath64 ) as @xmath65.the calculation is made assuming a transition of a hadronic type star with a combined eos model including additional hyperons @xcite to a hybrid star with a quark content described by the mit bag model . two relativistic non - linear walecka - type eos models of glendenning - moszkowsky @xcite are tested , namely , gm1 ( blue curve ) and gm3 ( red curve ) usually used to describe the hadronic phase . the typical compressibility values @xmath66 for the gm1 model are stiffer than for the gm3 model . note that in this scenario of hybrid stars the maximum mass for the hybrid object must be somewhat lower than in the case of the pure hadronic star . although both of them predict maximum hadronic stars masses somewhat on the low side with @xmath67 , ( as compared to recent measurements reporting masses of about @xmath68 @xcite ) , they can be considered illustrative to show a general trend of the typical original configurations before transitioning to hybrid or pure qss . in this figure the value of some nuclear parameters such as the s - quark mass has been taken to be @xmath69 and the strong coupling constant @xmath70 . surface tension is @xmath71 . no curvature energy has been considered . in this situation the initial configuration masses and radii are not the same , since they depend on the value of the @xmath24 bag constant in the mit model . following @xcite we consider that the transition takes place between a configuration in the initial hadronic star with gravitational mass @xmath72 and with some baryonic mass @xmath73 and that of a final hybrid object ( computed with the hybrid eos ) with the same baryonic mass , @xmath74 , since that charge is conserved . @xmath75 and @xmath76 are the energy density and baryonic mass density for the baryonic object . physically , the transition occurs due to the fact that as the density or central pressure exceeds a threshold value , it is energetically allowed that , at the transition point , bubbles of quark matter form . this is due to the lowering of the chemical potential in the system as more degrees of freedom are available . these lumps of quark matter can grow very rapidly , driving a burning front and the original hadronic star will be converted into a hybrid star or quark star . in the mechanism involving self - annihilating dm this energy released could be considered as _ sparks _ that would coalescence or ignite the medium and allow quark deconfinement out of the baryons present ( this is b - dependent and therefore , eos dependent in our model ) . if we further include corrections due to slightly different masses for the initial and final configurations we have @xmath77 . we typically find @xmath78 , which illustrates that the transition mechanism discussed here indeed belongs to the class of the most energetic phenomena in the universe . the efficiency @xmath79 is plotted in fig  [ fig : eos ] as a function of the bag constant @xmath80 . it shows that the efficiency @xmath79 is higher as the bag constant @xmath24 grows , pointing to heavier dm particles in order to ignite the nucleation of quark matter lumps but well in the conservative range shown in fig . 2 in @xcite . further work is needed to clarify the role of the eos in the efficiency of the transition since the possible existence of a burning front able to fully convert the ns into a qs and proceed towards higher radii is a crucial point . numerically , using typical values @xmath81 , @xmath82 and @xmath83 results in @xmath84 . in the ns@xmath15qs transition most of the energy @xmath62 will be radiated as neutrinos and photons , as showed by detailed calculations @xcite . additionally gravitational radiation should also be emitted ( see  [ sect : gw ] ) . we assume now that a small fraction , @xmath85 , of this energy may be injected into the outer crust which is then ejected and becomes relativistic . the kinetic energy of the expelled crust is @xmath86 if acceleration is complete . the isotropic equivalent energy that could be radiated as gamma - rays by such an ejecta can be estimated by    @xmath87    where @xmath88 is the efficiency of gamma - ray energy extraction from the ejecta and could range from @xmath89 for the extraction of kinetic energy by internal shocks @xcite to @xmath90 for photospheric emission ( see e.g * ? ? ? * ) or magnetic reconnection @xcite . as discussed below , relativistic motion of the ejecta is favored by a small ejected mass , @xmath91 , which corresponds typically to the outer crust . the crust is defined as the region where the density drops below nuclear saturation density ( nsd ) at @xmath92 @xmath93 , and the outer crust is limited by the neutron drip ( nd ) at @xmath94 ( see  [ sect : engine ] ) . then , the value @xmath95 used in eq . [ eq : egammiso ] would correspond for instance to a situation where 1% of @xmath62 is injected in the crust and 10% of this energy is injected preferentially in the outer crust , so that @xmath96 . as there is large uncertainty in this estimate we use a safe approximation below the @xmath97 quoted in other detailed calculations @xcite . this estimate of @xmath52 is in reasonable agreement with observations of sgrbs : the ns@xmath15qs conversion scenario investigated here can reproduce measured energies in sgrbs for @xmath98 . + regarding the relativistic nature of the ejecta , the maximum lorentz factor , @xmath99 , that can be reached depends on the expelled fraction or ejected mass , @xmath100 , of the crust . the maximum lorentz factor can be deduced from the estimate of @xmath101 above , and from the ejected mass @xmath100 as : @xmath102 again , it seems that lorentz factors above @xmath103 , in agreement with the observational constraints described above , can be reached as long as the ejected mass remains low ( @xmath104 ) and the fraction of the energy injected in the outer crust is not too small ( @xmath105 ) . even ultra - high relativistic ejecta with @xmath106 could in principle be produced , if the ejected mass is really small . this could be the scenario where the _ crust is expelled . + we conclude that the dm self - annihilation triggered ns@xmath15qs scenario can , in principle , release enough energy to power a sgrb , and that the ejected crust can reach high lorentz factors , which is necessary to emit gamma - rays . this is however strongly dependent on the two parameters @xmath85 and @xmath100 which are very difficult to predict accurately at this stage . this will be briefly discussed in [ sect : engine ] . assuming that the transition of a ns to a qs triggered by the self annihilation of accreted dm in the core can inject enough energy into relativistic ejecta to produce a sgrb , it is worth comparing the observed rate of these phenomena with the predicted rate of ns@xmath15qs conversions . the local rate per unit volume of sgrbs , @xmath107 , can be estimated from their observed rate and distribution of flux using a population model ( luminosity function , comoving rate , etc ) , as has been done by @xcite , @xcite , who obtain @xmath108 the lower limit corresponds to a comoving sgrb rate that follows the cosmic star formation rate with a long delay , and the upper limit to a constant comoving rate . unfortunately , the unknown distribution of the beaming factor and its average @xmath109 is again a major source of uncertainty in this estimate . + in the scenario presented is this work , the local rate of ns formation , estimated as the local rate of type ii supernovae , gives an _ upper limit _ for the rate of ns @xmath15 qs conversions . it is of the order of @xcite @xmath110 then the ratio of the former two rates is @xmath111 from these estimates only , one can conclude that ns @xmath15 qs transition can be much more frequent than sgrbs , depending on the fraction of ns that will experience such a transition . if all sgrbs are due to ns @xmath15 qs conversions , the low ratio obtained in eq . [ eq : ratesnii ] could be ( i ) either due to the fact that only a fraction of ns @xmath15 qs transitions lead to short grbs ; ( ii ) or be related to the fact that only a small fraction of ns are converted into qs . having only a small fraction of ns converting to a qs is expected if the delay @xmath41 between the formation of a ns and its conversion to a qs is usually long , e.g. @xmath112 several gyr . for a broad probability distribution @xmath113 of the delay @xmath41 , with a high mean value @xmath114 of the order of the hubble time , most conversions would not have occured yet , resulting in a low ratio @xmath115 , the observed short grbs being produced by the conversions with the shortest delays . in addition , such a distribution of @xmath113 would make the scenario in good agreement with the properties of short grb afterglows and host galaxies : contrary to the case of lgrbs which are always observed in central regions of star forming galaxies @xcite , sgrbs can occur at any place ( sometimes at the periphery or outside ) in any type of galaxy @xcite . this indicates a delay between the end of the life of the massive progenitor star and the production of the short grb . it is already a well known fact that most nss are born with a natal velocity kick @xmath116 that can be as large at @xmath117 km / s @xcite . therefore , with high values of @xmath41 , not only any correlation with star formation is lost , but the ns can travel a distance @xmath118 and most likely experience the conversion to a qs far from the galactic central regions , or even outside the galaxy .    in the scenario presented here a lower limit on @xmath41 can be obtained from the physics of the transition , which is triggered by self - annihilation of accreted dm from the galactic halo . in our galaxy the dm density distribution can be taken to be of a type @xcite @xmath119}\ ] ] with parameters @xmath120 , @xmath121 , and @xmath122 so that at the solar neighbourhood the keplerian velocity is @xmath123 km / s and the local dm density is @xmath124 . dm from this halo can be accreted by gravitational capture @xcite at a rate at peak of ns distribution @xcite of@xmath125 but off - peak , at about solar circle it may be reduced somewhat . in this estimate , we assume a wimp - nucleon ( spin independent ) cross section @xmath126 @xcite . once the steady state , resulting from competing processes of annihilation and accretion , has been reached , the elapsed time is @xmath127 where @xmath128 is the volume of the star . typically , if we assume a light @xmath32 @xmath12 dm particle , as direct detections experiments seem to preliminary suggest , we obtain @xmath129 yr . for a velocity ( temperature ) dependent cross section and heavier dm particles @xmath130 @xmath12 , this delay can be longer , @xmath131 yr @xcite . from the condition that the transition should likely occur after reaching the steady state , we get a lower limit on the delay @xmath41 , @xmath132 notice that this delay is already much too large to allow to consider producing lgrbs with ns @xmath15 qs conversions , as an associated sn is sometimes found in association with such events within a few days @xcite . on the other hand , it is too small to have sgrbs uncorrelated with star formation , which is required by the observed diversity of sgrb host galaxies and afterglow locations @xcite . we conclude that @xmath41 is related to the microphysical processes happening in the burning of the ns . this , in turn , depends on the ability of the compact object ( mainly related to the eos ) and environment conditions to accrete dm and , therefore , can not be simply predicted and should present some spread and extend up to a large value @xmath133 that can be constrained by observations .    in our galaxy , there are hundreds of confirmed nss , with measured radii and masses @xcite . on the other hand , the subsample of confirmed nss with an estimate of the age is very small , due to the difficulty of the age determination , based on cooling theory @xcite . it seems that nss with an age of at least @xmath134 myr are identified @xcite which would put a lower limit on the maximum value of the delay @xmath41 , @xmath135 such delays , as shown by eq . [ eq : distance ] , lead to travelled distance of the order of 10 kpc or more , reaching the outskirts of a galaxy but are still too small to de - correlate from the star formation activity . one can not of course exclude that much older nss are present in the sample of confirmed nss , which would increase @xmath136 up to 100 my or more . nevertheless , a detailed comparison with the properties of sgrb host would require the knowledge of the distribution @xmath113 , which seems yet out of reach . another possible approach to constrain the rate of ns@xmath15qs transitions in the scenario proposed here is to focus on the kinematics of observed pulsars . the pulsar tangential velocity data can be fitted with a bimodal distribution peaked around @xmath137 km / s and an upper @xmath138 km / s @xcite . the high velocity pulsars with @xmath139 roughly account for the 10@xmath140 of the pulsar population . the first peak in the distribution is believed to be due to the kick velocity given to the ns when it is formed in a core collapse supernova . it has been suggested by @xcite that the second higher velocity peak could be due to a _ second _ kick when the ns@xmath15qs conversion takes place . in previous work @xcite , it was shown that dm seeding in nss may form a stable and long - lived strange quark matter ( sqm ) lump that could induce a partial ns conversion into a hybrid sqm star . this event may produce , as a consequence , an effect on the kinematics with a birth kick and rotation as a result of the partial burning of the ns @xcite able to produce up to @xmath141 km / s and relative changes in the angular velocity of @xmath142 as a result of the off - center mechanism driving the transition . other mechanisms quoted in the literature rely on some kind of asymetry @xcite in the front progress . from this interpretation of the observed pulsar velocity distribution , @xmath143 could be taken as an upper limit for the frequency of the ns@xmath15qs transitions , leading to an upper limit for the ns@xmath15qs rate which is more constraining than in eq . [ eq : ratesnii ] , i.e. @xmath144 since this rate remains higher than the sgrb rate , at this stage the only possibility in this scenario is to to assume that only a fraction @xmath145 of ns @xmath15 qs transitions produce a short grb , leading to @xmath146 this additional factor @xmath147 can be related to internal processes , such as the capacity of the burning front to proceed to the crust ( see  [ sect : engine ] ) . note that the value of the efficiency @xmath148 has been obtained here assuming that all short grbs are produced by ns @xmath15 qs transitions . however , we will show below (  [ sect : duration ] ) that this scenario naturally leads to short grb durations @xmath149 s , so that only very short grbs are good candidates for counterparts of these ns @xmath15 qs transitions . then , it reduces in principle even more the value of @xmath147 .    on the other hand , observations of afterglows of ultra - short grbs , identifications of their host galaxy and measurements of their distance are extremely rare so that their intrinsic rate is unknown . the distribution of the duration of batse bursts show that @xmath150 of the short bursts have a duration below 100 ms @xcite . this factor can not however be directly applied to the estimate of the intrinsic rate given by eq . [ eq : ratesgrb ] . indeed , this population of very short bursts may very well be a separate group with different properties : they are usually made of a single short and hard spike with possible substructure on a timescale of a few 10 @xmath151s @xcite . the analysis ( @xmath152 and @xmath153 diagram ) of the distribution of very short bursts observed by batse and konus gives some evidence for a local origin @xcite . this is however a bit contradictory with more recent results obtained by _ swift _ : 10 very short bursts with a duration of less 100 ms have been detected by swift until june 2012 . all of these show indeed a single short duration hard spike in the bat . in many cases , the afterglow has not been identified or is very weak at the limit of the detection ( grb 050925 , grb 051105a , grb 070209 , grb 070810b , grb 070923 , grb 090417a , grb 100628a , grb 120305a ) . there are however two very short bursts where the afterglow has been well detected and localized and where there is a good candidate for the host galaxy . in both cases , the host candidate is an early type galaxy and the afterglow shows a large offset of a few 10 kpc : grb 050509b seems to be associated to an elliptical galaxy at @xmath154 with an offset of 35 - 55 kpc @xcite ; grb 090515 is probably associated to an early type galaxy at @xmath155 with a large offset of 75 kpc @xcite . these two examples indicate a population at cosmological distance which is uncorrelated to star formation , in agreement with the discussion above . the sample is however much too small to allow for a determination of the intrinsic rate of very short grbs and an estimate of @xmath147 . in this section , we model the basis of the central engine mechanism of the internal burning front that will induce a resultant outflow with several relativistically moving emitting regions . this discussion is based on a series of works @xcite . nuclear processes involving quark deconfinement in the hadronic phase may happen if the @xmath156 @xmath12 dm particle candidate self - annihilates liberating @xmath157 photons and other light particle pair products . the corresponding lump of strange quark matter ( @xmath6 matter ) evolves towards the formation of a fireball that may cause stress and tension on the base of the inner crust of a ns . since there are only a few preliminar simulations @xcite developed so far on the full process of energy transport from the inner deconfined regions to outer regions through a burning front there is not much information where this front may stop or whether it fully proceeds to the outer crust . in these simulations the ns burning condition is dynamically analyzed showing the possibility that a hybrid star may form if the conversion front is not able to proceed as _ burning_. however , a full detailed treatment has not hitherto been performed . + in previous work @xcite , it was found that the seeding is most likely a non central process , and therefore , geometrically , the burning front progression may not be a radially symmetric dynamical process ( see fig .  2 in @xcite ) . the possibility of a beamed ejection of the outer crust arises then from the anisotropy in the progression of the burning front . this has been somewhat explored in the work of @xcite where they discuss the possibility of preferred ejection of a fireball through the polar caps . in the present work , we discuss the constraints on the ejected mass as a result of the ns@xmath15qs conversion . similar to what may happen in the heavy ion collision events in large colliders , a fireball may be formed and grow rapidly . then , a pure nucleonic eos of matter , would no longer be valid as nucleon quark content may be deconfined . since the newer eos is softened , later evolution may lead to the fact that the original hydrostatic structure is not longer energetically possible and re - adjustement of the object to favor lower radii and masses and then to build up tension in the crust tending to eject it and break it up . the crust mainly corresponds to matter where the density is below the nsd . therefore for lower densities a myriad of nuclei with mass number @xmath158 populate this phase . since the particular distribution of nuclei depend on the competition of short - range hadronic interaction and long range coulomb interaction a set of irregular shapes different from the spherical one can arise , forming what is known as the _ pasta phase_. as a result , low density matter in the crust of nss is mostly neutron - rich due to the deleptonization caused by neutrino escape in the first stages of cooling . its isospin content is closer to that of neutron matter than to regular nuclei where proton and neutron content are balanced @xmath159 . from the @xmath160fe iron content usually assumed in the lower density region in the crust , there is a series of neutron - rich nuclei going through heavier @xmath161ni , @xmath162ge , @xmath163sr and after this the nd transition takes place , signaling the inner crust of the ns . in the inner crust , surrounding these non - uniform pasta structures , a neutron gas is filling the system , as has been directly simulated in previous work @xcite . fragmented emission of ejecta is therefore possible since the stress in the base of the crust from a burning front may liberate the most abundant structures and the rest of lower @xmath158 nuclei . the gradient of composition ( heavy @xmath15 light ) should also produce some variability during the crust ejection , all regions of the crust being not necessarily ejected with the same lorentz factor . an additional source of uncertainty is related to the fraction of the initial energy release associated to the transition in the core which will be injected into gamma - ray photons , and the associated photo - disintegration of heavy nuclei . an efficient photo - disintegration would lead to a modified chemical composition biased towards light elements , and would enrich the medium by free neutrons that can be an additional source of energy ( neutron decay ) and internal dissipation in the ejecta ( see  [ sect : duration ] ) . in order to size the importance of this ejection , we plot in fig . [ fig3 ] the crust mass @xmath164 as a function of the stellar radius . these data are obtained integrating the tov @xcite equations for eight representative different eos @xcite up to the core . we compute the mass of the crust by integrating above a critical density , either the neutron drip density @xmath165 @xmath166 to estimate the mass of the outer ( solid ) crust only , or the nuclear saturation density @xmath167 @xmath168 ( where crust - core boundary sets in ) to estimate the mass of the entire crust . we find that the condition @xmath169 needed for the relativistic motion (  [ sect : energetics ] ) can be fulfilled if only the outer crust is ejected ( @xmath170 ) , whereas it becomes much more difficult if the whole crust is expelled ( @xmath171 ) . the details of the physics of the propagation of the burning front and the associated energy deposition are required to estimate precisely the fraction of the crust which is ejected . if this fraction varies from a ns@xmath15qs transition to another , this would naturally lead to @xmath172 as discussed in the previous section . in this section we discuss some expected properties for sgrbs produced in the scenario proposed in this work . we focus on the identification of distinct features related to the specific central engine that could help in distinguishing this mechanism from others proposed in the literature . let us assume that the ejected outer crust has a mass @xmath173 , an initial energy @xmath174 and a width @xmath175 , where @xmath176 is the light crossing time ( @xmath177 ) . the maximum final lorentz factor that can be reached in the ejection is @xmath178 due to the large physical uncertainties regarding the energy deposition in the crust and the following ejection , we do not attempt here a detailed calculation of the relativistic ejection ( see e.g. * ? ? ? * for a self - similar solution of the propagation of a strong shock wave within the ns and the following shock breakout ) . for a thermal acceleration , the saturation to this value of the lorentz factor will occur at radius @xmath179 assuming an initial radius @xmath180 km for the ejection . the ejecta will become transparent for its own radiation at the photospheric radius @xmath181 where we take the thomson opacity @xmath182 . here we assume @xmath183 free electron per nucleon in the expanding gas , whereas the dynamical chemical composition discussed in the previous section may lead to lower values . this does not affect too much the discussion as the dependence goes moderately as @xmath184 . this expression of @xmath185 is valid for @xmath186 . the radius @xmath187 is defined below and is of the order of a few @xmath188 cm so that the condition is always true for the typical parameters considered here . the estimates of @xmath189 and @xmath185 are based on standard fireball theory for grbs ( see e.g. * ? ? ? * ) and are only rough estimates for the scenario considered here as the physics of the ejection of the crust is much more complex . we should bear in mind that the ejecta composition @xcite and fragmentation may affect both the dynamics ( @xmath189 ) and the interaction with radiation ( @xmath185 ) @xcite . therefore , if the energy is not deposited in an homogeneous way in the expelled crust , the final lorentz factor in the ejecta may not be uniform . in addition , fragmentation of the crust during its ejection will also lead to some variability in the ejecta . if variations of @xmath190 are present on length scales @xmath191 , this will induce collisions ( internal shocks ) that will dissipate energy at a typical radius @xmath187 given by @xmath192 clearly , this possible internal dissipation will always occur well below the photosphere , and , depending on the value of the lorentz factor , even before the acceleration is complete . most of the dissipated energy should contribute again to the acceleration and the internal shock phase will only tend to smooth out the initial internal variability , without contributing to the emission .    the ejecta will expand freely initially , but will eventually be decelerated by the external medium . however , due to the expected delay between the formation of the ns and the ns @xmath15 qs transition , this external medium can correspond to the periphery of the host galaxy or even the surrounding intergalactic medium , i.e. have a low density . we assume a uniform medium with a number density @xmath193 . then the deceleration will start at radius @xmath194 @xmath195 is the proton mass . from these different estimates , we find for the proposed scenario that @xmath196 this would naturally lead to two episodes of emission , a single spike emitted at the photosphere followed by an afterglow starting at late time due to the high value of @xmath197 . the duration of the prompt spike should be fixed by the intrinsic curvature of the emitting region and its lateral extension , which gives @xmath198 except if the ejection is highly beamed , the minimum is usually given by the first term . nevertheless , this estimate clearly points out towards short ( @xmath199 s ) and even probably very short ( @xmath200 ms , see figure  [ fig : grbnsqs ] ) grbs without any strong variability ( one main single spike ) . due to the low external density , the afterglow should rise slowly and reach a maximum around @xmath201 , i.e. a few 10 ms to a few hours after the grb , depending on the external density . in addition , the combination of a low external density and a moderate energy will naturally lead to a weak afterglow . note that if free neutrons are present in the ejecta , due to efficient photo - disintegration ( see  [ sect : engine ] ) , these neutrons will decay at a typical radius @xmath202 , fixed by the mean lifetime @xmath203 , which could lead to an early additional signature at @xmath204 ( see e.g. * ? ? ? vs efficiency of the energy injection in the crust @xmath85 , the following constraints are plotted : ( 1 ) lines of constant lorentz factor are plotted in blue for @xmath205 ( non relativistic limit ) , @xmath206 , @xmath207 and @xmath208 . the limit @xmath209 obtained from the compactness argument ( see  [ sect : energetics ] is plotted in thick line and the forbidden region is shaded ; ( 2 ) the limit where the radius of the internal dissipation @xmath187 is equal to the radius of the photosphere is plotted in red ( most of the parameter space is well below this line , i.e. @xmath210 ) ; the limit where the observed duration of the prompt emission of photospheric origin is equal to 100 ms ( 1 s ) is plotted in magenta solid ( dashed ) line ; the limit where the observed peak energy of the photospheric emission is 100 kev is plotted in green ; the limit where the isotropic equivalent gamma - ray energy emitted by the photosphere is equal to @xmath211 is plotted in black . the effect of the redshift of the source on the duration and the spectrum are not included . other parameters are @xmath212 ( i.e. the width of the outer crust is 300 m ) and @xmath213 ( i.e. the ejecta is beamed within @xmath214 ) . as can be observed , a large fraction of the parameter space ( top - left region ) corresponds to ultra - relativistic outflows ( @xmath215 ) producing a very short ( @xmath216 ms ) but bright ( @xmath217 ) spike of hard ( @xmath218 kev ) photons , i.e. a very short grb . ] if most of the gamma - rays are produced at the photosphere , one should expect a thermal ( quasi - planckian ) spectrum , possibly modified at high energy by comptonization @xcite . the peak energy of the observed spectrum will then be located at @xmath219 , where @xmath220 is the temperature of the photosphere . it can be computed assuming an adiabatic radial expansion from the ejection to the photosphere : @xmath221    the efficiency of the photospheric emission can also be deduced from the adiabatic evolution and equals @xmath222 . this leads to a better estimate of the isotropic equivalent energy radiated in gamma - rays , @xmath223 that stands on the lower values for grbs . of course , there is still a large uncertainty due to the unknown factors @xmath47 , @xmath224 and @xmath100 . however , these two estimates confirm the capacity to produce bright and hard spikes of gamma - rays in the considered scenario , as illustrated in figure  [ fig : grbnsqs ] where all the constraints on the prompt gamma - ray emission expected in the ns @xmath15 qs conversion scenario are summarized .    another possible signature of the scenario would be the presence of spectral features and lines associated to the specific chemical composition ( heavy elements ) of the ejected material . following the work by @xcite where @xmath225 were considered , the spectrum could be influenced below the mev range . in addition to the expected short duration burst of @xmath226-rays and x - rays and to the afterglow , it is likely that a multi - messenger approach must be followed to spot this progenitor scenario for sgrbs . the emission of gravitational waves by the merger of ns+ns or ns+bh binary is the most promising source for detectors such as virgo and ligo and their advanced versions @xcite , or the einstein telescope @xcite . the predicted emission during the three main stages of the merger has been extensively studied in the literature ( see * ? ? ? * for a review ) . in the inspiral stage , the signal is very well known up to the last stable orbit . then , the emission during the merger is more uncertain and must be modeled using supercomputer simulations which provide information about the gravitational waveform @xcite ( see the recent simulations by @xcite which compute the evolution of the merger up to black hole formation , including or not magnetic fields , realistic eos , etc . ) . the final ringdown stage is also very well known as the inspiral . therefore , the detection of gravitational waves in association with a sgrb would undoubtedly prove if the progenitor is a merger or not . with a horizon of @xmath227 mpc for ns+ns mergers and @xmath228 mpc for ns+bh mergers , there may be merger detections with advanced virgo , ligo@xcite ( 0.4 to 400 mergers / yr for ns+ns , a slightly smaller rate for ns+bh , @xcite ) . however , the simultaneous detection with a sgrb if the merger scenario is correct is more uncertain , both for theoretical ( beaming of the gamma - ray emission ) and instrumental ( localization of sgrbs ) reasons . the gravitational wave signature of the scenario studied here is not as well known as for compact binary mergers . it is expected that a change in the moment of inertia is caused by deformations in the ns@xmath15qs transition . some preliminary estimates of the transient gravitational wave signal from an explosive quark - hadron phase transition have been done @xcite . it could in principle be detected out to 20 mpc with advanced virgo / ligo , which makes unfortunately the probability of detection with an associated sgrb quite low , even if the intrinsic rate of very short grbs is quite uncertain ( see  [ sect : rate ] ) . the strategy for the detection of gravitational waves associated to a grb is to combine searches , already having identified typical patterns in temporal and directional coincidence with sgrbs that had sufficient gravitational - wave data available , although it is a very challenging task @xcite . an additional signal that may be used to discriminate between progenitor models for sgrbs is the neutrino emission . the specific signal expected from ns+ns mergers has been studied using supercomputer simulations ( see e.g. * ? ? ? * ) . in this work and within the present scenario we do not attempt to describe such a neutrino emission since it crucially depends on the central engine details . however , it should be expected a neutrino flux originating from hadronic reactions happening in the central engine ( conversion in the nucleon burning front of quark deconfinement and strangeness production ) or in the ejecta ( photo - meson interactions between shock - accelerated protons / nuclei and gamma - ray photons ) . in addition , if produced neutrons do not interact they will decay being accompanied by anti - neutrinos . emission of prompt muon neutrino fluxes have been performed in some grb general scenarios @xcite and seem to be testable as recent preliminary estimated sensitivities for ice cube 86-strings quote values of @xmath229 . additionally , experiments as amanda - ii and icecube have the capability @xcite of detecting anisotropies from the emission @xcite of neutrinos from gamma ray induced air showers . therefore , as motivated , the discovery of high energy neutrinos in correlation with a sgrb and gw signal would help disentangling the current scenario . in this work we discuss the possibility that a ns@xmath15qs transition may be a central engine model for short ( @xmath230 1 s ) or more probably very short ( @xmath216 ms ) grbs . this is an alternative to the popular ns+ns or ns+bh merger scenario for sgrbs . note that this scenario is known to be compatible with observations of sgrbs but has not been proved yet , and that in addition , there are a few observations suggesting that very short bursts could be a separate population . we suggest that these very short bursts could be produced by the ejection and acceleration to relativistic speed of the ( outer ) crust of the ns during the conversion to a qs . we find that    * the isotropic equivalent gamma - ray energy @xmath231 can be accounted for , assuming that @xmath232 of the gravitational energy released by the transition is injected in the outer crust with , however , a large uncertainty due to the unknown beaming factor of the ejection ; * high lorentz factors , necessary for the emission of @xmath226-rays on short time - scales ( compactness problem ) , can be reached , as long as the mass of the expelled crust is less than @xmath233 ; this is attainable for the outer crust in ns models . * the rate of very short grbs can probably be reproduced , assuming that only a fraction of transitions lead to a grb and that there is on average a large delay between the formation of the ns and the conversion into a qs . such a delay is expected due to the fact that the transition is triggered by self - annihilation of dm , which needs first to be accreted in the core of the ns . such delays would then naturally at least partially suppress the correlation between star formation and very short grbs , which should be observed in any type of galaxy with a large offset ( at the present time , there are only two host galaxies of very short grbs which have been possibly identified , both being early - type , and the offset is a few 10 kpc in both cases ) ; * the prompt gamma - ray emission should be mainly produced at the photosphere , without a strong variability which should be washed out by internal dissipation at much smaller radii . * for a large fraction of the parameter space , a hard ( @xmath234 kev ) and short ( duration @xmath230 100 ms ) spike of gamma - rays is expected , in general agreement with observations of very short grbs ; * the afterglow should rise slowly and be rather weak , due to a low density of the external medium . a possible additional signature can be expected at early time if the ejected material initially contains free neutrons . * fragmentation of the ejecta arises naturally in this model since non - uniform nuclei arranged in lattice or even pasta phases are present in the low density matter . * spectral features of heavy nuclei relativistically accelerated are expected below @xmath235 mev .    to summarize , possible _ signatures _ compared to the binary ( ns , bh ) merger scenario are the shortness of the prompt gamma - ray emission , with possibly a thermal spectrum and spectral features due to the heavy composition , the associated gw emission , and possibly the properties of the host galaxies and the distribution of the afterglow position in the host , this latter signature being however difficult to characterize due to the uncertainties on the typical delay between the ns formation and the transition to a qs . clearly , a multi - wavelength / multi - messenger approach is needed to reach a firm conclusion . we thank the micinn ( spain ) multidark , fis-2009 - 07238 , fis2011 - 14759-e and fis2012 - 30926 projects and the esf - funded compstar project for partial financial support . we acknowledge useful discussions with i. bombaci , j. horvath , k. kotera , r. ouyed and c. providencia . m. a. p. g. would like to thank the iap for its kind hospitality .
we present a mechanism based on internal self - annihilation of dark matter accreted from the galactic halo in the inner regions of neutron stars that may trigger the full or partial conversion into a quark star . 
 we explain how this effect may induce a gamma ray burst that could be classified as short , according to the usual definition based on time duration of the prompt gamma - ray emission . 
 this mechanism differs in many aspects from the most discussed scenario associating short gamma - ray bursts with compact object binary mergers . 
 we list possible observational signatures that should help to distinguish between these two possible classes of progenitors 
 .    short gamma ray burst , dark matter , neutron star , quark star .