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double neutron star ( dns ) systems , i.e. binaries consisting of a radio pulsar and a usually undetected second neutron star , have provided an excellent test bed for general relativity theory . the orbital decay observed in dnss is the first indirect evidence for gravitational - wave radiation . the merger of the two neutron stars in dnss is expected to be a major source for gravitational - wave detection by the laser interferometer gravitational wave observatory ( ligo ) , virgo , or the laser interferometer space antenna ( lisa ) . such mergers are also thought to be potential progenitors of the short - duration gamma - ray bursts ( grbs ) . the most commonly discussed formation channel of dnss , which we refer to as the standard scenario ( e.g. bhattacharya & van den heuvel 1991 ) , involves a high - mass x - ray binary ( hmxb ) phase at an intermediate stage . the hmxb eventually undergoes roche - lobe overflow ( rlof ) which leads to a common - envelope ( ce ) phase . the expected outcome of this phase is a binary consisting of the helium core of the massive star and an x - ray emitting neutron star . chevalier ( 1993 ) argued that a neutron star which moves in the dense environment of a stellar envelope can accrete a considerable amount of matter , which may push the neutron star above the maximum mass allowed for neutron - star matter and lead to the formation of a black hole . because of this argument , brown ( 1995 ) suggested that hmxbs passing through a ce generally produce helium - star / black - hole binaries rather than helium - star / neutron - star binaries  and hence do not lead to the formation of dnss in this standard scenario . to avoid the problem of hypercritical accretion onto a neutron star , brown ( 1995 ) ( see also wettig & brown 1996 ; bethe & brown 1998 ) suggested that dnss originate from binaries consisting of two helium stars in a close orbit , which we will refer to as the double core ce scenario . the first - born neutron star accretes part of the stellar wind from the other helium star which may weaken its magnetic field strength and spin up the neutron star . an important constraint for the formation of a double helium - star binary in a close orbit is that the systems start with two components of almost equal mass ( within 4 per cent ) . however , strong accretion might not have to occur if the companion is extended ( chevalier 1993 ) , if rotation of the magnetized neutron star is taken into account ( chevalier 1996 ) or if there is a strong outflow from a disc around the neutron star ( armitage & livio 2000 ) . furthermore , taam , king & ritter ( 2000 ) suggested that , considering the low rates of accretion characteristic of the low density envelopes of more evolved stars in combination with the short duration of the ce phase , accretion may not be important . these counter - arguments suggest that the formation of dnss via the standard channel can not be ruled out at this stage . moreover , there are good arguments suggesting that at least for some pulsars in binaries the neutron star must have passed through a common envelope ( e.g. tauris , van den heuvel & savonije 2000 ) .    we will not argue in this paper whether or not a neutron star in a ce phase will become a black hole . nevertheless , the standard scenario clearly is not valid for the situation where the initial binary has almost equal mass components , and hence it is interesting to investigate whether binary systems with these particular initial conditions could also lead to the formation of dnss , which is the main purpose of this paper . we refer to this channel with stars of almost equal initial masses as the double - core scenario . using binary population synthesis simulations , we study the expected observational properties as well as the birth and merger rates of dnss formed via the double - core scenario and compare them to the results of the standard scenario . we describe the detail of the double - core scenario , as well as the basic assumptions and the code used in this work , in sect . [ doublecore : sec : method ] . the results are presented in sect . [ doublecore : sec : result ] and discussed further in sect . [ doublecore : sec : conclusion ] . the double - core scenario we consider in this paper is a slight variation of the original proposal by brown ( 1995 ) , i.e.  it starts with a binary consisting of two stars of almost equal initial masses . the main difference to the original scenario is that we put more constraints on the initial masses and periods for the following reason . the pulsars in dnss , which are the first - born neutron stars , are recycled , and this recycling process is assumed to be due to mass accretion from the progenitors of the pulsar companions . therefore , it is necessary that the first neutron star has sufficient time to accrete matter from the companion . binary calculations to model the formation of contact binaries have been presented by , e.g. , pols ( 1994 ) , wellstein , langer & braun ( 2001 ) and nelson & eggleton ( 2001 ) . however , evolution through the contact phase has not been modelled ( webbink 2003 ) . here we assume that the outcome of a contact phase is a close binary consisting of the cores of the primary and the secondary star . if the masses of the components are very similar , i.e.  differ by less than 0.3 per cent ( podsiadlowski , joss & hsu 1992 ) , the outcome of the contact phase is that the two cores are more or less in the same evolutionary phase , i.e.  produces he + he or co + co binaries . in this case , the two cores also have almost equal masses and collapse into neutron stars with a relatively short time between the two collapse phases . in this situation , the first - born neutron star has a very limited possibility to accrete matter from the companion . moreover , the probability of having a binary system with such similar initial masses is extremely low , and therefore we would not expect to form many recycled dnss binaries in this case . a channel to form non - recycled dnss from almost - twin binaries has previously been studied by belczyski & kalogera ( 2001 ) .    to avoid having two cores of almost equal masses and to allow the first neutron star to accrete matter , we propose that at the onset of the contact phase , the primary is in a more advanced stage of evolution than the secondary . this can be achieved , e.g. , if the primary has developed a co core when the secondary starts core helium burning , or if the primary has started core helium burning while the secondary is at the end of main sequence or at the beginning of shell hydrogen burning . in this paper we will consider the first option , i.e.  the outcome of the contact phase is the co core of the primary and the helium core of the secondary . the co core collapses into a neutron star , which then accretes matter from the wind and/or the transferred matter during rlof from the helium star . the latest stage of this scenario is the same as in the standard scenario , i.e.  a helium - star / neutron - star ( hes - ns ) binary in a close orbit . this formation of dns through the double - core scenario is presented in fig . [ doublecore : fig : scenario ] . we performed monte carlo simulations of binary systems with almost equal mass components . the initial primary mass distribution was assumed to follow a salpeter mass function . since our main aim is to investigate the formation of dnss , we therefore limited the initial primary masses to be @xmath1 , i.e.  the presently favoured mass range in which single stars leave neutron stars as remnants . the secondary mass is chosen such that the mass ratio of the system , @xmath2 , follows a uniform distribution . because our investigation is on almost equal mass binaries , only systems with @xmath3 are taken into account , where the critical mass ratio @xmath4 is determined from single star models so that the secondary will already have finished its main - sequence phase when the primary has finished its helium - core burning phase . the value of @xmath5 is therefore a function of @xmath6 , varying from 0.97 for @xmath7 to 0.93 for @xmath8 . for the distribution of orbital periods we take a uniform distribution in @xmath9 , with @xmath10 .    to obtain the co core of the primary and the he core of the secondary at the end of the contact phase , we limit our simulations to binary systems in which the primary undergoes case c mass transfer , i.e.  its roche radius follows @xmath11 , where @xmath12 and @xmath13 are the minimum and maximum radius for case c mass transfer from the primary . the minimum radius for case c mass transfer depends on how the star evolves accross the hertzsprung - russell ( h - r ) diagram , in particular on whether it spends most of its helium core - burning phase as a blue supergiant or whether it first experiences an extended helium core - burning phase as a red supergiant ( see , e.g. , podsiadlowski et al . 1992 ) . in the latter case , the minimum radius for case c mass transfer would be substantially larger , leading to fewer systems that can experience case c mass transfer . the details of the radius evolution of massive stars is still a major unresolved problem in the theory of evolution of massive stars ; it depends on the treatment of convection , including the effects of convective overshooting and semi - convection , the treatment of mass loss and other mixing processes ( for further discussion see , e.g. , langer & maeder 1995 ) . in order to be able to assess the importance of these uncertainties , we consider two extreme options , where in one we assume that all stars first experience helium core - burning as red supergiants , leading to a high minimum radius for case c mass transfer , and where in the other we assume that the star spends most of its helium core - burning phase as a blue supergiant , leading to a low minimum radius for case c mass transfer . the corresponding radii , @xmath12 and @xmath13 were estimated from single - star models and their radii in the respective phases .    the separation after the contact phase , @xmath14 , is determined as in the case of the standard single - core common - envelope evolution ( webbink 1984 ) , i.e.  the envelopes are ejected on the expense of the change in the orbital energy , @xmath15 , where the envelope binding energy is @xmath16 and the change in orbital energy is @xmath17 at the onset of mass transfer , @xmath18 . the secondary is within its roche lobe but expands as soon as it accretes matter from the primary , such that at the onset of the contact phase @xmath19 . prior to the mass transfer phase , we neglect the stellar wind mass loss such that the roche radii do not change . using eqs . [ doublecore : eq : binding ] and [ doublecore : eq : orbital ] , the reduction in separation can be expressed as @xmath20 here @xmath21 is an efficiency parameter for the envelope ejection , taken to be unity . the masses @xmath22 , @xmath23 and @xmath24 ( @xmath25 for primary and secondary , respectively ) are the stellar mass , the core mass and the envelope mass . the co and he core masses were taken from standard single star models for solar metallicity and adopting the schwarzschild criterion for convection and included 0.25 pressure scale heights of convective overshooting . @xmath26 , where @xmath27 is the roche - lobe radius , obtained as in eggleton ( 1983 ) , and @xmath28 is the separation at the onset of the contact phase . @xmath29 is the envelope binding energy parameter , which depends on the stellar mass and evolutionary stage ( dewi & tauris 2000 ; tauris & dewi 2001 ) . for the purpose of this work we take a constant value of @xmath30 , i.e.  0.1  which is the average @xmath30 value for high - mass stars ( dewi & tauris 2001 ) . the exact value of @xmath30 derived from the whole binding energy can be as low as 0.02 in stars more massive than @xmath31 20  @xmath32  and as high as 0.7 in 10  @xmath32  on the giant branch . as alternative option , we also perform simulations with @xmath33 , a value commonly adopted in population synthesis studies involving ce evolution . for each simulation we apply the same @xmath30 value for both primary and secondary stars .    after the contact phase , we assume that there is no further episode of mass transfer from the co core to the helium core . the co core explodes in an asymmetric supernova ( sn ) , in which a natal kick is imparted at the birth of the neutron star . we apply a maxwellian kick velocity distribution with a dispersion @xmath34 190  @xmath35  ( model  hp ; hansen & phinney 1997 ) and a single gaussian distribution with @xmath34 290  @xmath35  ( model  acc ; arzoumanian , chernoff & cordes 2002 ) . the latter distribution is similar to the distribution found in the most recent study by hobbs et al . ( 2005 ) who derived a kick velocity distribution with @xmath34 265  @xmath35 . the orbital period of the post - sn binary , as well as the system velocity after the explosion , are determined as in brandt & podsiadlowski ( 1995 ) . the explosion is assumed to leave a 1.4  @xmath32  neutron star . if the binary survives the sn explosion , it continues its evolution as a hes - ns system . extensive studies on mass transfer phase in hes - ns binaries have been carried out by dewi et al . ( 2002 ) and dewi & pols ( 2003 ) , taken into account a wide parameter space in helium star masses and orbital periods . during the mass - transfer phase , it was assumed that the neutron star accretes matter up to its eddington limit and the rest of the transferred mass is lost to the system , carrying the specific angular momentum of the neutron star . we apply the results of the systematic studies by dewi et al . ( 2002 ) and dewi & pols ( 2003 ) to determine the orbital parameters of the system at the end of rlof , which are the same as those prior to the explosion of the second sn . we apply the same kick velocity distribution as in the first sn . we also consider the recent suggestion that the second neutron star experiences a much lower kick velocity ( dewi , podsiadlowski & pols 2005 ) , i.e.  by combining the above - mentioned kick distributions for the first neutron star and a distribution with @xmath34 20  @xmath35  for the second . these models are denoted by asterisks in table  [ doublecore : tab : dns ] ( models hp * and acc * ) . to calculate the birth rate of dns , we assume a sn rate of 0.01  @xmath36 . after a dns is formed , it emits gravitational - wave radiation causing the decay of the orbit . we calculate the merger timescale of each system due to the emission of gravitational waves by applying the formula in peters ( 1964 ) . if a system merges in less than the hubble timescale , which we assume to be 10  gyr , it contributes to the total merger rate of dnss . in table  [ doublecore : tab : dns ] we present the birth and merger rates of dnss for each simulation . with lower @xmath30 values ( @xmath37 ) , we obtain systems with smaller post - contact separations than applying @xmath33 , and hence we would expect fewer systems to survive the contact phase . in general , applying a lower minimum radius for case c mass transfer means allowing for more systems to be included as dns progenitors and hence we obtain higher birth and merger rates .    .birth and merger rates of dnss , and potential rate of long - duration grbs for each simulation . also shown in the table are the disruption rates of dnss . all rates are in units of @xmath0 . the first column indicates the kick velocity distribution ( see text for explanation ) . asterisks mark models applying low kick velocities to the second - formed neutron star . the second and third columns present the @xmath30 value and the criterion for the minimum radius for case c mass transfer . [ cols="<,^ , < , > , > , > , > " , ]     it is still an open question whether black - hole formation is accompanied by a natal kick imparted to the black hole . the distribution of black - hole x - ray binaries in the galaxy may indicate that black holes on the whole do not receive significant kicks at birth ( white & van paradijs 1996 ) . however , the high space velocity of nova sco strongly indicates a large natal kick in this particular system ( brandt , podsiadlowski & sigurdsson 1995 ) . the recent study by jonker & nelemans ( 2004 ) also supports the idea of a substantial natal kick for the majority of black holes . in this study , we apply two assumptions for the kick velocity imparted to the black hole at birth ; one is that black holes are formed without a kick velocity ( @xmath38 ) , and the other that a kick velocity of the same magnitude as in the case of neutron - star formation ( @xmath39  @xmath35 ) is imparted .    in the case of almost twin binaries passing through a contact phase , the more massive primary always collapses first with a more massive core . consequently , in the case of bh - ns binaries , the neutron star is formed later and does not experience any episode of mass transfer , i.e.  it is not recycled and can only be observable as a young pulsar . studies on the formation of recycled pulsar with black - hole companion have been carried out by , e.g. , voss & tauris ( 2003 ) , sipior , portegies zwart & nelemans ( 2004 ) , and recently pfahl et al . ( 2005 ) . table  [ doublecore : tab : bhns ] shows the birth rates of bh - ns and black - hole / black - hole ( bh - bh ) binaries . all bh - ns and bh - bh systems merge within a hubble time , and hence the numbers in the table represent both the birth and merger rates . the rates of bh - ns binaries are significantly lower than those of dnss . the reason is that only a very narrow range of primary masses , i.e.  @xmath40  @xmath32   can produce bh - ns binaries in the framework of the double - core scenario . the trend found in dnss , in which birth and merger rates are the highest for the combination of the low case - c criterion and the high @xmath30 values , and are the lowest for the high case - c criterion and the high @xmath30 value , is also applicable to bh - ns binaries . the case where the black - hole mass is equal to its immediate progenitor mass yields higher rates , by typically a factor of 1.5 , than the case where mass is lost in the black - hole collapse . however , when we apply zero kicks for black - hole formation , the rates for the two cases of black - hole mass are rather similar . one would expect to form more bh - ns or bh - bh binaries than ns - bh systems ( in which the neutron stars are formed before the black holes ) because one requires fine tuning in the initial masses and the orbital period distribution to allow the initially more massive component to have a less massive core at the end of its evolution . the formation of ns - bh binaries is similar to pulsars b2303 + 46 and j11416545 , in which white - dwarf companions are formed before the pulsars ( tauris & sennels 2000 ; davies , king & ritter 2002 ) . indeed , sipior et al . ( 2004 ) found that the birth rate of bh - ns is about 27 higher than ns - bh . this is about 10 times higher than the ratio obtained by voss & tauris ( 2003 ) . the birth rates of bh - ns binaries from our simulations are typically comparable or lower than the ns - bh rates found by voss & tauris ( 2003 ) or pfahl et al . the latter authors applied more or less similar assumptions of black - hole masses , kick velocities and @xmath30 values . the comparable rates between our bh - ns result and their ns - bh binaries is because bh - ns binaries formed by the double - core channel originate from a very narrow mass range , as opposed to the formation of bh - ns through the standard scenario which allows a much wider range of mass to form black hole . when the helium star in a hes - ns binary collapses into a neutron star , it is possible that the system may not survive the sn explosion and become unbound ; in this case the two neutron stars become runaway neutron stars . the second neutron star , i.e.  the descendant of the helium star , will be observed as a young , single radio pulsar , while the first - born neutron star can be observed as a single , recycled pulsar . pulsars j2235 + 1506 ( @xmath41 55.7  ms ; camilo , nice & taylor 1993 ) and j0609 + 2130 ( @xmath41 59.7  ms ; lorimer et al . 2004 ) are two single pulsars with characteristics resembling those of dnss , and thus have been proposed to have originated from disrupted dnss . adopting the commonly accepted high kick velocity at neutron star birth , lorimer et al . ( 2004 ) suggested that we should observe more disrupted recycled pulsars than dnss . table  [ doublecore : tab : dns ] displays the disruption rates which , in general , are indeed higher than the birth rates in models  hp and acc . the disruption rates are significantly higher than the birth rates in models using the high case - c criterion and high @xmath30 values because the systems are in relatively wide orbits and hence are more likely to become unbound by the sn . the difference between disruption and birth rates are higher in simulations using acc kick models due to the large kick velocities . when we apply a low kick velocity at the second sn , the disruption rates are significantly reduced . the fact that we observe seven dnss and only two disrupted dnss is consistent with the suggestion that kick velocities imparted at the birth of the second neutron stars in dnss are lower than commonly thought . we can derive the runaway velocities of the two neutron stars as in appendix b in pfahl , rappaport & podsiadlowski ( 2002 ) . for the first - born neutron stars , we can calculate the spin period as in dewi et al . ( 2005 ) and plot them against the runaway velocities . [ doublecore : fig : faildns ] presents this plot for models  acc and acc*. as a consequence of the high kick velocities , disrupted dnss from model  acc have significantly higher runaway velocities . the interesting difference can be seen in the distribution of spin periods ; while the spin periods of model  acc extends to periods as short as 10  ms , only single , recycled pulsars with spin period larger than 0.2  s are produced by model  acc*. these systems originate from hes - ns binaries with relatively high - mass helium stars which transfer little amount of mass ( hence the large spin period , see the discussion in dewi et al . ( 2005 ) ) . this rather striking difference may allow us in principle to constrain the kick velocity distribution for the second supernova kick from the spin period distribution of single recycled pulsars from disrupted dnss . we have performed monte carlo simulations for the formation of dnss in the double - core scenario . we found merger rates in this channel of 0.1  12  @xmath0 . these rates are subject to substantial uncertainties in the binary input physics . although it is clear that model  hp provides larger birth and merger rates than model  acc , we found that the rates are not very sensitive to the choice of kick velocity as both kick models yield rates of the same order of magnitude . the rates are sensitive to the kick velocity only for models hp * and acc * where we assumed a much lower kick velocity for the second supernova . the birth and merger rates depend mainly on the modelling of the contact phase . in this study we limit the investigation to a combination of @xmath30 values and the minimum radius for case c mass transfer . although we include primary masses between 8 and 25  @xmath32 , we found that the dnss mainly originate from primary stars in the range of @xmath31 12  23  @xmath32 . the @xmath30 values in this mass range depend sensitively on the stellar mass , but in any case are always substantially lower than 0.5 , a standard value used in the previous literature . our adopted value of @xmath37 , even though too low for stars less massive than @xmath31 14  @xmath32  and too high for @xmath4217  @xmath32 , represents the average @xmath30 value for stars in the range of @xmath31 8  25  @xmath32  and hence should provide a more reasonable value than @xmath33  at least for the primary stars .    throughout our simulations we apply the same @xmath30 for the secondary as for the primary . for stars of @xmath31 16  18  @xmath32 , the @xmath30 value is relatively constant for a wide range of radius , then increases steeply once the star had finished core helium burning . since we assume that the primary is in a more advanced stage of evolution and , moreover for this particular study , the primary is at least at the end of the core helium - burning phase , using the same @xmath30 value for both the primary and secondary is not always the best approach . estimating the @xmath30 value for the secondary relative to the value for the primary requires knowledge of the secondary radius at the onset of mass transfer phase and modelling of the early mass - transfer phase , which we were not able to investigate in this study . using different minimum radii for case c mass transfer , which simulates the effects of different evolutionary post - main - sequence evolutionary tracks , is one of the major sources of uncertainty for deriving the birth and merger rates of dnss . stars less massive than @xmath31 14  @xmath32  generally go through a blue loop and hence the high case - c criterion fits better for primary stars in this range of mass . the situation is not so certain for more massive stars . knowledge of the primary and secondary radii at the onset of the contact phase is very important for determining the outcome of the contact phase since the radii determine the envelope binding energy ( and hence the appropriate value of @xmath30 ) . it will require detailed binary evolution calculations to overcome the uncertainties on the radii and @xmath30 values , which we leave for further study . even when we know the stellar structure through detailed modelling , we are still left with one important uncertainty , i.e.  how to model the outcome of a contact phase . in this study we apply the so - called standard prescription in which the final separation is determined by the envelope binding energy .    it is worth noting that our results depend on the initial distributions of the binary parameters , in particular the mass - ratio distribution . if we bias the initial mass - ratio distribution more towards equal masses of both components , e.g. by simply restricting the mass ratio to a uniform distribution between 0.5 and 1 , the resulting rates in table  [ doublecore : tab : dns ] are increased by a factor of @xmath43 . the double ce scenario studied by bethe & brown ( 1998 ) yielded a merger rate of @xmath44 for dnss and @xmath45 for bh - ns binaries , which tends to be somewhat higher than most of the rates obtained in this study . we suspect that this huge difference is due to our constraint of only including primaries which go through case c mass transfer . we argue that our additional constraint is required to explain the presence of recycled pulsars . after discussing the possible uncertainties involved in this study , we will now compare our results with those derived from the standard scenario . dpvdh found birth rates of 0.95  87 @xmath0 , comparable and somewhat larger than this study . however , comparison between our results and those of dpvdh is not straightforward as the two studies are done with a very different approach . dpvdh use the bse binary population synthesis code of hurley , tout & pols ( 2002 ) which , among other factors , includes the loss of angular momentum due to stellar wind mass loss in the orbital evolution . our double - 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we present the results of a systematic exploration of an alternative evolutionary scenario to form double neutron - star binaries , first proposed by brown ( 1995 ) , which does not involve a neutron star passing through a common envelope . in this scenario , 
 the initial binary components have very similar masses , and both components have left the main sequence before they evolve into contact ; preferably the primary has already developed a co core . 
 we have performed population synthesis simulations to study the formation of double neutron star binaries via this channel and to predict the orbital properties and system velocities of such systems . 
 we obtain a merger rate for dnss in this channel in the range of 0.1  12  @xmath0 . 
 these rates are still subject to substantial uncertainties such as the modelling of the contact phase . 
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