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the latest measurement of the shapiro delay for the millisecond pulsar psrj1614 - 2230 provides reliable lower bound on the maximum mass to be @xmath2 @xcite . this measurement rules out all the equations of state ( eoss ) yielding the maximum mass less than that of the psrj1614 - 2230 of course , the eoss for the nucleonic matter can readily yield the compact stars with masses @xmath3 . the eoss with hadron - quark phase transition are also compatible with the mass measurement of the psrj1614 - 2230 , provided , the quarks are assumed to be strongly interacting and are in colour superconducting phase @xcite . however , at large , the maximum mass of the compact stars are found to be well below @xmath0 when the non - nucleonic degrees of freedom like hyperons and kaon condensates are considered @xcite . one might thus infer in the backdrop of previous calculations that the existence of hyperons and kaon condensates are unlikely in the psrj1614 - 2230 . recently , studies involving role of hyperons on the maximum mass of the compact stars are revisited @xcite . it is shown that the eos for the hyperonic matter at higher densities can be stiffened in several ways within the relativistic mean - field ( rmf ) models . the maximum mass for these eoss are above @xmath0 indicating the existence of hyperons in the psrj1614 - 2230 . the eos of the hyperonic matter are stiffened by including the vector - isoscalar strange @xmath4 mesons within the rmf model , in addition to the usual scalar - isoscalar @xmath5 , vector - isoscalar @xmath6 and vector - isovector @xmath7 mesons @xcite . the @xmath4 mesons stiffens the eos at densities far beyond the nuclear saturation density . further , the increase of about @xmath8 in the maximum mass of the compact stars is achieved by varying the hyperon - nucleon potential depths for the @xmath9 and @xmath10 hyperons which are not very well known . it has been also demonstrated @xcite that maximum mass of the compact stars containing hyperons are well above @xmath11 , provided , the @xmath6 mesons are coupled to hyperons as strongly as to the nucleons . such strong meson - hyperon couplings stemmed from the breaking of su(6 ) symmetry . another way to stiffen the eos is to include the non - linear terms for the @xmath4-mesons as suggested in ref . it may be pointed out that the nuclear eoss employed in ref . @xcite are generally quite stiff in comparison to those extracted from the heavy - ion data @xcite .    an alternative scenario has also emerged in which compact stars containing hyperons can have masses @xmath3 . in this scenario , one assumes the presence of hypothetical weakly interacting light bosons ( wilbs ) at densities several times of the nuclear saturation density . the role of wilbs on the eos or the internal structure of the compact stars crucially depends on the choice of the characteristic scale which is the square of the ratio of the coupling strength to the masses of wilbs . the values of the characteristic scale of the wilbs are poorly constrained at present by the laboratory data and the compact star observable @xcite . consequently , the nuclear eoss compatible with the heavy - ion data allow the hyperons to exist in the compact stars with mass @xmath3 @xcite . the required stiffness of the eos at very high density is achieved by adjusting the characteristic scale of the wilbs .    in the present work we explore the possibility of existence of hyperons in the psrj1614 - 2230 using a diverse set of nuclear eoss calculated within the rmf models . in particular , we examine whether the nuclear eoss compatible with the heavy - ion data can allow the hyperons to exist in the psrj1614 - 2230 without recourse to the wilbs . this makes our present investigation quite different than the ones performed earlier . most of the previous investigations either employed the nuclear eoss which are stiffer in comparison to the heavy - ion data or included the contributions of the wilbs . the paper is organized as follows . in sec . ii we describe the theoretical framework based on the rmf model . in sec . iii , we present our results for the eoss for the matter without and with hyperons . in sec . iv we present our results for the bulk properties of the static compact stars . finally , we state our conclusions in sec . v. we use standard and extended versions of the rmf models to compute the bulk properties of the compact stars . the standard rmf model includes the contributions from the non - linear self - interaction for the @xmath5 meson and extended rmf model includes the contributions from the self and/or cross interaction terms for the @xmath5 , @xmath6 and @xmath7 meson . we will discuss both versions of the rmf models . the derivations of the effective lagrangian density and corresponding energy density functionals for the extended rmf model are well documented in refs . @xcite . in rmf models , baryons interact through the exchange of scalar ( @xmath5 ) , vector ( @xmath6 and @xmath7 ) as well as two additional hidden - strangeness ( @xmath5 * and @xmath4 ) mesons . the baryons considered in this work are nucleon ( @xmath12 ) and hyperons ( @xmath13 ) . the total lagrangian density of rmf model including hyperons plus leptons ( l ) can be written as ,    @xmath14    where the free baryons lagrangian density is , @xmath15\psi_b,\ ] ] here , @xmath16 is baryons field and the sum is taken over @xmath12 , @xmath17 , @xmath9,and @xmath10 baryons . the lagrangian density for free mesons involved is , @xmath18 the @xmath19 , @xmath20 and @xmath21 are field tensors corresponding to the @xmath6 , @xmath4 and @xmath7 mesons field , and can be defined as @xmath22 , @xmath23 and @xmath24 . the lagrangian @xmath25 describing the interactions of the baryons through the mesons is , @xmath26\psi_b , \label{eq : llin}\ ] ] where @xmath27 are the baryons isospin matrices . the lagrangian describing nucleons self interactions for @xmath5 , @xmath6 , and @xmath7 mesons can be written as , @xmath28 while the free leptons lagrangian density is , @xmath29\psi_l.\ ] ] here @xmath30 is leptons ( electron and muon ) field . the meson - nucleon coupling constants and nonlinear parameters of rmf models are determined by adjusting them to reproduce ground state properties of finite nuclei and nuclear matter . here , we employed nl3 , gm1 , tm1 , g2 , bsr2 , bsr6 , bsr9 , bsr13 and bsp parameter sets for meson - nucleon coupling constants and nonlinear parameters @xcite . these parameterizations of the rmf models are associated with different form for the lagrangian density . they differ in their non - linear part of the effective lagrangian ( eq . [ eq : lnlin ] ) which are summarized in table [ tab : rmf ] . for instance , the lagrangian density associated with the parameter sets nl3 and gm1 correspond to the standard rmf model which includes non - linear term only for the self - interactions of the @xmath5 meson . other parameter sets tm1 , g2 and bsr correspond to the extended rmf models which include contributions from the self - interactions of the @xmath6 mesons and/or cross - interactions between @xmath31 and @xmath7 mesons . the meson - hyperon coupling strengths @xmath32(@xmath33 and @xmath34 ) in eq . ( [ eq : llin ] ) can not be determined very well at present . the properties of compact stars are quite sensitive to the choices for the values of @xmath35,@xmath36 and @xmath37 . the variations in the values of @xmath38 and @xmath39 do not appreciably alter the properties of compact stars . the values of @xmath38 and @xmath39 are kept fixed in our calculations . we take @xmath40 , this choice is consistent with @xmath41hypernuclear data which yields weak @xmath42 interaction @xcite . the values of @xmath38 are taken from the su(6 ) quark model . we make several choices for the values of @xmath43 and @xmath37 . one of which correspond to those obtained within the su(6 ) quark model . the su(6 ) quark model values for @xmath36 , @xmath38 and @xmath37 are @xmath44 for given values of @xmath36 the coupling strengths @xmath35 are usually obtained from potential depths for hyperons in the symmetric nuclear matter at the saturation density as , @xmath45 the values of potential depths @xmath46 chosen are as follows @xcite , @xmath47 for the sake of convenience we define ,    @xmath48    and , @xmath49    it has been shown earlier in ref . @xcite that the values of @xmath50 , which are larger compared to those for the su(6 ) model ( eq . [ eq : su6 ] ) , can yield heavier compact stars composed of hyperons without affecting the properties of the @xmath51hypernuclei . recent investigation @xcite suggests that the values of @xmath52 can significantly differ from those given by the su(6 ) quark model . the breaking of the su(6 ) symmetry yields @xmath53 ( i.e. , @xmath54 ) . in the present work we vary the values of @xmath55 and @xmath56 over a wide range to see in what limits the compact stars with hyperons can satisfy the constraints on the lower bound on the maximum mass imposed by the psrj1614 - 2230 . we use different versions of the rmf models , as summarized in table [ tab : rmf ] , to compute the eoss for the @xmath57-equilibrated nucleonic and hyperonic matters . our choice for the models are such that they yield wide variations in the various quantities associated with symmetric and asymmetric nuclear matter at the saturation density . in table [ tab : nmpro ] we provide the values of some of the quantities associated with nuclear matter at the saturation density @xmath58 , namely , the binding energy per nucleons @xmath59 , incompressibility coefficient for symmetric nuclear matter ( @xmath60 ) , symmetry energy coefficient ( @xmath61 ) , linear density dependence of the symmetry energy coefficient ( @xmath62 ) and various quantities ( @xmath63 ) , ( @xmath64 ) and ( @xmath65 ) . these quantities are evaluated as follows ,    @xmath66    where , @xmath67 is the energy per nucleon at a given density @xmath7 and asymmetry @xmath68 . in table [ tab : nmpro ] , we also list the values of the neutron - skin @xmath69 for the @xmath70pb nucleus . the values of @xmath60 , @xmath71 and @xmath62 vary over a wide range for the selected rmf model . this immediately indicates that the behaviour of the eoss for the different rmf models considered should be quite different even at the low densities .    in fig . [ fig : snm ] we plot the eoss for symmetric nuclear matter ( snm ) in terms of pressure versus nucleon density obtained for various rmf models . the bounds on the eoss as shown by shaded regions are the ones extracted from heavy - ion collision data @xcite . the eoss for the nl3 , gm1 , bsr2 and bsr6 are stiffer in comparison to those obtained from the heavy - ion data . whereas , the tm1 , g2 , bsr9 , bsr13 and bsp are consistent with the eos from the heavy - ion data . the eos for the bsr2 and bsr6 parameterizations are very much the same for the reasons as follow . both of the parameter sets belong to the same type of the rmf model as can be seen from table [ tab : rmf ] . further , the parameters of the bsr2 and bsr6 parameterizations are obtained by fit to exactly same set of experimental data for bulk properties of finite nuclei , but , for different values of the neutron - skin thickness in @xmath70pb nucleus . thus , the bsr2 and bsr6 parameterizations are expected to yield different behaviour only for the eoss of the asymmetric nuclear matter . similar is the case for the eoss obtained with the bsr9 and bsr13 parameterizations . our main goal is to investigate whether the nuclear eoss which are compatible with the heavy - ion data can allow the hyperons to exist in the @xmath0 pulsar psrj1614 - 2230 . for this purpose , the eoss for the @xmath72equilibrated hyperonic matter are calculated using different values for @xmath52 and @xmath56 . we present here the eoss only for two different choices for the @xmath52 and @xmath73 . we refer these choices as xsu6 and x180 . for the case of xsu6 , @xmath74 and @xmath75 which correspond to those given by the su(6 ) quark model as conventionally used . the x180 refers to @xmath76 and @xmath77 . the values of @xmath78 coupling strength are determined using the nucleon - hyperon potential depths as described in sec . it can be easily verified from eqs . ( [ eq : su6 ] , [ eq : xw ] and [ eq : xphi ] ) that the values of @xmath52 and @xmath56 for the case of x180 are augmented by a factor of @xmath79 with respect to their values for the su(6 ) model . in fig . [ fig : eos_bem ] , the eoss for the nucleonic and hyperonic matters are compared for a few different rmf models . the eoss for the nucleonic matter are labeled as no hyp. the eoss for the hyperonic matter are labeled as xsu6 and x180 . it can be seen that the eoss for the hyperonic matter corresponding to x180 are quite close to those obtained for the nucleonic matter . it should be pointed out that the threshold density is lowest for the @xmath17 hyperons for all the rmf models considered irrespective of the choice of the meson - hyperon coupling strengths . further , the augmented meson - hyperon coupling strengths results in marginal increase in the values of the threshold densities for the @xmath17 hyperons . for instance , the threshold densities for @xmath17 hyperons for the nl3(bsp ) parameterizations for the xsu6 and x180 cases are 0.28(0.38 ) and 0.32(0.42 ) @xmath80,respectively . thus , the augmented meson - hyperon coupling strengths might increases the maximum mass of the compact stars without significantly affecting its hyperonic contents .    before employing our eoss for the hyperonic matter to study the properties of the compact stars , we would like to look into the behaviour of the @xmath51h potentials @xmath81 . the values of @xmath51h for given meson - hyperon coupling strengths are obtained as , @xmath82 where , the values of the fields @xmath31 and @xmath4 are calculated for the pure @xmath17 matter at a given density @xmath7 . in fig . [ fig : ulh ] , we plot the results for the @xmath81 obtained using the meson - hyperon coupling strengths corresponding to xsu6 and x180 . for the comparison , we also plot the values of @xmath81 obtained for two different models based on the su(3 ) symmetry @xcite . the green dashed curve is obtained using ref . @xcite for @xmath83 which yields highest value for the maximum mass for the compact star . the values of @xmath84 and @xmath85 for the case of x180 lie within those obtained using other models . whereas , the potential @xmath86 is somewhat stiffer in comparison to the other models as considered . the properties of static or non - rotating compact stars for a given eos is obtained by solving the tolman - oppenheimer - volkoff ( tov ) equations @xcite . for the case of rotating compact stars we solve the einstein equations for stationary axi - symmetric spacetime . the numerical computations are performed using the code written by stergioulas @xcite . we describe the outer crust region of the compact star using the eos of rster _ et  al . _ @xcite which is the recent update of the one given by baym , pethick , and sutherland @xcite . due to the fact that the detailed eos of inner crust indeed is not yet certain , the polytropic pressure - energy density relation is used to interpolate the eos for the region between outer crust and the core @xcite . the core is assumed to be composed of either the nucleonic or the hyperonic matter in @xmath72equilibrium . the eos of the core is obtained from the different parameter sets of the rmf models as presented in sec . [ sec : eos ] .    in fig . [ fig : m - r ] we display our results for the mass - radius relationships for the static compact stars composed of @xmath57-equilibrated nucleonic matter ( upper panel ) and hyperonic matter ( lower panel ) . the shaded region represents the current lower limit on the maximum mass , @xmath87 , of the compact star obtained from the recent mass measurement of the psrj1614 - 2230 . the mass - radius relationships for the compact stars containing hyperons are obtained using standard values for the meson - hyperon coupling strengths as discussed in the previous section . it is evident from the upper panel that the maximum masses of the compact star in the absence of hyperons for all the rmf models considered are compatible with the current limit on its lower bound . the solid circles in the lower panel indicate the minimum mass of the compact star at which the hyperons begin to appear . this minimum mass ranges from @xmath88 for the various rmf models considered . the parameter sets nl3 , gm1 , bsr2 and bsr6 yield maximum mass larger than @xmath0 when the hyperons are included . thus , these parameter sets readily allow the hyperons to appear in the psrj1614 - 2230 . the nuclear eoss , however , for these cases are not compatible with the heavy - ion data ( see fig . [ fig : snm ] ) . on the other hand , the nuclear eoss for the parameter sets bsr9 , bsr13 , bsp , g2 and tm1 are compatible with the heavy - ion data , but , they yield the maximum mass in the range of @xmath89 with the inclusion of hyperons . it seems that the nuclear eoss , compatible with heavy - ion data , can possibly allow the hyperons to exist in the psrj1614 - 2230 for substantially larger values of the meson - hyperon coupling strengths in comparison to their standard values .    in fig . [ fig : mr_x180 ] we show the mass - radius relationships for the compact stars obtained by augmenting the meson - hyperon coupling strengths in comparison to their standard values . as discussed previously , the label x180 corresponds to @xmath76 and @xmath90 which is larger by a factor of @xmath91 with respect to their slandered values taken from the su(6 ) quark model . we plot the results only for those rmf model for which the nuclear eoss are compatible with the heavy - ion data . we find that the maximum masses for the tm1 and bsp parameter sets are consistent with the mass of the psrj1614 - 2230 . it may be pointed out to this end that the radius @xmath92 for the compact star with canonical mass of @xmath93 for the bsp case is 12.7 km which is consistent with @xmath94 km as determined from the recent observations of both transiently accreting and bursting sources @xcite . the values of @xmath92 determined in ref . @xcite are independent of assumptions about the composition of the core . we also look into the hyperon fractions at the maximum mass . in table [ tab : ns ] we present our results for the maximum mass configurations obtained for two different choices of meson - hyperon coupling strengths corresponding to xsu6 and x180 . these results are compared with their nuclear counterparts having no hyperons . we also list the values of the partial mass @xmath95 which is composed of the hyperonic matter . the values of @xmath95 are obtained by integrating the density profile , corresponding to the maximum mass configuration , from the central density to the threshold density at which hyperons begin to appear . it is interesting to note that the ratio @xmath96 is sizable and almost the same for both the choices of the meson - hyperon coupling strengths . the maximum mass obtained using augmented meson - hyperon coupling strengths are very close to their nuclear counter parts and yet significant fraction ( @xmath1 ) of the mass is composed of the hyperonic matter . further , the radius @xmath97 at the maximum mass for the case with no hyperons and the one obtained using augmented meson - hyperon coupling strengths are almost the same . thus , it seems possible to obtain the maximum mass configuration of the compact star , containing sizable fraction of hyperons , which masquareds its nuclear counterpart . the maximum mass of the compact stars with hyperons nearly same as their nuclear counterpart has also been found in ref . @xcite    in fig . [ fig : bsr28 ] we plot the variations of @xmath98 with @xmath52 and @xmath56 for the case of bsp . the value of @xmath98 increases with increasing @xmath52 and @xmath56 . the @xmath98 depends strongly on @xmath52 for smaller values of @xmath56 . as the @xmath56 increases , the value of @xmath98 tends to saturate and becomes more or less independent of @xmath52 . for @xmath99 , the @xmath98 increases by @xmath100 with increase in @xmath52 from 0.5 to 1 . also , the @xmath98 is less dependent on @xmath56 for larger @xmath52 . to this end , we would like to remind that the @xmath101 potential depth @xmath102 is taken to be 30 mev . the value of @xmath103 is not yet certain . in fig . [ fig : bsr281 ] , we compare our results for the @xmath98 obtained for @xmath104 and 30 mev . the value of @xmath98 depends somewhat on @xmath103 for smaller values of @xmath105 . for @xmath106 , the @xmath98 may increases by @xmath107 with increase in @xmath103 from -30 to 30 mev . we also calculate the maximum mass of the compact stars rotating with the frequency @xmath108 hz as that of the psrj1614 - 2230 . in fig . [ fig : bsp_rns ] , we display the variations for the @xmath98 with @xmath52 and @xmath56 . it can be easily seen that the value of @xmath76 with @xmath109 is sufficient to produce the compact star with mass compatible with the current lower bound on the @xmath98 . we use various rmf models to explore the possibility of existence of hyperons in the heaviest observed compact star psrj1614 - 2230 having mass @xmath110 . we have examined the conditions required for the hyperons to exist in the psrj1614 - 2230 when the nuclear eoss are subjected to the constrained imposed by the the heavy - ion data . the various rmf models are selected in such a way that they result in a diverse set of nuclear eoss . the values of maximum mass for these models , in the absence of hyperons , are consistent with the mass of psrj1614 - 2230 . the nuclear eoss which are consistent with the heavy - ion data require larger values of the meson - hyperon coupling strengths in order to allow the hyperons to exist in the psrj1614 - 2230 . particularly , the coupling of @xmath6 and @xmath4 vector mesons to the hyperons are required to be significantly augmented with respect to their standard values . these lager values of the coupling strengths increases the maximum mass to the desired limit without significantly affecting the fraction of maximum mass composed of hyperonic matter . we find that the maximum mass configuration of the compact star with sizable fraction of hyperons masquareds its nuclear counterpart . .[tab : rmf ] various self - interaction and cross - interaction terms included in the lagrangian density associated with different parameterizations of the rmf models considered in the present work . the index 1 and 0 is used to indicate whether or not the corresponding term is included . [ cols="^,^,^,^,^,^,^,^ " , ]
the possibility of existence of hyperons in the recently measured @xmath0 pulsar psrj1614 - 2230 is explored using a diverse set of nuclear equations of state calculated within the relativistic mean - field models . 
 our results indicate that the nuclear equations of state compatible with heavy - ion data allow the hyperons to exist in the psrj1614 - 2230 only for significantly larger values for the meson - hyperon coupling strengths . 
 the maximum mass configurations for these cases contain sizable hyperon fractions ( @xmath1 ) and yet masquared their counterpart composed of only nucleonic matter .