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there is no consensus regarding the generation of the magnetic field in neutron stars .
the field could either be a fossil remnant from the progenitor star in the form of abrikosov fluxoids of the core proton super - conductor ( baym , pethick & pines 1969 , ruderman 1972 , bhattacharya & srinivasan 1995 ) .
or it could be generated after the formation of the neutron star in which case the currents would be entirely confined to the solid crust ( blandford , applegate & hernquist 1983 ) .
evidently , the nature of the evolution would depend very much on the internal field configuration .
observations and statistical analyses of existing pulsar data , nevertheless , indicate that significant decay of magnetic field is achieved only if the neutron star is a member of an interacting binary ( bailes 1989 , bhattacharya 1991 , hartman et al .
+ the processes that are responsible for the field evolution in neutron stars in binaries are - a ) expulsion of the magnetic flux from the super - conducting core during the phase of propeller spin - down , b ) screening of the field by accreted matter and c ) rapid ohmic decay of the crustal field in an accretion - heated crust ( for a review see bhattacharya 2000 ) .
diamagnetic screening of the field by accreted matter does not seem likely to have any long - term effect ( konar 1997 ) and we shall exclude it from the present discussion .
the other models invoke ohmic decay of the current loops for a permanent decrease in the field strength . in either case
, the effect of accretion is two - fold .
the heating reduces the electrical conductivity and consequently the ohmic decay time - scale inducing a faster decay . at the same time
the material movement , caused by the deposition of matter on top of the crust , pushes the original current carrying layers into deeper and denser regions where the higher conductivity slows the decay down .
the mass of the crust of a neutron star changes very little with a change in the total mass ; accretion therefore implies assimilation of the original crust into the super - conducting core .
when the original current carrying regions undergo such assimilation , further decay is stopped altogether .
both the purely crustal model as well as the model assuming an expelled flux have been investigated by many authors ( see bhattacharya 2000 ) . the important difference between our work and that of the other investigators lies in our assumption of a _ flux freezing _ upon the assimilation of the original current carrying layers into the super - conducting core .
system & final field and period & comment + isolated & high field , long period & no significant field decay + radio pulsars & & in @xmath0   years + hmxb & high field , long period & high - mass binary pulsars + & & and solitary counterparts + & low field , long period & not active as pulsars + lmxb & high field , long period & high field low - mass + & & binary pulsars + & & and solitary counterparts + & low field , short period & low field low - mass + & & binary pulsars + & & and solitary counterparts , + & & millisecond pulsars +
the qualitative features of field evolution , as outlined below , are similar for a ) an initial crustal field and b ) an expelled flux .    * pure ohmic decay in isolated neutron stars * ( konar 1997 ) + 1 .
a slow / fast cooling of neutron star implies a fast / slow decay ; hence a low / high final field .
initial crustal currents concentrated at lower / higher densities gives rise to low / high final surface fields .
large impurity content makes the decay rapid and gives rise to smaller final fields .    * accretion - induced field decay in accreting neutron stars * + ( konar & bhattacharya 1997 - kbi ) + 1 . in an accreting neutron star the field undergoes an initial rapid decay , followed by slow down and an eventual _ freezing_. + 2 .
a positive correlation between the rate of accretion and the final field strength is observed , giving rise to higher final saturation field strengths for higher rates of accretion .
* magnetic field and spin period *  we have investigated the nature of the final ` magnetic field - spin period ' combination .
our results agree well with the observations and are summarised in table - i ( kbi , konar & bhattacharya 1999a - kbii ) .
the nature of field evolution is similar for the model of spin - down induced flux expulsion ( konar & bhattacharya 1999b - kbiii ) .
though there is one major difference as can be seen from fig.([f_lmxb ] ) . to produce millisecond pulsars in lmxbs for an expelled flux large values of impurities , in the prior - to - accretion original crust , are required . but this would result in extremely small surface fields in old isolated pulsars .
this is in complete contrast to a purely crustal model and expectation from statistical analyses of pulsar data .
the paradigm of field evolution that have emerged out of observations , statistical analyses and theoretical expectations have been summarized in fig .
( [ f_paradigm ] ) where the connection between the radio pulsars and their binary counterparts , namely the x - ray binaries is indicated . in table - ii we indicate the constraints on various physical parameters in the field evolution models placed by the requirement to match observed properties in a variety of systems ( kbii , kbiii ) . the parameters discussed here are - the density at which the initial crustal current distribution is located ( @xmath1 ) , the impurity strength in the crust ( @xmath2 ) , the duration of wind - accretion phase in different binary systems and the rate of accretion in the roche - contact phase for lmxbs .
parameter & model & system & requirement & parameter range + @xmath3 & crustal & hmxb & high field & high @xmath3 + @xmath2 & crustal & isolated & no decay over & @xmath4 for + & & radio & active pulsar & standard cooling , + & & pulsar & life - time & @xmath5 for + & & & & accelerated cooling + & expelled & lmxb & millisecond & @xmath6 with + & flux & & pulsar & wind accretion , + & & & generation & @xmath7 without + & & & & wind accretion + duration of & crustal & hmxb & high field & short + wind accretion & & & & +  in & crustal & lmxb & high field & eddington rate + roche - phase & & & & +
the results and conclusions stated above suffer from a number of uncertainties regarding the micro - physics of the neutron star .
as have been listed below . moreover , a lot of the new theoretical results as well as the observational facts have recently become available . in this section
we mention some of the more important aspects that need to be incorporated in any future work on the evolution of the magnetic fields of neutron stars .
* thermal behaviour * + 1 . isolated phase - the present data can be made to fit scenarios with both a _ slow _ or an _ accelerated _ cooling .
therefore , it is not clear which is the correct cooling behaviour of an isolated neutron star .
accreting phase - the crustal temperature corresponding to a given rate of accretion has not been determined with any degree of certainty . also , the existing results are limited in their scope .
post - accretion phase - no calculation exists for the thermal behaviour of this phase at all .
* transport properties * - several factors affect the transport properties and hence both thermal and magnetic field evolution .
prominent among them is the change in the * chemical composition * due to a ) accretion and b ) spin - down .
recently it has been shown that the impurity content of the accreted crust for near - eddington accretion rates could be extremely large ( schatz et al .
this , along with a temperature inversion near or beyond the neutron drip ( brown 1999 ) might modify the transport properties significantly . moreover
the presence of dislocations , defects , non - spherical nuclei have so far not been taken into account in the calculation of transport properties .
these are also expected to have an impact on the field evolution in isolated as well as binary pulsars .
+ * multi - polar structure * - all of our and similar investigations have been based on an assumption of a pure dipolar model for the magnetic field .
though calculations for isolated neutron stars does not show any appreciable change in multi - polar structures ( mitra , konar & bhattacharya 1999 ) - the situation would change in presence of accretion or a very strong magnetic field ( geppert et al .
1999 ) due to the importance of the hall term requiring further investigation . +
* the magnetar question * - amongst some of the more recent developments the magnetars pose a great challenge for the existing theories of field evolution since they require a very rapid field evolution in isolated neutron stars . though some work have already been done in this area ( heyl & kulkarni 1998 , geppert et al .
1999 ) - more detailed investigation is needed .
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the evolution of the magnetic field is investigated for isolated as well as binary neutron stars . 
 the overall nature of the field evolution is seen to be similar for an initial crustal field and an expelled flux . 
 the major uncertainties of the present models of field evolution and the directions in which further investigation are required are also discussed in detail .