Dark matter ( DM ) particles in the Universe accumulate in neutron stars ( NSs ) through their interactions with ordinary matter .
It has been known that their annihilation inside the NS core causes late-time heating , with which the surface temperature becomes a constant value of T _ { s } \simeq ( 2 - 3 ) \times 10 ^ { 3 } K for the NS age t \gtrsim 10 ^ { 6 - 7 } years .
This conclusion is , however , drawn based on the assumption that the beta equilibrium is maintained in NSs throughout their life , which turns out to be invalid for rotating pulsars .
The slowdown in the pulsar rotation drives the NS matter out of beta equilibrium , and the resultant imbalance in chemical potentials induces late-time heating , dubbed as rotochemical heating .
This effect can heat a NS up to T _ { s } \simeq 10 ^ { 6 } K for t \simeq 10 ^ { 6 - 7 } years .
In fact , recent observations found several old NSs whose surface temperature is much higher than the prediction of the standard cooling scenario and is consistent with the rotochemical heating .
Motivated by these observations , in this letter , we reevaluate the significance of the DM heating in NSs , including the effect of the rotochemical heating .
We then show that the signature of DM heating can still be detected in old ordinary pulsars , while it is concealed by the rotochemical heating for old millisecond pulsars .
To confirm the evidence for the DM heating , however , it is necessary to improve our knowledge on nucleon pairing gaps as well as to evaluate the initial period of the pulsars accurately .
In any cases , a discovery of a very cold NS can give a robust constraint on the DM heating , and thus on DM models .
To demonstrate this , as an example , we also discuss the case that the DM is the neutral component of an electroweak multiplet , and show that an observation of a NS with T _ { s } \lesssim 10 ^ { 3 } K imposes a stringent constraint on such a DM candidate .