RX J0720.4-3125: Implications for neutron star cooling and the dense matter equation of state

The soft X-ray source RX J0720.4-3125 appears to be a clean example of a co oling neutron star. Its X-ray emission is well-fit by a 79 +/- 4 eV blackbo dy and displays a periodic modulation with period P = 8.391 sec and semi-am plitude similar to 10%. The observational upper limit to the period derivat ive implies a minimum spindown age of t(0) = 1.7 x 10(5) yr if the star was born rapidly rotating. The absence of a visible supernova remnant independ ently suggests an age for this source of greater than or similar to 10(5) y r. With the interpretation of this source as a cooling-driven, magnetized, rotating neutron star, we explore the implications for the dense matter equ ation of state (EOS), the mode of energy loss (modified URCA vs. direct URC A), and the rate of internal heating due to superfluid friction. For the st andard (modified URCA) cooling models, we study two types of stars: those b orn slowly rotating, with relatively small spindown rates and conventional dipole magnetic fields (similar to 10(12) G), and those born rapidly rotati ng with large spin-down rates and. magnetar-scale dipole fields (similar to 10(14) G). We find that standard cooling with a stiff or moderately stiff EOS is consistent with the observations of RX J0720.4-3125 provided the sta r's age is less than or similar to 3 t(0) = 5 x 10(5) yr. If the EOS is ver y stiff, the star must be born with a short rotation period and significant internal heating by superfluid friction is required. More moderate heating suffices only if the star is very massive (similar to 2 M.) and has an age similar to t(0) Stars with M similar to 1.4 M. and a moderately stiff EOS give modulations about a factor of five below that observed. However, the i nclusion of atmospheric effects or more complex field geometries could incr ease the modulation to a level consistent with the observations. Stars with a stiff EOS give modulations close to that observed. As an illustration of the effects of accelerated cooling processes, we consider direct quark URC A cooling. We find that these models cool too fast and are cleanly ruled pu t for this source. Hence, exotic matter is an insignificant component in th e stellar core, or does not participate in accelerated cooling. Direct URCA reactions in nucleonic matter are similarly ruled out. A measure of RX J07 20.4-3125's spin-down age would afford crucial tests of our conclusions.