Millisecond Pulsar Ages: Implications of Binary Evolution and a Maximum
  Spin Limit
  In the absence of constraints from the binary companion or supernova remnant,
the standard method for estimating pulsar ages is to infer an age from the rate
of spin-down. While the generic spin-down age may give realistic estimates for
normal pulsars, it can fail for pulsars with very short periods. Details of the
spin-up process during the low mass X-ray binary phase pose additional
constraints on the period (P) and spin-down rates (Pdot) that may consequently
affect the age estimate. Here, we propose a new recipe to estimate millisecond
pulsar (MSP) ages that parametrically incorporates constraints arising from
binary evolution and limiting physics. We show that the standard method can be
improved by this approach to achieve age estimates closer to the true age
whilst the standard spin-down age may over- or under-estimate the age of the
pulsar by more than a factor of ~10 in the millisecond regime. We use this
approach to analyze the population on a broader scale. For instance, in order
to understand the dominant energy loss mechanism after the onset of radio
emission, we test for a range of plausible braking indices. We find that a
braking index of n=3 is consistent with the observed MSP population. We
demonstrate the existence and quantify the potential contributions of two main
sources of age corruption: the previously known "age bias" due to secular
acceleration and "age contamination" driven by sub-Eddington progenitor
accretion rates. We explicitly show that descendants of LMXBs that have
accreted at very low rates will exhibit ages that appear older than the age of
the Galaxy. We further elaborate on this technique, the implications and
potential solutions it offers regarding MSP evolution, the underlying age
distribution and the post-accretion energy loss mechanism.
