2010ApJ...715..335K

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 (LMXB) phase pose additional constraints on the period (P) and spin-down rates {({dot}P)} 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 while the standard spin-down age may overestimate or underestimate 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 {({dot}m≪{dot}M_{Edd})} 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.