Millisecond Pulsar Ages: Implications of Binary Evolution and a Maximum Spin Limit

Abstract: 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.

• The paper proposes an enhanced methodology incorporating binary evolution and maximum spin limits to improve millisecond pulsar age estimates over traditional spin-down methods.
• It highlights shortcomings of standard spin-down age estimation for MSPs and incorporates binary evolution processes and maximum spin limits for refined age estimates.
• The study constrains MSP ages and has implications for understanding binary evolution and WD cooling models, suggesting a significant fraction experience low accretion rates.

Estimating Millisecond Pulsar Ages: An Enhanced Methodology

The paper in question revisits the traditional approach to estimating the ages of millisecond pulsars (MSPs) and proposes a novel methodology that incorporates additional constraints related to binary evolution and spin dynamics. The focus is on improving the accuracy of age estimates for MSPs, particularly those in binary systems and those nearing the theoretical spin limit.

Shortcomings of the Standard Spin-Down Age Estimation

For many pulsars, age estimation relies on measuring the period (P) and spin-down rate ($\dot{P}$), calculating an inferred "characteristic age." However, this method often fails for MSPs due to their rapid spin rates. Key assumptions about initial spin periods and energy loss mechanisms often lead to age overestimations or underestimations by up to an order of magnitude. The traditional spin-down age is captured as:

$\tau_{c} = \frac{P}{2 \dot{P}}$

This characterization assumes pure magnetic dipole radiation with a braking index of $n=3$, which may not always hold true for MSPs, particularly those that have undergone complex evolutionary processes.

Incorporating Binary Evolution and Spin Constraints

The researchers propose a more comprehensive framework that takes into account:

• Spin-Up Processes during LMXB Phases: MSPs can be spun up to very short periods in low mass X-ray binaries (LMXBs), which adds complexity to the age estimation. The authors introduce a method that considers these phases and recalibrates age estimates based on expected maximum spin-up limits.
• Maximum Spin Limits: Neutron stars experience a centrifugal force limit, given by Keplerian spin velocities, influencing the maximum possible spin rate. This limit helps define a realistic upper bound for redistributing the MSP population on the P-$\dot{P}$ diagram.

Introducing these factors allows for a refined age estimate, denoted as $\widetilde{\tau}$, resulting in more accurate portrayals of pulsar evolutionary stages.

Testing and Implications

The paper examines different plausible braking indices, confirming that an index of $n=3$ is consistent with observed populations. It introduces two forms of data "corruption": observed "age bias" due to secular acceleration and "age contamination" from low accretion rates during progenitor phases. By correcting these factors, MSP ages poised to appear older than their respective galaxies are more meaningfully constrained.

MSPs are individually subject to tracking evolutionary constraints to obtain realistic ages, providing significant implications for the study of binary evolution, WD cooling models, and the broader understanding of stellar dynamics. A key finding is that a significant fraction of the MSP population likely experiences low accretion rates, contradicting earlier estimates. Consequently, the study provides implications for MSP age distributions, underscoring the importance of addressing systematic biases when estimating their ages.

Future Directions

The research suggests that further observational studies of MSP kinematics and magnetic field properties could refine current age estimates. Also, continuing advancements in understanding WD cooling models and supernova remnant structures could provide additional independent means to verify pulsar age estimates.

In essence, this work significantly contributes to the field of pulsar astrophysics, offering a methodological improvement that considers evolving dynamics and the intricacies of neutron star physics. As future observations and models develop, especially concerning gravitational wave detections and MSP progenitor environments, these findings could be further refined, enhancing our understanding of these complex systems.