MSP Ages
Millisecond Pulsar Ages
Implications of Binary Evolution & a Maximum Spin Frequency
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 fornormal 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..
Millisecond Pulsar Ages
where the critical magnetic field is Bc~3.3*10^8 G for a putative mass shedding limit Psh~1ms, and alpha=2.58*10^6 (s^4/7).
Millisecond Pulsar Evolution [Movie: 2.8 MB ]
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The observed distribution of Galactic millisecond pulsars
- The observed distribution of Galactic millisecond pulsars. Black dots (•) indicate unbiased spin-down rates for MSPs that have proper motion measurements. Vertical solid lines are the corresponding Shklovskii correction. MSPs with no proper motion measurements are corrected for an assumed vt =100 km/s in order to see the potential level of bias. The magenta squares are MSPs (PSRs J1022+1001, J1216–6410, J1829+2456, J1933–6211) for which the spin-down rates are corrected only for an assumed vt =50 km/s while these MSPs will otherwise appear to be spinning-up.
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The expected true age distribution of the underlying millisecond pulsar population
- Color represents the true age. Downward arrows (↓) are the neutron star spin frequencies measured in LMXBs which are used as progenitor seeds to reconstruct the synthetic population.
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Age Corruption
The underlying age distribution of millisecond pulsars (a) before and (b) after correcting for effects of secular acceleration. Color represents the true age and the diagonal dashed lines are the inferred characteristic age lines. The progenitor seeds used to produce the synthetic population are randomly sampled from the period distribution of observed millisecond X-ray pulsars (downward arrows). a) The transverse velocities and distances are chosen to be consistent with the observed millisecond radio pulsar population in order to see the potential bias in the P-Pdot demographics. b) The P-Pdot distribution for the same sample MSP population after correcting for effects of secular acceleration. The process that disguises older MSPs as younger sources can be reversed by properly correcting (unbiasing) for the Shklovskii effect, whereas the population will still harbor young MSPs with apparent older ages. This (downward) age contamination is driven by the lower mass accretion rates experienced during the LMXB phase. We predict that a significant fraction of millisecond radio pulsars (~30%) will be born with characteristic ages older than the age of the Galaxy.
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Age Distribution
- The effects of secular acceleration on the MSP age distribution: Ages inferred from measured P and Pdot values will over- or under-estimate the true age (dashed line). Unbiased characteristic ages reflect mere overestimates (solid line) where ~30% of MSPs will have an unbiased characteristic age overestimating the true age by more than a factor of two.
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Ages of observed millisecond pulsars
- PSRs J1024-0719, J1801-1417 & J2229+2643 have Pdot'< 0 for vt=146, 208 &115 km/s respectively.
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- We assume vt=100 km/s for the Shklovskii correction in order to see the potential bias. PSRs J1022+1001, J1216-6410, J1829+2456 & J1933-6211 have Pdot'<0 for vt=100 km/s.
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