1. Constraining the braking indices of magnetars
数字化校园建设解决方案
Constraining the braking indices of magnetars
Zhi-Fu Gao
Xinjiang Astronomical Observatory, Chinese
Academy of Sciences，China
29 July
沈阳职业技术学院信息中心

2. Contents Introduction Constraining the ages of magnetars
Constraining the braking indices of magnetars
Explaining magnetars’ braking indices
Summary

3. Introduction
It is commonly accepted that pulsars are produced in a core-collapse supernova explosions. Therefore, pulsars and their associated supernova remnants (SNRs ) should therefore have the same ages.
Since the characteristic age of a is not available to estimate its true age , and the physically meaningful criterion to estimate is NS-SNR association. Their suggestions are in the same way applicable to magnetars with associated SNRs.
A puzzle is that we can not measure magnetars’ braking indexes observationally due to strong timing noise and the lack of long-term persistent emission and strong timing noise.

4. Introduction A pulsar spins down with a power law
The standard way to define the braking index n is

5. Braking indices of young radio pulsars

6. Observational braking indices of magnetars

7. Magnetars and their SNRs

9. Our assumptions
Firstly, we assume that a NS's braking index keeps constant since its birth.This is a strong necessary assumption when estimating the age of a very young NS. In deed, one cannot derive an analytical expression, Eq. (8), to estimate the age of a NS, if we consider either K or n in Eq. (1) is a time-dependent quantity. The measured braking index is obviously influenced by the variation in the braking torque during the observational intervals.

10. Our Assumptions
We assume that the age of a SNR is the age of a NS. Zhang \& Xie (2012) suggested that the physically meaningful criterion to estimate the true age of a NS is NS/SNR association. This suggestion is surely in the same way applicable to magnetars with SNRs.
Finally, we assume that , the initial spin-period of a magnetar is far less than current period, because magnetars are supposed to be formed from rapidly rotating NSs ( Thompson \& Duncan 1996).

11. Our methods
Note that t in Eq.(9) is the upper limit of the inferred age due to an approximation in Eq. (8), and n denotes the mean braking index of a magnetar since its formation due to the assumption of a constant n.

12. Our calculation results

13. Why magnetars appear `older’ or `younger’

14. Why n > 3? Due to the decay of crustal magnetic field
Due to the decay of magnetospheric current
Due to the decline in magnetic-cline angle

15. Why n < 3?

18. Thank you very much!