Extensive population synthesis studies of isolated neutron stars with magnetic fi eld decay

1. Extensive population synthesis studies of isolatedneutron stars with magnetic field decay Sergei Popov (SAI MSU) J.A. Pons, J.A. Miralles, P.A. Boldin, B. Posselt MNRAS (2009) arXiv: 0910.2190

2. Diversity of young neutron stars • Young isolated neutron starscan appear in many flavors: • Compact central X-ray sources • in supernova remnants. • Anomalous X-ray pulsars • Soft gamma repeaters • The Magnificent Seven • Unidentified EGRET sources • Transient radio sources (RRATs) • Calvera …. All together these NSs have total birth rate higher than normal radio pulsars(see discussion in Popov et al. 2006, Keane, Kramer 2008) We need more sources to have better statistics! Estimates show that eROSITA can find ~ few dozensof NSs like the M7 (if soft X-ray sensitivity is not reduced).

3. NS birth rate [Keane, Kramer 2008, arXiv: 0810.1512]

4. Too many NSs??? [Keane, Kramer 2008, arXiv: 0810.1512] It seems, that the total birth rate is larger than the rate of CCSN. e- - capture SN cannot save the situation, as they are <~20%. Note, that the authors do not include CCOs. So, some estimates are wrong, or some sources evolve into another. See also astro-ph/0603258.

5. Magnetic field decay Magnetic fields of NSs are expected to decay due to decay of currents which support them. Crustal field of core field? It is easy to decay in the crust. In the core the filed is in the formof superconducting vortices. They can decay only when they aremoved into the crust (during spin-down). Still, in most of models strong fields decay.

6. Magnetars Pdot B=const M7 PSRs P Magnetars, field decay, heating A model based on field-dependent decay of the magnetic moment of NSscan provide an evolutionary link between different populations (Pons et al.).

7. Period evolution with field decay An evolutionary track of a NS isvery different in the case of decaying magnetic field. The most important feature isslow-down of spin-down. Finally, a NS can nearly freezeat some value of spin period. Several episodes of relativelyrapid field decay can happen. Number of isolated accretors can be both decreased or increasedin different models of field decay. But in any case their average periods become shorter and temperatures lower. It is important to look at old sources,but we have only young …. astro-ph/9707318

8. Magnetic field decay vs. thermal evolution Magnetic field decay can be an important source of NS heating. Heat is carried by electrons. It is easier to transport heat along field lines. So, poles are hotter. (for light elements envelope thesituation can be different). Ohm and Hall decay arxiv:0710.0854 (Aguilera et al.) τHall depends on B0: τHall ~ 1/B0

9. Joule heating for everybody? It is important to understandthe role of heating by thefield decay for different typesof INS. In the model by Pons et al.the effect is more importantfor NSs with larger initial B. Note, that the characteristicage estimates (P/2 Pdot)are different in the case ofdecaying field! arXiv: 0710.4914 (Aguilera et al.)

10. Magnetic field vs. temperature The line marks balancebetween heating due to the field decay and cooling.It is expected that a NSevolves downwards till itreaches the line, then theevolution proceeds along the line: Selection effects are notwell studied here.A kind of populationsynthesis modeling iswelcomed. Teff ~ Bd1/2 (astro-ph/0607583)

11. Extensive population synthesis We want to make extensive population synthesis studies using as many approaches as we can to confront theoretical modelswith different observational data • Log N – Log S for close-by young cooling isolated neutron stars • Log N – Log L distribution for galactic magnetars • P-Pdot distribution for normal radio pulsars

12. Cooling curves: field dependence

13. Cooling curves: mass dependence

14. Luminosity vs. field and age

15. Cooling curves with decay Magnetic field distribution is more important than the mass distribution.

16. Fields and models We make calculations for seven different fields, which cover the whole range for young objects. To compare our results with observations we usesix different models of field distribution.

17. Log N – Log S with heating • Log N – Log S for 7 different magnetic fields. • 3 1012 G 2. 1013 G • 3. 3 1013 G 4. 1014 G 5. 3 1014 G • 6. 1015 G 7. 3 1015 G Different magnetic field distributions. [The code used in Posselt et al. A&A (2008) with modifications]

18. Statistical fluctuations For each model we run5000 tracks all of whichare applied to 8 masses,and statistics is collectedalone the track withtime step 10 000 years till 3 Myrs. However, it is necessaryto understand the levelof possible fluctuations, as we have the birth rate270 NSs in a Myr.

19. Fitting Log N – Log S We try to fit theLog N – Log Swith log-normal magnetic field distributions, as it is oftendone for PSRs. We cannot select the best oneusing only Log N – Log S forclose-by cooling NSs. We can select a combinationof parameters.

20. Populations and constraints Birthrate of magnetars is uncertain due to discovery of transient sources. Just from “standard” SGR statistics it is just 10%, then, for example,the M7 cannot be aged magnetars with decayed fields, but if there are many transient AXPs and SGRs – then the situation is different. Limits, like the one by Muno et al., on the number of AXPs from asearch for periodicity are very important and have to be improved(the task for eROSITA? MAXI?!). Such limits can be also re-scaledto put constraints on the number ofthe M7-like NSs and the number ofisolated accretors with decayed field. Lx> 3 1033 erg s-1 [Muno et al. 2007]

21. Log N – Log L for magnetars Magnetic field distributions:with and without magnetars(i.e. different magnetic fielddistributions are used). 7 values of initial magnetic field, 8 masses of NSs. SNR 1/30 yrs-1. “Without magnetars” means“no NSs with B0>1013 G”. Non-thermal contribution is nottaken into account. Justified but total energy losses.

22. Transient magnetars at youth Young magnetars can be transient sources. In the model we usewe cannot take this intoaccount self-consistently. We can make a simple test. Clearly, transient periodsat youth help to havemore bright magnetars. Here 5% of time L=10 L0 50% - just L0 And for 45% of time the source is dim.

23. P-Pdot diagram and field decay Let us try to see how PSRs with decaying magnetic fields evolvein the P-Pdot plot. At first we can use a simple analyticalapproximation to theevolutionary law forthe magnetic field. τOhm=106 yrs τHall=104/(B0/1015 G) yrs

24. Decay parameters and P-Pdot τOhm=107 yrs τHall =102/(B0/1015 G) τOhm=106 yrs τHall =103/(B0/1015 G) τOhm=105 yrs τHall =103/(B0/1015 G) Longer time scale for the Hall field decay is favoured. It is interesting to look at HMXBs to see if it is possibleto derive the effect of field decay and convergence.

25. Realistic tracks Using the model by Pons et al.(arXiv: 0812.3018) we plotrealistic tracks for NS withmasses 1.4 Msolar. Initial fields are: 3 1012, 1013, 3 1013, 1014, 3 1014, 1015, 3 1015 G Color on the track encodessurface temperature. Tracks start at 103 years,and end at ~3 106 years.

26. Observational evidence Kaplan & van Kerkwijk arXiv: 0909.5218

27. Population synthesis of PSRs Best model: <log(B0/[G])>= 13.25, σlogB0=0.6, <P0>= 0.25 s, σP0 = 0.1 s

28. Conclusions • There are several different populations of neutron stars which must be studied together in one framework • Population synthesis calculations are necessary to confront theoretical models with observations • We use different approaches to study different populations using the same parameters distribution • In the model with magnetic field decay we focused on log-normal distributions of initial magnetic fields • We can describe properties of several populations • ◊close-by cooling NSs◊magnetars◊ normal PSRs • with the same log-normal magnetic field distribution Best model: <log(B0/[G])>= 13.25, σlogB0=0.6, <P0>= 0.25 s, σP0 = 0.1 s • We exclude distributions with >~20% of magnetars • Populations with ~10% of magnetars are favoured

29. Extensive population synthesis:M7, magnetars, PSRs M7 Magnetars M7 Using one populationit is difficult or impossibleto find unique initialdistribution for themagnetic field PSRs All three populations are compatible with a unique distribution. Of course, the resultis model dependent. PSRs