Extensive population synthesis studies of

isolated neutron stars with magnetic field decay

Sergei PopovSergei Popov(SAI MSU)(SAI MSU)

J.A. Pons, J.A. Miralles, P.A. Boldin, B. Posselt

MNRAS (2009) arXiv: 0910.2190

Diversity of young neutron starsDiversity of young neutron stars

Young isolated neutron starscan appear in many flavors:

o Compact central X-ray sources in supernova remnants. o Anomalous X-ray pulsarso Soft gamma repeaterso The Magnificent Seveno Unidentified EGRET sourceso Transient radio sources (RRATs)o 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).

NS birth rateNS birth rate

[Keane, Kramer 2008, arXiv: 0810.1512]

Too many NSs???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.

Magnetic field decayMagnetic field decayMagnetic 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.

Magnetars, field decay, Magnetars, field decay, heatingheating

A model based on field-dependent decay of the magnetic moment of NSscan provide an evolutionary link between different populations (Pons et al.).

P

Pdot

PSRs

M7

B=const

Magnetars

Period evolution with field decayPeriod evolution with field decay

astro-ph/9707318

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 ….

Magnetic field decay vs. Magnetic field decay vs. thermal evolutionthermal evolution

arxiv:0710.0854 (Aguilera et al.)

Magnetic field decay can be an important source of NS heating.

Ohm and Hall decay

Heat is carried by electrons.It is easier to transport heat along field lines. So, poles are hotter.(for light elements envelope the

situation can be different).

τHall depends on B0: τHall ~ 1/B0

Joule heating for everybody?Joule heating for everybody?

arXiv: 0710.4914 (Aguilera et al.)

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!

Magnetic field vs. temperatureMagnetic field vs. temperature

(astro-ph/0607583)

The line marks balancebetween heating due tothe 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

Extensive population Extensive population synthesissynthesis

We want to make extensive population synthesis studies using as many approaches as we can to confront theoretical models

with 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

Cooling curves: field Cooling curves: field dependencedependence

Cooling curves: mass Cooling curves: mass dependencedependence

Luminosity vs. field and Luminosity vs. field and ageage

Cooling curves with Cooling curves with decaydecay

Magnetic field distribution is more important than the mass distribution.

Fields and modelsFields 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.

Log N – Log S with heatingLog N – Log S with heating

[The code used in Posselt et al. A&A (2008) with modifications]

Log N – Log S for 7 different magnetic fields.

1. 3 1012 G 2. 1013 G 3. 3 1013 G 4. 1014 G 5. 3 1014 G6. 1015 G 7. 3 1015 G

Different magnetic field distributions.

Statistical fluctuationsStatistical fluctuationsFor each model we run5000 tracks all of whichare applied to 8 masses,and statistics is collectedalone the track withtime step 10 000 yearstill 3 Myrs.

However, it is necessaryto understand the levelof possible fluctuations, as we have the birth rate270 NSs in a Myr.

Fitting Log N – Log SFitting Log N – Log SWe try to fit the Log 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.

Populations and constraintsPopulations 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 aremany 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.

[Muno et al. 2007]

Lx> 3 1033 erg s-1

Log N – Log L for magnetarsLog 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.

Transient magnetars at Transient magnetars at youthyouth

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.

P-Pdot diagram and field P-Pdot diagram and field decaydecay

τOhm=106 yrsτHall=104/(B0/1015 G) yrs

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.

Decay parameters and P-PdotDecay parameters and P-Pdot

τOhm=107 yrsτHall =102/(B0/1015 G)

τOhm=106 yrsτHall =103/(B0/1015 G)

τOhm=105 yrsτHall =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.

Realistic tracksRealistic 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.

Observational evidenceObservational evidence

Kaplan & van Kerkwijk arXiv: 0909.5218

Population synthesis of Population synthesis of PSRsPSRs

Best model: <log(B0/[G])>= 13.25, σlogB0=0.6, <P0>= 0.25 s, σP0 = 0.1 s

ConclusionsConclusions 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

Extensive population Extensive population synthesis:synthesis:

M7, magnetars, PSRsM7, magnetars, PSRsM7

M7Magnetars

PSRs

Using one populationit is difficult or impossibleto find unique initialdistribution for themagnetic field

All three populations are compatible with a unique distribution.Of course, the resultis model dependent.

PSRs