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

Diversity of young neutron stars Young isolated neutron stars can appear in many flavors: o Compact central X-ray sources in supernova remnants. o Anomalous X-ray pulsars o Soft gamma repeaters o The Magnificent Seven o Unidentified EGRET sources o 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 dozens of NSs like the M7 (if soft X-ray sensitivity is not reduced).

NS birth rate [Keane, Kramer 2008, arXiv: ]

Too many NSs??? [Keane, Kramer 2008, arXiv: ] 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/

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 form of superconducting vortices. They can decay only when they are moved into the crust (during spin-down). Still, in most of models strong fields decay.

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

Period evolution with field decay astro-ph/ An evolutionary track of a NS is very different in the case of decaying magnetic field. The most important feature is slow-down of spin-down. Finally, a NS can nearly freeze at some value of spin period. Several episodes of relatively rapid field decay can happen. Number of isolated accretors can be both decreased or increased in 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. thermal evolution arxiv: (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). τ Hall depends on B 0 : τ Hall ~ 1/B 0

Joule heating for everybody? arXiv: (Aguilera et al.) It is important to understand the role of heating by the field decay for different types of INS. In the model by Pons et al. the effect is more important for NSs with larger initial B. Note, that the characteristic age estimates (P/2 Pdot) are different in the case of decaying field!

Magnetic field vs. temperature (astro-ph/ ) The line marks balance between heating due to the field decay and cooling. It is expected that a NS evolves downwards till it reaches the line, then the evolution proceeds along the line: Selection effects are not well studied here. A kind of population synthesis modeling is welcomed. T eff ~ B d 1/2

Extensive population synthesis 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 dependence

Cooling curves: mass dependence

Luminosity vs. field and age

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

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 use six different models of field distribution.

Log 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 G G G G G G G Different magnetic field distributions.

Statistical fluctuations For each model we run 5000 tracks all of which are applied to 8 masses, and statistics is collected alone the track with time step years till 3 Myrs. However, it is necessary to understand the level of possible fluctuations, as we have the birth rate 270 NSs in a Myr.

Fitting Log N – Log S We try to fit the Log N – Log S with log-normal magnetic field distributions, as it is often done for PSRs. We cannot select the best one using only Log N – Log S for close-by cooling NSs. We can select a combination of parameters.

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 a search for periodicity are very important and have to be improved (the task for eROSITA? MAXI?!). Such limits can be also re-scaled to put constraints on the number of the M7-like NSs and the number of isolated accretors with decayed field. [Muno et al. 2007] L x > erg s -1

Log N – Log L for magnetars Magnetic field distributions: with and without magnetars (i.e. different magnetic field distributions are used). 7 values of initial magnetic field, 8 masses of NSs. SNR 1/30 yrs -1. “Without magnetars” means “no NSs with B 0 >10 13 G”. Non-thermal contribution is not taken into account. Justified but total energy losses.

Transient magnetars at youth Young magnetars can be transient sources. In the model we use we cannot take this into account self-consistently. We can make a simple test. Clearly, transient periods at youth help to have more bright magnetars. Here 5% of time L=10 L 0 50% - just L 0 And for 45% of time the source is dim.

P-Pdot diagram and field decay τ Ohm =10 6 yrs τ Hall =10 4 /(B 0 /10 15 G) yrs Let us try to see how PSRs with decaying magnetic fields evolve in the P-Pdot plot. At first we can use a simple analytical approximation to the evolutionary law for the magnetic field.

Decay parameters and P-Pdot τ Ohm =10 7 yrs τ Hall =10 2 /(B 0 /10 15 G) τ Ohm =10 6 yrs τ Hall =10 3 /(B 0 /10 15 G) τ Ohm =10 5 yrs τ Hall =10 3 /(B 0 /10 15 G) Longer time scale for the Hall field decay is favoured. It is interesting to look at HMXBs to see if it is possible to derive the effect of field decay and convergence.

Realistic tracks Using the model by Pons et al. (arXiv: ) we plot realistic tracks for NS with masses 1.4 Msolar. Initial fields are: , 10 13, , 10 14, , 10 15, G Color on the track encodes surface temperature. Tracks start at 10 3 years, and end at ~ years.

Observational evidence Kaplan & van Kerkwijk arXiv:

Population synthesis of PSRs Best model: = 13.25, σ logB0 =0.6, = 0.25 s, σ P0 = 0.1 s

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: = 13.25, σ logB0 =0.6, = 0.25 s, σ P0 = 0.1 s We exclude distributions with >~20% of magnetars Populations with ~10% of magnetars are favoured

Extensive population synthesis: M7, magnetars, PSRs M7 Magnetars PSRs Using one population it is difficult or impossible to find unique initial distribution for the magnetic field All three populations are compatible with a unique distribution. Of course, the result is model dependent. PSRs