Transcript Document

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: 0910.2190
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: 0810.1512]
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 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
Pdot
A model based on field-dependent decay of the magnetic moment of NSs
can provide an evolutionary link between different populations (Pons et al.).
Magnetars
M7
PSRs
P
Period evolution with field decay
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.
astro-ph/9707318
It is important to look at old sources,
but we have only young ….
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 the
situation can be different).
Ohm and Hall decay
arxiv:0710.0854 (Aguilera et al.)
τHall depends on B0: τHall ~ 1/B0
Joule heating for everybody?
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!
arXiv: 0710.4914 (Aguilera et al.)
Magnetic field vs. temperature
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:
1/2
Teff ~ Bd
Selection effects are not
well studied here.
A kind of population
synthesis modeling is
welcomed.
(astro-ph/0607583)
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
Log N – Log S for 7 different
Different magnetic field distributions.
magnetic fields.
1. 3 1012 G
2. 1013 G
3. 3 1013 G
4. 1014 G 5. 3 1014 G
6. 1015 G
7. 3 1015 G
[The code used in Posselt et al. A&A (2008) with modifications]
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 10 000 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.
Lx> 3 1033 erg s-1
[Muno et al. 2007]
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 B0>1013 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 L0
50% - just L0
And for 45% of time
the source is dim.
P-Pdot diagram and field decay
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.
τOhm=106 yrs
τHall=104/(B0/1015 G) yrs
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 possible
to derive the effect of field decay and convergence.
Realistic tracks
Using the model by Pons et al.
(arXiv: 0812.3018) we plot
realistic tracks for NS with
masses 1.4 Msolar.
Initial fields are:
3 1012, 1013, 3 1013, 1014,
3 1014, 1015, 3 1015 G
Color on the track encodes
surface temperature.
Tracks start at 103 years,
and end at ~3 106 years.
Observational evidence
Kaplan & van Kerkwijk arXiv: 0909.5218
Population synthesis of PSRs
Best model: <log(B0/[G])>= 13.25, σlogB0=0.6, <P0>= 0.25 s, σP0 = 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: <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 synthesis:
M7, magnetars, PSRs
M7
Magnetars
M7
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
PSRs