1. J.A. Pons, J.A. Miralles, P.A. Boldin, B. Posselt
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
Tarusa, May 2009

2. The old Zoo: young pulsars & old accretors

3. Diversity of young neutron stars
Young isolated neutron stars can appear in many flavours:
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 ….

4. Compact central X-ray sources in supernova remnants
Cas A
RCW 103
6.7 hour period
(de Luca et al. 2006)
Problem: small emitting area

5. CCOs in SNRs Age Distance J232327.9+584843 Cas A 0.32 3.3–3.7
J − G266.1− – –2
J − Pup A – –3.3
J − G – –3.9
J Kes ~ ~10
J − G347.3−0.5 ~ ~6
[Pavlov, Sanwal, Teter: astro-ph/ , de Luca: arxiv: ]
For two sources there are strong indications for large (>~100 msec) initial spin periods and low magnetic fields: 1E in PKS /52 and PSR J in Kesteven 79 [see Halpern et al. arxiv: ]

6. Magnetars dE/dt > dErot/dt
By definition: The energy of the magnetic field is released
Magnetic fields 1014–1015 G

7. Magnetic field estimates
Spin down
Long spin periods
Energy to support bursts
Field to confine a fireball (tails)
Duration of spikes (alfven waves)
Direct measurements of magnetic field (cyclotron lines)
Ibrahim et al. 2002

8. Spectral lines claims
All claims were done for RXTE observations (there are few other candidates).
All detections were done during bursts.
1E Gavriil et al. (2002, 2004)
4U Gavriil et al. (2007)

9. Known magnetars AXPs SGRs CXO 010043.1-72 0526-66 4U 0142+61 1627-41
CXO J
1 RXS J
XTE J 1E
AX J 1E 1E
SGRs
– Aug.2008!
(?)
(?)
(СТВ 109)

10. Israel et al. ATel #1837 (11 Nov)
The newest SGR
The most recent SGR candidate
was discovered in Aug. 2008
(GCN 8112 Holland et al.)
It is named SGR
Several recurrent bursts have been detected by several experiments
(see, for example, GCN 8132 by Golenetskii et al.).
Spin period sec.
Optical and IR counterparts.
SWIFT
P= (1) s
Pdot=7.4(1)E-12 s/s
Pdotdot=-4.3(1.1)E-19 s/s^2
Israel et al. ATel #1837 (11 Nov)

11. QPOs after giant flares
A kind of quasi periodic oscillations have been found in tail of two events (aug. 1998, dec. 2004).
They are supposed to be torsional oscillations of NSs, however, it is not clear, yet.
(Israel et al astro-ph/ ,
Watts and Strohmayer 2005 astro-ph/ )
See a recent review in aXiv:

12. Extragalactic SGRs It was suggested long ago (Mazets et al. 1982)
that present-day detectors could alredy detect giant flares from extragalactic magnetars.
However, all searches in, for example, BATSE databse did not provide clear candidates (Lazzati et al. 2006, Popov & Stern 2006, etc.).
Finally, recently several good candidates have been proposed by different groups
(Mazets et al., Frederiks et al., Golenetskii et al.,
Ofek et al, Crider ...., see arxiv: and references therein, for example).
Burst from M31
[D. Frederiks et al. astro-ph/ ]

13. Transient radio emission from AXP
ROSAT and XMM images an X-ray outburst happened in 2003.
AXP has spin period 5.54 s
Radio emission was detected from XTE J during its active state.
Clear pulsations have been detected.
Large radio luminosity.
Strong polarization.
Precise Pdot measurement. Important for limting models, better distance and coordinates determination etc.
(Camilo et al. astro-ph/ )

14. Another AXP detected in radio
P= 2 sec
SNR G
Pdot changed significantly on the scale of just ~few months
Rotation and magnetic axis seem to be aligned
Also these AXP demonstrated weak SGR-like bursts (Rea et al. 2008, GCN 8313)
Radio
[simultaneous]
X-rays
(see also arxiv: )

15. Transient radiopulsar
However, no radio emission detected.
Due to beaming?
PSR J
P=0.326 sec
B= G
Among all rotation powered PSRs it has the largest Edot. Smallest spindown age (884 yrs).
The pulsar increased
its luminosity in X-rays.
Increase of pulsed X-ray flux.
Magnetar-like X-ray bursts (RXTE).
Timing noise.
See additional info about this pulsar at the web-site ,

16. Bursts from the transient PSR
Chandra: Oct June 2006
Gavriil et al

17. Mysterious bursts of SWIFT J195509.6+261406
Optical bursts which is some sense similar to magnetars weak X-ray bursts.
[Stefanescu et al. arXiv: ]
See also arXiv:
Periodicity ~7 sec is suspected.
However, in our opinion, this can be not a magnetar, but a magnetic WD. Optic vs. X-ray, longer time scales, lower energies etc.
[Kaslival et al. arXiv: ]

18. Magnificent Seven Name Period, s RX 1856 7.05 RX 0720 8.39 RBS 1223
10.31
RBS 1556
6.88?
RX 0806
11.37
RX 0420
3.45
RBS 1774
9.44
Radioquiet (?)
Close-by
Thermal emission
Absorption features
Long periods

19. The isolated neutron star candidate 2XMM J104608.7-594306
A new INS candidate.
B >26, V >25.5, R >25 (at 2.5σ confidence level)
log(FX/FV) >3.1
kT = 118 +/-15 eV
unabsorbed X-ray flux:
Fx ~1.3 10−12 erg s−1 cm−2
in the 0.1–12 keV band.
At 2.3 kpc (Eta Carina) the luminosity is
LX ~ erg s−1
R∞ ~ 5.7 km
M7-like? Yes!
[Pires & Motch arXiv: and Pires et al ]

20. Discovery of radio transients
McLaughlin et al. (2006) discovered a new type of sources– RRATs
(Rotating Radio Transients).
For most of the sources periods about few seconds were discovered.
The result was obtained during the Parkes survey of the Galactic plane.
These sources can be related to The Magnificent seven.
Thermal X-rays were observed from one of the RRATs
(Reynolds et al. 2006). This one seems to me the youngest.

21. P-Pdot diagram for RRATs
McLaughlin et al Nature
Estimates show that there should be about
Sources of this type in the Galaxy.
Young or old???
Relatives of the
Magnificent seven?
(astro-ph/ )

22. RRATs. Recent data
X-ray pulses overlaped on radio data of RRAT J
(arXiv: )

23. RRATs
11 sources detected in the Parkes Multibeam survey (McLaughlin et al 2006)
Burst duration 2-30 ms, interval 4 min-3 hr
Periods in the range s
Period derivative measured in 3 sources: B ~ G, age ~ Myr
RRAT J detected in the X-rays, spectrum soft and thermal, kT ~ 120 eV (Reynolds et al 2006)
Some of sources appeared to be radio pulsars

24. Calvera et al.
Recently, Rutledge et al. reported the discovery of an enigmatic
NS candidated dubbed Calvera.
It can be an evolved (aged) version of Cas A source,
but also it can be a M7-like object, who’s progenitor was a runaway (or, less probably, hypervelocity) star.
No radio emission was found.

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

26. 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/

27. Are SGRs and AXPs brothers?
Bursts of AXPs (from 6 now)
Spectral properties
Quiescent periods of SGRs ( since 1983)
Gavriil et al. 2002

28. Unique AXP bursts?
Bursts from AXP J Note a long exponential tail with pulsations.
(Woods et al. 2005)

29. RRATs
P, B, ages and X-ray properties of RRATs very similar to those of XDINSs
Estimated number of RRATs ~ 3-5 times that of PSRs
If τRRAT ≈ τPSR, βRRAT ≈ 3-5 βPSR
βXDINS > 3 βPSR (Popov et al 2006)
Are RRATs far away XDINSs ?
Some RRATs are radio pulsars
New discussion about birth rates in Keane, Kramer arXiv:

30. 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

31. 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.

32. 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.
It is important to look at old sources, but we have only young ….
astro-ph/

33. 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: (Aguilera et al.)

34. 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: (Aguilera et al.)

35. 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:
Selection effects are not well studied here. A kind of population synthesis modeling is welcomed.
Teff ~ Bd1/2
Pons et al. There is an extra free parameter b. It is the ratio B^2/B_d^2. B - field in the crust due to surrents, B_d – dipole field in the crust.
(astro-ph/ )

36. 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

37. Cooling curves: field dependence

38. Cooling curves: mass dependence

39. 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.

40. Log N – Log S with heating
Log N – Log S for 7 different magnetic fields.
G G
G G G
G G
Different magnetic field distributions.
[The code used in Posselt et al. A&A (2008) with modifications]

41. 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.

42. 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.

43. 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> erg s-1
[Muno et al. 2007]

44. Log N – Log L for magnetars
Magnetic field distributions: with and without magnetars (i.e. different magnetic field distributions are used).
7 values of inital 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.

45. 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.

46. 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

47. 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.

48. Realistic tracks
Using the model by Pons et al. (arXiv: ) we plot realistic tracks for NS with masses 1.4 Msolar.
Initial fields are:
3 1012, 1013, , 1014, , 1015, G
Color on the track encodes surface temperature.
Tracks start at 103 years, and end at ~3 106 years.

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

50. 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