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Magnetic fields of neutron
stars
G.S.Bisnovatyi-Kogan
IKI RAS, Moscow
and
JINR, Dubna
HISS: Nuclear theory and astrophysical applications
Dubna, August 2007
Estimations
Radiopulsars, magnetars
Binary X-ray sources, X-ray pulsars
Recycled pulsars
Neutron stars are the result of collapse.
Conservation of the magnetic flux
2
B(ns)=B(s) (Rs/Rns )
B(s)=10 – 100 Gs,
Rs
~ (3 – 10) R(Sun), Rns =10 km
B(ns) = 4 1011– 5 1013 Gs
Ginzburg (1964)
Radiopulsars
E = AB2  4 - magnetic dipole radiation (pulsar wind)
E = 0.5 I
2
I – moment of inertia of the neutron star
2
B = IPP/4  A
Single radiopulsars – timing observations
(the most rapid ones are connected with young supernovae remnants)
B(ns) = 2 1011– 5 1013 Gs
Neutron star formation
4E+51
E kinpol
E rot
E magpol
E magtor
3.5E+51
N.V.Ardeljan,
G.S.Bisnovatyi-Kogan,
S.G.Moiseenko MNRAS,
2005, 359, 333.
3E+51
2.5E+51
2E+51
B(chaotic) ~ 10^14 Gs
1.5E+51
1E+51
High residual chaotic
magnetic field after MRE
core collapse SN explosion.
5E+50
0
0.1
0.2
0.3
time,sec
0.4
0.5
Heat production during
Ohmic damping of the chaotic
magnetic field may influence
NS cooling light curve
Inner region: development of magnetorotational instability (MRI)
TIME= 34.83616590
( 1.20326837sec )
TIME= 35.08302173
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Z
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R
TIME= 35.26651529
0.01
0.015
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R
( 1.21813298sec )
TIME= 35.38772425
0.014
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( 1.22231963sec )
Z
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( 1.21179496sec )
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R
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R
Toy model of the MRI development: expomemtial growth of
the magnetic fields
 d 
 Hr  r
;
dt
 dr 
dH
at initial stages
 d 
  A  const,
 dr 
H   H * :  r
MRI leads to formation of multiple poloidal differentially rotating vortexes.
Angular velocity of vortexes is growing (linearly) with a growth of H.
dH r
 d 
 Hr0  v l 
dt
 dl 
 d v 
l    ( H   H  )

 dl 
d2 


H

H

AH

(
H

H
)




r
0



dt 2 

 H  H   H e A H r 0 (t  t ) 

r0
 

H r30 2 1 2
A H r 0 ( t  t  )
e
1 .
Hr  Hr 0 
A




Field decay depends on the position of the electrical currents.
Deep inside the currents do not decay because of a very high conductivity.
et al., 1997
Soft Gamma Repeaters (SGR)
Giant bursts in SGR similar to short GRB
SGR model:
Magnetar
B=10^14 – 10^15 Gs
Giant bursts in nearby galaxies (short GRB): 2 are observed by
KONUS:
M31 (Andromeda), 1February 2007
M81 3 November 2005
(statistically should be see about 10 short GRB)
Jumps in dP/dt -- not seen in other pulsars
Cyclotron lines: proton radiation (?)
Mazets et al., 1981
St. Peterburg, June 2005
Mazets et al., 1981
Mazets et al., 1981
The time history of the giant burst from the soft gamma
repeater SGR 1627-41. on June 18, 6153 s UT corrected for dead
time. Photon energy E > 15 keV. The rise time is about 100 ms
(Mazets, 1999a).
The giant 1998 August 27 outburst of the soft gamma repeater SGR
1900 + 14. Intensity of the E > 15 keV radiation (Mazets, 1999c).
The epoch folded pulse profile of SGR 1900 + 14 (2-20 keV) for
the May 1998 RXTE observations (Kouveliotou
et al., 1999).
The epoch folded pulse profile of SGR 1900 + 14 (2-20 keV) for
the August 28, 1998 RXTE
observation. The plot is exhibiting two phase cycles (Kouveliotou
et al., 1999).
The Power Density Spectrum of the May 1998 RXTE observations of
SGR 1900 + 14 . The highest peak in the spectrum corresponds to
the fundamental period of 5.159142 s; the three less intense peaks
are the harmonics (Kouveliotou et al., 1999)
PDS of the August 28, 1998 RXTE observation. The two highest peaks
are the fundamental period at 5.160199 s, and its second harmonic
(Kouveliotou et al., 1999).
The evolution of "Period derivative" versus time since the first
period measurement of SGR 1900+14 with ASCA. The time is given in
Modified Julian Days (MJDs) (Kouveliotou et al., 1999)
2004 December 27
giant outburst.
Reconstructed time
history of the initial
pulse. The upper part
of the graph is
derived from Helicon
data while the
lowerpart represents
the Konus-Wind data.
The dashed lines
indicate intervals
where the outburst
intensity still
saturates the KonusWind detector, but is
not high enough to be
seen by the Helicon.
Mazets et al., 2005
Time history of the 2004
December 27 giant outburst
recorded by the Konus-Wind
detector in three energy windows
G1 (16.5--65~keV), G2 (65-280~keV), and G3 (280-1060~keV), and the hardness
ratio G2/G1. The moderate initial
count rate growth to 10^2-10^3~counts~s^{-1} transforms
rapidly to an avalanche-type rise
to levels >5 \times
10^7~counts~s^{-1}, which
drives the detector to deep
saturation for a time \Delta T
\simeq 0.5~s. After the initial
pulse intensity has dropped to
\sim 10^6~counts~s^{-1}, the
detector resumes operation to
record the burst tail.
P=7.57 +- 0.07 s
Mazets et al., 2005
A spectrum of the burst tail
averaged over the pulsation
period. The low-energy
component is similar to spectra of
SGR's recurrent bursts with E_0
~30 keV. At high energies it
exhibits a hard power-law
component with \alpha = -1.8 \pm
0.2. This two-component model
is shown by the solid line.
Mazets et al., 2005
The hystory of the outburst from SRG
1806-20 (RXTE/PCA 2-60 keV). The
top panel (a) shows aq bright burst
preceded by a long, complex precursor.
The bottom panel (b) shows the
precursor intervals used in the spectral
analysis (Ibrahim et al., 2002).
SGR 1806-20:
spectrum and best-fit
continuum model for the
second precursor interval
with 4 absorption lines
(RXTE/PCA 2-30 keV),
Ibrahim et al. (2002)
astro-ph/0309402
First evidence of a cyclotron feature in an anomalous X-ray
pulsar
astro-ph/0309261
ATMOSPHERES AND SPECTRA
OF STRONGLY MAGNETIZED
NEUTRON STARS
Wynn C. G. Ho, Dong Lai,
Alexander Y. Potekhin and
Gilles Chabrier
We find that, for the higher magnetic field
models (B > BQ), vacuum polarization
suppresses both the proton cyclotron line
and spectral lines due to the boundspecies.
As a result, the thermal spectra are almost
featureless and blackbody-like.
A proton RCF feature at 8.1 keV
et al.
A radio pulsar with an 8.5-second period that challenges emission models
Young, M. D.; Manchester, R. N.; Johnston, S.
Nature, Volume 400, Issue 6747, pp. 848-849 (1999).
Radio pulsars are rotating neutron stars that emit beams of radiowaves from regions
above their magnetic poles. Popular theories of the emission mechanism require
continuous electron-positron pair production, with the potential responsible for
accelerating the particles being inversely related to the spin period. Pair production will
stop when the potential drops below a threshold, so the models predict that radio
emission will cease when the period exceeds a value that depends on the magnetic field
strength and configuration. Here we show that the pulsar J2144-3933, previously
thought to have a period of 2.84s, actually has a period of 8.51s, which is by far the
longest of any known radio pulsar. Moreover, under the usual model assumptions, based
on the neutron-star equations of state, this slowly rotating pulsar should not be emitting
a radio beam. Therefore either the model assumptions are wrong, or current theories
of radio emission must be revised.
Pulsar Astronomy - 2000 and Beyond, ASP Conference Series, Vol. 202; Proc. of the
177th Colloquium of the IAU held in Bonn, Germany, 30 August - 3 September 1999
Young, M. D.; Manchester, R. N.; Johnston, S.
Ha, ha, ha, ha, staying alive, staying alive: A radio pulsar with an
8.5-s period challenges emission models.
Radiopulsars with "magnetar" properties
PSR J1119-6127 has period P=0.407 s, and the largest period derivative known among radio
pulsars
characteristic spin-down age of only
a surface dipole magnetic field strength
G
The second pulsar, PSR J1814-1744, has P=3.975 s and
PSR J18470130
a 6.7 s spin period
This inferred dipolar magnetic field strength is the highest by far among all known radio pulsars
and over twice the quantum critical field above which some models predict radio emission
should not occur. The inferred dipolar magnetic field strength and period of this pulsar are in
the same range as those of the anomalous X-ray pulsars, which have been identified as being
magnetars whose luminous X-ray emission is powered by their large magnetic fields.
An upper limit on the X-ray luminosity of J1847-0130 is
lower than the luminosities of all but one anomalous Xray pulsar. The properties of this pulsar prove that
inferred dipolar magnetic field strength and period
cannot alone be responsible for the unusual high-energy
properties of the magnetars and create new challenges
for understanding the possible relationship between
these two manifestations of young neutron stars
X – ray pulsars
Her X-1: X ray pulsar
Period of pulsations P(p)=1.24 sec, orbital P(orb)=1.7 days,
P(precession)=35 days
Neutron star mass 1.4 Solar masses
Optical star mass about 2 Solar masses
Cyclotron line corresponds to B ~ 5 10^12 Gauss
(Truemper et al., 1978)
Inner disk radius is at
R~ 20 R(star)
Configuration of the inner edge of the disk and the neutron star; neutron star and the disk in
the "high-on" state (left top box), and in the "low-on" state (right bottom box).
Sheffer et al., 1992
Scott et al., 2000
Similar results have been
obtained from RXTE
data
Sample Ginga pulse profiles in five energy bands. The bands increase in energy from top to
bottom: 1.0--4.6, 4.6--9.3, 9.3--14, 14--23, 23--37 keV.
The bottommost panels display a hardness ratio (9.3--23 keV band divided by 1.0--4.6 keV band).
(a)---Leftmost panel set. Main High state observation on MJD 47643. Total exposure time is 8713 seconds. Main
pulse occupies phase interval 0.75--1.25, and the interpulse occupies phase interval 0.3--0.7. (b)---Center panel set.
Same profiles as in (a), but with close-up of interpulse. (c)---Rightmost panel set. Short High state observation on
MJD 47662, less than a day after Short High state turn-on. Total exposure time is 10118 seconds. At same scale as
center panel set.
Magnetodipole radiation
of highly anisotropic
relativistic electrons
Comparison of the observational and computational X-ray spectra
of Her X-1. The solid curve is the observational results taken from McCray et al. (1982),
the dot curve is the approximation with T_s=0.9 ~ keV, T_c=8 ~ keV, \tau_c=14,
Double peaked electron distribution at \gamma = 40, B=4 \times 10^{10} Gs.
Baushev, B.-K., 1999
Schematic structure of the accretion column near the
magnetic pole of the neutron star (top), and its radiation spectrum (bottom).
Baushev, B.-K., 1999
Santandgelo et al., 1999
Observational spectrum of
the main pulse of the X-ray
pulsar X0115+63 in hard
part of the spectrum with
harmonics, according to
observation by BeppoSAX
Nonequidistant lines
Baushev, 2002
Cyclotron harminics in magnetodipole radiation
X ray pulsars in LMXB:
Very high frequency: P ~ 2 msec
Very low magnetic fields: B ~ 10^8 Gs
Give birth to millisecond recycled pulsars:
NS + low mass WD
Recycled pulsars
Her X-1: this system should give birth to the binary radiopulsar (recycled)
Bisnovatyi-Kogan G.S. and Komberg B.V., 1974, Astron. Zh. 51,373
Reasons:
1. After 100 million years the optical star will become a white dwarf,
mass transfer will be finished, and the system will be transparant to
radio emission.
2. X ray pulsar is accelerating its rotation due to accretion, so after
the birth of the white dwarf companion the neurton star will rotate
rapidly, P(p) about 100 msec.
Question:
Why are the binary radiopulsars not found (1973) ?
Answer (B-K, K, 1974):
Because the magnetic field of the neutron star is decreasing about 100 times
during the accretion, so binary radiopulsars are very faint objects,
4
Pulsar luminosity L ~ B2 /P
At small B luminosity L is low even at the rapid rotation
Magnetic field is screened by the infalling plasma
Physics Today
1975, 28, No.11,
pp. 46-54
Informal discussion
at Landau Theor. Inst.
Left to right:
G.S.Bisnovatyi-Kogan,
I.D.Novikov,
Academicians
V.L.Ginzburg and
Ya.B.Zeldovich, and
David Pines.
(Photo G.Baym)
The properties of the first binary pulsar coinside with our predictions:
Rapid rotation and Small magnetic field
12
The average magnetic fields of single radiopulsars is about 10 Gauss.
2005: New class of neutron stars: recycled pulsars, more than 100 objects
discovered. All passed the stage of accreting pulsars, accelerating the
rotation and decreasing the magnetic field.
Ordinary pulsars
Recycled pulsars
P=0.033 – 8 sec
13
B= 1011- 10 Gauss
P=1.5 – 50 msec
B=108 - 1010 Gauss
Modeling calculations of screening: Lovelace et al. (2005), and references therein.
infalling of highly conducting matter versus instability, petentration of plasma
into the magnetosphere.
NS + NS RP are the best laboratories for checking of General Relativity
1913+16 timing had shown (indirectly) the existence of gravitational waves
A Double-Pulsar System — A Rare Laboratory for
Relativistic Gravity and Plasma Physics (Lyne et al., 2004)
The clock-like properties of pulsars moving in the gravitational fields of their unseen
neutron-star companions have allowed unique tests of general relativity and provided
evidence for gravitational radiation. We report here the detection of the 2.8-sec pulsar
J0737-3039B as the companion to the 23-ms
pulsar J0737-3039A in a highly-relativistic double-neutron-star system, allowing
unprecedented tests of fundamental gravitational physics. We observe a short eclipse
of J0737-3039A by J0737-3039B and orbital modulation of the flux density and pulse
shape of J0737-3039B, probably due to the influence of J0737-3039A’s energy flux
upon its magnetosphere. These effects will allow us to probe magneto-ionic properties
of a pulsar magnetosphere.
Timing of the pulsars J0737-3039A /B is the most
poweful
instrument for the verification of General Relativity
due to unpresedented precision of the
observations.
The observational constraints
upon the masses mA and mB.
The colored regions are those
which are excluded by the
Keplerian mass functions of the
two pulsars. Further constraints
are shown as pairs of lines
enclosing permitted regions as
predicted by general relativity:
(a) the measurement of the
advance of periastron , giving
the total mass mA+mB = 2:588
pm 0:003M (Sun) (dashed line);
(b) the measurement of R =
mA/mB = 1:069 pm 0:006 (solid
line); (c) the measurement of the
gravitational redshift/time
dilation parameter (dot-dash
line); (d) the measurement of
Shapiro parameter r giving mB =
1:2 pm 0.3M (Sun) (dot-dot-dotdash line) and (e) Shapiro
Lyne et
al., 2004,
parameter
s (dotted
line). Science,
303, 1153.
M.~Kramer et al.,
astro-ph/0503386.
Tests of general
relativity from
timing the double
pulsar
M. Kramer, et al.
astro-ph/0609417
14 Sep 2006
Conclusions
1. Magnetic fields of radiopulsars are in good correspondence with
theoretical estimations. Ohm damping, according to the best fit model,
is not important.
2. RP and LMXB have small magnetic fields, which very probably
had been decreased by damping or screening during accretion stage.
3. Contradiction between high B_{cycl} and other
observational estimations of B in the LMXB Her X-1 may be removed in
the model of relativistic dipole mechanism of the formation of a hard
spectral feature by strongly anisortopic relativistic electrons, leading to
conventional value of B ~ 5 10^{10} Gs.
4. Very high magnetic fields in magnetar model of SGR needs farther
confirmation and investigation.