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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
B(ns)=B(s) (R /R )s ns2
B(s)=10 – 100 Gs, R ~ (3 – 10) R(Sun), R =10 kms
B(ns) = 4 10 – 5 10 Gs Ginzburg (1964)
11 13
ns
Radiopulsars
E = AB - magnetic dipole radiation (pulsar wind)
E = 0.5 I
I – moment of inertia of the neutron star
B = IPP/4 A
2
2
2
4
Single radiopulsars – timing observations (the most rapid ones are connected with young supernovae remnants)
B(ns) = 2 10 – 5 10 Gs
11 13
time,sec0.1 0.2 0.3 0.4 0.5
0
5E+50
1E+51
1.5E+51
2E+51
2.5E+51
3E+51
3.5E+51
4E+51Ekinpol
Erot
Emagpol
Emagtor
N.V.Ardeljan, G.S.Bisnovatyi-Kogan, S.G.Moiseenko MNRAS, 2005, 359, 333.
B(chaotic) ~ 10^14 Gs
Neutron star formation
High residual chaotic magnetic field after MRE core collapse SN explosion.
Heat production duringOhmic damping of the chaotic magnetic field may influence NS cooling light curve
Inner region: development of magnetorotational instability (MRI)
R
Z
0.01 0.015 0.020.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )
R
Z
0.01 0.015 0.020.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )
R
Z
0.01 0.015 0.020.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )
R
Z
0.01 0.015 0.020.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )
Toy model of the MRI development: expomemtial growth of the magnetic fields
; r
dH dH r
dt dr
MRI leads to formation of multiple poloidal differentially rotating vortexes. Angular velocity of vortexes is growing (linearly) with a growth of H.
0r v
r
dH dH l
dt dl
( )vdl H H
dl
2
02( )
r
dH H AH H H
dt
0
0
( )0
3 2 1 2( )0
0 1 .
r
r
A H t tr
A H t trr r
H H H
H
e
H HA
e
at initial stages * :H H const,
dr Adr
et al., 1997
Field decay depends on the position of the electrical currents.Deep inside the currents do not decay because of a very high conductivity.
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
Mazets et al., 1981
St. Peterburg, June 2005St. Peterburg, June 2005
Mazets et al., 1981
The time history of the giant burst from the soft gammarepeater SGR 1627-41. on June 18, 6153 s UT corrected for deadtime. 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 SGR1900 + 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 (Kouveliotouet al., 1999).
The Power Density Spectrum of the May 1998 RXTE observations ofSGR 1900 + 14 . The highest peak in the spectrum corresponds tothe 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 peaksare the fundamental period at 5.160199 s, and its second harmonic
(Kouveliotou et al., 1999).
The evolution of "Period derivative" versus time since the firstperiod 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 Konus-Wind 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 sMazets 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
A proton RCF feature at 8.1 keV
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.
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
The second pulsar, PSR J1814-1744, has P=3.975 s and
PSR J1847-0130
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.
G
An upper limit on the X-ray luminosity of J1847-0130 is lower than the luminosities of all but one anomalous X-ray 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
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)
X – ray pulsars
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
Inner disk radius is atR~ 20 R(star)
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.
Scott et al., 2000
Similar results have been obtained from RXTE data
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
Magnetodipole radiation of highly anisotropic relativistic electrons
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
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,Pulsar luminosity L ~ B /P
At small B luminosity L is low even at the rapid rotation Magnetic field is screened by the infalling plasma
2 4
Recycled pulsars
Physics Today1975, 28, No.11,pp. 46-54
Informal discussionat Landau Theor. Inst.
Left to right:
G.S.Bisnovatyi-Kogan,I.D.Novikov,AcademiciansV.L.Ginzburg and Ya.B.Zeldovich, andDavid Pines.(Photo G.Baym)
The properties of the first binary pulsar coinside with our predictions:Rapid rotation and Small magnetic field
The average magnetic fields of single radiopulsars is about 10 Gauss.12
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 P=1.5 – 50 msecB= 10 - 10 Gauss B=10 - 10 Gauss11 13 8 10
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 Relativity1913+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-mspulsar 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-dot-dash line) and (e) Shapiro parameter s (dotted line).
Lyne et al., 2004, 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
1. Magnetic fields of radiopulsars are in good correspondence withtheoretical estimations. Ohm damping, according to the best fit model, is not important.
2. RP and LMXB have small magnetic fields, which very probablyhad been decreased by damping or screening during accretion stage.
3. Contradiction between high B_{cycl} and otherobservational estimations of B in the LMXB Her X-1 may be removed inthe model of relativistic dipole mechanism of the formation of a hardspectral feature by strongly anisortopic relativistic electrons, leading toconventional value of B ~ 5 10^{10} Gs.
4. Very high magnetic fields in magnetar model of SGR needs fartherconfirmation and investigation.
Conclusions
