Young neutron stars with soft gamma ray emission and anomalous X-ray pulsar
G. S. Bisnovatyi-Kogan






Young neutron stars with soft gamma ray emission and anomalous X-ray pulsar
    Gennady S. Bisnovatyi-Kogan 

Space Research Institute of Russian Academy of Sciences,
 Profsoyuznaya 84/32, Moscow 117997, Russia,
 and

National Research Nuclear University MEPhI 
 (Moscow Engineering Physics Institute),
 Kashirskoe Shosse 31, Moscow 115409, Russia

Email: gkogan@iki.rssi.ru
    
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The observational properties of Soft Gamma Repeaters and Ano­malous X-ray Pulsars (SGR/AXP) indicate to necessity of the energy source different from a rotational energy of  a neutron star. The model, where the source of the energy is connected with a magnetic field dissipation in a highly magnetized neutron star (magnetar) is analyzed. Some observational inconsistencies  are indicated for this interpretation.
The alternative energy source, connected with the nuclear energy of superheavy nuclei stored in the nonequilibrium layer of low mass neutron star is discussed.


Young neutron stars with soft gamma ray emission and anomalous X-ray pulsar
    Gennady S. Bisnovatyi-Kogan 

Space Research Institute of Russian Academy of Sciences,
 Profsoyuznaya 84/32, Moscow 117997, Russia,
 and

National Research Nuclear University MEPhI 
 (Moscow Engineering Physics Institute),
 Kashirskoe Shosse 31, Moscow 115409, Russia

Email: gkogan@iki.rssi.ru
    
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§  INTRODUCTION


Neutron stars (NS) are formed as a result of a collapse of the core of a massive star with a mass M>∼ 12 M_⊙.
Conservation of the magnetic flux gives an estimation of NS magnetic field as
 B_ns=B_s (R_s  /R_ns   )^2,
B_s=10 ÷ 100 Gs, at   R ∼ (3 ÷ 10) R_⊙,    R_ns   =10 km,
B_ns = 4· 10^11÷ 5· 10^13   Gs (Ginzburg 1964).

Estimation of the NS magnetic field is obtained in radio pulsars by measurements of
their rotational period and its time derivative, in the model of a dipole radiation, or
pulsar wind model, as (E, I, and Ω  are NS rotational energy,  moment of inertia, and
rotational angular velocity,  respectively):


    E_rot = 0.5 IΩ^2,   Ė_rot = AB^2Ω^4,  
    B  =  IPṖ/4A π^2,    A=R^6/6c^3,

B is NS surface dipole magnetic field at its magnetic pole.
Timing observations of single radiopulsars (the rapidly rotating ones  connected with young supernovae remnants are
marked by star)
give the following estimation   B_ns  =   2 · 10^11÷ 5· 10^13 Gs (Lorimer 2005).


The pulsars with a small magnetic field in the left lower angle decrease their magnetic field
during recycling by accretion in a close binary.  see Bisnovatyi-Kogan (2006).

SGR are single neutron stars with periods 2 ÷ 8 seconds
They produce "giant bursts", when their luminosity L in the peak increase 5 ÷ 6 orders of magnitude.
Having a slow rotation, and small rotational energy, their observed average luminosity
exceeds rotational loss of energy more than 10 times, and orders of
magnitude during the giant outbursts.

It was suggested by Duncan and Thompson (1995), that the source of energy is their huge magnetic field,
2 or 3 order of  a magnitude larger, then the average field in radiopulsars. Such objects were called  magnetars.





§ SGR,  GIANT BURSTS, AND SHORT GRB


First two Soft Gamma Repeaters (SGR) had been discovered by KONUS
group in 1979. The first one, FXP 0520 - 66, was
discovered after the famous giant 5 March 1979 burst
(Mazets et al. 1979b,c; Golenetskii et al. 1979), see also
Mazets et.al (1982). In another
source B1900+14 only small recurrent bursts had been observed (Mazets et al. 1979a). Now
these sources are known under names SGR 0520 - 66 and SGR 1900+14
respectively. The third SGR 1806-20 was identified as a repetitive
source by Laros et.al. (1986a,b). The first detection of this source as
GRB070179 was reported by Mazets et al.(1981), and it was indicated by
Mazets et al. (1982), that this source, having an unusually soft spectrum,
can belong to a separate class of repetitive GRB, similar to
FXP0520 - 66 and B1900+14. This suggestion was completely confirmed.
The forth known SRG1627-41, showing giant burst, was discovered in
1998 almost simultaneously by BATSE (Kouveliotou et al. 1998a), and BeppoSAX
(Feroci et al. 1998). The giant bursts had been observed until now in 4 sources.



 §.§ SGR0526-66


It was discovered due to a giant burst of 5 March 1979, projected to
the edge of the SNR N49 in LMC, and described by (Mazets et al. 1979b,c; Golenetskii et al. 1979, Mazets et.al 1982). Accepting the distance 55 kpc to LMC, the peak luminosity in the region E_γ>30 keV was
L_p ≥ 3.6× 10^45 ergs/s, the total energy release in the peak
Q_p ≥ 1.6 × 10^44 ergs, in the subsequent tail Q_t=3.6
× 10^44 ergs. The short recurrent bursts have peak
luminosities in this region L_p^rec=3× 10^41 -  3 ×
10^42 ergs/s, and energy release Q^rec=5× 10^40 -  7
× 10^42 ergs. The tail was observed about 3 minutes and had
regular pulsations with the period P≈ 8 s. There was not a
chance to measure Ṗ in this object.




 §.§ SGR1900+14


Detailed observations of this source are described by
Mazets et al. (1999b,c), Kouveliotou et al. (1999), Woods et al. (1999).
 The giant burst was observed 27
August, 1998. The source lies close to the less than 10^4 year old
SNR G42.8+0.6, situated at distance ∼ 10 kpc. Pulsations had
been observed in the giant burst, as well as in the X-ray emission
observed in this source in quiescence by RXTE and ASCA. Ṗ was
measured, being strongly variable. Accepting the distance 10 kpc,
this source had in the region E_γ>15 keV: L_p > 3.7×
10^44 ergs/s, Q_p > 6.8× 10^43 ergs, Q_t=5.2 ×
10^43 ergs, L_p^rec=2× 10^40 -  4× 10^41
ergs/s, Q^rec=2× 10^39 -  6× 10^41 ergs,
P=5.16 s, Ṗ=5 × 10^-11 -  1.5× 10^-10 s/s.
The X-ray pulsar in the error box of this source was discovered by Hurley et al. (1999b).
This source was discovered also in radio band, at frequency 111 MHz as a faint,
L_r^max=50 mJy, radiopulsar (Shitov 1999), with the same P and
variable Ṗ, good corresponding to X-ray and gamma-ray
observations. The values of P and average Ṗ correspond to
the rate of a loss of rotational energy Ė_rot=3.5 ×
10^34 ergs/s, and magnetic field B=8 × 10^14 Gs. The age
of the pulsar estimated as τ_p=P/2Ṗ=700 years is much less
than the estimated age of the close nearby SNR. Note that the observed X-ray
luminosity of this object L_x=2× 10^35   -    2×
10^36 ergs/s is much higher, than rate of a loss of rotational
energy, what means that rotation cannot be a source of energy in
these objects. It was suggested that the main source of energy comes
from a magnetic field annihilation, and such objects had been called
as magnetars by Duncan and Thompson (1992). The light curve of the giant burst is given in Fig.<ref>.






 §.§ SGR1806-20


The giant burst from this source was observed in December 27, 2004
(Palmer et al. 2005, Mazets et al. 2005, Frederiks et al. 2007).
 Recurrent bursts had been studied by Kouveliotou et al. (1998b), Hurley et al. (1999a). Connection with the Galactic radio SNR G10.0-03
was found. The source has a small but significant displacement from
that of the non-thermal core of this SNR. The distance to SNR is
estimated as 14.5 kpc. The X-ray source observed by ASCA and RXTE in
this object shows regular pulsations with a period P=7.47 s, and
average Ṗ=8.3× 10^-11 s/s. As in the previous case, it
leads to the pulsar age τ_p ∼ 1500 years, much smaller that
the age of SNR, estimated by 10^4 years. These values of P and
Ṗ correspond to B=8× 10^14 Gs. Ṗ is not
constant, uniform set of observations by RXTE gave much smaller and
less definite value Ṗ=2.8(1.4)× 10^-11 s/s, the value
in brackets gives 1σ error. The peak luminosity in the burst
reaches L_p^rec∼ 10^41 ergs/s in the region 25-60 keV, the
X-ray luminosity in 2-10 keV band is L_x≈ 2× 10^35
ergs/s is also much higher than the rate of the loss of rotational
energy (for average Ṗ) Ė_rot≈ 10^33 ergs/s.

 The burst of December 27, 2004 in SGR 1806-20 was the greatest flare, ∼ 100 times brighter than ever. It was detected by many satellites: Swift, RHESSI, Konus-Wind, Coronas-F, Integral, HEND et al..


Very strong luminosity of this outburst permitted to observe the signal, reflected from the moon by the HELICON instrument on the board of the satellite Coronas-F. The position of satellites Wind and Coronas-F relative to the Earth and Moon during the outburst are given in Fig.<ref>, and the reconstructed full light curve of the outburst is given in Fig.<ref> from Mazets et al. (2005), Frederiks et al. (2007a).








 §.§ SRG1627-41


Here the giant burst was observed 18 June 1998, in addition to
numerous soft recurrent bursts. Its position coincides with the SNR
G337.0-0.1, assuming 5.8 kpc distance. Some evidences was obtained
for a possible periodicity of 6.7 s, but giant burst did not show
any periodic signal (Mazets et al. 1999a), contrary to three other giant burst
in SGR. The following characteristics had been observed with a time
resolution 2 ms at photon energy E_γ> 15 keV:
 L_p ∼ 8× 10^43 ergs/s,
Q_p ∼ 3× 10^42 ergs, no tail of the giant burst had been
observed. L_p^rec=4× 10^40 -  4× 10^41 ergs/s,
Q^rec=10^39 -  3× 10^40 ergs. Periodicity in this
source is not certain, so there is no Ṗ.



 §.§ SRG giant bursts in other galaxies


The similarity between giant bursts in SGR, and short GRB was noticed by
by Mazets et al. (1999), Bisnovatyi-Kogan (1999).
The experiment KONUS-WIND had observed two short GRB, interpreted as giant bursts of SGR.
The first one, GRB070201, was observed
in M31 (Andromeda),  1 February, 2007.
The energy of the burst is equal to 1 · E^45 erg, in consistence with
giant bursts of other SGR   Mazets et al. (2008).
The second short burst, GRB051103, was observed in the galaxy M81,  3 November 2005.
The energy of the burst is equal  to 7· E^46 erg
(Golenetskii et al. 2005, Frederiks et al. 2007).



§ ESTIMATIONS OF THE MAGNETIC FIELDS
 IN SGR/AXP


Despite the fact, that rotation energy losses are much smaller than the observed luminosity, for estimation of the magnetic field strength in these objects used the same procedure as in radio pulsars, based on measurements of P and Ṗ, and using (<ref>). The first measurements have been done for  SGR 1900 + 14, in different epochs by measurements of satellites RXTE and ASCA
(Kouveliotou et al. 1999), presented in Figs.<ref>-<ref>.







The pulse shape is changing from one epoch to another, inducing errors in finding derivative of the period. The big jump in Ṗ, visible in Fig <ref> looks out surprising. for magnetic dipole losses, because it needs a considerable jump in the magnetic field strength, prohibited by self induction effects. Contrary, in the model of pulsar wind rotational energy losses it looks quite reasonable, that these losses strongly increase during the giant burst, when the Ṗ jump was observed.




 Another evidence in favour of the magnetar magnetic field was connected with the absorption lines in the spectrum of SGR 1806-20, observed by RXTE in November 1996 (Ibrahim et al. 2002). The main line corresponds to magnetic field (5÷ 7)·
10^11 Gs, when interpreted as an electron cyclotron line. In order to preserve the magnetar model, the authors <cit.> suggested that this line is connected with the proton motion, increasing the magnetic field estimation almost 2000 times. It is connected, however, with a drastic, ∼ 4· 10^6, decrease in the absorption cross-section, compared to the electron cyclotron line. Therefore, if this cyclotron line is real, its connection with the proton is very improbable.






§ RADIOPULSARS WITH VERY HIGH MAGNETIC 
 FIELDS AND SLOW ROTATION



Radio pulsars are rotating neutron stars that emit beams of radio waves 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. It was shown by Young et al. (1999a,b)
 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.
The period 8.51 second is characteristic for SGR/AXP objects, but this pulsar does not show any violent behaviour, and behave like ordinary radio pulsar.

Soon after this discovery, several other  radio  pulsars were found, where also Ṗ, and therefore magnetic field strength was measured
(Manchester et al. 2001, Camilo et al. 2000, McLaughlin et al. 2003,2004). These pulsars include:

 1. PSR J1119 - 6127,  P = 0.407 s,  Ṗ = 4.0 · 10^-12 s/s, B=4.1· 10^13 G;

 2. PSR J1814 - 1744, P = 3.975 s,  Ṗ = 7.4 · 10^-13 s/s, B = 5.5 · 10^13 G;

It was noted by Camilo et al. (2000), that "Both PSR J1119 — 6127 and PSR J1814 —1744 show apparently normal radio emission in a regime of magnetic field strength where some models predict that no emission should occur. Also, PSR J1814 —1744 has spin parameters similar to the anomalous X-ray pulsar (AXP) IE 2259 + 586, but shows no discernible X-ray emission. If AXPs are isolated, high magnetic field neutron stars (“ magnetars ”), these results suggest that their unusual attributes are unlikely to be merely a consequence of their very high inferred magnetic fields."

 3.  PSR J1847 - 0130, P=6.7 s, Ṗ = 1.3 · 10^-12 s/s, B=9.4 · 10^13 G.

 It was noted in the paper of McLaughlin et al. (2003), with the title "PSR J1847—0130: A RADIO PULSAR WITH MAGNETAR SPIN CHARACTERISTICS",  that "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."

 4. PSR J1718 - 37184, P= 3.4 s ,     B= 7.4 · 10^13 G.

 It was noted in the paper of McLaughlin et al. (2004), that "These fields are similar to those of the anomalous X-ray pulsars (AXPs), which growing evidence suggests are “magnetars”. The lack of AXP-like X-ray emission from these radio pulsars (and the non-detection of radio emission from the AXPs) creates new challenges for understanding pulsar emission physics and the relationship between these classes of apparently young neutron stars."



§ SGR/AXP WITH LOW MAGNETIC FIELDS AND MODERATE ROTATION



SGR/AXP  J1550-5418 (1E 1547.0-5408) was visible in radio band, showing pulsations with a period P=2.069 s )Camilo et al. 2007). The pulsations with the same period  have been observed first only in the soft X ray band by XMM-Newton (Halpern et al. 2008). In the hard X ray region statistics of photons was not enough for detection of pulsations. In the strong outbursts in 2008 October and in 2009 January and March, observed by Fermi gamma-ray burst monitor, the  period of 2.1s was clearly visible up to the energy ∼ 110 keV (Kaneko et al., 2010).
The INTEGRAL detected pulsed soft gamma-rays from SGR/AXP 1E1547.0-5408 during its Jan-2009 outburst, in the energy band 20÷ 150 keV, showing a periodicity with P=2.1s (Kuiper et al. 2009).	
 This object is the only SGR/AXP with a relatively low period, all previous has periods exceeding ∼ 4s.

  A low-magnetic-field  SGR0418+5729 was detected by Fermi gamma-ray burst detector (Rea et al. 2010). This soft gamma repeater with low magnetic field SGR0418+5729 was recently detected after it emitted bursts similar to those of magnetars. It was noted by Rea et al. (2010) that  "X-ray observations show that its dipolar magnetic field cannot be greater than
7.5·  10^12 Gauss, well in the range of ordinary radio pulsars, implying that a high surface dipolar magnetic field is not necessarily required for magnetar-like activity".





§ THE MAGNETAR MODEL


In the paper  of Duncan and Thompson (1992) was claimed, that dynamo mechanism in the new born rapidly rotating star may generate NS with a very strong  magnetic field 10^14÷ 10^15 G, called magnetars. These magnetars could be responsible for cosmological GRB, and may represent a plausible model for SGR. In the subsequent paper  (Duncan and Thompson 1995) the connection between magnetars and SGR was developed in more details.
The authors presented a  model for  SGRs, and the energetic 1979 March 5 burst, based on the existence of neutron stars with magnetic fields  much stronger than those of ordinary pulsars. They presented the following arguments point to a neutron star with B(dipole) 5· 10^14 G as the source of the March 5 event (Duncan and Thompson 1995).

 1. Existence of such a strong magnetic field may spin down the star to 8 s period in the 10^4yr, what is the age of the surrounding supernova remnant N49.

 2. Magnetic field provide enough energy for the March 5 event.

 3. In presence such magnetic field  a large-scale interchange instability is developed with the growth time comparable to the  0.2-s, close to the width of the initial hard transient phase of the March 5 event.

 4. A very strong magnetic field can confine the energy that was radiated in the soft tail of that burst.

 5.  A very strong magnetic field reduce the Compton scattering cross-section sufficiently to generate a radiative flux that is ∼ 10^4 times the (non-magnetic) Eddington flux;

 6. The field decays significantly in ∼ 10^4 ÷ 10^5 yr, as is required to explain the activity of soft gamma repeater sources on this time-scale; and

 7. The field power the quiescent X-ray emission L_X ∼ 7· 10^35 erg s^-1 observed by Einstein and ROSAT, as it diffuses the stellar interior. It is proposed that the 1979 March 5 event was triggered by a large-scale reconnection/interchange instability of the stellar magnetic field, and the soft repeat bursts are produces at cracking of the crust.

These suggestions were justified only by semi-qualitative estimations. Subsequent observations of P and Ṗ in several SGR (McGill 2014), seems to support this model. However, when the rotation energy losses are much less than observed X-ray luminosity, B estimations using Ṗ are not justified, because
magnetic stellar wind could be the main mechanism of angular momentum losses.
The jump in Ṗ observed in the giant burst of PSR1900+14 (Fig.<ref>) is plausibly explained by a corresponding increase of the magnetic stellar wind power, while the jump in the dipole magnetic field strength is hardly possible.
The jumps in Ṗ, as well as in the pulse form (Figs.<ref>,<ref>) have not been seen in the radio pulsars.
In the fall-back accretion model of SGR (Chatterjee et al. 2000, Alpar 2001, Trümper et al. 2010, 2013) the estimations of the magnetic field using P and Ṗ give the values characteristic for usual radiopulsars, when there is a  presence of a large scale magnetic field in the fall back accretion disk (Bisnovatyi-Kogan and Ikhsanov 2014).

When the energy density of the magnetic field is much larger that that of matter, as expected in the surface layers of the magnetar, the instability should be suppressed by magnetic forces.

The observations of radio pulsars, showing no traces of bursts, with magnetar magnetic fields and slow rotation (Section <ref>), detection of SGR with a small rotational period and low magnetic field, estimated from P and Ṗ values similar to radio pulsars (Section <ref>), gives a strong indication that inferred dipolar magnetic field strength and period cannot alone be responsible for the unusual high-energy properties of SGR/AXP. Therefore, another characteristic parameter should be responsible for a violent behaviour
of SGR/AXP. The unusually low mass of the neutron star was suggested by Bisnovatyi-Kogan (2012), Bisnovatyi-Kogan and Ikhsanov (2014) as a parameter, distinguishing SGR/AXP neuron stars from the majority of neutron stars in radio pulsars and close X-ray binaries.



 §.§ Angular momentum losses by a magnetized stellar wind


A magnetic stellar wind carries away the stellar angular momentum J as (Weber and Davis 1967)


    J̇_wind=2/3ṀΩ r_A^2,

here r_A  is Alfven radius, where the energy density of the wind E_w is equal to the magnetic energy density E_B=B^2/(8π).
We consider the wind with a constant outflowing velocity w, which energy density is E_w=0.5ρ w^2. In a stationary wind
with a mass loss rate Ṁ the density is equal to


    ρ=Ṁ/4π w r^2.

For the dipole stellar field we have B=μ/r^3, where μ=B_s r_*^3 is the magnetic dipole moment of the star.
At the Alfven radius we have


    ρ_A=Ṁ/4π w r_A^2,    E_wA=Ṁ w/8π r_A^2,   E_BA=μ^2/8π r_A^6.

From the definition of the Alfven radius r_A we obtain its value as


    E_wA=E_BA,   r_A^4=μ^2/Ṁ w.

The angular momentum of the star J=IΩ, and when the wind losses (<ref>) are the most important, we obtain the
value of stellar magnetic field  as


    B^2_wind=9/4I^2Ω̇^2 w/Ω^2 Ṁ r_*^6.

The angular momentum and energy losses by the dipole radiation which are main losses in
ordinary radiopulsars are written as (Pacini 1967)

 
    L=B_s^2 Ω^4 r_*^6/c^3,   Ė=IΩΩ̇= L,   J̇_PRS=L/Ω.

We obtain from (<ref>) the magnetic field if the dipole radiation losses are the most important


    B^2_PSR=3I c^3Ω̇/2Ω^3 r_*^6.

The ratio of these two values is written as


    B^2_PSR/B^2_wind=2 c^3Ṁ/3I ΩΩ̇w=4/3Ṁ w^2/2/I ΩΩ̇(c/w)^3
    =4/3F_wind/Ė_rot(c/w)^3.

Here F_wind is the the energy flux carried away by the wind, and Ė_rot is rate of the loss of
rotational energy. For estimation of the energy flux carried away by the wind could be used the average
X and γ-ray luminosity of SGR/AXP L_xγ, and the wind velocity is of the order of the free fall velocity of the neutron star.
For low mass neutron star M≤ 0.8 M_⊙ we have v_ff=√(2GM/r_*)≈ (c/3) at M=0.6 M_⊙,
r_*=15km, and

  
    B^2_PSR/B^2_wind=36L_xγ/Ė_rot.

Using data from McGill(2014) and (<ref>) we obtain for the magnetic fields of SGR  0526-66, SGR 1806-20, SGR 1900+14 the values
10^13, 1.7· 10^14, 6· 10^13 Gs respectively. While  the mechanical loss of the energy could exceed L_xγ,
these values of the magnetic field are suppose to be the upper limit if the magnetic field of these SGR.



§ MODEL OF NUCLEAR EXPLOSION



It was shown by Bisnova­tyi-Kogan and Chechetkin (1974), that in the neutron star crust full thermodynamic equilibrium is not reached, and a non-equilibrium layer is formed there during a neutron star cooling, see also Bisnovatyi-Kogan 2001.

 


The non-equilibrium layer is formed in the region of densities and pressure ρ_2<ρ<ρ_1, P_1<P<P_2, with


    ρ_1≃μ_e 10^6 (8/0.511)^3≃ 3.8· 10^9μ_e    g/cm^3≃ 1.5· 10^10   g/cm^3


    ρ_2≃μ_e 10^6 (33/0.511)^3≃ 2.7· 10^11μ_e    g/cm^3≃  10^12   g/cm^3


    P_1= 7.1 · 10^27   in   cgs   units,    P_2 = 2.1 · 10^30   in   cgs   units.


The mass of the non-equilibrium layer is defined as (Bisnovatyi-Kogan and Chechetkin 1974)

    M_nl=4π R^4/GM(P_2 - P_1) ≃ 0.1 (P_2-P_1)≃ 2· 10^29   g  ≃ 10^-4  M_⊙,


and the energy stored in this non-equilibrium layer is estimated as

    E_nl≃ 4· 10^17 (P_2 - P_1) ≈ 10^48   erg

Here a neutron star of a large (∼ 2  M_⊙) was considered, where the nonequilibrium layer is relatively thin, and its mass, and the energy store are estimated in the approximation of a flat layer. The nuclei in the non-equilibrium layer are overabundant with neutrons, so the number of nucleons per one electron is taken as μ_e≃ 4, and the energy release in the nuclear reaction of fission is about 5· 10^-3 c^2 erg/g. A schematic cross-section of the neutron star is represented in Fig.<ref> from Baym (2007).


 Soon after discovery of gamma ray bursts the model of nuclear explosion was suggested (Bisnovatyi-Kogan et al. 1975), in which the non-equilibrium layer matter is brought to lower densities during a starquake. At the beginning GRB have been considered as objects inside the Galaxy, and the outburst was connected with period jumps in the neutron star rotation similar to those observed in the Crab nebula pulsar. It was suggested that: "Ejection of matter from the neutron stars may be related to the observed jumps of periods of pulsars. From the observed gain of kinetic energy of the filaments of the Crab Nebula (∼ 2· 10^41 erg) the mass of the ejected material may be estimated as (∼ 10^21 g). This leads to energies of the γ-ray bursts of the order of 10^38-10^39 erg, which agrees fully with observations at the mean distance up to the sources 0.25 kpc". A more detailed model of the strong 5 March 1979 burst, now classified as SGR 0526-66 in LMC,  was considered by  Bisnovatyi-Kogan and Chechetkin (1981). It was identified with an explosion on the NS inside the galactic disk, at a distance ∼ 100 ps.
 The schematic picture of the nuclear explosion of the matter from the non-equilibrium layer is  presented in Fig.<ref>.




Cosmological origin of GRB, and identification of a group of non-stationary sources inside Galaxy as SGR/AXP lead to considerable revision of the older model, presented by Bisnovatyi-Kogan et al. (1975). It becomes clear that SGR represent a very rare and very special type of objects, which produce bursts much more powerful, than it was thought before from comparison with quakes in Crab nebula pulsar. Besides, the SGR are the only sources for which the nuclear explosions could be applied, because the energy release in the cosmological GRB highly exceed the energy store in the non-equilibrium layer.

It was suggested by Bisnovatyi-Kogan (2012,2015), Bisnovatyi-Kogan and Ikh­sa­nov (2014), that the property, making the SGR neutron star so different from much more numerous of them in radio pulsars, single and binary X ray sources, is connected with the value of their mass, but not the magnetic field strength, see Camilo (2000), McLaughlin (2003), and Section <ref>. Namely, it was suggested that the neutron stars in SRG/AXP have anomalously low mass, (0.4 ÷ 0.8)M_⊙, compared to the well measured masses in binary systems of two neutron stars, where neutron stars have masses ≥ 1.23  M_⊙ (Ferdman et al. 2014). The violent behaviour of the low-mass NS may be connected with much thicker and more massive non-equilibrium layer, and accretion from the fall-back highly magnetized accretion disk could trigger the instability, leading to outbursts explosions  (Bisnovatyi-Kogan and Ikhsanov 2014). The NS radius is increasing with mass rather slowly, so in a flat approximation the mass of non-equilibrium layer is inversely proportional to the mass. More accurate estimations have been obtained from calculations of neutron star models, presented in Fig.<ref>.
In Sect.<ref> the calculated mass of the non-equilibrium layer M_nl≈ 10^-4 M_⊙ was belonged to the neutron star with the mass ∼ 2 M_⊙ (see Bethe and Johnson 1975, Malone et al. 1975). For M_ns=0.45  M_⊙ the mass of the non-equilibrium layer is ∼ 7 times larger. The energy store reaches ∼ 10^49 erg, what is enough for ∼ 1000 giant bursts.




 The observational evidences for existence of neutron stars with masses, less than the Chandrasekhar white dwarf mass limit have been obtained by Janssen et al. (2008).
Observations of the binary pulsar system J1518-4904 indicated the masses of the components to be
m_p =0.72(+0.51, - 0.58 M_⊙),  m_e = 2.00(+0.58, - 0.51) M _⊙ with a 95.4% probability.
It was suggested by Bisnovatyi-Kogan and Ikhsanov (2014)  that low mass neutron stars could be formed in the scenario of the off-center explosion (Branch and Nomoto 1986), but more detailed
numerical investigation is needed to prove it. X-ray radiation of SGR/AXP in quiescent states was explained by Bisnovatyi-Kogan and Ikhsanov (2014) as a fall back accretion from the disk with a large scale poloidal magnetic field, what could also be a trigger for development of instability, leading to the mixing in the neutron star envelope, and nuclear explosion of the matter from the non-equilibrium layer.




§ CONCLUSIONS


1. SGR are highly active, slowly rotating neutron stars.

2. Nonequilibrium layer (NL) is formed in the neutron star crust, during NS cooling, or during accretion onto it. It may be important for NS cooling, glitches, and explosions connected with SGR.

3. The mass and the energy store in NL increase rapidly with decreasing of NS mass.

4.  The properties of pulsar with high magnetic fields prove that inferred dipolar magnetic field strength and period cannot alone be responsible for the unusual high-energy properties of SGR/AXP.
The NL in low mass NS may be responsible for bursts and explosions in them.

5. The upper boundary of the magnetic fields in 3 most famous SGR, measured by the average L_xγ luminosity is
about one order of magnitude lower than the values obtained using the pulsar-like energy losses of the rotational energy
of the neutron star.

6. Magnetar model of SGR, in which the energy of the observed bursts is provided by magnetic field annihilation, seems to be not relevant. Observations of quiet radiopulsars with a "magnetar" magnetic field, and of a low-field "magnetar", is the most important indication to that conclusion. A rapid growth of rotational periods, what is a favorite argument for a "magnetar" origin, is naturally explained by action of the magnetic stellar wind.
Besides, the high pressure of the magnetic field suppresses convection, which is needed in all annihilation models.




Acknowledgments



The work of  was partially supported by the Russian Foundation for Basic Research Grants No. 14-02-00728 and  OFI-M 14-29-06045, and the Russian Federation President Grant for Support of Leading Scientific Schools, Grant No. NSh-261.2014.2.


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