On the nature of AXPs and SGRs

1
On the nature of AXPs and SGRs

• I.F.Malov
• Pushchino Radio Astronomy Observatory, Russia

2
Plan of the report

• 1. AXP and SGR
• 2. The magnetar model
• 3. Alternative models
• 4. The drift model
• i) real values of AXP and SGR parameters
  (rotation periods, their derivatives, magnetic
  fields)

3

• ii) Persistent X-ray emission, gamma-bursts
• iii) Radio pulsars with very long periods
• iv) What is the difference between normal
  radio pulsars and magnetars?
• iv) The possibilities of observational tests
• 5. Conclusions

4
Basic publications Malov I.F.
2001. Astron. Rep. 45, 389 Malov I.F., Machabeli
G.Z., Malofeev V.M. 2003. Astron. Rep. 47,
232 Malov I.F., Machabeli G.Z. 2005. Astron.
Rep. 49, 459 Malov I.F. 2006. Astron. Rep. 50,
398 Lomiashvili D., Machabeli G., Malov I.
2006. Ap J. 636, 1010 Malov I.F., Machabeli
G.Z. 2006. Astron. and Astrophys. Trans. 25, No.1
5

• Introduction. Magnetar model
• Two classes of astrophysical objects have been
  studied intensively during the last 10 years but
  their nature is unclear up to now. These are
  Anomalous X-ray Pulsars (AXPs) and Soft Gamma
  Repeaters (SGRs). Both classes are characterized
  by pulsed X-ray emission, and we can suggest that
  the central objects in these sources are isolated
  neutron stars because there are no any evidences
  for the presence of secondary companions in all
  cases

6

• The AXP group contains 5 confirmed sources and
  several candidates. All data were taken from
  Duncan Thompson (1992), Baring Harding
  (1998), Mereghetti (1999), Hurley (2000),
  Mereghetti (2000), Baring Harding (2001),
  Israel et al. (2001) and Hambarian et al (2002).
  The main difference of AXPs from "normal" X-ray
  pulsars is their monotonous slowing down with
  derivatives of periods dP/dt 10 -13 10-10 .

7
The model of the X-ray pulsar (Manchester and
Taylor. Pulsars).
8
Changes of X-ray pulse periods for Her X-1 and
Cen X-3.
9

• As for SGRs, they number 4 confirmed objects and
  one candidate. Their pulse periods are in the
  same range as the periods of AXPs (P 5 - 8 s)
  (Table 1). However pulsed components are observed
  from them during quiet stages (SGR 1627-41 and
  1806-20) only or vice versa when gamma-ray bursts
  occur (SGR 0525-66). Only SGR 190014 shows
  pulsed X-ray emission during all stages. The main
  distinctions of SGRs are episodic gamma-ray
  bursts with the total energy of each burst up to
  1044 erg (Mereghetti 2000). Sometimes there are
  more intensive flares. For example, SGR 1806-20
  had the total (isotropic) flare energy 2 x 1046
  erg on 2004 December 27 (Palmer et al. 2005).

10
Fig.1. The folded pulse profiles of eight
different magnetar candidates (Woods Thompson
2004)
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• If we use the known formula  B 6.4 1019
  (P dP/dt)1/2 (1) obtained from the
  model of the magneto-dipole slowing down, then
  magnetic fields at the surface of a neutron star
  in AXPs and SGRs must be 1014 1015 G, two
  orders of magnitude higher than fields in
  "normal" pulsars. This was the reason why such
  objects were named "magnetars". The second reason
  can be understood from the data of the Table 1
  showing the observational data for the best
  studied AXPs and SGRs. It is known that the main
  source of radio pulsar energy is connected with
  losses of the rotation energy of a neutron star
  with the rate dE/dt IO dO/dt.

14

• Here I is the moment of inertia of a neutron
  star, O 2p/P is its angular rotation velocity.
  But if we take I 1045 g cm2 then energy losses
  for AXPs and SGRs dE/dt 1033 erg/s are much
  less than their X-ray luminosities. To avoid this
  difficulty it was suggested that X-ray radiation
  took its energy from a magnetic reservoir. Let us
  consider this possibility.The total energy of
  such reservoir is  E (B2/8 p)(4 p R3 /3)
  1.7 1045-1.7 1047 erg (2)

15

• where R 10 km is the neutron star radius. The
  X-ray luminosity of SGR 1806-20 is 2 x 1035
  erg/s. For E 1047 erg this source will exist
  for 104 years only. Time of life for normal radio
  pulsars is 107 years. So, only one magnetar must
  be observed among 1000 known radio pulsars. This
  estimate is ten times less than the observed
  number. In fact, not all radio pulsars are
  observed. However we can say the same about
  "magnetars".

16

• We suggest here that the relative observed parts
  of these objects are equal each to another.
  Energetic difficulties become more serious if we
  take into account that SGR 1806-20 injects
  relativistic particles in the ambient SNR with
  the rate 1037 erg/s (Kouveliotou et al. 1998).
  In this case the magnetic reservoir will be
  exhausted during 360 years. However the age of
  SGR 1806-20 is 1400 years.

17

• To avoid this difficulty it is necessary to
  postulate the existence inside a neutron star of
  magnetic fields B 1016 G (Thompson Duncan
  1996). It is worth noting that the induced
  magnetic moment of the anisotropic neutron
  superfluid in neutron stars can give the maximal
  strength of the unduced magnetic field 1015 G
  only (Peng 2006).
• It is well known that the necessary stage to
  generate pulsar radio emission is creation of
  electron-positron pairs. But a gamma-quantum in
  very strong magnetic fields (B gtgt 1012 G) will
  convert into two othergamma-quanta (Baring
  Harding 1998).

18

• B ? ? B e e- (3)
• B ? ? B ?1 ?2
• ?
• Therefore AXPs and SGRs must be radio quiet
  objects.
• However Shitov et al. (2000) detected radio
  emission from SGR 190014 and Malofeev et
  al.(2005) registered pulse radio signals from the
  AXP 1E2259586.

19

• So there is the alternative either we do not
  understand how radio pulsars radiate or magnetic
  fields of "magnetars" are much less than
  10141015G.

20

• The braking index n is determined by the
  equation
• dO/dt C On (4)
• n (O d2 O/ dt2 ) / (dO/dt)2
• n 3 for the magneto-dipole slowing down
• n 0.20 0.47 for SGR 190014 (Shitov et al.
  2000).
• Hence we cant use the magneto-dipole model for
  calculating of magnetic fields in AXPs and SGRs

21
OTHER MODELS

• i)These difficulties compel some authors to use
  the accretion model to explain observable
  properties of AXPs and SGRs (see, for example,
  Marsden et al. 2001). The accretion from ambient
  plasma gives an additional energy source for Bs
  1012 G and it is not necessary to suggest
  super-strong magnetic fields.

22

• Moreover, the other mechanism describing the
  decreasing of an angular moment appears, and
  large values of dP/dt can be explained without
  the magneto-dipole slowing down. In this case the
  braking index must differ from the magneto-dipole
  value n 3 (see, for example, Malov 2003). In
  fact, the observations of SGR 190014 give n
  0.19 (Shitov et al. 2000).

23

• However, there is a number of difficulties in
  accretion models too. The accretion from the
  interstellar medium can provide luminosities L
  1032 erg/s, much less than the observable ones
  (see Table 1). If accretion is connected with a
  relic disk then time of life of this disk is
  very small (lt 1 year) and such accretion does not
  describe the observed slowing down of AXPs (Li
  1999).

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• Plasma from a secondary component could explain
  the observed luminosities for the rate of
  accretion dM/dt 10-11 M? /year (Mereghetti
  1999). However, there are no any evidences of the
  presence of such components in AXPs or SGRs in
  all cases. An ambient plasma certainly exists
  around these objects, and accretion processes
  can play a role in their slowing down and
  evolution. However, the accretion models can not
  explain the main properties of "magnetars".

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• ii) White dwarfs with B 108 109 G (Paczynski
  ApJ 1990, 365, L9,
• Usov ApJ 1993, 410, 761).
• The reasonable models of white dwarfs give
  log(dE/dt) 36. It is not enough to explain
  injection of relativistic particles in ambient
  SNRs.
• Extremely short periods are required.

26

• iii) Strange stars
• (Dar De Rujula 2000, Usov 2001)
• The existence of these objects is rather
  problematic.
• The possible models are not worked out.
• iv) Precession (Shaham 1977, Sedrakian et al.
  1999)
•  A long living free precession is doubtful
  realized.

27
The drift model

• In this report we discuss an other model for
  describing the magnetar" phenomenon using usual
  values of magnetic fields at the surface of a
  neutron star Bs 1012 G.
• Kazbegi et al. (1991), Chedia et al. (1997), and
  Machabeli et al. (2001) showed that besides l-
  and lt-waves generation of transverse
  electromagnetic drift waves was possible in
  pulsar magnetospheres with the characteristic
  frequency ?0 Re ? kx uxb
  (5)and the increment
•   G Im ? (nb / np)1/2 ?p1/2 kx uxb /?b1/2
  (6)
•  

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• These waves cause variations of curvature of
  field lines
• K 1/? 1 (dy/dx)2 - 3/2 d2y /dx2 (7)
• K (1 kf r Br /Bf) /r
  (8)
• If kf r gtgt1 the change of K could be
  significant. As far as radiation is emitted along
  a tangent to the local direction of magnetic
  field the change of its curvature leads to the
  change of the radiation direction.

29

• Fig.2. Scheme of the drift model

30

• These waves are stabilized due to a neutron
  star rotation and permanent injection of
  relativistic particles in a region of their
  generation.

31

• We can use the results of Malov Machabeli
  (2002) and Malov et al. (2003) to calculate the
  synchrotron luminosity
•  
•   31/2 p7/2 e I ?b3/2 dP/dt
• L -------- -------- , (9)
  
• 32 m1/2 c3/2 P7/2 ?p2
• the period of drift waves
• Pdrmax e B P2 / (4 p2 m c ?b )
  (10)
• and its derivative
• (dP/dt)dr e B P dP/dt /(2 p2 m c ?b )
  (11)
•  

32

• We can calculate P, dP/dt and B from the system
  (9)-(11)
•  
  (P? )-11
• P (s) 8.32 x 10-2 --------------2/5
  (12)
• (Lx)34
  (W/Pobs )2 Pobs pl
•  
• P (dP/dt)obs
• dP/dt -------
  (13)
•   2 ?obs
•  
• ? (G) 22.45 ?obs / P2
  (14)
• We assume that I 1045 g cm2 and use ?b 106
  -107 .
•  

33

• The results of our calculations can be seen from
  the Table . AXPs

34
Caclulated parameters of SGRs
35

• 4 p2 I dP/dt
• dE/dt ------- (15)
  
• P3
• is the loss of the rotation energy.
• The dependence of Lx (Table 1) on dE/dt from
  Table 2
• log Lx (0.60 0.28) log (dE/dt) 13.08
  7.52 (16)
•  and high correlation coefficient ( K 0.8)
  between Lx and dE/dt show that the losses of the
  rotation energy can be the real energy source of
  the X-ray emission in AXPs and SGRs.

36

• The relationship between the X-ray luminosity and
  dE/dt for 41 radio pulsars (Possenti et al.
  2002) has rather different form
•  
• log Lx ( 1.33 0.09) log (dE/dt) 15.28
  3.29 (17)
• However in these objects the rotation energy
  losses is the main source of their X-ray emission
  as well.
• It is worth noting that the values of dE/dt
  in Table 2 is higher than 1037 erg/s for many
  objects and they are quite enough to explain the
  observed injection of relativistic particles into
  ambient SNRs.

37

• The objects in our sample and radio pulsars with
  X-ray emission have as a rule short periods. For
  AXPs and SGRs in Table 2 ltPgt 89 ms, and for 41
  pulsars from (Possenti et al.2002) ltPgt 128 ms
• The distributions of periods for these objects
  are identical as well. Indeed, among 41 sources
  from Possenti et al. (2002) there are pulsars
  with periods P from milliseconds to dozens of
  milliseconds (1.56 89 msec) and with P 0.1
  0.53 sec. Table 2 contains also AXPs and SGRs
  with P 10 msec (1E2259586 and RXS 1709-4009),
  with periods of order tens milliseconds
  (1E1048-5937) and with P gt 0.1 sec ( SGR
  190014).

38

• The braking index n  is near to 0 for AXPs and
  SGRs. This means that some other braking
  mechanisms operate in these objects (Malov 2001,
  Illarionov Sunyaev 1975, Lovelace et al. 1999,
  Zhang et al. 2003, Malov 2003).
• n 3 2 (d2Pdr/dt2)/(dPdr /dt)2 (18)
• n - 0.6 as for pulsars with P lt 0.1 sec
• (Malov 2004)

39

• Fig.3. Location of AXPs and SGRs on the diagram
  (dP/dt)- P in the frame of
  our model (black circles) and the magnetar
  model (Woods Thompson 2004).

40

• Quiescent X-ray emission
• It is well known that near the surface of a
  neutron star the process describe by the equation
  (3) takes place, and new born electrons and
  positrons populate the Landau levels. Let us
  consider the question what is the frequency
  range corresponding to radiation near the
  surface.
• The frequency ? in the observers coordinate
  system depends on the frequency ?0 in the system
  where V 0 and it is determined by the
  equation
• ( 1 V2
  / c2 )1/2
• ? ?0 ??????? ,
  (19)
• 1 V Cos
  ? / c
•  

41

• If the Lorentz-factor of emitting particles ?
• ( 1 V2/c2 )-1/2 gtgt 1, and the angle ? is small,
  the formula (19) can be presented in the
  following form
• 
  2?0
• ? ?????
  (20)
  
• 1/?
  ?2 ?
• If ?2 ? ltlt 1/?, then
• ? ? 2?0
  ? (21)
•  In the opposite case
• ? ?
  ?0?? (22)
  
  
• For
• 1 ? ?2 ? ? 10 ,
  (23)
•  and B 1012 G the electron cyclotron frequency
•  
•  
•  
•  
•  

42

• e Bs
• ?0 ????
  (24)
• 2 ? m c
•  
• is in the soft X-ray range ( 1 10 keV) in the
  observers system. This emission can penetrate
  through the e - magnetosphere and arrive to the
  observer. The diapason of angles ? can be very
  wide, and the distribution function of emitting
  particles is not mono-energetic, therefore the
  resulting spectrum must be wide too.

43

• The magnetic field of a neutron star falls with
  the increasing distance, and the frequency
  coincides with one of the Landau harmonics
•   ?m - ?n ( p?m2 - p?n2 ) / 2 me h ?0 S,
  (25)
• S ( m n ) ? 1, ?2,
• near the surface only.
• Lines corresponding to such harmonics have been
  detected in fact (Rea et al. 2003). They
  correspond to B 1011 1012 G if they are
  emitted by electrons. There are some attempts
  (Zane et al. 2001) to interpret them as the
  absorption lines of non-relativistic protons in
  magnetic fields 1014 1015 G.

44

• However according to Ho et al.( 2002) vacuum
  polarization effect not only suppresses proton
  cyclotron lines, but also suppresses spectral
  features due to bound species.
• . Therefore spectral lines or features in thermal
  radiation are more difficult to observe when the
  neutron star magnetic field is ? 1014 G.

45

• Moreover in this case the electron cyclotron
  lines in the range near 1 MeV must be observed.
  Their detection will be the good evidence for the
  magnetar model.
• The emission beam of relativistic particle has
  the width ? 1 / ? .
• We believe that this near-surface emission is
  the main part of the observed quiescent X-ray
  radiation of AXPs and SGRs. As we said earlier
  near the light cylinder the pulsed emission was
  generated. So, we must observed two emission
  cones as it is shown in Fig. 4.

46

• Fig.4. Two cones of X-ray emission in
• AXPs and SGRs

47

• Irregular gamma-ray bursts
• If a is near to 0 (for example due to any
  catastrophic event at the surface of the neutron
  star) the boosting effect must take place
• 1
• P? P?0 ???????? (26)
• 1 V Cos ? / c
•   For ?? 0 P? increases drastically and
  becomes equal to 
• P? ? 2 P?0 ?2

48

• So, the power in the gamma-ray range can be 2 ?2
  times higher than in X-ray one. If X-ray power
  is 1036 erg/s, the Lorentz-factor must be ?
  104 to provide a gamma-ray burst with the power
  1044 erg/s. In the traditional model such energy
  characterizes the tail of the distribution
  function for the secondary particles (Fig.5). To
  achieve the power 2 x 1046 erg / sec as in SGR
  1806-20 we must put ? 105. There are such
  particles in the tail of the secondary plasma as
  well.

49
Fig.5. Distribution function of relativistic
plasma in a pulsar magnetosphere (Arons 1981).
Broken line is the positron
distribution.
50

• Radio pulsars with very long observed periods
• Recently radio pulsars with long periods were
  discovered (see table 4).They must be in the
  radio-quiet zone. PSR J2144-3933 , discovered in
  1999 (Yong et al.), has the longest (8.5 s) pulse
  period among the known radio pulsars. PSR
  J2144-3933 is distinguished by some other
  characteristics. It has the lowest spin-down
  luminosity ( dE/dt 3.2 1028 erg/s) among any
  known pulsar. The beaming fraction (that is, the
  fraction of the celestial sphere swept across by
  the beam) is also smallest, W10 / P 1/300.

51

• On the other hand PSR J1847-0130 59 and PSR
  J1814-1744 60 are isolated radio pulsars having
  the largest inferred surface dipole magnetic
  fields Bs yet seen in the population 9.4 1013 G
  , and 5.5 1013 G, respectively. These pulsars
  show apparently normal radio emission in a regime
  of magnetic field strength (Bs Bcr 4.4
  1013G) where some models predict no emission
  should occur.
• The model explaining the phenomenon of radio
  emission from all these pulsars and all special
  properties of PSR J2144-3933 does not exist up to
  now.

52

• We proposed a model, which provides the natural
  explanation of the peculiarities of pulsars under
  consideration. We believe that the observed
  interval between successive pulses is not equal
  to the rotation period, but is determined by the
  period of drift waves as in AXPs and SGRs.
  Variation of the ?eld line curvature can be
  estimated as
• ??/? kfr?Br/Bf (27)
  
•  
• It follows that even the drift wave with a modest
  amplitude Br ?Br 0.01Bf alters the ?eld
  line curvature substantially, ??/? 0.1

53

• Since radio waves propagate along the local
  magnetic ?eld lines, such curvature variations
  cause changes of emission direction.
• There is unequivocal correspondence between
  the observable intensity and a (angle between
  observers line of sight and emission direction
  (see Fig. 6)). Maximum of intensity corresponds
  to minimum of a. The period of pulsar is the time
  interval between neighboring maximums of
  observable intensity (minimums of a). According
  to this fact, we can say that the observable
  period is the representative value of a and as it
  will appear below it might differ from the spin
• period of pulsar.

54

• Fig.6. Geometry under consideration. K is
  emission axis, A is observers one. Angles d
  and ? are
• constant, while ß and a are oscillated with time.

55

• cos a AK
  (28)
• a arccos (sin d sin ß cos Ot cos d cos ß)
• In the absence of the drift wave ß ß0
  constant and consequently the period of a equals
  to 2p/O.
• According to equation (27), in the case of the
  presence of the drift wave, fractional variation
  ??/? is proportional to the magnetic ?eld of the
  wave Br , which changes periodically. So
• ß ß (t) is harmonically oscillating about ß0
  with an amplitude ?ß ??/? and rate ?dr 2p/Pdr
  . So, we can write that
• ß ß0 ?ß sin (?dr t F)
  (29)
•  
•  

56

• According to equations (69) and (70) we obtain
• a arccos (sin d sin (ß0 ?ß sin (?dr t F))
  cos Ot cos d cos (ß0 ?ß sin (?dr t F)))
• Parameters of the pulse pro?le (e.g. width,
  maximal intensity etc.) signi?cantly depend on
  what would be minimal angle between the emission
  axis and the observers axis while the first one
  passes the other (during one revolution). If the
  emission cone does not cross the observers line
  of sight entirely (i.e. minimal angle between
  them is more than cone angle ?
•   amin gt ? ,
  (30)
• then pulsar emission is unobservable for us.

57

• Opposite to this, inequality
• amin lt ? (31)
• de?nes condition that is necessary for emission
  detection (Fig.7). In this case observed pulses
  must be quite narrow, as seen in pulsars under
  consideration. Sometimes we can see several
  subpulses as a result of subsequent neutron star
  rotations. Our model predicts a detection of such
  objects in future.

58

• Fig.7. The oscillating behaviour of a with time
• for ß0 d 0.12,
• ?ß 0.12,
• ?dr 2p/17 sec-1,
• O 2p/0.85 sec-1,
• F 0.

59

• In that case the observable period Pobs does not
  represent the real pulsar spin period, but is
  divisible by it
• Pobs mP
  (32)
• It follows from this
• (dP/dt)obs mdP/dt
  (33)
• From equations (1), (74) - (75) follows that
• B Bobs/m
  (34)

60

• After inserting equations (32) and (34) in
  equation of death line for a sunspot
  configuration field (Chen Ruderman 1993)
  (Fig.8)
• 7 log Bs 13 log P 78
  (35)
• we obtain
• 7 log B - 13 log P (7 log Bobs - 13 log Pobs )
• 6 log m 78
  (36)
• Then
• 6 log m 78 - 7 log Bobs 13 log Pobs
  (37)

61

• It can be veri?ed that there exists value for m
  which satis?es equation (37) and simultaneously
• the condition
• B Bobs/m lt Bcr (38)
• So, it is possible ful?lment of conditions
  necessary for (e e-) pair production for some
  values of m

62

• If we consider all pulsars in framework of our
  model, their parameters (spin, magnetic fields
  etc.) will get new real values, shown in Table
  4.
• If we use the observed values of parameters
  (Table 3) the location of pulsars under
  consideration on the Bs P diagram are presented
  by Fig.8.
• According to the obtained results, considered
  pulsars will be placed on Bs P diagram as
  shown in Fig. 9.

63
Table 3. Observed parameters of long periodic
radio pulsars
64
Table 4.Calculated values of pulsar parameters
65

• Fig.8. A, B and C are death lines for the
  dipole magnetic field, the sunspot configuration
  and the multipolar magnetic field
• (Chen Ruderman 1993). The broken line
  represents B Bcr. The values of parameters are
  taken from Table 3

66

• Fig.9. Real positions of the considered
  pulsars on Bs P diagram (Table 4).

67

• Discussion
• One of the main characteristics of observed
  emission is the stability of pulse periods. As we
  said already the drift waves are stabilized due
  to the neutron star rotation and the permanent
  injection of relativistic particles in the region
  of their generation. Moreover as was shown by
  Gogoberidze et al. (2005) that the nonlinear
  induced scattering leads to a transfer of waves
  from higher to lower frequencies. As the result
  one eigen mode becomes dominant.

68

• So the wave energy accumulates in waves with the
  certain azimuthal number m, characterizing the
  lowest frequency. This means that the period of
  the modulation and the interval between observed
  pulses must be rather stable.
• It follows from (12) and (13) that if the
  rotation period P and its derivative dP/dt
  undergo to glitches then similar glitches must be
  observed in Pdr and (dP/dt)dr as well.
•   We have used the suggestion on the small
  angles between rotation axes and magnetic
  moments of neutron stars in AXPs and SGRs. In
  fact observed X-ray pulses in these objects are
  quite wide, and this indicates that they are
  nearly aligned rotators.

69

• Two peculiarities of magnetarsi) A small
  angle ß ( ß lt 100 )
• between rotation and magnetic axes,
• ii) a rotation period P 0.1 sec.
• The first group (i) contains about 10 of the
  whole population, if neutron stars are formed
  with an arbitrary angle ß.
• The second one (ii) number approximately 0.1
  part of all pulsars.
• So, we can expect 1 of magnetars in the
  whole sample of radio pulsars. In fact we observe
  about 15 magnetars among 1500 radio pulsars

70

• Recently discovered transient radio pulsars
  (McLaughlin et al. 2005) may belong to the
  population of objects described by our model.
  Indeed, 5 of them have rather long visible
  periods (P gt 4 sec) and one of them has the
  surface magnetic field obtained in the
  magneto-dipole model Bs 5 1013 G gt Bcr.
• Precession, star-quakes or other reasons can lead
  to the fulfillment of the condition (31) for a
  short time and to an appearance of a number of
  visible pulses.

71
CONCLUSIONS

• 1. It is shown that there are many difficulties
  in the magnetar model.
• 2. In the framework of the drift model P, dP/dt,
  and B are calculated for AXPs and SGRs.
• P 10-520 ??, ltPgt 89 ??
• dP/dt 3.7 10(-16)- 5.5 10(-12)
• log B 2.63 6.25
• 3. The high correlation L (dE/dt) is detected,
  as for 41 radio pulsars with detected X-ray
  emission.

72

• 4.Magnetic fields at the surface of AXPs and
  SGRs are estimated
• lg Bs 11.22 12.79
•  ltlg Bs gt 11.73
• 5. In the drift model a modulation of emission
  with periods of order 0.1 sec should be observed.
  The detection of oscillations in SGR 1806-20 with
  frequencies 18, 26, 92.5 and 626.5 Hz (Watts
  Strohmayer 2006) may be the first evidence of
  such modulation.
• 6. The persistent X-ray emission in the range 1
  10 keV can be explained by cyclotron radiation of
  electrons at the surface with magnetic fields Bs
  1012 G.

73

• 7. Cyclotron lines can be observed in this
  diapason.
• 8. Any cataclysms at the surface of a neutron
  star in AXP or SGR should cause bursts of
  emission in X-ray or gamma-range with power 2
  ?2 times higher than persistent X-ray one.
• 9. If the magnetar model is realized an
  absorption line with energy of order 1 MeV must
  be observed.
• 10. Radio pulsars with observed periods P gt 4 sec
  can be described in the framework of the drift
  model too.

74
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Thank you