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ISSN 1063-7729, Astronomy Reports, 2012, Vol. 56, No. 1, pp. 29–34. c Pleiades Publishing, Ltd., 2012. Original Russian Text c I.F. Malov, 2012, published in Astronomicheskii Zhurnal, 2012, Vol. 89, No. 1, pp. 32–37. Do Magnetars Really Exist? I. F. Malov * Puschino Radio Astronomy Observatory, Astro Space Center, Lebedev Physical Institute, Russian Academy of Sciences, Puschino, Moscow region, Russia Received July 28, 2011; in nal form, August 17, 2011 AbstractWe perform a comparative analysis of the properties of isolated single neutron stars and show the absence of any single typical feature providing unambiguous evidence that they belong to the classes of AXPs or SGRs. Several objects with features intermediate between AXPs and radio transients (RRATs) have been discovered recently: radio pulsars with high magnetic elds, radio-emitting AXPs, etc. Assuming the existence of elds of 10 16 G in the stellar interiors cannot explain the giant gamma-ray outbursts of SGRs. It appears necessary to invoke other energy sources, such as nuclear reactions in the matter that breaks through the crust of the neutron star. For the recently discovered AXP PSR J16424950, we nd that the angle β between its spin axis and magnetic moment is 15.6 . This agrees with earlier estimates for the AXPs J1810197 and 1E 1547.05408, which have β< 10 . The similarity of these objects to aligned rotators enables a description using the drift model. This model yields a rotational period for PSR J16424950 of P =0.32 s, a magnetic eld in the radiation generation region of B = 950 G, and a surface magnetic eld of B s =3.39 × 10 12 G. It is shown that the cyclotron instability in the neighbourhood proximity of the light cylinder, associated with particles in the tail of the secondary-plasma distribution, can explain the generation of the radio emission of PSR J16424950, which should be observed predominantly at low frequencies (100 MHz). DOI: 10.1134/S1063772912010064 1. INTRODUCTION In recent years, active surveys and observations of anomalous X-ray pulsars (AXPs) and recurrent sources of soft gamma-ray radiation (soft gamma-ray repeaters, SGRs) have been carried out. Simulta- neously, many theoretical eorts have been invested in models aiming to explain the observed features of these objects. This activity is motivated by the need to understand the evolution of isolated neutron stars, to which AXPs and SGRs belong. Among currently developed models for these sources, the most popular is the magnetar modela neutron star with a surface magnetic eld of the order of 10 14 10 15 G and an even stronger eld in the interior (10 16 G) [1]. It is supposed that the magnetic-eld energy stored in the interior of the neutron star is high enough to explain all the observed features of the emission in various wavebands of the electromagnetic spectrum, and all the proposed assumptions of the model are sucient to explain all the peculiarities of AXPs and SGRs. In this paper, we compare the properties attributed to these objects with the characteristics of other classes of neutron stars, and discuss the possibility of describing the collected observational data using a magnetar model and a drift model [2]. We * E-mail: [email protected] emphasize that we restrict our consideration to iso- lated neutron stars and leave completely untouched the processes describing the behavior of usual X- ray pulsars associated with binaries, where the main factor is accretion of matter from a companion onto the neutron star. 2. WHAT ARE AXPs AND SGRs? To respond to the question raised in the title of this paper, we muat rst dene the term magnetar.Some features of such sources are considered in [3]. Let us discuss the most frequently mentioned pecu- liarities of AXPs and SGRs. 1. As we noted already, the term magnetaritself was introduced after a dipolar surface magnetic eld of B s 10 14 10 15 G was inferred for the neutron star, using a model with magnetic-dipole braking. However, there is a number of arguments providing evidence of the incorrectness of applying this formula to both normalpulsars [4] and to AXPs and SGRs [5]. The discovery of SGR 0418+5729, whose mag- netic eld does not exceed 7.5 × 10 12 G [6], shows that the main attribute of a magnetar (a magnetic eld exceeding the Schwinger critical value B cr =4.4 × 10 13 G) is not necessary for all AXPs/SGRs. More- over, the question arises of whether the magnetic-eld 29

Do magnetars really exist?

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Page 1: Do magnetars really exist?

ISSN 1063-7729, Astronomy Reports, 2012, Vol. 56, No. 1, pp. 29–34. c© Pleiades Publishing, Ltd., 2012.Original Russian Text c© I.F. Malov, 2012, published in Astronomicheskii Zhurnal, 2012, Vol. 89, No. 1, pp. 32–37.

Do Magnetars Really Exist?

I. F. Malov*

Puschino Radio Astronomy Observatory, Astro Space Center, Lebedev Physical Institute,Russian Academy of Sciences, Puschino, Moscow region, Russia

Received July 28, 2011; in final form, August 17, 2011

Abstract—We perform a comparative analysis of the properties of isolated single neutron stars andshow the absence of any single typical feature providing unambiguous evidence that they belong to theclasses of AXPs or SGRs. Several objects with features intermediate between AXPs and radio transients(RRATs) have been discovered recently: radio pulsars with high magnetic fields, radio-emitting AXPs,etc. Assuming the existence of fields of 1016 G in the stellar interiors cannot explain the giant gamma-rayoutbursts of SGRs. It appears necessary to invoke other energy sources, such as nuclear reactions in thematter that breaks through the crust of the neutron star. For the recently discovered AXP PSR J1642–4950, we find that the angle β between its spin axis and magnetic moment is 15.6◦. This agrees with earlierestimates for the AXPs J1810–197 and 1E 1547.0–5408, which have β < 10◦. The similarity of theseobjects to aligned rotators enables a description using the drift model. This model yields a rotational periodfor PSR J1642–4950 of P = 0.32 s, a magnetic field in the radiation generation region of B = 950 G, and asurface magnetic field of Bs = 3.39× 1012 G. It is shown that the cyclotron instability in the neighbourhoodproximity of the light cylinder, associated with particles in the tail of the secondary-plasma distribution, canexplain the generation of the radio emission of PSR J1642–4950, which should be observed predominantlyat low frequencies (∼100 MHz).

DOI: 10.1134/S1063772912010064

1. INTRODUCTION

In recent years, active surveys and observationsof anomalous X-ray pulsars (AXPs) and recurrentsources of soft gamma-ray radiation (soft gamma-rayrepeaters, SGRs) have been carried out. Simulta-neously, many theoretical efforts have been investedin models aiming to explain the observed features ofthese objects. This activity is motivated by the needto understand the evolution of isolated neutron stars,to which AXPs and SGRs belong. Among currentlydeveloped models for these sources, the most popularis the magnetar model—a neutron star with a surfacemagnetic field of the order of 1014−1015 G and aneven stronger field in the interior (∼1016 G) [1]. Itis supposed that the magnetic-field energy stored inthe interior of the neutron star is high enough toexplain all the observed features of the emission invarious wavebands of the electromagnetic spectrum,and all the proposed assumptions of the model aresufficient to explain all the peculiarities of AXPs andSGRs. In this paper, we compare the propertiesattributed to these objects with the characteristicsof other classes of neutron stars, and discuss thepossibility of describing the collected observationaldata using a magnetar model and a drift model [2]. We

*E-mail: [email protected]

emphasize that we restrict our consideration to iso-lated neutron stars and leave completely untouchedthe processes describing the behavior of usual X-ray pulsars associated with binaries, where the mainfactor is accretion of matter from a companion ontothe neutron star.

2. WHAT ARE AXPs AND SGRs?

To respond to the question raised in the title ofthis paper, we muat first define the term “magnetar.”Some features of such sources are considered in [3].Let us discuss the most frequently mentioned pecu-liarities of AXPs and SGRs.

1. As we noted already, the term “magnetar” itselfwas introduced after a dipolar surface magnetic fieldof Bs ∼ 1014−1015 G was inferred for the neutronstar, using a model with magnetic-dipole braking.However, there is a number of arguments providingevidence of the incorrectness of applying this formulato both “normal” pulsars [4] and to AXPs and SGRs[5]. The discovery of SGR 0418+5729, whose mag-netic field does not exceed 7.5 × 1012 G [6], showsthat the main attribute of a magnetar (a magnetic fieldexceeding the Schwinger critical value Bcr = 4.4 ×1013 G) is not necessary for all AXPs/SGRs. More-over, the question arises of whether the magnetic-field

29

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30 MALOV

energy is sufficient to feed these objects. It becomesnecessary to suppose that, for a usual pulsar magneticfield in the magnetosphere, the field in the interiorof the neutron star must be maintained at a level of1016 G during the entire lifetime of the star.

2. The second main reason for devising the mag-netar model was substantial excess of the X-ray lumi-nosities of AXPs/SGRs over their rotational-energyloss rates, which were considered to be the mainsource of the pulsar’s energy. However, at the sametime, the energy of the pulsars was estimated assum-ing that the period of the pulsar is equal to the ob-served time interval between pulses. The young radiopulsar PSR J1846–0258 in the supernova remnantKes 75, with a characteristic age τ = P/(2dP/dt) =884 yr and a period 326 ms [7], displays X-ray out-bursts accompanied by large deviations in the pulse-arrival times; i.e., it behaves like an AXP or SGR.At the same time, its X-ray luminosity, which variesbetween Lx = 1.85× 1034 and 1.16× 1035 erg/s, canbe entirely supported by the loss of the rotationalenergy of the star, dE/dt = 8.3 × 1036 erg/s.

3. Outbursts of radiation are considered to becharacteristic of magnetars. We should stress thatnormal radio pulsars also display nonstationary emis-sion on all studied time scales (from fractions of amicrosecond to tens of years), with the intensity ofindividual outbursts varying over a wide range. For“normal” pulsars, outbursting components of pulses[8, 9] and giant pulses (see, e.g., [10, 11]) are ob-served. The intensities of the latter are hundreds oreven thousands of times higher than the average valuein quiescence. AXPs and SGRs are also variable overlong time scales (up to several years). In principle,strong intensity variations and time variations of thespectra of individual pulses of AXP XTE J1810–197[12] do not differ from the behavior of normal pul-sars, whose individual pulses not only strongly differin power, but even change the sign of the spectralindex [13]. On this basis, anomalous pulsars differfrom radio pulsars in the scale of the energy param-eters and the characteristics of the variability. Hence,this feature is likewise not an exclusive peculiarity ofAXPs and SGRs.

4. It is usual to represent the X-ray spectra ofAXPs/SGRs as the sum of a blackbody and power-law radiation. For several radio pulsars, both ther-mal and non-thermal components are observed out-side the radio, and these objects (for instance, PSRB0531+21 in the Crab) have rather complex spectra.

In essence, this comparison of AXPs/SGRs withnormal pulsars shows the absence of any single ex-plicit attribute or several attributes that enable unam-biguous classification of a certain object as a “mag-netar.” In practice, it is sometimes difficult to clas-sify newly discovered objects related to neutron stars.

One example is SWIFT J195509+261406, which ex-perienced 40 outbursts over three days in optical, withinfrared outbursts also observed [14, 15]. The opticallight curves appeared to be similar to the high-energylight curves of AXPs and SGRs. A feature at 0.12–0.16 Hz corresponding to a period of 6–8 s is presentin the power spectrum of the source. It was proposedto classify this source as a transient magnetar, whileits X-ray luminosity is intermediate between those ofSGRs, with Lx ∼ (2−4) × 1035 erg/s, and XDINSs,with Lx ∼ (2−20) × 1030 erg/s. Another example isthe transient AXP XTE J1810–197, which not onlyemits in the radio, but is the radio-brightest neutronstar at frequencies above 20 GHz [16]. Observationsof AXP 1E 1547.0–5408 (PSR J1550–5418), whichhas features similar to those of XTE J1810–197, atfrequencies from 1.4 to 45 GHz displayed flux vari-ations and a high degree of polarization [17]. TheINTEGRAL space mission discovered the transientsource J11321–5211, which can be classified an AXPbecause it has outbursts at frequencies from 20 to300 keV with a peak luminosity of ∼1037 erg/s [18].Apart from the radio, the RRAT J1819–1458 wasdetected in the X-ray, where its pulsing componentat 0.3–5 keV reaches 34% [19]. These data provideevidence for the existence of intermediate types ofanomalous objects, while also suggesting that theseobjects are related to each other and to normal pul-sars, and that all isolated neutron stars can be de-scribed by a single model. We have attempted tosuggest such a description based on a drift model inseveral papers and the monograph [20]. Here, we willconsider several questions related to the possibility ofdescribing the observed peculiarities of AXPs/SGRsusing the magnetar model and the drift model.

3. MAGNETAR MODEL

Even if magnetic fields of the order of 1014 to1015 G exist, their energy is not sufficient to providethe energies of AXPs and SGRs [20]. The existenceof 1016 G fields in the interiors of these stars is itselfproblematic, and does note resolve the situation. Therelease of up to 1046 erg of magnetic energy in a giantburst (as in SGR 1806-20) requires

B2R03/6 ∼ 1046 erg. (1)

If B = 1016 G, a sphere with a radius R0 ∼ 1 km (i.e.,10% of the stellar radius) must be ejected from thestar, if the conversion of the magnetic energy intoradiation is 100% efficient (this radius would be largerfor lower efficiencies). This would lead to a substantialchange in the structure of the neutron star, for whichthere is no evidence from observations. Explainingthe giant gamma-ray bursts of SGRs is the main

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DO MAGNETARS REALLY EXIST? 31

difficulty of all models, without exception. Invokingnuclear reactions in the matter ejected from beneaththe crust is probably unavoidable. Let us assume that

σMc2 = ηE, (2)

where M is the mass of matter involved in the nuclearreactions, σ is the efficiency of the conversion of en-ergy into radiation, and η is a coefficient associatedwith beaming. If σ ∼ η ∼ 0.01, then

E ∼ Mc2 ∼ 1046 erg

and

M ∼ 1025 g < 10−8M�.

This requirement is much less demanding than inthe case of the ejection of matter and reprocessing ofmagnetic energy.

4. THE DRIFT MODEL

The anomalous X-ray pulsar PSR J1642–4950,with an observed interval between pulses Pobs = 4.3s and magnetic field Bs ∼ 4 × 1014 G (calculated us-ing the magnetic-dipole formula), was recently dis-covered [21]. This pulsar has a very long switch-off time, extreme flux variability, and variations ofthe shapes of the integrated pulse profiles in the onstate. Moreover, it displays a high noise level in thepulse-arrival times. These peculiarities are typicalfor most observed AXPs, and the observed proper-ties of PSR J1642–4950 are very similar to those of1E 1547–5408 and XTE J1810–197.

To verify applicability of the drift model for PSRJ1642–4950 and the calculation of its parametersusing the method described in [22, p. 120], we esti-mated the angle β between its spin axis and magneticmoment. We first calculated the angle ζ betweenthe spin axis and the viewing angle. We use a cubicequation for y = cos ζ :

b3y3 + b2y

2 + b1y + b0 = 0, (3)

where the coefficients bi are functions of the parame-ters C and D, with C being the maximum derivativeof the linear-polarization position angle in the averageprofile and D = cos(W10/2), where W10 is the widthof the profile at the 10% level. For PSR J1642–4950,the observed change of the position angle correspondsto C = 1, while the width of the pulse implies D =cos 76.9◦ [21]. These parameters give y = 0.8554,ζ = 31.2◦, and β = 15.6◦. Hence, PSR J1642–4950is a nearly aligned rotator, and it is justified to applyour drift model to this object.

In this model, assuming a synchrotron nature forthe pulsed X-ray emission, we can calculate the rota-tion period of the neutron star P , its time derivative,

Ωμ

β

r

rLC

Schematic of the magnetosphere of a pulsar with a smallangle β.

and the magnetic field in the region of formation of theobserved pulses [20, pp. 65–66]:

P [s] = 8.32 × 10−2

[(dPdr/dt)−11

(Lx)34(W/Pdr)2Pdrfpl

]2/5

,

(4)

dP

dt=

P (dPdr/dt)2Pdr

, (5)

B[G] = 22.45Pdr

P 2. (6)

Here, (dPdr/dt)−11 = (dPdr/dt)/10−11.The data given in [21] suggest that the fraction

of pulsed radiation of PSR J1642–4950 is fpl =0.3. Then, P = 0.32 s, dP/dt = 6.29 × 10−13, B =950 G, and, if the magnetic field is dipolar from thesurface to the light cylinder, log Bs = 12.53.

If β = 15.6◦, the boundary of the magnetosphereis at a distance of the order of 4 · rLC , where rLC isthe radius of the light cylinder (see the figure). Thismakes possible the formation of appreciable pitchangles and the generation of synchrotron emission,

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32 MALOV

since the ratio of the magnetic-energy and plasma-energy densities becomes less than unity. Theseconsiderations enable us to apply relation (4). Letus analyze the possibility of generating radio emissionat a distance of the order of the light cylinder radius,where the cyclotron instability begins to operate (see,for example, [23]). Two conditions for the develop-ment of this instability are presented in [23]: (i) thedistance rc from the center of the neutron star to theinstability region must be less than the radius of thelight cylinder, and (ii) the time scale for the instabilityto develop tc = 1/Γc, where Γc is the increment of thecyclotron instability, must be shorter than the timefor the escape of relativistic plasma from the pulsarlight cylinder, t0 = rLC/c = P/2π. These conditionsare justified for pulsars with large angles β; for nearlyaligned rotators, the magnetosphere may extend toseveral light cylinder radii, and these conditions areno longer required.

It was shown in [24] that transverse waves ariseas a result of the development of cyclotron instability,whose frequency is

ω =4ω3

Bγ3p

ω2pγb

, (7)

where ωB = eB/mc is the cyclotron frequency, ωp2 =

8πnpe2/m is the square of the plasma frequency, γp is

the Lorentz factor of the secondary electron–positronplasma, and γb is the Lorentz-factor of the primarybeam.

Let us estimate the distance at which emission atthe frequency ν = ω/2π is generated, assuming thatthe magnetic field is dipolar out to the boundary of themagnetosphere:

r

R∗=

(e2B2

sPγ4p

2π2m2c2γ2b ν

)1/6

. (8)

Here, Bs is the magnetic field at the surface of theneutron star and R∗ is the stellar radius. It is assumedin (8) that the energy of the primary beam is almostentirely transferred to the secondary plasma,

nbγb ∼ 2npγp, (9)

and the density of the primary beam is equal to theGoldreich–Julian density [25]

nb =B

ceP. (10)

If γ3/2b /γ2

p = 4.37 × 108, as is typical for radio pul-sars with X-ray emission [26], and γb = 107, whichcorresponds to γp = 8.5, then

r/R∗ = 1.42 × 103(PB212/ν8)1/6. (11)

Here, B12 = B/1012 and ν8 = ν/108.

For the values of P and Bs calculated above, weobtain

r/R∗ = 1.76 × 103ν−1/68 . (12)

The light cylinder radius corresponding to the pe-riod P = 0.32 is rLC = 1.53 × 103R∗; i.e., emissionat 100 MHz will be generated just beyond the lightcylinder, at a distance that is slightly larger thanrLC (r = 1.15rLC ). This is quite possible for smallangles β. We stress that the dependence r(ν) isvery weak. For example, emission at 1 GHz will begenerated at r/R∗ = 1.20× 103, also in the vicinity ofthe light cylinder. However, the proximity of the levelsof generation of the emission at different frequenciesdoes not mean that the intensities at these frequencieswill also be similar. The increment of the cyclotroninstability [24],

Γc = πω2pres/ωγt, (13)

decreases with increasing frequency. Here, ωpres isthe plasma frequency of the resonant particles andγT the thermal range of their Lorentz factors. As isshown in [24], a cyclotron resonance is possible onlyif

δ =ω2

p

4ω2Bγ3

p

� 12γ2

res

. (14)

This condition is justified for the particles of theprimary beam and the tail of the secondary-plasmadistribution only. For the parameter values appliedabove and γT = 100, the increment (13) for the beam,

Γcb =2πeBs(R∗/r)3

mcPνγT= A1(R∗/r)3ν−1, (15)

is equal to Γcb = 21.5 × ν−18 . For the particles of the

tail,

Γct =2πeBsγb(R∗/r)3

mcPνγT γt= A2(R∗/r)3ν−1. (16)

For γt = 105, we obtain Γct = 2.15 × 103ν−18 .

To estimate the efficiency of the cyclotron instabil-ity during the generation of coherent radio emission,we must calculate

τ =∫

Γdr

c, (17)

which characterizes the rate of increase of the ampli-tude of the generated waves. Let us assume that thelayer where emission is formed efficiently is confinedbetween rLC and 2rLC , and let us use the expressionsobtained above for Γc. This yields for the particles inthe beam

τb = 3A1R3∗/8cr

2LCν = 0.63ν−1

8 , (18)

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DO MAGNETARS REALLY EXIST? 33

and for the tail

τt = 3A2R3∗/8cr

2LCν = 62.6ν−1

8 . (19)

Expressions (18) and (19) show that the gener-ation of fairly intense waves by the particles of theprimary beam is not efficient, while the particles of thetail are able to provide the observed emission at longwavelengths (ν ∼ 100 MHz). The amplification ofthe waves at higher frequencies is substantially lower.For example, the amplification at 1 GHz will be bymore than 20 orders of magnitude weaker. Hence, weexpect a currently measurable low-frequncy flux andan absence of measurable emission at substantiallyhigher frequencies. We emphasize that the expectedflux is also low at low frequencies, since the density ofthe particles in the tail,

nt = nbγb

γt=

Bs(R∗/r)3γb

cePγt(20)

is very small for the parameters used above(∼104 cm−3).

5. CONCLUSION AND DISCUSSION

1. We have shown that there is no single propertythat provides unambiguous evidence that an object isan AXP or SGR.

2. The discovery of SGR 0418+5729, whosemagnetic field does not exceed 7.5 × 1012 G, castsdoubt on the idea that supercritical magnetic fieldsplay a decisive role in the activity of AXPs and SGRs.

3. It is proposed that gamma-ray bursts, and pos-sibly other dramatic variability of AXPs and SGRs,could be associated with the ejection of plasma frominner layers of the neutron star into the magneto-sphere, with the subsequent release of nuclear energy.

4. Using data on the polarization of the recentlydiscovered AXP PSR J1642–4950, we have esti-mated the angle between its spin axis and magneticmoment to be 15.6◦. The fact that this object is anearly aligned rotator enables us to apply the driftmodel in this case.

5. We have estimated the parameters ofPSR J1642–4950 in this model: the spin period P =0.32 s, magnetic field in the region of generation ofthe observed emission B = 950 G, and the magneticfield at the neutron-star surface Bs = 3.39 × 1012 G.

6. The cyclotron instability can develop close tothe light cylinder of PSR J1642–4950, resulting inthe generation of radio emission.

7. It is expected that all the radio emission willbe generated in a very narrow layer, and that the fluxat low frequencies (of the order of 100 MHz) will bemuch higher than at higher frequencies.

More rigorous numerical estimates require data onthe structure of the magnetosphere at distances of theorder of the light cylinder radius; all our estimates herehave assumed that the field is dipolar at all distancesfrom the neutron star. It is also necessary to studyrigorously the processes of wave generation and am-plification; in the present paper, we have used onlyestimates of the increments, i.e., we have assumedamplification in the linear regime. However, it is clearthat, at some stage, nonlinear processes will switchon, possibly substantially changing the conditions foremission generation (in particular, the efficiency ofthe transformation of plasma-wave energy into radia-tion). These problems are the topics of separate stud-ies. Here, we wished only to show, using the recentlydiscovered anomalous pulsar PSR J1642–4950 asan example, that the generation of radio emissionin AXPs/SGRs is possible in the drift model. Asconcerns the question raised in the title of this paper,based on the evidence of modern observational dataand theoretical considerations, we suggest that theanswer is negative.

ACKNOWLEDGMENTS

This study was supported by the Russian Founda-tion for Basic Research (project code 09-02-00584)and the Basic Research Program of the Presidiumof the Russian Academy of Sciences “The Origin,Structure, and Evolution of the Universe.” The au-thor thanks R.D. Dagkesamanskii for several usefulremarks.

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Translated by L. Yungel’son

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