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Astronomy Reports, Vol. 47, No. 8, 2003, pp. 681­686. Translated from Astronomicheski Zhurnal, Vol. 80, No. 8, 2003, pp. 738­743. i Original Russian Text Copyright c 2003 by Abubekerov, Lipunov.

The Lower Temperature Limit of Accretors
M.K. Abubekerov1 and V.M. Lipunov
1 2

1, 2

Physics Department, Moscow State University, 119992 Moscow, Russia Sternberg Astronomical Institute, 13Universitetski i pr., 119992 Moscow, Russia
Received June 20, 2002; in final form, January 10, 2003

Abstract--There should be a universal correlation between the main observational parameters of magnetized accreting stars (neutron stars, white dwarfs, and possibly T Tauri stars): their luminosities, periods, and temperatures. To first approximation, such a dependence is obeyed reasonably well for Xray pulsars, intermediate polars, and T Tauri stars. In contrast, the parameters of anomalous pulsars (socalled "magnetars") and soft gamma-ray repeaters differ sharply from this dependence, and even occupy a "forbidden" region in the parameter space. This presents a serious argument against the idea that these are accreting neutron stars. c 2003MAIK "Nauka/Interperiodica".

1. INTRODUCTION The theory of accretion onto magnetized stars was developed in connection with the discovery and subsequent study of X-ray pulsars in binary systems [1]. Although we are still far from being able to construct a complete theory, to first approximation, the main elements of the theory discussed as early as the 1970s can still be considered to be on firm ground. The most important of these include the following. (1) The size of the magnetosphere of the accreting star is close to the so-called Alfven radius: RA = µ2 2M 2GMx
2/7

the main observational quantities associated with Xray pulsars are their luminosity L, period P , period derivative (P ), and characteristic spectral temperature (kTspec ). The first three quantities are obviously interconnected, since the luminosity is determined by the accretion rate, which also determines the rate of change of the period. Here, we concentrate on the fact that the three points listed above imply that the luminosity and period of any accreting star (accretor) should be correlated with the characteristic temperature of its radiation. 2. A NEW PICTURE FOR X-RAY PULSARS Let us consider a lower limit for the characteristic temperature of the radiating region of an accretor. As a first approximation, we can use the Stefan­ Boltzmann formula L = S T 4 . (1)

,

(2) During its evolution under the action of the accelerating and decelerating torques in the system, the accreting star tends to approach an equilibrium state in which the size of the magnetosphere is close to the corotation radius ( 1) [2]: RA = Rc = (GMx / )
2 1/3

, We can estimate the size of the region onto which the accreting material falls based on the dipole structure of the magnetic field of the accretor [3]: S = 2R
22 x

(3) The time over which this equilibrium is attained is always less than the characteristic lifetime of the star in the accretion stage: t
eq

I Mx = = GM Rc M M

Rx Rc

3

Mx . M

,

(2)

Generally, speaking, these last two points suppose that a disk-accretion regime is realized; this is obviously applicable for systems in which there is a flow of material through the inner Lagrange point, but is also a quite likely scenario for accretion of material from a stellar wind. Here, we are not considering only systems in which there is disk accretion. Recall that

where is the opening angle of the polar column, which is determined by the accretor's radius Rx and the size of the Alfven zone RA via the expression = Rx RA
1/2

.

(3)

Let us now also take into consider the fact that, during its evolution, the accretor tends toward a state

1063-7729/03/4708-0681$24.00 c 2003 MAIK "Nauka/Interperiodica"


682 Table 1. Temperatures of accretors Type Neutron stars

ABUBEKEROV, LIPUNOV

Name Her X-1 4U 0115+63 X0331+53 Cen X-3 Vela X-1 AXJ 1845­0258 1E 2259+586 1E 1841­045 4U 0142+615 1E 1048­5937 1RXS J17084.9 SGR 1900+14 SGR 1806­20 SGR 1627­41 SAXJ 1808.4­36 AM Her DQ Her SW UMa TTau

kT

min

,eV

kT

spec

,eV

kT

ef f

,eV

f (L) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 .398 .421 .398 .680 .335 .182 .121 .182 .240 .206 .190 .027 .680 .10 .896 .68 .68 .68 .68

Magnetars

Soft gamma-ray repeaters

Burster Polar Intermediate polars T Tauri star


3754 4965 4633 7045 6954 1752 1259 1911 2456 1964 1986 696 76000 1107 81 3.868 0.937 3.307 0.290

19000 8000 15500 14300 17500 640 410 550 390 640 460 500 9000 1300 200 28 20 70 0.43

13593 5631 11089 8511 13112 541 365 465 314 530 386 486 5357 1181 223 16 11.9 41.6 0.25

The temperature of the X-ray flare of the source is indicated.

in which the Alfven radius approaches the corotation radius Rc , i.e., RA = Rc , (4) where is a dimensionless coefficient that is close to unity. Further, using the definition of the corokT 105 104 103 102 101 100
SW UMa AM Her DQ Her

tation radius and (1)­(4), we obtain the minimum temperature of the accretion zone in the blackbody approximation kTmin = 0.94 M1
1/12

L

R

1/4 35 3/4 6

P

1/6

kev.

(5)

kTmin kTspec

Her X ­ 1 Vela X ­ 1 X0331 + 53 4U0115 + 63 SGR 1627 ­ 41 SGR 1900 + 14 SAX J1808.4 Cen X ­ 3 SGR 1806 ­ 20

1 E 1841 ­ 045 1 E 1048 ­ 5937 AXJ 1845 ­ 025 1 E 2259 + 586 1 RXS J1708.4 4U 0142 + 615

T Tau

0.0001

0.001

0.1 0.01 1 M1/12 L1/4 P1/6 R3/4

10

100

Dependence of the spectral temperature on the parameters of the accretor. kT is measured in eV, M in , L in 1035 erg/s, in s, and R in 106 cm.

In (5), the mass is normalized to one solar mass, the luminosity to 1035 erg/s, the period to one second, and the radius to 106 cm. The corresponding relation is shown by the line in Fig. 1. We emphasize again that (5) gives a lower limit for the temperature of the accretor's radiation zone. As a consequence of Rayleigh­Taylor instability, the accreting material channeled in the near-polar zones by the magnetic force lines falls not onto the polar cap of the accretor, but instead into a narrow ring of much smaller area [1]. It is obvious that the resulting lower limit for the temperature can be applied to any magnetized accretor independent of its nature--aneutron star, white dwarf, or ordinary star. The main thing is that we are dealing with magnetized objects accreting from a disk. There is no doubt that such objects are found among X-ray pulsars, X-ray bursters, cataclysmic variables (polars and intermediate polars), and possibly T Tauri stars [4].
ASTRONOMY REPORTS Vol. 47 No. 8 2003


Lower Temperature Limit of Accretors Table 2. Used numerical values of main accretor characteristics Type Neutron stars Name Her X-1 4U 0115+63 X0331+53 Cen X-3 Vela X-1 Magnetars AXJ 1845­0258 1E 2259+586 1E 1841­045 4U 0142+615 1E 1048­5937 1RXS J17084.9 Soft gamma-ray repeaters SGR 1900+14 SGR 1806­20 SGR 1627­41 Burster Polar Intermediate polars SAXJ 1808.4­36 AM Her DQ Her SW UMa T Tauri star


683

P ,s 1.24 3.61 4.38 4.84 283 6.97 6.98 11.76 8.69 6.44 10.99 5.16 7.47 6.41 0.0025 11139.2 71.07 954 432000

L, 10

35

erg/s

R, 106 cm 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 700 700 700 140000

M/M 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.0 1.0 1.0 1.0

200 300 200 1000 63 3 0.8 3 10 5 3.6 0.09 107 0.5 0.003 0.0002 0.00002 0.0005 0.0044

TTau

The luminosity of the X-ray flare is indicated. The masses and radii of neutron stars are not intended to be extremely accurate, but to represent their most likely values.

3. THE ROLE OF COMPTONIZATION In the case of accreting neutron stars, we will use the model atmosphere of [5] to specify the relationship between the spectral X-ray temperature of the accretor kTspec (which we will take to be the temperature in the best-fit approximation to the observed spectrum of the form I exp-h /kTspec ) and the effective temperature of the radiating region. We wish to elucidate the effect of comptonization on the spectrum. We write for the relationship beASTRONOMY REPORTS Vol. 47 No. 8 2003

tween kTspec and kTeff Tspec = f (L)Teff , where the function f (L) has the form f (L) = 1.51(L/L 1.68
edd

(6)

)0.

04

L L

Ledd Ledd

The results of correcting for the effect of comptonization are presented in Table 1. We can see that, as before, the temperatures of observed accretors


684

ABUBEKEROV, LIPUNOV

Table 3. References to observational data for the accretors Type Neutron stars Name Her X-1 4U 0115+63 X0331+53 Cen X-3 Vela X-1 Magnetars AXJ 1845­0258 1E 2259+586 1E 1841­045 4U 0142+615 1E 1048­5937 1RXS J17084.9 Soft gamma-ray repeaters SGR 1900+14 SGR 1806­20 SGR 1627­41 Burster Polar Intermediate polars SAXJ 1808.4­36 AM Her DQ Her SW UMa T Tauri star TTau Reference [6, 7] [6, 7] [6, 7] [6, 7] [6, 7] [8, 9, 10] [8, 9, 10] [8, 9, 10] [8, 9, 10] [8, 9, 10] [8, 10, 11, 12] [13, 14, 15, 16] [17, 18, 19, 20] [21, 22, 23] [24, 25] [6, 26, 27] [6, 28] [6, 29] [4, 6]

are higher than their minimum values. The effect of comptonization is somewhat smaller in the case of other types of accretors--polars and T Tauri stars-- but the discrepancy between the effective temperature and the minimum temperature remains large, even when the largest value of f (L) is used for the correction (Table 1). 4. POLAR AND T TAURI SYSTEMS The cataclysmic variable AM Her is a member of the subclass of polars. It is a binary system containing a magnetized white dwarf and a red dwarf. The red dwarf fills its Roche lobe. The orbital period and rotational period of the white dwarf are nearly coincident,

Pspin = 0.77Porb . It is thought that the magnetic field at the white-dwarf surface is 109 G[6]. DQ Her is a cataclysmic variable classified as an intermediate polar. It is a binary system containing a white dwarf and a K­M star (the latter star's spectral type has not been established more precisely). The synchronization coefficient is Pspin = 0.004Porb . The magnetic field at the white-dwarf surface is believed to be 106 G[6]. SW UMa is another intermediate-polar cataclysmic variable, and periodically produces novalike flares. It is a binary system containing a white dwarf and an M2 or later-type companion. The relationship between the orbital period of the sysASTRONOMY REPORTS Vol. 47 No. 8 2003


Lower Temperature Limit of Accretors

685

tem and the rotational period of the white dwarf is Pspin = 0.195Porb [6]. T Tauri stars are young stars whose accretion luminosities lie in the range from 0.02L to 0.2L ; we have adopted the luminosity 0.1L ) for our calculations for T Tau. The period of T Tau varies from 3 to 10 days, being on average 5 days. The mass of the white dwarf is 1 - 1.5M , and the magnetic field at its surface reaches 104 G[4]. The numerical values for the characteristics of the accretors we have considered are listed in Table 2. References to this information are given in Table 3. 5. DISCUSSION Let us consider the dependence for the lower limit of the accretor temperature (5) shown in the Figure, which plots the X-ray spectral temperature as a function of the generalized coordinate M
1/12

For example, one possible mechanism is the dissipation of magnetic fields 1014 ­1015 G [30, 31]. Thus, our proposed universal dependence based on the relationships between the characteristic temperature of the radiation zone of an accretor and its main properties--luminosity, period, mass, and radius-- can add weighty arguments that the X-ray radiation of an individual object has an accretional (or nonaccretional) origin. 6. ACKNOWLEDGEMENTS The authors thank S.A. Lamzin, N.I. Shakura, and S.B. Popov for useful discussions. This work was supported by the Russian Foundation for Basic Research (project code 00-02-17164a), the State Science and Technology Program "Astronomy" (1.4.4.1), and the Science and Technology Program "Astronomy" (1.4.2.3). REFERENCES
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L1/4 P R3/4

1/6

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We chose the generalized coordinate so as to transform (5) into a linear relationship. Recall that 2. the collection of accretor parameters in (5) is the result of combining expressions (1)­(4), so that the 3. right-hand side of (5), and therefore the generalized coordinate plotted in the Figure, carries information 4. about the accretor's rotational period, its luminosity, and, indirectly, its moment of inertia. 5. This same plot shows the temperatures kTspec characterizing the observed spectra. Since the the6. oretical area of the accretion zone is clearly overestimated, and taking into account the effect of comptonization on the emerging radiation, we can be confident that points with kTspec should lie above their the7. oretical values, or at the very least not be below them. The region below the theoretical line (5) is therefore 8. a "forbidden zone" for sources whose luminosities are associated with accretion. 9. We can see from the Figure that the anomalous X-ray pulsars (magnetars) and soft gamma-ray re- 10. peaters lie in the "forbidden zone". Only SGR 1627­ 41 deviates slightly from this tendency. However, 11. in contrast to the undoubted accretors, for which 12. kTmin ,we have kTmin kTspec for SGR 1627­ kTspec 41. We also emphasize that the position of SGR 1627­ 13. 41 above the line corresponding to minimum accretor temperatures does not necessarily imply that the 14. luminosity of this source cannot have a non-accretion 15. nature. The above discussion brings into doubt the ac- 16. cretional nature of the radiation of magnetars and soft gamma-ray repeaters. It is possible that another 17. mechanism is responsible for their X-ray radiation.
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Translated by D. Gabuzda

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No. 8

2003