Multiple X-ray bursts and the model of a spreading layer of accreting matter over the neutron star surface
aa r X i v : . [ a s t r o - ph . H E ] A ug to be published in Astronomy Letters, 2017, v. 43, n. 9, pp. 583-594(in Russian: Pis’ma v Astronomicheskii Zhurnal, 2017, v. 43, No. 9, pp. 643-654) MULTIPLE X-RAY BURSTS AND THE MODEL OF ASPREADING LAYER OF ACCRETING MATTER OVER THENEUTRON STAR SURFACE
S. A. Grebenev ∗ , I. V. Chelovekov Space Research Institute, Russian Academy of Sciences,Profsoyuznaya ul. 84/32, Moscow, 117997 Russia
Submitted on September 26, 2016We report the detection during the JEM-X/INTEGRAL observations of several X-raybursters of series of close type I X-ray bursts consisting of two or three events with a recur-rence time much shorter than the characteristic (at the observed mean accretion rate) timeof matter accumulation needed for a thermonuclear explosion to be initiated on the neutronstar surface. We show that such series of bursts are naturally explained in the model ofa spreading layer of accreting matter over the neutron star surface in the case of a suffi-ciently high ( ˙ M ∼ > × − M ⊙ yr − ) accretion rate (corresponding to a mean luminosity L tot ∼ > × erg s − ). The existence of triple bursts requires some refinement of the model— the importance of a central ring zone is shown. In the standard model of a spreadinglayer no infall of matter in this zone is believed to occur. DOI:
Keywords:
X-ray bursters, neutron stars, X-ray bursts, thermonuclear explosion, accretion,boundary layer, spreading layer. ∗ e-mail < [email protected] > INTRODUCTION
In the period of the discovery of type I X-ray bursts (Belian et al. 1972, 1976; Babushkinaet al. 1975; Grindlay et al. 1976; Heise et al. 1976) and their theoretical explanation asthermonuclear explosions of a mixture of hydrogen and helium on the surface of a neutron starwith a weak magnetic field (Hansen and van Horn 1975; Woosley and Taam 1976; Maraschiand Cavaliere 1977), the question of precisely where the explosion occurred was not discussedspecially. It was believed that the accreting matter spreads rapidly over the entire neutronstar surface, and the explosion could begin in a more or less arbitrary place in which criticalconditions favorable for this were accidentally created at a given time. But, most importantly,it was believed that after the initiation of an explosion the thermonuclear burning propagatesover the entire stellar surface in fractions of a second with a supersonic (detonation wave)speed, v det ∼ km s − ≫ a s = (2 kT /m p ) / ≃ kT /
10 keV) / km s − ; therefore,the specific place of ignition is of no importance (Joss et al. 1978; Fryxell and Woosley1982a). Here, T is the temperature at the base of the neutron star atmosphere, a s is thecorresponding sound speed, and m p is the proton mass. Except for the short ( ≤ ≃ −
15 s)of X-ray photons undergoing multiple Compton scatterings in it and free-free production-absorption (Paczinski 1983a, 1983b; Ebisuzaki et al. 1984; Ebisuzaki 1987; Sunyaev andTitarchuk 1986; London et al. 1986).Subsequently, however, it became clear that the detonation wave in the neutron staratmosphere should rapidly decay and could not ignite an appreciable area of its surface(Timmes and Niemeyer 2000). The deflagration wave propagates too slowly (Fryxell andWoosley 1982b; Nozakura et al. 1984; Bildsten 1995), with a speed v def ∼ . − . − (for conductive energy transfer from the burning region to the surrounding matter) or ∼ . − − (for convective energy transfer). In this case, the flame propagation time ismuch longer than the observed burst duration. There were doubts that the explosion wascapable of affecting the entire surface of the star.The conclusion about fairly slow flame propagation was confirmed by the RXTE dis-covery of high-frequency (ms) coherent oscillations of the X-ray flux from bursters duringbursts, which were explained by the neutron star spin with a frequency Ω s ∼ −
600 Hz 3 –(Strohmayer et al. 1996, 1997; Smith et al. 1997; Galloway et al. 2008). The flame speed v must be less than πR ∗ Ω s /N ∼ s / (400 Hz) km s − ≪ a s , where R ∗ is the neutronstar radius, which is assumed here and below to be 12 km, and N ∼ >
100 is the number ofsuccessive pulsations needed for their reliable detection ( T = N/ Ω s ∼ > .
25 s is the detectionperiod). However, it is apparently still higher than the deflagration speed v def .Quite recently, three-dimensional theoretical computations of an explosion on the surfaceof a neutron star (Simonenko et al. 2012; see also Gryaznykh 2013a, 2013b) have shown thatthe flame can propagate in a qualitatively different, three-dimensional way. These authorspointed out that the heat flux from the explosion along the stellar surface should weakengreatly, because the bulk of the explosion energy (radiative and kinetic) is carried awayupward due to the atmosphere being exponential. The horizontal heat flux may turn out tobe insufficient for direct ignition of the surrounding matter. In these conditions the flamewill propagate through the inflow of matter expanding during the explosion onto the layerof the unperturbed atmosphere surrounding the place of explosion, its pressing and, thus,the creation of conditions for thermonuclear ignition at the base of the atmosphere. Thespeed of this process v can exceed appreciably the deflagration speed v def , while duringpowerful explosions it can reach and even exceed the sound speed a s . Such a process allowsthe observed duration of ordinary bursts to be explained.In this paper we discuss the detection of series of multiple (triple and double) type I X-ray bursts from a number of known bursters occurring with a recurrence time t r ∼ t a ∼ π Σ c R ∗ ˙ M − ≃ ˙ M − h needed for a thermonuclear explosionto be initiated on the neutron star surface. Here, Σ c = 10 Σ g cm − is the critical surfacedensity of the accumulated matter (for explosive helium ignition), ˙ M = 10 ˙ M g s − isthe accretion rate corresponding to the total luminosity of the neutron star in the periodbetween bursts L X = GM ∗ ˙ M /R ∗ ≃ . × ˙ M erg s − , G is the gravitational constant,and M ∗ is the neutron star mass, which is assumed to be 1 . M ⊙ . The time t a determines themean frequency of ordinary bursts < ν > = 1 /t a observed from each specific burster, and,of course, most of the bursts from the bursters being discussed were detected precisely withthis frequency. The detection of multiple bursts recurring on a time scale t r ∼
10 min ≪ t a from the same bursters seems surprising. 4 –Multiple bursts were also detected previously, in particular, double bursts were observedby Murakami et al. (1980) and Ohashi et al. (1982) from the sources 4U 1608-522 and4U 1636-536, more rare triple ones were observed by Boirin et al. (2007) from the transientburster EXO 0748-676 and by Keek et al. (2010) from several more sources. Sanchez-Fernandez et al. (2011) detected a triple burst from the burster 4U 1608-522 with the JEM-Xtelescope onboard the INTEGRAL observatory, the same one whose data are analyzed inthis paper. In addition to bursts with a recurrence time t r ∼
10 min, double bursts with t r ∼
10 s were detected. Bhattacharyya, Strohmayer (2006) observed such a burst fromthe source 4U 1636-536; they assure that the burst profile was formed without involving anyphotospheric expansion effects.The nature of multiple bursts is not yet clear. Having studied the properties of suchbursts detected during superlong (158 h) continuous observations of the burster EXO 0748-676 by the XMM-Newton satellite, Boirin et al. (2007) revealed: (1) a reduction in theexponential decay time of the profile for the recurrent events compared to the initial ones(which, in their opinion, is related to a decrease of the hydrogen abundance in the explodedmatter) and (2) a decrease in the intensity of events in the series compared to the separatebursts from this source. Based on these properties of multiple bursts, they assumed thatstepwise burning of the layers of stratified material with different chemical compositions(hydrogen, helium, and CNO abundances) is observed on the neutron star surface duringthem. Hydrogen burns out during the first flash, whereupon conditions for the ignition ofhelium are created etc. Indeed, the computations by Fujimoto et al. (1981) and Peng et al.(2007) show that at a sufficiently low accretion rate the hydrogen burning on the neutron starsurface can be explosive and, at the same time, may not accompanied by the simultaneousignition of helium. It is only unclear why the helium burning is resumed ∼
10 min after thefirst flare and why triple events are observed.In this paper, based on the JEM-X/INTEGRAL observations of multiple events, we offera different possible explanation of this phenomenon: the thermonuclear explosions producingsuccessive flashes occur in physically separated regions on the neutron star surface in whichthe matter efficiently accumulates during its nonuniform (in the meridional direction) infallas it is accreted. Such infall of matter should be expected at a sufficiently high, though muchlower than the Eddington level, accretion rate in the model of a spreading layer proposed byInogamov and Sunyaev (1999, 2010). According to this model, falling from the accretion disk 5 –into the boundary equatorial region of the star, the accreting matter has an excessively large(Keplerian) angular momentum, that completely compensates the gravitational attraction,which together with the radiation pressure does not allow it to immediately settle to thestellar surface. Continuing to rotate, the matter is displaced toward higher latitudes andonly there, often in the immediate vicinity of the neutron star poles, does it slow down andsettle to the stellar surface. Depending on the accretion rate, the ring regions where the infallof matter occurs can be at different distances from the equator and can have different widths.The bulk of the accretion energy of the infalling matter accounted for by the spreading layeris released and radiated in the zones of these regions more distant from the equator. Notethat in the Newtonian approximation the luminosity of the spreading layer is equal to theluminosity of the entire accretion disk L b ≃ . M R ∗ (Ω K − Ω s ) ≃ . GM ∗ ˙ M /R ∗ (Shakuraand Sunyaev 1988; Kluzhniak 1988). Here, Ω K = ( GM ∗ /R ∗ ) / is the Keplerian angularvelocity near the stellar surface.Suppose that the subsequent spreading of the fallen matter from these regions over thestellar surface is much slower than its accumulation, so that a critical surface density Σ c isreached at some time. The amount of matter fallen in the northern and southern regionsmust be approximately the same. However, it is obvious that the explosion initially beginsin one of them, let this be the northern region. After the explosive burnout of hydrogenand helium in it (for example, in the regime proposed by Simonenko et al. 2012), the flameslowly (as a deflagration wave) propagates over a less dense layer of matter with a speed v def ∼ .
01 km s − until it reaches the boundary of the southern region, where a new flashbegins. Let us examine how well this explanation agrees with the observed picture of theseries of multiple bursts. OBSERVATIONS
We revealed multiple events when working on the full catalog of X-ray bursts detected bythe JEM-X telescope onboard the INTEGRAL observatory in 2003-2014 (Chelovekov et al.2017). This is the final, third part of our investigation of thermonuclear X-ray bursts withthe INTEGRAL telescopes. The first two parts (Chelovekov at al. 2006; Chelovekov andGrebenev 2011) were the catalogs of bursts detected by the IBIS/ISGRI telescope sensitivein a harder X-ray band ( ∼ >
18 keV) than the JEM-X band (4–30 keV). Although it is clear 6 –
Fig. 1:
JEM-X/INTEGRAL photon count rates (the 3–20 keV energy band) in the observingsessions on March 24, 2004 (top), and March 28, 2009 (bottom), during which triple thermonuclearX-ray bursts were detected from the X-ray bursters Aql X-1 and 4U 1608-522. In the inserts theburst profiles are shown with a better time resolution.
Date,a Time,a δT, b C b ( C c ) , c F b , d F c , e ∆ T , f ∆ T , g Λh SourceUTC UTC s counts 10 − erg 10 − erg h h bursts − s − cm − s − cm − h m s
16 166 (8) 1 . ± . . ± . . . h m s
10 186 (9) 1 . ± . h m s
19 273 (7) 1 . ± . . ± . . h m s . ± . h m s
20 194 (7) 3 . ± . h m s
30 197 (7) 3 . ± . . ± . . . h m s
20 110 (7) 1 . ± . h m s . ± . . ± . . . h m s . ± . h m s . ± . . ± . . . h m s . ± . . ± . h m s
39 256 (11) 3 . ± . . ± . . . h m s
14 149 (11) 1 . ± . h m s
22 263 (7) 5 . ± . . ± . . . h m s
17 256 (7) 4 . ± . h m s
10 201 (8) 16 . ± . . ± . . . h m s . ± . h m s
13 144 (8) 1 . ± . . ± . . . h m s
15 160 (8) 1 . ± . h m s . ± . . ± . . h m s
10 100 (5) 1 . ± . h m s
14 196 (6) 1 . ± . . ± . . . h m s
14 145 (6) 2 . ± . h m s . ± . . ± . . h m s . ± . h m s
24 359 (13) 7 . ± . . ± . . h m s
12 101 (13) 1 . ± . h m s
12 289 (13) 2 . ± . h m s
21 135 (6) 1 . ± . . ± . . . h m s
13 116 (6) 1 . ± . . ± . h m s
11 305 (31) 6 . ± . . ± . . h m s . ± . . ± . h m s . ± . . ± . . h m s . ± . . ± . h m s . ± . . ± .
3a Date and time (UTC) of the peak count rate in the burst.b The burst duration.c The peak C b and mean C c count rate of photons from the source in the 3–20 keV band.d The peak flux in the 3–20 keV band.e The persistant flux from the burster during several previous exposures in the 3–100 keV bandf The time from the first burst in the series to the nearest burst not from the series ∆ T .g The minimum time between ordinary bursts from this burster for the entire sample ∆ T .h The interval between the bursts in the series excceeds 30 min. ∼
8) and better corresponded to the main goal ofour investigation, i.e., revealing hitherto unknown bursters. Two such bursters have indeedbeen discovered (see Chelovekov and Grebenev 2007, 2010).The full catalogue of bursts detected with JEM-X is accessible at < http: //dlc.rsdc.rssi.ru > . The main characteristics of the series of double and tripleevents selected from this catalog are given in the table. It provides the date of observation,the time of the peak count rate T and the duration δT of each burst in the series, thepeak and observation-averaged ( ∼ C b and C c , the recorded peak flux in the burst F b , and the mean flux F c from the source inseveral consecutive previous exposures (for more details, see Chelovekov et al. 2017).The fluxes in the bursts were measured in the 3–20 keV band; the persistent flux wasmeasured in the 3–100 keV band. Note that the characteristic persistent flux from thebursters being discussed F c ∼ × − erg s − cm − corresponds to an X-ray luminosity L X ∼ . × erg s − under the assumption that the source is near the Galactic center ata distance of 8 kpc, i.e. these are all sources with a fairly high accretion rate.The data from the table allow us to estimate the mean time interval between singlebursts (or a single burst and a series of bursts) t a ≃ . α Σ( δ T F b ) / F c using the so-calledparameter α ∼
40 (Lewin et al. 1993), which characterizes the efficiency of energy releaseduring accretion compared to explosive helium burning. Here, the factor 0.24 allows forthe deviation of the measured burst duration δT from the exponential time and Σ denotessummation over the bursts of the series. In particular, for the known bursters Aql X-1 and4U 1608-522 t a ≃ . − . T from the first burstin the series to the nearest burst from this burster not from this series and the minimuminterval ∆ T between ordinary bursts from this burster for the entire sample. These intervalsallow one to judge the mean frequency of bursts < ν > = t − a from a given burster at thecurrent and mean accretion rates, respectively. Since the INTEGRAL observations of eachspecific source were generally episodic, though they could last tens of hours, some burstsmust have undoubtedly been missed; therefore, these intervals should be considered only asupper limits on the time t a . For this reason, we, in particular, used a fairly stringent criterionfor the inclusion of bursts in the series: the interval between them should not exceed 30 min. 9 – Fig. 2:
JEM-X/INTEGRAL photon count rates (the 3–20 keV energy band) in the observingsessions on April 29, 2005 (top), and March 12, 2006 (bottom), during which double thermonuclearX-ray bursts were detected from the X-ray bursters Aql X-1 and SAX J17470-2853. In the insertsthe burst profiles are shown with a better time resolution.
10 –The asterisks in column 9 of the table mark several possible double bursts that did not passthis criterion. These were detected from the known bursters GX 3+1 and XTE J1739-285;the interval between them was 40–70 min, while the time ∆ T for these sources was 2.6 and16.5 h, respectively. It is unclear whether these bursts are events similar to the remainingmultiple events in the table and their long recurrence time t r reflects some of their uniquephysical properties or these are ordinary single bursts distinguished by an unusually shortaccumulation time t a of the critical matter density. Estimates based on the data from thetable similar to those given above for the bursters Aql X-1 and 4U 1608-522 show that thisis possible at least for the source GX 3+1. On the other hand, in this case, it is most likelyinsufficient for the source to have an enhanced accretion rate compared to other bursters; itis also necessary that at such an accretion rate the explosive development of a flash does notpass into continuous burning (see, e.g., Strohmayer and Bildsten 2006).As an example, Fig. 1 shows the light curves of the triple events observed from the knownbursters Aql X-1 and 4U 1608-522; Figs. 2–4 show those of the double events observed fromthe mentioned burster Aql X-1 and the equally known bursters SAX J17470-2853, 4U 1636-536, and XTE J1739-285. The insets present the profiles of individual bursts with a bettertime resolution demonstrating a fast rise to the maximum and a long exponential decay,which is characteristic for type I (thermonuclear) bursts. The burst duration varied between ∼ ∼
15 s, i.e., it was also typical for such bursts. In all the observed cases oftriple events, the second burst was noticeably fainter than the first and third bursts and waslocated almost halfway between them (closer to the third burst by ∼ −
70 s). The thirdburst was slightly fainter than the first one. The total duration of the shown series of tripleevents was ∼
800 s ( ∼
13 min). In the double events in Figs. 2–4 the second burst was, as arule, fainter than the first one; in some cases, the bursts had a comparable intensity. As arule, the duration of the second burst was shorter than that of the first one. For a number ofsources the time interval between the double bursts was comparable to the duration of thetriple events ( ∼ −
13 min, cf. Figs. 1 and 2); for others it was noticeably longer ( ∼ − Fig. 3:
JEM-X/INTEGRAL photon count rates (the 3–20 keV energy band) in the observingsessions on August 8, 2004 (top), and August 26, 2005 (bottom), during which double thermonuclearX-ray bursts were detected from the X-ray burster 4U 1636-536. In the inserts the burst profilesare shown with a better time resolution. . 12 –
Fig. 4:
JEM-X/INTEGRAL photon count rates (the 3–20 keV energy band) in the observingsessions on October 10–11, 2005 (top), and March 21, 2006 (bottom), during which double ther-monuclear X-ray bursts were detected from the X-ray burster XTE J1739-285. In the inserts theburst profiles are shown with a better time resolution. . 13 –
Fig. 5:
JEM-X/INTEGRAL photon count rates (the 3–20 keV energy band) from the sourceGX 3+1 in the observing sessions on April 2 (top) and 13 (bottom), 2010, during which double andtriple thermonuclear X-ray bursts were detected by this telescope. The time interval between thebursts is shorter than the sample-averaged interval between the bursts from this source only by afew times. In the inserts the burst profiles are shown with a better time resolution. . 14 –that the series duration reflects the neutron star properties, the accretion rate characteristicfor a given source, and/or the composition of the accreting matter. On the other hand, bothanomalously long ( ∼
42 min, Fig. 4a) and anomalously short ( ∼ ∼ >
40 min (Fig. 5). The recurrence time of ordinary bursts from this sourceaveraged over the entire sample of events recorded by the JEM-X telescope, t a , was longeronly by a factor of ∼ − × − erg s − cm − . It exceeds the fluxes fromother bursters by several times and clearly suggests a high accretion rate onto this source.On the other hand, it is interesting that apart from the double bursts, a triple burst wasalso detected from this source (Fig. 5, bottom panel), whose properties, except for the timescale on which it developed, are very close to those of the triple bursts from other bursters(Fig. 1). In particular, the middle event in this burst also occurred with a delay by ∼ DISCUSSION
Our analysis of a sample of multiple X-ray bursts detected by the JEM-X telescope onboardthe INTEGRAL observatory has revealed several trends that can give a key to understandingthis interesting phenomenon.1. The profiles of such bursts and especially triple bursts with powerful first and lastevents and a much fainter middle event are unique and uniform for different sources;these are very difficult to explain in the model of successively resuming thermonuclearburning of stratified (consisting of the layers of different elements) fuel.2. The double bursts can be failed triple bursts in which the middle burst was too faintto be detected.3. The duration of the series of bursts is, on average, unique for each specific source,probably reflecting the parameters of the neutron star in it, the characteristic accretionrate, and the composition of the accreting matter. 15 –4. The intermediate (second) burst of the triple events is delayed relative to the middleof the interval between the first and last events by 10–15%.5. In addition to the previously discussed series of bursts with a total duration ∼
10 min,there can exist series of bursts with a duration ∼ >
40 min from some sources.The unique profiles of multiple bursts are naturally explained in the model of a spreadinglayer of accreting matter over the neutron star surface (Inogamov and Sunyaev 1999, 2010).In this model, reaching the surface of the neutron star in the equatorial region, the accretiondisk matter is displaced in a spiral toward its poles and only there does it lose its angularmomentum in two ring zones, radiate the energy being released, and settle to the surface.The probability of reaching the critical conditions for thermonuclear ignition of the matteraccumulated during accretion is high precisely in these regions. Since it is obvious that theflash begins initially only in one of the ring zones, it will be responsible for the first mostpowerful burst in the series. Once the matter accumulated in this zone has burnt out, thethermonuclear flame propagates with a deflagration wave speed v def ≃ .
01 km s − over thestellar surface toward the equator and then toward the opposite stellar pole and the secondring zone. On reaching it, the last burst in the series begins. Note that although the bulkof the matter during accretion falls in these ring zones, some moderate amount of mattermust also settle from the spreading layer on its way to these zones; otherwise there would beno radiative energy for its maintenance (recall that the layer must be a radiation-dominatedand levitating one). It is through this settled matter that the deflagration wave propagatesafter the first explosion. The matter from the ring zones that slowly spreads over the neutronstar surface can also contribute to the layer of fuel accumulated here.There are several points that do not seem natural in the model of a spreading layer andrequire an explanation. The Origin of the Middle Burst in a Series
One would think that the intermediate (second) burst in a triple series of bursts cannotbe explained in any way in the model of a spreading layer. Proposing it, Inogamov andSunyaev (1999) assumed that all of the matter from the disk spread in meridional directions.Actually, this cannot be the case, because the matter in the disk has quite a distinct radialvelocity v r = ˙ M / (2 πR ∗ Σ d ) , that must not be ignored. This velocity can be slowed down 16 –only through viscosity in a narrow equatorial ring layer like the boundary layer describedby Shakura and Sunyaev (1988, 1999) and Kluzhniak (1988). In this case, at least for partof the accreting matter, not only the radial velocity but also the rotation velocity decreasesdown to the stellar rotation velocity. This matter settles to the stellar surface straight inthe equatorial zone. Although the amount of matter settling in this zone and the energybeing released in this case are small compared to the matter and the energy settling andbeing released, respectively, in the polar ring zones of the neutron star, it may turn out to besufficient to explain the intermediate burst in series of triple burst events. If, alternatively,little matter fell in this zone, then we will be able to see only a double burst. The infall ofmatter in this zone will be considered in more detail in Grebenev (2017). Explaining the Asymmetry of the Profile fot Triple Bursts
It has been noted above that the intermediate burst in the triple events observed from thebursters Aql X-1 and 4U 1608-622 is delayed by ∼ −
70 s relative to the middle of thetime interval between the first and third bursts. At first glance this delay contradicts thedescribed symmetric picture. Note, however, that the ring zones in which the matter settlesand accumulates can be quite extended, depending on the accretion rate (Inogamov andSunyaev 1999). The first burst begins in the region of maximum surface density that canbe near the high-latitude edge of the ring zone. Thereafter, all this zone (or is sufficientlydense part) will be affected by the flame in a time comparable to the duration of the firstburst. At the same time, the ignition of the opposite zone begins from its low-latitude edgeby the flame front going away from the equator. Thus, the third burst will begin earlier thanthe first burst relative to the time of passage of the equatorial zone by the flame front andits ignition (i.e., the second burst in the series). In principle, the observation of such triplebursts will allow one to investigate the parameters of the spreading layer and to check thecomputations performed by Inogamov and Sunyaev (1999).
Series of Bursts of Greater Multiplicity
Keek et al. (2010) reported the detection of a series of X-ray bursts from the source 4U 1636-538 consisting of four events. Such bursts of greater multiplicity can be explained in theproposed model by assuming that shortly before their observation the accretion rate ontothe source changed abruptly. In this case, as the burning front passed over the neutron 17 –star surface, the flashes should have occurred in two ring zones associated with the infall ofmatter at the initial accretion stage and two other ring zones associated with the infall ofmatter at the final stage. Clearly, this event requires the fulfillment of certain conditionsand can occur very rarely, much more rarely than double and triple bursts. This is generallyobserved.
Why are Single Bursts observed?
Or why are double and triple bursts encountered quite rarely? The point is that the modelof a spreading layer acts only at sufficiently high accretion rates ˙ M ∼ > .
01 ˙ M ed , where ˙ M ed is the critical Eddington accretion rate (Inogamov and Sunyaev 1999). As the accretion ratedecreases, the ring zones of the main energy release and the infall of accreting matter narrowdown and are displaced toward low latitudes. At ˙ M ∼ < .
01 ˙ M ed the entire matter settles inthe equatorial zone; accordingly, only one X-ray burst is observed during the thermonuclearexplosion in this zone. Moreover, the picture is complicated by the fact that as the accretionrate increases, the thermonuclear burning may not be accompanied by an explosion but becontinuous. The exact conditions under which it is possible to observe multiple bursts can beclarified only in future, through detailed numerical simulations of the thermonuclear burningin the physical model being discussed. ACKNOWLEDGMENTS
This work is based on the INTEGRAL data retrieved via its Russian and Europian sciencedata centers. It was financially supported by the “Transitional and Explosive Processesin Astrophysics” Subprogram of the Basic Research Program P-7 of the Presidium of theRussian Academy of Sciences, the Program of the President of the Russian Federation forsupport of leading scientific schools (grant NSh-10222.2016.2) and the “Universe” theme ofthe scientific research program of the Space Research Institute, the Russian Academy ofSciences. 18 –
REFERENCES
1. O.P. Babushkina, L.S. Bratolyubova-Tsulukudze, M.I. Kudryavtsev, A.S. Melioranskii,I.A. Savenko, and B.I. Yushakov,
Sov. Astron. Lett. , 32 (1975).2. R.D. Belian, J.P. Conner, and W.D. Evans, Astrophys. J. , L87 (1972).3. R.D. Belian, J.P. Conner, and W.D. Evans,
Astrophys. J. , L135 (1976).4. S. Bhattacharyya and T.E. Strohmayer,
Astrophys. J. , L121 (2006).5. L. Bildsten,
Astrophys. J. , 852 (1995).6. L. Boirin, L. Keek, M. M´endez, A. Cumming, J.J.M. in’t Zand, J. Cottam, F. Paerels,and W.H.G. Lewin,
Astron. Astrophys. , 559 (2007).7. I.V. Chelovekov and S.A. Grebenev,
Astron. Lett. , 807 (2007).8. I.V. Chelovekov and S.A. Grebenev, Astron. Lett. , 895 (2010).9. I.V. Chelovekov and S.A. Grebenev, Astron. Lett. , 597 (2011).10. I.V. Chelovekov, S.A. Grebenev, I.A. Meriminsky, and A.V. Prosvetov, Astron. Lett. , in press (2017).11. I.V. Chelovekov, S.A. Grebenev, and R.A. Sunyaev, Astron. Lett. , 456 (2006).12. T. Ebisuzaki, Publ. Astron. Soc. Japan , , 539 (1987).13. T. Ebisuzaki, D. Sugimoto, and T. Hanawa, Publ. Astron. Soc. Japan , 551 (1984).14. B.A. Fryxell and S.E. Woosley, Astrophys. J. , 733 (1982a).15. B.A. Fryxell and S.E. Woosley,
Astrophys. J. , 332 (1982b).16. M.Y. Fujimoto, T. Hanawa, and S. Miyaji,
Astrophys. J.
Astrophys.J. Suppl. Ser. , 360 (2008).18. S.A. Grebenev,
Astron. Lett. , in preparation (2017).19. J. Grindlay, H. Gursky, H. Schnopper, D.R. Parsignault, J. Heise, A.C. Brinkman, andJ. Schrijver, Astrophys. J. , L127 (1976).20. D.A. Gryaznyh,
Astron. Lett. , 586 (2013a).21. D.A. Gryaznyh, Astron. Lett. , 602 (2013b). 19 –22. C.J. Hansen and H.M. van Horn, Astrophys. J. , 735 (1975).23. J. Heise, J. Grindlay, and W. Liller,
IAU Circ. n. 2929 (1976).24. N.A. Inogamov and R.A. Sunyaev,
Astron. Lett. , 269 (1999).25. N.A. Inogamov and R.A. Sunyaev, Astron. Lett. , 848 (2010).26. P.C. Joss, Astrophys. J. , L123 (1978).27. L. Keek, D.K. Galloway, J.J.M. in’t Zand, and A. Heger,
Astrophys. J. , 292 (2010).28. W. Kluzhniak,
PhD Thesis (Stanford University, 1988).29. W.H.G. Lewin, J. van Paradijs, and R.E. Taam,
Space Sci. Rev. , 223 (1993).30. R.A. London, R.E. Taam, and W.M. Howard, Astrophys. J. , 170 (1986).31. N. Lund, C. Budtz-Jorgensen, N.J. Westergaard, S. Brandt, I.L. Rasmussen, A. Horn-strup, C.A. Oxborrow, J. Chenevez, et al.,
Astron. Astrophys. , L231 (2003).32. L. Maraschi and A. Cavaliere, in
Highligths of Astronomy, Proceedings of the 16th IAUGeneral Assembly on “X-Ray Binaries and Compact Objects” , Grenoble, France, Aug.24 – Sept. 2, 1976, Ed. E.A. M¨uller, v. , p. 127 (1977).33. T. Murakami, H. Inoue, K. Koyama, K. Makishima, M. Matsuoka, M. Oda, Y. Ogawara,T. Ohashi, et al., Publ. Astron. Soc. Japan , 543 (1980).34. T. Nozakura, S. Ikeuchi, and M.Y. Fujimoto, Astrophys. J. , 221 (1984).35. T. Ohashi, H. Inoue, K. Koyama, K. Makishima, M. Matsuoka, T. Murakami, M. Oda,Y. Ogawara, et al.,
Astrophys. J. , 254 (1982).36. B. Paczynski,
Astrophys. J. , 282 (1983a).37. B. Paczynski
Astrophys. J. , 315 (1983b).38. F. Peng, E.F. Brown, and J.W. Truran,
Astrophys. J. , 1022 (2007).39. C. Sanchez-Fernandez, E. Kuulkers, and E. Aranzana,
Proceedings of “Fast X-ray tim-ing and spectroscopy at extreme count rates (HTRS 2011)” , (Champ´ery, Switzerland,February 7–11, 2011), PoS, , id. 69 (2011).40. N.I. Shakura and R.A. Sunyaev,
Adv. Space Res. , 135 (1988).41. N.I. Shakura and R.A. Sunyaev,
Astrophys. Lett. Comm. , 197 (1999).42. V.A. Simonenko, D.A. Gryaznyh, I.A. Litvinenko, V.A. Lykov, and A.N. Shushlebin, Astron. Lett. , 231 (2012). 20 –43. D.A. Smith, E.H. Morgan, and H. Bradt, Astrophys. J. , L137 (1997).44. T. Strohmayer and L. Bildsten,
Compact stellar X-ray sources , Cambridge AstrophysicsSeries (Ed. W.Lewin, M. van der Klis, Cambridge: Cambridge Univ. Press, 2006), n. , p. 113 (astro-ph/0301544).45. T.E. Strohmayer, W. Zhang, and J.H. Swank, Astrophys. J. , L77 (1997).46. T.E. Strohmayer, W. Zhang, J.H. Swank, A. Smale, L. Titarchuk, C. Day, and U. Lee,
Astrophys. J. , L9 (1996).47. R.A. Sunyaev and L.G. Titarchuk,
Sov. Astron. Lett. , 359 (1986).48. F.X. Timmes and J.C. Niemeyer, Astrophys. J. , 993 (2000).49. C. Winkler, T.J.-L. Courvoisier, G. Di Cocco, N. Gehrels, A. Gimenez, S. Grebenev,W. Hermsen, J.M. Mas-Hesse, et al.,
Astron. Astrophys. , L1 (2003).50. S.E. Woosley and R.E. Taam, Nature , 101 (1976)., 101 (1976).