Restless quiescence: thermonuclear flashes between transient X-ray outbursts
aa r X i v : . [ a s t r o - ph ] J u l Astronomy&Astrophysicsmanuscript no. 10981 c (cid:13)
ESO 2018October 26, 2018
Restless quiescence: thermonuclear flashes between transientX-ray outbursts
E. Kuulkers , J.J.M. in ’t Zand , and J.-P. Lasota , ESA, European Space Astronomy Centre (ESAC), P.O. Box 78, 28691, Villanueva de la Ca˜nada (Madrid), Spain e-mail:
[email protected] SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands Institut d’Astrophysique de Paris, UMR 7095 CNRS, UPMC Univ Paris 06, 98bis Bd Arago, 75014 Paris, France Astronomical Observatory, Jagiellonian University, ul. Orla 171, 30-244 Krak´ow, PolandReceived; accepted
ABSTRACT
For thermonuclear flashes to occur on neutron-star surfaces, fuel must have been accreted from a donor star. However, sometimesflashes are seen from transient binary systems when they are thought to be in their quiescent phase, during which no accretion, orrelatively little, is expected to occur. We investigate the accretion luminosity during several such flashes, including the first-ever andbrightest detected flash from Cen X-4 in 1969. We infer from observations and theory that immediately prior to these flashes theaccretion rate must have been between about 0.001 and 0.01 times the equivalent of the Eddington limit, which is roughly 2 ordersof magnitude less than the peak accretion rates seen in these transients during an X-ray outburst and 3–4 orders of magnitude morethan the lowest measured values in quiescence. Furthermore, three such flashes, including the one from Cen X-4, occurred within 2to 7 days followed by an X-ray outburst. A long-term episode of enhanced, but low-level, accretion is predicted near the end of thequiescent phase by the disk-instability model, and may thus have provided the right conditions for these flashes to occur. We discussthe possibility of whether these flashes acted as triggers of the outbursts, signifying a dramatic increase in the accretion rate. Althoughit is di ffi cult to rule out, we find it unlikely that the irradiance by these flashes is su ffi cient to change the state of the accretion disk insuch a dramatic way. Key words.
Accretion, accretion disks – binaries: close – binaries: general – Stars: neutron – X-rays: binaries – X-rays: bursts
1. Introduction
In low-mass X-ray binaries (LMXBs) a neutron or black holeaccretes matter via an accretion disk from a less massive Roche-lobe filling companion star. In many LMXBs the accretion fromthe disk on the compact object is transient. After a transient out-burst (hereafter referred to as outburst), lasting typically a fewmonths, the system settles in quiescence for a few months to sev-eral decades. The disk-instability model (DIM; Osaki 1974, seeLasota 2001 for a review) predicts that, if in quiescence the diskextends down to the stellar surface (or the last stable Keplerianorbit), the accretion rate is negligibly low ( ∼ g s − ; Lasota etal. 2008, see Eq. (1) in Sect. 4). However, in general the X-rayemission of quiescent transient sources corresponds to accretionrates that cannot be qualified as negligible (e.g., van Paradijs etal. 1987, Campana et al. 2004).In the case of neutron-star transients there has been a con-troversy on the origin of the quiescent X-ray luminosity. Onthe one hand, quiescent-disk truncation easily explains the lu-minosity (Lasota et al. 1996, Dubus et al. 2001, Narayan &McClintock 2008), is also applicable to black-hole systems, andhas been confirmed by observations (e.g., Done 2002). On theother hand, Brown et al. (1998) propose that quiescent X-rayshave their origin in heating of the neutron-star crust by nuclearreactions and not in accretion. Both models have their di ffi cul-ties. The observed rapid variability of the quiescent X-ray fluxand the presence of a substantial power-law component (as seen Send o ff print requests to : E. Kuulkers in, e.g., the LMXB transient Cen X-4, see Campana et al. 1997,2004, Rutledge et al. 2001), as well as a very low quiescentX-ray luminosity (less than about several times 10 erg s − for1H 1905 + ffi cult to reconcile withthe deep crustal heating model (see, e.g., Jonker 2008 for a re-cent discussion). The lack of a well understood disk-truncationmechanism (see, however, Liu et al. 2002) and the overpredictedratio of neutron-star to black-hole quiescent X-ray luminosi-ties (Menou et al. 1999) are the weaknesses of its competitor.Therefore, any independent estimate of the quiescent accretionrate in transient systems would be a great help in resolving thecontroversy.Type I X-ray bursts (Grindlay et al. 1975, Belian et al. 1976,Ho ff man et al. 1978) are thermonuclear flashes at the surface ofa neutron star (Joss 1977, Maraschi & Cavaliere 1977, Lamb &Lamb 1978; for reviews see, e.g., Lewin et al. 1993, Strohmayer& Bildsten 2006). We hereafter refer to these events as flashes.If the energy release during a flash is fast and large enough,the local luminosity on the neutron star surface can surpass theEddington limit, resulting in a lift-up of the photosphere. Suchflashes are referred to as photospheric radius-expansion X-raybursts. During the expansion phase the inferred temperature de-creases, whereas the inferred emitted area increases (see, e.g.,Lewin et al. 1993, for a review).The first observed flash, in retrospect, was the event detectedon July 7, 1969, with Vela 5B from Cen X-4 (Belian et al. 1972;see Sect. 2). The event lasted for about 10 min, and is still the
E. Kuulkers et al.: Restless quiescence brightest ever observed with a peak flux of about 60 Crab (3–12 keV). Two days after the flash Cen X-4 went into an X-rayoutburst, which peaked at about 25 Crab (3–12 keV) and lastedfor about 80 days (Conner et al. 1969; Evans et al. 1970; seealso Sect. 2). Except for the flash, no other X-ray emission wasdetected from Cen X-4 before the outburst (Belian et al. 1972).Interestingly, a similar situation recently occurred in anothersource: a ≃
40 s long flash was detected from IGR J17473 − −
245 (Cornelisse et al. 2007). Our inspectionof the
RXTE
All Sky Monitor (ASM) light curve shows that thefirst flash, which lasted for about 40–50 s, occurred when therewas no detectable X-ray emission. The following two flashes oc-curred when the source showed X-ray emission at a slightly ele-vated level. About a week later the source developed into a brightX-ray outburst.A few other LMXB transients have shown flashes afterand / or in between X-ray outbursts when their X-ray emis-sion was below the detection thresholds and the systemswere inferred to be in their quiescent phase: 2S 1711 − − −
312 (Cornelisse et al.2002a, in ’t Zand et al. 2001, 2003b, respectively). Also Cen X-4may have shown a flash ∼ : that the flashes serve as triggers for accretion-disk instabilities resulting in X-ray outbursts. We study in Sect. 4the viability of this idea in the context of Cen X-4.
2. Cen X-4: revisiting old data
Cen X-4’s 1969 flash was reported to reach a peak flux of about1.4 × − erg cm − s − . The event rose to an observed maximum The commonly used Crab unit is equivalent to about2 × − erg cm − s − in the classical 2–10 keV photon-energy band. Belian et al. (1972) called Cen X-4’s 1969 flash a probable precur-sor to its subsequent X-ray outburst. They suggested the two events tobe associated, but no physical scenario was discussed. Whether the flux is bolometric or in the 3–12 keV band is not en-tirely clear from Belian et al. (1972). Assuming the X-ray detectorsonboard
Vela 5B to be ideal detectors (i.e., with a 100% quantum ef-ficiency), we can translate the quoted 3–12 keV count rate (2850 c s − ,Belian et al. 1972) into a photon flux, and subsequently estimate thebolometric flux assuming a black body with a temperature of 3 × K(see Belian et al. 1972). This results in a bolometric flux estimateof about 1.8 × − erg cm − s − , i.e., higher than the quoted peak flux.Since the X-ray detectors are not ideal, quantum e ffi ciencies are lower,which results in even higher estimated bolometric flux values. This andthe fact that Belian et al. (1972) speak of an “energy” flux, suggests thequoted peak value to be the 3–12 keV flux. However, given the uncer-tainties involved and that the quoted peak flux is closer to the bolometric within up to about 1 min and lasted about 10 min; the shape ofthe decay after the peak was more consistent with a power-lawthan with an exponential (see also below). During the decay theemission softened: at the peak it could be described by a black-body with a temperature of about 2.6 keV, whereas in the tailthe temperature was about 1.3 keV (Belian et al. 1972). We notethat the e ff ective black-body radius at the peak would be about6.5 km (at 1.2 kpc, see below). The energy release during theflash was estimated to be about 5 × erg (at 1.2 kpc; Matsuokaet al. 1980). It was recognized later that these are the characteris-tics of a flash, although it was noted that the event lasted unusu-ally long (Fabbiano & Branduardi 1979, Matsuoka et al. 1980,Kaluzienski et al. 1980; see also Hanawa & Fujimoto 1986).However, such long flashes, although rare, have since been seenin other LMXBs as well (see, e.g., Kuulkers 2004, in ’t Zand etal. 2007, Falanga et al. 2008).The position of Cen X-4 has been refined (Hjellming 1979,Canizares et al. 1980) since the early Vela 5B reports; we, there-fore, decided to re-analyse the
Vela 5B data. The raw data filesare archived at HEASARC (see Whitlock et al. 1992, Whitlock& Tyler 1994).
Vela 5B (see Conner et al. 1969) provided the firstX-ray all-sky monitor; it was, however, designed to be a nuclear-test detection satellite. The satellite rotated about its nadir-fixedspin axis with a 64-s period, and orbited the Earth in around112 hrs. The scintillation X-ray detector (XC) was located atabout 90 ◦ from the spin axis, and so covered the X-ray sky twiceper satellite orbit. Data were telemetered in 1-s count accumula-tions. The X-ray detector provided data in two energy channels,3–12 keV and 6–12 keV. A slat collimator limited the field ofview to a FWHM aperture of 6.1 ◦ × ◦ ; the e ff ective detectorarea was about 26 cm .We extracted the light curves, assuming that no other strongX-ray sources were in the field of view. We used two time scales.For the X-ray outburst we used 56 hrs (i.e., half the Vela 5B satel-lite orbital period), and included data up to the recommended 5 ◦ o ff -axis from the position of Cen X-4. For the flash we used the1-s info. The beginning of the flash occurred at a larger o ff -axisangle than the recommended value; here we therefore includeddata from up to 6 ◦ . Data flagged for an unstable spin period andfor pointing errors were not included. The data were correctedusing a sinusoidally modelled background. For some sources, re-moval of the fitted background leaves a slightly negative averagein the count rate; this is also the case for Cen X-4. We correctedthe 56-hrs average light curve for the observed negative averagein the count rate just before and after the X-ray outburst (about − − ). The 1-s data are corrected for the collimator responseand the time stamps are corrected to solar-system barycentrictime. The errors on these data are determined as follows: weassumed Poisson counting statistics in the light curves uncor-rected for background and collimator; the errors were then prop-agated when all corrections were made. The 56-hrs count ratesare weighted averages of the 1-s data; the errors take into ac-count uncertainties introduced by background removal and col-limator response correction, as well as counting statistics (seeWhitlock et al. 1992). We normalized the count rates to the Vela5B
Crab rate observed in the 3–12 keV band between 1969, May28 and Oct 29, i.e., around the time of the 1969 X-ray outburst(43.2 ± − ).The flash (Fig. 1, left panel) rose to the observed peak withinup to 62 s. We find a peak flux of 57 ± peak flux of that observed during Cen X-4’s flash seen with Hakucho ,we use the quoted value as the bolometric flux.. Kuulkers et al.: Restless quiescence 3 −500 0 500 1000 F l u x ( C r ab ) Time (sec after peak)1969 July 7 flash Cen X−4
400 450 500 . . F l u x ( C r ab ) Time (MJD − 40000)1969 outburst Cen X−4 flash
Fig. 1.
Left: Vela 5B light curve (3–12 keV) of the X-ray event from Cen X-4 which occurred on July 7, 1969. Time = Right: Vela 5B light curve (3–12 keV) of the X-ray outburst of Cen X-4 which lasted from 1969, July-September. See also Evans et al. (1970). Data are shown from near the start (1969 May 28) up to about 155 days after the start (1969 Oct 29) ofthe Vela 5B mission. The time of the flash is indicated with an arrow. pre-flash level (see Fig. 1, right panel). Our revised peak inten-sity is a factor of ≃ × − erg cm − s − .We only have sparse timing information. Because of the datagaps the actual peak flux may have been even higher; we alsocan not say with certainty whether the event showed a photo-spheric radius-expansion phase indicative of (super-)Eddingtonfluxes from the flash or not.Until about 150 s after the peak the exponential decay timeis about 44 s. After that excess emission above the expected ex-ponential decay is observed. Such excess emission is similarto that seen in other flashes from, e.g., Aql X-1 (Czerny et al.1987), X1905 +
000 (Chevalier & Ilovaisky 1990) and GX 3 + ± ◦ satel-lite temperature change from one side of the satellite orbit to theother. This has not been (and can not be any more) taken intoaccount in the data reduction, because of the lack of pre-launchtests, and the lack of information regarding the temperature val-ues in our time frame of interest (see Whitlock et al. 1992).A second X-ray outburst occurred in 1979, which reached apeak flux of about 4 Crab (3–6 keV) and lasted about a month(Kaluzienski et al. 1980). During the late stages of the outbursta flash was observed with Hakucho (Matsuoka et al. 1980). Thisflash reached a peak flux of about 25 Crab (1.5–12 keV; with anestimated uncertainty of about 5%, M. Matsuoka, private com-munication) or a bolometric peak flux of 1 × − erg cm − s − ,attained a peak black-body temperature of 2.5 ± ≃
100 s, and had an energy output of about 1 × erg (at1.2 kpc; Matsuoka et al. 1980). There is no clear evidence of aradius-expansion phase in this flash either.The peak fluxes of the 1969 and 1979 flashes have been usedto estimate the proximity of the system; the upper limit wasabout 1.2 kpc (Matsuoka et al. 1980, Kaluzienski et al. 1980,Chevalier et al. 1989). Our revised 1969 flash peak flux andthe theoretical value for the Eddington-limited luminosity, L Edd ( ≃ × erg s − ) , for a 1.4 M ⊙ star which accretes materialwith solar composition (see Sect. 3.1) translate again to an upperlimit of about 1.2 kpc (assuming isotropic radiation). This upperlimit is consistent with that derived from other constraints, i.e.,between 0.9 kpc and 1.7 kpc (Gonz´alez Hern´andez et al. 2005a).In this paper we adhere to a distance of 1.2 kpc.No significant X-ray emission was detected before and justafter the 1969 flash of Cen X-4 (Belian et al. 1972; see alsoConner et al. 1969). The 1-day average 3 σ detection limit of Vela 5B is about 250 Uhuru Flux Units (see Priedhorsky &Holt 1987), which corresponds to about 6 × − erg cm − s − (2–10 keV). Using our light curves with 56 hrs time resolu-tion during the ≃
40 days before the X-ray outburst we findthat the spread in values of the count rates is 32.4 mCrab (3–12 keV). We, therefore, infer a 56 hrs-average 3 σ upper limit of ≃
97 mCrab (3–12 keV) on the emission before the X-ray out-burst. The error on the average of the count rates over the 40days is ≃ σ upper limit on theemission over the whole 40-day time interval of ≃
17 mCrab (3– The Eddington luminosity as measured by a distant observer is L Edd = (4 π cGM /κ )[1 − GM / ( Rc )] / , where c , G , M , κ and R are thespeed of light, the gravitational constant, the mass of the object, theelectron scattering opacity and the radius of the object, respectively(see, e.g., Lewin et al. 1993). = Uhuru c s − = × − erg cm − s − (2–10 keV), assuming a Crab-like spectrum (Forman et al. 1978). E. Kuulkers et al.: Restless quiescence
12 keV). Assuming a Crab-like spectrum (see, e.g., Kirsch et al.2005) the above 3 σ limits translate to 2–10 keV pre-flash fluxesof about 2 × − erg cm − s − and 3 × − erg cm − s − , respec-tively. The non-detection of the source during 1977–1978 in theHEAO-A2 sky survey corresponds to an upper limit of about1 × − erg cm − s − (2–10 keV; see Kaluzienski et al. 1980), in-dicating that the source approached quiescent values in betweenthe two X-ray outbursts. The quiescent flux observed long af-ter the second X-ray outburst is about 1–3 × − erg cm − s − (0.5–10 keV; see Rutledge et al. 2001). It is, however, variable onlong-term time scales ( ∼
40% in 5 years; Rutledge et al. 2001),as well as on short-term time scales (factor of about 3 in a fewdays and at a level of ∼
45% rms down to about 100 s; Campanaet al. 1997, 2004).
3. Limits on pre-flash accretion rates
What is the level of accretion prior to the flashes, allowingthem to occur? During none of the flashes mentioned in theIntroduction was emission detected just before and after theflash, so in principle no accurate measurement of the luminos-ity, and therefore accretion rate, can be made around the time ofthese flashes. Nevertheless, the observed upper limits may stillgive us useful constraints on the accretion rate.The ratio of (the upper limit to) the pre-flash emission andthe Eddington-limited flux provides an estimate of the fractionof the Eddington limit at which a source is accreting (see, e.g.,Cornelisse et al. 2002a). For ease of comparison between theobservations and flash theory, we therefore denote the observedX-ray luminosities in terms of the Eddington luminosity, L Edd ,and the accretion rates, ˙ M , in terms of the Eddington accre-tion rate, ˙ M Edd . The Eddington accretion rate is defined as theaccretion rate at which the corresponding accretion luminos-ity, L acc , equals L Edd . The secondary star in Cen X-4 is a late-type K3-K7 star in a ∼
15 hr orbit with the neutron star (e.g.,Casares et al. 2007, and references therein). We can fairly as-sume that the secondary provides a solar mix of H and He; themetallicity is only slightly over-solar (Gonz´alez Hern´andez etal. 2005b). For the other systems this is not clear. Assumingthat the metallicity of these sources does not deviate much fromsolar, L Edd ≃ × erg s − (see Sect. 2), while correspondingly˙ M Edd ≃ g s − (see footnote 7, using L acc = L Edd ).Since X-ray instruments provide information in a limited en-ergy range only, one has to correct the observed X-ray fluxes tobolometric values. To determine the bolometric correction factorone has to make assumptions on the spectrum outside the instru-ment’s energy window. For the purpose of this paper we employa bolometric correction factor of about 2 (see in ’t Zand et al.2001, 2003b, 2007), whenever necessary. We also assume thatthe pre-flash emission as well as the flash emission is isotropic. L acc = GM ˙ M / R ≃ × ˙ M ( M / M ⊙ )(10 km / R ) erg s − , where L acc is the accretion luminosity and where we used ˙ M = ˙ M g s − Notethat this corresponds to an accretion e ffi ciency of ∼ ⊙ and a radius of 10 km, L acc ≃ × ˙ M erg s − . See, e.g., Frank et al. (1992). The secondary of SAX J1808.4 − ∼ ⊙ brown dwarf (Bildsten & Chakrabarty 2001), while the secondary inGRS 1747 − For photospheric radius-expansion flashes the peak bolomet-ric black-body flux, F bb , peak , equals the Eddington flux, and,therefore, L x , bol / L Edd = F pers , bol / F bb , peak , where L x , bol and F pers , bol refer to the (estimated) bolometric pre-flash source luminosityand flux, respectively. When a flash does not show such an ex-pansion phase, F bb , peak represents a lower limit to the Eddingtonflux, and, therefore, L x , bol / L Edd < F pers , bol / F bb , peak . The flux val-ues and corresponding luminosity information are shown inTable 1. Note that the values for L x , bol / L Edd are in the samerange as the upper limits derived on the emission of the burst-only sources around the flashes (Cocchi et al. 2001, Cornelisseet al. 2002a, and references therein), where L x , bol / L Edd . F pers , bol and L x , bol can be up to about a factor of 2 higher. This does, however, nothave an e ff ect on our principal conclusions.Assuming L x , bol / L Edd equals ˙ M / ˙ M Edd (keeping in mind theuncertainties introduced by the bolometric corrections, the as-sumption here of a radiation e ffi ciency of ∼ M around thetime of the flashes in our sample is . − ˙ M Edd , i.e., at leastabout 2 orders of magnitude lower than what is typically ob-served when the systems are in outburst. We note here that thelowest measured accretion flux for an active burster is about0.03 L Edd (in ’t Zand et al. 2007).
The characteristics of a flash (such as duration and peak lumi-nosity) depend primarily on ˙ M and the composition of the ac-creted material, for a given neutron star mass (e.g., Fujimotoet al. 1981, Fushiki & Lamb 1987; see also Peng et al. 2007,Cooper & Narayan 2007, and references therein). In general, Heignites completely in a fraction of a second, while unstable hy-drogen burning is prolonged to about 100 s through slow beta de-cays in the rp process (e.g., Cumming 2003, Woosley et al. 2004,Heger et al. 2007, Fisker et al. 2008). The duration of a flash isa convolution of the burning process time and the cooling time.For ˙ M . − ˙ M Edd flashes occur deeper in the neutron star andthe duration is mainly determined by the cooling time. At facevalue, the duration of the 1969 flash from Cen X-4 is consistentwith burning of a H-rich layer with e-folding decay times closeto values found for the prototypical burster GS 1826 −
24 (e.g.,Heger et al. 2007, Galloway et al. 2008). However, since the ac-cretion rate at the time of Cen X-4’s flash was low, the decayrate is likely to be limited also by the relatively large depth ofthe ignition. Although the available literature on the theoreticaldescription of the flash behaviour at the low accretion rates rele-vant to our sample (typically . − ˙ M Edd ) is sparse and has onlyrecently been developed in more detail (Peng et al. 2007, Cooper& Narayan 2007), we can use it to infer additional constraints onthe accretion rate around the time of the observed flashes.Below ˙ M of a few times 10 − ˙ M Edd , one expects mixed H / Heflashes triggered by thermally unstable H burning. The decaytimes of such flashes are on the order of tens of seconds, dueto the long waiting times involved in β -decays. During the peakof these kinds of flashes the fluxes are sub-Eddington, but areexpected to exceed about 10% of the Eddington limit. Betweena few times 10 − ˙ M Edd and 10 − ˙ M Edd , unstable H burning doesnot trigger unstable He burning and a layer of He is being builtup, which may eventually lead to an energetic (approaching oreven reaching the Eddington limit) and long flash. These ˙ M lim-its depend, however, on the emergent flux from the neutron starcrust and whether sedimentation is important or not. For exam- . Kuulkers et al.: Restless quiescence 5 Table 1.
Overview of the properties of the observed flashes discussed in this paper.Source F bb , peak (10 − F pers F pers , bol / F bb , peak L x , bol (10 ∆ t last ∆ t next erg cm − s − ) (10 − erg cm − s − ) ≡ L x , bol / L Edd erg s − ) (days) (days)Cen X-4 ∼
120 [1] < a (2–10 keV) [1] . . >
40 [1,2] ≃ −
339 3.0 ± b [4] < . . ∼
340 [4] ≃ − ≃ c [6] < . . ≃
26 [6] ≃
28 [6]IGR J17473 − ≃ d [7] < . . ∼
960 [9,10] ≃ −
245 3.1 ± < e (2–28 keV) [4] . . ∼ ≃ − ± c [14] < . . ≃
17 [14] ≃
543 [15] a Vela 5B
56 hrs upper limit. b Highest peak flux among the flash sample in [4]. c Photospheric radius-expansion flash. d Peak flux observed during another flash reported by [7]. e No limits are quoted in [12]; we, therefore, assume the highest
BeppoSAX / WFC flux upper limit from [4].
Note 1.
In the first two columns we give the observed flash bolometric peak fluxes ( F bb , peak ) and the 3 σ upper limits on the flux around the flashes( F pers ). From these we infer the flash peak luminosities in terms of the Eddington luminosity ( L Edd ), assuming L x , bol / L Edd ≡ F pers , bol / F bb , peak (seeSect. 3), where F pers , bol and L x , bol are the bolometric pre-flash source flux and luminosity, respectively. Assuming L Edd = × erg s (see Sect. 2)we derive an upper limit on L x , bol . In the last two columns we provide the time since the last and to the next detected X-ray outburst with respectto the time of the flash, ∆ t last and ∆ t next , respectively. References are given in brackets: [1] this paper, [2] Conner et al. (1969), [3] Belian et al.(1972), [4] Cornelisse et al. (2002a), [5] Markwardt & Swank (2004), [6] in ’t Zand et al. (2003b), [7] Altamirano et al. (2008), [8] Markwardt etal. (2008), [9] Grebenev et al. (2005), [10] Markwardt & Swank (2005), [11] Del Monte et al. (2008), [12] Cornelisse et al. (2007), [13] Jernigan(1976), [14] in ’t Zand et al. (2001), [15] Marshall (1998). ple, a factor of 10 higher flux from the crust results in ˙ M limitswhich are about a factor of 10 lower, while including sedimen-tation has the e ff ect of increasing the ˙ M limits by about a factorof 2 (see Peng et al. 2007, Cooper & Narayan 2007).The minimum accretion rate below one expects no flashesat all (i.e., completely stable burning all the time), is even lesswell-studied nor well-determined, but it is probably of the orderof 10 − ˙ M Edd (see Fushiki & Lamb 1987).It is important to realize that the above quoted ˙ M values fromflash theory are presumed to sustain for at least a few months(i.e., the thermal time scale of the crust). If there were a tempo-rary increase in ˙ M on a shorter time scale, the temperature of thelayer where the flash originates may still be higher than would beexpected from the lower long-term averaged ˙ M , thus influencingthe flash behaviour. We reiterate that, when comparing the observed limits on ˙ M withthat inferred from flash theory, one has to keep in mind the un-certainties and assumptions mentioned at the end of Sect. 3.1,as well as the uncertainties in the flash theory. The minimum˙ M below one expects no flashes, translates to an accretionluminosity of a few times 10 erg s − . This is interestinglyclose, but above, to that observed for our sample of sources,as well as other neutron star X-ray transients, in quiescence(10 − erg s − ; e.g., Cornelisse et al. 2002a,b, 2007, Campanaet al. 2004, Jonker et al. 2007, Heinke et al. 2007, and refer-ences therein). The neutron stars in our source sample, there-fore, must have been accreting at levels above that of quiescence,i.e., ˙ M & − ˙ M Edd . In this respect we note, however, the sub-luminous ( L bb , peak ∼ × erg s − ) flash seen from a source inM28 with a pre-flash luminosity of L x , bol . erg s − (Gotthelf& Kulkarni 1997), which may counter the suggestion. For thissource L x , bol / L Edd . × − (assuming solar type compositions),which is about a factor of 1000 lower than the values found forthe sources in our sample (Table 1).The 1969 flash from Cen X-4 was bright, but we can not in-fer whether it had a photospheric radius-expansion phase (i.e.,reached the Eddington limit). It could thus have been either a flash fueled by a deep layer of nearly pure He or a longmixed H / He flash triggered by an unstable H flash. The ex-pected ˙ M is thus . − ˙ M Edd , which is consistent with the ob-served upper limit based on the Vela 5B non-detection prior tothe flash (see also Hanawa & Fujimoto 1986). This also holdsfor the flashes seen from 2S 1711 − − − − −
312 didreach the Eddington limit and lasted on the order of minutes (in’t Zand et al. 2001, 2003b). For these sources we thus infer thatthe expected ˙ M was between about a few times 10 − ˙ M Edd and10 − ˙ M Edd , roughly consistent with the observed upper limits onthe pre-flash source luminosity. The expected ˙ M are 3–4 ordersof magnitude higher than that inferred from observations in qui-escence.One can make simple analytic estimates how long such anenhanced accretion period has to last in order to show a flash(assuming the flash is produced from only the freshly accretedmaterial, and that all of this fresh material is used during theflash). Burning H to He to C (using a H mass fraction X = = × erg g − , whereasburning He to C (using X =
0, Y =
1) gives roughly 6 × erg g − (see, e.g., Bildsten 1998). In the case of Cen X-4’s long 1969flash, if it is due to unstable mixed H / He burning, we need atleast 10 g to get a flash fluence of more than 5 × erg. If ˙ M onto the neutron star is about 10 − –10 − ˙ M Edd , one needs to waitat least 115–12 days for a flash to occur. If the flash is due to un-stable pure He burning, one needs even more matter and one hasto wait longer (assuming the steadily burning H does not leaveHe behind). Then the He mass needed is about 8 × g, andthe neutron star needs to accrete at least an order of magnitudelonger than estimated above. This enhanced accretion time scalegrows inverse proportionally with mass accretion rate for evenlower values of ˙ M . Note that for ˙ M . − ˙ M Edd , in the mixedburning case, the time scale starts to become as long or evenlarger than the thermal time scale of the crust.Inspection of Fig. 1 (right panel) shows, in the case ofCen X-4, no evidence of any increased X-ray activity (aboveabout 10 erg s − ), i.e., no enhanced accretion onto the neutronstar, above the Vela 5B detection level during the 40 days prior
E. Kuulkers et al.: Restless quiescence to the 1969 outburst (see also Conner et al. 1969). The othersources show comparable limits on the existence of temporaryincrease in ˙ M , mainly based on observations with X-ray moni-toring instruments such as the RXTE / ASM and
BeppoSAX / WFC.However, these limits (more than 3 orders of magnitude higherthan the quiescent luminosity) are not very constraining, andthus enhanced ˙ M could have occurred with maximum accre-tion luminosities of about 5 × –10 erg s − , around the timeof their flashes. We conclude that the presence of the flashes discussed here re-quire an enhancement of the accretion rate above that of purequiescence, either temporary or on longer time scales. In the firstcase the enhancement can occur in the phases just before or af-ter the bright outburst, or be the result of a weak (presumablyunobserved) outburst.Indeed, Cornelisse et al. (2002a) already suggested that theburst-only sources either accrete persistently at “medium” ˙ M (with L x , bol ≃ − erg s − ), or that their flashes occur duringor after faint outbursts (with L x , bol . erg s − ). Interestingly,one of the burst-only sources, XMMU J174716.1 − L x , bol ≃ × erg s − (see Del Santo et al. 2007).Similarly, over the years AX J1754.2 − − − − −
312 and 2S 1711 −
339 have shown X-ray out-bursts with L x , bol > erg s − . Ten to eleven months afterthe SAX J1808.4 − −
339 has been detectedat low-intensity levels at various times before and after its1998 / − ∼
10) after its main outbursts, before going toquiescence (Keek et al. 2008). During its quiescence phaseSAX J1808.4 − − −
29, have shown exponential decaying low-levelintensity light curves after their main outburst over a period ofseveral years (from about 2–5 × erg s − to an apparent baselevel of 2–5 × erg s − ; e.g., Cacket et al. 2006). All of theabove suggests the possibility of ongoing accretion episodesafter the main outburst, which may be universal among the(neutron-star) X-ray transients.Although quiescence is reached some time after theX-ray outbursts of SAX J1808.4 − −
312 and2S 1711 − M had not reached quiescent values yet. The smoothness of the decay of KS 1731 −
260 and MXB 1659 − M as the cause of it; they favour a cooling neutron star. Wenote, however, that the decay light curves are not too well sampled (ef-fectively 5 observations over about 4 years). For 2S 1711 −
339 this was almost a year after the X-ray outburst(Table 1). On the other hand, it could be that at the end of the qui-escent phase of Cen X-4, IGR J17473 − − M was enhanced as predicted by the DIM (see Sect. 4). No evi-dence is found of a long-term increase of the accretion rate; theincrease is of temporary nature. It is di ffi cult to estimate the dura-tion of this temporary enhancement, however, due to insu ffi cienttime coverage and sensitivity.
4. Do flashes trigger X-ray outbursts, or is it theopposite?
Flashes have an impact on the region around the neutron star,i.e., the corona and / or the inner parts of the accretion disk. Thiscan be seen in those flashes where the residual X-ray emissionduring the photospheric radius-expansion phase is lower thanthe pre-flash emission (e.g., Molkov et al. 2000, Strohmayer &Brown 2002), and / or in those flashes where the decay showspronounced irregularities from canonical exponential-like de-cay (e.g., van Paradijs et al. 1990, Strohmayer & Brown 2002,Molkov et al. 2005, in ’t Zand et al. 2005b, 2007; excluding thosesources which are viewed at high inclination). We here pose thequestion whether a flash can be influential enough to enhancethe accretion onto the neutron star; in other words, was the 1969Cen X-4 flash the trigger of Cen X-4’s subsequent X-ray outburst(and similarly for IGR J17473 − − ff erence is thatin LMXBs irradiation by the central X-ray source strongly influ-ences the disk’s stability (van Paradijs 1996, Dubus et al. 1999)and the properties of the outburst cycle (Dubus et al. 2001).According to the DIM, outbursts are driven by a thermal-viscous instability which triggers heating fronts that bring an ini-tially ‘cold’ disk into a ‘hot’, high accretion-rate, state. The hotoutburst phase is ended by an inward-propagating cooling frontwhich brings the disk back to a cold state. During the subsequentquiescent phase the disk fills up with matter until it reaches theinstability limit, which corresponds to the critical accretion rategiven by:˙ M − crit = . × α . . R . M − . g s − (1)where α = α . is the disk viscosity parameter, R = cm R the radius and M = ⊙ M the mass of the accreting object. Thesuperscript ‘ − ’ refers to the maximum accretion rate for stablecold disks (see Lasota et al. 2008).During quiescence the accretion rate in the disk must ev-erywhere be lower than the critical value given by Eq. (1).Therefore, for disks extending down to the neutron star surface(or to the innermost stable circular orbit) the resulting rates areridiculously low, as mentioned in the Introduction. However,for disks truncated at, say, ∼ cm, the accretion rate at theinner disk’s edge is about 7 × g s − , i.e., ∼ × − ˙ M Edd (inagreement with observations of Cen X-4 in quiescence ). Whenthe accretion rate reaches somewhere the critical value givenby Eq. (1), an outburst starts. In LMXBs the outbursts alwaysstart near the inner edge of the (truncated) disk (see Dubus Given the 1.2 kpc distance and a bolometric correction factor of 2the observed X-ray luminosity in quiescence (see Sect. 2) correspondsto L x , bol ∼ × erg s − . This leads to inferred accretion rates in qui-escence of about 2–5 × g s − , or 2–5 × − ˙ M Edd .. Kuulkers et al.: Restless quiescence 7 et al. 2001). In the model of Dubus et al. (2001) correspond-ing roughly to the parameters of Cen X-4, outbursts start at˙ M ∼ × g s − (see their figure 19), i.e., at ˙ M ∼ × − ˙ M Edd ,which, (consistently) implies an accumulation time for a criticalpile of flash fuel of several months to more than a year, depend-ing on the sort of flash produced (see Sect. 3.3).In outburst (when accretion rates can reach Eddington lim-ited values) the X-ray irradiation stabilizes the disk (van Paradijs1996, Dubus et al. 1999), but in quiescence the X-ray accretionluminosity is too low to a ff ect the stability properties. However,external disk irradiation (e.g., by a flash) can a ff ect the disk’sproperties by significantly lowering the value of the critical den-sity and accretion rate. In general, the irradiation temperaturecan be written as: σ T = C L x π R , (2)where L x is the X-ray luminosity and C represents the fraction ofthe X-ray luminosity that heats up the disk and contains informa-tion on the irradiation geometry, the X-ray albedo and the X-rayspectrum. Based on observations of irradiated disks in low-massX-ray binaries, Dubus et al. (1999, 2001) found that in outburst,when L x is the accretion luminosity, C≈ ff ect of varying X-ray luminositycan be mimicked by varying C . The upper continuous line infigure 15 of Dubus et al. (2001) shows the column-density profileof a disk just before the onset of the outburst: in its inner parts thedensity is very close to the critical one represented by a dottedline in that figure. This is the standard situation when irradiationin quiescence is negligible because of low accretion luminosity.The second (lower) dotted line in that figure corresponds to thecase of a disk irradiated in quiescence ( C multiplied by 100).In this case the outburst would have started at lower surface-density, i.e., earlier than in the case of a non-irradiated disk. Canthis represent the e ff ect of irradiation by a flash such as observedin Cen X-4?As discussed in Sect. 3, the X-ray luminosity before the flashwas not higher than L x ≃ erg s − . Therefore, the e ff ect of theflash can be roughly described by an increase in C by a factorof at least 100 which corresponds to the situation represented atfigure 15 of Dubus et al. (2001). The numerical values of thesurface-density and truncation radius correspond to a 7 M ⊙ ac-cretor as it is the only available example in Dubus et al. (2001).The relative amplitude of the e ff ect, however, does not dependon the mass of the compact object. So, in principle, a flash canaccelerate the start of an outburst.However, since the flash lasted only about 10 min, one has tocheck that the disk had the time to modify its thermal structure,i.e., that it had enough time to react to irradiation. The character-istic thermal time scale of the disk is t th ∼ / ( α Ω K ), where Ω K isthe Keplerian angular velocity. Assuming an inner disk radius at ∼ cm and α = t th ∼ ff ectingthe disk structure. ( α could have a value up to, say, 0.03, but thiswould not help much).As mentioned above, in the relevant non-irradiated modelof Dubus et al. (2001), outbursts start at ˙ M ∼ × g s − . FromEq. (1) this corresponds to a radius of ∼ × cm. Therefore,it is rather unlikely that the flash triggered the outburst. If any-thing, the opposite is true: according to the model, in the lasttwo years preceding the outburst the accretion rate increases to alevel, which may have provided the right conditions for the flashto occur (see above). One should, however, keep in mind that the exact value of the truncation radius depends on an ‘evaporation’mechanism model.
5. Summary
The detection of a flash at the end of the quiescent phasesin Cen X-4, IGR J17473 − − − − − to 10 g s − might have pro-vided the right conditions for the flashes to occur in just beforethe outbursts of Cen X-4, IGR J17473 − − Acknowledgements. We thank Jorge Casares for discussions regarding the sec-ondary star of Cen X-4, Randy Cooper regarding ˙ M limits from flash theory,Masaru Matsuoka regarding the flash seen from Cen X-4 by Hakucho , PaulGorenstein and Rick Harnden for discussions about the
Apollo 15
X-ray burstevent, Arne Åsnes, Bob Lin, David Sibeck and Matt Taylor for discussions aboutsolar wind particles and their interaction with the earth’s magnetosphere, andPeter Jonker for commenting on an earlier draft of the paper. EK and JZ ac-knowledge support from the Faculty of the European Space Astronomy Centre(ESAC). JPL was supported by the Centre National d’Etudes Spatiales (CNES).
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Appendix A: A flash from Cen X-4 in quiescencerecorded by
Apollo 15 ? A.1.
Apollo 15 observations
The X-ray Fluorescence Spectrometer (1– > Apollo 15 mission, was mainly used for orbitalmapping of the lunar surface composition (see, e.g., Adler et al.1972a,b, 1975). Galactic X-ray observations were made duringthe trans-Earth coast for several periods of about an hour (e.g.,Adler et al. 1972b). Among the various other instruments werethe Gamma-ray Spectrometer (500 keV–30 MeV; e.g., Arnold etal. 1972) and the Alpha Particle Spectrometer (4.5–9.0 MeV;e.g., Gorenstein & Bjorkholm 1972). The X-ray FluorescenceSpectrometer was pointed towards various constellations over aperiod of about 3 days (1971, Aug 5–7) with an attitude stabilitywithin a degree for approximately 1 hr of observation (Adler etal. 1972b).A large increase in the X-ray count rate for about 10 minwas recorded on UT 1971, August 5, 00:34 (Gorenstein et al.1974). The burst event occurred when the spacecraft was pointedtowards the Centaurus constellation, for a period of about 65 min(Adler et al. 1972b, Gorenstein et al. 1974). According to theApollo 15 Flight Journal , it was aimed at Centaurus A. The X-ray Fluorescence Spectrometer had all the known X-ray sourcesin Centaurus at that time in the full-width conal field of view of50 ◦ (Gorenstein et al. 1974); Cen X-4 was about 21.5 ◦ fromthe center of the field of view.At the peak of the burst event the intensity was several timeshigher than Sco X-1, and Gorenstein et al. (1974) noted that thelight curve and strength of the burst event was similar to that re-ported for the flash from Cen X-4 by Belian et al. (1972). Basedon the above characteristics Gorenstein et al. (1974) suggestedtheir event to be a similar flash from Cen X-4. See http://history.nasa.gov/ap15fj/ . The nominal field of view is about 60 ◦ full-width at half-maximum(see, e.g., Adler et al. 1972a,b); in practice, however, it proved out to bemore complicated (Adler et al. 1975).. Kuulkers et al.: Restless quiescence 9 c t s / s e c Apollo 15 − August 5, 1971 c t s / s e c >3 keV H a r dne ss Time (sec) >3 keV/1−3 keV
Fig. A.1.
Top and middle:
Light curves recorded by the X-rayFluorescence Spectrometer on-board
Apollo 15 in the 1–3 keV band andat > Bottom:
Hardness curvederived from the ratio of the count rates at > t = The burst event was observed in the 1–3 keV band, at > > > > ≃
50 s from start to peak) andexponential-like decay (decay time of ≃
100 s and ≃
25 s, respec-tively in the 1–3 keV band and at > t = > RXTE
All-SkyMonitor (ASM) show that the daily average flux of Sco X-1 is roughly 11–13 Crab (2–12 keV). The Apollo 15 burst event peakflux is thus indeed in the range observed for the flashes seen by
Vela 5B (Belian et al. 1972) and
Hakucho (Matsuoka et al. 1980).Although there were a couple of (currently) known flash sources(see, e.g., in ’t Zand et al. 2004) in the field of view of the X-ray Fluorescence Spectrometer at the time of the event, they areall known to not show flashes like that seen from Cen X-4, andcertainly not as bright.Cen X-4 was in quiescence around the time of the event (seeSect. 2). During the event itself
Vela 5B was operating, but didnot look at Cen X-4’s region. Prompted by the
Apollo 15 find-ings, we searched the
Vela 5B data base for similar flashes asseen in 1969 (see Sect. 2), but found none. Also the
RXTE / ASMdata base on Cen X-4 does not reveal any similar events abovethe level of about 0.5 Crab. It would be interesting to find out ifsimilar events exist in other databases, such as of
CGRO / BATSE.
A.2. Particleeventor not?
Energetic electron bursts at energies of keV to tens, or even hun-dredths, of keV (but below about 500 keV) are common aroundthe Earth’s magnetosphere. They occur especially in the Earth’smagnetotail in the anti-Sun direction, but also in the magne-tosheath which extends to ±∼ ◦ from the anti-Sun direction,and around the bow shock (to ±∼ ◦ from anti-Sun); see, e.g.,Sarris et al. (1976), Baker & Stone (1978), Meng et al. (1981).They arise during geomagnetic activity. If Apollo 15 was in theseregions then there is a likelihood of such a burst; either the space-craft passed through a static particle region or such a regionswept across the spacecraft.The position of the Sun and Moon on Aug 5, 1971, i.e., thelongitude φ and latitude λ in ecliptic coordinates were roughly φ , λ = ◦ ,0 ◦ and φ , λ = ◦ , − ◦ , respectively. The Earth-Moondistance was around 374307 km on that day. According to theApollo 15 Flight Journal the spacecraft was about 15200 kmfrom the Moon around the time of the Centaurus region obser-vations, so we may assume it was close to the position of theMoon. Apollo 15 was thus about 24 ◦ from the anti-Sun direc-tion, placing it near the boundaries of the Earth’s magnetotail.The Interplanetary magnetic field was southward on Aug 5,1971 , favouring geomagnetic activity and the production of en-ergetic particles in the Earth’s magnetosphere. This was particu-larly true for the first half day, from UT 00:00–12:00. However,the activity was not exceptional in any way, peaking from UT03:00–04:00 and gradually decaying the rest of the day. Furtherinspection also reveals a moderately strong geomagnetic sub-storm in progress at this time and a weak geomagnetic storm.If the burst event originated from increased geomagneticactivity, one would expect, however, to see more such events.Gorenstein et al. (1974) report that, apart from the 1971, Aug 5event, during a total about 20 hours of observing time of the X-ray Fluorescence Spectrometers onboard Apollo 15 and Apollo16, two other events of two minute durations were seen, as wellas one other event of longer duration. Also, as mentioned inSect. B.1, the X-ray flux was reported to be stable before andafter the event. This suggests that the Aug 5 burst event is arather isolated event. Moreover, a changing slope of the spec-trum of a particle burst in the magnetotail is not likely to pro-duce a dramatic change of spectral hardness, as observed in thisburst event. We, therefore, conclude that the Aug 5 burst eventhas most probably a celestial origin. See http://omniweb.gsfc.nasa.gov . See .0 E. Kuulkers et al.: Restless quiescence
List of Objects ‘Cen X-4’ on page 1‘Cen X-4’ on page 1‘Cen X-4’ on page 1‘1H 1905 + − − − − − + +
1’ on page 3‘Cen X-4’ on page 3‘Crab’ on page 3‘Crab’ on page 4‘Cen X-4’ on page 4‘SAX J1808.4 − − −
24’ on page 4‘Cen X-4’ on page 4‘Cen X-4’ on page 5‘2S 1711 − − − − − − − − − − − − − − − − − − − − − − −
29’ on page 6‘SAX J1808.4 − − − − −
29’ on page 6‘2S 1711 − − − − − − − − − − − −−