Drifts of the marginally stable burning frequency in the X-ray binaries 4U 1608--52 and Aql X--1
G. C. Mancuso, D. Altamirano, M. Méndez, M. Lyu, J. A. Combi
MMNRAS , 000–000 (0000) Preprint 3 February 2021 Compiled using MNRAS L A TEX style file v3.0
Drifts of the marginally stable burning frequency in theX-ray binaries 4U 1608–52 and Aql X–1
G. C. Mancuso, , (cid:63) D. Altamirano, M. M´endez, M. Lyu, and J. A. Combi , Instituto Argentino de Radioastronom´ıa (CCT-La Plata, CONICET; CICPBA), C.C. No. 5, 1894 Villa Elisa, Argentina Facultad de Ciencias Astron´omicas y Geof´ısicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina Physics & Astronomy, University of Southampton, Southampton, Hampshire SO17 1BJ, UK Kapteyn Astronomical Institute, University of Groningen, PO BOX 800, NL-9700 AV Groningen, the Netherlands Department of Physics, Xiangtan University, Xiangtan, Hunan 411105, China
ABSTRACT
We detect millihertz quasi-periodic oscillations (mHz QPOs) using the Rossi X-ray Time Explorer (RXTE) fromthe atoll neutron-star (NS) low-mass X-ray binaries 4U 1608–52 and Aql X–1. From the analysis of all RXTEobservations of 4U 1608–52 and Aql X–1, we find mHz QPOs with a significance level > σ in 49 and 47 observations,respectively. The QPO frequency is constrained between ∼ Key words: accretion, accretion discs − stars: neutron − X-rays: binaries.
Low-mass X-ray binaries (LMXBs) are systems harbouring acompact object, either a neutron star (NS) or a black hole,and a low-mass ( (cid:46) M (cid:12) ) donor star. The compact object ac-cretes material from the companion star through an accretiondisc (Pringle & Rees 1972; Shakura & Sunyaev 1973). TheseLMXBs can be always active, showing a persistent X-ray lu-minosity in the 10 − erg s − range, for years to decades,or transient, spending most of the time in a low luminos-ity or quiescence state ( L X (cid:46) erg s − ; see, e.g., Chenet al. 1997). This quiescence state is occasionally interruptedby outbursts when the X-ray luminosity increases by up toseveral orders of magnitude ( L X (cid:39) − erg s − ; see, e.g.,Lasota 2001 for a review).Bright NS LMXBs are divided into two subclasses, basedon their spectral and timing features: atoll sources, with lowluminosities ( (cid:46) L Edd ) and Z sources, with luminositiesnear (or even above) the Eddington limit (Hasinger & vander Klis 1989; Homan et al. 2010). Different spectral stateswere identified within each of these groups. In particular, themain states of the atoll sources are the extreme island, the (cid:63)
E-mail: [email protected] island, and the banana branches, a.k.a. hard, intermediate(or transitional), and soft states, respectively (e.g., van derKlis 2006 and reference therein).Many NS LMXBs show second to millisecond X-ray vari-ability in their light curves. This variability can be decom-posed into separate components in the Fourier power densityspectrum (e.g., van der Klis 1989). Depending on the charac-teristics, they are usually called broad-band noise (with fre-quencies <
100 Hz) and quasi-periodic oscillations (QPOs;see, e.g., van der Klis 2006 for a review). QPO appear ina power density spectrum as peaks of finite width which aregenerally well described by a Lorentzian (Belloni et al. 2002).The QPOs display a wide range of frequencies, from millihertz(mHz) to kilohertz (kHz, with frequencies in the 300 − ∼ ∼
15 mHz,and show properties that make them different from all otherQPOs seen in NSs: (i) their fractional rms amplitudes area few percent, increasing with energy from ∼ ∼ © a r X i v : . [ a s t r o - ph . H E ] F e b G. C. Mancuso et al. keV and then decreasing from ∼ ∼ L −
20 keV (cid:39) (0 . − . × erg s − ; and (iii) they are affected by the presence of a ther-monuclear (type I) X-ray burst, disappearing at the onsetof the burst (Revnivtsev et al. 2001; Altamirano et al. 2008;Mancuso et al. 2019; Lyu et al. 2020); furthermore, there isa strong correlation between the properties of these burstsand mHz QPOs (Lyu et al. 2016). Although they could notrule out an explanation due to disc instabilities, Revnivtsevet al. (2001) related the mHz QPOs with a special regime ofnuclear burning on the NS surface. This interpretation wasstrengthened by the findings of Yu & van der Klis (2002) whoreported an anti-correlation between the kHz QPO frequencyand the 2–5 keV X-ray count rate associated with a 7.5 mHzQPO in 4U 1608–52. This result is consistent with the innerdisc being pushed outward due to the increasing flux duringeach mHz QPO cycle.In addition to the six sources mentioned above, thereare two other sources with mHz QPOs, but whose featuresare different compared with those of the previous systems.On one hand, Linares et al. (2010) detected QPOs in themHz range from the NS and 11 Hz pulsar IGR J17480–2446(Strohmayer & Markwardt 2010). The mHz QPOs in thissource were found at a persistent luminosity L −
50 keV ∼ erg s − , i.e., roughly an order of magnitude higher than inthe other sources, and the QPO frequency was in the range2.8–4.5 mHz (Linares et al. 2010, 2012). Linares et al. (2012)also discovered that the thermonuclear X-ray bursts smoothlyevolved into mHz QPOs as accretion rate increased, and viceversa. This is a distinct behaviour compared with the above-mentioned six sources, where mHz QPOs and bursts can beseen within an observation. On the other hand, Ferrigno et al.(2017) reported an ∼ ∼ ≈
100 sec). They also found that the oscillations are onlyexpected in a small range of mass accretion rates, what ex-plains the narrow range of X-ray luminosities where the mHzQPOs are observed. Heger et al. (2007) proposed that thephysical mechanism behind this oscillatory mode of burningis the marginally stable nuclear burning of He on the surfaceof an NS. This mode of burning takes place near the bound-ary between the non-stable and stable burning, where thetemperature dependence of the nuclear heating and coolingrates almost cancel.Although Heger et al. (2007) simulations explain the maincharacteristics of the mHz QPOs, some discrepancies betweenobservations and models are still present. Whereas Heger et al. (2007) model predicts that the mHz QPOs should beseen at the transition from unstable to stable burning at prac-tically the Eddington mass accretion rate, ˙ M Edd , mHz QPOsare observed at ∼
10% ˙ M Edd . In order to explain this differ-ence, Heger et al. (2007) proposed that the accreting materialwould just cover a tenth of the NS surface, so that the localaccretion rate is of the order of the Eddington rate. This ex-planation was reinforced by the results of Lyu et al. (2016)who found that in 4U 1636–53 all the type I X-ray burststhat started immediately after mHz QPOs had positive con-vexities. This, in turn, is related with ignition site of burstsat the NS equator, where the mass accretion rate per unitarea might be higher compared with high latitudes. An al-ternative solution was given by Keek et al. (2009). Using ahydrodynamic stellar evolution code, the authors found thatthe mixing processes due to rotation (and rotationally in-duced magnetic fields) combined with a larger energy releasefrom the crust might explain the observed transition bound-ary. Keek et al. (2009) also showed that by lowering the heatflux from the crust, a decrease of the oscillation frequencyis seen followed by a flash. This showed that the frequencydrift could be the result of the cooling of deep layers as it wasproposed by Altamirano et al. (2008).Other major efforts have been made in order to furtherunderstand the physical mechanism that produces the mHzQPOs. Lyu et al. (2014, 2015, 2016) did not find any cor-relation between the persistent flux and frequency evolutionnor between the mHz QPO frequency and the temperatureof the NS surface in 4U 1636–53. This is at odds with theanti-correlation predicted theoretically (Heger et al. 2007).Moreover, Stiele et al. (2016) studied the phase-resolved en-ergy spectra of the mHz QPOs in 4U 1636–53 and found thatthe oscillations were consistent with changes in the size of theemission region and not with variations in the temperatureof the NS.From the six sources that exhibit mHz QPOs, there areonly reports of downward frequency drift in two of them,namely, 4U 1636–53 and EXO 0748–676. Strohmayer et al.(2018) analysed all the available observations of GS 1826–238 obtained with the Neutron Star Interior CompositionExplorer (NICER) and concluded that the observations weretoo short to measure potential drifts. They also studied allthe observations of GS 1826–238 taken with the Rossi X-rayTiming Explorer (RXTE), but the source was most of thetime in the hard state and no mHz QPOs were observed.4U 1323–619 is a dipper system (van der Klis et al. 1985;Parmar et al. 1989) so mHz QPOs can potentially be mim-icked by regular absorption (dipping) behaviour; therefore adetailed analysis of 4U 1323–619 will be presented elsewhere.In this work we analyse all the RXTE available observationsof the remaining two systems: 4U 1608–52 and Aql X–1.
4U 1608–52 is a transient LMXB discovered in 1972 (Belianet al. 1976; Grindlay & Gursky 1976; Tananbaum et al. 1976)that undergoes outbursts with a recurrence period rangingfrom ∼
85 d to (cid:39)
MNRAS , 000–000 (0000)
Hz QPO frequency drift in 4U 1608–52 and Aql X–1 at 619 Hz (Muno et al. 2001; Galloway et al. 2008). This fre-quency was associated with the spin period of the NS, making4U 1608–52 one of the most rapidly rotating accreting NSs(Galloway et al. 2008). Single bursts, multi-peak bursts (Pen-ninx et al. 1989; Galloway et al. 2008) and a superburst havebeen observed in this source (Keek et al. 2008).The distance to the source was constrained to the range (cid:39) i to the range (cid:39) o – 40 o .Based on the spectral and timing behaviour, Hasinger & vander Klis (1989) classified the system as an atoll source. Aquila X–1 (hereafter Aql X–1) is a transient LMXB discov-ered in 1965 by Friedman et al. (1967). Aql X–1 undergoesoutbursts quite regularly, with a recurrence time between ∼
125 and ∼
300 d (Priedhorsky & Terrell 1984; Kitamoto et al.1993; Campana et al. 2013). Koyama et al. (1981) detectedtype I X-ray bursts, concluding that the compact object inthis system is an NS. Similarly to 4U 1608–52, multi-peakedbursts (Galloway et al. 2008), as well as a superburst (Serinoet al. 2016) have been observed from Aql X–1.Using type I X-ray bursts, Jonker & Nelemans (2004) es-timated a distance to this system of 4.5–6 kpc, while MataS´anchez et al. (2017) derived a distance of d = 6 ± ∼ o – 47 o (Mata S´anchezet al. 2017, but also see Galloway et al. 2016). Reig et al.(2000, 2004) studied the colour, spectral and timing proper-ties of Aql X–1, and classified the system as an atoll-typesource (Hasinger & van der Klis 1989). Casella et al. (2008)detected coherent millisecond X-ray pulsations in the persis-tent X-ray emission at a frequency of 550.27 Hz for (cid:38) We analysed all public archival observations of both 4U 1608–52 and Aql X–1 taken with the Proportional Counter Array(PCA; Jahoda et al. 2006) onboard the Rossi X-ray TimingExplorer (RXTE) satellite. We used a total of 1134 and 603pointed observations of 4U 1608–52 and Aql X–1, respec-tively, sampling the period comprised between 1996 Marchand 2011 December. An observation covers one to multipleconsecutive RXTE data segments of different lengths sep-arated by data gaps of at least ∼ ∼ ∼ ≈ ≈ > σ . To calculate the 3 σ level, we fol-lowed Press et al. (1992) which assumes white noise and takesas number of trials the number of frequencies searched. Totest our assumption on the white noise, we followed Vaughan(2005) and fitted a power law to the LSP excluding the QPO.The powerlaw index was consistent with white noise. This isas expected given that the red-noise found in some NS spec-tral states is the strongest at higher energies than the onewe used to search for the mHz QPOs (see, e.g., van der Klis2006). For the number of trials, we took the number of fre-quencies searched in each LSP (which changes as it is depen-dent on the length of the data-segment; in our case between500 and 5,000 seconds) so as to take into account the factQPOs could be detected in a wider range of frequencies. Wedetermined the exact mHz QPO frequency, ν QPO , fitting asinusoidal function to the 1 sec light curve.We constructed hardness-intensity and colour-colour di-agrams (CCD) of both sources, using the 16-sec time-resolution Standard-2 mode data following the approach de-scribed in Altamirano et al. (2005). In particular, to excludethe X-ray bursts, we removed the data from 10 seconds beforeto 100 seconds after the onset of each burst. We computedthe soft colour as the ratio between the count rates in the 3.5-6.0 keV and 2.0-3.5 keV bands, and the hard colour as theratio in the 9.7-16.0 keV and 6.0-9.7 keV bands. We definedthe intensity as the 2.0-16.0 keV count rate. We normalisedall the quantities to those of the Crab in the same energyranges. Given that both sources transitioned from outburstto quiescence several times, we discarded those observationswhere the intensity was lower than 5 mCrab.
We detected mHz QPOs in 58 and 57 data segments (in someoccasions, the QPO was not present along a whole data seg-ment), in a total of 49 and 47 observations, in 4U 1608–52and Aql X–1, respectively. In 4U 1608–52, the mHz QPOfrequency was between ∼ ∼ In a total of 13 segments (9 of 4U 1608–52 and 4 of Aql X–1),the significance was ∼ σ . In order to test whether these detectionswere significant, we created light curves using the channels 0–8 andcomputed the LSP again. We found that the significance increasedwith respect to the value obtained using the channels 0–10, andtherefore kept all these segments. MNRAS , 000–000 (0000) G. C. Mancuso et al. H a r d C o l ou r ( C r ab )
4U 1608-52 (RXTE/PCA)mHz QPOmHz QPO with drift
Soft Colour (Crab)
Aql X-1 (RXTE/PCA)mHz QPOmHz QPO with evidence of drift
Figure 1.
Colour-colour diagrams (CCDs) of all RXTE observations of 4U 1608–52 (left) and Aql X–1 (right). Each open grey circlecorresponds to the averaged colour of the source per RXTE observation, normalised to the colours of the Crab. To calculate the colours,type I X-ray bursts have been removed. Filled red circles mark the location of the source in the CCD when the mHz QPOs were found.Filled blue squares indicate those cases where we found the mHz QPOs and we observed a frequency drift. filled red circles in Fig. 1). In a few cases, we observed the os-cillations with harder colours, sampling the island state (IS).In each source we found one case when the mHz QPOs weredetected at hard colour > .
8, significantly harder coloursthan for all other observations with mHz QPOs. In Figs. 4 &5 we show the light curves of those two observations. Whilein the case of 4U 1608–52 (Fig. 4) the mHz QPOs are not asclear as those seen in Figs. 2 & 3 (even if significant underour assumptions; see Section 2), the mHz QPOs in Aql X–1(Fig. 5) can clearly be seen in the light curve.We found that the mHz QPOs disappeared at the time ofthe occurrence of a type I X-ray burst in 3 cases, 2 in 4U 1608–52 and 1 in Aql X–1. One of our 4U 1608–52 cases was previ-ously reported by Revnivtsev et al. (2001). The other case inthis source corresponds to a later observation (obsID 70059-03-01-000; 2002 September). Revnivtsev et al. (2001) alsoreported a QPO peak at 6–7 mHz that disappeared after theonset of a type I X-ray burst in Aql X–1. However, we couldnot confirm this finding given that the significance of the pos-sible QPO was below the 3 σ level. In those cases in which wedetected the mHz oscillations before the burst, but not afterit, we found an average rms of ∼ σ upper limitof less than ∼ (cid:38) < All data subsets where we detected mHz oscillations havelengths of at most ∼ ∼ ∼ ν =11 . ± .
03 mHz and at the end of it was ν = 8 . ± .
02 mHz.The observation lasted ∼ ∼ .
97 mHz ksec − . Another case is thatof obsID 30062-02-01-01 (3 data segments). In this case, wetook 1100 sec at the beginning of the first data segment and1400 sec at the end of the third data segment. The frequencyof the oscillations decreased from ν = 10 . ± .
04 mHz inthe first segment down to ν = 6 . ± .
03 mHz in the secondone (see Fig. 3). Assuming that the mHz QPOs were presentduring the data gaps, the drift lasted for about 13.4 ksec,giving an average rate of ∼ − . Figs. 2 and 3suggest a correlation between the QPO frequency and the av-erage count rate. However, we note that Fig. 3 data leads toa high-scattered correlation (the average intensity decreasesand increases while the frequency decreases or remains con-stant; see Fig. 3). Given that we only have two cases where MNRAS , 000–000 (0000)
Hz QPO frequency drift in 4U 1608–52 and Aql X–1 we observe this potential correlation, we do not discuss it fur-ther (see, e.g., Altamirano et al. 2008; these authors foundthat for 4U 1636–53 the frequency of the mHz QPO is notalways correlated to the intensity). In the last case (obsID95334-01-04-00), we fitted the same sinusoidal function tothe first 750 sec and to the last 1000 sec of the observation.The QPO frequency dropped from ν = 13 . ± .
08 mHz to ν = 10 . ± .
03 mHz within ∼ ∼ − . In all these cases, 4U 1608–52 was in thelower part of the IS, close to the BB (see filled blue squaresin Fig. 1, left). We also found evidence of a downward fre-quency drift in other 4 cases (group 2). In all these cases, theinitial frequency of the QPO was below 9 mHz and decreasedby (cid:46) ∼ (cid:46) ≈ ∼ In Aql X–1 we only found one case with a significant evidenceof a downward frequency drift. In this observation (obsID92034-01-03-00), the frequency of the oscillations was ν =9 . ± .
15 mHz in the first 1000 sec, and decreased to ν =6 . ± .
11 mHz in the last 1000 sec. The mHz QPO frequencydrifted at an average rate of ∼ − through the ∼ ∼ ∼ ∼ <
500 1000 1500 2000 2500 3000
Time [sec] F r e q u e n c y [ H z ]
70 80 90 100 110 120 0 500 1000 1500 2000 2500 3000 3500 R X T E c t s / s e c / P CU ( - k e V ) TIME (seconds)
Figure 2.
Top:
Dynamical power spectrum (DPS) of the secondorbit of the RXTE observation 95334-01-03-06 of 4U 1608–52. Toconstruct the plot, we used a 600-s window sliding with a step of50 s. The DPS shows that the mHz QPO frequency drifts from ∼
12 mHz down to ∼ > σ ) second harmonic is visible. Bottom:
RXTE/PCAbackground subtracted light curve ( ≈ ∼ also observed in 4U 1636–53 (Altamirano et al. 2008; Lyuet al. 2015). We used nearly 16 years of RXTE archival data to performthe first systematic search and characterisation of the mHzQPOs in the NS LMXBs 4U 1608–52 and Aql X–1. We de-tected the QPO in the ∼ MNRAS , 000–000 (0000)
G. C. Mancuso et al.
Time [ksec] F r e q u e n c y [ H z ]
120 125 130 135 140 145 150 0 1 2 3 R X T E c oun t r a t e ( c oun t s / s e c / P CU )
6 7 8 9
Time since start of observation (ksec)
12 13 typical error
Figure 3.
Top:
Dynamical power spectrum (DPS) of the RXTEobservation 30062-02-01-01 of 4U 1608–52. To construct the plot,we used a 700-s window sliding with a step of 50 s. The DPS showsthat the mHz QPO frequency drifts from ∼ ∼ Bottom:
RXTE/PCA background subtracted light curve( ≈ ∼ inally discovered by Revnivtsev et al. (2001). Therefore, as-suming that the current interpretation of (marginally stable)nuclear burning is correct, then the mHz QPOs observed in4U 1608–52 and Aql X–1 are the result of He burning on theNS surface (e.g., Heger et al. 2007; Keek et al. 2009).Up to now, only two sources had shown a decrease of theQPO frequency with time (Altamirano et al. 2008; Mancusoet al. 2019). Altamirano et al. (2008) found a systematic fre-quency drift of the QPOs in 4U 1636–53 at an average ratebetween 0.07 and 0.15 mHz ksec − . The average rate of de-creasing measured by Mancuso et al. (2019) in EXO 0748–676was of 0.26 and 0.56 mHz ksec − in two separate occasions. Inour three instances of frequency drift detected in 4U 1608–52,we estimated a decrease at an average rate of ∼ ∼ ∼ − . In particular, these last two values arethe fastest average rate measured for a frequency drift. How-ever, we note that these average rates depend on the lengthof the observations. If we take as an example the observationshown in Fig. 3, we would have measured different frequencydrifts if we had only used one or two of the 3 data segments(e.g., no drift if we had used the 3rd data segment). The factthat the observation was long enough while the mHz QPOswere drifting made possible to estimate an average rate. In In 4U 1636–53, EXO 0748–676 and 4U 1608–52, the average ratewas calculated, when needed, interpolating through data gaps.
45 50 55 60 65 0 200 400 600 800 1000 1200 1400 R X T E c t s / s e c / P CU ( - k e V ) TIME (seconds)
4U 1608-52 (RXTE/PCA)
Figure 4.
Background-subtracted 16 s binned light curve ( ≈ the same way, faster rates within a data segment might haveoccurred in any of the sources where the drift has been ob-served.We also found that the highest values of the rate corre-spond to those two observations with the hardest colours.Although this is a result based on only three cases, it sup-ports the suggestion by Mancuso et al. (2019) that the rateat which the frequency drops decreases as the source becomessofter.In the case of Aql X–1, we only found one observation withstrong evidence of a downward in the mHz QPO frequency.We calculated an average drift rate of ∼ − ,consistent to one of the 4U 1608–52 cases, and higher thanthose reported in the previous sources. Although the down-ward drift is significant and the source is in the intermedi-ate state (as expected based on the results on 4U 1636–53,4U 1608–52 and EXO 0748–676), we consider this case only asa strong evidence as the QPO has been seen to vary stochas-tically when the average frequency is below 9 mHz (e.g., thiswork and Altamirano et al. 2008).It is possible that the reason we did not detect more signif-icant downward frequency drifts in Aql X–1 is that we wereunlucky with the observational sampling of Aql X–1 interme-diate states. However, the explanation is probably related tothe length of the data segments: RXTE monitored Aql X–1many times with single-orbit snapshots per day, most of themwith integration times lower than 2.0 ksec (and only few withintegration times as long as ∼ . In atoll sources, the position of a system in the CCD canbe parametrised by the length, S a , of the curve along thepath traced by the source in that diagram (see, e.g., Fig. 1in M´endez et al. 1999). This length is commonly normalised,taking the value S a = 1 at the top right-hand vertex, and S a = 2 at the bottom left-hand vertex of the CCD. M´endezet al. (1999) found that in 4U 1608–52 the kHz QPO fre-quency increased while the system moved from the island tothe banana state. The fact that the kHz QPO frequency and S a were well correlated, while there was no single correlation MNRAS , 000–000 (0000)
Hz QPO frequency drift in 4U 1608–52 and Aql X–1
35 40 45 50 55 0 200 400 600 800 1000 1200 1400 1600 1800 R X T E c t s / s e c / P CU ( - k e V ) TIME (seconds)
Aql X-1 (RXTE/PCA)
Figure 5.
Background-subtracted 16 s binned light curve ( ≈ between the frequency and the count rate when the sourcewas observed at different luminosities, led the authors to sug-gest that S a is a good proxy for ˙ M (see also Hasinger & vander Klis 1989).Altamirano et al. (2008) found that, in 4U 1636–53, allthe mHz oscillations occurred when the system was in eitherthe BB, or in the transition between this state and the IS.We find something similar in both 4U 1608–52 and Aql X–1.However, we also found two cases (one per source, see Figs.4 & 5), in which mHz QPOs are detected in the upper partof the IS, i.e., at lower values of S a . If we assume that therelation between S a and the mass accretion rate is correct(see, e.g., Hasinger & van der Klis 1989; M´endez et al. 1999;Zhang et al. 2011), then our results show that the marginallystable burning occurs in a larger range of mass accretion ratethan models predict (e.g., Heger et al. 2007). In fact, for4U 1608–52, and assuming a distance of 3.7 kpc, we foundthat the luminosity when the source was in the upper part ofthe IS was ∼ . × erg s − in the 3–20 keV energy range,i.e., an order of magnitude lower than the highest luminosityobserved by Revnivtsev et al. (2001). We note that if Hegeret al. (2007) model is correct, then our results would indicatethat the local accretion rate onto the NS is always close tothe Eddington limit, even if we see significant changes in thesource spectra (parametrised by the position in the CCD)and average X-ray luminosity. Altamirano et al. (2008) discovered that, when 4U 1636–53was near to the transition between the IS and the BB, themHz QPO frequency decreased systematically with time (seealso Lyu et al. 2014, 2015), and once it dropped below 9mHz, an X-ray burst took place within a few kiloseconds af-terwards. The case of EXO 0748–676 is similar, as Mancusoet al. (2019) found two instances of frequency drift, in an areaof the CCD that the authors identified as close to the inter-mediate state. We found a similar result in 4U 1608–52: the This is similar to what it was found by Mancuso et al. (2019) inEXO 0748–676; see their Fig. 2; however we note that EXO 0748–676 colours are affected by the high inclination of the system. three cases where we found significant downward frequencydrift occurred at a time when the source was near the tran-sition between the soft and hard states. The fact that thesefrequency drifts are detected roughly in the same part of theCCD independently of the source (4U 1636–56, EXO 0748–676, and 4U 1608–52; our Aql X–1 results are still consistentwith this picture) strongly suggests a relation between thesource state (which is likely set by the mass accretion rate)and the expected QPO frequency evolution.Keek et al. (2009) showed that the QPO frequency de-creases with time if the heat flux from the crust decreases,i.e., the drift could be the result of the cooling of deep layers.However, Keek et al. (2009) did not discuss why the cool-ing of the deep layers could change depending on the sourcestate. We speculate that the change of behaviour might berelated to the change in accretion rate. Assuming that theaccretion rate is an increasing function of the parameter S a (see above), as the source changes its spectral state, from theIS to the BB, the mass accretion rate increases, as well as theluminosity. This implies, in turn, an increase of the tempera-ture of the layer where the burning takes place. Consequently,this increasing in the temperature balances the cooling of thedeeper layers, until it becomes high enough to compensatecompletely the cooling, and therefore no drift would occur atall. We speculate that this would happen near the bottomleft-hand vertex of the CCD, i.e., at a mass accretion ratecompatible with S a (cid:39) ∼
13 mHz in one of theircases. In 4U 1608–52, we detected a similar result: an initialfrequency above 9 mHz, between 10.2 and 13.4 mHz. Ourfindings, combined with the previous ones, suggest that theonset of the QPOs that show a downward drift is at a fre-quency (cid:38)
10 mHz. Moreover, given the relatively wide rangeof initial QPO frequency and the different hard-colour valueswhere the downward frequency drift was observed, a relationbetween the initial mHz QPO frequency drift and the spectralstate cannot be excluded.
Previous works showed that mHz QPOs with systematicfrequency drifts occur in the NS LMXBs 4U 1636–53 andEXO 0748–676. Here we discovered a significant drift of thefrequency of the mHz QPOs in 4U 1608–52, and strong evi-dence of such drift in the mHz QPOs observed in Aql X–1.Our results are consistent with previous findings in other sys-tems, and strongly suggest that the mHz QPOs can undergodownwards frequency drifts if they are observed when thesystems in which they occur is in the intermediate spectralstate.
DATA AVAILABILITY
The data underlying this article are publicly available inthe High Energy Astrophysics Science Archive Research In the another case, the authors began to observe the QPO fre-quency at ∼ , 000–000 (0000) G. C. Mancuso et al.
Center (HEASARC) at https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3browse.pl . ACKNOWLEDGMENTS
GCM acknowledges support from the Royal Society Inter-national Exchanges “the first step for High-Energy Astro-physics relations between Argentina and the UK”. DA ac-knowledges support from the Royal Society. JAC and GCMwere partially supported by PIP 0102 (CONICET). Thiswork received financial support from PICT-2017-2865 (AN-PCyT). Lyu is supported by National Natural Science Foun-dation of China (grant No.11803025), and Hunan Provin-cial Natural Science Foundation (grant No. 2018JJ3483).JAC was also supported by grant PID2019-105510GB-C32/AEI/10.13039/501100011033 from the Agencia Estatalde Investigaci´on of the Spanish Ministerio de Ciencia, In-novaci´on y Universidades, and by Consejer´ıa de Econom´ıa,Innovaci´on, Ciencia y Empleo of Junta de Andaluc´ıa as re-search group FQM-322, as well as FEDER funds. This re-search has made use of data and/or software provided by theHigh Energy Astrophysics Science Archive Research Center(HEASARC), which is a service of the Astrophysics ScienceDivision at NASA/GSFC and the High Energy AstrophysicsDivision of the Smithsonian Astrophysical Observatory. Thisresearch has made use of NASA’s Astrophysics Data System.
REFERENCES
Altamirano D., van der Klis M., M´endez M., Migliari S., JonkerP. G., Tiengo A., Zhang W., 2005, ApJ, 633, 358Altamirano D., van der Klis M., Wijnands R., Cumming A., 2008,ApJ, 673, L35Belian R. D., Conner J. P., Evans W. D., 1976, ApJ, 206, L135Belloni T., Psaltis D., van der Klis M., 2002, ApJ, 572, 392Campana S., Coti Zelati F., D’Avanzo P., 2013, MNRAS, 432, 1695Casella P., Altamirano D., Patruno A., Wijnands R., van der KlisM., 2008, ApJ, 674, L41Chen W., Shrader C. R., Livio M., 1997, ApJ, 491, 312Chevalier C., Ilovaisky S. A., 1991, A&A, 251, L11Degenaar N., Miller J. M., Chakrabarty D., Harrison F. A., KaraE., Fabian A. C., 2015, MNRAS, 451, L85Ferrigno C., et al., 2017, MNRAS, 466, 3450Friedman H., Byram E. T., Chubb T. A., 1967, Science, 156, 374Galloway D. K., Muno M. P., Hartman J. M., Psaltis D.,Chakrabarty D., 2008, ApJS, 179, 360Galloway D. K., Ajamyan A. N., Upjohn J., Stuart M., 2016, MN-RAS, 461, 3847Grindlay J., Gursky H., 1976, ApJ, 209, L61G¨uver T., ¨Ozel F., Cabrera-Lavers A., Wroblewski P., 2010, ApJ,712, 964Hasinger G., van der Klis M., 1989, A&A, 225, 79Heger A., Cumming A., Woosley S. E., 2007, ApJ, 665, 1311Homan J., et al., 2010, ApJ, 719, 201Jahoda K., Markwardt C. B., Radeva Y., Rots A. H., Stark M. J.,Swank J. H., Strohmayer T. E., Zhang W., 2006, ApJS, 163,401Jonker P. G., Nelemans G., 2004, MNRAS, 354, 355Keek L., in’t Zand J. J. M., Kuulkers E., Cumming A., BrownE. F., Suzuki M., 2008, A&A, 479, 177Keek L., Langer N., in’t Zand J. J. M., 2009, A&A, 502, 871Kitamoto S., Tsunemi H., Miyamoto S., Roussel-Dupre D., 1993,ApJ, 403, 315Koyama K., et al., 1981, ApJ, 247, L27Lasota J.-P., 2001, New Astron. Rev., 45, 449 Linares M., et al., 2010, The Astronomer’s Telegram, 2958Linares M., Altamirano D., Chakrabarty D., Cumming A., KeekL., 2012, ApJ, 748, 82Lochner J. C., Roussel-Dupre D., 1994, ApJ, 435, 840Lomb N. R., 1976, Ap&SS, 39, 447Lyu M., M´endez M., Altamirano D., 2014, MNRAS, 445, 3659Lyu M., M´endez M., Zhang G., Keek L., 2015, MNRAS, 454, 541Lyu M., M´endez M., Altamirano D., Zhang G., 2016, MNRAS,463, 2358Lyu M., Zhang G., M´endez M., Altamirano D., Mancuso G. C.,Xiang F.-Y., Xiao H., 2020, ApJ, 895, 120Mancuso G. C., Altamirano D., Garc´ıa F., Lyu M., M´endez M.,Combi J. A., D´ıaz-Trigo M., in’t Zand J. J. M., 2019, MNRAS,486, L74Mata S´anchez D., Mu˜noz-Darias T., Casares J., Jim´enez-Ibarra F.,2017, MNRAS, 464, L41M´endez M., van der Klis M., Ford E. C., Wijnands R., van ParadijsJ., 1999, ApJ, 511, L49Muno M. P., Chakrabarty D., Galloway D. K., Savov P., 2001,ApJ, 553, L157Paczynski B., 1983, ApJ, 264, 282Parmar A. N., Gottwald M., van der Klis M., van Paradijs J., 1989,ApJ, 338, 1024Penninx W., Damen E., Tan J., Lewin W. H. G., van Paradijs J.,1989, Astronomy and Astrophysics, 208, 146Poutanen J., N¨attil¨a J., Kajava J. J. E., Latvala O.-M., GallowayD. K., Kuulkers E., Suleimanov V. F., 2014, MNRAS, 442,3777Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P.,1992, Numerical recipes in FORTRAN. The art of scientificcomputingPriedhorsky W. C., Terrell J., 1984, ApJ, 280, 661Pringle J. E., Rees M. J., 1972, A&A, 21, 1Reig P., M´endez M., van der Klis M., Ford E. C., 2000, ApJ, 530,916Reig P., van Straaten S., van der Klis M., 2004, ApJ, 602, 918Revnivtsev M., Churazov E., Gilfanov M., Sunyaev R., 2001, A&A,372, 138Scargle J. D., 1982, ApJ, 263, 835Serino M., Iwakiri W., Tamagawa T., Sakamoto T., Nakahira S.,Matsuoka M., Yamaoka K., Negoro H., 2016, Publications ofthe Astronomical Society of Japan, 68, 95Shakura N. I., Sunyaev R. A., 1973, A&A, 500, 33Stiele H., Yu W., Kong A. K. H., 2016, ApJ, 831, 34Strohmayer T. E., Markwardt C. B., 2010, The Astronomer’s Tele-gram, 2929, 1Strohmayer T. E., Smith E. A., 2011, The Astronomer’s Telegram,3258Strohmayer T. E., et al., 2018, ApJ, 865, 63Tananbaum H., Chaisson L. J., Forman W., Jones C., MatilskyT. A., 1976, ApJ, 209, L125Vaughan S., 2005, A&A, 431, 391Wachter S., Hoard D. W., Bailyn C. D., Corbel S., Kaaret P., 2002,ApJ, 568, 901Welsh W. F., Robinson E. L., Young P., 2000, AJ, 120, 943Yu W., van der Klis M., 2002, ApJ, 567, L67Zhang W., Jahoda K., Kelley R. L., Strohmayer T. E., Swank J. H.,Zhang S. N., 1998, ApJ, 495, L9Zhang G., M´endez M., Altamirano D., 2011, MNRAS, 413, 1913ˇSimon V., 2004, A&A, 418, 617van der Klis M., 1989, in ¨Ogelman H., van den Heuvel E. P. J.,eds, NATO Advanced Science Institutes (ASI) Series C Vol.262, NATO Advanced Science Institutes (ASI) Series C. p. 27van der Klis M., 2006, Rapid X-ray Variability. pp 39–112van der Klis M., Jansen F., van Paradijs J., Stollman G., 1985,Space Sci. Rev., 40, 287MNRAS000