Decades-long variations in NS-LMXBs observed with MAXI/GSC, RXTE/ASM, and Ginga/ASM

Abstract

We investigate the decades-long X-ray variations in bright low-mass X-ray binaries containing a neutron star (NS-LMXBs). The light curves of MAXI/GSC and RXTE/ASM cover ∼26 yr, and high-quality X-ray light curves are obtained from 33 NS-LMXBs. Among these, together with Ginga/ASM, two sources (GX 3+1 and GX 9+1) showed an apparent sinusoidal variation with respective periods of ∼5 and ∼10 yr in the 34 yr light curve. Their X-ray luminosities were (1–4) × 10³⁷ erg s⁻¹ in the middle of the NS-LMXB luminosity distribution. Seven other sources (Ser X-1, 4U 1735−444, GX 9+9, 4U 1746−37, 4U 1708−40, 4U 1822−000, and 1A 1246−588) have similar sinusoidal variations, although the profiles (amplitude, period, and phase) are variable. Compering the 21 sources with known orbital periods, one possible cause of the long-term sinusoidal variation might be mass-transfer cycles induced by irradiation to the donor star.

1 Introduction

Many bright X-ray sources are low-mass X-ray binaries with a weakly magnetized neutron star (NS-LMXBs; see Barret 2001 for a review). Based on the temporal activity, NS-LMXBs are divided into two types: persistent and transient. Furthermore, many persistent NS-LMXBs and bright phases of transient NS-LMXBs are divided into two groups, Z sources and Atoll sources, based on their behavior on the color–color diagram and the hardness–intensity diagram (Hasinger & van der Klis 1989). Z sources are very bright, and the luminosities sometimes become close to the Eddington luminosity (L_E). On the other hand, Atoll sources are generally less bright (⁠|$\lesssim\! 0.5 L_{\rm E}$|⁠).

The orbital periods of NS-LMXBs range from minutes to ∼20 d (Liu et al. 2007). Moreover, long-term variations on the timescale beyond the orbital period are known. These super-orbital periods range from tens to hundreds of days and are thought to be related to the properties of the accretion disk, such as radiation-induced warping and precession (see Charles et al. 2008 for a review). On the other hand, several NS-LMXBs display very long-term quasi-periodic modulations (approximately several to tens of years). The variations are thought to have a different origin. Kotze and Charles (2010) (hereafter KC10) suggest that the long-term variations are due to the variation of the mass-transfer rate from the donor, which is a consequence of solar-like magnetic cycles (Applegate & Patterson 1987; Warner 1988). Solar-like cycles of ∼10 yr are observed from many late-type stars (Baliunas et al. 1995).

The importance of irradiation in NS-LMXBs for the outburst properties and their long-term evolution has been pointed out (Ritter 2008). The former is relevant to irradiating the accretion disk. Irradiation during an outburst leads to drastic changes in the outburst properties because the irradiation changes the conditions for the occurrence of disk instabilities. The latter is relevant to the irradiating donor star. The irradiation of the donor star can destabilize mass transfer and lead to irradiation-driven mass-transfer cycles, i.e., to a secular evolution. However, it is not easy to estimate the effect of irradiation on secular evolution because of several unclear factors.

GX 3+1 shows a long-term variation on a timescale of years superimposed with a short-term variations on a timescale of hours (Seifina & Titarchuk 2012). The short-term variations are due to transitions between branches in terms of its color–color diagram, which are independent of the long-term variation. The spectral index is constant during the long-term variations.

In this paper, we focus on the sinusoidal variation and report the analysis of long-term variations during 1996–2021 for 41 NS-LMXBs. In section 2, we present the details of the X-ray light-curve analysis. We show the results in section 3. We discuss the cause of the sinusoidal variation in section 4.

2 Observations and data analysis

The long-term X-ray activity has been continuously monitored with MAXI (Monitor of All-sky X-ray Image: Matsuoka et al. 2009) since 2009 August. We obtained long-term one-day bin light curves of MAXI/GSC (Gas Slit Camera: Mihara et al. 2011; Sugizaki et al. 2011)¹ for 41 NS-LMXBs from 2009 August to 2021 December. We also analyzed the data for the same sources observed with the ASM (All Sky Monitor: Levine et al. 1996) on board RXTE (Rossi X-ray Timing Explorer: Bradt et al. 1993) in the 2–10 keV band from 1996 February to 2011 December. The ASM data are obtained from the archived results provided by the RXTE/ASM teams at MIT and NASA/GSFC.²

The obtained count rates of GSC and ASM were converted to luminosities by assuming a Crab-like spectrum (Kirsch et al. 2005) and the distance listed in table 1. ASM data are converted to a flux in Crab units using the nominal relation of 1 Crab = 75 counts s⁻¹ for ASM.³ GSC data are converted to a flux in Crab units using the nominal relation of 1 Crab = 3.45 photons s⁻¹ cm⁻² in the 2–10 keV band for GSC.⁴ The assumption of a Crab-like spectrum is acceptable in the hard state (low luminosity ≤5 × 10³⁶ erg s⁻¹) because the energy spectrum is approximated by a power law with a photon index of 1–2. On the other hand, in the soft state (high luminosity ≥10³⁷ erg s⁻¹), the energy spectrum is dominated by the thermal emission, and the luminosity obtained by assuming a Crab-like spectrum is underestimated in the 2–10 keV band (Asai et al. 2015). In this paper, we do not concern ourselves with this because we handle only the relative difference.

We excluded the following data in each source:

GX 3+1: Data for MJD = 56187–56287 and 56652–56997 for contamination by Swift J174510.8−262411. Data for MJD = 55916–55922 for another south-west source.

SLX 1735−269: Data for MJD = 56187–56287 and 56652–56997 for contamination by Swift J174510.8−262411.

4U 1624−490: Data for MJD = 58460–58580 for contamination by MAXI J1631−479.

4U 1708−40: Data for the count rate above 1 photons cm⁻² s⁻¹ by solar X-ray leakage.

4U 1916−053: Data for MJD = 55945–55951 and MJD = 56311–56315 by solar X-ray leakage.

4U 1323−619: Data for MJD = 58509–58610 for contamination by MAXI J1348−630.

Ser X-1: Data with errors above 0.012 Crab in the 2–10 keV band.

We analyzed the ASM and GSC data for the 41 NS-LMXBs and investigated the long-term variability over ∼26 yr (see table 1). The X-ray light curves are shown in the Appendix. Here we have used GSC data for the overlapping period of MJD = 55100–55800. Table 1 shows the flux ratio of ASM and GSC during the overlapping period.

We estimated the luminosity in the 2–10 keV energy band from MJD = 55100 to MJD = 59662 for the 41 NS-LMXBs using GSC data and listed it in L_ave. High-quality persistent light curves are obtained from 33 sources. The remaining eight sources are excluded from the following analyses. Six of the excluded eight sources are transient sources. The active period of HETE J1900.1−2455 is too short (≤10 yr) to investigate the long-term variability. Other sources (EXO 1745−248, Aql X-1, XTE J1709-267, 4U 1608−522, and 4U 1745−203) are below the GSC detection limit during quiescence. The two other excluded sources, SAX J1747.0−2853 and 4U 1724−307, have contamination from nearby sources.

KC10 indicated that all the 20 sources in their paper were considered to be better fitted with a single sine wave than with a constant value. We also focus on the properties of the sinusoidal variation. Here, we have tried to classify the observed variations into five types as follows. The types are described in the comment column of table 1.

CP (clear periodic variation): Two bright Atoll sources (GX 3+1 and GX 9+1) show clear sinusoidal variations. We define CP sources as those that can be fitted with a single sinusoidal curve and a tilted line. We focus on these sources in the next section.

MP (modified periodic variation): Seven sources (Ser X-1, 4U 1735−444, GX 9+9, 4U 1746−37, 4U 1708−40, 4U 1822−000, and 1A 1246−588) show modified periodic variation. It is difficult to fit their light curves with the periodic model functions. We also focus on these sources in the next section.

NP (no periodic variation): 19 sources show no periodic variation. Eight (Z sources and GX 13+1) of them show almost constant baselines although there are small variations around the baseline. Another eight (X-ray luminosities ≲ 3 × 10³⁷ erg s⁻¹) are almost constant. The remaining three sources (4U 1543−624, 4U1916−053, and 1H 1556−605) show a decreasing trend in luminosity.

FV (fast variation): Two sources (4U1820−303 and 4U1705−440) show a luminosity change with a shorter variability than 1 yr. The variation seems to have a different origin from that of the sinusoidal variation investigated in this paper.

LV (large variation): Three sources (Cir X-1, 4U 1636−536, and GS 1826−238) show a large luminosity change of one to two orders of magnitude. Again, the large luminosity change seems to have a different origin from that of the sinusoidal variation investigated in this paper.

Figure 1a shows the average luminosity against the binary separation for 21 sources. Of the 33 sources, the orbital periods of 21 are known. The binary separation was estimated by Kepler’s third law assuming a neutron star mass of 1.4 |$M_{\odot}$| and a donor-star mass of 0.5 |$M_{\odot}$|⁠, although their actual masses are uncertain. We also display the types in the figure. In particular, filled marks indicate periodic variation, which is relevant to the long-term variation investigated in this paper.

Figure 1b shows the irradiating flux on the donor star against the binary separation. Here we have treated the donor star as a point source and simply calculated the irradiation flux F = L/4πd², where L and d denote the average luminosity and the binary separation, respectively.

Next, we discuss CP and MP sources with periodic and modified periodic variations. To confirm the property of variation, we also analyzed archive data from the X-ray All Sky Monitor (ASM: Tsunemi et al. 1989) on board the Ginga satellite (Makino & ASTRO-C Team 1987). The Ginga/ASM data from 1987 to 1991 are obtained from the archived site of DARTS.⁵ The 1–6 keV counts s⁻¹ are converted to the 2–10 keV flux assuming the spectrum of the Crab nebula. For 1A1246−588 (MP), there were no data from Ginga/ASM.

3 Results

Figure 2 shows the light curves of two CP sources (GX 3+1 and GX 9+1) with an apparent sinusoidal variation from 1987 to 2021. First, we fitted the light curves of GX 3+1 and GX 9+1 with a sinusoidal and linear function model. The fitting parameters are shown in table 2.

Next, in order to investigate the variability of the sinusoidal profile of two CP soures and seven MP sources, we fit each peak with a Gaussian profile (figures 3 and 4). The parameters are the width (sigma) of the Gaussian profile (GW) and the peak luminosity (GN). These correspond to the period and amplitude of the sinusoidal variation, respectively. In order to see the variability of the peak luminosity and width, we plotted the GN against the GW in figure 5. The amplitudes and periods of two CP sources (GX 3+1 and GX 9+9) are more stable than those of MP sources. The average GWs for each source are ∼300–2300 d, which correspond approximately to a half-sinusoidal period of GX 3+1 (∼2.5 yr) and a period of GX 9+1 (∼10 yr), respectively.

The individual properties of the nine sources are as follows:

GX 3+1 (figures 2a and 3a): The sinusoidal variation is clear, although the shapes of the sinusoidal profiles are complex with some peaks. The baseline decreases. The long-term period is ∼6 yr, which is similar to the results of KC10. The long-term periodic variation becomes stable over twice the time length of KC10.

GX 9+1 (figures 2b and 3b): The sinusoidal variation is also clear but with a slightly longer period (∼11 yr) than that of GX 3+1. The baseline has gradually increased over ∼25 yr, which is contrasts with the KC10 report that the baseline was constant for ∼13 yr, observed by RXTE/ASM. The long-term period is similar to the results (∼12 yr) of KC10.

Ser X-1 (figure 4a): Quasi-periodic modulation is clear. The period is not constant, but seems to become longer. KC10 reported a period of ∼7.3 yr, observed by RXTE/ASM. In the MAXI/GSC era, the period is longer and the amplitude may be larger.

4U 1735−444 (figure 4b): The sinusoidal variation is clear. However, the period is not constant, but seems to become shorter. KC10 reported a period of ∼10 yr from the large hump around MJD = 53000. In the MAXI/GSC era, the period is shorter, about half, and the amplitude may be smaller.

GX 9+9 (figure 4c): Although KC10 reported that the baseline was increasing, it cannot be extrapolated in the MAXI/GSC era. The light curve dropped after RXTE/ASM. Since then the baseline has stayed almost constant. However, the long-term period is similar to the results (∼4 yr) of KC10 throughout by RXTE/ASM and MAXI/GSC. The amplitude of the sinusoidal variation seems to be smaller in the MAXI/GSC era.

4U 1746−37 (figure 4d): Quasi-periodic modulation is clear. However, the period and amplitude are not constant. KC10 reported a period of ∼4.36 yr, observed by RXTE/ASM.

4U 1708−40 (figure 4e): Quasi-periodic modulation is clear. However, the period and amplitude are not constant. Although we divided the data into a small peak with a short period, the data from the MAXI/GSC era can also be fitted with one Gaussian profile for one large peak. KC10 did not report this source, because they focused on the Z and Atoll sources.

4U 1822−000 (figure 4f): Quasi-periodic modulation is clear. However, the period and amplitude are not constant. Although we divided the data between MJD = 54800 and 57000 into two small peaks with a short period, the data can also be fitted with one Gaussian profile for one large peak. KC10 did not report this source.

1A 1246−588 (figure 4g): Quasi-periodic modulation is seen. However, the period and amplitude are not constant. KC10 did not report this source.

4 Discussion

Long-term sinusoidal variations are presented for two CP sources (GX 3+1 and GX 9+1). The long-term periods range from ∼5 to ∼10 yr as shown in tables 2 and 3 and figures 2 and 3. We also investigated seven MP sources with modified periodic variation, and estimated the periods of quasi-periodic modulation (table 3 and figure 4). The range of each average period was approximately ∼2.5 to ∼10 yr. These timescales are much longer than the orbital period (∼2–5 hr), although, strictly speaking, those of four sources (CP: GX 3+1, GX 9+1; MP:4U 1708−40, 1A 1246−588) are unknown.

We discuss the mechanisms of long-term variation. First, we focus on the physical motion of the accretion disk. Precession of the accretion disk may occur due to excitation of resonances in the case of a mass ratio of q = M_c/M_NS ∼ 0.25–0.33 (Whitehurst & King 1991). This is likely to occur in the case of LMXBs with donor masses of 0.35–0.46|$\, M_{\odot}$|⁠. Although the donor masses of our CP and MP sources are not known, precession of the accretion disk could be possible. In general, according to Inoue (2012), precession occurs when the ratio of the precession period P_p to the binary orbital period P_B is P_p/P_B = 10–100. The ratios of our results are P_p/P_B ≥ 10⁴. There is no such case in figure 2 of Inoue (2012). However, if we extrapolate one line for P_p/P_B = 10⁴, a range of donor masses of 0.14–0.42|$\, M_{\odot}$| (q ∼ 0.1–0.3) would be possible. Since the donor mass is not known, the disk-precession scenario could be possible.

On the other hand, another possibility of radiation-induced warping is excluded. Kotze and Charles (2012) explicitly discuss the stability of radiation-induced warping. In the region below the bottom solid line in their figure 1, radiation-induced warping of the disk is unlikely, and there is in fact no super-orbital cycle observed in this region. Our four sources lie below the bottom solid line for typical values of mass ratio, q = M_c/M_NS ∼ 0.3, and orbital period, ∼2–5 hr. Thus, radiation-induced warping of the accretion disk is unlikely.

Next, we consider the possibility of variation of the mass-transfer rate from the donor. KC10 suggested that this is a consequence of the solar-like magnetic cycles seen in late-type stars (Applegate & Patterson 1987; Warner 1988). They pointed out that the flux modulation of a sine wave of ≤30% is plausible by the magnetic cycles. In our result, the flux modulation (see the amplitude in table 2) is ≤30%. Thus solar-cycle-like variations could be responsible for the long-term variations.

Here, we discuss another possibility for the variation of mass-transfer rate from the donor. This is irradiation by the central X-ray source to the donor star. Ritter (2008) shows that irradiation-driven mass-transfer cycles could only occur when the irradiation is sustained for a sufficiently long time. Büning and Ritter (2004) show the numerical results in terms of irradiation-driven mass-transfer cycles and then indicate the possibility that NS-LMXBs undergo these cycles. Their numerical results show that the stability of the mass-transfer rate from the donor star is a function of the orbital period.

In figure 1, filled marks represent quasi-periodic modulation (MP: Ser X-1, 4U 1735−444, GX 9+9, 4U 1746−37, 4U 1822−000) in our analysis. In figure 1b, the five filled marked MP sources are located in a region with medium binary separation and high irradiation average flux. The region may tend to show a periodic modulation.

However, in the region, there are also three sources (GS 1826−238, 4U 1636−536, and 4U 1254−690) of non-periodic modulation. The two LV sources (GS 1826−238 and 4U 1636−536) show a large luminosity change of one to two orders of magnitude, and it is difficult to see the flux modulation of the amplitude (≤30%) that a change of the mass-transfer rate induces. The one NP source (4U 1254−690) has similar binary properties to that of GX 9+9 (CP). The cause of the lack of clear periodic variation is unclear.

We discuss the features of the region in which long-term variation to occur. One feature is high irradiation average flux (≥1 × 10¹³ erg s⁻¹ cm⁻²). Even in the high irradiation flux, there are four NP sources (Sco X-1, GX 349+2, LMC X-2, and 4U1624−490) without a long-term variation in the larger binary-separation region. Here, the three sources (Sco X-1, GX 349+2, and LMC X-2) are Z sources. KC10 reported that the amplitudes of the long-term variation of Z sources are small and noted that this is because their luminosity is close to the Eddington luminosity. Although the luminosity of 4U 1624−490 is not close to the Eddington luminosity, the intrinsic luminosity is uncertain because it is an accretion-disk corona source. Here, we focus on the donor star. The three sources (Sco X-1, GX 349+2, and LMC X-2) are Z sources, and the donor stars are suggested to be evolved stars (Hasinger & van der Klis 1989 for Z sources; Cherepashchuk et al. 2021 for Sco X-1). 4U 1642−490 does not belong to the Z sources. However, Jones and Watson (1989) reported that the flaring behavior of the source shows a similarity to the flaring blackbody component (in temperature and radius) of Sco X-1 and other Z sources. Although the donor star of 4U 1624−490 has not been identified, it is possible for it to be an evolved star, similar to the Z sources. In this case, the mass-transfer rate on to the neutron star may be above the Eddington luminosity.

On the other hand, in the high irradiation flux but smaller binary-separation region, there are four sources (FV: 4U 1820−303 and three NPs: 4U 1543−624, 4U 2127+119, and 4U 1916−053). The sources are ultra-compact X-ray binaries (UCXBs). The donors in UCXBs may be white dwarfs (WDs) or He stars (4U 1820−303: Rappaport et al. 1987; 4U 1543−624: Nelemans et al. 2004; 4U 2127+119: Dieball et al. 2005; and 4U 1916−053: Joss 1978; Nelemans et al. 2006). Lü et al. (2017) suggest that, if the donor star is a WD, the irradiation flux can only penetrate into a very thin layer of the WD surface, and the irradiation hardly affects the evolution of the persistent UCXB. The irradiation flux would not affect the mass-transfer rate from the donor star.

In summary, intense irradiation may induce variation of the mass-transfer rate, and a sinusoidal periodic variation may appear. Our results also seem to show a dependence on the donor. A WD donor would not be affected by the irradiation. The periodicity might be related to the mass-transfer cycles caused by the irradiation pointed out by Ritter (2008).

Appendix. Light curves of 41 NS-LMXBs observed with MAXI/GSC and RXTE/ASM

The light curves used to analyze the long-term variation are presented in figures 6–14. The energy band is 2–10 keV, and the data period is from 1996 February to 2021 December. The data from RXTE/ASM are shown to the left of the vertical dashed line, those from MAXI/GSC to the right.

Footnotes

References