Seven Reflares, a Mini Outburst, and an Outburst: High-amplitude Optical Variations in the Black Hole X-Ray Binary Swift J1910.2–0546

Swift J1910.2–0546 (MAXI J1910−057, hereafter J1910.2) was independently discovered by the Neil Gehrels Swift Observatory (Swift; Burrows et al. 2005) and the Monitor of All-sky X-ray Image (MAXI; Matsuoka et al. 2009), when the source went into an outburst in 2012 May (Krimm et al. 2012a; Usui et al. 2012). The 2012 outburst was extensively studied using X-ray spectral and timing analysis (e.g., Degenaar et al. 2014; Nakahira et al. 2014), optical photometry (Saikia et al. 2023) and spectroscopy (Casares et al. 2012; Charles et al. 2012). From these detailed studies, J1910.2 was was found to be a likely BH candidate at a distance of d > 1.7 kpc (Nakahira et al. 2014). Optical variability of the source suggests the orbital period to be fairly short (∼2–4 hr; Lloyd et al. 2012) with an upper limit of ≤6 hr (Saikia et al. 2023), although we note that a larger value is expected from spectroscopic studies (≥6.2 hr; Casares et al. 2012).

Following the 2012 outburst, Swift and MAXI continued to detect J1910.2 until 2013 January, after which the flux levels of the source had decreased below the detection limits. Radio detections were obtained on 2013 March 9 and May 3, along with Swift observations on March 9 (optical detection, X-ray nondetection) and May 10 (X-ray detection; Tomsick et al. 2013). No further observations of J1910.2 have been reported since 2013 May, except optical (2015 July) and near-infrared (NIR; 2017 April) detections in quiescence (López et al. 2019), until the recent enhancement of activity of the source in 2022. A new X-ray outburst from J1910.2 was detected in 2022 February (Tominaga et al. 2022), when it was also found to be prominent in the radio (Williams et al. 2022) and optical (Hosokawa et al. 2022; Kong 2022). The source quickly and steadily decayed at all wavelengths, and was found to be back in optical quiescence by the end of 2022 March (Saikia et al. 2022a).

Here we report the long-term optical monitoring of J1910.2 with the Faulkes Telescopes ⁷ and Las Cumbres Observatory (LCO) ⁸ network of telescopes from 2012 to 2022. We mainly focus on two periods of activity that were previously undocumented—a series of strong flaring in 2013, and a faint mini outburst in 2014. We combine our optical data with Swift and MAXI monitoring (at UV and X-ray wavelengths) and radio data from the literature to discuss the optical emission processes in J1910.2 throughout quiescence and outbursts, and explore the various physical explanations behind the flaring activity and the mini outburst. The observations are described in Section 2, and the results are presented and discussed in Section 3. We include a comparative analysis of the reflares with other BHXB systems in Section 4, and a summary is provided in Section 5.

We have been monitoring J1910.2 at optical wavelengths since its discovery in 2012, using the 2 m Faulkes Telescopes at Haleakala Observatory (Maui, Hawai"i, USA) and Siding Spring Observatory (Australia), as well as the 1 m telescopes at Siding Spring Observatory (Australia), Cerro Tololo Inter-American Observatory (Chile), McDonald Observatory (Texas), Teide Observatory (Tenerife), and the South African Astronomical Observatory (SAAO, South Africa) of the LCO network (Brown et al. 2013). The observations were performed in the Bessell B, V, R and Sloan Digital Sky Survey (SDSS) ${i}^{{\prime} }$ filters, as part of an ongoing monitoring campaign of ∼50 LMXBs (Lewis et al. 2008). We use the "X-ray Binary New Early Warning System (XB-NEWS)" data analysis pipeline (Russell et al. 2019; Goodwin et al. 2020; Pirbhoy et al. 2020) for calibrating the data and performing aperture photometry (see Saikia et al. 2023, for more details). This process resulted in photometric measurements of J1910.2 in a total of 123 (B), 74 (V), 85 (R), and 211 (${i}^{{\prime} }$) images (see Tables A1–A4) between 2012 June 14 (MJD 56092) and 2022 March 20 (MJD 59658).

We note that J1910.2 lies in the Galactic plane, with a few faint stars within 2'' of the source position (López et al. 2019). These stars may contribute to the quiescent flux measurements, but are too faint to affect the active interval photometry. Due to the limitation in the resolution and sensitivity of the Faulkes and LCO Telescopes, it is difficult to provide a proper numerical estimate of the contribution of the two neighboring stars to the quiescent magnitude of the source.

We acquired the X-ray detections of J1910.2 obtained with the X-Ray Telescope (XRT; Burrows et al. 2005) onboard Swift, using the online Swift/XRT data products generator ⁹ maintained by the Swift data center at the University of Leicester (see Evans et al. 2007; Evans et al. 2009). The source was observed for 67 days during its 2012 outburst (see Saikia et al. 2023) in the Windowed Timing (WT) mode (Hill et al. 2004). Due to Sun constraints, no observations were taken by Swift/XRT from 2012 November until 2013 March. It was again observed in Photon Counting (PC) mode (Hill et al. 2004) for five days between 2013 March to September, with exposures ranging from ∼1000 to ∼2000 s (Observation ID 00032742), and was detected only once (see Table A5). In addition to the Swift/XRT light curve, we also acquired the 2–10 keV MAXI/GSC light curve. ¹⁰ Unfortunately, during the flaring activity of J1910.2, MAXI only detected the system once above 3σ significance.

We also retrieved the publicly available Swift Ultraviolet and Optical Telescope (UVOT; Roming et al. 2005) observations from the NASA/HEASARC data center. We use the pipeline processed images and follow the uvotsource HEASOFT routine to obtain the magnitudes of the source using an aperture size of 5'' centered on the source. During the 2012 outburst, the source was detected in almost all the epochs observed by Swift/UVOT, for a varying range of exposures between ∼20 and 1000 s (see Saikia et al. 2023). However, most of the observations during the flaring period and the faint mini outburst during 2013 and 2014 were nondetections (the significance of the detection above the sky background is lower than 5σ, see Table A5), despite having much longer exposure times (even for ∼1000 s exposures).

We searched the literature for detections of J1910.2 after the 2012 outburst. In 2013, detections were acquired by the Australia Telescope Compact Array (ATCA) in March and May at 5.5 and 9 GHz on both dates, with average flux densities of 0.06 mJy in March and 0.3–0.4 mJy in May (no errors are given; Tomsick et al. 2013). It was again detected during its 2022 outburst with the Arcminute Microkelvin Imager Large Array (AMI-LA; Zwart et al. 2008; Hickish et al. 2018) at 15.5 GHz (Williams et al. 2022).

From MAXI and Swift X-ray data, Nakahira et al. (2014) report that the 2012 outburst of J1910.2 ended around 2013 January 26 (MJD 56318). Due to Sun constraints we have no optical coverage during the 2012 outburst decay, and when monitoring was resumed in 2013 March we found J1910.2 in a flaring state. It displayed at least seven, high-amplitude (∼3 mag), quasi-periodic optical reflares (with the interval between reflares increasing from ∼42 to ∼49 days), which continued for at least eight months. Due to the lack of coverage before 2013 March, it is not evident if and when the source entered quiescence before the rebrightening, and it is also not possible to constrain the exact date when the reflaring started or ended.

We plot the 2013 rebrightening activities of the source in Figure 2. During the interval of 2013 February 27 to November 4 (MJD 56350 to MJD 56600), the source had unusually extreme reflares in all optical bands, which had not been seen before. The optical magnitude during the peak of these reflares reached $i^{\prime} \sim$ 17–17.5. Between any two consecutive flares, the magnitudes did not drop to the quiescent value, and remained around $i^{\prime} \sim$ 19–20. For a rough comparison, J1910.2 is found to have a quiescent $i^{\prime}$ of 22.18 ± 0.04 using the William Herschel Telescope with the auxiliary port camera (ACAM; 2015 July 19; López et al. 2019). The optical color (V – $i^{\prime}$) roughly decreased during the rise of the flare, following a bluer-when-brighter behavior (see Figures 2(c) and 7). It was seen to be the lowest during the peak of the flares, and the color reddened during the decay of the flares. Radio and X-ray observations carried out in this period with ATCA (2013 March 9 and May 3) and Swift/XRT (2013 March 9 and May 10) show that the source was probably flaring in these bands as well (Tomsick et al. 2013). While in 2013 March, the authors report a radio flux of 0.06 mJy, it increased to 0.3–0.4 mJy in 2013 May. On the other hand, the source was not detected above 3σ significance with Swift/XRT (0.6–10 keV) during the 2013 March observation, but it was observed to be brighter in 2013 May (see Table A5). Inspecting the MAXI light curves in the energy band 2.0–10.0 keV for the same period, we found that J1910.2 was only detected once (MJD 56451) above 3σ significance. Taking into account the Swift/XRT and MAXI detections, we estimate lower and upper limits for the X-ray flux in the energy band 2.0–10.0 keV of ∼4.0 × 10⁻¹² erg cm⁻² s⁻¹ and ∼3.0 × 10⁻¹⁰ erg cm⁻² s⁻¹, respectively.

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The average optical cycle time of the reflares increases with time from ∼42 to ∼49 days. In Figure 2(f) we show the first six reflares folded on a period of 41.9 days (the time between the fast rises of flares 3 and 4). As evident from the figure, the four initial reflares have a very similar duration consistent with ∼41.9 days. The first two reflares (flares 1 and 2) have a fairly sharp peak before decaying, with comparable rise and decay times. The next two (flares 3 and 4) have a rise time similar to the previous ones, but show an extended peak lasting ∼15 days, before the decay. For these first four reflares, the rise time from the minimum to the peak of the reflare is ∼6 days. The last two flares (flares 5 and 6) have a double-peaked morphology, with the first peak being faint and the second peak being a similar magnitude to the first four flares, and a slightly longer period (seen in Figure 2(f) as a delay in the bright peak for these flares). Multiple reflares displaying such periodic behavior have been previously observed in many dwarf novae (DNe; see, e.g., Kato 2015), but they are rarely seen in LMXBs (see Section 4 for a detailed discussion).

When optical monitoring of J1910.2 was resumed in 2014, the source was found in a variable state close to quiescence ($i^{\prime} \sim$ 20.7–21.7, see Section 3.6). Shortly thereafter, the source became brighter again (see Figure 3), showing two consecutive peaks on MJD 56853.5 ($i^{\prime}$ = 18.93 ± 0.21) and a brighter one on MJD 56874.3 ($i^{\prime}$ = 17.30 ± 0.01). There was a single LCO detection of the source between the 2013 reflares and the 2014 rebrightening (2014 March 17, MJD 56733.6, $i^{\prime}$ = 19.89 ± 0.09), which is much fainter than the reflares, but brighter than the typical quiescence value obtained with LCO ($i^{\prime} \sim$ 20.7–21.7, see Section 3.6). Due to the lack of continuous observations during that period, it cannot be confirmed if the 2013 reflares were going on for the whole year and the rebrightening events seen in 2014 were just a continuation of the 2013 reflares.

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The peak of the 2014 rebrightening on May 8 (MJD 56874.3, $i^{\prime}$ = 17.30 ± 0.01) is almost ∼2 mags fainter than the 2012 outburst peak on MJD 56103.6 ($i^{\prime}$ = 15.41 ± 0.01). Although comparable to the peak magnitudes observed during the 2013 reflares ($i^{\prime}$-band range ∼17.0–17.5, see Table 1), we classify the 2014 rebrightening as a mini outburst because the source had reached close to quiescence before the apparent brightening. Moreover, it follows a typical double-peaked outburst profile with a sudden rise from quiescence followed by an exponential decay after the second peak. The evolution of the optical color (V – $i^{\prime}$) during the mini outburst also follows a bluer-when-brighter behavior, similar to the 2013 reflares. This is clearly observed during the second peak of the mini outburst, where the source is bluest at the peak, and slowly reddens as it decays during the return of the mini outburst to quiescence.

Recently, renewed X-ray activity was detected in J1910.2 by MAXI/GSC on 2022 February 4 (MJD 59614), with the 2–6 keV flux reaching 17 mCrab on February 5 (MJD 59615), and then gradually declining to ∼7 mCrab on February 7 (MJD 59617; Tominaga et al. 2022). The source quickly faded below the detection limit in soft X-rays, and returned to close to quiescence (see Figure 4(d)). It was detected in the radio by AMI-LA (Hickish et al. 2018; Zwart et al. 2008) at 15.5 GHz, with integrated fluxes of 4.1 ± 0.6 mJy on 2022 February 7 (MJD 59617.377), 7.0 ± 0.8 mJy on February 9 (MJD 59619.411), and 9.0 ± 1.0 mJy on February 10 (MJD 59620.376), indicating that the source was rapidly brightening (see Figure 4(c); values obtained from Williams et al. 2022).

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LCO first detected J1910.2 during the recent activity on 2022 February 13 (MJD 59623.27), after the source came out of a Sun constraint (see Figure 4(a)). At that time, it was already at peak, or at an early decline stage of the outburst (with $i^{\prime} \,\sim$ 16.45 ± 0.01). This is brighter than the previous rebrightening events of 2013 (flares with peaks in the range of i' ∼ 17.0–17.5 mag,) and the mini outburst of 2014 ($i^{\prime} \,\sim$17.30 ± 0.01), and fainter than the previous 2012 outburst with $i^{\prime} \sim$ 15.41 ± 0.01 on 2012 June 25 (MJD 56103.6, see Table 1). An optical nondetection was reported on 2022 February 8 (MJD 59618.85) with the MITSuME 50 cm telescope Akeno, implying 5σ upper limits of R_c > 17.0 and I_c > 16.6, before brightening and being detected on 2022 February 15 (MJD 59625.84) with R_c = 16.9 ± 0.1 and I_c = 16.7 ± 0.1 (Hosokawa et al. 2022). It was also detected by the Zwicky Transient Facility (ZTF; Bellm et al. 2019) on 2022 February 11 (MJD 59621) with r ∼ 16.4, which got gradually fainter with r ∼ 16.6 on February 12 (MJD 59622) and r ∼ 17.2 on February 18 (MJD 59628; Kong 2022). Following the rebrightening classification scheme based on Zhang et al. (2019), we classify the recent activity as a new outburst, as the flux reached quiescence before the rebrightening event, and the time separating the start of the quiescent period (after the end of the last activity) from the start of the recent rebrightening is much larger than the duration of the outburst.

We build the dereddened spectra and spectral energy distributions (SEDs) of J1910.2 using quasi-simultaneous observations (within 24 hr) both in quiescence (see Figure 5), and in the bright episodes of the 2013 reflares, the 2014 mini outburst, and the 2022 outburst (see Figure 6). We also overplot a few SEDs from different spectral states of its discovery outburst in 2012 for comparison (see Saikia et al. 2023, for the evolution and the naming of the spectral states in J1910.2). Dereddened fluxes were obtained from the calibrated magnitudes using a hydrogen column density value of N_H = (3.5 ± 0.1) × 10²¹ cm⁻² (Degenaar et al. 2014) and the Foight et al. (2016) and Cardelli et al. (1989) extinction laws to estimate the absorption coefficients (see Table 1 in Saikia et al. 2023, for more details).

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For J1910.2, a simple fitting of the quiescent spectra (using values obtained from López et al. 2019) with a single-temperature blackbody gives a value of ∼3040 K (Figure 5). Assuming that there is no accretion activity at these lowest fluxes, then this temperature is consistent with an M4-type star, of mass ∼0.3 M_⊙ and radius ∼0.3 R_⊙ (see Saikia et al. 2023).

During the outbursts and rebrightening episodes, the optical/UV spectra are found to be fairly smooth. For the brighter outburst epochs, we find a slightly positive to flat slope in the optical (α_R−b = −0.04–0.35, where F_ν ∝ ν^α ), and a negative slope in the UV (α_u−w2 = −1.0 to −1.2, see Figure 6). The SEDs peak around V or B for the brighter epochs of the 2012 outburst, but appear redder (around $i^{\prime}$) for the 2022 outburst. During the rebrightening epochs of the 2013 reflares and 2014 mini outburst, the $i^{\prime}$ flux is generally found to be brighter than the higher frequencies, unlike the brighter epochs of the 2012 outburst (see Table 2 for a comparison of the optical spectral indices). This could be a hint of the blackbody peak shifting to lower frequencies, as the luminosity decreases. The overall shapes of the optical/UV spectra are consistent with the outer regions of a blue, X-ray irradiated accretion disk (e.g., Hynes 2005).

Table 2. List of Optical Spectral Indices for the Spectra Presented in Figure 6

Year	MJD	State	Spectral Index
2012	56092	Soft	αR−b = 0.35 ± 0.09
2012	56140	Soft	${\alpha }_{i^{\prime} -b}\,=$ –0.04 ± 0.06
2012	56220	HS3/HIMS	${\alpha }_{i^{\prime} -v}\,=$ 0.09 ± 0.01
2012	56229	Hard	${\alpha }_{i^{\prime} -R}\sim$ −0.11 a
2012	56235	Hard	${\alpha }_{i^{\prime} -v}\,=$ −0.85 ± 0.30
2013	56475	Reflares	${\alpha }_{i^{\prime} -b}\,=$ −0.74 ± 0.01
2013	56542	Reflares	${\alpha }_{i^{\prime} -v}\,=$ 0.11 ± 0.03
2013	56564	Reflares	${\alpha }_{i^{\prime} -v}\,=$ −1.83 ± 0.63
2014	56866	Mini outburst	${\alpha }_{i^{\prime} -v}\,=$ −1.45 ± 0.48
2014	56874	Mini outburst	${\alpha }_{i^{\prime} -v}\,=$ 0.24 ± 0.02
2014	56894	Mini outburst	${\alpha }_{i^{\prime} -v}\,=$ −0.50 ± 0.07
2022	59623	Hard	${\alpha }_{i^{\prime} -b}\,=$ −0.38 ± 0.08
2022	59625	Hard	${\alpha }_{i^{\prime} -b}\,=$ −0.23 ± 0.11
2022	59628	Hard	${\alpha }_{i^{\prime} -b}\,=$ 0.05 ± 0.16
2022	59632	Hard	${\alpha }_{i^{\prime} -b}\,=$ −0.04 ± 0.26

Note. ${\alpha }_{{i}^{{\rm{{\prime} }}}-b}$ is shown unless otherwise specified.

^a As only two data points are available, we are unable to calculate the uncertainty.

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In order to analyze the color evolution of J1910.2, we plot the optical color–magnitude diagram (CMD) using quasi-simultaneous V-band and $i^{\prime}$-band magnitudes (Figure 7, top panel), and the optical/UV CMD using uvm2-band and V-band magnitudes (Figure 7, bottom panel). The different states of the 2012 outburst, the subsequent rebrightening events, and the 2022 outburst are shown in different colors and symbols to distinguish their temperature ranges and study their comparative behaviors. We also plot the single temperature blackbody model of Maitra & Bailyn (2008), which approximates the emission of an X-ray irradiated outer accretion disk (see also Russell et al. 2011; Zhang et al. 2019; Baglio et al. 2020b, 2022; Saikia et al. 2022c). The normalization of the blackbody model depends on various factors, including the accretion disk radius, which can be estimated from the system masses, orbital period, inclination, source distance, disk filling factor, disk warping, etc. As many of these parameters are poorly constrained, we fix the normalization value to what best describes the trend in the optical CMD as it has the most amount of data. Among the observations, we optimize the normalization so as to cover the widest range of observed optical color (V – $i^{\prime}$). We use the same normalization also for the optical/UV CMD.

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We find that the observations taken during the reflares in 2013 and the mini outburst in 2014 are well represented by the disk model (shown as a solid black line in Figure 7). During these rebrightening events, the outer disk temperature is approximately between 4500 and 9500 K. This covers the expected temperature range where hydrogen in the disk gets ionized (∼7000–10,000 K). We find that the disk temperature during these rebrightening events repeatedly increases and then decreases, suggesting that the reflares are caused by continuous waves of heating and cooling flowing through the accretion disk.

However, the initial outburst of 2012 does not completely follow the same model of single-temperature blackbody heating and cooling. The temperature during this main outburst is higher than the H ionization temperature (∼11,000 K), and the emission is redder and/or brighter than what is expected from the disk model. We find that the data are better represented by a single-temperature blackbody model with a different normalization (shown as a solid gray line in Figure 7). This could either be due to significant contribution to the optical emission from additional components such as synchrotron emission from a jet, or because the viscous disk starts to dominate, or else because of disk warping. The factor difference between the two normalizations is 2.75 in flux, indicating the expected increase in the surface area needed to explain the brighter points from the initial outburst, compared to the reflares and mini outburst.

We note that synchrotron emission is unlikely to be the dominant cause, as the brighter and redder trend is also observed in the soft state, when we do not expect the jet to be present. Jets have been observed in the IR/optical during transition from the soft state to the soft-intermediate state (e.g., Russell et al. 2020), but for a prolonged time, and not in the soft state. The observations taken during the 2012 outburst in the pure hard state are much redder compared to all the other data points, especially in the optical CMD representing longer wavelengths (V versus V – $i^{\prime}$), which trace the highest jet contribution. In this case, the significant deviation of the data points away from the disk model can be confidently attributed to a jet, as it starts to dominate the optical emission during the transition to the pure hard state.

Even for the optical/UV CMD, where we plot the bluer wavelengths (uvm2 versus uvm2 – V) that are generally dominated by the disk with a negligible jet contribution, we find that the data in the soft as well as the hard–intermediate state (HIMS) and hard state diverged from the disk model. This suggests that the deviation of the 2012 data from the blackbody model is not because of a jet contribution, but probably has its origin in the disk.

The 2022 data are also comparatively brighter and/or redder than the disk model. As these data points are taken during the hard state, and the spectral index is too low for a viscous disk, we attribute this deviation to a jet contribution, just as in the case of the pure hard-state data of the 2012 outburst. This is also supported by the AMI-LA radio detections, which showed a considerable rise just before the LCO observations were taken (Williams et al. 2022).

After the end of the mini outburst in 2014, we continued the LCO monitoring of J1910.2. In Figure 8, we plot the long-term (2014–2022) optical ($i^{\prime}$) light curve of J1910.2, and find that it remained in quiescence throughout this interval, but was variable over a range of $i^{\prime}$ band ∼ 20.7–21.7. However, we do note that, during quiescence, the LCO magnitudes (mostly with forced multiaperture photometry by XB-NEWS at the source position; Goodwin et al. 2020) include some contaminating flux from two nearby stars (within 2'' of the source position), with similar brightnesses as J1910.2.

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López et al. (2019) detected J1910.2 at $i^{\prime}$ = 22.18 ± 0.04 on 2015 July 19 (MJD 57222) using the William Herschel Telescope with ACAM. This is the only other published quiescent magnitude of the source at optical wavelengths, in which the magnitudes obtained are not contaminated by neighboring stars. From the finding chart of López et al. (2019), we know that the two neighboring stars have brightnesses comparable to J1910.2. Assuming that the ACAM magnitudes are representative of the average magnitude of J1910.2 in quiescence, and that the two neighboring stars are of the same magnitude, we speculate that having all three stars in the same aperture (as should be the case for LCO data) would give us a flux which is thrice the real flux. This translates to an optical magnitude of $i^{\prime} \sim$ 21.01 ± 0.10. In fact, we find that the average quiescent LCO mags is comparable to this, with $i^{\prime}$ = 21.16 ± 0.29. As we do not have an LCO detection of the source on the same date, a direct comparison of the magnitudes is not possible, but the closest observation with LCO (MJD 57230) is also ∼1 mag brighter. As shown in Figure 8, the long-term LCO light curve suggests accretion variability in quiescence with a range of quiescent magnitudes that are ∼0.4 to ∼2.0 mag brighter in LCO compared to the López et al. (2019) value (a range that could either be due to varying seeing conditions and/or due to intrinsic accretion variability). As the amount of flux in the blend depends on the seeing conditions, we cannot completely trust the variability observed. However, we note that although some quiescent variability is expected due to fluctuating seeing, we cannot rule out intrinsic variability, as is seen in many other BHXBs (e.g., Koljonen et al. 2016; Wu et al. 2016; Russell et al. 2018).

We compile a list of all BHXB sources (see Table 3) where significant rebrightening was observed within one year of the last detection of the initial outburst (either after it reached quiescence or after a gap where it is uncertain if it reached quiescence). We do not include recurrent transients (e.g., GX 339-4; Tetarenko et al. 2016) and multipeak outbursts (e.g., GRO J1655-40; Chen et al. 1997). Along with BHXBs (e.g., MAXI J1535–571 and V404Cyg; Parikh et al. 2019; Muñoz-Darias et al. 2017; Cuneo et al. 2020), such rebrightening events (at different timescales) after the main outburst are also seen in NSXBs (e.g., IGR J00291+5934; Lewis et al. 2010), as well as WZ Sge-type DNe (see, e.g., Kato 2015). We use the observation-based labeling scheme explained in Zhang et al. (2019) to classify the different rebrightening phenomena in this sample, in which a rebrightening is termed as a "reflare" if the flux did not reach quiescence before the rise in amplitude. If the flux reaches quiescence before the rebrightening, we term it a "mini outburst," provided that the flux ratio between the rebrightening peak and the primary outburst peak is less than 0.7, and the time separating the start of the quiescent period from the start of the rebrightening is less than the duration of the main outburst. On the other hand, if the duration of the main outburst is shorter, or if the flux ratio between the peak of the rebrightening and the peak of the primary outburst is more than 0.7, we term it as a "new outburst" (Zhang et al. 2019).

Table 3. Sample of LMXB Outbursts with Rebrightenings within One Year of the Last Detection of the Initial Outburst

Source	BH/NS a	Year b	Classification c	tflaring (d) d	${N}_{\mathrm{flares}}$ e	Band f	Δtpeaks g	State h	References i
A 0620–00	BH	1975	mini outburst	∼60	1	optical	⋯	⋯	1
GRO J0422+32	BH	1992	mini outbursts	>271	2	optical	∼113	⋯	2
GRS 1716−249	BH	1993	reflares	>400	5	X-ray	50–90	hard	3
XTE J1859+226	BH	1999	mini outbursts?	∼75	3	optical	20–30	hard	4
XTE J1650–500	BH	2001	reflares?	>150	≥7	X-ray	14.2	hard	5, 6
Swift J1753.5–0127	BH	2005	mini outburst	>151	1	both	⋯	hard	7
IGR J00291+5934	NS	2008	new outburst	>49.0	1	both	⋯	hard	8
XTE J1752–223	BH	2010	reflare?	⋯	1	both	⋯	hard	9
MAXI J1659–152	BH	2010	mini outburst	89 ± 15	1	both	⋯	hard	10, 11
MAXI J1836–194	BH	2011	reflare?	∼75	1	both	⋯	hard	12, 13
Swift J1910.2–0546	BH	2012	reflares	>245.8	≥7	optical	42–49	hard	14, 15
GRS 1739–278	BH	2014	mini outbursts	>150	3	X-ray	∼62	hard, soft	16
V404 Cyg	BH	2015	reflares	>33	>10	both	<1	hard	17, 18
MAXI J1535–571	BH	2017	reflares	>165	≥5	X-ray	31 − 32	hard, soft	19, 20
MAXI J1820+070	BH	2018	mini outbursts	>474	3	both	∼177	hard	21–28
MAXI J1348–630	BH	2019	mini outbursts	∼280	≥3	both	∼90	hard	29–34
4U 1543–47	BH	2022	mini outburst, reflares	>240	≥5	both	20–30	hard, soft	35–37

Notes.

^a BH = black hole; NS = neutron star. ^b Year of initial outburst. ^c Rebrightening classification based on Zhang et al. (2019). ^d Total duration of rebrightening interval after the initial outburst. ^e Number of reflares during the rebrightening interval. ^f Wave band(s) of the reported rebrightening(s) (optical, X-ray, or both). ^g Reflare recurrence times (when >1 flare recorded). ^h Rebrightening X-ray state (if known). ⁱ References: (1) Charles (1998); (2) Callanan et al. (1995); (3) Hjellming et al. (1996); (4) Zurita et al. (2002); (5) Tomsick et al. (2003); (6) Tomsick et al. (2004); (7) Zhang et al. (2019); (8) Lewis et al. (2010); (9) Corral-Santana et al. (2010a); (10) Homan et al. (2013); (11) Corral-Santana et al. (2018); (12) Yang et al. (2012); (13) Krimm et al. (2012b); (14) this paper; (15) Tomsick et al. (2013); (16) Yan & Yu (2017); (17) Muñoz-Darias et al. (2017); (18) Kajava et al. (2018); (19) Parikh et al. (2019); (20) Cuneo et al. (2020); (21) Ulowetz et al. (2019); (22) Bahramian et al. (2019); (23) Baglio et al. (2019); (24) Hambsch et al. (2019); (25) Xu et al. (2019); (26) Adachi et al. (2020); (27) Sasaki et al. (2020); (28) Shaw et al. (2021) (29) Al Yazeedi et al. (2019); (30) Pirbhoy et al. (2020); (31) Shimomukai et al. (2020); (32) Zhang et al. (2020); (33) Baglio et al. (2020a); (34) Carotenuto et al. (2021); (35) Alnaqbi et al. (2022); (36) Wang et al. (2022); (37) Negoro et al. (2022).

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As discussed in Section 3.1, the 2013 rebrightenings observed in J1910.2 are reflares, and not mini outbursts. We find that it is one of the very few systems to display such unusually extreme flaring (with more than seven optical reflares). In most cases, the number of reflares or mini outbursts seen during the period of rebrightening is fewer than five. The only other BHXBs displaying more than five reflares within one year of their outbursts are XTE J1650–500 (Tomsick et al. 2003, 2004), MAXI J1535–571 (Parikh et al. 2019; Cuneo et al. 2020), and V404 Cyg (Muñoz-Darias et al. 2017; Kajava et al. 2018).

In MAXI J1535–571, at least four reflaring events were seen after the first outburst, all having an approximately constant interval between reflares of ∼31–32 days (Cuneo et al. 2020). However, unlike MAXI J1535–571, where a progressive faintness of the reflares is observed, likely due to an emptying reservoir of mass available for accretion (Parikh et al. 2019), the peak magnitude of the 2013 reflares in J1910.2 stayed almost constant. The MAXI J1535–571 reflares also exhibited state transitions and the hysteresis pattern in the HID, which is generally observed only in the main outbursts of LMXBs (except for the mini outbursts in GRS 1739–278; Yan & Yu 2017). Such a comparison is not possible for J1910.2, as there is only one X-ray detection and a few upper limits available from Swift/XRT during the reflaring behavior. The single X-ray detection is as hard as the 2012 outburst hard-state decay, so at least for one date during the reflares we can confirm that the source was in the hard state. Moreover, as transitions are usually at higher luminosities, and these reflares are barely detected by Swift/XRT, we argue that all the reflares are probably happening in the hard state. We note that the reflares hysteresis loops observed in MAXI J1535–571 occurred at almost 100 times lower luminosities than the peak of the main outburst, with the state transitions occurring at a luminosity of L_X ≤ 7 × 10³⁶ erg s⁻¹ (which is the lowest luminosity at which hard-to-soft transitions have been observed in a BHXB; see Cuneo et al. 2020). However the only X-ray detection of J1910.2 available during the reflares is more than 1000 times lower than the outburst peak, suggesting that the 2013 reflares of J1910.2 happened in the hard state.

One important observation from the CMD of J1910.2 (see Section 3.5) is that it repeatedly crosses the temperature needed to ionize/neutralize the hydrogen present in the accretion disk during the rebrightening events. Typically at the end of the outburst, the temperature in the outer disk decreases, causing the hydrogen in the disk to recombine, and this sends a cooling wave that propagates inwards (Dubus et al. 2001; Lasota 2001). It eventually reaches matter in the inner disk that is so hot it cannot be cooled lower than the recombination temperature, so the cooling wave halts. At the radius where the surface density behind the cooling front becomes high enough, the disk becomes thermally unstable, initiating a new heating front to propagate outwards (Dubus et al. 2001). The CMD of J1910.2 suggests that the repeated 2013 reflares are probably due to the back-and-forth propagation of cooling and heating waves in the disk.

If the instability causing the reflares is originating at the inner disk and then propagating outwards, then the rise time of the repeated reflares, which estimates the propagation time of the heating front, suggests a viscous timescale of ∼6 days. A viscous timescale of ∼6 days is also measured from the dip in intensity seen during the 2012 outburst, provided it is also caused by a reduction in mass transfer into the inner disk (Degenaar et al. 2014; Saikia et al. 2023). A measurement of the disk viscosity parameters from the observed light-curve profile (as done using a hierarchical Bayesian approach with Markov Chain Monte Carlo fitting after removing flares in Tetarenko et al. 2018) is difficult in this case due to the lack of good coverage during the decay of the reflares. However, overall the general structure of the reflares follow a pattern of rapid heating and a relatively slower fading, similar to what is observed during main outbursts.

Numerical simulations of the DIM automatically predict reflares which are spontaneously created through repeated heating/cooling waves that cyclically ionize and recombine in the accretion disk, although the numerically produced light curves do not generally resemble those observed (Dubus et al. 2001; Meyer & Meyer-Hofmeister 2015; Hameury & Lasota 2021). Moreover, the reflares predicted by the DIM require the density of matter to be depleted with each subsequent reflare, and hence a progressive faintness in amplitude is expected (Dubus et al. 2001); which is not observed in the case of J1910.2. However, we speculate that a heated-up companion can continuously dump matter in the disk, due to its expansion from being heated by the X-rays of the 2012 outburst. This enhanced mass transfer from the companion (in addition to the steady accretion from the companion that happens all the time) can result in an almost constant amplitude during the reflares. Another possibility is that the X-ray and optical emission show different things. X-rays trace the mass accretion rate close to the BH, and a decreasing trend of peak X-ray luminosities is expected (as seen in the X-ray light curves of MAXI J1535–571 reflares; Cuneo et al. 2020). However, the constant peak optical magnitude could correspond to the position in the CMD where the disk reaches above the H ionization temperature. From the CMDs of J1910.2 (see Figure 7), we find that the data follow the disk model very well, suggesting that the emitting area is roughly constant during the reflares. Hence it is possible that we are probing different mechanisms in both wavelengths: we could be looking at constant-area blackbody heating and cooling in the optical, while tracing the mass accretion rate in X-rays. This could be another reason why we do not have a decreasing trend of peak optical fluxes, as also seen in the optical light curves of GRO J0422+32 reflares by Callanan et al. (1995).

Overall, it is not completely clear if the reflares are caused by the same hydrogen ionization instability which triggers the main outburst or they have a different origin mechanism. However, from the changes in temperature observed during the reflares (which repeatedly cross the H ionization temperature), we consider the back-and-forth propagation of heating/cooling waves to be the most likely explanation for the 2013 reflares.

Large-amplitude optical oscillations or violent reflares seen on shorter timescales (on timescales of hours) in sources like V404 Cyg are expected in long-period systems. The disk in such systems is much larger, and the surface densities in the outer disk will be too low to have sustained mass accretion in the inner disk, which is required for longer-timescale reflares (Kimura et al. 2016). In fact, the longer-timescale 2014 mini outburst as seen in J1910.2 is expected to be more common in BHXB systems with shorter orbital periods (<7 hr). In such short-period systems, it is speculated that the outer disk has a high enough temperature for the heating front to remain hot, thereby triggering a mini outburst (Zhang et al. 2019). Due to the lack of any deep soft X-ray observation during the outburst fade, or before this 2014 mini outburst, we do not have direct confirmation for the presence of a hot inner disk. However, recent optical fast photometry of J1910.2 indeed suggests an orbital period of <7.4 hr (Saikia et al. 2023). Previously, Casares et al. (2012) had reported an orbital period >6.2 hr from their spectroscopic study, assuming that the velocity changes in Hα emission are cause by binary motion. Later, a fairly short orbital period (∼2–4 hr) was proposed based on the small size of its disk with a radius of ∼4 × 10⁹ cm (Degenaar et al. 2014) and its variable optical emission (Lloyd et al. 2012). Such a short orbital period can ensure the presence of a hot inner disk at the end of the outburst decay, which could have triggered the mini outburst seen in J1910.2.