Rapid Optical Variations Correlated with X-rays in the 2015 Second Outburst of V404 Cygni (GS 2023$+$338)

TL;DR

This study analyzes rapid optical and X-ray variations during the 2015 outburst of V404 Cygni, revealing correlated short-term fluctuations and a time delay consistent with disc reprocessing.

Contribution

It provides the first Bayesian estimate of a ~30 second optical delay relative to X-rays during the outburst, supporting disc reprocessing as the origin of optical variability.

Findings

Optical and X-ray variations are correlated with a ~30 s delay.

Optical luminosity scales with X-ray luminosity as L_opt ∝ L_X^{0.25-0.29}.

Rapid optical variations occur even at low luminosity levels.

Abstract

We present optical multi-colour photometry of V404 Cyg during the outburst from December, 2015 to January, 2016 together with the simultaneous X-ray data. This outburst occurred less than 6 months after the previous outburst in June-July, 2015. These two outbursts in 2015 were of a slow rise and rapid decay-type and showed large-amplitude ($\sim$2 mag) and short-term ($\sim$10 min-3 hours) optical variations even at low luminosity (0.01-0.1$L_{\rm Edd}$). We found correlated optical and X-ray variations in two $\sim$1 hour time intervals and performed Bayesian time delay estimations between them. In the previous version, the observation times of X-ray light curves were measured at the satellite and their system of times was Terrestrial Time (TT), while those of optical light curves were measured at the Earth and their system of times was Coordinated Universal Time (UTC). In this version, we have corrected the observation times and obtained a Bayesian estimate of an optical delay against the X-ray emission, which is $\sim$30 s, during those two intervals. In addition, the relationship between the optical and X-ray luminosity was $L_{\rm opt} \propto L_{\rm X}^{0.25-0.29}$ at that time. These features can be naturally explained by disc reprocessing.

Tables

Table 1. Table 2: Bayesian estimates of the time delays for interval (1) during the day 8.18–8.22 and interval (2) during the day 8.246–8.292. The 68% interval indicates the quantile-based interval and the 68% HPD interval represents the highest posterior density interval.

Intervals	Median∗	68% Interval	68% HPD Interval
(1)	22.5 s	(22.4 s, 22.9 s)	(22.3 s, 22.8 s)
(2)	34.8 s	(34.6 s, 35.0 s)	(34.6 s, 35.0 s)
∗We report posterior medians because posterior means are not reliable indicators for the centre of a multi-modal distribution. The posterior mode and median of time delays are identical up to three decimal places.

Table 2. Table A1: Initial values of the parameters for each of three Markov chains used in the function bayesian of the R package timedelay for interval (1) during the day 8.18-8.22 and interval (2) during the day 8.246-8.292. The explanation of each parameter is the same as that in Table A1.

Names of parameters	(1)	(2)
theta.ini ($\mu$, $\sigma$, $\tau$)∗	(5.23, 100, 0.01)	(6.54, 100, 0.01)
	(5.23, 10, 0.1)	(6.54, 10, 0.1)
	(5.23, 1, 1)	(6.54, 1, 1)
delta.ini†	0.0003187326	0.0004607528
	0.0002608622	0.0004028825
	0.0002029918	0.0003450121
delta.uniform.range‡	($-$0.04, 0.04)	($-$0.046, 0.046)
delta.proposal.scale§	0.0001	0.0001
tau.proposal.scale#	1	1
tau.prior.shape¶	1	1
tau.prior.scale∗∗	2/107	$2/{10}^7$
sigma.prior.shape††	1	1
sigma.prior.scale‡‡	1	1
adaptive.delta§§	FALSE	FALSE
multimodality##	TRUE	TRUE
micro¶¶	0	0

Full text

††pubyear: 2017††pagerange: ERRATUM: Rapid Optical Variations Correlated with X-rays in the 2015 Second Outburst of V404 Cygni (GS 2023$+$338)–S2

In the published paper (Kimura et al., 2017), the observation times of X-ray light curves were measured at the satellite and their system of times was Terrestrial Time (TT), while those of optical light curves were measured at the Earth and their system of times was Coordinated Universal Time (UTC). We have converted the times of these light curves to the common time system BJD (TT) with the tool barycent in OSA, and made time-delay analyses. In addition, we have reduced the X-ray data again by using the updated version of the tool ii_shadow_build from the one in OSA v10.2. In calculating the background normalization in the imaging step, the affected pixels by the bright sources V404 Cyg, Cyg X-1, and Cyg X-3 were taken into accounted by adding their names in the parameter ’brSrcDOL’ in the IBIS Graphical User Interface. As a result of the time delay estimations with the new data, we found that the optical variations are delayed against the X-ray ones by 22.5${}^{+0.4}_{-0.1}$ s for time interval (1) and by 34.8${}^{+0.2}_{-0.2}$ s for time interval (2), although Kimura et al. (2017) described that $\sim$30–50-s X-ray delays were detected. The correct tables and figures on the time delay estimations, which are presented in Tables 2, A1 and Figures 4, 5, A1, replace the original ones. Additionally, the LNDCF estimates averaged with a time bin size equal to 34.56 s, which are displayed in Figure S2 and replace the original ones, are consistent with the Bayesian results as described in Kimura et al. (2017).

Under the assumption that photons move at the light speed from the inner region to the outer region of the disc, the estimated distance between the vicinity of the black hole to the optical emission region from the $\sim$30-s optical delay is $\sim$1012 cm, which is only about a few times smaller than the disc size in the 2015 June–July outburst (Kimura et al., 2016). The optical delays are, therefore, naturally explained by X-ray reprocessing, and then the optical variations would reflect the X-ray activity, though Kimura et al. (2017) concluded that the time delays are caused by propagating mass accretion flow in the inner disc. As Kimura et al. (2017) described in Sec. 4.2, the optical flux ratios against the X-ray flux were smaller than those in the June–July outburst, and the relation between the optical and X-ray luminosity did not follow the relation of the canonical X-ray reprocessing $L_{\rm opt}\propto L_{\rm X}^{1/2}$. They, however, do not deny the existence of X-ray reprocessing, since the degree of X-ray reprocessing vary with the energy spectral shape, the radial distribution of the disc temperature, the X-ray albedo, the optical depth of the disc, and the disc structure. For example, Coriat et al. (2009) showed that the relation $L_{\rm opt}\propto L_{\rm X}^{1/4}$ is derived from the assumption that the optical frequency lies in the Rayleigh-Jeans tail of the energy spectra and this relation seems to agree with our results. In addition, the possibly low surface density discussed in Sec. 4.2 in Kimura et al. (2017) also seems to be relevant to the small optical flux.

Acknowledgements

We appreciate to Julia Alfonso Garzón for notifying us of the discrepancies of the times between the X-ray and optical light curves. Mariko Kimura thank the INTEGRAL helpdesk for helpful comments on the X-ray data reduction.