# An elevation of 0.1 light-seconds for the optical jet base in an accreting Galactic black hole system

Poshak Gandhi, Matteo Bachetti, Vik S. Dhillon, Robert P. Fender, Liam K. Hardy, Fiona A. Harrison, Stuart P. Littlefair, Julien Malzac, Sera Markoff, Tom R. Marsh, et al.

► To cite this version:

Poshak Gandhi, Matteo Bachetti, Vik S. Dhillon, Robert P. Fender, Liam K. Hardy, et al. An elevation of 0.1 light-seconds for the optical jet base in an accreting Galactic black hole system. Nature Astronomy, 2017, 1 (12), pp.859-864. 10.1038/s41550-017-0273-3. hal-01758370

HAL Id: hal-01758370

https://hal.science/hal-01758370v1

Submitted on 7 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# An elevation of 0.1 light-seconds for the optical jet base in an accreting Galactic black hole system

P. Gandhi<sup>1*</sup>, M. Bachetti<sup>2</sup>, V. S. Dhillon<sup>3,4</sup>, R. P. Fender<sup>5</sup>, L. K. Hardy<sup>3</sup>, F. A. Harrison<sup>6</sup>, S. P. Littlefair<sup>3</sup>, J. Malzac<sup>7</sup>, S. Markoff<sup>8</sup>, T. R. Marsh<sup>9</sup>, K. Mooley<sup>5</sup>, D. Stern<sup>10</sup>, J. A. Tomsick<sup>11</sup>, D. J. Walton<sup>12</sup>, P. Casella<sup>13</sup>, F. Vincentelli<sup>13,14,15</sup>, D. Altamirano<sup>1</sup>, J. Casares<sup>4,5,16</sup>, C. Ceccobello<sup>8</sup>, P. A. Charles<sup>1,5</sup>, C. Ferrigno<sup>17</sup>, R. I. Hynes<sup>18</sup>, C. Knigge<sup>1</sup>, E. Kuulkers<sup>19</sup>, M. Pahari<sup>20</sup>, F. Rahoui<sup>21</sup>, D. M. Russell<sup>22</sup> and A. W. Shaw<sup>23</sup>

Relativistic plasma jets are observed in many systems that host accreting black holes. According to theory, coiled magnetic fields close to the black hole accelerate and collimate the plasma, leading to a jet being launched<sup>1-3</sup>. Isolating emission from this acceleration and collimation zone is key to measuring its size and understanding jet formation physics. But this is challenging because emission from the jet base cannot easily be disentangled from other accreting components. Here, we show that rapid optical flux variations from an accreting Galactic black-hole binary are delayed with respect to X-rays radiated from close to the black hole by about 0.1 seconds, and that this delayed signal appears together with a brightening radio jet. The origin of these subsecond optical variations has hitherto been controversial<sup>4-8</sup>. Not only does our work strongly support a jet origin for the optical variations but it also sets a characteristic elevation of ≲10<sup>3</sup> Schwarzschild radii for the main inner optical emission zone above the black hole<sup>9</sup>, constraining both internal shock<sup>10</sup> and magnetohydrodynamic<sup>11</sup> models. Similarities with blazars<sup>12,13</sup> suggest that jet structure and launching physics could potentially be unified under mass-invariant models. Two of the best-studied jetted black-hole binaries show very similar optical lags<sup>8,14,15</sup>, so this size scale may be a defining feature of such systems.

In June 2015, the Galactic X-ray binary V404 Cygni underwent the brightest outburst of an X-ray binary so far this century. We coordinated simultaneous optical observations from the William Herschel Telescope (WHT) with X-ray observations from the NuSTAR space observatory on the morning of 25 June. These were high-frame-rate optical observations taken by the ULTRACAM

instrument, sampling timescales down to 35.94 milliseconds (ms). Both optical and X-ray light curves show variability on a broad range of timescales characteristic of this source<sup>15,16</sup> (Fig. 1). The Arcminute Microkelvin Imager (AMI) telescope provided contiguous radio coverage throughout this period. Details of the observations may be found in Methods.

These coordinated observations occurred on 25 June, the day preceding the peak of the 2015 outburst. When the optical observations began, the X-ray intensity was two orders of magnitude below peak, and the spectrum was dominated by low-energy X-rays (that is, it was in a state characterized as being relatively 'soft'). Steady, compact jet activity is not expected in such a state, and consistent with this, the radio spectral index is negative, as is typical of emission from discrete optically thin ejecta. NuSTAR observations were interrupted about 2,000 seconds later by a period of Earth occultation, which separates the two halves (hereafter, 'epochs') of the sequence under consideration.

At some point during this occultation, the source underwent a striking and very rapid change in its X-ray spectral state. When NuSTAR emerged from Earth occultation, the spectrum was instead found to have pivoted towards high energies, with a larger fraction of X-ray counts above 10 keV than below (that is, the state was significantly 'harder'). In addition, there was a sharp rise in radio flux as well as spectral index, all of which signal the strengthening of compact radio jet emission in an X-ray hard state. The fractional root-mean-square amplitude characterizing the strength of the variations also increased in both optical and X-rays. Together, these facts indicate that we serendipitously caught a rapid state transition, with a sharp divide in observed properties between the first and

<footnote n="1">¹Department of Physics and Astronomy, University of Southampton, Southampton SO17 3RT, UK. ²INAF-Osservatorio Astronomico di Cagliari, via della Scienza 5, I-09047 Selargius, Italy. ³Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK. ⁴Instituto de Astrofísica de Canarias, 38205 La Laguna, Santa Cruz de Tenerife, Spain. ⁵Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK. ⁶Cahill Center for Astrophysics, California Institute of Technology, 1216 East California Boulevard, Pasadena, CA 91125, USA. ⁷IRAP, Université de toulouse, CNRS, UPS, CNES, Toulouse, France. ⁸Anton Pannekoek Institute for Astronomy, University of Amsterdam, 1098 XH Amsterdam, The Netherlands. ⁹Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK. ¹⁰Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail Stop 169-221, Pasadena, CA 91109, USA. ¹¹Space Sciences Laboratory, University of California, 7 Gauss Way, Berkeley, CA 94720-7450, USA. ¹²Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK. ¹³INAF-Osservatorio Astronomico di Roma, Via Frascati 33, I-00040 Monteporzio Catone, Italy. ¹⁴DiSAT, Università degli Studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy. ¹⁵INAF-Osservatorio Astronomico di Brera Merate, via E. Bianchi 46, I-23807 Merate, Italy. ¹⁶Department of Astrofísica Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain. ¹⁷ISDC, Department of Astronomy, University of Geneva, Chemin d'Ecogia 16, CH-1290 Versoix, Switzerland. ¹⁸Department of Physics and Astronomy, Louisiana State University, 202 Nicholson Hall, Tower Drive, Baton Rouge, LA 70803, USA. ¹⁹ESA/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands. ²⁰Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411007, India. ²¹European Southern Observatory, K. Schwarzschild-Strasse 2, D-85748 Garching bei München, Germany. ²²New York University Abu Dhabi, PO Box 129188 Abu Dhabi, United Arab Emirates. ²³Department of Physics, University of Alberta, CCIS 4-183, Edmonton AB T6G 2E1, Canada.
*e-mail: P.Gandhi@soton.ac.uk</footnote>
<figure><img src="image_2.png" /></figure>

**Fig. 1** | Multiwavelength light curves and timing correlations of V404 Cygni on 25 June 2015. All times have been transformed to the common Solar System barycentre (BMJD). **a**, WHT/ULTRACAM optical *r*-band light curve at a time resolution of 35.94 ms. The inset zoom-in highlights a short, fast flaring episode, probably marking the moment of the serendipitously caught state transition. **b**, NuSTAR full band X-ray light curve. There are two epochs of strict simultaneity with the optical, corresponding to two satellite orbits, separated by an Earth occultation gap. **c**, NuSTAR hardness ratio between bands 10–79 keV and 3–10 keV, lightly binned with a 5 s kernel for display purposes. **d**, AMI 15.4 GHz light curve. Uncertainties for panels **a–d** are typically smaller than symbol sizes. **e**, Radio spectral index ($\alpha_{radio}$) between frequencies ($\nu$) of 15.4 GHz and 13.9 GHz (defined such that flux density $F_s \propto \nu^{\alpha_{radio}}$) with errors denoting 1 standard deviation over the approximately 350-s-long segments used for binning. **f, g**, Optical versus X-ray discrete cross-correlation functions (DCF) between lag times of -1 and +1s, for the two epochs. Uncertainties denote 1 standard error of the mean for each lag bin. A positive delay corresponds to the optical lagging of the X-rays.

second epochs. This was the final transition leading up to the over-all outburst peak on the following day (Fig. 2), when the source displayed enhanced gamma-ray emission¹⁷, exceedingly bright X-ray¹⁶ and radio¹⁵ emission, and pronounced subsecond optical flaring¹⁵. Pinpointing any one instant as the moment of the transition is not possible, but we note the sudden appearance of a short-lived rapid optical flaring episode about midway into the occultation (Fig. 1a), which may be regarded as the likely point of transition.

Cross-correlating the light curves reveals the short optical time delay with respect to X-rays (Fig. 1). Whereas no lag is apparent during the first epoch, a significant signal appears in the timing correlation function during the second epoch. The signal is skewed towards positive optical lags, with a weighted time delay $\tau=+0.13 \pm 0.04$ s of the optical with respect to X-rays. The delay is

present in shorter light-curve segments, and also in the Fourier domain lags, confirming its robust detection (Supplementary Information). The percentage probability of the signal arising by chance is less than 1%. Correlations between the optical and X-rays on longer (seconds to minutes) timescales have already been reported¹⁸,¹⁹ and are visually apparent for the broad flares in Fig. 1 also. The rapid and regular cadence of our observations, combined with exquisite data quality due to the brightness of the outburst, has allowed us to push time-lag detections to the subsecond regime.

A handful of other black-hole binaries are known to show considerable optical variability, including both positive and negative responses to X-ray variations, on characteristic timescales of order seconds and less²⁰. Their origin remains under debate, with possibilities including a magnetically active corona, an advective flow,
<figure><img src="image_3.png" /><figcaption>**Fig. 2** | X-ray evolution of V404 Cygni leading to outburst peak. **a,** The full NuSTAR light curve for the hardness ratio between 10–79 keV and 3–10 keV, plotted using 5 s time bins. Uncertainties (1 standard deviation) are typically less than 10% on any point and are omitted for clarity of display. **b,** INTEGRAL IBIS/ISGRI 25–200 keV light curve covering the period of 24–26 June 2015. Uncertainties denoting 1 standard deviation are plotted but are typically smaller than symbol sizes. The peak of the outburst occurred on 26 June, following which the outburst gradually declined to quiescence. The red arrows in panel **a** denote the times of ULTRACAM optical observations on 25 June covering the state transition (see Fig. 1) and 26 June (when rapid optical flaring was highly developed; ref. 15). Bin widths denote the time interval of data averaging.</figcaption></figure>

a jet or a combination of components$^{4–8}$. Evidence to distinguish between these models has been lacking so far.

We now have this evidence for V404 Cygni. There is a clear change in the timing correlation between the optical and X-rays as a function of radio flux across the state transition. The subsecond delay is significantly detected only during the second epoch, when both radio flux and spectral index rose sharply. This strongly supports a causal link between the jet and the subsecond fluctuations. The delay $\tau$ corresponds to a maximal distance scale of the order $c\tau = 1.4(\pm0.4) \times 10^3$ Schwarzschild radii ($R_s = 2GM_{BH}/c^2$, with G being the gravitational constant and c the speed of light) for a black-hole mass $M_{BH} = 9$ solar masses, $M_\odot$ (ref. 21). The expected timescales for X-ray heating of the outer disk or the companion are of the order of tens of seconds, much longer than the fast delay under question here. Any reprocessing of X-rays in an axisymmetric disk wind known in this system is expected to occur on similarly long timescales (Supplementary Information). An inner hot flow powering the fast optical and X-ray variations is, likewise, incompatible with the data because it predicts the two bands to be anticorrelated$^7$. We therefore associate the inferred compact scale with the inner jet, where optical emission is expected to arise as synchrotron radiation. Detection of a lag alone cannot fully constrain the geometry of the optical emission zone in the inner jet. But additional support for this hypothesis comes from the fact that the subsecond flaring is significantly redder (as expected from optically thin synchrotron) than other emission components$^{15}$. Moreover, a red spectral shape argues against an origin due to standard thermal reprocessing$^5$. Finally, a rise in optical polarization was detected together with rising radio fluxes during the present outburst$^{22}$, interpreted as evidence for optical synchrotron radiation.

Spectral analysis of the NuSTAR data constrains the X-ray emission region also to be compact. In particular, the brightest flares seem to be extremely hard spectral events confined to $\lesssim 5 R_s$ (ref. 17). The emission source for these X-rays can be attributed to the hot electron corona overlying the disk, or the base of the jet, which may be cop spatial. Emission during fainter episodes instead originates in a geometrically thick and absorbed flow$^{23}$. Irrespective of the

physical mechanism of X-ray emission, there seems to be no doubt that it must occur in a compact region very close to the black hole.

Based upon the above observational facts, we interpret our measurement of $\tau$ as the characteristic propagation delay between the X-ray and the first optical emission zone (the ‘optical base’) in the inner jet (Fig. 3). This association is important because it constrains the physical scale over which plasma is accelerated in the inner jet. The physics of feeding, acceleration and collimation of the plasma within this acceleration and collimation zone (ACZ) is thought to be governed by magnetohydrodynamic (MHD) processes$^3$. In the blazar BL Lacertae, which is a jet-dominant supermassive black hole, synchrotron flaring is observed both within the ACZ at elevations of several hundred $R_s$ above the black hole as radiation from accelerated plasma knots is beamed toward the line-of-sight, and also as the plasma crosses a standing shock at an elevation of $\sim 10^4 R_s$ where the ACZ is estimated to terminate$^{12}$. Disruptions leading to shocks in a MHD flow probably require a combination of being beyond the causality surface for fast magnetosonic waves, and some change in external pressure or other perturbative forces. Where exactly this occurs, and why, is currently unknown and must be determined observationally, but once determined provides a critical constraint on numerical models. With the X-rays arising from very close to the black hole in V404 Cygni, and the origin of the rapid optical flares being inner jet synchrotron, the simplest interpretation is that our measured delay $\tau$ corresponds to the ACZ crossing time of the plasma (in the observed frame of reference), thus placing a limit of $\sim 10^3 R_s$ on its elevation above the black hole. Some of the flares may instead arise from within the ACZ, as in BL Lac. However, our timing cross-correlations here measure a bulk property of the flow of the continuous jet, rather than the location of any single knot, and thus provide a robust limit to the ACZ elevation in V404 Cygni.

Once a steady jet has been launched, its characteristic broadband emission spectrum must also be explained. These spectra are typically flat in flux density units, which requires that adiabatic expansion losses be somehow compensated for. This has motivated internal shock models in which collisions between plasma shells with a velocity shear provide the requisite energy injection mechanism$^{10,24}$. The location of the optical base of the jet corresponds to the zone where such shocks are first produced. If the jet is fed by the accretion flow, a time lag between the X-ray emitting accretion flow and the shock synchrotron radiation is expected, with the magnitude of this lag depending mostly on the characteristic timescale of velocity fluctuations driving the shocks. Lags $\tau$ of order 0.1 s may naturally be obtained under the assumption that the power spectrum of the distribution of shock Lorentz factors is similar to that powering the X-ray emission$^{10}$. However, despite the presence of flux variations on all timescales, the power spectra of the X-ray emission of V404 Cygni during the present observations are dominated by slow fluctuations (Supplementary Information), thus predicting a much longer lag. This is strongly constraining in that it rules out the jet Lorentz-factor fluctuations being driven by the observed X-ray variability during this state transition, arguing for a revision of current models. We cannot, however, exclude the possibility that complex absorption$^{23}$ or reflection$^{16}$ effects are conspiring to suppress the fastest X-ray fluctuations from being observed.

Much of the physics of jets is considered to be scale-invariant, with supermassive black-hole jets being the scaled-up counterparts of the stellar-mass systems under consideration here$^{25,26}$. State-of-the-art MHD models allow for a wide range of standing shock elevations, depending upon conditions at the jet formation zone (C.C. et al., manuscript in preparation). Our measured elevation of $\lesssim 10^3 R_s$ in V404 Cygni is similar to (although perhaps closer to the lower end of) the scales over which flaring occurs in BL Lac, suggestive of mass-scaled similarities in the relevant MHD physics. Whether it is a combination of MHD effects and environmental pressure or some other perturbation that governs this location will
<figure><img src="image_4.png" /></figure>

**Fig. 3** | Schematic of the post-transition accretion and jet geometry of V404 Cygni. The black hole and accretion disk are situated to the right. X-rays originate in a compact region within ~5R<sub>s</sub> of the black hole owing to redistribution of photon energies through the Compton effect (either jet or coronal). Optical photons are delayed with respect to X-rays by ~0.1s. This 'optical base' lies ≤10<sup>3</sup> R<sub>s</sub> from the X-ray core, and should power broadband synchrotron radiation extending to high frequencies. The above time delay limits the extension of the putative acceleration and collimation zone (ACZ). Beyond the optical base, shocks in the longitudinally and laterally expanding jet inject energy that power the broadband lower-frequency radiation down to the radio.

need to be explored. Our work provides the boundary conditions enabling such an investigation.

Only two other low-mass X-ray binaries with strong jet optical emission have high-quality timing observations allowing a detailed search for subsecond correlation signals. These are XTE J1118+480<sup>27</sup> and GX 339–4<sup>8</sup>, both with strictly simultaneous data in optical and X-rays at high time resolution. There are, however, important differences from our work reported here. XTE J1118+480 was observed in a different state during outburst decline with falling optical, infrared and X-ray emission, and showed a broad continuum range of optical time lags interpreted as continuous dissipation of a reservoir of energy<sup>5</sup>. The declining emission implies that the jet was probably not at peak at this time. On the other hand, GX 339–4 displayed a clear ~0.1 s optical delay<sup>8</sup>, but no corresponding state transition with changing jet activity was probed in that case. Our observations of such changes in V404 Cygni firmly support the association with inner jet activity argued for GX 339–4. This is true despite differences between the two systems. In particular, V404 Cygni has an orbital period almost four times as long as GX 339–4 and thus a much larger accretion reservoir. This large reservoir may be responsible for the pronounced slower (~100–1,000 s long) variations exclusive to V404 Cygni, and interpreted either as instabilities in the disk<sup>28</sup> or as an extended corona (Dallilar et al., manuscript in preparation). Irrespective of this, the subsecond flaring can be cleanly separated from these slower fluctuations in terms of colour and characteristic timescales<sup>15</sup>, implying an independent origin.

## Methods

**Observations.** ULTRACAM. ULTRACAM<sup>29</sup> is a fast optical imager capable of high sampling rates (up to several hundred Hz) in three filters simultaneously. The ULTRACAM data on the 2015 outburst of V404 Cygni, without any X-ray analyses, have been described previously<sup>15</sup>, focusing on 26 June, the day following the light curve described herein. The time resolution (ΔT) during the 25 June observation used here was 35.94 ms, constant throughout the observation. This is the cycle time between consecutive exposures and includes a short dead time of approximately 1 ms. Data were obtained in three optical filters simultaneously

(u', g' and r'), but the r' data had by far the best combination of signal-to-noise ratio (SNR) and time resolution. The SNR is a factor of 2 better in r' than g', and the time resolution is a factor of 15 worse in u' because of the need for coadding frames to gain sensitivity. Hence, we focus on the r' data in this work, although the source behaviour is qualitatively similar in all optical filters. The light curve times were transformed to the Solar System barycentre by using custom ULTRACAM software, based upon the positional astronomy library SLALIB.

**NuSTAR.** NuSTAR (the Nuclear Spectroscopic Telescope Array)<sup>30</sup> is the first X-ray telescope in orbit capable of focusing photons above 10 keV and is highly sensitive up to approximately 80 keV. NuSTAR carried out a long (~3 day) Target of Opportunity observation triggered by the outburst of V404 Cygni, and we were able to coordinate an ~2 hour optical observation with the WHT/ULTRACAM in the early morning hours of 25 June 2015 which is the focus of the analysis herein.

The NuSTAR data are described in more detail elsewhere<sup>16</sup>. Here we give salient details only. The NuSTAR detectors are not affected by pileup issues. But at high count rates above several hundred per second, dead time becomes important, and the X-ray light curves herein were all corrected for dead time<sup>11</sup>. The full energy range of 3–79 keV is used, summing up counts from both focal plane modules (FPMA and FPMB). Events were barycentred using BARYCORR with FTOOLS<sup>32</sup> with a clock correction file that covered the full observation. For cross-correlating the multiwavelength light curves, the X-ray data were sampled using identical time bins to the optical. In order to do this, the X-ray barycentred event times were converted to Universal Time Coordinated (UTC) and then binned using the exact time bin boundaries (which are uniformly spaced in UTC). The binned X-ray light curves then exactly match the barycentred optical data. Background is ignored as the source completely dominates the NuSTAR field of view.

**Epochs of simultaneity.** After removing the Earth occultation gap and a few data points at the edges of the gap, there are two epochs of strict simultaneity between optical and X-rays. Epoch 1 is 2,112.6s long, starting at barycentric Modified Julian Date (BMJD) 57198.15404876 and finishing at 57198.17850000. Epoch 2 has a duration of 1,820.3s and lasts between BMJD 57198.20800000 and 57198.22906829.

**AMI.** Radio imaging data were obtained by the AMI<sup>13</sup>. Those data will be described elsewhere (R.P.F. et al., manuscript in preparation). For the analysis here, we use light curves extracted using time bins of 20 s at 13.9 and 15.4 GHz. The light curve in Fig. 1 shows a brightening in radio flux by a factor of approximately 5 in Epoch 2, as compared with Epoch 1. In addition, the radio spectral index also rises considerably, from being significantly negative in Epoch 1 to being consistently
above 0 in Epoch 2, with a maximum value of 0.68±0.17. Segments approximately 350 s in length were binned to increase the SNR of the spectral index trend.

INTEGRAL. The INTEGRAL³⁴ mission provided some of the best coverage of the 2015 outburst. Light curve data products in standard bands for all instruments have been made publicly available³⁵. The IBIS/ISGRI instrument³⁶ light curve covering the energy range of 25–200 keV is displayed in Fig. 2 to show the long-term evolution starting from before our ULTRACAM/NuSTAR campaign and continuing until outburst peak on 26 June. The light curve demonstrates that the state transition that we caught was unique during this period, with the source remaining bright and flaring until the end, even after the NuSTAR observation had finished.

**Timing correlation and lag.** One popular estimator of the degree of correlation between two bands is the discrete correlation function (DCF), which measures the averaged cross product between all pairs of lags defined by the sampling times of the two light curves. We computed the DCF between the optical and the X-rays according to the algorithm of ref. ³⁷, for the strictly simultaneous epochs separately. Each epoch was divided into 10⁴ independent segments, and the DCF computed over time lags between ±1 s after pre-whitening to remove any red noise trend³⁸. The mean DCF and its standard error were computed at each time lag, and the results for the two epochs are shown in Fig. 1.

We quantified the lags by computing their centroid, which is defined as the mean of the individual lags ($t_i$) weighted by the DCF coefficients $c_i$ (refs. ³⁹,⁴⁰):

$$ \tau = \sum_{i} (c_{t_i}) / \sum_{i} (c_i) $$

Following standard practice⁴⁰, the summation is over all $t_i$ where the DCF coefficients $c_i$ have values above half of the peak (representing an approximate weighted mean of the full-width DCF at half-maximum). The error on $\tau$ is computed by generating an ensemble of 10⁴ DCFs by using the scatter in the coefficients from the independent data segments to randomize the coefficients at all lags. This results in 10⁴ mean-weighted centroid lags ($\tau_{random}$), and the standard deviation of $\tau_{random}$ is used as the error estimator of $\tau$.

**Data availability.** The data that support the plots within this paper and other findings of this study are available from public archives and the corresponding author upon reasonable request.

Received: 24 February 2017; Accepted: 7 September 2017; Published online: 30 October 2017

## References

1. Blandford, R. D. & Znajek, R. L. Electromagnetic extraction of energy from Kerr black holes. *Mon. Not. R. Astron. Soc.* **179**, 433–456 (1977).

2. Blandford, R. D. & Payne, D. G. Hydrodynamic flows from accretion discs and the production of radio jets. *Mon. Not. R. Astron. Soc.* **199**, 883–903 (1982).

3. Meier, D. L., Koide, S. & Uchida, Y. Magnetohydrodynamic production of relativistic jets. *Science* **291**, 84–92 (2001).

4. Merloni, A. et al. Magnetic flares and the optical variability of the X-ray transient XTE J1118+480. *Mon. Not. R. Astron. Soc.* **318**, L15–L19 (2000).

5. Malzac, J. et al. Jet-disc coupling through a common energy reservoir in the black hole XTE J1118+480. *Mon. Not. R. Astron. Soc.* **351**, 253–264 (2004).

6. Yuan, F. et al. An accretion-jet model for black hole binaries: interpreting the spectral and timing features of XTE J1118+480. *Astrophys. J.* **620**, 905–914 (2005).

7. Veledina, A. et al. Hot accretion flow in black hole binaries: a link connecting X-rays to the infrared. *Mon. Not. R. Astron. Soc.* **430**, 3196–3212 (2013).

8. Gandhi, P. et al. Rapid optical and X-ray timing observations of GX 339–4: flux correlations at the onset of a low/hard state. *Mon. Not. R. Astron. Soc.* **390**, L29–L33 (2008).

9. Markoff, S. et al. A jet model for the broadband spectrum of XTE J1118+480. Synchrotron emission from radio to X-rays in the Low/Hard spectral state. *Astron. Astrophys.* **372**, L25–L28 (2001).

10. Malzac, J. The spectral energy distribution of compact jets powered by internal shocks. *Mon. Not. R. Astron. Soc.* **443**, 299–317 (2014).

11. Polko, P. et al. Linking accretion flow and particle acceleration in jets: II. Self-similar jet models with full relativistic MHD gravitational mass. *Mon. Not. R. Astron. Soc.* **438**, 959–970 (2014).

12. Marscher, A. et al. The inner jet of an active galactic nucleus as revealed by a radio-to-gamma-ray outburst. *Nature* **452**, 966–969 (2008).

13. Cohen, M. H. et al. Studies of the jet in Bl Lacertae. I. Recollimation shock and moving emission features. *Astrophys. J.* **787**, 151–160 (2014).

14. Casella, P. et al. Fast infrared variability from a relativistic jet in GX 339–4. *Mon. Not. R. Astron. Soc.* **404**, L21–L25 (2010).

15. Gandhi, P. et al. Furiously fast and red: sub-second optical flaring in V404 Cyg during the 2015 outburst peak. *Mon. Not. R. Astron. Soc.* **459**, 554–572 (2016).

16. Walton, D. J. et al. Living on a flare: relativistic reflection in V404 Cyg observed by NuSTAR during its summer 2015 outburst. *Astrophys. J.* **839**, 110–132 (2017).

17. Loh, A. et al. High-energy gamma-ray observations of the accreting black hole V404 Cygni during its 2015 June outburst. *Mon. Not. R. Astron. Soc.* **462**, L111–L115 (2016).

18. Gandhi, P. et al. Correlated optical and X-ray variability in V404 Cyg. *Astron. Telegr.* **7727** (2015).

19. Rodriguez, J. et al. Correlated optical, X-ray, and γ-ray flaring activity seen with INTEGRAL during the 2015 outburst of V404 Cygni. *Astron. Astrophys.* **581**, L9–L13 (2015).

20. Durant, M. et al. High time resolution optical/X-ray cross-correlations for X-ray binaries: anticorrelation and rapid variability. *Mon. Not. R. Astron. Soc.* **410**, 2329–2338 (2011).

21. Khargharia, J., Froning, C. S. & Robinson, E. L. Near-infrared spectroscopy of low-mass X-ray binaries: accretion disk contamination and compact object mass determination in V404 Cyg and Cen X-4. *Astrophys. J.* **716**, 1105–1117 (2010).

22. Shahbaz, T. et al. Evidence for magnetic field compression in shocks within the jet of V404 Cyg. *Mon. Not. R. Astron. Soc.* **463**, 1822–1830 (2016).

23. Motta, S. et al. The black hole binary V404 Cygni: an obscured AGN analogue. *Mon. Not. R. Astron. Soc.* **468**, 981–993 (2017).

24. Jamil, O., Fender, R. P. & Kaiser, C. R. iShocks: X-ray binary jets with an internal shock model. *Mon. Not. R. Astron. Soc.* **401**, 394–404 (2010).

25. Falcke, H., Körding, E. & Markoff, S. A scheme to unify low power accreting black holes. *Astron. Astrophys.* **414**, 895–903 (2004).

26. Merloni, A. et al. A fundamental plane of black hole activity. *Mon. Not. R. Astron. Soc.* **345**, 1057–1076 (2003).

27. Kanbach, G. et al. Correlated fast X-ray and optical variability in the black-hole candidate XTE J1118+480. *Nature* **414**, 180–182 (2001).

28. Kimura, M. et al. Repetitive patterns in rapid optical variations in the nearby black-hole binary V404 Cygni. *Nature* **529**, 54–58 (2016).

29. Dhillon, V. S. et al. ULTRACAM: an ultrafast, triple-beam CCD camera for high-speed astrophysics. *Mon. Not. R. Astron. Soc.* **378**, 825–840 (2007).

30. Harrison, F. et al. The Nuclear Spectroscopic Telescope Array (NuSTAR) high-energy X-ray mission. *Astrophys. J.* **770**, 103–131 (2013).

31. Bachetti, M. et al. No time for dead time: timing analysis of bright black hole binaries with NuSTAR. *Astrophys. J.* **800**, 109–120 (2015).

32. Blackburn, J. K. FTOOLS: A FITS data processing and analysis software package. *Astr. Soc. P.* **77**, 367–370 (1995).

33. Zwart, J. T. L. et al. The Arcminute Microkelvin Imager. *Mon. Not. R. Astron. Soc.* **391**, 1545–1558 (2008).

34. Winkler, C. et al. The INTEGRAL mission. *Astron. Astrophys.* **411**, L1–L6 (2003).

35. Kuulkers, E. INTEGRAL observations of V404 Cyg (GS 2023+338): public data products. *Astron. Telegr.* **7758** (2015).

36. Ubertini, P. et al. IBIS: the imager on-board INTEGRAL. *Astron. Astrophys.* **411**, L131–L139 (2003).

37. Edelson, R. A. & Krolik, J. H. The discrete correlation function: a new method for analyzing unevenly sampled variability data. *Astrophys. J.* **333**, 646–659 (1988).

38. Welsh, W. F. On the reliability of cross-correlation function lag determinations in active galactic nuclei. *Publ. Astron. Soc. Pac.* **111**, 1347–1366 (1999).

39. Koratkar, A. P. & Gaskell, C. M. Structure and kinematics of the broad-line regions in active galaxies from IUE variability data. *Astrophys. J. Suppl.* **75**, 719–750 (1991).

40. Peterson, B. M. et al. On uncertainties in cross-correlation lags and the reality of wavelength-dependent continuum lags in active galactic nuclei. *Publ. Astron. Soc. Pacific.* **110**, 660–670 (1998).

## Acknowledgements

This research has made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA), as well as the High Energy Astrophysics Science Archive Research Center. P.G. thanks the Science and Technology Facilities Council (STFC) for support (grant reference ST/J003697/2). ULTRACAM and V.S.D. are supported by STFC grant ST/M001350/1. P.G. thanks C.B. Markwardt, C.M. Boon, A.B. Hill, M. Fiocchi, K. Forster, A. Zoghbi and T. Muñoz-Darias for help and discussions. J.C. acknowledges financial support from the Spanish Ministry of Economy, Industry and Competitiveness (MINECO) under the 2015 Severo Ochoa Program MINECO SEV-2015-0548, and to the Leverhulme Trust through grant VP2-2015-04.
T.R.M. acknowledges STFC (ST/L000733/1). J.M. acknowledges financial support from the French National Research Agency (CHAOS project ANR-12-BS05-0009), and D.A. thanks the Royal Society. S.M. acknowledges support from Netherlands Organisation for Scientific Research (NWO) VICI grant no. 639.043.513. We thank P. Wallace for use of his SLA C library. P.A.C. is grateful to the Leverhulme Trust for the award of a Leverhulme Emeritus Fellowship. Part of this research was supported by the UK-India UKIERI/UGC Thematic Partnership grants UGC 2014-15/02 and IND/ CONT/E/14-15/355. This work profited from discussions carried out during a meeting organized at the International Space Science Institute (ISSI) Beijing by T. Belloni and D. Bhattacharya.

**Author contributions**

P.G. wrote the ULTRACAM proposal, analysed the data and wrote the paper. The ULTRACAM observations were coordinated and carried out by L.K.H., S.P.L., V.S.D. and T.R.M. The X-ray observations were proposed by D.J.W., coordinated by D.S., J.A.T. and F.A.H., and the timing data analysed by M.B. Radio data were obtained and analysed by

R.P.F. and K.M. INTEGRAL data were arranged by E.K. The remaining authors provided insight into jet physics constraints (S.M., J.M., C.C.), cross-correlation analyses (P.C., R.I.H., C.K., C.F., M.P., F.V.) and placing the source in context (D.A., J.C., P.A.C., D.M.R., F.R., A.W.S.). All authors read and commented on multiple versions of the manuscript.

**Competing interests**

The authors declare no competing financial interests.

**Additional information**

**Supplementary information** is available for this paper at https://doi.org/10.1038/s41550-017-0273-3.

**Reprints and permissions information** is available at www.nature.com/reprints.

**Correspondence and requests for materials** should be addressed to P.G.

**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.