Simultaneous X-ray and optical spectroscopy of V404 Cygni supports the multi-phase nature of X-ray binary accretion disc winds

Observational signatures of accretion disc winds have been found in a significant number of low-mass X-ray binaries at either X-ray or optical wavelengths. The 2015 outburst of the black hole transient V404 Cygni provided a unique opportunity for studying both types of outflows in the same system. We used contemporaneous X-ray (Chandra Observatory) and optical (Gran Telescopio Canarias, GTC) spectroscopy, in addition to hard X-ray light curves (INTEGRAL). We show that the kinetic properties of the wind, as derived from P-Cyg profiles detected in the optical range at low hard X-ray fluxes and in a number of X-ray transitions during luminous flares, are remarkably similar. Furthermore, strictly simultaneous data taken at intermediate hard X-ray fluxes show consistent emission line properties between the optical and the X-ray emission lines, which most likely arise in the same accretion disc wind. We discuss several scenarios to explain the properties of the wind, favouring the presence of a dynamic, multi-phase outflow during the entire outburst of the system. This study, together with the growing number of wind detections with fairly similar characteristic velocities at different wavelengths, suggest that wind-type X-ray binary outflows might be predominantly multi-phase in nature.


Introduction
Active low-mass X-ray binaries (LMXBs), where a stellar-mass black hole or a neutron star is accreting material from a lowmass donor, provide one of the best opportunities for studying accretion and outflows processes in strong gravity conditions (e.g. Fender et al. 2004). Multiwavelength observations of these systems (e.g. Corral-Santana et al. 2016;Tetarenko et al. 2016) have revealed the presence of two main (X-ray) accretion states (hard and soft), as well as associated outflows in the form of collimated jets (mainly detected in radio waves) and massive winds (e.g. Remillard & McClintock 2006;Done et al. 2007;Belloni et al. 2011;Fender & Muñoz-Darias 2016 for reviews). In particular, accretion disc winds have been detected in a number of LMXBs at (mainly) X-ray and optical wavelengths. They are thought to have a fundamental impact on the accretion process, as they can carry significant amounts of mass and angular momentum (see e.g. Neilsen et al. 2011;Ponti et al. 2012;Tetarenko et al. 2018;Casares et al. 2019;Dubus et al. 2019).
The so-called hot winds are detected via X-ray spectroscopy in systems seen at high orbital inclination (i.e. closer to edgeon) during relatively soft accretion states (e.g. Ueda et al. 1998;Miller et al. 2006;Neilsen & Lee 2009;Ponti et al. 2012Ponti et al. , 2014Díaz Trigo & Boirin 2016). Likewise, optical spectroscopy has revealed the presence of P-Cyg line profiles and other conspicuous signatures of colder winds in several LMXBs (e.g. Muñoz-Darias et al. 2016, hereafter MD16;Muñoz-Darias et al. 2018). More recently, the intense follow-up of the black-hole transient MAXI J1820+070 throughout its entire discovery out-burst showed that optical P-Cyg profiles were solely present during the hard state, while near-infrared wind signatures could be still detected during the soft state . This picture is consistent with optical and near-infrared observations of up to ten other systems (see Table 2 in Panizo-Espinar et al. 2022), including outbursts with more limited coverage (e.g. Mata Sánchez et al. 2022), hard state-only outburst (e.g. Cúneo et al. 2020), and persistent sources (Bandyopadhyay et al. 1997). While the above works have demonstrated that both hot and cold winds are common (if not ubiquitous) in X-ray binaries, it is unclear whether they are different types of outflows or whether they represent different faces of the same phenomenon. Simultaneous wind detections have been reported in the optical and the near-infrared (Sánchez-Sierras & Muñoz-Darias 2020), as well as in the optical and the ultraviolet Castro Segura et al. 2022) regimes. However, a simultaneous study of hot (Xray) and cold (optical) wind-type outflows has not been possible to date.
The 2015 outburst of the black hole transient V404 Cygni was arguably among the most revealing ones ever recorded. During this luminous and violently variable event, the system displayed a rather unique phenomenology across the electromagnetic and time domains (e.g. Rodriguez et al. 2015;Kimura et al. 2016;Gandhi et al. 2016;Siegert et al. 2016;Motta et al. 2017a;Tetarenko et al. 2017;Miller-Jones et al. 2019). However, the outburst was surprisingly short, with the most active phase merely lasting two weeks, which has been proposed to be a consequence of the massive wind that was repeatedly detected via

Observations and data reduction
We analysed the two Chandra observations (hereafter, obs-1 and obs-2) taken during the luminous phase of the outburst (see Plotkin et al. 2017 for additional pointings taken during the decay), together with two contemporaneous spectroscopic epochs taken with the Gran Telescopio Canarias (GTC): one taken 28 minutes after the first Chandra observation ended (hereafter, GTC-1) and another one that was strictly simultaneous with the second Chandra window (hereafter, GTC-2). The start and end times for each observation are summarised in Table 1.

X-rays
In an effort to avoid radiation damage as a result of the exceptional brightness of V404 Cygni, the Chandra observations were performed with the ACIS-S array in continuous clocking mode and with the zeroth-order position located off the detector array. Therefore, only positive and negative orders are available for the medium-energy grating (MEG) and high-energy grating (HEG), respectively. The Chandra data were reprocessed with the chandra_repro task of the ciao software and the keyword recreate_tg_mask set as yes, in order to improve the location of the zeroth-order. Spectra and response matrices were computed with tgextract and mktgresp tasks, respectively, applying the proper selection in time. To check the accuracy of the zeroth-order location, we compared our spectra with the ones downloaded from the Chandra Grating-Data Archive and Catalog (TGCat; Huenemoerder et al. 2011 1 ), finding a good agreement.
In order to optimise the signal-to-noise ratio (S/N), we used MEG data (with a resolution of ∆λ ∼ 0.023 Å) above 6.5 Å (<1.9 keV), while the spectral range below 4 Å (i.e. > 3.1 keV) is covered by HEG data only (at ∆λ ∼ 0.012 Å) 2 . Within 4-6.5 Å we combined both HEG and MEG datasets (at the MEG resolution and wavelength scale). In addition, we made use of the X-ray light curve (25-200 keV) from INTEGRAL (Winkler et al. 2003), which covers obs-2 entirely. We used this dataset (Kuulkers 2015) with a time resolution of ∼ 64s (see MD16 for details and Rodriguez et al. 2015 for the full INTEGRAL analysis during the first part of the outburst).

Optical
Optical spectroscopy (3630-7500 Å) was obtained using the instrument OSIRIS (Cepa et al. 2000) at the GTC (La Palma, Spain). For this work we used the average spectra for each of the two epochs (see Table 1), that were already presented in MD16 and MS18, where we refer the reader for further details on the data reduction. We note that the velocity resolution of this dataset is ∼ 250 km s −1 , significantly better than that of MEG and HEG data (∼ 1100 and 580 km s −1 , respectively at 6 Å). We focus the study on the He i-5876 Å (hereafter He i) and Hα emission lines, the two optical transitions showing the strongest wind features throughout the outburst. These recombination lines are arguably the most relevant optical wind tracers in LMXBs, accreting white dwarfs (e.g. Kafka & Honeycutt 2004) and massive stars (e.g. Prinja et al. 1996).

Analysis and results
An analysis of the Chandra data was presented in K15. To allow for an easy comparison with this work, we initially divided each Chandra pointing into 10 × 3.2 ks (hereafter, spec-1.1 to -1.10) and 9 × 3.2 ks (hereafter, spec-2.1 to -2.9) spectra, respectively. As reported in K15, the data are very rich in emission lines, which show significant variability across the 19×3.2 ks intervals. Figure 1 (bottom panel) shows the average spectrum of obs-2, which is qualitatively very similar to that of obs-1. This work is focussed on the analysis of the recombination line of Si xiv (6.184 Å; 2.005 keV). This is the strongest spectral feature in the soft X-ray band and is covered by both MEG and HEG data. Furthermore, it is a singlet (Lyα) and is located in a spectral region with a relatively flat continuum. These properties make it particularly suited for identifying blue-shifted absorptions and their associated blue-edge velocities. In addition, we also included S xvi (4.732 Å; 2.620 keV) and Mg xii (8.423 Å; 1.472 keV), which are also Lyα transitions sharing to some extent some of the above properties. Each of these lines was treated separately by normalising their adjacent continuum to unity. Finally, for the most interesting epochs the high energy part of the spectrum, and in particular the Fe xxvi Lyα transition (1.778 Å; 6.973 keV), was also studied. For clarity reasons, a slight Gaussian smooth of one pixel was used when representing the X-ray data. The data analysis was performed using molly, xspec and custom routines developed under python.

Chandra observation-1
In agreement with K15, no strong wind features are detected during obs-1 (although spec-1.4 at high flux shows features compatible with weak wind signatures). Given the lack of conspicuous wind-related absorptions and simultaneous INTEGRAL and GTC observations, we decided to use the average spectrum for the entire obs-1 to be compared with the different sets of data derived from obs-2, which will be the main focus of our analysis (see below). We note that a very significant count-rate drop was observed in the last spectrum (i.e. spec-1.10), which resulted in a significantly lower S/N. This is consistent with the flux drop observed in the optical light curves presented in Kimura et al. (2016, see fig. 1) around that time. Therefore, even though GTC-1 started merely 28 minutes after obs-1 ended, this strong flux variability suggest that the properties of the source might be very different between obs-1 and GTC-1, and thus we will treat these windows as completely independent datasets (see Sec. 4).
Interestingly, strong optical wind signatures are present during GTC-1. In particular, He i shows a P-Cyg profile with a blue absorption component at ∼ 1500 km s −1 (dotted vertical line) and a blue-edge velocity of ∼ 3000 km s −1 (blue, dotteddashed vertical line). The Hα line profile is redshifted but shows a prominent blue wing in emission (Fig. 2, right panel). A detailed view of the Hα evolution throughout this observation can be found in Fig. 15 of MS18.  2 ks spectra (also used in K15). Following the hard X-ray evolution, we have divided the observation into three intervals: obs-2.A (spectra 1 to 4; low flux), obs-2.B (5 to 7; plateau), and obs-2.C (8 to 9; flares). Bottom panel: Combined MEG+HEG spectrum. We have labelled the emission lines included in this analysis (see Section 3).

Chandra observation-2
Obs-2 was fully covered by INTEGRAL data (Fig. 1), where large flux variations become evident. In particular, the last two spectra (spec-2.8 and -2.9) include two large flares, with the hard X-ray flux increasing by more than three orders of magnitude with respect to the beginning of the observation. P-Cygni profiles are witnessed during these two epochs, the strongest being those during spec-2.8, in correspondence with the most luminous flares. In order to increase the S/N of the spectra, we divided obs-2 in three intervals based on the INTEGRAL light curve, which is much less affected by intrinsic absorption than soft X-rays and therefore provides a more realistic estimation of the true luminosity of the system (i.e. unabsorbed; see Section 4.2). Thus, obs-2.A includes spec-2.1 to -2.4 (low-flux), obs-2.B covers spec-2.4 to -2.7; (plateau) and obs-2.C includes spec-2.8 and -2.9 (flares). Fig. 2 (left panel) shows how the equivalent width of the Si xiv emission line decreases across obs-2, following the increase in hard X-ray luminosity. In addition, obs-2.C

Fig. 2.
Chandra spectra of Si xiv (top panels) compared with GTC spectroscopy in the He i and Hα regions (mid and bottom panels). The right panels are zoomed version of the left ones aimed at highlighting the blue-shifted absorption features. Dotted vertical lines mark the core velocity (-1500 km s −1 ) of the He i absorption component, while the dotted-dashed vertical lines mark (approximately) its blue-edge velocity (blue; -3000 km s −1 ) and the corresponding receding velocity (red; 3000 km s −1 ).
is characterised by strong P-Cyg features with blue-shifted absorptions reaching values ∼ 20 per cent below the continuum level. Both the core velocity of the absorption component and its blue-edge velocity are comparable to those observed in He i in GTC-1 ( Fig. 2; right panel). The blue emission line wings observed in obs-2.A and obs-2.B (and also in obs-1) reach similar velocities than the blue-edge velocities determined in GTC-1 (i.e. He i) and obs-2.C (dotted-dashed, blue lines). This is also true for the red-edge of the emission line profile, which roughly match the velocity observed in the blue-edge of the P-Cyg absorptions (dotted-dashed lines; red when taken positive).
The P-Cyg profile observed in Si xiv is also detected in S xvi and Mg xii with roughly similar properties, although slight variations in the core and blue-edge velocities of the blue-shifted absorption components might be present ( Fig. 3; see Sec. 4).

Emission line variability
Si xiv is the strongest emission line in the soft part of the spectrum and shows strong variability throughout obs-2, including blue-shifted absorptions during obs-2.C. In order to characterise this variability we performed a Gaussian fit to the line profile of the 9×3.2 ks spectra, with the velocity offset (from the rest wavelength), the width (corrected from the MEG velocity resolution), and the height of the Gaussian as free parameters. The results are presented in Fig. 4 and Table 2. The centroid of Si xiv is observed to shift towards larger velocity values as the hard X-ray activity increases. In particular, the largest velocity offsets are measured in the spectra that include flaring activity (see Fig. 1): spec-2.5, -2.6 and particularly spec-2.8 and -2.9. Contrastingly, the lowest values are found at low X-ray fluxes (i.e. obs-2.A) and also in spec-2.7 during the plateau phase (but without clear flaring events present). Also, S xvi and Mg xii show significant variability throughout obs-2. However, their worse S/N results in larger error bars when fitting the 9×3.2 ks spectra. Nonetheless, when using the three spectra of the obs-2 intervals we obtained velocity offsets that are consistent with the trend seen in Si xiv (see Table 2). We note that although the theoretical (absolute) wavelength accuracy at Si xiv (6.184 Å) varies between 290 and 530 km s −1 (HEG and MEG), it has been empirically found to be as good as ∼ 30 km s −1 for both HEG and MEG data (Ishibashi et al. 2006). Nevertheless, the relative wavelength accuracy between observations is expected to be in the range of ∼ 50-100 km s −1 . The above indicates that the observed trend is real and that significant redshifts are associated with the epochs dominated by luminous hard X-ray flares. The FWHM of Si xiv is observed to be 1166 ± 57, 1207 ± 96 and 950 ± 156 km s −1 for obs-2A, -2B, and -2C, respectively. S xvi and Mg xii show roughly consistent values (see Table 2). The narrower lines observed during obs-2C are in agreement with the detection of P-Cyg profiles. Table 2 also reports the fits for the three Lyα transitions for the entire obs-1 and obs-2. In agreement with K15, we obtain small velocity offsets in the range of ∼ ± 100 km s −1 for both observations, although values tend to be redshifted for obs-2, as expected given the presence of P-Cyg profiles. The typical FWHM for both observations is ∼ 1200 km s −1 .

Strictly simultaneous data
Observation GTC-2 was partially covered by Chandra spec-2.5 and spec-2.6. In order to perform a more direct comparison we computed the Chandra spectrum during the 2.3 ks simultaneous with GTC-2. The associated hard X-ray flux during GTC-2 is one order of magnitude lower than the peak of the flares in obs-2.C. However, it includes a smaller flare that occurred during the transition between spec-2.5 and spec-2.6 ( Fig. 1). Fig. 4 (right panels) shows the line profiles of the X-ray and optical lines in-cluded in our analysis. None of the emission lines show P-Cyg profiles, but they are all significantly redshifted (see Table 2). In particular, Si xiv is roughly symmetric and centred at ∼ 400 km s −1 , while the optical lines are centred at ∼ 140 km s −1 (MD16). S xvi and Mg xii show nominal redshifts consistent with those of Si xiv. However, these lines are more complex and non-symmetric, with a secondary red component clearly present and a main emission line peak that is only slightly redshifted (similar to that of the optical lines).
The FWHM of Hα during GTC-2 is ∼ 940 km s −1 (varying in the range of 875 -993 km s −1 ; MS18), which is lower than observed in obs-2.A and -2.B (1100-1300 km s −1 ). However, when computing the FWHM of Si xiv during GTC-2, we obtain 889 ± 207, which is consistent with that measured in the optical emission lines (see also Fig 4).

High-energy spectrum
The Chandra high-energy spectrum is significantly more complex than the soft one. A detailed analysis of this spectral region is beyond the scope of this work. However, we note that blueshifted absorptions are present during obs-2.C (see also K15). Figure 5 shows the Fe xxvi (Lyα) transition together with Fe xxv. These components are broader than those observed at lower energies but their core velocities match (rather precisely) that of He i (and, consequently, the soft X-ray transitions during obs-2.C; Fig. 2). The continuum of the high-energy spectrum is more complex than that of the soft X-rays lines, which hampers a clear identification of the blue-edge velocity. However, it might be still consistent with the ∼ 3000 km s −1 observed in the optical and soft X-ray emission lines (as we discuss below).

Discussion
The black hole transient V404 Cygni displayed strong X-ray (K15) and optical (MD16) accretion disc wind signatures during the most active part (∼ 12 days) of its 2015 outburst. In this work, we have analyse the only contemporaneous observations (including simultaneous data) taken with Chandra and GTC over two consecutive days within this activity period. Although our study includes recombination lines of species with largely different excitation potentials, the kinetic properties of the wind are remarkably similar. In particular, we find a common characteristic velocity (as derived from the core of the optical and Xray blue-shifted absorption lines) of ∼ 1500 km s −1 and a blueedge velocity (a proxy for the wind terminal velocity) ∼ > 3000 km s −1 (e.g. Fig. 3). However, while we do observe strictly simultaneous redshifts in both the optical and the X-ray emission lines (Fig. 4), the P-Cyg features (i.e. blue-shifted absorptions) are observed at different times and hard X-ray fluxes.

Observational properties of the wind
As discussed in MD16 and MS18, conspicuous optical P-Cyg profiles are only observed at low optical (and hard X-ray) fluxes. Observations characterized by a low average flux but including flaring activity are particularly revealing, since they show how the optical P-Cyg profiles briefly disappear and reappear in correspondence to flares (e.g . Fig 2 in MD16). This behaviour is accompanied by a sudden increase in the intensity ratio of the higher excitation emission lines (e.g. He ii and N iii) to the low excitation ones (e.g. He i, Hα) during the flares. This indicates that (at least during low-flux epochs) the wind is permanently ac-Article number, page 5 of 10 A&A proofs: manuscript no. V404-Cyg_wind_FINAL  tive, but its detection via P-Cyg profiles is most likely driven by ionisation effects. As a matter of fact, throughout the entire outburst the optical P-Cyg profiles are solely detected when these line ratios indicate a low-ionisation optical spectrum, while other observables (e.g. redshifted lines, broad emission line wings) strongly suggest that the outflow was likely present during most, if not the entire event (MD16). Observation GTC-1 shows strong optical P-Cyg profiles as well as an optical flare, when the wind signatures briefly disappear (see Fig. 15 in MS18). This observation occurs during an optical flux drop, that starts right at the very end of Chandra obs-1 (day ∼ 7.5 in Fig. 1 in Kimura et al. 2016). Contrastingly, both the optical flux and, in particular, the ionisation state of the optical emitting accretion disc (traced by line ratios) are higher during GTC-2 and P-Cyg profiles are not observed.
In X-rays, a rather opposite behaviour is witnessed: P-Cyg profiles are only present during luminous flares, and these are seen in emission lines indicating mid (e.g. Si xiv) to high (e.g. Fe xxvi) ionisation parameters. K15 suggested that the terminal velocity of the X-ray wind, as measured from the blue-edge velocity of the P-Cyg absorption, increases with the ionisation potential of the atomic species from ∼ 1500 to 4000 km s −1 . However, we note that this is a particularly difficult measurement that requires a good determination of the continuum. Our results shows that while the high energy lines (Fig. 5) have broader absorptions profiles than the lower excitation ones, core velocities of ∼ 1500 km s −1 and blue-edge velocities of ∼ 3000 km s −1 are roughly compatible with all the optical and X-ray P-Cyg profiles observed (dotted and dashed-dotted lines in Figs 2, 3, 5). Nonetheless, terminal velocities of ∼ 4000 km s −1 are also consistent with the blue-edges of Fe xxvi and Fe xxv during obs-2.C, as proposed by K15.

Wind variability and actual luminosity of V404 Cygni
We have discussed how the observational properties of the optical and X-ray wind change with time, following the large variations in the observed luminosity. However, detailed X-ray spectral analysis favours the presence of variable X-ray absorption, which might reach very high values (N H ∼ 10 23−24 cm −2 ; e.g. Motta et al. 2017a,b), significantly exceeding the Galactic extinction along the line of sight (N H ∼ 10 22 cm −2 ). Variable Xray absorption was also reported for the 1989 outburst (e.g. Życki et al. 1999) and can be roughly accounted by the estimates of the wind mass outflow rate derived from the optical spectra (MD16; Casares et al. 2019). It is worth noting that this behaviour, namely, conspicuous outflows and variable absorption, is not exclusive of V404 Cygni and has, in fact, been seen in other systems (a relatively long orbital period seems to be a common feature; see e.g. Muñoz-Darias et al. 2018;Koljonen & Tomsick 2020). While this large and variable N H is expected to have a strong impact on the soft X-ray variability, it is less clear how much it affects the hard X-ray light curve. For instance, assuming a simple power-law spectrum, the INTEGRAL count-rate (25-200 keV) is expected to drop by ∼ 5-10 percent (intrinsic power-law index in the range of 1.5-3) when N H increases from 10 22 to 5 × 10 24 cm −2 . The same N H variation would produce a drop of four order of magnitudes in the 2-10 keV band. Incidentally, this level of variability is present in the soft X-ray light curve of the outburst (e.g. that from Swift, see e.g. MD16 and Motta et al. 2017a). Still, a fairly similar variability level (∼ three orders of magnitude) is also present in the INTEGRAL light curve (see also Fig. 1), as well as in the radio emission (MD16; see also Tetarenko et al. 2017Tetarenko et al. , 2019. This indicates that an important fraction of the hard X-ray variability is most likely intrinsic and, thus, it is expected that the soft X-ray light curves have also a significant intrinsic variability component. A similar conclusion was drawn by Hynes et al. (2019) from the study of the X-ray/optical correlations (see also Alfonso-Garzón et al. 2018) and the behaviour of the hard X-ray light curve, which often displays a harder-when-brighter trend during flares. These hard flares might be explained by a strong reflection component from a jet-illuminated disc, a scenario that would account for the hot seed photons derived in some spectral fits (Walton et al. 2017; see also Roques et al. 2015;Natalucci et al. 2015). However, very large N H values might also account for this problem (see e.g. Sánchez-Fernández et al. 2017).
On a related note, using soft X-ray data of GRS 1915+105 during a phase that is also characterised by high levels of intrinsic absorption, Neilsen et al. (2020) found that the flaring behaviour can be explained by a combination of enhanced intrinsic activity and reduced absorption by a similar factor (3-4). The latter is likely (to some extent) a direct consequence of ionisation effects on the obscuring material, which at least for the case of V404 Cygni seems reasonable to assume that must be linked somehow to the outflow.
Finally, we note that a large mass outflow rate, such as that inferred for V404 Cygni, might also drive violent intrinsic variability as a result of instabilities in the accretion rate (e.g. Neilsen et al. 2011, MD16).

A multi-phase accretion disc wind
As discussed above, the kinetic properties of the X-ray and optical outflows are remarkably consistent with each other. However, P-Cyg profiles -the most convincing evidence for the presence of winds -are not observed simultaneously, nor at the same range of luminosities. There are several scenarios that may explain this behaviour (see illustrative sketch 3 in Fig. 6): (i) Two different winds. There are two independent outflows that are triggered at different luminosities. The similarity between their kinetic properties would be merely casual or somehow related to the physical properties of the system (e.g. physical size), but not to the nature of the wind. It might be also expected that winds are launched from different regions within the disc. While it is difficult to fully rule out this scenario, the remarkably similar emission line properties derived from the simultaneous observations (assuming both X-ray and optical lines are formed in the wind; see below) implies significant fine-tuning to keep both outflows as totally independent phenomena.
(ii) A single-phase wind. The wind continuously responds to the changes in the properties of the irradiating luminosity (e.g. amount and spectral shape), which is expected to trigger changes in the ionisation parameter of the outflowing gas, and thus in its observability across the electromagnetic spectrum. Hence, there is either an X-ray wind or an optical wind, but not coexisting phases (e.g. hot and cold) of the outflow. This scenario would be ruled out if the cold wind is always active, as optical observations seem to indicate. For instance, excluding epochs with P-Cyg profiles, V404 Cygni showed optical emission lines systematically broader during the 2015 outburst than during quiescence. This is at odds with what is typically observed in other sources, that display narrower (and mostly double-peaked) lines during outburst than in quiescence, as they arise in outer disc regions characterised by lower velocities. In addition, optical lines are systematically red-shifted during the first ∼ 10 days of the outburst (see MS18; MD16). As a matter of fact, during the simultaneous Chandra/GTC window (GTC-2), the optical and X-ray lines are both redshifted and their breadths are consistent with each other (see Fig. 4), suggesting that they both arise in (the same) wind, which would rule out this scenario.
(iii) A multi-phase static wind. The wind has both hot (X-ray) and cold (optical) phases, but their physical properties are the same across the outburst. This is ruled out as we see variability in the observational properties of the wind as a function of the luminosity.
(iv) A stratified wind. The X-ray and optical winds coexist in time, but their balance and observability vary according to physical changes in the system and/or the irradiating spectrum. The ionisation parameters of the X-ray and optical emitting regions of the outflow are expected to be significantly different, namely, ξ X >> ξ V . From this, we can simply derive: where we assume that both the hot and cold ejecta see the same luminosity (L), while n X and n V are the densities for the X-ray and optical emitting gas, and r X and r V the corresponding distances from the irradiating source. Thus, if the density is constant throughout the wind (i.e. n X ≈ n V ), we would end up with a stratified wind (r V > r X ; i.e. the optical wind is further away from the black hole). From the simulations of optically thin nebulae by Kallman & McCray (1982), it seems reasonable to assume that, in order to detect the spices present in the optical and X-ray spectra, there is at least a three orders of magnitude difference between their corresponding ionisation parameters, that is, ξ X ∼ > 10 3 ξ V . This implies r V ∼ > 30r X . While this case (constant density) remains useful for illustrative purposes, it is probably unrealistic since the wind is expected to diffuse into the interstellar medium with a given opening angle. This implies that density naturally decreases with the distance (r) to the source. For instance, if we repeat the above exercise for a conical wind that diffuses uniformly (i.e. no clumps) following a r −1 density law, we obtain an even more restrictive solution of r V ∼ > 10 3 r X . It is important to bear in mind that the optical wind is observed to respond to the variations of the X-ray source on time scales ∼ < 80 seconds, which places the ejecta within the accretion disc outer radius (∼ 30 light-seconds; i.e. 9 × 10 6 km) or very close to it (MD16). Assuming that the wind velocity (∼ 1500 − 3000 km s −1 ) traces the escape velocity at the launching region, a radius of ∼ 1 light-second is obtained, which would set a lower limit for the distance to the X-ray wind, implying that the optically emitting ejecta would need to be placed at ∼ 30-1000 light-seconds. On the other hand, K15 derived a radius of a few times 10 6 km for the formation of some of the X-ray lineswhich, if arising in the wind, would put the optical outflow even further away. All the above strongly suggest that stratification, all by itself, cannot explain the observables.
(v) A multi-phase dynamic wind. Finally, one can also consider that the X-ray and optical winds coexist not only in time but also in space (i.e. r V ≈ r X ). Thus, ξ X ∼ > 10 3 ξ V implies n V ≈ 10 3 n X . In this case, the wind would be a combination of optically emitting denser and cooler blobs that are embedded in thinner and hotter gas regions which, under isobaric conditions follow n V T V = n X T X , with T V and T X the temperatures of the optical and X-ray emitting gas, respectively. This configuration is often found in nebulae in the interstellar medium (e.g. McKee & Ostriker 1977), albeit at lower densities. This is also commonly applied to active galactic nuclei in order to explain their co-spacial outflows, which, similarly to the case of V404 Cygni, cover several orders of magnitude in ionisation parameter (e.g. Krolik et al. 1981). As a matter of fact, theoretically oriented photoionisation studies (e.g. Chakravorty et al. 2013;Bianchi et al. 2017;Gatuzz et al. 2019) have shown that, for typical Xray binary spectral energy distributions, multiple gas phases can be stable in pressure equilibrium. Even if this condition is not satisfied (e.g. as a result of significant radiation pressure from the X-ray source) alternative solutions allow for largely different ionisation parameters within a single slab of gas (Stern et al. 2014a,b). Thus, if the irradiating X-ray source is strongly variable, as it is the case in V404 Cygni, this naturally becomes a very dynamic system, and therefore significant variability is expected in the observational properties of the outflow across the electromagnetic spectrum. This would be also true even if the variability is due to variable extinction (but see Sec. 4.2) as long as the main absorber is located between the X-ray source and the wind launching region (see e.g. Motta et al. 2017a). . Illustrative sketch depicting the different possibilities discussed in Sec. 4.3 on the relation between the optical and X-ray winds as the hard X-ray luminosity varies from low (L) to high (H) values. We find that a multi-phase, dynamic scenario is favoured by the observations. phase, clumpy, winds are also thought to be present in massive stars, where both observational and theoretical studies indicate that the wind perturbations originating the clumps occur from very inner regions of the wind (i.e. close to the launching region; see e.g. Sundqvist & Owocki 2013 and references therein).
We conclude that, although some degree of stratification might be present and it is probably not unexpected (e.g. predominately hotter gas to be present at the ionisation front in the very inner part of the wind), a multi-phase solution is able to explain the observables. Furthermore, we note that the similar kinematic properties found in both X-ray and optical winds in LMXBs (e.g. Ponti et al. 2015;Panizo-Espinar et al. 2022), which show similar velocities in the range of a few hundred to a few thousands kilometres per second, together with the simultaneous detection of optical and near-infrared (Sánchez-Sierras & Muñoz-Darias 2020) as well as optical and ultraviolet (Castro Segura et al. 2022) winds in two systems, suggest that multi-phase accretion disc winds might be the norm in X-ray binaries.

Some considerations on the wind launching mechanism
In the above, we have discussed the properties of the wind once it has been launched. However, the wind launching mechanism in X-ray binaries is an open question, and the case of V404 Cygni is no exception. The wind could have a magnetic origin (e.g. Waters & Proga 2018), but the observed wind velocities are compatible with large launching radii (thousands of gravitational radii) and thus do not require this mechanism, which is able to produce outflows with large velocities if launched from the very inner accretion flow. Given that the source approached the Eddington luminosity during some phases of the outburst, a radiation driven wind (i.e. via Thompson scattering) might be unavoidable. As a matter of fact, the large outflow mass (up to ∼ 100 times the accreted mass) derived from the evolution of the nebular phase (MD16; see also Rahoui et al. 2017) that followed the most active phase of the event suggests a contribution from radiation pressure to the launch of the wind (Casares et al. 2019). However, optical winds are observed at hard X-ray luminosities three orders of magnitude lower than the outburst peak. The most appealing mechanisms at these fainter epochs are Compton heated (a.k.a thermal wind; Begelman et al. 1983) and line driven winds. Both mechanisms require of significant shielding against X-rays in order to not overionise the ejecta. As discussed above, a multi-phase, clumpy outflow could explain the lower ionisation parameter associated with the optical lines.
Conspicuous P-Cyg profiles were seen in the optical lines across the first week of the outburst. During the first two days, the wind velocity (blue-edge) was significantly lower (∼ 1500 km s −1 ) than that observed later in outburst (∼ 3000 km s −1 ; e.g. GTC-1 in this paper; see Fig 1. in MD16). Interestingly, the observed luminosity of the system was lower in all the bands during these first two days of the event (Kimura et al. 2016;Motta et al. 2017a, MD16). Likewise, wind velocities were also lower (∼ 1000-1500 km s −1 ) during the December 2015 secondary (and fainter) outburst ) and the (somewhat less extreme) 1989 outburst (Casares et al. 1991, MS18), suggesting a relation between the average luminosity of the system at a given stage of the outburst and the wind velocity. In this regard, it is an appealing approach to consider that the thermal wind, which is expected to have a slower response to luminosity changes, plays a role. We note that the complex wind phenomenology seen in V404 Cygni suggests that more than one mechanism might be contributing to the launch of the outflow. This probably should not come as a surprise since these mechanisms are unavoidable for certain physical conditions, and this would go in line with theoretical work that propose hybrid solutions to explain accretion disc winds in X-ray binaries (e.g. see Higginbottom et al. 2020;Tetarenko et al. 2020 for recent studies).

Conclusions
We used contemporaneous (including simultaneous) X-ray and optical spectroscopic data, together with hard X-ray light curves, to study the main observational properties of the accretion disc wind of the black hole transient V404 Cygni. We have shown that the optical P-Cyg profiles observed at low hard X-ray fluxes are alike those seen in a number of X-ray transitions during luminous flares. Furthermore, strictly simultaneous data taken at intermediate hard X-ray fluxes show how the optical and the X-ray emission lines are both redshifted and have similar line profiles, indicating that they most likely arise in the same wind. All aspects considered, this study favours a scenario in which a dynamic, multi-phase accretion disc wind, whose observational properties dramatically change with the luminosity, was active during the entire 2015 outburst of V404 Cygni. New coordinated X-ray and optical/near-infrared observations of active LMXBs are highly encouraged to establish the predominantly multi-phase nature of X-ray binary winds, as the growing number of wind detections with similar properties (e.g. similar velocities) at largely different energies would suggest.