CHARACTERIZING X-RAY AND RADIO EMISSION IN THE BLACK HOLE X-RAY BINARY V404 CYGNI DURING QUIESCENCE

We obtained a 52.6 ks observation of V404 Cyg with XMM-Newton (ObsID 0723310201) on 2013 October 13–14, covering part of the first NuSTAR observation (see Table 1). We used the Scientific Analysis System (SAS) v13.0.1 software package to reduce the data from the pn, MOS1, and MOS2 instruments, which were all operated in full frame mode with the medium blocking filter. The 10–12 keV light curve from the full pn detector shows that proton flares occurred at the beginning and the end of the observation, and we filtered out the time when the 10–12 keV pn count rate was greater than 1 c s⁻¹, leaving a net exposure time of 31.5 ks for pn and 34.9 ks for each of the MOS units. The part of the observation used to make energy spectra started at 2013 October 13, 20.2 hr UT and ended at 2013 October 14, 6.0 hr UT.

We produced event files using epproc and emproc, and then applied the standard event filtering. For pn, this means keeping events with the "FLAG" parameter set to zero, the "PATTERN" parameter less than or equal to 4, and applying the #XMMEA_EP data selection. For the MOS units, the filtering criterion is a "PATTERN" parameter less than or equal to 12 along with applying the #XMMEA_EM data selection. The pn and MOS images clearly show the presence of a point source at the known location of V404 Cyg, which is the brightest source in the field.

We extracted a 0.5–10 keV pn light curve, a 0.5–10 keV pn spectrum and 0.3–10 keV MOS spectra using a circular extraction region centered on V404 Cyg with a radius of 720 pixels (0.6 arcmin). We used nearby source-free rectangular regions to estimate and subtract the contribution from background. We rebinned the pn spectrum to have at least 100 counts per bin and the MOS spectra to have at least 50 counts per bin. We produced pn and MOS response matrices with rmfgen and arfgen. The average count rates for pn, MOS1, and MOS2 are 0.105 ± 0.002 c s⁻¹, 0.036 ± 0.001 c s⁻¹, and 0.035 ± 0.001 c s⁻¹, respectively.

We reduced the NuSTAR data using the NuSTAR Data Analysis Software (NuSTARDAS v1.4.1) available as part of HEASOFT v6.16 and the latest CALDB files. The NuSTAR observations were taken during intervals of normal Solar activity, and we used standard filtering to remove periods of high background during South Atlantic Anomaly (SAA) passages and Earth occultation. We created cleaned, calibrated event files using the NUPIPELINE script with standard settings. The source spectra and light curves were extracted using a 50'' radius circular region around the source. For background estimation on FPMA, we used the nuskybgd tool that accurately generates the background by properly taking into account the non-uniformity of background across the focal plane (see Wik et al. 2014 for details).

FPMB, on the other hand, showed the presence of faint stray light leaking into the field of view from a nearby source during epochs 1 and 2. The nuskybgd tool does not account for stray light; thus, we did not use it for FPMB. Fortunately, for epoch 1, the source fell on a favorable position and we were able to remove stray light contamination by carefully selecting the background from a 100'' radius circular region and subtracting it from the source. However, for epoch 2 the source was right on the edge of the stray light pattern, making it difficult to remove the contamination. Therefore, to safely avoid any contamination issue, we did not use epoch 2 FPMB data for any further analysis. FPMB epoch 3 data and all FPMA data are clean and free from any stray light issue and we use them for detailed scientific analysis.

V404 Cyg was observed with the upgraded Jansky VLA (Perley et al. 2011, project 13B–016,PI: S. Corbel) on 2013 December 2 for a total time on source of ∼9 hr. The array was in the B-configuration and the observations were performed in the C band (4.74–7.96 GHz) with two $1024\;$ MHz basebands centered at 5.25 and $7.45$ GHz, with eight spectral windows of $64\times 2\;$ MHz channels for each baseband.

The quasar 3C286 (J1331+3030) was used for the bandpass calibration and to set the amplitude scale. We used the very nearby compact source J2025+3343 ($0\_\_AMP\_\_fdg;28$ away from V404 Cyg) to calibrate the antenna amplitude and phase gains. We performed a cycle of 10 minutes on V404 Cyg and 36 seconds on the phase-referenced secondary calibrator. Two additional three minute scans were allocated on the non-polarized compact source J2355+4950 to calibrate the polarization leakages. Flagging, calibration, and imaging of the data followed standard procedures and were carried out within the Common Astronomy Software Application (CASA, version 4.1.0) package (McMullin et al. 2007).

We set the primary calibrator 3C286 flux scales using the task setjy and the physical properties measured by Perley & Butler (2013). The routines bandpass and gaincal were used to solve for the complex bandpass, the amplitude, and the phase gains. Stokes parameter values of the linearly polarized calibrator 3C286 were assigned with setjy due to its fractional linear polarization and its polarization position angle listed in Perley & Butler (2013). We derived calibration solutions for the leakage terms using J2355+4950. The flux densities of the secondary calibrators were bootstrapped using the task fluxscale, based on the absolute calibration of 3C286. Finally, we applied the calibration to V404 Cyg, linearly interpolating the gain solutions from the secondary calibrator J2025+3343, assuming that the two sources are close enough so that the gains are slowly varying between the two nearby field of views.

We imaged V404 Cyg in all Stokes parameters using the Cotton-Schwab CLEAN algorithm for the deconvolution. Calibrated measurements were split into four distinct $512\;$ MHz bands in order to characterize the spectral evolution of V404 Cyg over the bandpass. We made $480\times 480\;$ pixel² images with $0\_\_AMP\_\_farcs;15$ pixel width. At $7.94$ GHz the maximum baseline is ∼270 kλ, corresponding to an angular scale of ∼$0\_\_AMP\_\_farcs;76$. We used the multi-frequency synthesis method with the Briggs' weighting robust parameter set to 0.5 for all I images in order to achieve the best compromise between angular resolution and signal-to-noise ratio (S/N). However, the U and Q images were deconvolved with natural weighting to maximize the S/N. V404 Cyg is consistent with a point source in all images, so the flux densities were measured by fitting a point source in the image plane, and we add a 1% systematic error as usual for the VLA in this frequency range.

V404 Cyg is detected with a mean flux density of $300\pm 2\;\mu$Jy (Stokes I over the full bandwidth), in good agreement with previous studies conducted during the quiescent state (e.g., Gallo et al. 2005; Miller-Jones et al. 2008; Hynes et al. 2009). The source is unresolved with a beamsize of $0.81\times 0.79$ arcsec² at $7.7$ GHz, consistent with previous high spatial resolution studies (Miller-Jones et al. 2008).

No significant polarized emission is detected at the location of V404 Cyg, as no point source can be fitted on the images in the Stokes U, Q, and V parameters. By extracting the flux from a reduced number of channels, we avoided smearing out of any polarized signal over a large frequency bandwidth due to Faraday rotation of the linear polarization vector. Therefore, we computed the upper limit on its polarized emission by taking into account the rms of the corresponding images, i.e., 1.51, $1.48$, and $1.47\;\mu$Jy for Stokes parameters Q, U, and V, respectively. The linear polarization, defined as $\mathrm{LP}\;=\;\sqrt{{Q}^{2}+{U}^{2}}$, can then be constrained not to exceed $\mathrm{LP}\leqslant 6.33\;\mu$Jy at a $3\sigma$ confidence level. Regarding the fractional polarization $\mathrm{FP}\;=\;100\mathrm{LP}/I$, an upper limit of 2.11% can be inferred. Similar amplitude measurements have been obtained for BH candidates in brighter hard states (e.g., GX 339-4; Corbel et al. 2000); however, it is close to the detection limit.

We studied the spectra for each X-ray observation separately in order to investigate any spectral variation from epoch to epoch. Throughout this work we performed spectral modeling using XSPEC v12.8.2 (Arnaud 1996). Figure 7 shows the NuSTAR FPMA spectra for the three epochs of observations. It is readily visible that the spectra follow each other very closely, suggesting there is very little spectral variation among these three epochs. In order to quantify any spectral variation, we examined each spectra separately (three NuSTAR spectra and one XMM-Newton). We started with a simple model consisting of a power law modified by photoelectric absorption due to the interstellar medium. To account for the absorption due to intervening material, we used the tbabs spectral model with updated solar abundances (Wilms et al. 2000) and photoionization cross-sections as described in Verner et al. (1996).

Zoom In Zoom Out Reset image size

For XMM-Newton, the EPIC (pn and MOS) spectra were fitted simultaneously. We obtained a best-fit value of the photon index of Γ = 2.04 ± 0.08 and absorption ${N}_{{\rm{H}}}$ = (1.18 ± 0.09) × 10²² cm⁻². The absorbed 0.3–10 keV flux is 5.5 × 10⁻¹³ erg s⁻¹ cm⁻², which agrees well with the previously reported value of 5.8 × 10⁻¹³ erg s⁻¹ cm⁻² (Bernardini & Cackett 2014). The absorption obtained from XMM-Newton is a little higher than the Galactic value of 8.10 × 10²¹ cm⁻² (Dickey & Lockman 1990). While performing fits with individual NuSTAR spectra, we fixed ${N}_{{\rm{H}}}$ to the value obtained with XMM-Newton as NuSTAR's energy range is not sensitive to such absorption values. The best-fit values for the power-law index for the three NuSTAR observations are ${2.54}_{-0.17}^{+0.18}$, 2.28 ± 0.17, and 1.90 ± 0.24, respectively. The spectrum apparently is flattening going from epoch 1 to epoch 3; however, the individual errors on the power-law indices overlap, suggesting that the difference may not be statistically significant. In order to investigate this, we fitted the data from each epoch simultaneously with an absorbed power-law model. All the parameters were linked between epochs and only the overall normalization constants were allowed to vary. This also provided an excellent fit to the data, with a reduced ${\chi }^{2}$ of 1.07 for 95 degrees of freedom and a best-fit power-law index of Γ = 2.35 ± 0.12. This suggests that any variations in the spectral parameters during the three epochs are not significant and the spectra can formally be considered to be consistent with each other. Further, we have also derived hardness ratios between the two NuSTAR energy bands, 3–8 keV (soft) and 8–30 keV (hard), to test for any X-ray spectral variations. We found no variation in the hardness ratio (hard/soft), indicating that there are no significant spectral changes in the X-ray data. This is consistent with the previous X-ray studies using Chandra (Hynes et al. 2009) and Swift (Bernardini & Cackett 2014).

In order to evaluate the broadband X-ray characteristics of V404 Cyg during quiescence, we simultaneously fitted XMM-Newton and NuSTAR data to achieve energy coverage from 0.3–30 keV. As shown above, there is no significant spectral variation between the three epochs of NuSTAR observations, therefore we combined the data from the three NuSTAR epochs to improve the S/N. We used the ftool addascaspec to combine the NuSTAR data, which properly combines the corresponding background and response files. In order to account for the cross-calibration between different instruments, we included a constant multiplicative factor in all the spectral modeling described below. This constant factor was held fixed to 1.0 for XMM-Newton EPIC-pn and allowed to vary freely for other instruments. The EPIC-pn to NuSTAR normalization differences are below the expected ≲10% level (Madsen et al. 2015).

We employed several different spectral models to characterize the broadband spectra of V404 Cyg during quiescence, including an absorbed power-law model, a cutoff power-law model, a thermal bremsstrahlung model, and a thermally comptonized continuum model (see Figure 8). The best-fit spectral parameters obtained through joint fitting of XMM-Newton and NuSTAR data are listed in Table 2. All these models provide statistically acceptable fits to the data. The power-law model provides a best-fit value of the photon index of Γ = 2.12 ± 0.07. The unabsorbed flux in the 0.3–30 keV energy band is (1.29 ± 0.07) × 10⁻¹² erg cm⁻² s⁻¹ and the corresponding luminosity is (8.9 ± 0.5) × 10³² erg s⁻¹ for a distance of 2.4 kpc (Miller-Jones et al. 2009). Although the power-law model provides an acceptable fit (${\chi }_{\nu }^{2}$ = 0.86), the residuals show a hint of a rollover in the high-energy data above ∼10 keV. We therefore tried a power-law model with a high-energy exponential cutoff (cutoffpl in XSPEC) to test if it accounted for the high-energy residuals. This model, with an e-folding energy of the cutoff of ${20}_{-7}^{+20}$ keV, further improves the fit, with ${\rm{\Delta }}{\chi }^{2}$ = 12 for one additional degree of freedom. The cutoff energy, being very close to the high end of the spectral data, is not tightly constrained.

Zoom In Zoom Out Reset image size

Table 2.  Best Fit Spectral Parameters from Joint Fit to XMM-Newton and NuSTAR Data

Model	${N}_{{\rm{H}}}$	Γ/${\tau }_{p}$	Ecut/kTe	Norm	${\chi }^{2}$/dof	Fluxa
	(1022 cm−2)		(keV)	(10−4)
Power-law	1.25 ± 0.08	2.12 ± 0.07	...	2.20 ± 0.20	173/200	3.31
Cutoff power-law	1.14 ± 0.10	1.86 ± 0.15	${20}_{-7}^{+20}$	${1.92}_{-0.20}^{+0.22}$	161/199	3.39
Bremsstrahlung	0.84 ± 0.05	...	${6.9}_{-0.6}^{+0.7}$	${1.58}_{-0.07}^{+0.08}$	199/200	3.60
CompTT	0.78 ± 0.06	${4.8}_{-0.8}^{+0.7}$	${4.0}_{-0.6}^{+1.2}$	${0.60}_{-0.13}^{+0.11}$	160/199	3.42

Note.

^aAbsorbed flux in 3–10 keV energy band with units of 10⁻¹³ erg cm⁻² s⁻¹.

Download table as:  ASCIITypeset image

In order to assess the significance of the potential cutoff, we performed a series of spectral simulations. Using the same responses, background files, and adopting the same exposure times as the data used here, we simulated 10,000 sets of XMM-Newton (pn, MOS1, MOS2) and NuSTAR (FPMA, FPMB) spectra with the FAKEIT command in XSPEC. These simulations were based on the best-fit power-law continuum, and each of the simulated data sets was rebinned in the same manner and analyzed over the same bandpass as adopted for the real data. We then fit each of the combined data sets with an absorbed power-law continuum with and without an exponential cutoff, again in the same manner as the real data, and noted the improvement in fit provided by the former over the latter. Of the 10,000 data sets simulated, only 28 showed a chance improvement equivalent to or greater than that observed, implying that the detection significance of the cutoff in the real data is at the 3σ level. Next, we performed another set of simulations with the best-fit cutoff power-law model as input in order to assess the expected distribution of ${\rm{\Delta }}{\chi }^{2}$ when compared to a simple power-law model given the available data. We found that it peaks near the observed value and this holds true even if we take into account that the power-law model already provides a good fit with reduced ${\chi }^{2}\quad \lt$ 0.9. All of these simulations favor the detection of a cutoff with 3σ significance in our broadband XMM-Newton+NuSTAR data. Such a feature has been measured for the first time in V404 Cyg during quiescence.

We next used a physically motivated thermal bremsstrahlung model to characterize the broadband spectra. Again, this model provides a statistically acceptable fit to the data. The derived plasma temperature is ${6.9}_{-0.6}^{+0.7}$ keV. However, this fit is poorer by ${\rm{\Delta }}{\chi }^{2}$ = 33 compared to the cutoff power-law model. Thus, the cutoff power-law is the favored spectral model for these data among the above three models. In addition, we also tried a thermally Comptonized continuum model, comptt, that describes Comptonization of soft photons in a hot plasma from a Comptonizing corona and the inner region of an ADAF flow (Hua & Titarchuk 1995; Titarchuk & Lyubarskij 1995). The comptt model has a higher number of free parameters, and not all of them are constrained simultaneously. The seed photon temperature kT₀ varies between 0 and 0.4 keV with a best-fit value of 0.32 keV, which is in excellent agreement with the previous measurement of 0.33 keV by Bernardini & Cackett (2014). Hence, we fixed the seed photon temperature to 0.32 keV during the fit. As listed in Table 2, the comptt model is characterized by a coronal electron temperature of ∼4 keV and an optical depth of ∼5. The goodness of fit with this Comptonization model is very similar to that found for the simple cutoff power-law model (see Table 2) and shows very similar residuals. Therefore, we have not shown it in Figure 8 for the sake of clarity.

Visual inspection of the X-ray spectra indicates that the data are featureless, showing only a smooth continuum over the broad X-ray band. However, there are predictions for the presence of X-ray emission lines from the hot plasma in an ADAF-like flow (Narayan & Raymond 1999). In order to derive an upper limit on the highly ionized Fe XXV ${{\rm{K}}}_{\alpha }$ line at 6.7 keV, we added a Gaussian component to our best-fit cutoff power-law model. We obtained an upper limit on the equivalent width of ∼200 eV (0.1 keV fixed width and 90% confidence limit) from the broadband XMM-Newton and NuSTAR spectra. This is somewhat higher than the upper limit derived by Bradley et al. (2007). However, it is nearly as large as the prediction of ∼230 eV for the sum of the equivalent widths for the total group of Fe emissoin lines (Narayan & Raymond 1999).

In order to characterize the SED at radio energies, we measured the flux density of V404 Cyg through four distinct frequency bands over the whole observing period. We report the results in Table 3. We use this information to constrain the radio spectral shape by fitting the function ${f}_{\nu }\propto {\nu }^{\alpha }$, where f_v is the flux density and ν is the frequency. Figure 9 shows the radio spectrum (black points) fitted with a power-law model (dotted line) and the corresponding 95% confidence region (gray shaded area). We obtain a spectral index of $\alpha \;=\;-0.27\pm 0.03$ (1σ error) for the average spectrum across the whole observation. The same fitting procedure was applied to two frequency bands to derive the evolution of the spectral shape during the observation. Figure 10 shows the spectral index variation over $\sim 10\;$ minute time bins. Interestingly, the spectral index changes rapidly between optically thick (0.0 to 0.5) and thin (−1.0 to −0.5) synchrotron emission regimes. In order to make sure that such extreme variability is associated with V404 Cyg, we performed a similar analysis on nearby field sources. We found that the flux density and the derived radio spectral index of the field sources were constant over the course of the observation, confirming that the observed spectral variability displayed in Figure 10 is associated with V404 Cyg.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Over the course of our observations, V404 Cyg showed strong variability at soft X-ray, hard X-ray, and radio wavelengths, represented as multiple flares with each flare lasting for a few hours. Similar temporal variability has been observed previously in long-term monitoring of this source with the Swift X-Ray Telescope (XRT; Bernardini & Cackett 2014) in the 0.3–10 keV energy band. That study showed that V404 Cyg is highly variable on a wide range of timescales from tens of minutes to years in 34 Swift observations of the source in quiescence. Hynes et al. (2004) also reported dramatic X-ray flux variability with much higher amplitude (more than a factor of 20) using 2003 Chandra observations in the 0.3–7 keV band. Our sensitive NuSTAR observations clearly demonstrated that the flaring behavior of V404 Cyg continues beyond 10 keV. In addition, new VLA radio light curve data, taken simultaneously with the NuSTAR hard X-ray data, also showed strong variability on short timescales, similar to that reported by Hynes et al. (2009). However, unlike these previous radio light curves, our new radio data show a persistent emission component with the flux level never going to zero. Although the simultaneous radio and X-ray data show strong variability, we do not find any significant correlation (or anti-correlation) between the two data sets. This is again consistent with previous multi-wavelength studies (Hynes et al. 2009).

The quiescent X-ray spectra of V404 Cyg have been studied previously with XMM-Newton, Chandra, and Suzaku (see Bradley et al. 2007; Corbel et al. 2008 and Reynolds et al. 2014) and are well characterized using absorbed power-law models. We measured the power-law index Γ = 2.12 ± 0.07 using our broadband XMM-Newton and NuSTAR data. This measurement is in excellent agreement with previously reported power-law spectra from Chandra (Γ = 2.17 ± 0.13) and XMM-Newton (Γ = 2.09 ± 0.08). Reynolds et al. (2014) recently studied quiescent X-ray spectra for a sample of accreting BHs, including V404 Cyg. They reported best-fit power-law index of 2.05 ± 0.06 from a simultaneous fit to XMM-Newton, Chandra, and Suzaku observations, which agrees with our measurement within 90% errors. The broadband XMM-Newton and NuSTAR spectra, along with excellent sensitivity, show the presence of a cutoff at around ∼20 keV with more than ∼3σ significance. A similar cutoff (at around 10 keV) was recently detected by NuSTAR in the quiescent spectra of the low-mass X-ray binary Cen X-4 (Chakrabarty et al. 2014), which these authors attribute to hard X-ray emission arising either from a hot, optically thin corona or from hot electrons in an optically thin RIAF. The broadband spectrum of Cen X-4 is well characterized by a thermal bremsstrahlung model with kT_e = 18 keV. For V404 Cyg, the bremsstrahlung model also provides a statistically acceptable fit, though the best-fit temperature, kT_e = ${6.9}_{-0.6}^{+0.7}$ keV, is significantly lower than that observed in Cen X-4. Recently, Bernardini & Cackett (2014) analyzed the Swift XRT spectra of V404 Cyg and reported that fits with a bremsstrahlung model find the temperature between 3.3 and 4.7 keV as a function of count rate, which is slightly lower than our measurement. However, Reynolds et al. (2014) reported a bremsstrahlung temperature of ${6.16}_{-0.89}^{+1.15}$ keV using Suzaku XIS data, in agreement with our measurement.

Corbel et al. (2008) revisited the radio-X-ray flux correlation for V404 Cyg by re-analyzing some of the 1989 outburst data and adding two points from their 2003 Chandra/VLA data and 2000 Ginga/VLA observations during quiescence. They found a strong correlation between the two energy bands and conclude that the correlation observed during the decay of the 1989 outburst holds down to the quiescent state. Using our new simultaneous NuSTAR/VLA observations, we were able to add one more point to that correlation, shown in Figure 11. Earlier data were taken from Corbel et al. (2008; see their Figure 4) and we did not attempt any fitting. Our new data point lies right on their best-fit curve, nicely following the long-term correlation from previous data. The quiescent flux level of V404 Cyg during our observations is higher compared to their Chandra/VLA observation, but it is significantly lower than the Ginga/VLA measurements. This long-term correlation between X-ray and radio flux is indicative of a common or related origin for the two components. Although the radio and X-ray fluxes are correlated on long timescale, the short timescale variations during the observations become more complicated and any correlation may be smoothed out by internal jet variability (Gleissner et al. 2004).

Zoom In Zoom Out Reset image size

The quiescent X-ray flux of V404 Cyg shows significant variability on a timescale of a few years, as reported in previous studies. Reynolds et al. (2014) reported that the 0.3–10 keV unabsorbed X-ray flux varies in the range of (0.8–3.42) × 10⁻¹² erg s⁻¹ cm⁻² using various observations between 2000 and 2009 from Chandra, XMM-Newton, and Suzaku. We measured the unabsorbed 0.3–10 keV flux to be 1.1 × 10⁻¹² erg s⁻¹ cm⁻², which is well within the above range; however, it is slightly lower compared to the average flux of 1.7 × 10⁻¹² erg s⁻¹ cm⁻² reported by Bernardini & Cackett (2014) using 75 days of Swift monitoring observations in 2012. Narayan et al. (1997) reported unabsorbed 1–10 keV flux of 8.2 × 10⁻¹³ erg s⁻¹ cm⁻² using 1994 ASCA observations. Thus, the X-ray flux of V404 Cyg shows significant variability; however, its spectral shape remains fairly stable with Γ = 2.1–2.3.

We can use the measured spectral cutoff to make inferences about the nature of the accretion flow onto the BH. We follow the general approach used by Chakrabarty et al. (2014) in interpreting the spectral cutoff in the quiescent accreting NS Cen X-4. A key difference here is that the observed X-ray luminosity in BH systems provides only a lower limit on the mass accretion rate, since matter can be accreted onto the BH without radiating. In the discussion below, we assume a BH mass of 10 ${M}_{\odot }$ and a distance of 2.4 kpc, and we write the Eddington luminosity and accretion rate for a 10 ${M}_{\odot }$ BH as ${L}_{E}\;=\;0.1{\dot{M}}_{E}\;{c}^{2}\;=\;1\times {10}^{39}$ erg s⁻¹. The observed X-ray luminosity is thus ${L}_{x}\simeq {10}^{-6}\;{L}_{E}$.

The hard X-ray emission in BH binaries is often ascribed to a Comptonizing corona of hot electrons. Our comptt fit yielded an electron temperature of ${{kT}}_{e}\;=\;4.0\;{\rm{keV}}$ and an electron scattering optical depth of $\tau \;=\;4.8$. This is a fairly high optical depth, and it is related to the electron density n_e by

$$\begin{eqnarray}&&\tau \;=\;{\sigma }_{{\rm{T}}}\int {n}_{e}(r){dr},\end{eqnarray} \tag{ 1 }$$

where ${\sigma }_{{\rm{T}}}$ is the Thomson cross-section. We assume a quasi-spherical RIAF inside a transition radius at ${r}_{t}\;=\;{10}^{4}{R}_{S}$, where ${R}_{S}\;=\;2{GM}/{c}^{2}\;=\;30$ km for a 10 ${M}_{\odot }$ BH. We then find that an accretion rate of $\dot{M}\approx 0.02{\dot{M}}_{E}$ is required to produce the measured value of τ. (We used Equations (5) and (8) of Chakrabarty et al. 2014 to relate n_e and $\dot{M}$, taking $\eta \;=\;0.1$ and $\mu \;=\;0.6$.) The resulting electron population has a high scattering optical depth but is optically thin to free-free absorption, and will thus itself be a source of bremsstrahlung emission. At a temperature of ${kT}\;=\;3.9\;{\rm{keV}}$, this would produce an X-ray luminosity 60 times brighter than what we observe. If we allow for the possibility of an outflow by setting

$$\begin{eqnarray}&&\dot{M}(r)\;=\;{\left(\displaystyle \frac{r}{{r}_{t}}\right)}^{p}\;{\dot{M}}_{t}\end{eqnarray} \tag{ 2 }$$

with $p\gt 0$ (Blandford & Begelman 1999), the discrepancy is even larger. We conclude that thermal Comptonization cannot be responsible for the spectral cutoff.

Thermal bremsstrahlung emission from the accretion flow is, however, a viable possibility. Our bremsstrahlung fit has an emission measure

$$\begin{eqnarray}&&\int {n}_{e}^{2}\;{dV}\;=\;4.7\times {10}^{57}\;{\mathrm{cm}}^{-3}\end{eqnarray} \tag{ 3 }$$

for a distance of 2.4 kpc. For the p = 0 case in Equation (2), an accretion rate of $\dot{M}\simeq {10}^{-3}{\dot{M}}_{E}$ is sufficient to yield this emission measure. Menou et al. (1999) suggested that V404 Cyg during its quiescent state is basically in the RIAF regime when mass loss via wind is included. If we allow for an outflow ($p\gt 0$), then we require ${\dot{M}}_{t}\sim {10}^{-2}{\dot{M}}_{E}$ at the transition radius. These are plausible accretion rates for the RIAF regime (Menou et al. 1999).

Another possibility is synchrotron and/or synchrotron self-Compton emission from the base of a jet outflow (Markoff et al. 2005). Such models are competitive with Compton coronal models for the X-ray emission in BH binaries and are capable of producing curvature in the power-law spectrum which could be consistent with our observed cutoff. Detailed modeling will be necessary to evaluate the viability of this model in V404 Cyg.

The hundreds of seconds to kiloseconds timescale flaring behavior of V404 Cyg in quiescence has already been reported at several wavelengths, including at 8.4 GHz in the radio (Miller-Jones et al. 2008; Hynes et al. 2009). Our new sensitive radio observations with the VLA confirm this behavior, but they also allow us for the first time to have additional radio spectral information during these periods of weak activity. The spectral index (Figure 10) evolved on a very fast timescale (as short as $10\;$ minutes) with clear switching between regimes of optically thick and optically thin synchrotron emission.

In order to explain the observed spectral variability, we explored several possibilities, one of them being intervening material along the line of sight. V404 Cyg lies behind the Cygnus super bubble, composed of interstellar structures shaped by supernova explosions and stellar winds of massive stars, all estimated to be located between 0.5 and $2.5\;$ kpc from the Earth (see, e.g., Uyanıker et al. 2001; Ackermann et al. 2011). Fluctuation of the electron density in these clouds can modify the refractive index of the plasma, inducing scintillation of the observed radio emission. However, Miller-Jones et al. (2008) estimated that the timescale of refractive scintillation should be between 140 and 1000 hr, given the source size constraints they derived from VLBI observations. The flux variability seen in our VLA observations on a timescale of a few minutes must therefore be intrinsic to V404 Cyg.

In the hard state, self-absorbed compact jets are usually observed with a radio spectrum that is either flat or slightly inverted (e.g., Corbel et al. 2000). However, it has been found that when the compact jets are building up during the soft to hard state transition, they are initially consistent with optically thin emission (e.g., Corbel et al. 2013; Kalemci et al. 2013). The quiescent state in V404 Cyg may be similar to such a situation with the accretion flow not being able to sustain stable compact jets due either to insufficient particle density and/or inefficient particle acceleration. One could possibly interpret the rapid spectral index changes in Figure 10 as jet ignition instabilities, rapidly moving between development/fading ($\alpha \lt 0$) and activated states (corresponding to flat/inverted spectra, $\alpha \geqslant 0$). A dedicated campaign with simultaneous observations in infrared and radio should provide an important diagnostic for such behavior.

Alternatively, the observed fast spectral modulations of the radio spectrum may originate from stochastic instabilities in the accretion flow. The synchrotron turnover frequency, ${\nu }_{b}$, of a compact jet (usually at infrared frequencies in the hard state, e.g., Corbel & Fender 2002; Russell et al. 2006; Hynes et al. 2009; Corbel et al. 2013) could move to lower frequencies as the mass accretion rate, $\dot{m}$, decreases (Falcke et al. 2004; Chaty et al. 2011). In quiescence, the accretion rate in V404 Cyg may fluctuate on very short timescales. Rapid modulations of the magnetic field intensity and/or the size of the particle acceleration zone may cause ${\nu }_{b}$ to shift over to the range of our observable bandwidth (Chaty et al. 2011; Gandhi et al. 2011), thus producing the switches between optically thick and thin synchrotron emission, as observed at infrared wavelengths on similar timescales for other sources (Gandhi et al. 2011; Rahoui et al. 2012). The fact that the new observations lie on the standard radio and X-ray flux correlation observed in the hard and quiescence states probably indicates an interpretation related to the compact jets. As observed in Gandhi et al. (2011) and Rahoui et al. (2012), even if the compact jets are strongly variable on short timescales, those variations smooth out on longer timescales.

The observed radio emission may also be unrelated to compact jets, which might be absent in quiescence. The radio flaring behavior might instead be related to synchrotron bubble ejection events, possibly triggered by magnetic reconnection events above the accretion disk, or be related to variations in the accretion rate. In the synchrotron bubble scenario, the high-frequency peak should lead the lower low-frequency flux maximum (van der Laan 1966; Hjellming & Johnston 1988). Considering averaging effects, this is consistent with the rapid switch between the observed positive and negative spectral indices (see Figure 10). However, in such a case, one would expect the higher frequency light curve to have higher maxima than observed at lower frequency. This is in contrast to what we observe (Figure 4), and indicates that the synchrotron bubble scenario is not the favored interpretation.