NO EVIDENCE OF INTRINSIC OPTICAL/NEAR-INFRARED LINEAR POLARIZATION FOR V404 CYGNI DURING ITS BRIGHT OUTBURST IN 2015: BROADBAND MODELING AND CONSTRAINT ON JET PARAMETERS

We performed simultaneous optical and NIR imaging polarimetry for V404 Cyg using the Hiroshima Optical and Near IR camera (HONIR; Akitaya et al. 2014) mounted on the Kanata 1.5 m telescope in Higashi-Hiroshima, Japan. The data presented here were taken on MJD 57193 and 57194. The HONIR polarization measurements utilize a rotatable half-wave plate and a Wollaston prism. We selected R_C and K_s bands as the two simultaneous observing filters. To study the wavelength dependence of polarization properties for the target, we also took ${{VR}}_{C}{I}_{C}{{JHK}}_{s}$ imaging polarimetric data on MJD 57194.50–57194.55 (the "C" subscripts are herein suppressed). Each observation consisted of a set of four exposures at half-wave plate PAs of 00, 225, 450, and 675. Typical exposures in each frame were 30 and 15 s for the R and K_s bands, respectively, but these exposures were sometimes modified depending on weather conditions (decreased when seeing became good, and increased when cirrus clouds passed over the target). ${VI}$- and JH-band exposures on MJD 57194 were 30 and 15 s, respectively.

To calibrate these data, we observed standard stars on MJD 57195 that are known to be unpolarized (HD 154892) and strongly polarized (HD 154445 and HD 155197; Turnshek et al. 1990; Wolff et al. 1996). We thereby confirmed that the instrumental PD is less than 0.2% and determined the instrumental polarization PA against the celestial coordinate grid. Absolute flux calibration, which is needed to construct the optical and NIR spectral energy distributions (SEDs), was performed by observing standard stars on the photometric night MJD 57200.

We also performed optical R-band imaging polarimetry monitoring for V404 Cyg using the Multi-Spectral Imager (MSI; Watanabe et al. 2012) mounted on the 1.6 m Pirka telescope located in Hokkaido, Japan, from MJD 57190 to 57193. The MSI observations were performed in a similar manner to the Kanata/HONIR ones, namely, the MSI utilizes a rotatable half-wave plate and a Wollaston prism, and a series of four exposures were taken for each polarization measurement. The typical exposure time of each frame was 15 s. To remove the instrumental polarization (p = 0.78%) and to calibrate the polarization PA, we used past MSI data of the two unpolarized stars (BD +32 3739 and HD 212311; Schmidt et al. 1992) and three strongly polarized stars (HD 154445, HD 155197, and HD 204827; Schmidt et al. 1992) obtained on MJD 57167 and 57169. We also confirmed the polarization efficiency of ∼99.7% using a polarizer and flat-field lamp.

We analyzed X-ray data for V404 Cyg taken with XRT on board the Swift satellite using HEASoft version 6.16. The Swift/XRT data analyzed here were taken on MJD 57193 and 57194 (observation IDs: 00031403040 and 00031403046), which were almost simultaneous (within less than 1 hr) with the Kanata/HONIR multiband photopolarimetry data. Clean events of grade 0–12 within the source rectangle region (because the observation was in window-timing mode) were selected. After subtracting background counts selected from both sides of the source with rectangle shapes, the 0.5–10 keV events were utilized for spectroscopy. We generated ancillary response files with the xrtmkarf tool. Using XSPEC version 12.8.2, we roughly fit the data by assuming a disk blackbody plus power-law model, both modulated by Galactic absorption (i.e., wabs∗(diskbb+pow)), and converted the deabsorbed spectra to ν F_ν fluxes.

The simultaneous Kanata/HONIR R- and K_s-band light curves showed almost the same temporal evolution, except the orphan K_s-band flare, which peaked around MJD 57193.54 and lasted for ∼30 minutes (see Figure 1). Apart from this orphan flare (which is discussed in detail later), the quite similar R- and K_s-band light curves naturally lead to an interpretation that the NIR and optical emissions come from the same component (or have the same origin). There are two possible options to explain the optical and NIR emissions: one is a disk origin, and the other is from a jet. To gauge which is the most plausible, we constructed a broadband spectrum of V404 Cyg from the radio to X-ray bands in $\nu -{F}_{\nu }$ representation (Figure 5). Note that the radio fluxes are not simultaneous, while the Kanata and Swift/XRT data were obtained within a 1 hr time span. The Kanata optical and NIR fluxes were dereddened by assuming A_V = 4.0 and R_V = 3.1. The A_V value of 4.0 was derived by Casares et al. (1993) from the spectral type of the companion star and B − V colors, which was also confirmed by subsequent studies (e.g., Shahbaz et al. 2003; Hynes et al. 2009). After we corrected the observed fluxes for extinction using A_V = 4.0, we found a slightly rising but almost flat (α ∼ 0) shape in the optical and NIR spectrum. This implies optically thick synchrotron emission from an outer jet. Indeed, the ∼2–20 GHz radio spectrum obtained about 1.5 days before our observation (on MJD 57191.95) can be smoothly extrapolated to the Kanata/HONIR spectral data assuming an ${F}_{\nu }\propto {\nu }^{0.2}$ form (see Figure 5). However, the flat optical/NIR spectral shape can also be interpreted in a disk model (see, e.g., Kimura et al. 2016, Extended Data Figure 6 therein). Thus, it is difficult to determine the optical/NIR emission mechanism solely from its spectral shape. No evidence of intrinsic linear polarization in the R and K_s bands is allowed in both scenarios because both optically thick synchrotron and blackbody radiation only generate weak linear polarization of order ≲10%.

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Here we focus on the orphan K_s-band flare, which lasted for only ∼30 minutes at MJD 57193.54. The observed red color and short duration imply synchrotron emission from a jet as the most plausible origin of the flare. Indeed, the K_s-band peak flux of the flare reached ∼2.0 Jy, which was the same level measured during the giant radio and submillimeter flares observed by RATAN-600 and Sub Millimeter Array on MJD 57198.933 and 57195.55 (Tetarenko et al. 2015; Trushkin et al. 2015b), respectively. As shown in Figure 5 (left panel), an extrapolation of the radio spectrum observed during the giant flare at GHz frequencies on MJD 57198.933 nicely connects to the K_s-band peak flux by assuming a flat spectral shape (i.e., ${F}_{\nu }\propto {\nu }^{0}$). More interestingly, even during the orphan flare, the K_s-band PD showed no significant temporal variation, indicating that the NIR emission is not strongly polarized. This result would be reasonably understood if the jet synchrotron emission in the K_s band is still in the optically thick regime. We therefore conjecture that this orphan K_s-band flare is produced by optically thick synchrotron emission from an outer jet. If the optically thick synchrotron emission extends up to the R band with a flat spectral shape and the baseline R-band flux is not as high as the flaring component of ∼2.0 Jy (after extinction correction, assuming ${A}_{V}=4.0$), it significantly contributes to the R-band flux as well, making the flare visible also in the R-band light curve. A spectral break between the K_s and R bands of the flaring emission component caused by the transition of synchrotron emission from optically thick to optically thin regimes, if present, would make the contribution of the flaring component negligible with respect to the baseline flux, as observed. The quasi-simultaneous F_ν Kanata/HONIR and Swift/XRT spectra measured on MJD 57194.52, together with the RATAN-600 nonsimultaneous radio fluxes, are also shown. The radio, optical/NIR, and X-ray spectra would be reasonably understood as optically thick synchrotron emission from the outer jet, disk emission, and disk plus corona emissions, respectively.

To constrain the jet parameters and physical quantities in the emission region, we attempted to model the SED of V404 Cyg by using a one-zone synchrotron plus synchrotron self-Compton (SSC) model (Finke et al. 2008), which is widely used for blazar SED modeling (e.g., Abdo et al. 2009, 2011; Tanaka et al. 2014, 2015). We show in Figure 6 (left panel) the quasi-simultaneous broadband SED of V404 Cyg during the K_s-band flare. This modeling assumes that a single emission region is located at the innermost part of the jet. Hence, the optically thick synchrotron emission from an outer jet, which has a flat spectrum of ${F}_{\nu }\propto {\nu }^{0}$ observed in the radio up to NIR band, is not modeled, while the optically thin synchrotron and SSC emissions at optical frequencies and higher are fitted. However, in the current case, we now know that the optical and X-ray emission are from a disk and disk plus corona, respectively. We therefore regard the Kanata/HONIR, Swift/XRT, and INTEGRAL data points (taken from Figure 3 of Rodriguez et al. 2015) as upper limits for the jet emission. Another constraint comes from the Kanata/HONIR observation that the K_s-band emission is not significantly polarized even during the orphan flare. This indicates that the K_s-band emission is still in the optically thick regime and that the break frequency (defined as ν_SSA) is due to synchrotron self-absorption (SSA). The transition from the optically thick to optically thin regime is above the K_s-frequency band; thus, ν_SSA ≳ 1.4 × 10¹⁴ Hz, and we adopt a value of ν_SSA = 3.0 × 10¹⁴ Hz. We also assume that the synchrotron peak flux is 2 Jy as observed by Kanata/HONIR (and also by RATAN-600 on MJD 57198.933). We can then derive the magnetic field B and the size of the emission region R by using the standard formulae for synchrotron absorption coefficient and emissitivity (e.g., Rybicki & Lightman 1979; Chaty et al. 2011; Shidatsu et al. 2011),

$$\begin{eqnarray}B & \approx & 1\times {10}^{5}{\left(\displaystyle \frac{{\nu }_{{\rm{SSA}}}}{3\times {10}^{14}{\rm{Hz}}}\right)}^{\displaystyle \frac{3s+10}{2s+13}}\\ & & \times {\left(\displaystyle \frac{{F}_{\nu }}{2{\rm{Jy}}}\right)}^{-\displaystyle \frac{2}{2s+13}}{\left(\displaystyle \frac{D}{2.4{\rm{kpc}}}\right)}^{-\displaystyle \frac{4}{2s+13}}\ {\rm{Gauss}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}R & \approx & 5\times {10}^{8}{\left(\displaystyle \frac{{\nu }_{{\rm{SSA}}}}{3\times {10}^{14}{\rm{Hz}}}\right)}^{\displaystyle \frac{-({s}^{2}+7s+8)}{2(2s+13)}}{\left(\displaystyle \frac{{F}_{\nu }}{2{\rm{Jy}}}\right)}^{\displaystyle \frac{s+6}{2s+13}}\\ & & \times {\left(\displaystyle \frac{D}{2.4{\rm{kpc}}}\right)}^{\displaystyle \frac{2(s+6)}{2s+13}}\ {\rm{cm}},\end{eqnarray} \tag{ 2 }$$

where s is the power-law index of electron distribution (see below) and D is the distance to V404 Cyg. Here we assumed almost equipartition between magnetic field and electron energy density, which was confirmed by the following SED modeling.

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The electron energy distribution is assumed to have a single power-law shape with exponential cutoff as ${dN}/d\gamma \;=K{\gamma }^{-s}\mathrm{exp}(-\gamma /{\gamma }_{{\rm{cut}}})$ for ${\gamma }_{{\rm{min}}}\leqslant \gamma \leqslant {\gamma }_{{\rm{max}}}$, where γ is the electron Lorentz factor, K is the electron normalization, s is the power-law index, γ_cut is the cutoff energy, and γ_min and γ_max are the minimum and maximum electron energies and are set to 1 and 10⁶, respectively. The jet inclination angle of V404 Cyg is estimated as ∼55° (e.g., Shahbaz et al. 1994; Khargharia et al. 2010), and assuming a jet velocity of 0.9c, the corresponding Doppler beaming factor is $\delta ={[{\rm{\Gamma }}(1-\beta \mathrm{cos}\theta )]}^{-1}\sim 0.9$. We can therefore safely neglect relativistic beaming effects.

By changing the parameters of the electron energy distribution, we calculated the resultant synchrotron and SSC emissions. The calculated model curves are shown in Figure 6 (left panel), and all the model parameters are tabulated in Table 2. The derived parameters for the electron energy distribution are K = 4.5 × 10⁴⁰, s = 2.2, and γ_cut = 10². Importantly, the Swift/XRT data allowed us to constrain the cutoff energy as 10² because larger γ_cut violates these upper limits in the soft X-ray band. This implies that particle acceleration in this microquasar jet is not very efficient. The electron energy distribution cutoff energy is determined by the balance between acceleration and cooling times, where the acceleration time is defined as ${t}_{{\rm{acc}}}=\eta E/({eBc})$ by using an electron energy E and parameter η, the number of gyrations an electron makes while doubling its energy (e.g., Finke et al. 2008; Murase et al. 2014). Since dominant cooling processes for electrons of $\gamma ={\gamma }_{{\rm{cut}}}={10}^{2}$ are both synchrotron and SSC, the cooling time is estimated as ${t}_{{\rm{cool}}}=3\gamma {m}_{e}c/(8{\sigma }_{T}{\gamma }^{2}({U}_{{\rm{B}}}+{U}_{{\rm{sync}}}))$, where ${U}_{{\rm{B}}}={B}^{2}/8\pi$ and ${U}_{{\rm{sync}}}={L}_{{\rm{sync}}}/4\pi {R}^{2}c$ are the energy densities of magnetic field and synchrotron photons, respectively (e.g., Finke et al. 2008). Thus, we obtain η ∼ 10⁶ by setting $E={\gamma }_{{\rm{cut}}}{m}_{e}{c}^{2}$ and B = 10⁵ G. This is much larger than η ∼ 10 in blazar jets (e.g., Rachen & Mészáros 1998), indicating much longer acceleration times and inefficient acceleration in this microquasar jet.

Table 2.  Model Parameters

Parameter	Symbol	MJD 57193	MJD 57194
Break frequency (Hz)	νSSA	3 × 1014	3 × 1014
Magnetic Field (G)	B	1.4 × 105	1.8 × 105
Size of emission region (cm)	R	5.3 × 108	1.7 × 108
Jet velocity (c)	β	0.9	0.9
Electron distribution normalization (electrons)	K	4.5 × 1040	7.0 × 1039
Electron power-law index	s	2.2	2.2
Minimum electron Lorentz factor	γmin	1.0	1.0
Cutoff electron Lorentz factor	γcut	102	102
Maximum electron Lorentz factor	γmax	106	106
Synchrotron luminosity $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	Lsync	2.8 × 1037	4.3 × 1036
SSC luminosity $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	LSSC	4.1 × 1037	7.2 × 1036
Total radiation luminosity $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	Lrad	6.9 × 1037	1.2 × 1037
Jet power in magnetic field $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	LB	3.7 × 1037	6.3 × 1036
Jet power in electrons $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	${L}_{{\rm{e}}}$	7.8 × 1036	3.7 × 1036
Jet power in cold protons $(\mathrm{erg}\;{{\rm{s}}}^{-1})$	Lp	2.1 × 1039	2.0 × 1039
Jet radiative efficiency (%)	${\epsilon }_{{\rm{rad}}}$	∼3	∼1

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Note that the electron power-law index of 2.2 we obtained from SED modeling has already been modified by rapid synchrotron and SSC cooling. In the current situation, because the magnetic field is strong (B ∼ 1 × 10⁵ G) and the emission region is small (R ∼ 5 × 10⁸ cm), we need to consider the following three energy-loss processes: adiabatic cooling (this is also equivalent to particle escape from emission region), synchrotron cooling, and SSC cooling. Note here that we can neglect synchrotron cooling for electrons of γ ≲ 40 because the optically thick regime is below ${\nu }_{{\rm{SSA}}}=3\times {10}^{14}{(\gamma /40)}^{2}(B/{10}^{5}\ {\rm{G}})\ {\rm{Hz}}$ (e.g., Piran 2004). Cooling timescales for these processes are estimated as ${t}_{{\rm{ad}}}\gtrsim R/c\sim 1.7\times {10}^{-2}(R/5\times {10}^{8}\ {\rm{cm}})$ and ${t}_{{\rm{SSC}}}\;\sim 5.1\times {10}^{-2}{\gamma }^{-1}{({U}_{{\rm{sync}}}/3\times {10}^{8}{\rm{erg}}{{\rm{cm}}}^{-3})}^{-1}$, respectively (e.g., Piran 2004; Chaty et al. 2011). Therefore, high-energy electrons of γ ≳ 3 rapidly lose their energy via SSC emission, and hence the electron power-law index becomes steeper by one power of E, if injection of high-energy emitting electrons continued over a few tens of minutes (which corresponds to the flare duration observed by Kanata/HONIR). Namely, the electron energy distribution at γ ≳ 3 is already in a fast-cooling regime, which indicates that the original (or injected) electron power-law index is 1.2. This is much smaller than the standard power-law index of 2.0 derived by the first-order Fermi acceleration theory (e.g., Blandford & Ostriker 1978).

We can now derive the total energy in electrons and magnetic field as ${W}_{{\rm{e}}}={m}_{e}{c}^{2}{\int }_{{\gamma }_{{\rm{min}}}}^{{\gamma }_{{\rm{max}}}}d\gamma \gamma {dN}/d\gamma =9.9\times {10}^{34}$ erg and ${W}_{{\rm{B}}}=(4/3)\pi {R}^{3}{U}_{{\rm{B}}}=4.7\times {10}^{35}$ erg, respectively; thus, the jet is Poynting flux dominated by a factor of ∼5. The jet power in electrons (L_e) and magnetic field (L_B) is calculated as ${L}_{{\rm{i}}}=2\pi {R}^{2}\beta {{cU}}_{{\rm{i}}}\ (\text{i = e, B})$, where ${U}_{{\rm{e}}}={W}_{{\rm{e}}}/(4\pi {R}^{3}/3)$ is the electron energy density, β = 0.9 is assumed, and the factor of 2 is due to the assumption of a two-sided jet (e.g., Finke et al. 2008). Then, we obtain L_e = 7.8 × 10³⁶ erg s⁻¹ and L_B = 3.7 × 10³⁷ erg s⁻¹, and the summed power (${L}_{{\rm{e}}}+{L}_{{\rm{B}}}$) amounts to 4.5 × 10³⁷ erg s⁻¹. On the other hand, we can also calculate the total radiated power using the SED modeling result as L_rad = L_sync + L_SSC = 7.0 × 10³⁷ erg s⁻¹, which is larger than the summed L_e + L_B = 4.5 × 10³⁷ erg s⁻¹. This indicates that the Poynting flux (L_B) and L_e are not sufficient to explain L_rad and another form of power is required. The simplest and most probable solution is to assume that the jet contains enough protons that have larger power than L_rad (e.g., Sikora & Madejski 2000; Ghisellini et al. 2014; Saito et al. 2015; Tanaka et al. 2015). This is another (though indirect) evidence of a baryon component in a microquasar jet. Note that we reached the above conclusion based on jet energetics argument, but the baryonic jet in a microquasar has already been claimed by a different, independent method based on the detection of blueshifted emission lines in the X-ray spectra for SS 433 and 4U 1630-47 (Kotani et al. 1994; Díaz Trigo et al. 2013).

By assuming that the jet contains one cold proton per one relativistic (emitting) electron, we can derive the total energy of cold protons as ${W}_{{\rm{p}}}={m}_{p}{c}^{2}{\int }_{{\gamma }_{{\rm{min}}}}^{{\gamma }_{{\rm{max}}}}d\gamma {dN}/d\gamma =5.4\times {10}^{37}$ erg, where m_p is the proton mass. This corresponds to the cold proton power (L_p) of 2.1 × 10³⁹ erg s⁻¹ by using the relation of ${L}_{{\rm{p}}}=2\pi {R}^{2}\beta {{cU}}_{{\rm{p}}}$ (e.g., Finke et al. 2008), where ${U}_{{\rm{p}}}={W}_{{\rm{p}}}/(4\pi {R}^{3}/3)$ is the energy density of cold protons and β = 0.9 is assumed. We therefore obtain the total jet power ${L}_{{\rm{jet}}}={L}_{{\rm{e}}}+{L}_{{\rm{B}}}+{L}_{{\rm{p}}}$ and radiative efficiency of the jet as ${L}_{{\rm{rad}}}/{L}_{{\rm{jet}}}\sim 3\%$ (see also Table 2).

During the moderate and steady state on MJD 57194, there were no observational constraints on ν_SSA owing to the dominance of the disk component in the optical and NIR bands; hence, we assume that it remained the same as that during the bright flare, ν_SSA = 3.0 × 10¹⁴ Hz. We estimated the synchrotron peak flux as 0.2 Jy, because such a flux level was observed in the GHz band during the high state (Trushkin et al. 2015a) and an extrapolation to the NIR band with a flat shape (α = 0) seems reasonable. We thereby obtained the following estimates of B ∼ 2 × 10⁵ G and R ∼ 2 × 10⁸ cm (see Equations (1) and (2)). Important information about the nonthermal jet emission, which should be included in the SED modeling, comes from the INTEGRAL detection of an additional power-law component of ${\rm{\Gamma }}={1.54}_{-0.45}^{+0.24}$ in the hard X-ray band (Rodriguez et al. 2015). The Kanata/HONIR, Swift/XRT, and INTEGRAL (exponential cutoff power-law component dominant up to ∼100 keV) data points are treated as upper limits. Based on these assumptions and the multiwavelength data, we calculated the broadband nonthermal jet emission by accelerated electrons using the one-zone synchrotron and SSC model. The result is shown by solid lines in Figure 6 (right panel), and the model parameters are tabulated in Table 2. We obtained the same parameter values of s = 2.2 and γ_cut = 10² for the electron energy distribution, but the electron normalization K = 7.0 × 10³⁹ is smaller owing to the fainter jet flux, as was observed in the radio band. We also found ${L}_{{\rm{B}}}/{L}_{{\rm{e}}}\sim 2$, suggesting again that the jet is slightly Poynting flux dominated. More interestingly, the total radiated power is again larger than the summed electron and magnetic field powers in the jet (see Table 2), implying the presence of a baryonic component even during the fainter state.

Our discussion of the jet properties of V404 Cyg in this section, particularly in relation to AGN jets, can be summarized as follows:

• 1.  
  The SSA frequency and peak flux density enable us to estimate the magnetic field strength and size of the emission region by assuming equipartition between magnetic field and relativistic electrons. The derived magnetic field of B ∼ 10⁵ G is much stronger, and the size of the emission region of R ∼ 10⁸ cm much smaller, compared to AGN jets (typically B ∼ 1–10 G and R ∼ 10^17–18 cm; see, e.g., Ghisellini et al. 2010).
• 2.  
  Based on modeling of the broadband spectrum of V404 Cyg, we found an upper limit to the cutoff Lorentz factor of electrons of ∼100. Because the cutoff is determined by the balance of the acceleration and cooling times, this result implies a longer acceleration time of η ∼ 10⁶ in this microquasar jet, suggesting that electron acceleration is much less efficient compared to AGN jets (which typically show η ∼ 10).
• 3.  
  The original (or injected) power-law index of the electron energy distribution was derived as s = 1.2. In the SED modeling of AGN jets, electrons are assumed to have a broken power-law shape. The power-law index below the break Lorentz factor γ_break (typically γ_break ∼ 100–1000) is estimated as s ∼ 1 (e.g., Ghisellini et al. 2010). Hence, s = 1.2 derived here in the V404 Cyg jet is comparable to that derived in AGN jets, implying that the same acceleration mechanism operates in these different systems.
• 4.  
  To account for the total radiated power of the jet of V404 Cyg, a cold proton component is required inside the jet. This is the same situation as in AGN jets.
• 5.  
  During the bright flare on MJD 57193, the jet radiative efficiency (${\epsilon }_{{\rm{rad}}}\equiv {L}_{{\rm{rad}}}/{L}_{{\rm{jet}}}={L}_{{\rm{rad}}}/({L}_{{\rm{e}}}+{L}_{{\rm{B}}}+{L}_{{\rm{p}}})$) is derived as ∼3%. This is roughly comparable to that of AGNs and GRB jets (∼10%; see, e.g., Nemmen et al. 2012; Ghisellini et al. 2014).