SPECTRAL STATE DEPENDENCE OF THE 0.4–2 MEV POLARIZED EMISSION IN CYGNUS X-1 SEEN WITH INTEGRAL/IBIS, AND LINKS WITH THE AMI RADIO DATA

Cyg X-1 has been extensively observed by INTEGRAL since the launch of the satellite; preliminary results of the very first observations are described by Pottschmidt et al. (2003a). In LRW11, we first considered all uninterrupted INTEGRAL pointings, also called "science windows" (ScWs), where Cyg X-1 had an offset angle of less than 10° from the center of the field of view. We then removed all ScWs from the performance verification phase so that our analysis covered the period from 2003 March 24 (MJD 52722, satellite revolution (rev.) 54) to 2010 June 26 (MJD 55369, rev. 938). We further excluded ScWs with less than 1000 s of good ISGRI and PICSiT time. This resulted in a total of 2098 ScWs. Polarization was detected when stacking this sample (LRW11).

In the present work, we added to the LRW11 sample all observations belonging to our Cyg X-1 INTEGRAL monitoring program (PI J. Wilms) made until 2012 December 28 (MJD 56289.8, rev.1246). We applied the same filtering criteria to select good ScWs. We consider both the data of the low energy detector of IBIS, ISGRI (Lebrun et al. 2003), and of the X-ray monitors JEM-X (Lund et al. 2003). ISGRI is sensitive in the ∼18–1000 keV energy range, although its response falls off rapidly above a few hundred keV. The two JEM-X units cover the soft X-ray (3–30 keV) band. All data were reduced with the Off Line Scientific Analysis (OSA) v.10.0 software suite and the associated updated calibration (Caballero et al. 2012), following the methods outlined by Rodriguez et al. (2008b).

The brightest and most active sources of the field, Cyg X-1, Cyg X-2, Cyg X-3, 3A 1954+319, and EXO 2032+375, were subsequently taken into account in the extraction of spectra and light curves. The Cyg X-1 spectra of each ScW were extracted with 67 spectral channels. All ScWs belonging to the same state were then averaged to produce one ISGRI spectrum for each spectral state. The spectral classification is described in Section 3 (see Grinberg et al. 2013 for details of the method). A systematic error of 1% was applied for all spectral channels. Low significance channels were rebinned when necessary.

The JEM-X telescopes have a much smaller field of view than IBIS. The number of ScWs during which Cyg X-1 can be seen by these instruments is therefore smaller. Since rev. 983 (MJD 55501) both units are on for all observations. Before rev. 983, both units were used alternately, so that the number of ScWs and time coverage is not the same. We derived images and spectra in the standard manner following the cookbook, separating the data into states following the same criteria as for the IBIS data. We applied systematic errors of 2% to all spectral channels of both units.

Thanks to its two position-sensitive detectors ISGRI and PICsIT, IBIS can be used as a Compton polarimeter (Lei et al. 1997). The concept behind a Compton polarimeter utilizes the polarization dependence of the differential cross section for Compton scattering,

$$\begin{eqnarray}&&\displaystyle \frac{d\sigma }{d{\rm{\Omega }}}=\displaystyle \frac{{r}_{0}^{2}}{2}{\left(\displaystyle \frac{E\prime }{{E}_{0}}\right)}^{2}\left(\displaystyle \frac{E\prime }{{E}_{0}}+\displaystyle \frac{{E}_{0}}{E\prime }-2{\mathrm{sin}}^{2}\theta {\mathrm{cos}}^{2}\phi \right)\end{eqnarray} \tag{ 1 }$$

where r₀ is the classical electron radius, E₀ the energy of the incident photon, E' the energy of the scattered photon, θ the scattering angle, and ϕ the azimuthal angle relative to the polarization direction. Linearly polarized photons scatter preferentially perpendicularly to the incident polarization vector. Hence by examining the scattering angle distribution of the detected photons (also referred to as polarigrams)

$$\begin{eqnarray}&&N(\phi )=S[1+{a}_{0}\mathrm{cos}(2(\phi -{\phi }_{0}))]\end{eqnarray} \tag{ 2 }$$

where S is the mean count rate, one can derive the polarization angle PA and polarization fraction Π. With $\mathrm{PA}={\phi }_{0}-\pi /2+n\pi$, Equation (2) becomes $N(\phi )=S[1-{a}_{0}\mathrm{cos}(2(\phi -\mathrm{PA}))][2\pi ]$. The polarization angle therefore corresponds to the minimum of $N(\phi )$. The polarization fraction is ${\rm{\Pi }}={a}_{0}/{a}_{100}$, where a₁₀₀ is the amplitude expected for a 100% polarized source, obtained from Monte-Carlo simulations of the instrument. Forot et al. (2008) obtained ${a}_{100}=0.30\pm 0.02$, hence a $\sim 6.7\%$ systematics uncertainty that should be taken into account in the derivation of Π. Recent simulations allowed us to reduce the uncertainty on a₁₀₀ to $\sim 3\%$ which is small compared to the statistical errors on $N(\phi )$ (see below), and is therefore neglected.

To measure $N(\phi )$, we followed the procedure described by Forot et al. (2008) that led to the successful detection of the polarized signal from the Crab Nebula. We consider events that interacted once in ISGRI and once in PICsIT. These events are automatically selected on board through a time coincidence algorithm. The maximum allowed time window was set to 3.8 μs during our observations. To derive the source flux as a function of ϕ, the Compton photons were accumulated in 6 angular bins, each with a width of 30° in azimuthal scattering angle. To improve the signal-to-noise ratio in each bin, we took advantage of the π symmetry of the differential cross section (Equation (2)), i.e., the first bin contains the photons with $0^\circ \leqslant \phi \lt 30^\circ$ and $180^\circ \leqslant \phi \lt 210^\circ$, etc. Chance coincidences, i.e., photons interacting in both detectors, but not related to a Compton event, were subtracted from each detector image following the procedure described by Forot et al. (2008). The derived detector images were then deconvolved to obtain sky images. The flux of the source in each ϕ bin was then measured by fitting the instrumental point-spread function to the source peak in the sky image.

The uncertainty of $N(\phi$) is dominated by statistic fluctuations in our observations that are background dominated. Confidence intervals on a₀ and ${\phi }_{0}$ are not derived by a $N(\phi )$ fit to the data, but through a Bayesian approach following Forot et al. (2008), based on the work presented in Vaillancourt (2006). The applicability of this method was recently thoroughly discussed in Maier et al. (2014). In this computation, we suppose that all real polarization angles and fractions have a uniform probability distribution (non-informative prior densities; Quinn 2012; Maier et al. 2014) and that the real polarization angle and fraction are ${\phi }_{0}$ and a₀. We then need the probability density distribution of measuring a and ϕ from N_pt independent data points in $N(\phi )$ over a period π, based on Gaussian distributions for the orthogonal Stokes components (Vaillancourt 2006; Forot et al. 2008; Maier et al. 2014):

$$\begin{eqnarray}{dP}(a,\phi ) & = & \displaystyle \frac{{N}_{\mathrm{pt}}\;{S}^{2}}{\pi {\sigma }_{S}^{2}}\mathrm{exp}\Bigg[-\frac{{N}_{\mathrm{pt}}{S}^{2}}{2{\sigma }_{S}^{2}}\left[{a}^{2}+{a}_{0}^{2}2{{aa}}_{0}\mathrm{cos}(2\phi -2{\phi }_{0})\right]\Bigg]a\;{da}\;d\phi \end{eqnarray} \tag{ 3 }$$

where ${\sigma }_{S}$ is the uncertainty of S. Credibility intervals of a and ϕ correspond to the intervals comprised between the minimum and maximum values of the parameter considered in the two-dimensional 1σ contour plot (not shown).

The 2002–2012 15 GHz light curve classified utilizing the same method as for the INTEGRAL data is shown in Figure 1. As known from previous studies of microquasars, including Cyg X-1, the LHS and the IS show a high level of radio activity, while the radio flux is at a level compatible with or very close to zero during the soft state (e.g., Corbel et al. 2003; Gallo et al. 2003).

Cyg X-1 shows a high level of radio variability with a mean flux $\langle {F}_{15\;\mathrm{GHz}}\rangle \sim 12$ mJy and flares. The most prominent flare occurred on MJD 53055 (2004 February 20) and reached a flux of 114 mJy.¹¹ Flares occur frequently (Figure 1), and are connected with the X-ray behavior of the source (Fender et al. 2006; Wilms et al. 2007). The main flares seem to mostly coincide with the IS. The radio behavior in the LHS is usually steadier (although there is, e.g., a flare at MJD 53700, Figure 1).

We obtained state resolved mean radio fluxes of $\langle {F}_{15\;\mathrm{GHz},\ \mathrm{LHS}}\rangle =13.5$ mJy, $\langle {F}_{15\;\mathrm{GHz},\mathrm{IS}}\rangle =15.4$ mJy, and $\langle {F}_{15\;\mathrm{GHz},\ \mathrm{HSS}}\rangle$ = 4.6 mJy. Given the typical rms uncertainty of $\mathrm{rms}(5\;\mathrm{minutes})$ = 3.0 mJy (e.g., Pooley & Fender 1997; Rodriguez et al. 2008a), the mean radio flux in the HSS is not detected at the $3\sigma$ level. The few clear radio detections in this state (Figure 1) do not correspond to a steady level of emission that would indicate a compact radio core (see also Fender et al. 1999). Such detections preferably occur after radio flares and thus likely represent the relic emission of previously ejected material (e.g., Corbel et al. 2004).

We analyzed the state resolved energy spectra of each instrument using XSPEC v.12.8.0 (Arnaud 1996). For JEM-X we considered the 10–20 keV range¹² and 20–400 keV for the ISGRI data. We used Compton data between 300 keV and 1 or 2 MeV, depending on their statistical quality. We started by fitting the spectra in the 10–400 keV range since the contribution of the 1 MeV power-law tail is supposed to be negligible here (LRW11). When an appropriate model was found for this restricted range, we added the 0.3–2 MeV Compton spectra and repeated the spectral analysis.

In order to find the most appropriate models describing the 10–400 keV spectra for all three spectral states, we proceeded in an incremental way. We started with a simple power-law model and added spectral model components until an acceptable fit according to ${\chi }^{2}$ statistics was found. The phenomenological models were then replaced by more physical Comptonization models. Since the $\geqslant 10$ keV data are not affected by the absorption column density of ${N}_{{\rm{H}}}\sim {\rm{a}}$ few ${10}^{22}\;{\mathrm{cm}}^{-2}$ (e.g., Böck et al. 2011; Grinberg et al. 2015), no modeling of the foreground absorption is necessary. Cross-calibration uncertainties and source variability during different exposure times are taken into account by a normalization constant. The ISGRI constant was frozen to one and the others left free to vary independently. We required that the values of the free constants were in the range [0.85, 1.15]. The best-fit parameters obtained with the best phenomenological and with the Comptonization models are reported in Table 1 for all three spectral states.

Table 1.  Spectral Parameters of Fit to the 10–400 keV Spectra

reflect*highecut(powerlaw)
State	Γ	Ecut	Efold	Fluxesb
		(keV)	(keV)	10–20 keV	20–200 keV	200–400 keV
LHS	1.43 ± 0.01	$\leqslant 12$	155 ± 4	4.48 ± 0.02	22.30 ± 0.03	3.56 ± 0.03
IS	${1.87}_{-0.03}^{+0.02}$	${56}_{-6}^{+4}$	198 ± 8	5.10 ± 0.03	18.47 ± 0.04	2.52 ± 0.05
HSSa	2.447 ± 0.007	${130}_{-16}^{+11}$	${198}_{-59}^{+135}$	1.83 ± 0.01	3.33 ± 0.01	0.18 ± 0.03
reflect*comptt
State	${\rm{\Omega }}/2\pi$	kTe	τ	Fluxesb
		(keV)		10–20 keV	20–200 keV	200–400 keV
LHS	0.13 ± 0.02	${59.4}_{-1.2}^{+1.3}$	1.06 ± 0.03	4.37 ± 0.03	22.60 ± 0.03	3.70 ± 0.03
IS	0.04 ± 0.03	${54.4}_{-2.8}^{+3.6}$	0.82 ± 0.06	5.30 ± 0.03	18.42 ± 0.06	1.93 ± 0.07
HSS	0.36 ± 0.03	279 ± 15	$\lt 0.013$	1.84 ± 0.09	3.7 ± 0.6	0.36 ± 0.01

Notes. Errors and limits on the spectral parameters are given at the 90% confidence level, while the errors on the fluxes are at the 68% level.

^aA reflection component with ${\rm{\Omega }}/2\pi$ = 0.46 ± 0.04 was included for a good spectral fit to be obtained. ^bIn units of 10⁻⁹ $\mathrm{erg}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$.

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4.2.1. Hard state

A power law (Figure 2(a)) gives a very poor representation of the 10–400 keV data with a reduced ${\chi }^{2}={\chi }_{\nu }^{2}\sim 70$ for 87 degrees of freedom (dof). The broadband spectrum clearly departs from a straight line, which indicates a curved spectrum. A power law modified by a high energy cutoff (highecut*power in XSPEC) provides a highly significant improvement with ${\chi }_{\nu }^{2}\;=\;0.89$ for 85 dof (Figure 2(b)). We note, however, that the value of the high energy cutoff is unconstrained (Table 1), and deviations are seen at high energies.

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As a cutoff power law in this energy range is usually assumed to mimic the spectral shape produced by an inverse Compton process, we replaced the phenomenological model by a more physical model comptt (Titarchuk 1994; Titarchuk & Hua 1995; Titarchuk & Lyubarskij 1995). Due to our comparably high lower energy bound, the temperature of the seed photons could not be constrained. We fix it to a typical LHS value of 0.2 keV (Wilms et al. 2006). Although the high energy part is better represented, the fit is statistically unacceptable (${\chi }_{\nu }^{2}\;=\;2.9$ for 88 dof, Figure 2(c)) and significant residuals are visible in 10–80 keV range. In this range, hard X-ray photons can undergo reflection on the accretion disk. This effect is usually seen as an extra curvature, or bump in the 10–100 keV range in the spectra of microquasars and AGNs (García et al. 2014 and references therein). We thus included a simple reflection model (reflect) convolved with the Comptonization spectrum and fixed the inclination angle to 30°. The residuals are much smaller, yielding an acceptable fit (${\chi }_{\nu }^{2}\;=\;1.67$ for 87 dof).¹³ The normalization constants are 0.99, 1.06, and 0.98 for JEM X-1, JEM X-2, and the Compton mode respectively. The best fit results of this model are listed in Table 1, while the $\nu \;F\nu$ broad band 10–400 keV spectrum is shown in the rightmost panel of Figure 2.

Next, we added the ≥400 keV Compton mode spectrum (Figure 3) to our data. These points are significant at the $8.2\sigma$, $7.8\sigma$, $6.9\sigma$, and $6.5\sigma$ levels in the 451.4–551.9 keV, 551.9–706 keV, 706–1000.8 keV, and ∼1–2 MeV energy bands. A significant deviation from the previous best fit model is clearly visible above 400 keV. An additional power law improves the fit significantly (${\chi }_{\nu }^{2}=1.4$ for 90 dof). The photon index of this additional power law is hard (${\rm{\Gamma }}={1.1}_{-0.4}^{+0.3}$) and marginally compatible with the values reported earlier (1.6 ± 0.2, LRW11).

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We model the reflection component using several distinct approaches, assuming (1) that the power-law component undergoes the same reflection as the Comptonization component (reflect*(power+comptt)), (2) that both components undergo reflection but with different solid angles ${\rm{\Omega }}/2\pi$ (reflect₁*(power)+reflect₂*(comptt)), and (3) that the power law is not reflected (power+reflect*(comptt)). In model 2, the value for the reflection of the power-law component is unconstrained. Model 3 results in a better ${\chi }_{\nu }^{2}$, but the value of the power-law parameters are physically not acceptable. The normalization is too high and Γ too soft to reproduce the Compton data well. We therefore discard model 3, and consider model 1 as the most valid one. The value of the fit statistics is, however, still high with ${\chi }_{\nu }^{2}=1.8$ for 89 dof. The residuals show deviations in the ∼50–200 keV range that may be due to the accumulation of a large set of ScWs taken at different calibration epochs and at different off-axis and roll angles of Cyg X-1.

In the final fit to the 10 keV–2 MeV broad band spectrum the parameters of the Comptonized component are ${{kT}}_{e}=53\pm 2$ keV and $\tau =1.15\pm 0.04$, the reflection fraction is unchanged, and the photon index of the hard tail is ${\rm{\Gamma }}={1.4}_{-0.3}^{+0.2}$, i.e., essentially compatible with the value reported in LRW11. The 0.4–1 MeV flux of the hard tail (${F}_{\mathrm{pow},0.4-1\;\mathrm{MeV}}\;=1.9\times {10}^{-9}\;\mathrm{erg}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$) accounts for 86% of the total 0.4–1 MeV flux.

4.2.2. Intermediate State

4.2.3. Soft State

Polarigrams were obtained for each of the three spectral states. The low statistics of the IS (the source significance in the Compton mode is $5.7\sigma$) does not permit us to constrain the 250–3000 keV polarization fraction.

In the HSS, the detection significances of Cyg X-1 with the Compton mode are $4.2\sigma$ and $7.7\sigma$ in the 300–400 keV and 400–2000 keV bands respectively. A weighted least square fit procedure was used to fit the polarigrams. A constant represents the 400–2000 keV polarigram rather well (${\chi }_{\nu }^{2}=1.6$, 5 dof, not shown). The 1σ upper limit of the 400–2000 keV polarization fraction in the HSS is ∼70%.

Figure 4 shows the LHS polarigrams in two energy ranges: 300–400 keV and 400–2000 keV. Note that the data selection described in Section 3 is at the origin of the different count rates between the polarigrams shown here and those in Figure 2 or LRW11. This effect is more obvious at the highest energies where the different spectral slopes have the largest impact (Figure 3). In the lower energy range, the Compton mode detection significance of Cyg X-1 is 12.3σ. The polarigram can be described by a constant (${\chi }_{\nu }^{2}=0.87$, 5 dof). We estimate an upper limit for the polarization fraction of ${{\rm{\Pi }}}_{300-400\;\mathrm{keV},\ \mathrm{LHS}}=22\%$ in this energy range. The 400–2000 keV energy range polarigram shows clear deviation from a constant and a constant poorly represents the data (${\chi }_{\nu }^{2}=3.5$, 5 dof). The pattern and fit indicate that the photons scattered in ISGRI are not evenly distributed in angle, but that the scattering has a preferential angle as is expected from a polarized signal (Section 2.2). We describe the distribution of the polarigram with the expression of Equation (2) and obtain the values of the parameters a₀ and ${\phi }_{0}$ with a least square technique. The fit is better than that to a constant, although not formally good (${\chi }_{\nu }^{2}=2.0$, 3 dof) due to the low value of the periodogram at azimuthal angle 100° (Figure 4). Assuming that the non constancy of the polarigram is evidence for a real polarized signal (an assumption also consistent with the independent detections of polarized emission in Cygnus X-1 with SPI; Jourdain et al. 2012), we estimate that the polarization fraction is ≳10% at the 95% level, and greater than a few % at the 99.7% level. In other words we obtain a significance higher than $3\sigma$ for a polarized 400–2000 keV LHS emission. We determine a polarization fraction and a credibility interval of ${{\rm{\Pi }}}_{400-2000\;\mathrm{keV},\mathrm{LHS}}=$ 75% ± 32% at position angle ${\mathrm{PA}}_{\mathrm{Cyg}\ {\rm{X}}-1,\mathrm{LHS}}=40\buildrel{\circ}\over{.} 0\pm 14\buildrel{\circ}\over{.} 3$. The values of the polarization fraction and angle are consistent with those found by JRC12. We note that an error of 180° in the angle convention in LRW11 led to $\mathrm{PA}=140^\circ$, which after correction becomes 40°, in agreement with our state resolved result (see also JRC12). Note that the good agreement of our results with those obtained with SPI in the case of Cyg X-1, and also the fact that IBIS also detected polarization in the high energy emission of the Crab Nebula and pulsar (Forot et al. 2008) at values compatible with those obtained with SPI (Dean et al. 2008), increase the confidence in the reality and validity of our results.

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Our analysis shows that the $\gt 400$ keV spectral properties of Cyg X-1 depend on the spectral state, as already suggested previously (e.g., McConnell et al. 2002). We detect a strong hard tail in the LHS, but obtain only upper limits in the IS and HSS. In Figure 5 (left), we show a comparison of our LHS 0.75–1 MeV spectrum with those obtained with Compton Gamma Ray Observatory/COMPTEL during the 1996 June HSS and during an extended LHS observed with this instrument (McConnell et al. 2000, 2002). The IBIS hard tail is compatible in terms of fluxes to within $2\sigma$ to those seen with COMPTEL and also with the INTEGRAL/SPI hard tail reported in JRC12 (see their Figure 5). It is worth noting that Cyg X-1 is a notoriously highly variable source and flux evolution between different epochs is expected. To illustrate this behavior, we study data taken during two main periods, that covering 2003 March–2007 December (MJD 52722–54460) and 2008 March–2009 December (MJD 54530–55196), respectively. These intervals correspond to the analysis of LRW11. The two Compton spectra are shown in Figure 5 (right). It is obvious that the flux of the hard tail varied between the two epochs and an evolution of the slope may also be visible. We note that these data are not separated by states, but as they cover the period before 2009 December, they are dominated by the LHS (e.g., Figure 1). We therefore conclude that, even in the same state, the hard tail shows luminosity variations.

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A major difference from McConnell et al. (2002) is the non-detection of a hard tail in the HSS. McConnell et al. (2002) remark that between two epochs of HSS the hard tail either has a higher flux than in their averaged LHS or is not detected. Malyshev et al. (2013) also note that the 1996 HSS hard tail comes from a single occurrence of this state and may not reflect typical behavior. While detection of a hard tail during the LHS, even if it shows variations, indicates an underlying process that is rather stable over long periods of time, the apparent transience of the HSS hard tail may indicate a different origin for this feature. For example, in Cyg X-3 the very high energy (Fermi) flares are associated with transitions to the ultra soft state (Fermi LAT Collaboration et al. 2009). While this is similar to what is seen in Cyg X-1, all Fermi γ-ray flares of Cyg X-1 were reported during the LHS (Bodaghee et al. 2013; Malyshev et al. 2013). While the lack of simultaneous very high energy GeV–TeV data and/or polarimetric studies of the Comptel HSS hard tail prevent any further conclusion on the origin of this component, we conclude that the HSS hard tail and the LHS hard tail could be of different origins.

A clear polarized signal is detected from Cyg X-1 with both IBIS and SPI while accumulating all data regardless of the spectral state of the source (LRW11, JRC12). Here we separated the data into different spectral states and studied the state dependent high energy polarization properties. The HSS and 300–400 keV polarigram can be described by a constant, indicating no or very small levels of polarization. The 400–2000 keV LHS polarigram shows a large deviation from a constant, which indicates that the Compton scattering from ISGRI is not an evenly circular distribution on PICSiT. We interpret this as evidence for the presence of polarization in this energy range, even if the polarigram shows some deviations from the theoretically expected curve (Figure 4). In the 300–400 keV range, no evidence for polarization is found. This is consistent with the results obtained with SPI (JRC12) and shows that the polarization fraction is strongly energy dependent. Assuming a non-null level of polarization, a reasonable assumption given the above arguments, we estimate that the detection of polarized emission is significant at higher than $3\sigma$. Given the larger amount of data and the separation into different spectral states, one could have expected to obtain more robust results and more constrained polarization parameters compared to LRW11 and JRC12, while the uncertainties we obtained are, at best, of the same order. The reason for this lies in the behavior of Cyg X-1. While the earlier studies did not perform a state dependent analysis, our state classification reveals that both studies were dominated by data taken during the LHS and the IS (see also Figure 1). In fact, compared to LRW11 the number of ScWs measured during the LHS increased only by 13%, and 75% of the IS data comes from the period considered in these earlier studies, i.e., before ∼MJD 55200. On the other hand, about 94% of the HSS data are new. It is therefore not surprising that our hard state result is consistent with the earlier results, as these were fully dominated by the (polarized) hard state data. The exposure of the less polarized IS data was not large enough to significantly "dilute" the polarization. Our result clearly shows that larger amounts of data in each of the states are needed to refine the constraint on the polarization properties and their relation to the spectral states.

Our LHS spectral analysis shows that the 10–1000 keV spectrum can be decomposed into several spectral components: a (reflected) thermal Comptonization component in the range ∼10–400 keV, and a power-law tail dominating above ∼400 keV (Section 4.2.1). The origin of the seed photons for the Compton component may either be an accretion disk or synchrotron photons from a compact jet undergoing synchrotron self-Comptonization (SSC). As discussed elsewhere (e.g., Laurent et al. 2011), due to the large number of scatterings the Comptonization spectrum from a medium with an optical depth $\tau \geqslant 1$ is not expected to show intrinsic polarization, especially with such a high fraction as the one we detect here. Multiple Compton scattering, as expected in such a medium, will "wash out" the polarization of the incident photons even if the seed photons are polarized (e.g., jet photons). It is therefore not surprising that the LHS ≲ 400 keV component has a very low (or zero) polarization fraction (see also Russell & Shahbaz 2013).

The origin of the hard-MeV tail is much less clear and is highly model-dependent. Two main families of models can explain the (co-)existence of cutoff power-law and/or pure power-law like emissions in the energy spectra of BHBs. The first is based on the presence of a hybrid thermal–non thermal population of electrons in a "corona," and hybrid Comptonization has been successfully applied to the spectra of, e.g., GRO J1655–40 or GX 339–4 (e.g., Joinet et al. 2007; Caballero-García et al. 2009), and even to ∼1–10000 keV spectra of Cyg X-1, in both the HSS and LHS (McConnell et al. 2002). A double thermal component has been used to represent the 20–1000 keV SPI data of 1E 1740–2947 well (Bouchet et al. 2009).

The second family of models essentially contains the same radiation processes but is based on the presence of a jet emitting through direct synchrotron emission, thermal Comptonization of the soft disk photons on the base of the jet, and/or SSC of the synchrotron photons by the jet's electrons (e.g., Markoff et al. 2005). Such models have been used with success to fit the data of some BHs, and particularly GX 339–4 and XTE J1118+480 (Markoff et al. 2005; Maitra et al. 2009; Nowak et al. 2011). It should be noted, however, that they obviously rely on the presence of a compact jet and therefore can only be valid when/if a compact jet is present.

The capacities of the current high energy missions, albeit excellent, do not permit an easy discrimination between the different families of models. This has been nicely illustrated in the specific case of Cyg X-1 through the 0.8–300 keV spectral analysis of the Suzaku/RXTE observations (Nowak et al. 2011). Different and complementary approaches and arguments can, however, be used to try and identify the most likely origin for the hard power-law tail. The fundamental plane between radio luminosity and X-ray luminosity (e.g., Corbel et al. 2003) was originally used as an argument for a (small) contribution of the jet to the X-ray domain. Our approach here was to first separate the radio data sets into different spectral states, based on a model-independent classification. It was only because of this separation that we could show that a hard polarized tail is present in the LHS, with a high polarization fraction, together with a radio jet. The very high level of polarization can only originate from optically thin synchrotron emission (see below), and implies a highly ordered magnetic field similar to that expected in jets. The synchrotron tail coincides with thermal Comptonization at lower energies and with a radio jet. The presence of all these features is qualitatively compatible with the multi-component emission processes predicted by compact jet models such as those of Markoff et al. (2005). While polarization of the (compact) jet emission has already been widely reported in the radio domain (Brocksopp et al. 2013, and references therein), a thorough study of the multi-wavelength polarization properties of Cyg X-1 has only recently been undertaken by Russell & Shahbaz (2013). These authors, in particular, showed that the multi-wavelength spectrum and polarization properties of Cyg X-1 are quantitatively compatible with the presence of a compact jet that dominates the radio to IR domain and is also responsible for the MeV tail. A similar conclusion was drawn by Malyshev et al. (2013) under the assumption that "the polarization measurements were robust" and that therefore the MeV tail could only originate from synchrotron emission. This pre-requisite is reinforced by our refined and spectral-state dependent study of the polarized properties of Cyg X-1 at 0.3–1 MeV. A polarized signal is indeed suggested by the 400–2000 keV LHS data and the large degree of polarization measured in Section 4.3 implies a very ordered magnetic field. Assuming the magnetic field lines are anchored in the disk implies that the γ-ray polarized emission comes from close to the inner ridge of the disk where the magnetic energy density is highest. This constraint is difficult to reconcile with a spherically shaped corona medium, where the magnetic field lines are more likely to be tangled and where the polarized component necessarily comes from the outer shells of the corona where the optical depth is the lowest. We therefore conclude that in the LHS the 0.4–2 MeV tail detected with INTEGRAL/IBIS is very likely due to optically thin synchrotron emission, and that this emission comes from the detected compact jet.

The synchrotron spectrum of a population of electrons following a power-law distribution, ${dN}(E)\propto {E}^{-p}d(E)$, where p is the particle distribution index, can be approximated by a power-law function over a limited range of energy, i.e., ${F}_{{E}_{1},{E}_{2}}(E)\propto {E}^{-\alpha }$ over $[{E}_{1},{E}_{2}]$ (Rybicki & Lightman 1979). In the case of compact jets, two main domains are usually considered: the optically thick regime with $\alpha \lesssim 0$ and the optically thin regime with $\alpha \gt 0$. The break between the two regimes is typically in the infrared band (e.g., Corbel & Fender 2002; Rahoui et al. 2011; Corbel et al. 2013; Russell & Shahbaz 2013). The jet synchrotron spectrum is optically thin toward higher energies, and here $\alpha =(p-1)/2$. The jet emission becomes negligible in the range from the optical to hard X-rays when compared to the contribution from other components such as the companion star, the accretion disk, or the corona. Our results indicate that it again dominates above a few hundred keV (see also Russell & Shahbaz 2013, for a multi-components modeling of the multi-wavelength Cyg X-1 spectrum).

The degree of polarized emission expected in the optically thin regime is ${\rm{\Pi }}=\frac{p+1}{p+7/3}$ (Rybicki & Lightman 1979). Since the flux spectral index $\alpha ={\rm{\Gamma }}-1$, where Γ is the photon spectral index, it is possible to deduce p from the measured spectral shape. With ${\rm{\Gamma }}={1.4}_{-0.3}^{+0.2}$ (Section 4.2.1) we obtain $p={1.8}_{-0.7}^{+0.4}$ and thus expect ${{\rm{\Pi }}}_{\mathrm{expected}}={67.8}_{-5.5}^{+2.7}\%$. This value is consistent with the value measured in the LHS (${\rm{\Pi }}=75\%\pm 32\%$).

We determine a polarization angle of $\sim 40^\circ$ compatible with the SPI results (JRC12). This angle, however, differs by about 60° from the polarization angles measured in the radio and optical (Russell & Shahbaz 2013, and references therein). Assuming that the γ-ray polarized component comes from the region of the jet that is closest to the launch site (i.e., the inner ridge of the disk and/or the BH), the change in polarization angle implies that the field lines in the γ-ray emitting region have a different orientation than farther out in the jet. This could be indicative of a relatively large opening angle at the basis of the jet (as sketched in Figure 3 of Russell & Shahbaz 2013). Alternatively the large offset could simply be due to strongly twisted magnetic field lines close to the accretion disk.