A VARIABLE MID-INFRARED SYNCHROTRON BREAK ASSOCIATED WITH THE COMPACT JET IN GX 339–4

Despite decades of studies on accreting sources, observations of jets in X-ray binaries suffer from important limitations. Strong emission from accreting, stellar, or surrounding material dominates fainter jet radiation over infrared–X-ray frequencies in most sources (e.g., Russell et al. 2006). The transient nature of activity in many binaries makes it difficult to catch them contemporaneously with multiple observatories necessary to probe broadband emission and isolate the jet. Moreover, there has so far been a lack of sensitive monitoring instruments in the infrared where the jet flux density is expected to peak (e.g., Markoff et al. 2001).

According to the canonical model of emission from compact jets (Blandford & Königl 1979), this peak occurs because conservation of particle and magnetic flux leads to each location in the jet being associated with its own photospheric frequency, which falls linearly with distance from the base. The sum of all components conspires to give a flat/inverted spectrum (α ⩾ 0, where F_ν∝ν^α) up to a peak frequency associated with the optically thick-to-thin break (ν_b), above which optically thin synchrotron radiation (α < 0) reveals information about the underlying particle distribution. Constraints on this break remain sparse due to the limitations mentioned above (e.g., Fender 2001; Corbel & Fender 2002; Gallo et al. 2007; Migliari et al. 2007, 2010; \Pe'er & Casella 2009; Rahoui et al. 2011).

In this Letter, we present the first mid-infrared (MIR) study of GX 339–4, a binary hosting a black hole with mass ≳6 M_☉ (Hynes et al. 2003) and well known for its transient, multiwavelength variability on a broad range of timescales (Motch et al. 1982; Dunn et al. 2008; Gandhi 2009; Casella et al. 2010). Its donor star is a late-type companion in a long (∼1.7 days) orbit, much fainter than the primary when active (Shahbaz et al. 2001; Muñoz-Darias et al. 2008). GX 339–4 shows evidence of relativistic jets and has proven to be a key object for jet studies across the electromagnetic spectrum (Fender 2001; Corbel et al. 2003; Markoff et al. 2003; Gandhi et al. 2008).

A MIR detection with Spitzer has been reported, but only in a single filter during a faint, steep-power-law state (Tomsick et al. 2004). We now present multiband simultaneous MIR detections during the source outburst of 2010, which allow important new constraints on ν_b and on changing conditions in the inner jet. A distance of 8 kpc and a black hole mass of 10 M_☉ are taken as representative (Shidatsu et al. 2011). Interstellar line-of-sight extinction of A_V = 3.25 is assumed (F. W. Lewis et al. 2012, in preparation), with dereddening uncertainties described in detail.

2.1. WISE

2.2. Multiwavelength

Follow-up data will be presented in a number of upcoming papers, including (1) Cadolle Bel et al. (2011, hereafter CB11) who describe extensive X-ray, near-IR, and optical coverage; (2) F. W. Lewis et al. (2012, in preparation) presenting further optical and UV data; and (3) S. Corbel et al. (2012, in preparation) discussing the radio. Broadband monochromatic fluxes closest to the WISE observations are listed in Table 2 and plotted in Figure 1. Where multiple observations were available, averages were used for the mean spectral energy distribution (SED), with the mean error computed as the standard deviation divided by the square root of the number of exposures.

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Table 2. Quasi-simultaneous Dereddened Ultraviolet to Radio Mean Fluxes

Band (Telescope or Instrument)a	log Frequency	Mean MJDb	Flux Densityc	References
	(Hz)		(mJy)
UVW2 (UVOT)	15.19	55261.05	83.8(± 6.9)+203− 59	CB11; F. W. Lewis et al. (2012, in preparation)
UVW1 (UVOT)	15.06	55259.97	54.6(± 3.0)+93− 35	CB11; F. W. Lewis et al. (2012, in preparation)
U (UVOT)	14.94	55260.38	40.3(± 0.7)+44− 21	CB11; F. W. Lewis et al. (2012, in preparation)
V (FTS)	14.74	55273.72	54.5(± 1.8)+32− 20	CB11; F. W. Lewis et al. (2012, in preparation)
R (FTS)	14.67	55273.72	33.2(± 2.1)+14− 10	CB11; F. W. Lewis et al. (2012, in preparation)
i' (FTS)	14.60	55273.72	33.9(± 0.3)+12− 9	CB11; F. W. Lewis et al. (2012, in preparation)
V (REM)	14.74	55261.30	48.2(± 1.1)+28− 18	CB11
R (REM)	14.67	55261.30	30.7(± 0.7)+13− 9	CB11
I (REM)	14.58	55261.30	29.9(± 0.3)+7− 6	CB11
J (REM)	14.39	55261.30	32.4(± 0.8)+5− 4	CB11
H (REM)	14.26	55261.30	35.1(± 0.3)+3− 3	CB11
K (REM)	14.13	55261.30	41.9(± 0.7)+3− 3	CB11
W1 (WISE)	13.95	55266.363	55.2(± 3.9)+5− 4	This work
W2 (WISE)	13.81	55266.363	64.3(± 4.6)+5− 5	This work
W3 (WISE)	13.41	55266.363	79.9(± 7.3)+10− 9	This work
W4 (WISE)	13.13	55266.363	87.4(± 8.3)+12− 11	This work
9 GHz (ATCA)	9.95	55266.4	9.7(± 0.1) ± 1.7	S. Corbel et al. (2012, in preparation)
5.5 GHz (ATCA)	9.74	55266.4	9.1(± 0.1) ± 1.0	S. Corbel et al. (2012, in preparation)

Notes. ^aUVOT: Swift UltraViolet and Optical Telescope; FTS: Faulkes Telescope South; REM: Rapid Eye Mount telescope. ^bClosest available data to the WISE observation. ^cDereddened fluxes. Statistical error bars are in brackets; the following numbers are the total errors including systematics.

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Below we present some details on the X-ray analysis, the radio observations, and the UV-to-MIR dereddening, which are specific to our work.

2.2.1. X-Rays

Public X-ray data nearly simultaneous with WISE from the Rossi X-ray Timing Explorer (RXTE; Bradt et al. 1993) were available for analysis. A short observation (ObsId 95409-01-09-03) with goodtime ≈1360 s was conducted between WISE epochs 12 and 13. For data reduction, we followed standard procedures using HEASOFT v.6.10 and FTOOLS (similarly to Gandhi et al. 2010, hereafter G10).

We find an acceptable fit with a multicolor disk with inner temperature kT_in = 0.80^+0.15_{− 0.25} keV (90% confidence intervals), an Fe K line with equivalent width ranging over ∼70–450 eV, and coronal Comptonization with electron temperature kT_e = 32⁺⁴_{− 3} keV and optical depth τ = 1.87^+0.17_{− 0.20} (modeled with comptt; Titarchuk 1994). The Proportional Counter Array (PCA) and HEXTE fluxes are found to be F_3–20 keV = 3.70^+0.01_{− 0.20}× 10⁻⁹ and F_{20–200 keV} = 8.6^+0.1_{− 0.5}× 10⁻⁹ erg s⁻¹ cm⁻², respectively, giving a luminosity L_{1–200 keV} = 1.0 × 10³⁸ erg s⁻¹ or ≈0.08 × L_Eddington. The bright-state spectrum of GX 339–4 is known to be complex and the exact physical model is irrelevant for the work presented here. The derived luminosity is not overly sensitive to model parameterization. See CB11 for detailed X-ray evolution of the source over the outburst.

For timing analysis, we extracted net light curves from the RXTE event mode data, with 8 s time bins in order to approximately match the WISE exposure times. RXTE data probe variability shorter than 1360 s. For longer timescales, we used Swift Burst Alert Telescope (BAT) 15–50 keV light curves provided by the Hard X-ray Transient Monitor team.¹⁷ Swift sampling times are non-uniform, with intervals ranging from ∼10 minutes to ≳1 hr.

2.2.2. Radio

The Australia Telescope Compact Array (ATCA) observed GX 339–4 frequently during the outburst. Here, we have used the mean fluxes observed on the two closest dates straddling the WISE observation: MJD 55262.91 and 55269.80, with simultaneous observations in the 5.5 and 9 GHz bands. Variations of ≈25% and 40% are present between the bands. Note that the source does not display extreme radio variability on timescales of days (Corbel et al. 2000). Full details will be presented in S. Corbel et al. (2012, in preparation).

2.2.3. Dereddening

The UV-to-near-IR data were dereddened assuming a standard interstellar extinction law with R_V = 3.1 (Cardelli et al. 1989). Extinction beyond 3 μm, though certainly lower than in the near-IR, remains ill-constrained. We use the mean of three recent extinction laws for the WISE data, with their dispersion serving as a propagated systematic uncertainty on the corrected fluxes: (1) the R_V = 5.5 grain model of Draine (2003) which matches the Galactic center extinction of Lutz et al. (1996) below 8 μm; (2) the Galactic center extinction curve described by Chiar & Tielens (2006); and (3) that presented by Flaherty et al. (2007). The latter two provide updates on MIR silicate absorption strengths. Finally, we also include a systematic A_V uncertainty of 0.5 mag (G10).

3.1. Broadband Spectrum

3.2. Variability

Simultaneous four-band WISE light curves in Figure 2 show striking variability typically sampled at (multiples of) the WISE orbital period of 95 minutes. The shortest sampling interval was 11 s between epochs 3 and 4, when WISE caught GX 339–4 on two consecutive scans. We extracted light curves of randomly selected field stars for comparison. For each band, two field stars with brightness similar to GX 339–4 within 5' were selected. Variations in the target light curves are clearly much stronger than the field star variations and also display inter-band correlations, implying that they are not related to any instrumental or observational artifact.

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We measured the fractional variability amplitudes (F_var; Vaughan et al. 2003) of the MIR light curves and found them to increase with wavelength, with F^MIR_var ∼ 0.25 ± 0.03 for W1–2 and ∼0.32 ± 0.06 for W3–4, respectively (errors allow for WISE pipeline systematics as in Section 2.1). The peak-to-peak flux ratios also increase from 2.3 to 3.3 in W1–4. In X-rays, the Swift data show low mean variability over the timespan of WISE observations, with F_var(Swift) = 0.17 ± 0.02. This value may suffer from large systematics because BAT employs a coded mask with a wide field of view. RXTE is not affected by such complications, and we measure F_var(PCA) = 0.21 ± 0.01 and F_var(HEXTE) = 0.20 ± 0.01 for the full energy ranges of the instruments, and over the range of timescales of 8–1360 s.

Both the timing and spectral properties strongly favor a jet origin for the mid-infrared emission. The mean optically thick and thin slopes are fairly typical for binaries in the hard state when the jet is known to be strong. From closely simultaneous X-ray and MIR light curves, we find F^X-ray_var < F^MIR_var when comparing similar timescales. This argues against strong MIR variations originating via reprocessing, because the secondary (driven) variability cannot exceed the primary ones in strength. X-ray variations can also be ruled out as the driver of IR variations in the outer disk because the IR spectral slopes are inconsistent with thermal reprocessing. Dusty circumbinary disks found in some other sources (Rahoui et al. 2010) are unlikely here because of the strong variability (so dust grains should be destroyed by X-rays), and the MIR spectral slopes do not match thermal dust emission.

The strong variability implies dramatic changes in spectral slope across the WISE bands in the individual observation epochs. These are displayed in Figure 3. Parameterizing the spectra with single power laws results in slopes of α_WISE ∼ −0.5 to +0.2 (Table 1). In several epochs, additional spectral curvature appears to be present within the WISE bands. In particular, in epochs 12 and 13, W1 and W4 fluxes lie below the fit (while W2–3 lie above), returning large single-power-law null-hypothesis rejection probabilities (P). From W2 to W1, the slope is negative in most epochs ($\overline{\alpha _{{}_{W1}}^{{}_{W2}}}$ = −0.48 ± 0.07), meaning that these bands probe mostly optically thin emission. Thus carrying out a simple two-power-law fit to describe the W1 and W2 band pair and the W3 and W4 pair separately, the spectral break associated with this curvature is constrained to be at log(ν_b; Hz) = 13.65 ± 0.24 and 13.68 ± 0.26 in epochs 12 and 13, respectively.

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The position of ν_b depends strongly on the magnetic field strength (B) at the acceleration zone in the compact jet, and is comparatively insensitive to luminosity, geometry, and energy partition factors. Generalizing the homogeneous cylindrical single-zone emission model of Chaty et al. (2011), we find expressions for B and the zone radius R as follows:

$$\begin{eqnarray} B & = & 1.5\times 10^4\ \ \xi ^{-4z}\ h^{2z}\ d_8^{-4z} \nonumber\\ & & \times (F_{\nu _{\rm b}}/F_{70})^{-2z}\ (\nu _{\rm b}/4.5\times 10^{13})\ {\rm G}, \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} R & = & 2.2\times 10^9\ \ \xi ^{-z}\ h^{-z(p+6)}\ d_8^{2z(p+6)}\nonumber\\ & & \times (F_{\nu _{\rm b}}/F_{70})^{z(p+6)}\ (\nu _{\rm b}/4.5\times 10^{13})^{-1}\ {\rm cm}, \end{eqnarray} \tag{ 2 }$$

where z = (2p+13)⁻¹, ξ is the equipartition fraction of particles to magnetic energy density, h is the scale height of the optically thin region, d₈ is the distance in units of 8 kpc, and F₇₀ = 70 mJy. Since B depends only weakly on h and ξ (we fix both at 1), we have a robust estimate of B when ν_b can be measured. Both epochs 12 and 13 imply B ≈ 1.5(± 0.8) × 10⁴ G and R ≈ 2.5(±1.5) × 10⁹ cm, with errors determined from Monte Carlo sampling of all parameters (including also systematic distance uncertainty of 2 kpc).

In addition, the strong MIR slope changes between optically thick and thin imply that ν_b is varying over a range at least as wide as that which WISE is sensitive to. It is likely that uncertainties due to present WISE photometric calibration as well as the ill-constrained dereddening prevent accurate localization of ν_b in some other epochs. Setting the WISE systematic errors to zero and repeating the single-power-law fits returns P > 90% values in additional epochs 1, 2, 3, 6, and 7, consistent with ν_b falling within the WISE bandpass in these.

In order to understand the extent of changing jet physical conditions, we compare two extreme WISE epochs: (1) epoch 4, with very bright flux in W4 and a steep slope implying optically thin emission over the whole WISE range and (2) epoch 8, when the source was faintest in W4 with an inverted slope implying that ν_b has shifted to the high-frequency end. We assume (1) ν_b(epoch 4) = 1.3 × 10¹³ Hz and (2) ν_b(8) = 9 × 10¹³ Hz, corresponding to the extreme WISE frequencies and representing likely upper and lower limits to the true ν_b values, respectively. The dereddened fluxes are $F_{\nu _{\rm b}}$(4) ≈ 115 mJy and $F_{\nu _{\rm b}}$(8) ≈ 50 mJy. Comparing B and R, we find

$$\begin{equation} B(4)/B(8) = [F_{\nu _{\rm b}}(4)/F_{\nu _{\rm b}}(8)]^{-2z} [\nu _{\rm b}(4)/\nu _{\rm b}(8)] = 0.13 \end{equation} \tag{ 3 }$$

$$\begin{equation} R(4)/R(8) = [F_{\nu _{\rm b}}(4)/F_{\nu _{\rm b}}(8)]^{z(p+6)} [\nu _{\rm b}(4)/\nu _{\rm b}(8)]^{-1} = 10.4\,. \end{equation} \tag{ 4 }$$

Modulations by factors of ∼10 in the field strength or in acceleration zone size are required. The standard scaling of the B field along the jet is B ∼ R⁻¹ (Blandford & Königl 1979) which, if true, is consistent with the variability being dominated by changes in location of the acceleration zone along the jet. These modulations may ultimately originate from stochastic instabilities within the accretion flow, or as a result of changing dissipative shock conditions in the inner jet (e.g., Falcke & Biermann 1995; Meier et al. 2001; Polko et al. 2010). Multiwavelength monitoring coordinated with the mid-infrared opens up the possibility for studying these processes in the future. The characteristic timescales of change are ∼hours or less (Figure 2), though variability between epochs 3 and 4 means that some changes are faster than ∼11 s.

Simultaneous multiband observations over a broad frequency range with WISE have proved crucial for revealing complex and rapid changes occurring near the jet base. Based on the average data in Figure 1 alone, it would be impossible to accurately localize ν_b and to infer changes in its position. Whereas ν_b has been found to lie at similar MIR frequencies of (1–4) × 10¹³ Hz in 4U 0614+091 and Cyg X-1, observational limitations prevented simultaneous observations straddling the break in the former (Migliari et al. 2010), and the MIR is dominated by non-jet emission in the latter (Rahoui et al. 2011). We have cleanly probed jet-dominant MIR emission simultaneously in multiple bands and shown that inferences from long-term averages are not representative of the underlying behavior in GX 339–4 at least. Thus, time dependence must be incorporated as an integral parameter when modeling compact jets.

Scale-invariant jet models imply that similar break frequency variability could be present in active galactic nuclei, where ν_b is expected at millimeter frequencies (Kellermann & Pauliny-Toth 1969; Heinz & Sunyaev 2003). Long-term millimeter monitoring may have already found signatures for this (Trippe et al. 2011).

WISE is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory (JPL)/California Institute of Technology (Caltech), funded by the National Aeronautics and Space Administration (NASA). Data for individual scans are from NEOWISE (e.g., Mainzer et al. 2011), a project of JPL/Caltech funded by NASA's Planetary Science Division. We thank the referee for a prompt report. Individual support acknowledgments are as follows. P.Ga. acknowledges JAXA International Top Young Fellowship, D.M.R. and S.M. acknowledge Netherlands Organisation for Scientific Research Veni and Vidi Fellowship, respectively, J.M. acknowledges GDR PCHE (France), and P.C. acknowledges EU Marie Curie Intra-European Fellowship 2009-237722. Swift/BAT transient monitor results and RXTE HEASARC archive data are used herein. The Faulkes Telescope South (FTS) is maintained and operated by Las Cumbres Observatory Global Telescope Network. We thank Rosa Doran of NUCLIO, Portugal for FTS observations as part of the EU-Hands on Universe initiative for school scientific education.