THE COMPLETE SPECTRUM OF THE NEUTRON STAR X-RAY BINARY 4U 0614+091

4U 0614+091 was observed with the VLA in its relatively compact C-configuration on 2006 November 1–2. The observation at 8.46 GHz started at 09:26:45 UT with an exposure time of 290.4 minutes and the observation at 4.86 GHz started at 05:07:58 UT with an exposure time of 290.7 minutes. 3C 48 was used as the primary calibrator, setting the flux density scale according to coefficients derived at the VLA in 1999.2 by staff at National Radio Astronomy Observatory (NRAO). The secondary calibrator was J 0613+1306, 40 away from the target source. Six of the 26 telescopes in the array were retrofitted expanded VLA (EVLA) antennas, necessitating the determination of baseline-based gain solutions to prevent closure errors on EVLA–VLA baselines due to mismatched bandpass shapes. The observing frequencies were 8.46 and 4.86 GHz, and the observing bandwidth was 50 MHz in both cases. Data were reduced according to standard procedures in the 2008 December 31 version of AIPS (Greisen 2003) using a clean component model to determine the gain solutions for the primary calibrator. Since the source was so faint, no self-calibration was performed. The source flux density and position were measured after deconvolution by fitting the source as a point source and as an elliptical Gaussian in the image plane.

We observed 4U 0614+091 with Spitzer/Infrared Array Camera (IRAC) on 2006 October 30 starting at 17:41:39 UT for 384 s and with Spitzer/Multiband Imaging Photometer for Spitzer (MIPS) on 2006 November 3 starting at 06:57:43 UT for 3371 s. We have processed the 24 μm MIPS and the 3.6, 4.5, 5.8, and 8 μm IRAC basic calibrated data using the software mopex (Makovoz & Marleau 2005), following the procedure as in the manuals available online.¹¹ We created a mosaic from the 280 and 10 frames per band obtained in the MIPS and IRAC observations, respectively, and we extracted the source flux using aperture photometry. We have corrected the IRAC flux densities for interstellar extinction using A_v = 2 (derived from the equivalent hydrogen column density values in Juett et al. (2001) and using N_H = A_v × 0.179 × 10²² in Predehl & Schmitt (1995)), and following the standard optical-to-IR interstellar extinction law with 0.55 μm as a reference frequency for the V band (Rieke & Lebofsky 1985; Cardelli et al. 1989). These de-reddening values calculated from the X-ray spectra have to be considered upper limits (Juett et al. 2001). However, studies of the optical spectra of the source indicate that the reddening of the object should be close to the maximum in the Galaxy in its direction (see Nelemans et al. 2004). Therefore, we use these values (also adopted in Nelemans et al. 2004) as a fair approximation also for SMARTS and Swift/UV–Optical Telescope (UVOT) flux corrections, with an uncertainty of ∼30% (Bohlin et al. 1978). For Spitzer, the corrections for interstellar extinction are small, i.e., ∼10% for the flux density at 3.6 μm and less than 5% for the flux densities in the other three IRAC bands. No extinction correction was made at 24 μm. We add, quadratically to the rms, a 5% and 10% systematic error on the estimate of the flux densities in the IRAC and MIPS observations, respectively, to take into account the uncertainties on the photometric calibration (see Reach et al. 2005).

4U 0614+091 was observed on 2006 October 30 at 05:31 UT for 660 s using the Andicam dual-channel optical/IR camera on the SMARTS 1.3 m telescope at Cerro-Tololo, Chile. Optical photometry was obtained in the V and I bands, and IR in the J band. The data were reduced in IRAF¹² using standard procedures. In the optical, differential photometry was performed relative to a bright comparison star in the field, and this star was then calibrated on several nights in 2007 January relative to multiple stars in the standard field Ru 149 (Landolt 1992). IR data were obtained in a five-point dither pattern, and combined before measuring the brightness of the target relative to a nearby star in the field from the Two Micron All Sky Survey (2MASS) catalog. We have applied de-reddening corrections as described in Section 2.2.

We analyzed the Swift X-ray Telescope (XRT) and UVOT data from the observation of 4U 0614+091 that started on 2006 October 30, at 17:36 UT for 3256 s (ObsID 00030812001). We used the windowed timing mode for the XRT and obtained a total XRT exposure time of 3256 s. We reduced the XRT data in 2008 May using the HEASOFT v6.4.1 software. We used the HEASOFT routine xselect to produce source and background spectra. For the source spectrum, we included photons from the cleaned event list that are within 47'' of the source centroid, and we used a background region that is the same size but is offset by 28. After background subtraction, we measured a count rate of 44 counts s⁻¹ for the source. We generated a response using the calibration files that were current in 2008 May. For the UVOT data, we started by using the HEASOFT routine uvotimsum to sum the images for the different filters used. Then, we defined source and background regions and used uvot2pha to produce the spectra and response files, from which we obtained the flux measurements given in Table 1 for the V, B, U, UVW1, and UVM2 filters. We have applied de-reddening corrections as described in Section 2.2. Note that, contrary to the IR band, the extinction correction in the UV spectrum is large, up to 26%. Therefore, the uncertainty on the de-reddening value can be significant.

For the energy spectral analysis, we combined the data taken on the 2006 October 30, i.e., the observations 92411-01-06-07 and 92411-01-06-00 for a total exposure time of 4160 s. We have used Proportional Counter Array (PCA) Standard2 of all the Proportional Counter Units (PCUs) available, and HEXTE Standard Mode cluster B data. For the PCA data, we have subtracted the background estimated using pcabackest v.3.0, produced the detector response matrix with pcarsp v.10.1, and analyzed the energy spectra in the range 3–20 keV. A systematic error of 0.5% was added to account for uncertainties in the calibration. For the HEXTE data, we corrected for deadtime, subtracted the background, extracted the response matrix using HEASOFT v.6.4.1. We have analyzed the HEXTE spectra between 20 and 200 keV.

The low-frequency spectrum of 4U 0614+091 (4.86 GHz–8 μm) is consistent with synchrotron emission from a continuously replenished compact jet, as described in its first formulation by Blandford & Königl (1979). The spectrum is consistent with being optically thick from the radio to the mid-IR band, with a flat spectrum of spectral index α = 0.03 ± 0.04. At a frequency 1.25 × 10¹³ Hz<ν_break < 3.71 × 10¹³ Hz a break occurs and the spectrum steepens to a power law with spectral index α = −0.47 ± 0.15 at least up to 8 μm (i.e., 8.3 × 10¹³ Hz). In the near-IR band the accretion disk starts to dominate the emitting spectrum.

The synchrotron break frequency for the NS 4U 0614+091 is lower than the measured break frequency in the BH GX 339−4 by a factor of ∼10 (Corbel & Fender 2002; see Migliari et al. 2006). The lack of statistics and the fact that the break frequency has been observed to vary within the same source (in GX 339-4), possibly in relation to variations of the bolometric luminosity, make it premature to generalize any possible relation between the ν_break and the nature of the compact object. However, under certain assumptions, we can make some considerations on their possible dependence, as follows.

The break frequency is the frequency above which the jet is fully transparent to its emitting synchrotron radiation. The association between this break frequency and the geometrical parameters of the jet is still unknown. If we relate an emitting frequency to a specific position in the jet, parameterized by its distance from the jet base, and make the disk–jet symbiosis assumption that a fixed fraction of the mass accretion rate is channeled into the jet (Falcke & Biermann 1995), we may have some clues on the jet geometry. In the latest prescription of the disk–jet symbiosis model by Falcke et al. (2004), the ν_break is related to the size of the base of the jet R_nozzle and to the mass accretion rate $\dot{M}$, by $\nu _{\rm break} \propto \dot{M}^{2/3} R_{\rm nozzle}^{-1}$.

Corbel & Fender (2002) detected the ν_break in two observations of the BH GX 339−4 during its hard state (in one of the two, only a lower limit). The observation with the lower bolometric luminosity shows the higher ν_break. Therefore, assuming that at a higher bolometric luminosity corresponds a higher mass accretion rate, the predicted positive dependence of the ν_break to the $\dot{M}$ seems to be in contrast with the observations of the BH GX 339−4. Moreover, in the prescription of Falcke et al. (2004) the jet is attached to the inner radius of the disk. (1) If the disk is truncated, a lower luminosity would correspond to a lower mass accretion rate and a higher R_nozzle, implying a lower ν_break. (2) If instead the inner radius corresponds to the innermost stable orbit also in the hard state, R_nozzle should not change significantly with the accretion rate, and a lower bolometric luminosity would correspond to a lower mass accretion rate and therefore, according to the above formula, to a lower ν_break.

In the NS 4U 0614+091, the X-ray bolometric luminosity, i.e., in the range 0.6–100 keV¹³ is 3.4 × 10³⁶ erg s⁻¹ (at 3 kpc) and the break frequency is ∼(1–4) × 10¹³ Hz. In the BH GX 339−4 observation where the break frequency was detected, the X-ray bolometric luminosity was 4 × 10³⁷ erg s⁻¹ (1–200 keV integrated luminosity, using a distance of 4 kpc: Corbel & Fender 2002) and the break frequency ∼2 × 10¹⁴ Hz. Comparing these two observations, both the total accretion power and ν_break of GX 339−4 are higher than those of 4U 0614+091. There is an anticorrelation between the accretion power (i.e., X-ray bolometric luminosity) and the break frequency in the two GX 339−4 observations, therefore, if the accretion power–ν_break variations do not depend on the nature of the compact object, we would expect 4U 0614+091 to have a higher break frequency than GX 339−4. The lower break frequency observed in 4U 0614+091 would therefore point toward either a different jet formation mechanism between BHs and NSs or a different geometry of the jet (smaller in the NS) or less power channeled into the jet (i.e., the disk–jet symbiosis hypothesis is not valid), maybe due to an effect of the specific compact object, such as the presence of the magnetic field in the NS.

Given the X-ray bolometric luminosity of ∼3.4 × 10³⁶ erg s⁻¹ and using α = −0.47, the integral of the optically thin part of the synchrotron spectrum, from the thin–thick break frequency, is ∼5.7 × 10³² × E^0.53_c erg s⁻¹, where E_c is the high-energy cutoff of the synchrotron spectrum in eV. The optically thin synchrotron emission is observed up to 0.3 eV, which corresponds to a lower limit on the radiative power of the jet of 3 × 10³² erg s⁻¹.

The spectrum leads to a jet power of ∼1.1 × 10³⁴μ⁻¹_0.05E^0.53_c erg s⁻¹, where μ_0.05 is the radiative efficiency of the synchrotron emission in units of 0.05 (0.05 is the upper limit estimated for GRS 1915+105 by Fender & Pooley (2000), consistent with what is found in AGN (i.e., μ < 0.15; Celotti & Ghisellini 2003), and the theoretical prediction of μ < 0.15 in the jet model of Blandford & Königl (1979)). The jet power to X-ray bolometric luminosity ratio is L_J/L_Xbol ∼ 2 × 10⁻³ × μ⁻¹_0.05E^0.53_c.

Brightness temperature arguments, polarization studies (Shahbaz et al. 2008a; Russell & Fender 2008) and spectral studies indicate that the out-flowing matter in NSs during a steady state is in the form of a self-absorbed conical jet. In BHs this evidence has been corroborated by observations of spatially resolved jets of two systems (Stirling et al. 2001; Dhawan et al. 2000). However, a compact jet has never been spatially resolved in a NS. We were awarded 2.5 hr of time with the High Sensitivity Array (HSA; VLBA+Arecibo+GBT+phased VLA) to attempt to detect the compact jet in 4U 0614+091. The source was observed on 2008 March 27 at 4.86 GHz. The standalone data from the phased VLA measured a source with flux density ∼0.18 mJy, 30% less than the flux density measured during our multiwavelength campaign (Table 1); this is indicative of radio variability. However, the short duration of the observations, together with the extremely high sensitivity of the three big dishes (the GBT, phased VLA, and especially Arecibo) meant that the side-lobes of the naturally weighted dirty beam were too high (91% of the peak) to identify accurately the source (with a nominal rms of 23 μJy), particularly given the lack of an accurate position from other wavelengths. The VLA was in C configuration at the time, giving a position accurate to 200 mas, with respect to an HSA beamsize of 3.7 × 0.8 mas². A compact jet as inferred from our spectral study (this work) has never been spatially resolved.

Hard X-ray tails in XRBs are well fitted with a model where thermal accretion disk seed photons are Compton up-scattered by a "corona" of hot plasma. Markoff et al. (2005) analyzed a sample of BH XRBs' energy spectra and showed that fits of the hard X-ray tails using jet model's components (i.e., synchrotron and SSC) are statistically as good as single-component Comptonizing corona models (i.e., eqpair; Coppi 1999). This result would be in agreement with the possibility that the "corona" of hot plasma might be in fact the base of the jet itself, at least in BHs. In NS XRBs, the hard X-ray tails can also be well fitted by corona Comptonizing models with thermal electron with temperatures of 25–30 keV for low-luminosity NSs (e.g., Barret et al. 2000) tens of keV for accreting millisecond X-ray pulsars (e.g., Gierliński et al. 2002; Poutanen & Gierliński 2003; Gierliński & Poutanen 2005; Falanga et al. 2005a, 2005b, 2007) and a few keV for brighter sources (e.g., Paizis et al. 2006). Fits of energy spectra using the broadband jet model have not been attempted yet for NSs. In this work, we have detected both the optically thin spectrum of the jet and the hard X-ray tail in 4U 0614+091. Therefore, we are able for the first time to explore the possibility that in NSs, like BHs, the high-energy non-thermal energy spectrum might be reproduced, at least partially, with radiative processes taking place in the jet.

From the broadband spectrum in Figure 1, left, we see that the synchrotron emission alone, estimated as the extrapolation of the optically thin jet spectrum observed, at high energies (dashed line), cannot reproduce the high-energy X-ray tail observed (as it does in, e.g., the BH GX 339−4; Corbel & Fender 2002). As a first step, we test whether the hard X-ray tail could be produced by SSC emission from the same population which produces the synchrotron emission (i.e., post-shock accelerated jet; Markoff et al. 2005). We therefore constructed a simple, robust one-zone model for both synchrotron and SSC emission (e.g., Kirk et al. 1998). The emission region is taken to be a cylinder with variable aspect ratio and size, with the same population of electrons being responsible for synchrotron and inverse Compton emission. This simple model is appropriate, given that both the observed optically thin synchrotron tail and the SSC emission should come from the base of the jet (where photon and particle densities are highest). Different geometries (e.g., spherical) change the results only by factors of order unity.

Assuming uniform plasma density and isotropic synchrotron emission in the frame of the plasma, the SSC emission is then calculated analytically (e.g., Rybicki & Lightman 1979).

Since the emission is unresolved the problem is underconstrained and we have several free parameters at our disposal that can be varied in order to find a suitable SSC solution that is consistent with the observed spectrum:

• 1.  
  Radius and length of the cylindrical emission region.
• 2.  
  The bulk Lorentz factor of the emitting plasma.
• 3.  
  The viewing angle of the jet (relative to the direction of motion)
• 4.  
  The lower cutoff frequency of the synchrotron spectrum at the base of the jet (which is unobservable due to self-absorption).

The remaining parameters are determined by the observed synchrotron luminosity and spectrum. We then attempt to match the observed hard tail by varying the free model parameters.

We find that matching the observed high X-ray flux is not feasible for reasonable physical parameters: for reasonable jet bulk Lorentz factors of order Γ ≲ 5, the observed flux would require unrealistically low magnetic field values, roughly β ∼ 10⁴ (that is, the field is 4 orders of magnitude out of equipartition). For reasonable magnetic field values, with a β ≲ 10, the required Lorentz factors would require a bulk Lorentz factor of order 50 or larger, with a viewing angle close to 90°. Roughly, the relationship between the equipartition fraction β and Γ is β ∼ 10⁻⁴(Γ/5)^2.5.

However, even if the jet is either extremely undermagnetized or extremely relativistic, the spectral slope of the predicted SSC emission is too hard to match the observed X-ray spectrum: The optically thin synchrotron spectrum, which is imprinted on the SSC spectral slope, is −0.47, while the observed hard tail has a spectral slope of −1.25. We conclude that SSC emission alone, from the post-shock jet particles, is not a viable mechanism to explain the observed hard X-ray tail of NS 4U 0614+091. This result indicates that an extra Comptonizing population of hot plasma apart from that producing the direct synchrotron emission in the jet, exists close to the NS in the form of a corona where the hard X-ray emission is associated with the accretion disk boundary layers (e.g., Mitsuda et al. 1984; Kluźniak & Wilson 1991), a hot inner flow, an advection-dominated accretion flow (ADAF; Narayan et al. 1997; Barret et al. 2000; Medvedev & Narayan 2001; see also the discussion in Done & Gierlińsky 2003), a mildly outflowing corona (e.g., Beloborodov 1999), or a pre-shock, quasi-thermal, component at the base of the jet (Markoff & Nowak 2004). To assess in particular this last possibility, a broadband fit of the spectrum with a disk–jet model is necessary.