3 Results and discussion

3.1 Continuum spectral energy distribution: Model fitting and comparison with four Wolf-Rayet stars

Figure 2: Dereddened spectrum of Cygnus X-3 using either Draine (1989) law (left) or Lutz et al. (1996) law (right). The asterisks (*) in the lower panel represent the Ogley et al. (2001) ISOCAM results, after dereddening by Draine (1989) (left) and Lutz (right).

Figure 3: Best fitting of the two dereddened spectra of Cygnus X-3 shown in Fig. 2.

The dereddening of the Cygnus X-3 spectrum is made using either Lutz et al. (1996) or Draine (1989) laws, and using an absorption value of A_V= 20 mag (van Kerkwijk et al. 1996); the two dereddened spectra are shown in Fig. 2. They have clearly different shapes, but since the molecular composition of the absorbing material on the line of sight to Cygnus X-3 is unknown, we cannot choose between these two laws.
The spectral fitting of the dereddened spectra is shown in Fig. 3 and the results are given in Table 2. With the Lutz et al. (1996) law the best fit is obtained with a unique power law $S_\nu$ $\propto$ $\lambda$ $^{-0.6\pm}$  ^0.3_0.4 with a reduced $\chi^2$ = 4.3 in the 2.4-12 $\mu$m range, in good agreement with the Ogley et al (2001) result. With the Draine (1989) law the best fit is obtained with the sum of two components: a power law with slope $\lambda$ $^{-1.6\pm}$ ^0.2 and a black body at T=250 K with a radius of 5000  $R_{\odot}$ at a distance of 10 kpc, (reduced $\chi^2$ = 4.2 between 2.4 and 12 $\mu$m), a hint of the presence of circumstellar dust. The power law part of the continuum spectrum ($S_\nu$ $\propto$ $\lambda$ $^{-\alpha}$) can be explained by free-free emission of an expanding wind in the intermediate case between optically thick ($\alpha$ = 2) and optically thin ($\alpha$ $\sim$ 0) regimes (Wright & Barlow 1975).

Using the ISO archive data we have analysed the SWS spectra of four Wolf-Rayet stars: WR 147 (WN8+B0.5), WR 136 (WN6b), WR 134 (WN6) and WR 78 (WN7) whose main characteristics are given in Table 3. We compare them to the Cygnus X-3 spectrum, after smoothing the SWS spectra to the resolution of the ISOPHOT-S instrument (using an IDL routine of B. Schulz dowloaded from the Home Page of the ISO Data Centre at Vilspa). The observed WR spectra are shown in Fig. 4 on top of the observed Cygnus X-3 spectrum; the identification of the emission lines is from Morris et al. (2000).

 

Table 2: Comparison of the infrared continuum spectra of Cygnus X-3 and four WR stars: power law slopes $\alpha$ such as $S_\nu \propto \lambda ^{-\alpha }$ and 4.7 $\mu$m flux densities rescaled at 10 kpc.

Object	PL slopea	PL slopeb	Flux at 4.7$\mu$m (Jy)
Cygnus X-3	1.6 $\pm$ 0.2c	0.6 $\pm$ 0.30.4	0.079 $\pm$ 0.011
WR 78	1.4 $\pm$ 0.2d	1.4 $\pm$ 0.2	0.114 $\pm$ 0.008
WR 134	0.2 $\pm$ 0.2d	0.2 $\pm$ 0.2	0.081 $\pm$ 0.006
WR 136	1.0 $\pm$ 0.2e	1.0 $\pm$ 0.2	0.076 $\pm$ 0.006
WR 147	1.6 $\pm$ 0.1c	1.0 $\pm$ 0.1	0.085 $\pm$ 0.005

^a Dereddening with Draine (1989) law.
^b Dereddening with Lutz et al. (1996) law; fit between 2.4-12 $\mu$m.
^c Fit between 2.4-6.5 $\mu$m.
^d Fit between 2.4-12 $\mu$m.
^e Fit between 2.4-8 $\mu$m.

The dereddened spectra of the Wolf-Rayet stars, using either the Draine (1989) law or the Lutz et al. (1996) law with the A_V shown in Table 3, have been fitted with power law slopes given in Table 2. Wolf-Rayet stars emit free-free continuum radiation from their extended ionized stellar wind envelopes and the different slopes reflect different conditions in the wind (Williams et al. 1997). It is noticeable that the mean continuum flux density of Cygnus X-3 is the same (within a factor 1.5 at 4.7 $\mu$m as seen in Table 2) as that of the four WR stars when their flux density is rescaled to a Cygnus X-3 distance of 10 kpc.

 

Table 3: The four Wolf-Rayet stars observed with ISO/SWS.

Star	Type	Binarity	Distance	AVa	Reference	TDTNUM
WR 78	WN7ha WNL	No	2.0 kpc	1.48-1.87	Crowther et al. (1995a)	45800705
WR 134	WN6	possible	$\sim$2.1 kpc	1.22-1.99	Morel et al. (1999)	17601108
WR 136	WN6b(h) WNE-sb	possible	1.8 kpc	1.35-2.25	Stevens & Howarth (1999)	38102211
WR 147	WN8(h) WNL	B0.5V at 0.554''	630 $\pm70$ pc	11.2	Morris et al. (1999, 2000)	33800415

^a From van der Hucht (2001) except for WR 147.
^b From Crowther et al. (1995b).

Figure 4: Observed spectra of Cygnus X-3 and four Wolf-Rayet stars (not dereddened). An arbitrary vertical offset has been added to the WR spectra for clarity. The identification of the emission lines is from Morris et al. (2000).

The comparison between the Cygnus X-3 spectrum and that of the Wolf-Rayet WR 147 at 10 kpc is shown in Fig. 5 after dereddening with the Draine (1989) law (left) and with the Lutz et al. (1996) law (right). The WR 147 spectrum appears as the closest WR one to the Cygnus X-3 spectrum, with almost the same mean flux density at 10 kpc and the same power law slope (whithin the statistical errors).

Figure 5: Comparison between the spectral energy distribution of Cygnus X-3 and the one of WR 147 when rescaled at 10 kpc: both dereddened with Draine (1989) law (left) and the Lutz et al. (1996) law (right).

We note that WR 147 is known as a colliding-wind binary that has been spatially resolved (Williams et al. 1997; Skinner et al. 1999), with a separation on the sky large enough for the wind-wind collision zone between the stars to be resolved at near-infrared and radio (Williams et al. 1997), and X-ray energies (Pittard et al. 2002). The spectral energy distribution of WR 147 in the 0.5 $\mu$m to 2 mm wavelength range (including all components) shown by Williams et al. (1997) is dominated by the free-free emission from the stellar wind of the WN8 star; in the 2 to 10 $\mu$m range these authors find $\alpha$ = 1.0, in good agreement with our ISOPHOT-S measurement (when dereddened with the Lutz et al. 1996 law); and in the mid-infrared to radio range they find $\alpha$ = 0.66.

3.2 Emission lines; comparison with four Wolf-Rayet stars

The measured 4.3 $\mu$m line flux above the continuum in the Cygnus X-3 spectrum is 58 $\pm$ 11 mJy (dereddening with the Draine 1989 law), and 126 $\pm$ 25 mJy (dereddening with the Lutz et al. 1996 law), using respectively $\alpha$ = 1.6 and $\alpha$ = 0.6, the best fitted continuum slopes as given in Table 3, both detections being at more than 4.3 $\sigma$. This line is interpreted as the HeI (3p-3s) line at 4.295 $\mu$m, a prominent line in the WR 147 (WN8+B0.5) spectrum as seen in Morris et al. (2000) and in Fig. 4. Again WR 147 appears as the closest WR to Cygnus X-3 as being the only WR in our sample with a HeI emission line at 4.3 $\mu$m, the only line clearly seen in our Cygnus X-3 data. The other expected He lines at 2.62, 3.73, 4.05, 7.46 and 10.5 $\mu$m are not detected, probably due to the faintness of the object, at the limits of the instrument's sensitivity. We note (Fig. 4) that the second highest peak in the SS-part of the Cyg X-3 spectrum is at 3.73 $\mu$m, and there are also local maxima at 4.05 and 10.5 $\mu$m. These expected lines are all blended with H lines and the absence of H observed by van Kerkwijk et al. (1996) in the I and K band spectra of Cygnus X-3 could explain the weakness or absence of these lines in our data.

We note that the Br$\alpha$+HeI-II line at 4.05 $\mu$m is not detected in Cygnus X-3 in quiescence, but is present in the four Wolf-Rayet stars. Strong HeI and HeII lines have been previously observed in the K-range in Cygnus X-3 during quiescence (van Kerkwijk et al. 1992; 1996, Fender et al. 1999). These lines have been interpreted (van Kerkwijk et al. 1996; Cherepashchuk & Moffat 1994), as emission from the wind of a massive companion star to the compact object, and Fender et al. (1999) suggest that the best candidate is probably an early WN Wolf-Rayet star. We note that the close match we have found between the mid-infrared luminosity and the spectral energy distribution, the HeI emission line in Cygnus X-3 in quiescence, and that of the WR 147, is consistent with a Wolf-Rayet like companion of WN8 type to the compact object in Cygnus X-3, a later type than suggested by earlier works (van Kerkwijk et al. 1996; Fender et al. 1999; Hanson et al. 2000).

3.3 Mass loss rate evaluation

As Ogley et al. (2001), we evaluated the mass loss rate of this free-free emitting wind, following the Wright & Barlow (1975) formula (8) giving the emitted flux density (in Jansky) by a stellar wind assumed to be spherical, homogeneous and at a constant velocity:

$${S}_\nu ~ =~ 23.2 ~ \left(\frac{\dot{{M}}}{\mu {v}_\infty}\... ...rm kpc}^2} \ \gamma^{2/3}~{g}^{2/3}~{Z}^{4/3} \quad {\rm Jy}$$

where D is the distance to the source in kpc. It gives:

$$\dot{{M}}~ =~ 5.35\times 10^{-7} ~ {S}_\nu^{3/4}~ (\nu_ {\rm... ...^{-1/2} ~ \mu~{v}_\infty \quad {M_\odot \times \rm yr^{-1}}$$

(where $\nu$ is in GHz). With an assumed distance D=10 kpc, a Gaunt factor g=1, a flux density deduced from the continuum fitting (Lutz et al. 1996 law, Fig. 3) of $S_\nu=63$ mJy at 6.75 $\mu$m ( $4.44\times 10^{4}$ GHz), and for a WN-type wind (where the mean atomic weight per nucleon $\mu=1.5$, the number of free electrons per nucleon $\gamma_{\rm e}=1$ and the mean ionic charge Z=1), and with a velocity of $v_\infty=1~500$ km s^-1 (van Kerkwijk 1996), one obtains $\dot{M}=1.2\times 10^{-4}$ ${M}_\odot$ yr^-1. This is in agreement with the mass transfer rate estimated by van Kerkwijk et al. (1996) and (within a factor of 2) by Ogley et al. (2001). This result is in good agreement with the recent revised WN mass-loss rate estimates, which have been lowered by a factor of 2 or 3 due to clumping in the wind (Morris et al. 1999). Note that if we assume a flattened disc-like wind as reported by Fender et al. (1999), who detected double peaked emission lines, the mass loss rate decreases but remains within less than a factor of 2 of that obtained in the spherical case, in all but extreme cases when the ratio of structural length scales exceeds about 10, as shown by Schmid-Burgk (1982). It is noticeable that Churchwell et al. (1992), considering the radio flux from the southern, stellar wind component of WR 147, derived a mass-loss rate of $\dot{M}=4.2 \times 10^{-5}$ ${M}_\odot$ yr^-1 and Williams et al. (1997) found a non spherically symetric stellar wind with a mass-loss rate of $\dot{M}=4.6 \times 10^{-5}$ ${M}_\odot$ yr^-1.

3.4 Orbital modulation

Since the length of this spectrophotometric measurement was comparable to the 4.8 h modulation period seen in the K-band at the level of 5$\%$(Fender et al. 1995), we attempted to detect this modulation in our data set. The points in Fig. 6 refer to the average for the whole (2-12 $\mu$m) spectrum. Although, as shown in Fig. 6, the measurement uncertainty of the orbitally phase-resolved spectra was relatively high, the data clearly exclude periodic variations of amplitude higher than 15$\%$.

Figure 6: Flux density in the 2.4-12 $\mu$m range versus Cygnus X-3 orbital phase.

3.5 Radio and X-ray fluxes

Figure 7 shows the mean flux density of Cygnus X-3 on MJD 50180.3 from radio to hard X-rays. The quiescent state observed in the mid-infrared range with ISO was also seen during monitoring radio observations of Cygnus X-3 with the Ryle telescope (Mullard Radio Observatory, Cambridge) shortly before and after the ISO observations, the mean flux density at 15 GHz being about 120 mJy (Pooley 1999), and with the Green Bank Interferometer (GBI) monitoring program (McCollough et al. 1999) during a quiescent period before the ISO observations, the mean flux densities being 80 $\pm$ 30 mJy at 2.25 GHz and 125 $\pm$ 60 mJy at 8.3 GHz and the spectral index $\alpha$ = 0.3 $\pm$ 0.1 . These flux densities are at least one order of magnitude higher than that observed during the quench periods of very low radio emission preceeding the major flares of Cygnus X-3 (McCollough et al. 1999). In fact, this quiescent state was still present in 1996 May, June and July (Fender et al. 1999).

Figure 7: Quasi-simultaneous observations of Cygnus X-3 in the radio, infrared, soft and hard X-rays on April 7, 1996, averaged over the orbital phase; the ISOPHOT-S spectrum is dereddened with the Lutz et al. (1996) law and rebinned to the resolution of 0.3 $\mu$m; note that the GBI was dormant after 1996 April 1 till November 1996, and that the given flux densities (in dash lines) are mean values during the quiescent period March 17 to April 1, 1996.

In the X-ray range, at the same epoch, the $\it {Rossi}$ XTE/All Sky Monitor count rate was $\sim$7.5 count s^-1 corresponding to a mean flux of $\sim$1 mJy from 2 to 12 keV (see XTE archive and Levine et al. 1996), and the BATSE instrument on board the Compton Gamma Ray Observatory observed a mean photon flux of 0.039 count s^-1 corresponding to a flux density of 0.04 mJy in the 20-100 keV range. Thus the mid-infrared continuum spectrum whose shape is explained by thermal free-free emission in an expanding wind has a different origin than the non-thermal radio emission and the hard X-ray emission which are closely coupled (Mioduszewski et al. 2001; Choudhury et al. 2002).