Is WR 104 a face-on, colliding-wind binary?

ABSTRACT

Two decades of extensive spectroscopic monitoring of WR 104 is used to confront what we think we understand about this iconic prototype of the dust-producing pinwheel stars. Convincing SB1 orbital solutions are obtained for both the WC9d star and its OB companion. The period (⁠|$241.54 \pm 0.14$| d) and circular orbit agree perfectly with results from modelling images of the rotating dust spiral. Contrary to those results though, the orbit is found to be significantly inclined instead of face-on. The two SB1 solutions each indicate |$i \sim 45^{\circ }$| but could be as low as |$\sim 34^{\circ }$|⁠. This result naturally provides an explanation for the long puzzling photometric and emission line strength variations but is difficult to reconcile with the imaging. Confirmation that colliding winds are present is found by the detection of variable excess emission in two of the lines where it would be most expected. The changing shapes of this excess emission are not perfectly phase-locked though, which will complicate future modelling.

1 INTRODUCTION

WR 104 is one of the first few Wolf–Rayet stars found to exhibit an infrared excess that seemed to indicate the presence of circumstellar dust (Allen, Swings & Harvey 1972). This discovery was remarkable in that dust was not expected to be able to form or survive in the harsh environment near a Wolf–Rayet star. One of the keys to understanding how this could occur was the discovery (Williams et al. 1987) that dust appears to form briefly and episodically near periastron in another WR star, WR 140. The shielding, compression, and chemistry of a colliding-wind zone between a WC-type WR star and an OB companion is now thought to facilitate dust creation.

The first hint that WR 104 might be a binary was the observation that the emission lines appeared diluted by the possible presence of an OB companion (Cohen & Kuhi 1977). The detection of absorption lines by Williams & van der Hucht (1996) and Crowther (1997) provided further proof that WR 104 may be a binary and supported the hypothesis that dust production was initiated by colliding winds between the two stars. The discovery by Tuthill, Monnier & Danchi (1999) of a spiral plume of dust formed by the star and rotating with a period of about 8 months solidified this theory.

Subsequent analysis over the next two decades of the images of WR 104 (Soulain et al. 2023, and references therein) has cemented the status of WR 104 as the prototype for a class of persistently dust-producing ‘pinwheel stars’. Interest in these objects is not abating. Besides their marvellous appearance when resolved, they provide fascinating laboratories to study the physics and chemistry of colliding winds with phenomena ranging from high-energy X-ray production to formation of carbonaceous materials. These WC + OB binaries may be significant contributors to galactic dust production rates, perhaps rivalling that of AGB stars, especially in low-metallicity environments (Lau et al. 2021).

Despite its now iconic status, the study of WR 104 via spectroscopy has been less common. Preliminary velocity curves for each binary component were obtained by Hill (2006, 2008, 2009), but these were based on a limited data set. Orbital parameters inferred from images of the dust spiral have not been confirmed with a definitive spectroscopic solution. A crucial one of these parameters is the inclination, which within the uncertainties is face-on. The nature of the OB companion to the WC9d star is still somewhat uncertain. The range of possibilities include a mid-to-late main-sequence O star or an early B giant or supergiant (Williams & van der Hucht 2000). These points are somewhat critical. In order to effectively model and study the colliding-wind environment and geometry, the orbit and the luminosity and wind characteristics of both stars need to be accurately known.

Two other enduring puzzles and what they may mean for our understanding of WR 104 also remain. The relative contribution of the WC9d star to the spectrum has been known for some time to show considerable variations (Crowther 1997; Williams & van der Hucht 2000). Similarly perhaps, dramatic photometric variations frequently occur with a depth, duration, and timing that seem random (Williams 2014). Explanations for these phenomena that involve obscuration by either the dust plume or clumps that are more isotropically emitted are frustrated by the apparent face-on orientation and the lack of emission between coils of the dust spiral.

Finally, there is one other crucial benefit that spectroscopy might offer. A well-known signature of colliding winds is the presence of variable excess emission, particularly in certain lines such as C iii|$\lambda$|5696 and He i|$\lambda$|10830 (Hill, Moffat & St-Louis 2018). As post-collision plasma streams along the shock cone and cools, it can produce additional line emission, the shape of which can vary as the orientation with respect to the observer changes. The detection of such phase-locked excess emission would offer a convincing confirmation that colliding winds are present. Moreover, modelling of the profiles can return numerous parameters related to the orbit, and the geometry, orientation, and material motion for the shock cone (Hill et al. 2018).

The preliminary work cited above was based on only about a dozen spectra in just the yellow–green portion of the optical. These have been added to with substantially more spectra now covering most of the optical and into the infrared. The intention here is to confront what we think we know about WR 104 with extensive spectroscopy. The investigation is framed in the form of a single question with multiple aspects. Is WR 104 a face-on colliding-wind binary?

2 OBSERVATIONS

2.1 LRIS 2001–2008

Observations of WR 104 for this paper were begun in 2001 using the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck I telescope on Maunakea. The red arm of LRIS was used until 2008 to obtain a total of 17 spectra using a 0.7 arcsec long slit and a 1200 grooves mm⁻¹ grating. Exposure times varied between about 10 min and 1 h depending on conditions. These spectra covered the 4900–6100 Å region with a resolving power of about 2600 based on the full width at half-maximum (FWHM) of comparison lines. The S/N in the continuum, near 5500 Å, was typically a few hundred. LRIS is a Cassegrain instrument and does not have flexure control, so comparison spectra were obtained before and after each observation.

iraf¹ was used for LRIS data reduction and followed the steps described in Hill et al. (2018). A representative spectrum is shown in Fig. 1.

2.2 ESI 2013–2023

Optical observations of WR 104 continued in 2013 using the Echellette Spectrograph and Imager (ESI; Sheinis et al. 2002) on the Keck II telescope on Maunakea. A further 10 spectra were obtained through 2023. The wide spectral range of ESI provides complete coverage in 10 orders between 3900 and 10 900 Å. A 0.5 arcsec slit was used, providing a resolving power of 8000. Exposure times ranged between 20 min and 1.4 h. Given the wide spectral range of ESI and the considerable reddening of WR 104, the S/N of these spectra varies significantly from order to order and with the blaze function of the echellette grating. For the same continuum point referred to above for LRIS though, the S/N was typically about 150. Comparison lamps with suitably short exposure times were obtained before and after each observation. The Cu/Ar lamps are very faint though and were only taken at the start and end of each night. Even though ESI is (like LRIS) a Cassegrain instrument, it has a flexure compensation system, so this was not anticipated to be a significant issue.

Data reduction for the ESI spectra was very similar to that for LRIS. Actual bias frames were subtracted from the data rather than using the overscan region though. Each echellete order was extracted as if it were a single long-slit spectrum. Fig. 2 presents such a single extraction of order 9.

2.3 NIRSPEC 2004–2018

The two optical data sets described above are spanned by a third set of spectra in the near-infrared. NIRSPEC, (a near-infrared echelle spectrograph) on the Keck II telescope (McLean et al. 1998), was used to obtain 18 spectra between 2004 and 2018. These data cover 0.95–1.13 |$\mu$|m. The instrument was used in low-resolution mode, albeit with a 0.38 arcsec slit to provide a resolving power of 2000. As is typical for many near-infrared instruments, spectra were obtained via ABBA nodding and each integration consisted of multiple co-adds. The combined integration times usually totalled about 8 min. Typical S/N in the continuum was a few hundred. NIRSPEC is used at one of the two Nasmyth foci of Keck II, so comparison lamp spectra were only taken at the beginning and end of each night.

Initial frame combination and preparation for the NIRSPEC data was done with iraf, but most of the reductions were made using the redspec package. This latter software was produced at UCLA by S. Kim, L. Prato, and I. McLean and tailored for use with NIRSPEC data. Further information and the code itself can be found on the W.M. Keck Observatory NIRSPEC web pages.² The final rectification of the stellar spectra was accomplished using the CONTINUUM task within iraf. Fig. 3 shows one of these spectra.

3 A SPECTROSCOPIC ORBIT FOR WR 104

As noted earlier, the premise that WR 104 is a colliding-wind binary is consistent with various observations presented over the past few decades, but a confirmed orbital solution is still lacking. Absorption lines from a presumed OB companion are often visible but are generally weak compared to the WR emission lines. As noted though by Crowther (1997) and Williams & van der Hucht (2000), there have been occasions where the emission lines have appeared weakened and the absorption lines more obvious. In the spectra studied here, this phenomenon is readily apparent. In one instance (the ESI spectrum obtained on HJD 2456890.757), the emission lines were even too weak to measure reliably.

For WR + OB binaries, radial velocity curves fit to different emission lines do not always find identical values for various orbital parameters such as the semi-amplitude, initial epoch, and especially the systemic velocity. This complicates any attempt to determine an SB2 orbit via simultaneous fits to both emission and absorption lines. Combined with the general weakness of the absorption lines, the strategy was to begin by searching for an SB1 solution based on emission lines and then, if possible, bridge from that to a separate SB1 orbit for the absorption lines.

3.1 Emission line measurements and SB1 orbit

Ideally, any emission line chosen for radial velocity measurements should be somewhat narrow, fairly strong, isolated (free of blending), and not possess the changing substructure that is commonly thought to represent extra emission arising from a wind–wind collision zone. In addition, in order to gain better statistics, it would be beneficial for it to be present in more than one data set, i.e. LRIS + ESI or ESI  + NIRSPEC. Visual examination of the spectra presented here shows that such perfect lines may not exist. The best example is likely C iii|$\lambda$|9711, which is present in both the ESI and NIRSPEC data sets but is somewhat affected by telluric lines in the ESI spectra. This line seems remarkably well fit by a simple Gaussian. C iii|$\lambda$|5696 (LRIS + ESI) would be a good candidate except for the presence of variable excess emission that may affect radial velocity measurements. To some extent, this can be dealt with by avoiding the central/peak part of the line and measuring bisectors near or below half-maximum.

Table 1 presents radial velocities measured for the two lines described above. For C iii|$\lambda$|9711, these were measured by using the SPLOT task within iraf to fit a Gaussian. For C iii|$\lambda$|5696, the bisector was measured at 20, 30, 40, and 50 per cent of the peak and these four measurements were then averaged. C ii|$\lambda$|7118 appears to be fairly well fit by a simple Gaussian but is only present in the ESI spectra and somewhat weak. The same is true for C iii|$\lambda$|8500 and |$\lambda$|8664, but they are a bit stronger. He ii|$\lambda$|10124 is fairly well fit by a Gaussian, and although weak, it is measurable in all the NIRSPEC spectra. Velocities for these additional four lines were measured by fitting with SPLOT and are also presented in Table 1.

He i|$\lambda$|10830 is an iconic near-infrared line that, like C iii|$\lambda$|5696, is noted for displaying excess emission from colliding-wind regions (Stevens & Howarth 1999; Hill 2007). This quality poses the same challenge as for C iii|$\lambda$|5696 but in addition it has a P Cygni absorption component that presents significant phase dependent variations which further hamper attempts to measure a radial velocity for the Wolf–Rayet star. There may be an absorption component due to the OB companion but this could also be mimicked by double-peaked excess emission. Due to these numerous complications, this line was not used.

The rest wavelengths indicated in Table 1 are taken from the version v3.00b5 compilation of van Hoof (2018). For instances where the lines are multiplet blends, weighted means were formed using gf values.

The search for an SB1 orbit for the WR component in WR104 began by evaluating the NIRSPEC C iii|$\lambda$|9711 velocities presented in Table 1 for periodicity. The zero-point offset between the ESI and NIRSPEC velocities was unknown at this point. The phase dispersion minimization method (Stellingwerf 1978), as implemented in the pdm task within iraf, was used to search for possible periods between 0 and 2000 d. The lowest value of the PDM |$\theta$| statistic was found at 241.3 d. Other candidate periods were multiples of this, or, when phased, exhibited considerably more scatter.

With an initial value for the orbital period in hand, the C iii|$\lambda$|9711 velocities were then fit using

where |$\gamma _{\rm \scriptscriptstyle WR}$| is the systemic velocity, |$K_{\scriptscriptstyle \rm WR}$| is the RV semi-amplitude, |$\upsilon$| is the true anomaly, |$\omega$| is the angular separation between the ascending node and periastron, and e the eccentricity. The period was allowed to vary. In order to combine the ESI and NIRSPEC velocities an additional variable was utilized, that of a possible instrumental zero-point shift between the two sets. The velocities presented in Table 1 do not include this offset.

Although only preliminary at this point, a small but non-zero eccentricity was found (0.1). Initial estimates of the uncertainty implied the significance was marginal but e was retained as a variable pending incorporation of additional velocities which might clarify whether or not to adopt a circular orbit.

Following this preliminary derivation of an SB1 solution using just the C iii|$\lambda$|9711 radial velocities, orbits were calculated with each of the other lines mentioned above and produced similar parameters. Four of these six results are based on velocities from C iii lines. Although these four features may not originate in identical line forming regions, they at least arise from the same species. With this in mind, velocities from the C iii lines were combined and used to derive a more robust orbit for the WR component of WR 104. For this solution the zero-point shifts necessary for each of these velocities in Table 1 to be brought onto the same scale as those for the NIRSPEC |$\lambda$|9711 measurements were treated as free parameters in the fit. Shifts of 91.2, 178.6, 56.2, 137.3, and 162.3 km s⁻¹ were found for ESI/|$\lambda$|9711, ESI/|$\lambda$|8664, ESI/|$\lambda$|8500, LRIS/|$\lambda$|5696, and ESI/|$\lambda$|5696, respectively. The velocities listed in Table 1 do not include these increments. Much of the need for these shifts is due to simple zero-point differences between instruments. A significant contributor though is also the well known differences in systemic velocities found between different emission lines in the spectra of WR stars.

The best fit eccentricity found at this point was now only |$0.04 \pm 0.03$|⁠, consistent with a circular orbit. Orbital parameters obtained with |$e \equiv 0.0$| are presented in Table 2. The C iii emission line systemic velocity included in Table 2 is the actual one for NIRSPEC |$\lambda$|9711 since the zero-point shifts described above bring the others into alignment with it. The data and fit are shown in Fig. 4. Uncertainties were obtained using what is commonly known as a bootstrap method. Velocities were randomly sampled with replacement and an orbital fit calculated. This was repeated 1000 times. This set of elements is adopted as the SB1 orbit for the WR star going forward and used to calculate the phases listed in Table 1. Following common convention for circular WR + OB orbits, phase zero is set to inferior conjunction for the WR star.

3.2 Absorption line measurements and SB1 orbit

Absorption lines are visible in many of the spectra discussed here but are much more challenging to measure. Besides their general weakness, they are often blended with the corresponding emission lines that arise from the WR star. Moreover, since variable excess emission arising from colliding-wind regions can take the form of double peaks one has to be cautious not to interpret a possible gap between two peaks as an absorption line.

Proceeding with due caution then, Table 3 lists the measured radial velocities for a number of absorption lines. Measurements of extremely weak features and ones that are only reliably determined in a few spectra are excluded. As was the case for the emission lines, these velocities utilize the compilation of rest wavelengths of van Hoof (2018).

Procedurally, for fitting the absorption line velocities, there were a few changes from that for the emission lines. All but one of the sets presented in Table 3 arise from He i. There was no clear preference to start with one of them as was the case for C iii|$\lambda$|9711 with the emission lines. Accordingly, the He i velocities were combined from the start.

With the expectation that an absorption line orbit would be close to |$180^{\circ }$| out of phase with that for the emission lines the fit used

A circular solution was adopted from the start. |$E_{0}$| was allowed to vary since small differences between absorption and emission lines are not uncommon in WR + OB binaries. As an experiment, the period was allowed to vary. Within the uncertainties, the best-fitting value was identical to that found using the C iii emission line RV’s and so that value of the period was adopted.

It should be possible to use all absorption line velocities together to derive a combined solution but I harboured some reservations with regard to those of He ii|$\lambda$|5412. One concern related to excess emission mimicking an absorption line as described above. Perhaps more significantly, for the ESI spectrum obtained on HJD 2456890.757 where the WR emission lines almost disappear entirely, the He i lines are strong and easily visible but lines of He ii are not. Fig. 5 shows part of this spectrum. Conversely, with the LRIS spectrum from HJD 2452852.897 (Fig. 6) the emission lines are also very weak but still measurable and He ii|$\lambda$|5412 is clearly seen in absorption. Due to this puzzling dichotomy the He ii|$\lambda$|5412 velocities are retained in Table 3 but are not combined with those from He i.

Table 2 includes the parameters for a combined He i orbital fit. The uncertainties are derived using the bootstrap technique described above. Solutions for the OB stars in WR + OB binaries do not typically show large line-to-line variations in systemic velocities like those derived for the WR stars using emission lines. Accordingly, only a single free parameter corresponding to a zero-point offset between LRIS and ESI velocities was utilized for this combined fit. This was found to be |$-11.1 \pm 5.2$| km s⁻¹. The velocities presented in Table 3 do not include this shift. Fig. 7 shows the fit to the combined He i radial velocities.

A circular orbital solution using the He ii|$\lambda$|5412 velocities showed considerable more scatter than that for the He i lines. The rms(O–C) was about twice as large. The period was allowed to vary and again, within the errors, the same value as found for the C iii emission lines was found so that period was adopted. All but one of the orbital parameters found were then, within the (larger) errors, the same as for the combined He i line orbit. |$K_{OB}$| was found to be |$59 \pm 14$| km s|$^{-1}$|⁠.

4 PERIODIC, VARIABLE EXCESS EMISSION?

It is now widely thought that one of the possible hallmarks of a colliding-wind binary is the presence of excess line emission, the shape and position of which, can vary periodically with orbital phase. This extra line emission is thought to arise as plasma heated by the collision cools and flows along a shock surface. In the case of a WR + OB binary, this phenomenon can blend with emission arising from the undisturbed wind of the Wolf–Rayet star. As a result the appearance is often that of a line with two components. The underlying emission profile seems constant in shape but can appear to shift back and forth due to orbital motion. The excess emission can also shift in position but the shape may also change as the orientation of the shock surface with respect to the observer varies around the orbit.

Does the spectroscopy presented here demonstrate this phenomenon? One complication, already mentioned, is that there are dramatic variations in the overall strength of most, if not all, of the emission lines in the spectra of WR 104. Are these changes periodic? Do they primarily affect the underlying component (that which arises from the undisturbed wind), or the excess emission, or both? A key question, is whether any variations in shape are phase-locked as one might expect if they mainly arise from a changing viewing angle to the line emitting region.

It was noted above that the C iii|$\lambda$|9711 emission line appears unusually free of excess emission. It is well fit by a simple Gaussian. One might thus infer that very little of the flux in this line arises in the colliding-wind region and it therefore might provide a good indication of whether the underlying component exhibits variations in strength and if they are periodic. Fig. 8 (left) shows the equivalent width, full width at half maximum, and skewness of this line. The equations presented in Barclay et al. (2024) were used to calculate the latter two quantities. The FWHM is set to |$2.35\sqrt{\mu _{2}}$|⁠. In order to present measurements free of complications related to differing resolutions, instrumental zero-point shifts, imperfect telluric correction, etc. only the NIRSPEC data is used for this plot.

There are, clearly, considerable variations in the equivalent width but they do not appear to be periodic with orbital phase. A search for repeatability using the pdm task in iraf did not find any clear result for other periods either. The FWHM appears roughly constant and only exhibits variations of the order of 1 or 2 per cent. The skewness is small and any variations with the orbital period are not obvious.

What of any excess emission that might be present? A natural first place to look is C iii|$\lambda$|5696. This line is known to exhibit excess emission in the spectra of colliding-wind binaries as shown by Lührs (1997), Hill et al. (2018), and numerous other works. Examination of this line amongst the WR 104 spectra does show what appears to be variable excess emission. Moreover, it often shows the kinds of shapes that are expected to arise from a colliding-wind region. Fig. 8 (right) presents the same quantities for |$\lambda$|5696 as shown for |$\lambda$|9711. The equivalent width shows similarly dramatic, perhaps even larger, changes. Both FWHM and skewness show about twice the scatter compared to |$\lambda$|9711 but similarly, the modulations are not obviously tied to the orbital period though.

A detailed examination of the C iii|$\lambda$|5696 profiles reveals striking departures from simple Gaussian or flat-topped shapes. Fig. 9 shows two examples of sets of spectra that, although very close in phase, exhibit markedly different profiles and implies their variations seem to depend on more than just viewing angle (i.e. orbital phase) to the colliding-wind region.

As noted previously, He i|$\lambda$|10830 is another line well known for its sensitivity to colliding-wind regions. As with C iii|$\lambda$|5696, the overall strength of the line varies which complicates the search for phase-locked excess emission changes. In addition, there is also a somewhat variable P-Cygni component and possible absorption from the OB companion. Despite these challenges, examination of individual profiles reveals shapes that are reminiscent of colliding-wind excess emission. Although possibly not as striking as demonstrated for C iii|$\lambda$|5696 there also appears to be a lack of strict phase-locking for the He i|$\lambda$|10830 variations as well. Fig. 10 presents a stack plot of all the profiles where each one is scaled so that, on average, they have the same strength.

5 DISCUSSION

5.1 Is WR 104 a binary?

The question posed via the title of this work might actually be separated into three questions. One of those is simply whether WR 104 is a binary. At the outset, there was little doubt this is the case. As shown by Crowther (1997) and Williams & van der Hucht (2000), both absorption and emission lines are well known to be present in the spectra. The spiral structure of dust emission is aptly explained by presuming an origin in colliding winds between the two stars. Preliminary velocity curves based on the first few years of LRIS observations were presented by Hill (2006, 2008, 2009). With considerably more spectra, extending over a much longer baseline, the orbits presented here definitively confirm that WR 104 is a spectroscopic binary. Significantly, the period found agrees perfectly with that found for rotation of the spiral dust structure.

Fig. 5 may provide some insight regarding the nature of the OB companion. If lines of He ii are present in absorption, they are not obvious. The equivalent width of Si iii|$\lambda$|4553 is greater than that of both Si iv|$\lambda$|4089 and Mg ii|$\lambda$|4481, which implies a spectral type of B0.2 to B1 if a dwarf or B1 to B2 if a supergiant (Evans et al. 2015). The equivalent width of H|$\gamma$| (⁠|$3.2 \pm 0.4$| Å) may exclude a supergiant luminosity class. Since emission lines from the WR star are barely visible in Fig. 5, presumably any correction for dilution from the WR star is small. As listed in Walker & Millward (1985) and Hill, Walker & Yang (1986), early B supergiants typically present H|$\gamma$| strengths of about 2.0 Å, or less. The equivalent widths listed in Millward & Walker (1985) for early B dwarfs are around 4 or 5 Å. This may indicate that the most appropriate spectral type to infer for the OB companion is B1 III.

Conversely, Fig. 6 shows a spectrum where He ii|$\lambda$|5412 is clearly visible in absorption. Measuring the equivalent width of this line, along with that of He i|$\lambda$|4922 indicates a spectral type of O6 V using the calibration of Kerton, Ballantyne & Martin (1999). No correction for dilution by the WR star is included, presuming that |$\lambda$|5412 and |$\lambda$|4922 are close enough to negate the need.

Williams & van der Hucht (2000) discuss the nature of the OB component of WR 104 and conclude that it could be a mid-to-late O-type main sequence star or an early B giant or supergiant. Based on luminosity arguments they include the possibility of an O dwarf as early as O5. This range of possibilities spans the two conflicting indications above.

WR 104 is known to have a faint OB companion with a separation of about 1 arcsec (Soulain et al. 2018). An intriguing possibility is that the ESI spectrum shown in Fig. 5. is in fact that of this companion and the LRIS spectrum shown in Fig. 6 actually provides the better indication of the spectral type of the close companion to the WR star. WR 104 is known to show significant photometric variations (Williams 2014). If a particularly extreme incidence of this were occurring at the time, the faint companion may have been put on the ESI slit instead. This would also explain the near complete absence of emission lines in Fig. 5. Although the emission lines are much weaker in Fig. 6, they are still strong enough to be easily measurable. If the spectrum shown in Fig. 5 is that of the faint companion then the He i velocities from that night should not be included in the absorption line orbital solution. Removing them results in changes that are within the errors quoted in Table 2. Of most interest to the discussion below though is that |$K_{OB}$| increases to |$25.9 \pm 2.9$| km s|$^{-1}$|⁠.

5.2 Is the orbit face on?

A second question is whether the orbit is face on (or nearly so). Modelling of the spiral structure indicates that |$i \le 16^{\circ }$| (Harries et al. 2004; Tuthill et al. 2008). In principle, it is possible to estimate the inclination with knowledge of the distance, the proper motion of the dust plume’s outward motion, and the streaming velocity of material in the spiral. Tuthill et al. (2008) presents an argument that the streaming velocity of dust in the spiral is that of the WR wind terminal velocity. The other possibility (as used by Harries et al. (2004)) might be the post-shock flow velocity which could be much lower. These two approaches may represent a range of about 800–1600 km s|$^{-1}$|⁠. It is unclear how the parallax listed with |$Gaia$| DR3 (Vallenari et al. 2023) may have been affected by the nature of WR 104. The distance indicated by this parallax (⁠|$\sim 640$| pc) is much less than the distances discussed by Soulain et al. (2018) (1.6–3.4 kpc). Taking the |$Gaia$| parallax at face value and using the proper motion from Tuthill et al. (2008) implies an inclination of about |$70^{\circ }$| to |$80^{\circ }$| for the range of streaming velocity noted above.

What do the radial velocity curves found here imply regarding the stellar masses for |$i = 16^{\circ }$|⁠, or, alternatively, what orbital inclination is implied for reasonable estimates of the masses? Using the equations

and setting |$i = 16^{\circ }$| produces a startling result, |$M_{\scriptscriptstyle \mathrm{ WR}} = 217 \pm 32$| M|$_{\odot }$| and |$M_{\scriptscriptstyle \mathrm{ OB}} = 584 \pm 54$| M|$_{\odot }$|⁠.

For their study of the spiral dust structure, Soulain et al. (2018) adopted masses for the WR and OB star of 10 and 20 M|$_{\odot }$|⁠, respectively. Doing so here indicates an inclination of |$50^{\circ } \pm 3^{\circ }$| and |$58^{\circ } \pm 3^{\circ }$|⁠, respectively. Based on fig. 9 of Harries et al. (2004), an inclination near |$60^{\circ }$| seems very unlikely. I infer from the discussion of inclination in Tuthill et al. (2008), that their fits to the spiral structure might allow a higher inclination than |$16^{\circ }$|⁠. That is only the 1|$\sigma$| upper limit to their modelling. Moreover, they describe a limitation of their model that could lead to an underestimate of inclination. Nevertheless, it is worth emphasizing though that images of the dust spiral very much look to the eye to be face on. This is especially true for animations made by combining images.

How small an orbital inclination is possible if the uncertainties for |$K_{\scriptscriptstyle \mathrm{ WR}}$| and |$K_{\scriptscriptstyle \mathrm{ OB}}$| were underestimated and higher masses are allowed for the WR and OB stars? For the sake of this exercise, the RV amplitude uncertainties will be doubled. From the compilation of Sander et al. (2019), a reasonable mass estimate for WC9d stars is |$13.0 \pm 5.5$| M|$_{\odot }$|⁠. Based on the discussion above regarding the nature of the OB companion, it seems a wide range of masses are possible for the OB companion. I will use |$30 \pm 15$| M|$_{\odot }$|⁠. These changes result in |$i = 44^{\circ } \pm 10^{\circ }$| and |$i = 47^{\circ } \pm 12^{\circ }$| based on candidate masses and RV curves for the WR star and OB star, respectively.

An inclination as low as |$\sim 34^{\circ }$| can be regarded as possible given the calculations above. Something like a factor of 2 difference compared to that obtained from imaging of the spiral structure still remains though. Could the use of multiple zero-point shifts between different instrument and C iii line combinations have somehow produced an erroneous result? This seems unlikely but was tested by using just the NIRSPEC |$\lambda$|9711 velocities. The result (⁠|$K_{\scriptscriptstyle \mathrm{ WR}} = 62.8 \pm 4.4$| km s|$^{-1}$|⁠) is virtually identical to that obtained using all the C iii lines so it is unlikely that the discrepancy arises this way. How might a small, but non-zero, eccentricity contribute? The inclination derived from orbital fits should be insensitive to this source of error since sin i scales as |$\sqrt{1-e^2}$|⁠. It is unclear how sensitive models of the dust spiral might be to a small eccentricity. Tuthill et al. (2008) found that |$e \le 0.06$| though. Rejecting the He i velocities that might be from the faint companion does not help. That actually increases |$K_{\mathrm{ OB}}$| as was mentioned above. Given the minimal variations in the FWHM and skewness of C iii|$\lambda$|9711, it seems unlikely that some fraction of its formation in a colliding-wind shock cone has conspired to produce an erroneously high |$K_{\mathrm{ WR}}$|⁠. In any case, the velocities of C iii|$\lambda$|5696 were measured via bisectors designed to avoid excess emission and agree very well.

Comparing again to fig. 9 of Harries et al. (2004) implies these results may be palatable since spiral structure is still easily discernible up to at least |$30^{\circ }$|⁠. Concern about the difference presumes the dust spiral is in the orbital plane. Until now there has been no motivation to consider otherwise, nor is it obvious why this would not be the case. As to the second question considered here though, based on RV orbits, WR 104 is not a face on binary.

5.3 Is the spiral structure of WR 104 due to colliding winds?

The third question relates to a colliding-wind origin for the rotating dust spiral. What evidence is there in the spectra discussed here that also indicates the presence of colliding winds?

C iii|$\lambda$|5696 and He i|$\lambda$|10830 are two lines that, via the presence of variable excess emission, are known to be sensitive indicators of colliding winds in WR + OB binaries, albeit generally those in which the WR star is of an earlier type. In the spectra shown here, they both demonstrate such changing line profiles. Certainly for |$\lambda$|5696 though, the profile changes exhibited by these lines do not appear to be phase-locked with the orbit as would be expected. To some extent, the same may be true for |$\lambda$|10830.

Interpretation of WR 104 emission line profile variations is complicated by the dramatic changes in the equivalent width of most, if not all, emission lines. As shown above, these do not seem to be strictly tied to viewing angle (orbital phase). The photometric modulations of WR 104 studied by Williams (2014) (and called ‘eclipses’) appear equally random and take the form of fadings or obscurations by as much as 2 mag or more followed by recovery to nominal levels. Sometimes, a brightening is interrupted by another eclipse before a full restoration occurs. An earlier study by Kato et al. (2002) seemed to indicate that the variations were tied to the 241.5-d period, but Williams (2014) showed this was not the case. Might the fluctuations in brightness be related to some of the spectral changes?

There is some overlap between the photometry presented by Williams (2014) and the LRIS and NIRSPEC spectra shown here. The lowest point in the equivalent width plot for |$\lambda$|5696 (Fig. 8 here) falls in the deep 2003 eclipse shown in fig. 6 of Williams (2014). Three other very low EW points fall in the deep, and possibly wide, 2007 dimming illustrated in fig. 8 of Williams (2014). One of them is the lowest measurement for |$\lambda$|9711 presented in Fig. 8 here. The other two are |$\lambda$|5696 but were obtained on back-to-back nights, so are indistinguishable from a single point in Fig. 8 here. Conversely though, a NIRSPEC spectrum obtained near the minimum of the deep and well-defined eclipse in 2005 shows |$\lambda$|9711 with an equivalent width near the median of the points presented in Fig. 8.

The high rate of significant eclipses and the mystery of their origin are discussed by Williams (2014). The possible explanations that invoke variable obscuration by dust presented difficulties at that time. If the orbit is nearly face-on and the dust spiral is mostly in the plane of the sky, then it is hard to imagine how the dust plume could intercept the line of sight to the central binary. If clumps of dust are ejected isotropically, then there would be far more infrared emission between spiral arms. If those clumps were somehow beaming towards us along the orbital axis, then there would be a very bright (in the infrared) spot that is not observed.

A significant orbital inclination, as indicated here, may offer a solution to the puzzle described above. Tuthill et al. (2008) discuss the opening angle of the colliding-wind shock cone and determine that if radiative braking from the OB companion is included, the cone opening half-angle (⁠|$\theta _{s}$|⁠) could be as high as |$\cong 58^{\circ }$|⁠. In combination with the minimum inclination found here, this would allow the dust plume to graze our line of sight. Since i may in fact be higher, |$\theta _{s}$| could be lower and the combination would still admit the possibility of the plume entering the line of sight.

One aspect of this solution may still pose a challenge. If the photometric variations presented by Williams (2014) are caused by the dust spiral intercepting the line of sight, why are they not more periodic? The rotating spiral appears to be a very repeatable clock. Perhaps, the answer lies in the choice of words above. If the line of sight to the central stars grazes the dust plume, then the extinction may vary as stochastic variations in plume density and cone thickness combine with multiple arms of the spiral passing (nearly) in front to create modulations that do not have a strict or simple periodicity. One can extend this vision of the geometry to imagine how the excess emission line forming region in the shock cone might be wholly or partially blocked as well. This, in turn, would modulate the shape of the excess emission profile in a non-periodic fashion, creating the phenomenon presented in Fig. 9.

Returning to the third question, does the spectroscopy presented here support the premise that the rotating dust spiral originates in a colliding-wind region? Arguably, the strongest confirmation would be variable excess emission in certain lines that is phase-locked and that can be modelled presuming it arises in a colliding-wind region (Hill et al. 2018). Modelling the line profiles discussed here is beyond the intended scope of this work, even without the multiple complications discussed so far. Nevertheless, there is, what appears to be, significant and variable excess emission in two of the lines most expected to display it. That it is not strictly phase-locked may have an explanation that still fits within the colliding-wind paradigm. To this extent then, the spectroscopy does support the scenario of colliding winds.

6 CONCLUSIONS AND FUTURE WORK

Since 2001, LRIS (on Keck I), and ESI and NIRSPEC (both on Keck II) have been used to obtain numerous spectra of this object covering most of the optical and out to 1.13 |$\mu$|m in the infrared. Although for decades now, several lines of evidence have pointed towards the binary nature of WR 104, there has not been a definitive spectroscopic orbit. These data close this gap and convincingly demonstrate WR 104’s binarity via radial velocity curves for both components. The |$241.54 \pm 0.14$|-d period found here agrees perfectly with that obtained from images of the dust spiral (Tuthill et al. 2008) and reduces the uncertainty by over a factor of 3. The finding of a circular orbit agrees with models of that imaging as well.

Some uncertainty remains with regard to the nature of the OB component of the central binary of WR 104. The relative contribution of the WC9d star to spectra is known to vary, a phenomenon that is confirmed here. Although a nagging complication in some regards, this provides a chance to better study the absorption lines when the emission lines are weak. Based on such an ESI spectrum, the most likely spectral type for the OB star is B1 III. Similarly (and possibly related), WR 104 shows significant photometric variations. The timing, depth, and duration of these events appear random. If the ESI spectrum mentioned above was obtained during an extreme example of one of these fadings, it could in fact be a spectrum of the faint OB companion to WR 104. If so, then the most likely spectral type for the close companion to the WC9d star is indicated by an LRIS spectrum as O6 V.

The most surprising result here relates to the orbital inclination. WR 104 is widely believed to be a face-on binary. Not only do images of the dust spiral very much look to the eye to be face-on modelling of them finds |$i \le 16^{\circ }$|⁠. Such a low value of i is at odds with the radial velocity curves that would require unrealistically high masses for the stars. When combined with a mass of |$13.0 \pm 5.5$| M|$_{\odot }$| for the WC9d star and a mass of |$30 \pm 15$| M|$_{\odot }$| for the OB star, the velocity curves indicate |$i = 44^{\circ } \pm 10^{\circ }$| and |$i = 47^{\circ } \pm 12^{\circ }$|⁠, respectively. With a spectroscopic orbital inclination of least |$\sim 34^{\circ }$|⁠, exploring the upper boundary of i derived from modelling the images now becomes a very desirable avenue for future research. Likewise, any mechanism that can be conceived of, and shown to possibly tilt the dust spiral out of the orbital plane, would be a very interesting pursuit.

An unexpected and intriguing possibility follows from finding that the orbit of WR 104 is not face-on. The photometric changes and varying strengths of emission lines are two long-standing puzzles. Obscuration of the stars by the dust plume rotating through the line of sight is difficult to reconcile with a face-on geometry. The inclination found here is, alone, possibly not sufficient to bring the spiral into the line of sight. However, in addition, radiative braking from the OB companion may widen the shock cone opening angle enough to do so, or at least into grazing the line of sight. This then opens the possibility that random fluctuations in the cone thickness or density can then create varying obscurations of one or both stars or the excess emission line forming region of the shock cone.

The rotating spiral structure of WR 104 is well explained to be dust forming downstream in material that was compressed in a wind–wind collision. Support for this scenario appears to reside in the spectra studied here. Variable emission profiles are visible in both C iii|$\lambda$|5696 and He i|$\lambda$|10830. These lines are known as sensitive indicators of colliding winds. This interpretation is complicated though by the lack of strict phase locking between the orbital period and the excess emission profiles.

Modelling the excess emission profiles is not within the scope of this work but could be a next step. The fits would need to either account for or work around the two points mentioned above. If the excess emission profile shapes were strictly tied to orbital phase, the overall equivalent width modulations might be corrected for by simply scaling individual spectra. The fact that the profile changes are not phase-locked is something not so easily addressed. If dust is occasionally obscuring part of the shock region, then longer wavelengths are preferable; i.e. between the two lines discussed here, He i|$\lambda$|10830 may be less affected. If a similarly sensitive line is known at even longer wavelengths, then the best course might be to acquire those spectra. If the upper boundary of equivalent width measurements indicates spectra with little or no obscuration of the excess emission line forming region, then it might be easier to attempt modelling using just that subset of the data. This sort of modelling offers the possibility of learning more about the excess line forming region. In addition, one of the free parameters is the orbital inclination, a quantity now of considerable interest.

Known as the prototype of colliding-wind pinwheel stars, WR 104 still provides a source of mysteries and wonder. The results presented here show that there is still much to learn about this object and offer ample motivation for further studies.

ACKNOWLEDGEMENTS

The author wishes to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

I thank Peter Tuthill, Tony Moffat, Noel Richardson, and Nicole St-Louis for engaging discussions on Wolf–Rayet stars in general and WR 104 in particular. I gratefully acknowledge comments from the referee that have improved this paper.

The data presented herein were obtained at Keck Observatory, which is a private 501(c)(3) non-profit organization operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

DATA AVAILABILITY

The data presented here may be shared on reasonable request to the author.

Footnotes

REFERENCES