AN APPARENT PRECESSING HELICAL OUTFLOW FROM A MASSIVE EVOLVED STAR: EVIDENCE FOR BINARY INTERACTION

Observations of WR102c were made using FORCAST (Herter et al. 2013) on the 2.5 m telescope aboard SOFIA. FORCAST is a 256 × 256 pixel dual-channel, wide-field mid-infrared camera sensitive from 5 to 40 μm with a plate scale of 0768 per pixel and field of view of 34 × 32. The two channels consist of a short-wavelength camera (SWC) operating at 5–25 μm and a long-wavelength camera (LWC) operating at 28–40 μm. An internal dichroic beam splitter enables simultaneous observation from both LWCs and SWCs. A series of bandpass filters are used to image at selected wavelengths.

SOFIA/FORCAST observations of the Sickle H ii region were taken on the OC1-B Flight 110 on 2013 July 2 (altitude ∼39,000 ft) at 19.7, 25.2, 31.5, and 37.1 μm. Measurements at 19.7 and 31.5 μm, as well as 25.2 and 31.5 μm, were observed simultaneously in dual-channel mode, while the 37.1 μm observations were made in single-channel mode. Chopping and nodding were used to remove the sky and telescope thermal backgrounds. An asymmetric chop pattern was used to place the source on the telescope axis, which eliminates optical aberrations (coma) on the source. The chop throw was 7' at a frequency of ∼4 Hz. The off-source chop fields (regions of low mid-infrared Galactic emission) were selected from the Midcourse Space Experiment 21 μm image of the Galactic center. The source was dithered over the focal plane to allow removal of bad pixels and to mitigate response variations. The total integration time was 100 s at 19.7, 25.2, and 37.1 μm and 200 s at 31.5 μm. The quality of the images was consistent with near-diffraction-limited imaging: the FWHM of the point-spread functions was 32 at 19.7 μm and 38 at 37.1 μm.

Calibration of the images was performed by observing standard stars and applying the resulting calibration factors as described in Herter et al. (2013). Raw data were processed applying the latest techniques for artifact removal and calibration (Herter et al. 2013) and deconvolved to the same final point-spread function of 38. Color correction factors were negligible (≲5%) and were therefore not applied. The 1σ uncertainty in calibration due to photometric error, variation in water vapor overburden, and airmass is ±7%; however, owing to flat-field variations (∼15%), which we are unable to correct for, we conservatively adopt a 1σ uncertainty of ±20%.

We utilized Paschen-α line (1.87 μm) and continuum (1.90 μm) images of the Galactic center (Wang et al. 2010; Dong et al. 2011) taken by the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) on the Hubble Space Telescope (HST). Additionally, we incorporated in our analysis archival mid-IR (5.8 and 8.0 μm) observations obtained by the Spitzer Space Telescope's Infrared Array Camera (IRAC; Fazio et al. 2004) in the Galactic Legacy Infrared Midplane Survey Extraordinaire (GLIMPSE; Stolovy et al. 2006), as well as archival 24 μm Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al. 2004) observations performed in the MIPSGAL survey (Carey et al. 2009).

Large column densities of dust and gas lead to extreme extinction along lines of sight toward the Galactic center (A_V ≳ 30). We adopt the extinction curve derived by Fritz et al. (2011) from hydrogen recombination line observations of the minispiral, the H ii region in the inner 3 pc of the Galactic center, at 1–19 μm made by the Short Wave Spectrometer (SWS) on the Infrared Space Observatory (ISO) and the Spectrograph for Integral Field Observations in the Near Infrared (SINFONI) on the Very Large Telescope (VLT). We assume a distance toward the Galactic center of 8 kpc (Reid 1993).

Follow-up spectroscopic observations of the WR102c helix (R.A. = 17:46:12.90, decl. = −28:49:12.5 J2000) were performed on 2015 August 6 using the TripleSpec instrument on the 200'' Hale Telescope at Palomar Observatory. TripleSpec is a medium-resolution (λ/Δλ ∼ 2500) slit spectrograph (Wilson et al. 2004; Herter et al. 2008) that obtains spectra from 1.0 to 2.4 μm. The TripleSpec slit size is 1 × 30'', and each spectral resolution element is ∼2.7 pixels on the 2048 × 1024 pixel array. Spectra were averaged over 6 spatial pixels (∼18) and smoothed by preforming a 3 spectral pixel moving average.

Owing to crowded stellar fields along lines of sight toward the Galactic center and the high background of atomic hydrogen emission lines, ∼03 amplitude nods were performed to an off-source field of minimal stellar contamination and background emission. Observations were taken in an alternating ABBA nod sequence with 240 s exposures at each slit position. The total integration time spent on the WR102c helix was 1200 s. The centroids of prominent atmospheric OH emission lines in the off-source nod positions were used to calibrate spectral shifts of the Brackett-γ (λ = 2.16 μm) along the slit.

Barniske et al. (2008) adopt H and K_S fluxes of 11.84 and 9.93, respectively, for the photospheric emission from WR102c. However, at 1.9 μm, which falls in between the H and K_S bands, the flux from WR102c is reported to be 12.3 mag from observations with HST/NICMOS (Wang et al. 2010). Since the 1.9 μm flux is not consistent with the brighter H- and K-band fluxes, we claim that Barniske et al. (2008) mistakenly adopt the H and K_S band fluxes from another bright star for their stellar models of WR102c. These models therefore overestimate the stellar luminosity, radius, and mass of WR102c. Since the spectral analysis from Barniske et al. (2008) is unaffected by the photometric misidentification, its initial classification as a WN6 star remains unchanged (Figer et al. 1999b).

The Two Micron All Sky Survey ${{K}}_{S}$ and H fluxes of WR102c are 11.6 and 13.4, respectively, and were initially reported by Figer et al. (1999b), who studied the population of massive stars in the Quintuplet cluster and initially identified WR102c. We estimate the stellar luminosity of WR102c from the K-band bolometric correction for WN6 stars provided by Crowther et al. (2006a; BC_K ∼ 3.8) and the dereddening correction from the extinction curve derived by Fritz et al. (2011; A_K = 2.5). A K-band flux of 11.6 mag thus implies a luminosity of ∼4 × 10⁵ L_⊙. This luminosity is consistent with scaling down the flux stellar model of Barniske et al. (2008) by a factor of ∼5, which is consistent with the ratio of the misreported and newly assigned K-band fluxes. Follow-up analysis of WR102c by Steinke et al. (2015) using the proper photometry indeed indicates stellar luminosities of (3–4) × 10⁵ L_⊙.

In the mid- and far-IR, the helix extends ∼1.5 pc from WR102c at the southern base of the Sickle "handle" (Figure 1(A)) toward the Quintuplet cluster. Although the projected morphology of the handle appears linear, it traces the edge of the dense molecular cloud associated with the Sickle and likely has significant depth along the line of sight. The apparent spatial "wavelength" of the helix is ∼1 pc with a maximum peak-to-trough extent of ∼0.75 pc (Figure 1(B)). No other features perpendicular other than the helix are detected along the handle. The inconsistency of the helix with the handle morphology strongly suggests that the helix is not physically linked to the dusty, extended filaments composing the handle, which are shaped by the powerful winds from the Quintuplet cluster and aligned with the magnetic field embedded in the Sickle molecular cloud (Figer et al. 1999b; Dotson et al. 2000; Chuss et al. 2003). We will show, however, that the handle and the helix are close to each other in projection since they both appear to be heated by the radiation field of the Quintuplet cluster.

There is an identical ionized gas counterpart to the far-IR helix that appears in the image of the Paschen-α ($\lambda \quad =\quad 1.87\;\mu {\rm{m}}$) line emission (Wang et al. 2010; Dong et al. 2011; Figure 1(C)). The morphology of the Paschen-α helix is consistent with the structure that appears in the IR, which traces warm dust. At its leading, northwest end the helix coincides with one of two ∼0.1 pc sized lobes that extend from WR102c. Although WR102c itself appears as a Paschen-α line-emitting star, the He ii (8–6, λ = 1.8753 μm) emission line can reproduce the measured flux (M. Steinke 2015, private communication) since it is claimed to be an H-poor W-R star with a stellar temperature of 70,000 K (Steinke et al. 2015). The orientation of these lobes is aligned with the apparent trajectory of the helix near WR102c, indicating that they may be linked with the structure of the helix. In the IR, there is a local flux peak at the position of the lobes; however, the emission along lines of sight toward these regions is likely dominated by larger quantities of warm dust in the handle. We note that the helix also appears in the 8.3 GHz continuum map taken by Lang et al. (1997); however, the signal from the helix is comparable to that of the background flux from which there is also a non-thermal component.

We produce a color temperature map using the 19 and 31 μm images of the Sickle (Figure 2(A)) assuming that the emission of the dust is optically thin and takes the form ${F}_{\nu }\propto {B}_{\nu }({T}_{d})\;{\nu }^{\beta }$, where ${B}_{\nu }({T}_{d})$ is the Planck function, which depends on the emission frequency ν and dust temperature T_d, and β is the index of the emissivity power law and assumed to be 2. Although the 19 and 37 μm images would provide a longer spectral baseline, the signal-to-noise ratio of the extended helix flux detected at 37 μm is too low to determine a reliable map of color temperatures. Overlaid on the temperature map are the predicted temperature contours for 0.1 μm sized (red dashed) and 0.01 μm sized (blue dotted) silicate grains at the location of the handle heated in equilibrium by the Quintuplet cluster and WR102c. The radiation inputs from the Quintuplet cluster and WR102c are modeled as 35,000 K, 3 × 10⁷ L_⊙ (Figer et al. 1999b) and 35,000 K, 4 × 10⁵ L_⊙ (Steinke et al. 2015) point sources, respectively. For 0.1 μm sized grains, the observed temperatures at the handle (T_d ∼ 130 K) far exceed the predicted 85 K and are uniform on projected size scales of ∼1 pc in the vicinity of WR102c. Within the helix, the discrepancy between predicted and observed temperatures is even greater: T_d ∼ 95 K versus 180 K, respectively.

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First, we address the temperature discrepancy at the handle. Although the Quintuplet cluster dominates the heating, WR102c will contribute ∼25% of the total radiative flux in the surrounding ∼0.5 pc vicinity. Despite the inclusion of the heating contribution from WR102c, it is not possible to heat dust in the surrounding ∼0.5 pc vicinity of the handle to ∼130 K (Figure 2(A)) if the dust grains are 0.1 μm in size. However, given that the handle has been carved out by the powerful Quintuplet cluster winds (Simpson et al. 1997; Figer et al. 1999b), we expect the dust to be kinetically sputtered by the interaction with the gas in the winds (Tielens et al. 1994). Smaller grains exhibit higher temperatures under the same heating conditions as larger grains owing to lower heat capacities. By adopting a smaller distribution of grains (a = 0.01 μm) for the handle, the predicted equilibrium temperature ∼0.5 pc away from WR102c and ∼3 pc from the Quintuplet cluster is ∼125 K, which is consistent with the observed temperatures (Figure 2(A)). We rule out the possibility that the handle is heated by multiple luminous sources embedded within the Sickle molecular cloud since there are no observed local temperature peaks.

We now discuss the hotter temperatures observed from the helix (T_d ∼ 180 K), which are ∼50 K higher than the handle and ∼85 K higher than the predicted temperatures assuming heating by both the Quintuplet cluster and WR102c. It is difficult to reconcile such high and uniform temperatures, especially across large size scales (∼1 pc). These high and uniform temperatures strongly suggest that the helix is composed of transiently heated VSGs that are smaller than 0.01 μm. VSGs will not be heated in equilibrium with the incident radiation field given their small absorption cross sections and will therefore exhibit much greater temperatures when struck by individual photons (Draine & Li 2001). Importantly, the spectral shape of the emission from transiently heated VSGs is not sensitive to changes in distance (i.e., incident flux) from its heating source, which is consistent with the temperature uniformity of the helix. In the following section, we perform detailed models of the spectral energy distributions (SEDs) from dust throughout the helix and Sickle to substantiate our claims on the dust sizes.

Dust models are produced using DustEM (Compiègne et al. 2011), which is capable of evaluating spectra of VSG emission. We fit the models to the observed mid- and far-IR SEDs of two regions at the helix (east and west; Figures 2(B) and (C), respectively) and two regions around the Sickle (the handle and blade; Figures 2(D) and (E), respectively). The observed fluxes extracted from square 825 × 825 apertures at each region (see Figure 2(A)) are listed in Table 1. The free parameters of the models are the dust mass abundances and the grain size. The dust is assumed to be heated radiatively by WR102c and the Quintuplet cluster, which are modeled as a 4 × 10⁵ L_⊙ point source (Steinke et al. 2015) with a 35,000 K Castelli & Kurucz (2004) stellar atmosphere and a 3 × 10⁷ L_⊙ point source (Figer et al. 1999b) with a 35,000 K Castelli & Kurucz (2004) atmosphere, respectively. Separation distances between WR102c and dust in the helix are assumed to be the projected distance divided by cos(θ_p), where θ_p is the conical opening angle of the helix (∼16°; see Section 4.1). Given the greater uncertainties in the distances between both heating sources and the Sickle and between the Quintuplet cluster and the helix, a multiplicative factor of $\sqrt{2}$ is included to these projected distances. The 70 μm flux measurements from the Photoconductor Array Camera and Spectrometer (PACS, Poglitsch et al. 2010) on Herschel (Molinari et al. 2010; Pilbratt et al. 2010) are plotted on the SEDs as a diagnostic for the presence of a cooler distribution of dust and are therefore not included in the model fits.

Table 1.  Observed Mid- and Far-infrared Fluxes (in Jy)

Region	Δx	Δy	F5.8	F8.0	F19	F25	F31	F37	F70
Helix East	−225	−75	...	0.86	17.06	20.21	18.15	17.55	≲7
Helix West	−11.3	−90	...	0.49	17.79	23.00	22.02	19.97	≲7
Sickle Handle	68	−105	0.19	0.85	15.25	33.28	33.88	33.28	≲31
Sickle Blade	−1125	62.5	0.33	1.23	8.52	22.92	30.37	34.73	≲40

Note. Δx and Δy indicate the angular offset of the region from WR102c (R.A.: 17:46:11.14 and decl.: −28:49:05.9 J2000; Dong et al. 2011). Square 825 × 825 apertures were used to extract the fluxes. The 1σ errors for the fluxes are assumed to be 20%.

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Model fits show that the dust in the helix can indeed be modeled by a single distribution of transiently heated silicate-type VSGs (a ∼ 10 Å), whereas dust in the blade and handle, which trace the edge of the Sickle molecular cloud, is composed of two distributions of small (a ∼ 100 Å) and very small (a ∼ 10 Å) grains. Notably, the 70 μm flux at the east and west helix regions agrees very closely with the models fit to the mid- and far-IR fluxes and indicates that the helix is not associated with cooler dust in a molecular cloud along the line of sight. This is in direct contrast with SED models of the handle and helix, where the 70 μm flux excess reveals the presence of cooler dust within the Sickle molecular cloud. The difference in the grain size distributions between the helix and Sickle regions demonstrates that dust composing the helix is independent of the Sickle.

Spectroscopic measurements of the Brackett-γ emission line were fit assuming a Gaussian profile at three different spatial positions along the helix (Figure 3(A)): northeast (NE), center (C), and southwest (SW). The centroids of the emission lines at SW and NE are found to be shifted by +0.38 ± 0.26 and +0.62 ± 0.28 spectral pixels relative to the line at C, respectively (Figure 3(B)). Since the NE line centroid falls within the error of the SW line centroid, we average their relative displacements to the C line centroid and claim that there is a ∼0.5 spectral pixel shift between the outer edges of the helix and the central position along the axis of symmetry. A spectral pixel corresponds to ∼45 km s⁻¹, which implies a relative radial velocity shift of 23 ± 12 km s⁻¹ between the center and the edges of the helix. The observed velocity shifts along the helix are consistent with the kinematics of a conical outflow, where the motion of gas at the edges is perpendicular to our line of sight and exhibits the highest radial velocity.

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Electron densities are derived at the SW, C, and NE positions along the helix in order to characterize the density profile and estimate the total ionized gas mass. The densities are estimated from the extinction-corrected (Fritz et al. 2011; Mills et al. 2011) Paschen-α flux assuming case B recombination with an electron temperature identical to that of the Sickle (T_e ∼ 5500 K; Lang et al. 1997) and an adopted volume based on the spatially resolved thickness of the helix, t, at each position. We determine densities of 1.8, 1.6, and 1.4 × 10³ cm⁻³ for positions SW, C, and NE, respectively (Table 2). Adopting a 20% error in the extinction correction (Fritz et al. 2011) implies that the error of the density estimates is ±150 cm⁻³. A power-law fit to the densities as a function of projected distance from WR102c, d_*, yields a relatively shallow density gradient with an index of −0.37 ± 0.27. Assuming a radial density power law $\propto \;{d}_{*}^{-.37}$ and a uniform thickness of 0.16 pc throughout the helix, we integrate over the volume of the helix from d_* = 0.1 pc, the distance between WR102c and the edge of the lobes (see Figure 1(C)), to d_* = 1.5 pc and derive a total ionized gas mass of ∼0.8 M_⊙. The total mass of dust composing the helix derived from the best-fit DustEM models is ∼0.008 M_⊙, which implies a dust-to-gas mass ratio of ∼1%.

Table 2.  Physical Properties at Different Regions along the Helix

Region	${d}_{*}$ (pc)	${\rm{\Delta }}v$ (km s−1)	t (pc)	ne (×${10}^{3}\;{\mathrm{cm}}^{-3}$)
SW	0.6	+28 ± 13	0.14 ± 0.02	1.8
C	0.8	0	0.16 ± 0.01	1.6
NE	1.1	+17 ± 12	0.18 ± 0.02	1.4

Note. The electron density, n_e, velocity shift of the Brackett-γ emission-line peak relative to region C, ${\rm{\Delta }}v$, and the thickness of the helix, t, are provided at different regions along the helix located ${d}_{*}$ away from WR102c in projection. The error for the electron densities is $\pm 150\;{\mathrm{cm}}^{-3}$.

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We interpret the helix as a precessing, highly collimated outflow from WR102c. The morphology of the helix is fit to an analytical model of a precessing, collimated outflow (e.g., Kraus et al. 2006), the apparent shape of which is determined by the outflow velocity, v_H, precession period, τ_p, precession angle, θ_p, position angle, Θ, and inclination angle with respect to the plane of the sky, i. Based on the Paschen-α morphology of the helix, we adopt 240° for Θ, and the outflow velocity is assumed to be 23 ± 12 km s⁻¹ (see Section 3.5) divided by $\mathrm{sin}({\theta }_{p})$. The free parameters are therefore θ_p, τ_p, and i, the latter of which we assume is close to 0°. We fit a precession angle of 16° ± 4°, from which we infer an outflow velocity of 83 ± 48 km s⁻¹. The precession period can then be fit with a value of (1.4 ± 0.8) × 10⁴ yr, which is consistent with the wavelength of the helix (∼1 pc) divided by the outflow velocity (Figure 4). The model fit implies that the helix has existed for almost one and a half precession periods with a dynamical age of (1.8 ± 1.0) × 10⁴ yr. The total gas mass of the helix (∼0.8 M_⊙) infers a mean mass-loss rate of ${4.4}_{-1.5}^{+5.6}\times {10}^{-5}\;{M}_{\odot }\;{\mathrm{yr}}^{-1}$. This estimate of the mean mass-loss rate should be regarded as a lower limit since the helix only traces a confined, polar outflow from WR102c.

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Given the density and velocity of the helix and the outflow properties of the winds from the Quintuplet cluster, we can determine whether or not the morphology of the helix has been influenced by the luminous cluster. We verify that the expansion of the helix is unimpeded by the winds from the Quintuplet cluster by estimating the ram pressure ratio between the Quintuplet winds and the most extended regions of the helix. We define this ram pressure ratio as ${\chi }_{P}\quad =\quad {P}_{{\rm{H}}}/{P}_{\mathrm{QC}}$, where

$$\begin{eqnarray}&&{P}_{{\rm{H}}}={\rho }_{{\rm{H}}}{v}_{{\rm{H}}}^{2},{P}_{\mathrm{QC}}=\displaystyle \frac{{\dot{M}}_{\mathrm{QC}}}{4\pi \;{r}_{\mathrm{QC}}^{2}}\;{v}_{\mathrm{QC}},\end{eqnarray} \tag{ 1 }$$

and ${\rho }_{{\rm{H}}}$ is the density of the helix, v_H is the helix outflow velocity, ${\dot{M}}_{\mathrm{QC}}$ is the mass-loss rate of the Quintuplet cluster, r_QC is distance from the Quintuplet, and v_QC is the velocity of the Quintuplet winds. If ${\chi }_{P}\gg 1$ at regions in the helix most adjacent to the Quintuplet, then we do not expect the Quintuplet winds to have significantly disrupted the morphology of the helix. We assume that the helix extends ∼1.5 pc from WR102c ({−1, −1} in Figure 4), which is where r_QC ∼ 2 pc when including the $\sqrt{2}$ projection factor to account for distance uncertainties between the helix and the Quintuplet. Simulations of mass loss from the Quintuplet cluster reveal average radial outflow velocities <400 km s⁻¹ at distances of 02–10 (∼0.5–2.4 pc) from the cluster (Rockefeller et al. 2005). We therefore adopt an outflow velocity of v_QC = 400 km s⁻¹. Given the other mass-loss and outflow properties of the Quintuplet (Lang et al. 2005; Rockefeller et al. 2005) and the helix, the ram pressure ratio at r_QC = 2 pc can be expressed as

$$\begin{eqnarray}{\chi }_{P} & \sim & 50\;{\left(\displaystyle \frac{{\dot{M}}_{\mathrm{QC}}}{5\times {10}^{-4}{M}_{\odot }{\mathrm{yr}}^{-1}}\right)}^{-1}{\left(\displaystyle \frac{{v}_{\mathrm{QC}}}{400\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-1}\\ & & \times {\left(\displaystyle \frac{{d}_{*}}{1.5\mathrm{pc}}\right)}^{-0.37}{\left(\displaystyle \frac{{v}_{{\rm{H}}}}{80\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{2},\end{eqnarray} \tag{ 2 }$$

where d_* is the distance from WR102c. As expected, the ram pressure from the helix dominates that of the Quintuplet winds, which indicates that the winds have not yet disrupted the helix. The helix is therefore freely expanding into the cavity of the Sickle, and its morphology is consistent with the outflow model (Figure 4).

The disagreement between the observed wind velocity of WR102c (∼1600 km ${{\rm{s}}}^{-1};$ Steinke et al. 2015) and the outflow velocity of the helix (∼80 km ${{\rm{s}}}^{-1}$) indicates that the helix did not form in its high-velocity winds. Additionally, Steinke et al. (2015) reveal that the bipolar Paschen-α emitting lobes in the ∼0.15 pc vicinity of WR102c (Figure 1(C)) do not exhibit velocities consistent with the winds from WR102c. Discrepant nebular and wind velocities from W-R stars are not uncommon since the nebulae are interpreted as ejecta from a previous RSG or LBV phase (Toalá et al. 2015 and references therein), where the star has undergone enhanced mass loss at speeds of $\sim 10-100$ km ${{\rm{s}}}^{-1}$. Observations of nebulae around H-poor WN-type stars have revealed expansion velocities of $\sim 10-100$ km ${{\rm{s}}}^{-1}$ and enriched metal abundances consistent with ejecta from massive, evolved stars (e.g., S308, RCW58, M1-67, NGC 6888; Chu et al. 1999 and references therein). These nebulae have not been significantly accelerated by the more tenuous winds from their central W-R stars. Steinke et al. (2015) also suggest that the spectral and morphological characteristics of the bipolar emission around WR102c are consistent with those of a typical W-R nebula ejected from a previous phase of enhanced mass loss.

Evolutionary tracks of rotating stars with solar metallicty from Ekström et al. (2012), which were adopted by Steinke et al. (2015) to derive an initial mass of ∼40 ${M}_{\odot }$ for WR102c, indicate that stars with an initial mass $\geqslant 30$ ${M}_{\odot }$ will not go through an RSG phase (Georgy et al. 2012). We therefore favor the LBV interpretation as the origin of the helix; however, we do not rule out the RSG outflow scenario. The dynamical timescale of the helix ($\sim 2\times {10}^{4}\;{\rm{yr}};$ Section 4.1) is also comparable to the estimated duration of the LBV phase ($\sim {10}^{4}\;{\rm{yr}};$ Garcia-Segura et al. 1996) and supports our claim that WR102c has recently transitioned to a WN star.

The precession of WR102c that dictates the morphology of the helix must be provoked by gravitational interactions with either a binary companion or a disk with orbital axes misaligned with the spin axis of WR102c. We rule out the possibility that the precessing outflow is due to interactions with a disk since the strong winds from WR102c would disrupt a nearby disk on very short timescales. The disruption timescale, τ_d, can be estimated as the time it takes a shock driven by winds from WR102c to propagate through the disk. For a disk density and outer radius of ρ_d and r_d, respectively, the disruption timescale can be expressed as

$$\begin{eqnarray}&&{\tau }_{d}\quad =\quad \sqrt{\displaystyle \frac{{\rho }_{d}}{{\rho }_{w}}}{r}_{d}/{v}_{w},\end{eqnarray} \tag{ 3 }$$

where ρ_w is the density of the winds from WR102c and v_w is the wind velocity. In order to estimate τ_d, we adopt a gas density of ρ_d ∼ 10⁻¹⁰ g cm⁻³ and radius of r_d ∼ 200 R_⊙, which are consistent with near-IR observations of disks inferred around rapidly rotating B-type (Be) stars (Gies et al. 2007). Assuming that the density of the medium surrounding the disk is dominated by the mass loss, ${\dot{M}}_{w}$, and winds from WR102c (i.e., ${\rho }_{w}\approx {\dot{M}}_{w}/4\pi \;{r}_{d}^{2}{v}_{w}$), the disruption timescale is

$$\begin{eqnarray}{\tau }_{d} & \sim & 1.8\;{\left(\displaystyle \frac{{\dot{M}}_{w}}{4\times {10}^{-5}{M}_{\odot }{\mathrm{yr}}^{-1}}\right)}^{-1/2}{\left(\displaystyle \frac{{v}_{w}}{80\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{-1/2}\\ & & \times {\left(\displaystyle \frac{{r}_{d}}{200{R}_{\odot }}\right)}^{2}{\left(\displaystyle \frac{{\rho }_{d}}{{10}^{-10}{\rm{g}}{\mathrm{cm}}^{-3}}\right)}^{1/2}\;\mathrm{year},\end{eqnarray} \tag{ 4 }$$

where we have adopted the mass-loss rate derived in Section 4.1 and a wind velocity equivalent to the estimated helix outflow speed. Even if the disk were several orders of magnitude denser, the disruption timescale due to the shocks driven by WR102c would still be shorter than the inferred lifetime of the helix, ∼1.8 × 10⁴ yr. We also note that it is unlikely that a disk formed owing to enhanced equatorial mass loss from WR102c via rotational distortion since the resulting disk would be aligned with the star's rotational axis and thus provide no torque for the star to precess. Additionally, equatorial mass loss is predicted to be considerably suppressed for massive, oblate stars owing to gravity darkening at the equator and poleward latitudinal line-driven forces (Owocki et al. 1996).

We therefore conclude that the perturber must be a binary companion. The binarity of WR102c not only explains its precession but also provides a plausible scenario for the ejection and subsequent isolation from its likely birth site, the Quintuplet cluster, as well as a rapid spin-up of WR102c that can produce an enhanced polar outflow (Dwarkadas & Owocki 2002).

We hypothesize that WR102c and an initially more massive binary companion were formed and subsequently ejected from the Quintuplet cluster. The association of WR102c with the Quintuplet is substantiated by the presence of similarly evolved, massive stars within the cluster (Liermann et al. 2009). Based on the gainer/donor scenario for massive stars in interacting, mass-exchanging binaries (e.g., Smith & Tombleson 2015), we interpret the progenitor of WR102c to be the mass gainer of the system and its companion the mass donor. The donor, which is the star with the greatest initial mass in the system, evolves faster than the gainer and begins to fill its Roche lobe as its envelope swells while leaving the main sequence. Mass from the envelope of the donor accretes onto the gainer owing to Roche-lobe overflow and also spins up the gainer to near Keplerian, breakup speed (e.g., de Mink et al. 2013). The donor then explodes as an SN, and assuming that its explosion is spherically symmetric, the gainer and remnant core of the donor will still remain bound since the donor lost a significant fraction of its initial mass to winds and mass transfer. The SN explosion will, however, provide a velocity kick to the center of mass of the bound system and eject it from its birth site (e.g., Blaauw 1961). Based on population synthesis models of massive stellar binaries, ∼20% of binaries are expected to remain bound after the initial SN (Eldridge et al. 2011).

We do not rule out the possibility that the WR102c system was ejected via dynamical interactions with other members of the Quintuplet. However, it is unlikely that the companion is a closely orbiting MS or post-MS star given the lack of a detectable X-ray counterpart within a ∼30'' radius of WR102c that typically arises from wind collision zones between two massive stars (Mauerhan et al. 2009). We also rule out the possibility that the outflow originates from an accretion disk around a compact companion owing to the lack of a hard X-ray counterpart and the hostile conditions for dust surival in a high-velocity jet-like outflow from a compact object.

The binary companion will exert a torque on WR102c that attempts to align its spin axis with the angular momentum vector of the orbital plane, ${{\boldsymbol{\ell }}}_{\mathrm{orb}}$. A torque is also applied on ${{\boldsymbol{\ell }}}_{\mathrm{orb}}$ from the misaligned spin angular momentum vector of WR102c, ${{\boldsymbol{\ell }}}_{*}$. The result is a mutual precession of both spin and orbital axes about the net angular momentum vector of the system, ${{\boldsymbol{\ell }}}_{\mathrm{tot}}={{\boldsymbol{\ell }}}_{\mathrm{orb}}+{{\boldsymbol{\ell }}}_{*}$. This precession scenario is analogous to planetary systems with a hot Jupiter in a misaligned orbit with its host star's spin axis (e.g., Barnes et al. 2013). Figure 5 illustrates the precession geometry of the WR102c system where the z-axis is aligned with ${{\boldsymbol{\ell }}}_{\mathrm{tot}}$, φ_* is the angle between ${{\boldsymbol{\ell }}}_{*}$ and ${{\boldsymbol{\ell }}}_{\mathrm{tot}}$, ${\varphi }_{\mathrm{orb}}$ is the angle between ${{\boldsymbol{\ell }}}_{\mathrm{orb}}$ and ${{\boldsymbol{\ell }}}_{\mathrm{tot}}$, and $\varphi ={\varphi }_{*}+{\varphi }_{\mathrm{orb}}$. The angles and amplitudes of the angular momentum from WR102c's spin and the orbital motion of the companion can be related by

$$\begin{eqnarray}&&{{\ell }}_{*}\;\mathrm{sin}({\varphi }_{*})={{\ell }}_{\mathrm{orb}}\;\mathrm{sin}({\varphi }_{\mathrm{orb}}).\end{eqnarray} \tag{ 5 }$$

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In the case where ${{\boldsymbol{\ell }}}_{\mathrm{orb}}\gg {{\boldsymbol{\ell }}}_{*}$ with low orbital eccentricity and $\varphi \ll 90^\circ$, ${{\boldsymbol{\ell }}}_{\mathrm{orb}}\approx {{\boldsymbol{\ell }}}_{\mathrm{tot}}$ and the spin axis of WR102c precesses about the angular momentum vector of the orbital plane at a frequency of

$$\begin{eqnarray}&&{{\rm{\Omega }}}_{*}\equiv \displaystyle \frac{2\pi }{{\tau }_{p}}=\displaystyle \frac{3{\pi }^{2}}{{\omega }_{*}{P}^{2}}\left(\displaystyle \frac{{M}_{B}}{{M}_{A}+{M}_{B}}\right)\left[1-{\left(\displaystyle \frac{{R}_{p}}{{R}_{\mathrm{eq}}}\right)}^{2}\right]\mathrm{cos}(\varphi ),\end{eqnarray} \tag{ 6 }$$

where τ_p is the precession period, P is the orbital period of the system, M_A is the mass of WR102c, M_B is the mass of the binary companion, ω_* is the rotational frequency of WR102c, and R_p and R_eq are the polar and equatorial radii of WR102c, respectively. In the case where ${{\boldsymbol{\ell }}}_{\mathrm{orb}}\sim {{\boldsymbol{\ell }}}_{*}$, the precession rate of WR102c is faster since the angle ${\varphi }_{*}$ between ${{\boldsymbol{\ell }}}_{*}$ and ${{\boldsymbol{\ell }}}_{\mathrm{tot}}$ is now smaller than the angle φ between ${{\boldsymbol{\ell }}}_{*}$ and ${{\boldsymbol{\ell }}}_{\mathrm{orb}}$. The precession rate of WR102c in this more general case can be expressed as

$$\begin{eqnarray}&&{{\rm{\Omega }}}_{*}^{\prime }\equiv \displaystyle \frac{2\pi }{{\tau }_{p}^{\prime }}={{\rm{\Omega }}}_{*}\displaystyle \frac{\mathrm{sin}(\varphi )}{\mathrm{sin}({\varphi }_{*})},\end{eqnarray} \tag{ 7 }$$

where ${\tau }_{p}^{\prime }$ is the precession period of WR102c about the net angular momentum vector. It can be shown that ${{\ell }}_{\mathrm{orb}}\gtrsim {{\ell }}_{*}$ for the WR102c system, which implies ${\varphi }_{*}\gtrsim {\varphi }_{\mathrm{orb}}$ (Equation (5)) and $\varphi \lesssim 2{\varphi }_{*}$. Since the observed half-opening angle of the helix, θ_p, is the precession angle of WR102c, φ_*, it follows that $\varphi \lesssim 2{\theta }_{p}\sim 32^\circ$ (Section 4.1). We may therefore approximate $\mathrm{sin}(\varphi )$, $\mathrm{sin}({\varphi }_{*})$, and $\mathrm{sin}({\varphi }_{\mathrm{orb}})$ as φ, φ_*, and φ_orb, respectively. Equation (7) can then be re-expressed as

$$\begin{eqnarray}&&{{\rm{\Omega }}}_{*}^{\prime }\approx {{\rm{\Omega }}}_{*}\displaystyle \frac{\varphi }{{\varphi }_{*}}={{\rm{\Omega }}}_{*}\left(1+\displaystyle \frac{{\varphi }_{\mathrm{orb}}}{{\varphi }_{*}}\right)\approx {{\rm{\Omega }}}_{*}\left(1+\displaystyle \frac{{{\ell }}_{*}}{{{\ell }}_{\mathrm{orb}}}\right),\end{eqnarray} \tag{ 8 }$$

where we have also applied Equation (5). The magnitude of the spin angular momentum of WR102c is given by ${{\ell }}_{*}=k\;{M}_{A}\;{R}_{\mathrm{eq}}^{2}\;{\omega }_{*}$, where k is the moment-of-inertia coefficient (e.g., k = 0.4 for a uniform density sphere and k ∼ 0.06 for the Sun). For the binary companion with an orbital radius, a, and orbital frequency, ${n}_{B}\equiv 2\pi /P$, the magnitude of the orbital angular momentum is simply ${{\ell }}_{\mathrm{orb}}={M}_{B}\;{a}^{2}\;{n}_{B}$. The upper limit of ${{\ell }}_{*}/{{\ell }}_{\mathrm{orb}}$ can be obtained by assuming the physical limits where a ∼ R_eq and that WR102c is rotating near the Keplerian breakup velocity, ${\omega }_{*}\sim \sqrt{G\;{M}_{A}/{R}_{\mathrm{eq}}^{3}}$. Given our scenario from the previous section, the companion is interpreted as the remnant core of a massive star that will exhibit a mass no less than ${M}_{B}\sim 2\;{M}_{\odot }$. Recall that Steinke et al. (2015) estimate an initial mass of ∼40 M_⊙ for WR102c based on evolutionary tracks for rotating stars from Ekström et al. (2012). In the limit where ${M}_{B}\ll {M}_{A}$ and a ∼ R_eq, we assume that the system is tidally locked and that ${n}_{B}\sim {\omega }_{*}$. The moment-of-inertia coefficient is estimated to be k ∼ 0.05 from formulae fit to evolutionary models of k by Pols et al. (1998) as a function of initial stellar mass and radius (see Section A.2.1 in de Mink et al. 2013). Adopting these limiting physical properties of the WR102c system, the upper limit of ${{\ell }}_{*}/{{\ell }}_{\mathrm{orb}}$ is

$$\begin{eqnarray}&&\displaystyle \frac{{{\ell }}_{*}}{{{\ell }}_{\mathrm{orb}}}=\displaystyle \frac{k\;{M}_{A}\;{R}_{\mathrm{eq}}^{2}\;{\omega }_{*}}{{M}_{B}\;{a}^{2}\;{n}_{B}}\lesssim 1\left(\displaystyle \frac{k}{0.05}\right)\left(\displaystyle \frac{{M}_{A}}{40\;\;{M}_{\odot }}\right){\left(\displaystyle \frac{{M}_{B}}{2{M}_{\odot }}\right)}^{-1},\end{eqnarray} \tag{ 9 }$$

which shows that ${{\ell }}_{\mathrm{orb}}\gtrsim {{\ell }}_{*}$. Equations (6) and (8) can then be combined to redefine ${{\rm{\Omega }}}_{*}^{\prime }$ as

$$\begin{eqnarray}{{\rm{\Omega }}}_{*}^{\prime } & \approx & \displaystyle \frac{3{\pi }^{2}}{{\omega }_{*}{P}^{2}}\left(\displaystyle \frac{{M}_{B}}{{M}_{A}+{M}_{B}}\right)\left[1-{\left(\displaystyle \frac{{R}_{p}}{{R}_{\mathrm{eq}}}\right)}^{2}\right]\\ & & \times \mathrm{cos}(\varphi )\;\left\{1+\displaystyle \frac{k\;{M}_{A}\;{R}_{\mathrm{eq}}^{2}\;{\omega }_{*}}{{M}_{B}\;{(2\pi /P)}^{1/3}\;{[G({M}_{A}+{M}_{B})]}^{2/3}}\right\},\end{eqnarray} \tag{ 10 }$$

where we have also utilized Kepler's third law: ${n}_{B}^{2}\;{a}^{3}=G({M}_{A}+{M}_{B})$. With the observed and adopted parameters of the WR102c system, we can utilize Equation (10) to constrain the orbital period of the binary system. Since we claim that the helix was formed during a previous LBV phase of WR102c (Section 4.2), the stellar radius inferred from recent observations ($\sim 4\;{R}_{\odot };$ Steinke et al. 2015) is unlikely to be consistent with its radius while an LBV. We therefore adopt the measured radius and rotational velocity for AG Carinae (Groh et al. 2006), an LBV that exhibits rapid rotation, a bipolar nebula, and a dusty helical "jet" (Paresce & Nota 1989; Nota et al. 1992, 1995). The radius and spin of AG Carinae averaged over three observed epochs are ${R}_{\mathrm{eq}}=82\;{R}_{\odot }$ and ${\omega }_{*}=0.68\;{\omega }_{{\rm{K}}}$, respectively, where ${\omega }_{{\rm{K}}}$ is the Keplerian breakup velocity and the inclination of the star is assumed to be 90° (Groh et al. 2006). Optical observations show that fast rotation is typical for all bona fide, strong variable galactic LBVs (Groh et al. 2009); thus, a rapidly rotating LBV progenitor for WR102c is not unexpected. Binary population synthesis models performed by de Mink et al. (2013) also predict that $\sim 20\%$ of all massive MS stars are rapid rotators owing to binary interaction, which is consistent with the observed fraction of rapid rotators (e.g., Penny & Gies 2009).

The remaining parameters required to constrain P from Equation (10) are ${R}_{\mathrm{eq}}/{R}_{p}$, φ, ${{\rm{\Omega }}}_{*}^{\prime }$, M_A, and M_B. The oblateness of the star, ${R}_{\mathrm{eq}}/{R}_{p}$, can be related to its spin (see A.2.2 of de Mink et al. 2013). Since ${\theta }_{p}\lt \varphi \lesssim 2{\theta }_{p}$ and ${\theta }_{p}$ is a relatively small angle ($\sim 16^\circ$), it follows that $\mathrm{cos}(\varphi )\sim \mathrm{cos}({\theta }_{p})$. The stellar precession rate of WR102c, ${{\rm{\Omega }}}_{*}^{\prime }$, is simply $2\pi {/\tau }_{p}^{\prime }$, where ${\tau }_{p}^{\prime }$ is the measured precession period of the helix ($\sim 1.4\times {10}^{4}\;{\rm{yr}}$; Section 4.1). For the mass of WR102c during the production of the helix, M_A, we adopt the estimated initial mass value of $40\;{M}_{\odot }$ estimated by Steinke et al. (2015). The orbital period can then be constrained by assuming the range of masses exhibited by compact, remnant cores from core-collapse SNe (neutron stars and black holes) for M_B. Since current observations of stellar mass black holes in the Milky Way exhibit a narrow mass distribution at $7.8\pm 1.2\;{M}_{\odot }$ (Özel et al. 2010 and references therein), we use 2 and 8 ${M}_{\odot }$ as the lower and upper mass limit for M_B, respectively. We determine from Equation (10) that the orbital period of the WR102c binary system is constrained to $800\;\mathrm{days}\lt P\lt 1400\;{\rm{days}}$. The limits derived for P are consistent with the dynamical regime for a relatively wider orbit for massive binary systems where accretion and spin-up are predicted to occur without a merger event ($2\;\mathrm{days}\lesssim P\lesssim 1500\;{\rm{days}};$ Podsiadlowski et al. 1992; Sana et al. 2012; de Mink et al. 2013). Orbital and outflow properties of the WR102c system are summarized in Table 3.

Table 3.  Derived Helix Outflow and Orbital Properties of the WR102c System

vH (km s−1)	$\dot{M}$ (${10}^{-5}\;{M}_{\odot }\;{\mathrm{yr}}^{-1}$)	${\theta }_{p}{(}^{\mathring })$	${\tau }_{p}$ (104 yr)	P (days)
80 ± 43	${4.4}_{-1.5}^{+5.6}$	16 ± 4	1.4 ± 0.8	$800\lt P\lt 1400$

Note. The helix outflow velocity, v_H, is derived from the velocity shift of the Brackett-γ emission-line peak along the helix, and the mass-loss rate, $\dot{M}$, is the total observed gas mass in the helix divided by its dynamical timescale, $1.8\times {10}^{4}\;{\rm{yr}}$. The precession period of WR102c, ${\tau }_{p}$, and the precession angle, ${\theta }_{p}$, are derived from an analytical precessing outflow model. P is the orbital period of the system constrained from Equation (10).

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The presence of a helix due to a precessing, collimated outflow is unlikely unique to WR102c given the prevalence of binarity in massive stars (Sana et al. 2012). However, we expect helical trails from massive binary systems to be relatively rare since they require a bound system after the more massive companion explodes as an SN (Eldridge et al. 2011) and inclination angles favorable for observations. We investigated ∼60 nebulae surrounding massive evolved stars identified by Spitzer/MIPS imaging observations at 24 μm (Wachter et al. 2010) and found two sources that exhibit helical morphologies. The stars consistent with the helices are HD 316285 (Figure 6(A); Hillier et al. 1998) and the source number 54 (WMD 54; Figure 6(B)) identified by Wachter et al. (2010).

HD 316285 is classified as a candidate LBV based on its spectral variability and is believed to be located ∼2 kpc away (Hillier et al. 1998). The 24 μm nebular emission surrounding HD 316285 exhibits a bipolar morphology consistent with the orientation of the apparent helix detected at 8 μm (Figure 6(A)), which resembles the bipolar Paschen-α lobes and helix of WR102c (Figure 1(C)). Proper-motion measurements of HD 316285 indicate that the star is moving south–southwest at a rate of ∼5 mas yr⁻¹ (van Leeuwen 2007). If the nebula is a product of the interaction of an outflow from HD 316285 with the surrounding medium, the enhanced emission at its southern edge at 24 μm is consistent with HD 316285's direction of motion. This may explain the one-sided appearance of the helix in HD 316285, which is similar to the scenario we infer for WR102c. Additionally, the proper-motion velocity of HD 316285 is ∼45 km s⁻¹ assuming a distance of 2 kpc and is consistent with velocities exhibited by systems that remained bound after the initial SN kick (van den Heuvel et al. 2000). The size of the spatial wavelength of the helix is ∼0.8 pc and its total length is ∼1.6 pc assuming that HD 316285 is located 2 kpc away. If the helix is indeed associated with a precessing outflow from HD 316285, we infer a precession period of ${\tau }_{p}\sim 1900\;{\rm{yr}}$ and a total dynamic lifetime of ∼3800 yr given the measured wind velocity of ∼410 km s⁻¹ (Hillier et al. 1998). The lifetime of the helix is therefore consistent with HD 316285 being an LBV since it is less than the estimated timescale for the LBV phase ($\sim {10}^{4}$ yr). By adopting ${\tau }_{p}\sim 1900\;{\rm{yr}}$ for Equation (10) and assuming the same physical parameters as we did for WR102c, the orbital period of a hypothetical HD 316285 binary system may be constrained to $300\;\mathrm{days}\lt P\lt 520\;{\rm{days}}$, which agrees with the range of orbital periods where massive binaries are expected to interact.

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WMD 54 is broadly characterized as an emission-line B-type star, LBV candidate, or late-type nitrogen-rich W-R star based on the presence of both hydrogen and helium emission lines (Wachter et al. 2011). Unlike WR102c and HD 316285, the apparent helix at 24 μm around WMD 54 exhibits a symmetric morphology (Figure 6(B)). The symmetric appearance of the helix may be consistent with the dynamics of the system if the enhanced emission at the eastern edge of the nebula is indicative of an eastward proper motion of the star. However, neither the distance to WMD 54 nor its proper motion is well constrained since the system is not well studied. Preliminary analyses of near-IR spectra of the WMD 54 helix taken recently by Palomar/Triplespec do not reveal the presence of Br-γ emission lines, and we are therefore unable to infer its kinematics. The lack of Br-γ emission, which suggests that the radiation field from WMD 54 is softer than typical W-R stars, and the absence of broad ∼1000 km s⁻¹ helium emission lines (Wachter et al. 2011) indicate that WMD 54 is not likely a W-R star. An LBV classification of WMD 54 would strengthen our claim of the formation of dusty helices during the LBV phase if the helical feature is indeed associated with an outflow from the central star. Further observations are required to verify this hypothesis.