Discovery of a 310 Day Period from the Enshrouded Massive System NaSt1 (WR 122)

PGIR is a wide-field, time-domain imaging survey located at Palomar Observatory. It utilizes a 30 cm telescope and J-band filter similar to the 2MASS J filter with an effective wavelength of λ_eff = 1.235 μm and an effective filter bandwidth of Δλ = 0.1624 μm. PGIR achieves a 496 × 496 field of view (FoV) with its 2k × 2k HAWAII-2RG detector and a scale of 87 pixel⁻¹. The entire sky visible from Palomar is imaged by PGIR every ∼2 nights down to a 5σ detection limit of 14.8 Vega mag. ¹⁵ The PGIR image processing and photometric calibration are described by De et al. (2020a). The J-band saturation limit of PGIR was initially ∼8.5 mag, but has been subsequently improved to J ≈ 6 mag after implementing a new readout mode described by De et al. (2020b).

NaSt1, which is located at α(J2000) = 18^h52^m1755 and δ(J2000) $=\,+00^\circ 59^{\prime} 44\buildrel{\prime\prime}\over{.} 3$ (Gaia Collaboration 2018), was well covered by PGIR imaging fields. In order to investigate the J-band variability of NaSt1, forced-aperture photometry was performed at its coordinates using a 3 resampled-pixel radius (∼13'') aperture in PGIR images taken between 2018 November and 2021 June. Importantly, source confusion is not an issue since NaSt1 is >3.8 mag brighter in J than all objects within 15'' of its coordinates (Cutri et al. 2003). Photometry from PGIR and all other platforms included in this work are provided in Table 1.

Optical BVRI photometry of NaSt1 was obtained with the robotic 0.76 m Katzman Automatic Imaging Telescope (KAIT; Filippenko et al. 2001) at Lick Observatory. Additional Clear-band (close to the R band; see Li et al. 2003) images were also obtained with KAIT. A series of 66 imaging observations of NaSt1 was performed with KAIT between 2014 July and 2015 November. The KAIT observing frequency of NaSt1 ranged from a few days to a few weeks when visible.

All images were reduced using a custom pipeline (Ganeshalingam et al. 2010; Stahl et al. 2019). Point-spread-function (PSF) photometry was then obtained using DAOPHOT (Stetson 1987) from the IDL Astronomy Users Library. ¹⁶ Several nearby stars were chosen from the Pan-STARRS1 ¹⁷ catalog for calibration. Their magnitudes were first transformed into Landolt magnitudes (Landolt 1992) using the empirical prescription presented by Tonry et al. (2012) and then transformed to the KAIT natural system.

Apparent magnitudes were all measured in the KAIT4 natural system. The final results were transformed to the standard system using local calibrators and color terms for KAIT4 as given in Table 4 of Ganeshalingam et al. (2010), except for KAIT Clear-band data, where no reliable color term is measured owing to the broad response function. We therefore present the Clear magnitude relative to the reference stars in Landolt R magnitude, which is essentially in the KAIT natural system.

Mid-IR observations of NaSt1 were made using The Broadband Array Spectrograph System (BASS) sensor (Hackwell et al. 1990) at the 3.6 m Advanced Electro-Optical System (AEOS) telescope on Haleakela, HI, on 2017 October 23, 2018 May 13, 2019 April 6, and 2019 August 24 (UT dates are used throughout this paper). AEOS utilizes a chopping secondary mirror, run at 7 Hz for rapid sampling of the background. While observing, a chop-and-nod strategy was used with a chop throw of $\sim 11^{\prime\prime}$ and a telescope nod of the same distance between exposures. Integrations of 30 s were obtained per nod position, and 12–26 samples were obtained for each of the AEOS observations (6–13 min total integration).

An off-axis visible-wavelength CCD was used for guiding to keep the source centered in the 42 instrument aperture during exposures. The resolving power of BASS is 30–125 across a 3–13 μm bandpass. Flux calibration was obtained via observations of the standard star α Lyr (Vega) at an airmass similar to that of the NaSt1 observations. Flux calibration was performed by dividing the target spectrum by the Vega spectrum and then multiplying the result by a Kurucz model atmosphere of Vega matched to the resolution of the data. This process also removes most of the telluric features. However, residual telluric artifacts remained, particularly in the deep water absorption band over 5–8 μm, so those data were removed for clarity. Although the stellar-atmosphere model does not account for dust excess, Vega's debris excess does not emit significantly shortward of 13 μm. For example, at the long-wavelength end of our BASS spectrum, Vega's 13 μm debris disk excess is <2%–3% of the photosphere (Su et al. 2013).

Wavelength calibration of each BASS channel was performed in the lab using a monochrometer and either checked on-sky with observations of a strong mid-IR emission-line source (planetary nebula NGC 7027) or in the dome using a blackbody source (hot plate) measured at two temperatures (40°C and 60°C) and attenuated by films of polystyrene and polysulfone to superimpose absorption features for reference.

We present historical IR ${JHKL}^{\prime} M$ photometry of NaSt1 (Table 2) taken from the 3.8 m United Kingdom Infrared Telescope (UKIRT) and the European Southern Observatory (ESO) 1 m photometric telescope between 1983 July and 1989 May (MJD 45,528–47,671). The UKIRT and ESO photometry taken on 1983 July 13 (MJD 45,838) and 1983 May 18 (MJD 45,528), respectively, were previously published by Williams et al. (1987). Subsequent photometry is presented in this work for the first time. Since these observations were taken as a continuation of the photometry published by Williams et al. (1987), the observations follow the same procedures described in their paper. ESO ${JHKL}^{\prime} M$ filter properties are described by van der Bliek et al. (1996). The UKIRT JHK and $L^{\prime} M$ filter properties are provided by Hawarden et al. (2001) and Leggett et al. (2003), respectively.

Table 2. NaSt1 Historical IR Magnitudes

MJD	J	H	K	${L}^{{\prime} }$	M	Source
45,528	9.54	8.51	6.50	4.12		UKIRT a
45,838	9.52	8.46	6.39	3.99	3.30	ESO a
46,237	9.19	8.27	6.25	3.90	3.46	UKIRT
46,302	9.05	7.95	5.94	3.78	3.16	UKIRT
46,715	9.49	8.18	6.19	3.91	3.18	UKIRT
46,960	9.10	7.82	5.88	3.71	3.04	ESO
47,258	8.99	7.85	5.87	3.66	2.98	ESO
47,259	8.99	7.82	5.87	3.66	3.02	ESO
47,261	9.04	7.89	5.87	3.68	2.96	ESO
47,304	9.18	7.97	6.02	3.76	3.12	ESO
47,670	9.40	8.25	6.25	3.89	3.19	ESO
47,671	9.39	8.25	6.25	3.90	3.23	ESO

Notes. IR photometry of NaSt1 from UKIRT and the ESO 1 m photometric telescope. Uncertainties are assumed to be 0.1 mag for ${JHKL}^{\prime}$-band photometry and 0.15 mag for M-band photometry.

^a Previously published by Williams et al. (1987).

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UKIRT ${{JHKL}}^{{\prime} }$ photometry was obtained using a 124 diameter aperture, and M photometry was obtained with a 5'' diameter aperture. ESO photometry was measured through a 15'' diameter aperture except for the observation taken on 1987 June 14 (MJD 46,960), where a 22'' diameter aperture was used. The photometry is shown in Table 2 and provided in Vega magnitudes.

We utilize the g-band and r-band PSF-fit photometry of NaSt1 from the Zwicky Transient Facility (ZTF; Bellm et al. 2019; Masci et al. 2019) Public Data Release 6. ¹⁸ ZTF observations of NaSt1 were taken between 2018 April and 2021 April with a ∼1 day cadence when visible. Only the photometry with clean extractions (i.e., "catflags = 0") from ZTF DR6 were used for the analysis. Several nights included multiple observations of the field containing NaSt1. For example, high-cadence r-band observations were taken on MJD 58,347 and MJD 58,348, where each night consisted of ∼100 images. Multiple ZTF g- and r-band observations taken over a night were therefore averaged in single-night bins. Since ZTF photometry from the DR6 catalog was provided in units of AB magnitude, we converted the photometry to Vega units by applying the conversions m_g,AB − m_g,Vega = −0.08 and m_r,AB − m_r,Vega = 0.16.

We also utilize the V-band photometry of NaSt1 from the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014; Kochanek et al. 2017). Photometry of NaSt1 was obtained from the ASAS-SN Variable Star Database ¹⁹ (Jayasinghe et al. 2020), where it was identified as a variable with the reference ID ASASSN-V J185217.55+005944.3. ASAS-SN photometry of NaSt1 from the Variable Star Database spans from 2015 February to 2018 November with an observing cadence of ∼1 week when visible.

Lastly, we use photometric measurements of NaSt1 obtained by the Asteroid Terrestrial-impact Last Alert System (ATLAS) project between 2015 October 23 (MJD 57,318) and 2021 July 9 (MJD 59,404) from the ATLAS forced-photometry server ²⁰ (Heinze et al. 2018; Tonry et al. 2018; Smith et al. 2020). ATLAS surveys the entire visible sky at declinations north of −50° every two nights with the ATLAS orange ("o-band"; λ_eff = 6632 Å) and cyan ("c-band"; λ_eff = 5184 Å) filters. ATLAS photometry obtained from the forced-photometry server were filtered by ignoring observations where the NaSt1 was within 100 pixels of the edge of the FoV and where the magnitude error was greater than 0.1 mag. Multiple observations of NaSt1 taken over a night were averaged in single-night bins. PSF photometry of NaSt1 was converted from Jy to Vega magnitudes using zero-points of 3585.79 and 2846.76 Jy for the c- and o-band filters, respectively, which were derived by the Spanish Virtual Observatory Filter Profile Service (Rodrigo et al. 2012; Rodrigo & Solano 2020).

The near-IR and optical light curves of NaSt1 taken between 2014 July and 2021 July are shown in Figure 1 and present clear evidence of smooth variability on a roughly year-long timescale. Since the variations are sufficiently smooth and symmetric about maxima, sinusoidal functions were fit to the PGIR, ZTF, ATLAS, ASAS-SN, and KAIT photometry using a least-squares fitting routine from the SciPy library in Python v.3.8.5. The free parameters were the period, variability amplitude, magnitude offset, and phase. The sinusoidal fits to each light curve reveal variability consistent with a period of ∼300 days. The best-constrained period was derived from the fit to the ZTF r-band light curve of P_r = 309.7 ± 0.7 days, which we adopt as NaSt1's photometric variability period. All other light curves were then refitted with an adopted period of P = 309.7 days. The results from the adopted-period sinusoidal fits are shown in Table 3. The following analysis utilizes the results from these adopted-period (P = 309.7 day) sinusoidal fits.

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Interestingly, the sinusoidal variability amplitudes differ across the different wavelengths, which is shown in Figure 2. The ZTF r, KAIT R, ATLAS o, and PGIR J bands exhibit higher-variability amplitudes relative to the other photometric bands. The KAIT I-band amplitude is comparable to the ZTF g- and ATLAS c-band amplitudes, which demonstrates that there is no obvious trend in the amplitudes as a function of wavelength. The apparent wavelength dependence of NaSt1's variability amplitude notably differs from the expected trend for stellar pulsations (e.g., Cepheids), where an increased amplitude is expected toward shorter wavelengths (Klagyivik & Szabados 2009).

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The amplitude fit from the ASAS-SN V-band photometry is discrepant with the KAIT V-band amplitude despite the similar wavelength coverage of the instrument filters (Table 3). Owing to the much larger 8'' pixels of ASAS-SN compared to the 08 KAIT pixels and the two-pixel (16'') radius aperture used for ASAS-SN photometry (Kochanek et al. 2017), the lower ASAS-SN amplitude is likely due to confusion with a nearby source of V-band brightness comparable to that of NaSt1. Photometry from the Pan-STARRS Data Release 1 catalog (Chambers et al. 2016) supports this explanation and shows that there is a source located ∼16'' from NaSt1 with a PS1 g-band brightness 57% that of NaSt1. Synthetic Johnson V-band photometry derived from optical spectroscopy of NaSt1 presented by Crowther & Smith (1999), where V = 14.47 mag also shows closer agreement with the 14.41 mag offset derived from the KAIT V-band light-curve fit (Table 3). The 0.066 ± 0.004 mag amplitude derived from the KAIT V-band photometry therefore more accurately traces the NaSt1 variability than the lower-amplitude ASAS-SN photometry.

The phase-folded PGIR J-band and ZTF r-band light curves, which show the highest variability amplitude, are shown in Figure 3 (left). These phase-folded light curves and the fitted-model residuals demonstrate close agreement with sinusoidal variability. The phase-folded light curves also show the cycle-to-cycle consistency of NaSt1's photometric variability.

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The ZTF r-band and PGIR J-band light curves from NaSt1 between MJD 58,550 and MJD 58,900 and the adopted-period sinusoidal fits indicate a significant (>5σ) phase offset of +17 ± 2.5 d, where the J-band peak lags behind the r-band peak (Figure 3, right). There is a similar phase offset between the ZTF r-band and g-band light-curve fits, where the g-band offset agrees with the PGIR J-band offset within the uncertainties. The phase offsets suggest that the PGIR J-band and ZTF r-band emission originate from distinct stellar and/or circumstellar components of NaSt1.

Adopted-period (P = 309.7 day) light-curve fits to the UKIRT and ESO 1 m ${JHKL}^{\prime}$-band observations of NaSt1 taken in 1983–1989 reveal that the periodicity of the past photometric variability is consistent with the present-day observations (Figure 4). Adopted-period light-curve fits to the M-band observations were unsatisfactory, which was likely due to the larger photometric uncertainties. Figure 4 also shows the predicted J-band emission based on the adopted-period fit to the PGIR light curve. Note that despite the small uncertainties in the period (1σ = 0.6 day) used for the light-curve fitting, the extrapolation from MJD ∼ 58,600 to MJD ∼46,500 leads to large uncertainties in the predicted phase. The consistent fit to the historic photometry strengthens our adopted period and demonstrates coherence of the periodic variability over decades.

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The results from the adopted-period fits to the historical IR light curves are shown in Table 4. Similar to the results from the recent optical/IR light-curve analysis (Table 3), the variability amplitudes differ at different filter wavelengths. Interestingly, the results from the light-curve fits indicate that the past J-band emission was brighter and showed variability amplitudes larger than the recent PGIR J-band observations.

Table 4. NaSt1 Historical IR Light-Curve Fit Results

Filter	Amplitude (mag)	Mag. Offset	MJD (φ = 0)
UKIRT/ESO J U: 1.24 (0.23) μm E: 1.21 (0.19) μm	0.25 ± 0.02	9.25 ± 0.02	45,607.8 ± 7.0
UKIRT/ESO H U: 1.65 (0.26) μm E: 1.64 (0.27) μm	0.33 ± 0.02	8.18 ± 0.02	45,636.8 ± 3.7
UKIRT/ESO K U: 2.18 (0.37) μm E: 2.22 (0.36) μm	0.29 ± 0.02	6.17 ± 0.02	45,633.4 ± 3.9
UKIRT/ESO $L^{\prime}$ U: 3.77 (0.53) μm E: 3.74 (0.58) μm	0.18 ± 0.02	3.87 ± 0.02	45,634.4 ± 7.9

Note. Instrument filter details (effective wavelength and bandwidth) and results from adopted-period (P = 309.7 day) sine fits to the historical ${JHKL}^{\prime}$-band light curves of NaSt1 observed by UKIRT and ESO 1 m. Fitted properties include the variability amplitude, magnitude offset at the mid-line of the fitted sine function, and the MJD where the phase of the sine function φ = 0. The phase fitting assumed an initial φ = 0 estimate of MJD 45,630.

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It is important to consider the color and magnitude conversions between the different IR photometric systems of UKIRT/ESO and PGIR. Based on the UKIRT and 2MASS transformation Equations (37)–(40) from Carpenter (2001) and the measured magnitude offsets from the adopted-period light-curve fits (Table 4), the 2MASS and UKIRT J-band photometry conversion is J_UKIRT = J_2MASS − (0.21 ± 0.06 mag). Owing to their similar filter properties, J_2MASS ≈ J_PGIR, which implies that the change in J_PGIR between the past and recent observations is ΔJ_PGIR = 0.17 ± 0.06 mag. This suggests that NaSt1 does indeed exhibit variability on longer (≳decade) timescales.

Mid-IR spectroscopy of NaSt1 with BASS taken in 2017–2019 reveals variability at 3–13 μm (Figure 5), where the mid-IR flux from NaSt1 is likely dominated by thermal emission from circumstellar dust (Crowther & Smith 1999; Rajagopal et al. 2007). The IR-dominated spectral-energy distribution (SED) in Figure 5 (left) also demonstrates that NaSt1 is enshrouded by circumstellar dust in addition to being obscured by interstellar material.

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Figure 5 (center) shows the semicontemporaneous ZTF gr, ATLAS co, and PGIR J photometry taken within 20 days (Δφ ≈ 0.06) of the BASS spectroscopy in 2019 April (MJD 58,579) and within 7 days (Δφ ≈ 0.02) of BASS spectroscopy in 2019 August (MJD 58,719). Figure 5 (center) also shows the ZTF and ATLAS photometry taken within 4 days (Δφ ≈ 0.01) of the BASS spectroscopy in 2018 May (MJD 58,251). The timing of the 2019 April (φ = 0.71) and 2019 August (φ = 0.17) observations sample near the NaSt1 minimum and peak emission, respectively (see Figure 1). The NaSt1 SED at these two epochs shows that the trend in the mid-IR variability is consistent with the optical/near-IR variability (Figure 5, right). The ZTF, ATLAS, and PGIR photometry increased by 10%–30% between the 2019 April and 2019 August. The 3–13 μm emission increased similarly by ∼10%–30% between 2019 April and 2019 August, where the largest variations (>20%) were observed at shorter mid-IR wavelengths (λ ≈ 3 μm). Variability from the circumstellar dust emission in the mid-IR is therefore likely linked to the optical/near-IR variability.

In order to investigate the color variability of NaSt1, KAIT, and ZTF/PGIR color curves were produced with simultaneous or nearly contemporaneous observations. Figure 6 (left) presents KAIT V − I, V − R, and R − I color curves, which are derived directly from the simultaneous multiband KAIT observations. Since PGIR and ZTF observations were not performed simultaneously, the PGIR/ZTF g − J, g − r, and r − J light curves in Figure 6 (right) were produced by utilizing observations taken within <3 days (Δφ < 0.01).

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KAIT color curves in Figure 6 (left) each show different variability trends. The V − R color curve varied consistently with the R-band brightness; however, the R − I curve indicates the opposite trend. The V − I color curve exhibits no significant variability, which is likely due to the lower amplitude of the I-band variability relative to that of the shorter wavelength R-band filter (Figure 2). The ZTF and PGIR g − J, g − r, and r − J color curves all show variability correlated with increasing r-band brightness. The discrepancies in the color evolution reflect the inconsistency of the variability amplitude from NaSt1 as a function of wavelength and suggest that different wavelength filters trace emission from different stellar and/or circumstellar components. The observed phase offsets between different filters (Figure 3, right) likely influence the color evolution as well.

Optical and near-IR spectroscopy of NaSt1 by Crowther & Smith (1999) revealed prominent narrow nebular emission lines such as He i λ6678, Hα, and [N ii] λ5755, which may contribute to the photometric measurements and variability. In order to determine whether the emission lines are influencing the variability, the NaSt1 emission-line list from Crowther & Smith (1999) was used to quantify the relative observed flux-density contribution to the model-derived photometry (i.e., "Mag. Offset" in Table 3). A 10% absolute flux-calibration uncertainty was assumed for both the emission-line measurements from Crowther & Smith (1999) and the PGIR, KAIT, ATLAS, ZTF, and ASAS-SN photometry.

Table 3 shows F_line/F_phot, the ratio of the flux density from NaSt1's observed emission lines over the filter bandwidths relative to the observed photometry. The nebular emission lines from NaSt1 do indeed appear to contribute ∼5%–30% to the optical photometry, where the strongest emission lines in NaSt1 are associated with He i, He ii, and [N ii]. However, the emission-line contribution is much lower in J. Since the amplitudes in the optical light curves are in the range ∼0.03–0.13 mag, or ∼ ±3%–11% of the "Mag. Offset," it is possible that the photometric variability may be due to changes in the observed strength of the emission lines in these filters. Interestingly, the ATLAS o, ZTF r, and KAIT R observations which exhibit the largest photometric variability amplitudes at optical wavelengths (Figure 2) are the only bands that include coverage of He i λ6678, the strongest optical emission line observed from NaSt1 (Crowther & Smith 1999). These are also the only filter bands that include coverage of Hα and [N ii] λ6583, where emission from the latter appears as an extended and asymmetric nebula around NaSt1 (Mauerhan et al. 2015; Figure 7, top)

The emission-line contribution to the PGIR J-band photometry is negligible, which indicates that the large J variability amplitude does not arise from variable near-IR emission lines. There is also minimal (F_line/F_phot < 0.01) emission-line contribution to the past JHK photometry from UKIRT/ESO (Table 4), which suggests that the apparent change in the J-band amplitude variability between the UKIRT/ESO and PGIR observations is not due to emission-line variations. J-band emission from NaSt1 may instead be dominated by thermal emission from circumstellar dust.

It is possible that the PGIR J, ATLAS o, ZTF r, and KAIT R bands exhibit high-amplitude variability because the filter bands trace emission with a significant contribution from circumstellar material. The other filter bands with lower variability amplitudes may instead be more influenced by stellar continuum emission.

NaSt1's asymmetric nebula (Figure 7, top; Mauerhan et al. 2015) combined with the discovery of its regular period suggests that NaSt1 hosts a binary. Photometric variability arising from pulsations or other intrinsic instability in hot, single, massive stars also do not typically appear as regular or sinusoidal as we observe from NaSt1 (e.g., Soraisam et al. 2020). We therefore postulate that the smooth 310 day photometric variability is most likely modulated by the orbit of a binary in NaSt1. This discussion is notably reminiscent of the long debate on the binary versus single-star hypotheses on η Car, where the binary interpretation is favored based on observations of its stable periodic variability (Damineli 1996; Corcoran 2005; Damineli et al. 2008). However, it is still important to consider the possible single-star mechanisms that may also account for the observed variability in NaSt1.

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One of the most common origins of stellar variability is stellar pulsations. This mechanism can result in near-sinusoidal photometric variations, which have been observed from stars such as Cepheids, Miras, and red supergiants (RSGs). However, the amplitude of the photometric variability arising from stellar pulsations exhibits a characteristic wavelength dependence where the amplitudes increase toward shorter wavelengths owing to associated changes in the star's effective temperature (e.g., Klagyivik & Szabados 2009). This is inconsistent with the observed variability amplitudes of NaSt1 at different wavelength filters as shown in Figure 2. We therefore argue against stellar pulsations as the origin of NaSt1's photometric variability.

Another possibility for a single-star variability origin is rotational modulation that occurs in a rare class of highly magnetized O stars with the peculiar "Of?p" classification (Walborn 1973; Howarth et al. 2007; Grunhut et al. 2017). Of?p stars exhibit near-sinusoidal variability on the order of ∼0.05 mag and are attributed to phase-dependent occulations of a wind-trapped magnetosphere (Nazé et al. 2015; Munoz et al. 2020). They can also be slow rotators with rotation periods that range from weeks to years (Nazé et al. 2015). Of?p stars also exhibit dramatic spectral variability. For example, the well-known Galactic Of?p star HD 191612 exhibits both photometric variations and strongly variable Balmer and He i lines on a 540 day period (Howarth et al. 2007). Interestingly, another Galactic Of?p star, HD 148937, is surrounded by an extended dusty and N-rich circumstellar nebula (Mahy et al. 2017), which is similar to the properties of NaSt1's nebula. The photometric variability of Of?p stars, however, is modulated by wavelength-independent electron scattering opacity from a wind-trapped magnetosphere (Munoz et al. 2020). The variability amplitudes should therefore show no significant deviations as a function of wavelength. Howarth et al. (2007) also show that the photometric variations in HD 191612 must arise from continuum-level variability rather than changes in the line emission strength. Although it is unlikely, we cannot completely rule out the Of?p phenomenon as a contributor to NaSt1's photometric variability.

Given our discussion in the previous section, we assume that NaSt1's photometric variability is associated with the orbital period of a binary system as opposed to a single-star origin. Here, we examine the possible binary origins of NaSt1's variability and the relation to its orbital period. First, we can infer some orbital properties of the binary system assuming that the orbital period is consistent with the observed 310 day variability period. Assuming a combined stellar mass in the range ∼20–100 M_⊙ for the binary and a circular orbit, a 310 day orbital period corresponds to an orbital separation of ∼2–4 au. We note that a circular orbit is expected for a system that recently underwent RLOF. The orientation of the binary system can be inferred from NaSt1's extended N-rich nebula, which exhibits a nearly edge-on geometry with an inclination angle of i = 78° ± 3° (Mauerhan et al. 2015). Figure 7 (top) shows the resolved HST imaging by Mauerhan et al. (2015) of NaSt1's N-rich nebula and our schematic illustration of the embedded central binary. In this section, we discuss three possible binary-related scenarios given NaSt1's 310 day period and smooth sinusoidal variations (Figure 7, bottom): disk eclipses, colliding-wind dust formation, and ellipsoidal variability. We acknowledge that other scenarios are also possible given the limited observational constraints, but for the sake of brevity they will not be considered here.

4.2.1. Disk Eclipses

4.2.2. Colliding-wind Dust Formation

4.2.3. Ellipsoidal Variability

4.2.4. Preferred Interpretation and Unresolved Issues

Assuming that the photometric variability is modulated by the orbital motion of a binary in NaSt1, we can speculate on its nature in the context of the mass-transfer interpretation presented by Mauerhan et al. (2015). The ∼2–4 au binary orbital separation (Section 4.1) allows us to estimate the Roche-lobe radius that the mass-donor star must have approached in order to trigger mass transfer. Adopting a binary mass ratio of 0.25–4.0, the Roche-lobe radius is in the range 140–450 R_⊙. Although such a large stellar radius might suggest an RSG mass donor, an RSG is not consistent with the high temperatures (≳30,000 K) inferred from NaSt1's high-excitation nebular emission lines and there are no spectroscopic RSG features in the the IR where its emission should be directly observable (Crowther & Smith 1999).

Crowther & Smith (1999) suggested that the highly CNO-processed composition of the nebula and the temperature of the hot ionizing source is consistent with an early-type nitrogen-rich WR (WN) star; however, they demonstrated that NaSt1 does not exhibit any broad features consistent with an early WN star. It is important to note that the absence of spectroscopic confirmation of WR features does not preclude the presence of a WR star in NaSt1. The LBV system η Car is also enshrouded by dense circumstellar material and hosts an unseen hot massive companion that is thought be a WR star (see Smith et al. 2018 and references therein).

Interestingly, Smith et al. (2020) presented observations of an Ofpe/WN9 star, which are stars that show properties intermediate between those of Of and WN stars (Walborn 1977; Bohannan & Walborn 1989), and confirmed that these types of stars can undergo an LBV-like eruption. During this eruptive phase, the radius of the Ofpe/WN9 star can expand to double the size of its quiescent radius (Smith et al. 2020). Ofpe/WN9 stars in the Galactic center exhibit radii of R_2/3 ≈ 35–80 R_⊙, which corresponds to the radius where τ_Rosseland = 2/3 (Martins et al. 2007). We therefore suggest that mass transfer in NaSt1 could have been triggered during an eruptive phase from an Ofpe/WN9 star that is now obscured or outshined by dense circumbinary or circumstellar material. The massive RLOF binary RY Scuti is also believed to have undergone past LBV-like eruptions that led to the formation of its toroidal circumstellar nebula (Smith et al. 2011b).

Earlier, van der Hucht et al. (1989, 1997) had proposed that NaSt1 may host an Ofpe/WN9 star; however, this was based only on the nebular spectrum. Crowther & Smith (1999) instead suggested that NaSt1 hosts an early-type WN star based on the high temperatures required for the ionization source of its nebula. Our Ofpe/WN9 hypothesis on the nature of NaSt1 is still consistent with the interpretation by Crowther & Smith (1999): after its eruption, the mass donor may no longer resemble an Ofpe/WN9 star and could have transitioned to a hotter, earlier-type WN phase like the Ofpe/WN9 star MCA-1B studied by Smith et al. (2020). It is also possible that envelope stripping may have led to a more advanced chemical composition than the WN phase such as the WC phase. However, the deficiency of carbon in the circumstellar environment around NaSt1 would require a very recent transition to a WC star.

We can obtain insight on the enshrouded star(s) in NaSt1 from radio observations taken by the Karl G. Jansky Very Large Array telescope in the Global View of Star Formation in the Milky Way (GLOSTAR) survey (Medina et al. 2019). Interestingly, NaSt1 exhibits a radio spectral index of α = 0.61 ± 0.10 between 4 Ghz and 8 GHz, consistent with the spectral index expected for free–free emission from an ionized stellar wind (α ≈ 0.6; Panagia & Felli 1975; Wright & Barlow 1975). Such thermal radio emission properties are commonly identified from the ionized winds of OB and WR stars (Abbott et al. 1986; Bieging et al. 1989). We can then estimate the mass-loss rate of the ionized wind given the theoretical relation between the observed radio-flux density F_ν and the stellar-wind parameters (Wright & Barlow 1975):

$$\begin{eqnarray}&&{F}_{\nu }=2.32\times {10}^{4}{\left(\displaystyle \frac{\dot{M}Z}{{v}_{\infty }\,\mu }\right)}^{4/3}{\left(\displaystyle \frac{\gamma {g}_{\nu }\nu }{{d}^{3}}\right)}^{2/3}\,\mathrm{mJy},\end{eqnarray} \tag{ 1 }$$

where $\dot{M}$ is the mass-loss rate in M_⊙ yr⁻¹, v_∞ is the wind velocity in km s⁻¹, μ is the mean molecular weight, Z is the mean ionic charge, γ is the number of electrons per ion, g_ν is the Gaunt factor at observed frequency ν, and d is the distance in kpc. In order to estimate the mass-loss rate from the NaSt1 radio counterpart, we assume that μ ≈ 4.0, which is consistent with H-poor winds, and Z = 1.1, γ = 1.1, and g_5.8 ≈ 5.0 (Leitherer et al. 1997). Given the absence of any obvious stellar emission features from NaSt1's optical and near-IR spectrum (Crowther & Smith 1999), we must provide a guess for the wind velocity associated with the radio counterpart. Since the wind is most likely ionized by a hot central WR or OB star, we adopt a wind velocity of 1000 km s⁻¹. From NaSt1's observed 5.8 GHz flux density of F_5.8GHz = 4.38 ± 0.23 mJy (Medina et al. 2019), we then estimate a mass-loss rate of

$$\begin{eqnarray}&&\dot{M}\approx 2\times {10}^{-4}\left(\displaystyle \frac{{v}_{\infty }}{1000\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right){M}_{\odot }\,{\mathrm{yr}}^{-1}.\end{eqnarray} \tag{ 2 }$$

This mass-loss rate estimate is likely uncertain by factors of a few given NaSt1's unknown wind velocity. However, we note that a mass-loss rate of ∼10⁻⁴ M_⊙ yr⁻¹ is consistent with the upper range of mass-loss rates exhibited by Galactic WN stars (Hamann et al. 2019).

In this section, we address whether NaSt1 is undergoing RLOF mass transfer assuming the observed photometric variability is modulated by the orbital motion of the interacting (or previously interacting) binary. In order to assess the current state of mass transfer, we estimate the radius of the hot, ionizing star in NaSt1 and compare it to the Roche-lobe radius (R_L ≈ 140–450 R_⊙) derived above.

First, we obtain an estimate of the stellar luminosity from NaSt1's observed brightness V = 14.4 mag. By adopting the interstellar and/or circumstellar extinction correction toward NaSt1 by Crowther & Smith (1999) of A_V = 6.5 mag and using the Gaia-derived distance of d = 3.03 kpc (Rate & Crowther 2020), the absolute magnitude of NaSt1 is M_V = −4.5. The 30,000 K lower limit of the temperature derived for the ionizing source in NaSt1 by Crowther & Smith (1999) from optical spectroscopy implies a bolometric correction is BC_V = −3 mag, which indicates a stellar luminosity of L ≈ 7.9 × 10⁴ L_⊙. The radius of such a 30,000 K star would be R_* ≈ 10 R_⊙, an order of magnitude less than the estimated Roche-lobe radius. Stellar temperatures higher than 30,000 K will require larger bolometric corrections and thus lead to higher stellar luminosities; however, the resulting radii will be smaller than that of the 30,000 K star. For example, a star with a temperature of 200,000 K, which is the upper limit of the ionizing source temperature derived by Crowther & Smith (1999), would imply a luminosity of L ≈ 3.1 × 10⁶ L_⊙ and a stellar radius of R_* ≈ 1.5 R_⊙ given the appropriate bolometric correction of BC_V = −7 mag. Based on these constraints, we suggest that NaSt1 is not currently undergoing binary mass transfer.