Detection of the longest periodic variability in 6.7 GHz methanol masers G5.900$-$0.430

High-mass stars have significant impact on their surrounding environment through various feedback mechanisms, e.g., stellar winds, ultraviolet radiation, and supernovae. However, our understanding of the formation processes of high mass stars remains inadequate, hampered by the observational difficulties of their birth in distant, very deeply embedded dense gas. The Class II 6.7 GHz methanol maser is a well-known tracer of high-mass star-forming regions (HMSFRs) (e.g, Menten 1991; Minier et al. 2003; Pandian et al. 2007; Breen et al. 2013). Emission arises in most cases from regions of an interface between the protostellar disk and envelope at a typical distance of $\sim$1000 au from a protostar (Bartkiewicz et al. 2016). The 6.7 GHz maser is sensitive to the local physical conditions around high-mass protostars (e.g., Cragg, Sobolev, and Godfrey 2005; Sugiyama et al. 2008; Moscadelli et al. 2017; Burns et al. 2020), and thus is an excellent observational probe to study the high-mass star formation process.

Goedhart et al. (2003) first discovered a periodic flux variation of 243.3 days in the 6.7 GHz methanol masers associated with HMSFR G9.62$+$0.20E. Another 27 periodic methanol maser sources have been reported (Goedhart et al. 2004, 2009, 2014; Szymczak et al. 2011, 2014, 2015, 2016; Araya et al. 2010; Fujisawa et al. 2014; Maswanganye et al. 2015, 2016; Sugiyama et al. 2015, 2017; Proven-Adzri et al. 2019; Olech et al. 2019, 2022), and their periods range from 23.9 to 668 days. Systematic monitoring observations toward large sample have contributed significantly to the discovery of maser periodicity (e.g., Goedhard et al. 2004; Sugiyama et al. 2018; Szymczak et el. 2018; Olech et al. 2022). The variation pattern in the time series of the 6.7 GHz methanol maser are classified into two types: continuous (e.g., G188.95$+$0.89 reported by Goedhard et al. 2014) and intermittent (e.g., IRAS 22198$+$6336$=$G107.298$+$0.5639 reported by Fujisawa et al. 2014). Such differences in variation patterns are thought to be due to differences in the origin of 6.7 GHz maser periodicity. The mechanism of these maser periodicity remains an open question, and several explanations have been proposed; colliding wind binary (CWB) system (van der Walt 2011; van der Walt et al. 2016), protostellar pulsation (Inayoshi et al. 2013), spiral shock (Parfenov & Sobolev 2014), periodic accretion in a circumbinary system (Araya et al. 2010), or a very young low-mass companion blocking the ultraviolet radiation from the high-mass star in an eclipsing binary (Maswanganye et al. 2015). These models can explain the maser fluctuations of some sources well, however, there is no clear consensus.

In this paper, we present the new discovery of periodicity in 6.7 GHz methanol maser source in HMSFR G5.900$-$0.430, and discuss the mechanism of its flux variability.

Monitoring observations of the 6.7 GHz methanol maser were made with the Hitachi 32m telescope of Ibaraki station, a branch of the Mizusawa VLBI Observatory of the National Astronomical Observatories Japan (NAOJ), operated jointly by Ibaraki University and NAOJ (Yonekura et al. 2016). This is as a part of the Ibaraki 6.7 GHz Methanol Maser Monitor (iMet) program¹¹1http://vlbi.sci.ibaraki.ac.jp/iMet/.

Monitoring observations of G5.900$-$0.430 began on 2013 Jan. 03 (modified julian day (MJD) $=$ 56295). The cadence of observations is once par every $\sim$10 days from the start of the monitoring observations to 2015 Aug. 08 (MJD $=$ 57242), and once par every $\sim$5 days from 2015 Sep. 19 (MJD $=$ 57284) to the present. Observations after 2014 May 08 (MJD = 56785) were made at about the same azimuth ($\sim$187$\degree$) and elevation angle ($\sim$27$\degree$) to minimise intensity variations due to systematic telescope pointing errors. The half-power beam width of the telescope is $\sim$ \timeform4.6’ with the pointing accuracy better than $\sim$ \timeform30”. The coordinates of G5.900$-$0.430 adopted in observations are ${\rm R.A.}=$ \timeform18h00m 40s.86, Dec. $=$ \timeform-24D04’20.8” (J2000.0) (Caswell 2009; Caswell et al. 2010).

Observations are made by using a position-switching method. The OFF position is set to $\Delta{\rm R.A.}=+\ \timeform{60^{\prime}}$ from the target source. The integration time per observation is 5 minutes for both the ON and OFF positions. A single left circular polarization (LCP) signal was sampled at 64 Mbps (16 mega-samples per second with 4 bit sampling) by using a K5/VSSP32 sampler. The recorded bandwidth is 8 MHz (RF:6664-6672 MHz) and they are divided into 8192 channels. After averaging over 3 channels, the 1-sigma root-mean-squares noise level is approximately 0.3 Jy and the velocity resolution is 0.13 km s^-1. The antenna temperature was measured by the chopper-wheel method and the system noise temperature toward the zenith after the correction for the atmosphere opacity (${T}^{*}_{\rm sys}$) is typically 25–35 K. In our monitoring program, we observe $\sim$60 methanol maser sources per day, of which the variation of the flux density of sources that do not show the intrinsic variation are less than $\sim$20%.

The averaged spectrum and dynamic spectrum compiling all 437 scans of G5.900-0.430 is presented in Figures 1 and 2. In this source, seven velocity features are distributed from $V_{\rm LSR}$ $\sim$0 km s^-1 to $\sim$14 km s^-1. According to Caswell et al. (2010), the 6.7 km s^-1 feature (C and D in Figure 1) is associated with HMSFR G5.885$-$0.393, approximately 2.3 arcmin apart from G5.900$-$0.430. Therefore we exclude these features from the discussion below.

The results of periodicity analysis are summarized in Figures 3, 4 and Table 1. The periodicity was estimated eby mploying the Lomb-Scargle (LS) periodogram method (Lomb 1976 and Scargle 1982) and the asymmetric power function given by the equation adopted from Szymczak et al. (2011):

$$S(t)=C\times{\rm exp}^{s(t)}+D,$$

(1)

where C and D are constants and

$$s(t)=\frac{-B\ {\rm cos}(2\pi\frac{t}{P}+\phi)}{1-f\ {\rm sin}(2\pi\frac{t}{P}+\phi)}+A\ .$$

(2)

Here A and B are constants, P is the period, $\phi$ is the phase at $t=0$, and $f$ is the asymmetric parameter defined as the rise time from the minimum to the maximum flux (Szymczak et al. 2011). When $f=0$, the power function is symmetric with respect to the peak. The error of periods obtained by the LS method are estimated as the half width of half maximum (HWHM) of each peak in the periodgram.

A periodic and intermittent profile is found at 0.66 km s^-1 feature (A in Figure 1). Periods of 130.6$\ \pm\$2.8 and 65.2$\ \pm\$0.7 days were determined from the LS periodicity analysis. Note the latter appears to be a harmonic of the former, i.e. $P=$130.6/n where n = 2. In fact in figure 5, almost no flares can be detected in the period of 65.3 days (dashed line), which is half of 130.6 days (solid line). Thus the 130.6 days is the most plausible period for 0.66 km s^-1 feature. An asymmetric power function fitting determines a value of $P_{\rm fit}=$130.5 $\ \pm\$ 0.1 days and $f=$0.73. The periods obtained by the two methods are within the errors measured. The value of $f$ suggests that the 0.66 km s^-1 feature experiences an asymmetrical temporal flux density variation; a rapid onset followed by a slower decline. The HWHM of rising and decaying time obtained directly from fitting results are 8.16 and 13.88 days, respectively.

As shown in Figure 5, during our monitoring observation, there were 3 cases where no flares were detected at the expected flare date. In the first two of these three cases, observations were not made within 5 days before and after the expected flare date due to maintenance or other reasons. In the third case, we detected emissions with flux density of 2.5$\sigma$ and 2.6 $\sigma$ at 2 days before and 3 days after the expected flare date (MJD $=$ 59607), respectively, but no emissions above 3$\sigma$.

The 4.35 km s^-1 feature (B in Figure 1) is generally below detection limits after MJD $=$ 57363, and no periodicity is detected for this feature.

The 9.77 km s^-1 and 10.84 km s^-1 features (E and F in Figure 1) experience very long and continuous flux variation. The estimated period from LS method and power function fitting for 9.77 km s^-1 feature are 1264.9$\ \pm\$265.5 days and 1260.3 $\ \pm\$8.6 days, respectively, and those for 10.84 km s^-1 feature are 1264.9$\ \pm\$324.3 days and 1260.7$\ \pm\$9.6 days, respectively. The periods of each velocity features obtained by the two methods are consistent within the estimated errors. The results of fitting show that the flux variation of these features are symmetric with $f=$ -0.20 and -0.11 for 9.77 and 10.84 km s^-1, respectively.

MacLeod et al. (2022) detected periodic flux variation of maser features with two different periods in HMSFR G9.62$+$0.20E. According to MacLeod et al. (2022), G9.62$+$0.20E has secondary period of 52 days for 8.8 km s^-1 feature, along with the previously reported period of 243 days for another features. G5.900$-$0.430 may be the second example which has a secondary period. The temporal profiles of the 8.8 km s^-1 feature and the others are quite different, intermittent and continuous, respectively. This is similar to the present results for G5.900$-$0.430. On the other hand, the relationship in the flux variation profiles and the periods shows a completely opposite trend. In G5.900$-$0.430, the feature with a long period shows a continuous profile and the feature with a short period shows an intermittent profile, whereas in G9.62$+$0.20E has opposite tendency.

We present the new periodic 6.7 GHz methanol maser source G5.900$-$0.430, detected from long-term monitoring observations conducted by Ibaraki University. Periodic flux variabilities was detected at three velocity features among four in this source. The obtained periods are 130.6 days for low-velocity feature and $\sim$1260 days for two high velocity features. The period of 1260 days is the longest ever found. From the intermittent and asymmetric variability profile, the low-velocity feature is likely to be explained by the CWB model or spiral shock model, while the continuous and symmetric variation of the high-velocity features are likely to be caused by the protostellar pulsation. Consistency with the expected period-luminosity relation also supports the pulsation as the cause of the periodic variation of the high-velocity components. Simultaneous VLBI observations of the high-velocity and low-velocity components during the active phase of 0.66 km s^-1 feature will lead to a better understanding of the nature of this source.

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The authors are grateful to all the staff and students at Ibaraki University who have supported observations of the Ibaraki 6.7 GHz Methanol Maser Monitor (iMet) program. This work is partially supported by the Inter-university collaborative project “Japanese VLBI Network (JVN)” of NAOJ and JSPS KAKENHI Grant Numbers JP24340034, JP21H01120, and JP21H00032 (YY).