A kinematic analysis of the giant molecular complex W3: Possible evidence for cloud–cloud collisions that triggered OB star clusters in W3 Main and W3(OH)

Abstract

W3 is one of the most outstanding regions of high-mass star formation in the outer solar circle, and includes two active star-forming clouds: W3 Main and W3(OH). Based on a new analysis of the |${^{12}\text{CO}(J = 2-1)}$| data obtained at |$38^{\prime \prime }$| resolution, we have found three clouds that have molecular masses from 2000 to |$8000\, {M_\odot }$| at velocities |$-50\:\rm{km\: s^{-1}}$|⁠, |$-43\:\rm{km\:s^{-1}}$|⁠, and |$-39\:\rm{km\:s^{-1}}$|⁠. The |$-43\:\rm{km\:s^{-1}}$| cloud is the most massive one, overlapping with the |$-39\:\rm{km\:s^{-1}}$| cloud and the |$-50\:\rm{km\:s^{-1}}$| cloud toward W3 Main and W3(OH), respectively. In W3 Main and W3(OH), we have found typical signatures of a cloud–cloud collision, i.e., the complementary distribution with/without a displacement between the two clouds and/or a V-shape in the position–velocity diagram. We frame a hypothesis that a cloud–cloud collision triggered the high-mass star formation in each region. The collision in W3 Main involves the |$-39\:\rm{km\:s^{-1}}$| cloud and the |$-43\:\rm{km\:s^{-1}}$| cloud. The collision likely produced a cavity in the |$-43\:\rm{km\:s^{-1}}$| cloud that has a size similar to the |$-39\:\rm{km\:s^{-1}}$| cloud and triggered the formation of young high-mass stars in IC 1795 |$2\:$|Myr ago. We suggest that the |$-39\:\rm{km\:s^{-1}}$| cloud is still triggering the high-mass objects younger than |$1\:$|Myr currently embedded in W3 Main. On the other hand, another collision between the |$-50\:\rm{km\:s^{-1}}$| cloud and the |$-43\:\rm{km\:s^{-1}}$| cloud likely formed the heavily embedded objects in W3(OH) within |$\sim\! 0.5\:$|Myr ago. The present results favour an idea that cloud–cloud collisions are common phenomena not only in the inner solar circle but also in the outer solar circle, where the number of reported cloud–cloud collisions is yet limited (Fukui et al. 2021, PASJ, 73, S1).

1 Introduction

1.1 High-mass star formation

High-mass stars are important in our understanding of galaxy evolution because their influence on the interstellar medium is substantial via ultraviolet radiations, stellar winds, and supernova explosions. It was argued in the literature that the interstellar medium can form low to high-mass stars under the combined effects of turbulence, magnetic field, and gravity (for a review, see McKee & Ostriker 2007), whereas it was not directly shown that these effects alone can realize the formation of high-mass stars and massive clusters. It was also argued that the formation of high-mass stars may require some extra mechanism different from or additional to the mechanism for low-mass star formation (Zinnecker & Yorke 2007). The initial gas condition for star formation, for instance, may be a critical factor in order to realize the formation of high-mass stars. Numerical simulations have shown that the competitive accretion model (Bonnell et al. 2003) or the monolithic collapse model (Krumholz et al. 2009) are possible mechanisms, although they are not readily comparable with the observations. This is because the key signatures for comparison with observations are not always clearly pinpointed by the theoretical studies, allowing much room in the interpretation of observations.

In the competitive accretion model, the initial condition is a massive cloud-star system of more than a few |$1000\, \rm{M_\odot }$| where individual stars compete to acquire mass gravitationally, although the model fails to explain the formation of an isolated small-mass system including one or a few O stars which are distributed widely in the Galaxy (for a review see, e.g., Fukui et al. 2021a; Ascenso 2018). The monolithic collapse model assumes an initial condition including “a massive gas cloud of 100|$\, \rm{M_\odot }$| within a radius of 0.1 pc”, and it was numerically demonstrated that high-mass stars of 40 and |$30\, \rm{M_\odot }$| in a binary are formed (Krumholz et al. 2009). However, it remains an open question how such massive, dense initial clouds are prepared in interstellar space. The dense core has to be rapidly formed before the core is consumed by low-mass star formation. It has also been discussed in the literature that high-mass stars are formed in massive hot cores or in infrared dark clouds having very high column density (e.g., Egan et al. 1998). It is, however, a puzzle that they are not always associated with |${\small{H ii}}$| regions, which must be formed by O/early B stars, raising a doubt if they are real precursors of high-mass star formation (Tan et al. 2014). See also Motte, Bontemps, and Louvet (2018) for a review of relevant observations.

Another possibility to resolve the issue is external triggers to compress gas and induce star formation, which is called the triggered star formation. A model of such a trigger is the gas compression by expanding |${\small{H ii}}$| regions forming next-generation subgroups of OB associations, which is called the sequential star formation (Elmegreen & Lada 1977). According to the model, once high-mass stars are formed by a certain (unknown) mechanism, the stars can compress the surrounding gas by the stellar feedback to a gravitationally unstable gas layer, where the next-generation high-mass stars are formed. The trigger continues to form high-mass stars until the gas is exhausted, and the model may explain the age sequence of subgroups in OB associations such as those observed in Orion (Blaauw 1964). Another triggering mechanism is a cloud–cloud collision (CCC) between two clouds that have supersonic velocity separation. In this scheme, the gas is compressed in the interface layer between the clouds to a gravitationally unstable state, leading to the formation of high-mass stars. This mechanism explains the formation of high-mass stars in a state initially without high-mass stars, and also explains the distribution and age of all the high-mass stars involved as caused by the configuration of the two clouds; it is distinct from the sequential star formation, which assumes the first generation high-mass stars.

CCCs were proposed in 1950–1960 (Oort 1954; Oort & Spitzer 1955). Based on the optical spectroscopy of stellar absorption lines, Oort (1954) suggested that collisions between the interstellar clouds take place at a supersonic velocity of 10–|$15\:\rm{km\:s^{-1}}$|⁠. In NGC 1333, Loren (1976) observed two CO components of different velocities separated by |$2\:\rm{km\:s^{-1}}$| and proposed that a collision between two CO components triggered the star formation in NGC 1333. Numerical simulations of a CCC by Habe and Ohta (1992) demonstrated that the collision between two clouds of different sizes plays a role in efficiently compressing the gas to trigger star formation, which was supported by follow-up simulations by Anathpindika (2010) and Takahira et al. (2014). The simulations were refined by incorporating the magnetic field by Inoue and Fukui (2013) and Inoue et al. (2018), which showed that collisions are an effective process to trigger the formation of massive dense cores, a precursor of the high-mass star(s). Recently, Fukui et al. (2021b) compared these theoretical results with observations of CCCs and showed that the top-heavy mass spectra of the dense cores are consistent with observations. Fukui et al. (2021a) summarized the observational and theoretical understandings of star formation triggered by CCCs based on more than 50 candidate objects, which covers a wide range of the stellar mass from a single O star to massive clusters of |$10^{6}\, \rm{M_\odot }$| discovered by extensive CO surveys of our Galaxy and the Local Group members. Consequently, recent studies favour CCCs as an important mechanism of high-mass star formation rather than the turbulent clouds without external triggers.

1.2 W3 giant molecular complex

W3 is a radio continuum source discovered by Westerhout (1958) and is an |${\small{H ii}}$| region complex associated with a giant molecular complex (GMC; for a review, see Megeath et al. 2008). Located in the Perseus Arm at a distance of |$2\:$|kpc (Navarete et al. 2019), W3 is the most active site of star formation in the Perseus Arm (Ogura & Ishida 1976; Oey et al. 2005; Navarete et al. 2011, 2019; Kiminki et al. 2015), showing exceptionally active star formation in the outer solar circle. W3 is continuous to another |${\small{H ii}}$| region named W4 corresponding to Perseus/Chimney superbubble (Dennison et al. 1997) along the Galactic plane. In the boundary between W3 and W4, there is a high-density layer (HDL), which is a molecular layer nearly vertical to the Galactic plane (Lada et al. 1978). The HDL harbours several star-forming regions such as W3 Main, W3(OH), and AFGL 333, as well as diffuse the |${\small{H ii}}$| region IC 1795 and the more compact, bright |${\small{H ii}}$| region NGC 896. Each of these regions is associated with young stellar clusters with ages younger than |$5\:$|Myr, indicating recent star-forming activity.

Stellar clusters in the HDL have an age difference of a few Myr. The stellar cluster in IC 1795 is not associated with molecular gas but is associated with ionized gas, whereas OB stars in W3 Main and W3(OH) are deeply embedded in dense molecular material. According to the spectroscopic observations (Oey et al. 2005), OB stars in IC 1795 have ages of 3–|$5\:$|Myr, while the age determination has uncertainties due to the assumption of stellar evolution models and extinction law. The primary source of the ionization in IC 1795 is BD |$+$|61 411, an O6.5V star (Oey et al. 2005). W3 Main is associated with the most massive cluster in W3, which has a total stellar mass of |$4000\, \rm{M_\odot }$| according to the near-infrared observations (Bik et al. 2012). The members of the cluster are approximately 10 OB stars, hyper-compact and ultra-compact |${\small{H ii}}$| regions, as well as cold prestellar cores, which are localized within a diameter of |$\sim\! 3\:$|pc (Claussen et al. 1994; Tieftrunk et al. 1997; Bik et al. 2012; Mottram et al. 2020). In particular, the infrared source IRS 5 in W3 Main is known to harbor a trapezium-like cluster (Abt & Corbally 2000; Megeath et al. 2005; Rodón et al. 2008). In the W3(OH) region, OH masers and H|$_2$|O masers are localized within less than |$0.1\:$|pc (Forster et al. 1977; Reid et al. 1980). The OH maser is excited by an O9 star (Hirsch et al. 2012) and is associated with an ultra-compact |${\small{H ii}}$| region with a diameter of |$0.012\:$|pc. Further, five early-type stars of B0–B3 are distributed in the W3(OH) region (Navarete et al. 2011, 2019; Bik et al. 2012; Kiminki et al. 2015).

The sequential star formation model (Elmegreen & Lada 1977) has been discussed in W3 as a large-scale process of star formation. Lada et al. (1978) made a large-scale CO survey of the W3/W4/W5 region at |$8^{\prime }$| resolution covering over |$50\:$|pc in the |$^{12}$|CO(⁠|$J = 1$|–0) emission and proposed the sequential star formation. These authors discovered and mapped the HDL and found that the HDL is forming stars younger than those in W4 by |$\sim\! 10\:$|Myr, and suggested that the next generation stars were formed by the trigger of the expansion of W4. Oey et al. (2005) performed the UBV photometry and derived the age distribution of the stars in IC 1795. These authors proposed that W4 (stellar age |$\sim\! 20\:$|Myr) triggered the star formation in IC 1795 (stellar age |$\sim\! 3$|–|$5\:$|Myr), and IC 1795 triggered the star formation in W3 Main and W3(OH). The authors named the whole process “hierarchical triggering.”

Recent higher-resolution observations at multi-wavelengths, however, indicate that these simple pictures of sequential star formation may not work from distributions of stars and stellar ages. Feigelson and Townsley (2008) extensively studied stars of the low-mass populations with the Chandra X-ray satellite in W3 Main, IC 1795, and W3(OH). As a result, the authors agreed that stars in W3(OH) might have been triggered by IC 1795. On the other hand, the cluster of young stellar objects (YSOs) in W3 Main shows a large, spherical, centrally-condensed distribution, which was not interpreted as a consequence of the trigger by IC 1795.

Bik et al. (2012, 2014) conducted infrared photometry using the LBT (Large Binocular Telescope) Near Infrared Spectroscopic Utility with Camera and Integral Field Unit for Extragalactic Research (LUCI). As a result, these authors suggested that star formation in W3 Main began 2–|$3\:$|Myr ago, and is continuing until now, causing a dispersion in age of a few Myr. It was also shown that the youngest stars lie in the central part of the cluster. Further, these authors suggested that feedback from the older stars in the W3 Main region does not propagate deeply into dense clouds, by more than |$0.5\:$|pc, probably due to higher initial gas density even after a few Myr after the cluster formation, and does not influence the cluster formation as a whole.

Román-Zúñiga et al. (2015) carried out an extensive study of the YSO age distribution through a new |$JHK$| imaging by using the Calar Alto Observatory 3.5 m telescope combined with the Chandra Source Catalog, mosaics of SPIRE and PACS on board Herschel, and Bolocam |$1.1\:$|mm mosaic observations. These authors showed that there are many Class II sources in IC 1795 in spite of the molecular gas being largely dispersed already, and suggested that star formation has been very active until about |$2\:$|Myr ago. In addition, it was shown that W3 Main and W3(OH) include a stellar population with an age of more than |$2\:$|Myr. Based on these results, the authors concluded that it is hard to explain that the star formation in W3 Main and W3(OH) was triggered by stellar feedback from IC 1795 because of the lack of significant age difference among the ages of IC 1795, W3 Main, and W3(OH).

These previous works presented doubts about the sequential star formation model, but an alternative star formation scenario based on CO observation and analysis of gas kinematics is not provided. It therefore remains an open issue on how star formation took place in IC 1795, W3 Main, and W3(OH).

1.3 The aim of the present paper

Star formation in W3 has not been fully understood yet, in part due to the lack of a comprehensive study of the detailed gas kinematics. Recent studies extensively revealed the stellar properties in the region, which include both high-mass and low-mass stars at submillimetre and X-rays, as well as the deeply embedded stars. However, molecular gas kinematics has not been investigated deeply in spite of the high resolution and wide-field mapping of CO, and the other tracers have become available in the last two decades. We therefore commenced a systematic study of the molecular gas obtained by Bieging and Peters (2011) with the Heinrich Hertz Sub-millimeter Telescope (HHT), which is employed using the analysis tools of gas kinematics developed in the last decade by the Nagoya group on the molecular clouds (Fukui et al. 2021a): e.g., velocity channel distribution, position–velocity diagram, and separation of individual clouds. In the study, we aim to reveal a star formation mechanism that is dominant in W3 by utilizing the gas kinematic details and exploring its implications for high-mass star formation. Since the AFGL 333 region was investigated by Nakano et al. (2017) and Liang et al. (2021), we will deal with that region in the present paper.

This paper is organized as follows: Section 2 describes the datasets employed and section 3 gives the results of the present kinematical analysis. In section 4 we discuss the high-mass star formation in IC 1795, W3 Main, and W3(OH), and conclude the paper in section 5. We use the Galactic coordinate to depict directions; for example, “north” means “Galactic north” in this paper. We refer to the local standard of rest velocity (⁠|$\rm{V_\mathrm{LSR}}$|⁠) through the entire article.

2 Datasets

We used the |$J = 2$|–1 line of |$^{12}$|CO and |$^{13}$|CO archived data observed with HHT at the Arizona radio observatory (Bieging & Peters 2011). Observations were carried out in 2005 June to 2008 April. They used the on-the-fly (OTF) method to map a region of |$2.^{\!\!\!\circ}00$| times |$1.^{\!\!\!\circ}67$| square degrees. The map center was |$(l, b) = (133.^{\!\!\!\circ} 50, 0.^{\!\!\!\circ} 835)$|⁠. All the data were convolved to a spatial resolution of |$38^{\prime\prime}$|⁠. The velocity resolution is |$1.30\:\rm{km\:s^{-1}}$| at |$^{12}$|CO and |$1.36\:\rm{km\:s^{-1}}$| at |$^{13}$|CO, while they chose a common sample velocity of |$0.5\:\rm{km\:s^{-1}}$|⁠. The typical root-mean-square (RMS) noise temperatures of the |$^{12}$|CO emission and |$^{13}$|CO emission are |$0.12\:$|K and |$0.14\:$|K, respectively. We prefer to use |$^{12}$|CO mainly instead of |$^{13}$|CO in the present work because |$^{12}$|CO can better trace the low-density extended molecular gas. This is crucial in identifying the cloud interaction, as it may be saturated in small dense regions.

3 Results

3.1 The overall distributions of the molecular gas

Figure 1a depicts a pseudo-color image taken with Herschel¹/PACS at wavelengths of |$70\, \mu$|m (blue) and |$160\, \mu$|m (green), along with Herschel/SPIRE at |$250\, \mu$|m (red) (Rivera-Ingraham et al. 2013). The whole W3 GMC is dominated by the red color at |$250\, \mu$|m, while the areas around IC 1795, W3 Main, W3(OH), and AFGL 333 are bluer, indicating local dust heating due to nearby high-mass stars. Spectroscopically identified OB stars (Oey et al. 2005) are plotted as black crosses and show correspondence with “bluer” regions.

Figure 1b shows the integrated intensity of the |${^{12}\rm{CO}(J = 2-1)}$| emission. The diffuse gas is extended over the area, and three regions in the north-east-east edge of the cloud show intense |${^{12}\rm{CO}(J = 2-1)}$| emission, corresponding to the HDL where W3 Main, W3(OH), and AFGL 333 are located (Lada et al. 1978). W3 Main has the most prominent peak at |$(l, b) \sim (133.^{\!\!\!\circ} 70, 1.^{\!\!\!\circ} 22)$| with an integrated intensity of |$450\:\rm{K\:km\:s^{-1}}$|⁠, and most of the O stars in W3 are distributed within |$10\:$|pc of the peak position. W3(OH) at |$(l, b) \sim (133.^{\!\!\!\circ} 95, 1.^{\!\!\!\circ} 07)$| has an integrated intensity of |$300\:\rm{K\:km\:s^{-1}}$| and is associated with the OH and H|$_2$|O masers (Forster et al. 1977; Reid et al. 1980) as well as a few OB stars. AFGL 333 has the weakest integrated intensity among the three and is connected to W4 on the eastern edge. The HDL has a clear molecular cavity at |$(l, b) \sim (133.^{\!\!\!\circ} 80, 1.^{\!\!\!\circ} 13)$| and coincides with an |${\small{H ii}}$| region IC 1795 powered by an O6 star called BD |$+$|61 411 (Mathys 1989). The |${\small{H ii}}$| region corresponds to the “bluer” area in figure 1a, where we can see the intense |$70\, \mu$|m emission.

Figure 2 shows the velocity channel distributions of the W3 region. The distribution shows significant variation in velocity; the gas at |$\rm{V_{LSR}}= -54$| to |$-45\:\rm{km\:s^{-1}}$| (upper panels) is distributed in the southeastern part, while the gas at |$\rm{V_{LSR}}= -45$| to |$-36\:\rm{km\:s^{-1}}$| (lower panels) is distributed in the northwestern region. The two velocity components have different velocity ranges with the boundary at |$\rm{V_{LSR}}\sim -45\:\rm{km\:s^{-1}}$|⁠. The three peaks of the |$^{12}$|CO integrated intensity W3 Main, W3(OH), and AFGL 333 also show different velocity ranges at |$\rm{V_{LSR}}= -45$| to |$-36\:\rm{km\:s^{-1}}$|⁠, |$\rm{V_{LSR}}= -51$| to |$-42\:\rm{km\:s^{-1}}$|⁠, and |$\rm{V_{LSR}}= -54$| to |$-45\:\rm{km\:s^{-1}}$|⁠, respectively.

Figure 3 shows Galactic longitude–velocity diagrams of the W3 region. Figure 3a is for the |${^{12}\rm{CO}(J = 2-1)}$| emission, and figure 3b is for the |${^{13}{\rm CO}(J = 2-1)}$| emission, where the two diagrams show similar distributions. Specifically, W3 Main and W3(OH) show complex velocity distribution. W3 Main shows a velocity difference of 3–|$4\:\rm{km\:s^{-1}}$| between |$l = 133.^{\!\!\!\circ} 65$| and |$l = 133.^{\!\!\!\circ} 85$|⁠, and W3(OH) shows a velocity shift of |$\sim\! 4\:\rm{km\:s^{-1}}$| at |$l = 133.^{\!\!\!\circ} 85$| from the peak position at |$l = 133.^{\!\!\!\circ} 95$|⁠. In the following, we shall focus on the two peaks in W3 Main and W3(OH) and analyse their detailed distributions.

Figure 4a shows the integrated intensity distribution of the W3 Main and W3(OH) regions, where the brightest peak corresponds to W3 Main. About 10 O stars (white circles), including BD |$+$|61 411 (magenta cross), are concentrated in the W3 Main regions. The |${\small{H ii}}$| regions IC 1795 and NGC 896 correspond to the cavity of the molecular gas. We see that the OB stars (Navarete et al. 2011, 2019; Bik et al. 2012) are distributed toward the centre of IC 1795 and W3 Main. BD |$+$|61 411(O6.5V), the earliest type member of the IC 1795 cluster, is located inside the molecular cloud cavity toward IC 1795. IRS 2, the most massive star in W3, is associated with W3 Main (Bik et al. 2012). The molecular cavity coincides with these |${\small{H ii}}$| regions, whereas BD |$+$|61 411 has an offset from the centre of the |${\small{H ii}}$| region overlapping with the cavity. In the W3(OH) region, the molecular emission peak at |$(l, b) = (133.^{\!\!\!\circ} 95, 1.^{\!\!\!\circ} 07)$| is associated with an OH maser (Forster et al. 1977; Reid et al. 1980). Five O stars are within |$5\:$|pc of W3(OH).

Figure 4b shows the distribution of the first moment calculated from a velocity range of |$\rm{V_{LSR}}= -55$| to |$-35.0\:\rm{km\:s^{-1}}$|⁠. Only the voxels with intensity greater than |$6\, \times$|  |$T_\mathrm{rms} = 0.72\:$|K are included. Most of the emission is in a velocity range of |$\rm{V_{LSR}}= -45.5$| to |$-42.0\:\rm{km\:s^{-1}}$|⁠, whereas redshifted emission is seen at |$\rm{V_{LSR}}= -40.5$| to |$-37.0\:\rm{km\:s^{-1}}$| with a size of |$\sim\! 5\:$|pc in the east of W3 Main. On the other hand, in the W3(OH) region, the radial velocity of the gas is in a range |$\rm{V_{LSR}}= -53.0\:\rm{km\:s^{-1}}$| to |$-46.5\:\rm{km\:s^{-1}}$| on the eastern side, showing a clear velocity shift along the CO cloud elongation of the W3(OH) region.

Figures 5a to 5f show typical CO spectra in the W3 Main and W3(OH) regions, respectively. In the W3 Main region, the CO spectra are peaked in a velocity range of |$\rm{V_{LSR}}= -40.5$| to |$-37\:\rm{km\:s^{-1}}$| and/or |$\rm{V_{LSR}}$| = |$-45.5$| to |$-42.0\:\rm{km\:s^{-1}}$|⁠. In particular, in panel b at |$(l, b) = (133.^{\!\!\!\circ} 69, 1.^{\!\!\!\circ} 29)$|⁠, |$^{12}$|CO and |$^{13}$|CO spectra have a double peak in the two velocity ranges, indicating that two clouds are overlapped. Similarly, in the W3(OH) region, the CO cloud has two peaks in velocity ranges of |$\rm{V_{LSR}}= -53.0$| to |$-46.5\:\rm{km\:s^{-1}}$| and |$\rm{V_{LSR}}= -45.5$| to |$-42.0\:\rm{km\:s^{-1}}$|⁠, while |$^{12}$|CO and |$^{13}$|CO spectra have a double peak in panel e at |$(l, b) = (133.^{\!\!\!\circ} 94, 1.^{\!\!\!\circ} 02)$|⁠, indicating that two clouds are overlapped. The redshifted component in W3(OH) and the blueshifted component in W3 Main are part of a common, coherent component, as seen by the first moment (figure 4). Hence, the W3 Main and W3(OH) regions consist of three clouds, and we hereafter call |$\rm{V_{LSR}}= -40.5$| to |$-37.0\:\rm{km\:s^{-1}}$|⁠, |$\rm{V_{LSR}}= -45.5$| to |$-42.0\:\rm{km\:s^{-1}}$|⁠, and |$\rm{V_{LSR}}= -53.0$| to |$-46.5\:\rm{km\:s^{-1}}$| components the |$-39\:\rm{km\:s^{-1}}$|⁠, |$-43\:\rm{km\:s^{-1}}$|⁠, and |$-50\:\rm{km\:s^{-1}}$| clouds, respectively.

Figures 6a, 6b, and 6c show the integrated intensity distributions of the |$-39\:\rm{km\:s^{-1}}$|⁠, |$-43\:\rm{km\:s^{-1}}$|⁠, and |$-50\:\rm{km\:s^{-1}}$| clouds, respectively. We find that the |$-39\:\rm{km\:s^{-1}}$| cloud is compact, and its shape fits approximately the cavity of the |$-43\:\rm{km\:s^{-1}}$| cloud corresponding to IC 1795. The |$-50\:\rm{km\:s^{-1}}$| cloud is not distributed in the W3 Main region and is concentrated toward the W3(OH) region. Figure 7 shows an overlay of the three clouds, and the image of the |$-43\:\rm{km\:s^{-1}}$| cloud is superimposed over the |$-39\:\rm{km\:s^{-1}}$| (red contour) and |$-50\:\rm{km\:s^{-1}}$| (blue contour). The |$-39\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds overlap in the W3 Main region, while the |$-43\:\rm{km\:s^{-1}}$| and |$-50\:\rm{km\:s^{-1}}$| clouds overlap in the W3(OH) region. Thus, the two regions with significantly active star formation are the regions where the two clouds overlap.

Figure 8a shows the overlay of the three clouds, which are rotated by |$71^{\circ }$| counterclockwise relative to the Galactic plane centered on IRS 2. Figure 8b shows a position–velocity diagram along the horizontal axis in figure 8a. We find significant line broadening localized toward the CO peak at offset–|$X\sim\! 0.^{\!\!\!\circ }0$|⁠, indicating blue and red lobes of molecular outflows as mentioned by previous studies (e.g., Phillips & White 1988). The wings extend on both the redshifted and blueshifted sides, making it appear bipolar in the present beam, but in reality, the driving sources are different between the red lobe and the blue lobe; the blue lobe is associated with W3 IRS 4, while the red lobe is associated with IRS 5 (Phillips & White 1988). In addition to the broad linewidth, differences in the velocities of CO clumps associated with the infrared sources of W3 IRS 4 and W3 IRS 5 have been reported (Thronson et al. 1985). W3 IRS 5 corresponds to the peak at a velocity of approximately |$\rm{V_{LSR}}= -40\:\rm{km\:s^{-1}}$| for offset–|$X\simeq 0.^{\!\!\!\circ }01$| in figure 8b, while the peak at offset–|$X\simeq -0.^{\!\!\!\circ }01$| with a velocity of |$-43\:\rm{km\:s^{-1}}$| corresponds to W3 IRS 4.

Figure 9 shows the spatial and spectral distribution of the high-velocity component in the W3 Main region. Regarding W3 IRS 4, observations with a spatial resolution of |$3000\:$|au were conducted using IRAM-NOEMA by Mottram et al. (2020), and the results indicated that it is a hot core associated with a massive young stellar object (MYSO), and confirming the presence of bipolar outflows. For W3 IRS 5, observations were conducted using the Submillimeter Array (SMA) by Wang et al. (2013), detecting multiple outflows. Due to insufficient beam resolution, resolving each of these outflows individually is challenging, but line broadening originating from the outflows is localized within approximately |$1\:$|pc of W3 IRS 4 and 5. Hence, we find a V-shape by excluding the outflow lobes, as illustrated by the white line in figure 8b.

3.2 The physical parameters of the molecular clouds

In the above sections, we defined three velocity components at |$-39\:\rm{km\:s^{-1}}$|⁠, |$-43\:\rm{km\:s^{-1}}$|⁠, and |$-50\:\rm{km\:s^{-1}}$| in the HDL, where the most active star formation occurs. We calculated these parameters in the entire region shown in figure 6.

We derived column densities and masses of each molecular cloud under the local thermodynamic equilibrium assumption. First, we assumed the |${^{12}\rm{CO}(J = 2-1)}$| line is optically thick and obtained the excitation temperature in every pixel. Then, we calculated the optical depth of the |${^{13}{\rm CO}(J = 2-1)}$| line and derived the |$^{13}$|CO column density. Next, we obtained molecular hydrogen column densities assuming an abundance ratio of the |$^{13}$|CO molecules and the H|$_2$| molecules of |$7.1\times 10^5$| (Frerking et al. 1982). Finally, we obtained masses of the clouds from the column densities. The peak molecular hydrogen column densities toward W3 Main and W3(OH) calculated in the entire velocity cube are |$1.12\times 10^{23}\:$|cm|$^{-2}$| and |$4.1\times 10^{22}\:$|cm|$^{-2}$|⁠, respectively, giving the total molecular mass of |$2.1\times 10^4\, \rm{M_\odot }$|⁠. The physical parameters of each velocity component are summarized in table 1. For details of the analyses, see the Appendix. We also confirm that column densities and masses derived in the present study are consistent with those derived from Herschel’s observations within a factor of 1.5 (Rivera-Ingraham et al. 2013). See the Appendix for a detailed comparison of physical parameters from the present work and the previous derivation from the Herschel’s observations.

4 Discussion

Here, we discuss a possible scenario of high-mass star formation in W3 based on a detailed analysis of CO observation.

4.1 Trigger of star formation by the expansion of the H ii region

The scenario of sequential star formation driven by OB associations was proposed and discussed by Elmegreen and Lada (1977). In the W3 region, Lada et al. (1978) presented a model in which the W4 |${\small{H ii}}$| region expanded to compress the gas to form the HDL in the W3 region which led to trigger star formation. Subsequently, Oey et al. (2005) proposed a “hierarchical triggering” model where the expansion of the Perseus chimney/super-bubble in W4 triggered the formation of the IC 1795 cluster, and the feedback of the IC 1795 cluster triggered the active star formation in W3 Main and W3(OH). These previous studies are based on the stellar-age distribution, whereas detailed kinematics and distribution of the parental molecular gas were not analysed/considered in depth. We aim to understand the star formation better by using the velocity and density distribution of the CO molecular gas.

We find two molecular clouds in the W3 Main region (section 3). The two clouds have a velocity difference of |$\sim\! 4 \:\rm{km\:s^{-1}}$|⁠, and a usual explanation for the velocity difference is gas acceleration by the feedback of high-mass stars. In the present case, a possible scenario is that the momentum released by the IC 1795 cluster is responsible for the acceleration of the |$-39\:\rm{km\:s^{-1}}$| cloud relative to the |$-43\:\rm{km\:s^{-1}}$| cloud, because the |$-39\:\rm{km\:s^{-1}}$| cloud seems to be accelerated by |$\sim\! 4 \:\rm{km\:s^{-1}}$| from the systemic velocity if we regard the V-shape structure in the position velocity diagram as a redshifted half of the expanding shell (see figure 8b). Further, the |$-39\:\rm{km\:s^{-1}}$| cloud has an elongated structure toward BD |$+$|61 411, which may correspond to a blown-off cloud efficiently overtaken by the stellar wind (e.g., Fukui et al. 2017; Sano et al. 2018). To evaluate the expansion scenario, we first consider the stellar winds as the momentum source. The highest-mass star in IC 1795 is an O6.5V star BD |$+$|61 411 (Oey et al. 2005). The momentum delivered by the star to the surroundings in a time span of 3–|$5\:$|Myr, which is the age of the cluster (Oey et al. 2005), is expressed as follows:

where |$P_{\mathrm{winds}}$|⁠, |$\dot{M}$|⁠, and |$\Delta t$| are the wind momentum, the mass loss rate, and the cluster age, respectively. The typical wind mass loss rate of an O6.5V star is |$10^{-6.4}\, \rm{M_\odot }$| yr|$^{-1}$| (Vink et al. 2000) and its terminal velocity is |$2600\:\rm{km\:s^{-1}}$| (Kudritzki & Puls 2000). If we assume that IC 1795 contains 10 O6.5V stars, we estimate |$P_\mathrm{winds} = 3.1 \times 10^4\, \rm{M_\odot }\:\rm{km\:s^{-1}}$|⁠. The momentum required to accelerate a cloud of |$M_\mathrm{cloud}$| to a relative velocity |$V_\mathrm{rel}$| is given as follows if a complete coupling of the momentum to the cloud mass is assumed:

By taking the cloud mass accelerated by |$4\:\rm{km\:s^{-1}}$| to be |$1.17\times 10^4\, \rm{M_\odot }$| (⁠|$-39\:\rm{km\:s^{-1}}$| cloud and |$-43\:\rm{km\:s^{-1}}$| cloud), we obtain |$P_\mathrm{cloud} = 4.68 \times 10^4\, \rm{M_\odot }\:\rm{km\:s^{-1}}$|⁠. Similarly, in the W3(OH) region, we obtain |$P_\mathrm{cloud} = 6.86 \times 10^4\, \rm{M_\odot }\:\rm{km\:s^{-1}}$| assuming the gas with a mass of |$9800\, \rm{M_\odot }$| (⁠|$-43\:\rm{km\:s^{-1}}$| cloud and |$-50\:\rm{km\:s^{-1}}$| cloud) is accelerated by |$7\:\rm{km\:s^{-1}}$|⁠. These values are comparable to that supplied by the stellar winds. However, we need to consider the realistic geometry of the clouds and the stars further. The solid angle subtended by the cloud relative to IC 1795 seem to be significantly less than |$4\pi$| due to the inhomogeneous distribution of the clouds as shown by the weak CO emission toward the IC 1795 cluster (figure 6a). This indicates that the stellar feedback is hardly able to explain the cause of the velocity difference.

It has been a common thought for a long time that the |${\small{H ii}}$| regions can accelerate and compress the surrounding gas. This possibility was studied theoretically by Kahn (1954) and it was shown that there is a solution corresponding to the acceleration phase of the neutral gas driven by the |${\small{H ii}}$| gas under a range of two parameters: the stellar ultraviolet photons and the gas density. Through hydrodynamical numerical simulations without a magnetic field, Hosokawa and Inutsuka (2005) showed that the gas around an O star is accelerated and compressed, leading to star formation. Subsequently, Krumholz, Stone, and Gardiner (2007) made three-dimensional magnetohydrodynamical numerical simulations of the interaction between an |${\small{H ii}}$| region and magnetized neutral gas. They showed that the |${\small{H ii}}$| region expands in a direction parallel to the magnetic field lines, whereas the expansion is strongly suppressed by the magnetic pressure in the direction perpendicular to the field lines. They thus concluded that the triggered star formation is much less effective without a magnetic field than previously thought. It is also known that the champagne flow makes the |${\small{H ii}}$| gas escape from a low-density part of the surrounding gas (Tenorio-Tagle 1979; see figure 4 of Megeath et al. 2008), leading to even less compression. W3 seems to be one of such cases. In summary, recent numerical studies of the interaction of an |${\small{H ii}}$| region with the ambient neutral gas show that an |${\small{H ii}}$| region may not play a role in gas compression.

We are, in fact, able to see a trend of no acceleration of molecular gas in the present data. Figure 10 shows the first moment distributions of the |$-39\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds. The |$-43\:\rm{km\:s^{-1}}$| cloud in figure 10b shows that there is no appreciable velocity shift of the molecular gas facing the |${\small{H ii}}$| region at the present resolution, which contradicts the previous numerical simulations without magnetic field predicting a velocity shift (see figure 1 of Hosokawa & Inutsuka 2005). The |$-43\:\rm{km\:s^{-1}}$| cloud has shell-like distribution and has the first moment at |$-43\:\rm{km\:s^{-1}}$| over the whole extent with insignificant velocity variation. This may suggest that, while the cloud has a shell morphology, feedback by the IC 1795 cluster has a small effect on the overall cloud kinematics/distribution. On the other hand, the |$-39\:\rm{km\:s^{-1}}$| cloud shows a small velocity variation, less than |$\sim\! 1.5 \:\rm{km\:s^{-1}}$|⁠, in some places. Part of this may be due to the feedback of the stars, although the effect does not seem to be prevailing.

In summary, it seems that the usual scenario of feedback by high-mass stars is not able to explain the present observations of the W3 molecular gas in triggering star formation. This is along the lines of what has been argued for in recent works, although the trigger process by stellar feedback in star formation including the effects of small-scale clumps has not yet been fully tested. We note that small-scale triggering star formation at “sub-pc scale” has been discussed in previous works (Tieftrunk et al. 1997; Wang et al. 2013; Rivera-Ingraham et al. 2013); however, we do not deal with them further in the present work of pc-scale resolution.

4.2 An alternative scenario: Cloud–cloud collisions

We have discussed that it is unlikely that the sequential star formation model is able to explain the star formation in W3 Main and W3(OH). In this section, we test a scenario based on CCCs, which are suggested to be operating in the other typical young |${\small{H ii}}$| regions including the Orion region, the Carina region, and the M16 and M17 region (Fukui et al. 2021a, 2018; Enokiya et al. 2021a; Fujita et al. 2021; Nishimura et al. 2018, 2021).

Fukui et al. (2021a) summarized the main observational signatures of a CCC, where two clouds with a supersonic velocity separation associated with a young star/cluster or their candidates as follows:

• Complementary spatial distribution between the two clouds, and

• bridge feature(s) connecting the two clouds in velocity space, and

• U-shaped morphology in the integrated intensity map.

These three features are based on numerical modeling of colliding clouds by Habe and Ohta (1992) and subsequent observational tests summarized by Fukui et al. (2021a). This model assumes the collision between two clouds of different sizes, and the smaller cloud penetrates deeply into the large cloud and creates a cavity in the large cloud. Because this cavity is made by the motion of the small cloud, the small cloud and cavity show spatially complementary (or anti-correlated) distribution. In a case where the collision direction and line-of-sight have a non-zero angle, the complementary distribution between the small cloud and cavity undergoes displacement due to the projection effect. This displacement is predicted by the numerical calculation of Takahira et al. (2014) and its synthetic observation by Fukui et al. (2018), and has actually been observed (e.g., Fukui et al. 2018; Sano et al. 2021; Fujita et al. 2021; Yamada et al. 2021).

The two colliding clouds exchange momentum, and an intermediate velocity component arises, which is observed as a bridge feature in the position–velocity diagram. The bridge feature is often observed as a “V-shape” in the position–velocity diagram with the small cloud at the vertex and two bridges linking to the large cloud. The U-shape is due to the compression of the large cloud induced by the penetration of the small cloud. Because of the compression, the bottom of the “U-shape” is the densest in the colliding two-cloud system.

In W3 Main, we argue that the properties of the |$-39\:\rm{km\:s^{-1}}$| cloud and the |$-43\:\rm{km\:s^{-1}}$| cloud show the three observed signatures (i)–(iii) of CCC. The |$4\:\rm{km\:s^{-1}}$|⁠, a projected velocity separation, gives a lower limit to the actual collision velocity and is larger than the typical linewidth of the two clouds. A realistic local sound speed is provided by the Alfvenic speed, which is a few |$\rm{km\:s^{-1}}$| if density and magnetic field are assumed to be |$300\:$|cm|$^{-3}$| and |$20\:\mu$|G, respectively, being the typical conditions of the interstellar medium (Crutcher et al. 2010). The two clouds peaked toward IRS 2 in the cluster identified by Bik et al. (2012), which corresponds to the densest part in the U-shaped morphology and matches the picture of a U-shape formed by the Habe–Ohata model.

Figure 11a shows an overlay of the |$-39\:\rm{km\:s^{-1}}$| and the |$-43\:\rm{km\:s^{-1}}$| clouds. The |$-43\:\rm{km\:s^{-1}}$| cloud is extended beyond the outside of W3 Main as diffuse emission, while the |$-39\:\rm{km\:s^{-1}}$| cloud has a clear boundary of a |$5\:$|pc diameter. In order to test if a cloud–cloud collision is a possible scenario, we applied the algorithm of displacement by Fujita et al. (2021). This code optimises the correlation coefficient between the |$-39\:\rm{km\:s^{-1}}$| cloud and the |$-43\:\rm{km\:s^{-1}}$| cloud enclosed by the two boxes in figure 11a. We then obtained the lowest correlation coefficient of |$-0.53$| at the displacement of |$4.1\:$|pc to the southeast, achieving a good matching with the cavity in the large cloud. The correlation coefficient of |$-0.53$| is appropriate to fit the displacement (e.g., Fujita et al. 2021; Sano et al. 2021). Figure 8 shows a V-shape in the position velocity diagram as indicated by the white line superposed. The |$-39\:\rm{km\:s^{-1}}$| cloud is more compact than the |$-43\:\rm{km\:s^{-1}}$| cloud; the top of the V-shape is extended more toward the |$-39\:\rm{km\:s^{-1}}$| cloud.

We suggest that the W3(OH) region is also explicable by a CCC scenario. In this region, the |$-50\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds overlap and are associated with an OH maser source and an H|$_2$|O maser source as well as a few B stars. Figure 12a shows a complementary distribution between the two clouds. Figures 12b–12d show a strip map of figure 12a, which presents the integrated intensity in the dark shaded area averaged in Galactic Latitude. The blue, green, and black lines show the |$-50\:\rm{km\:s^{-1}}$|⁠, |$-43\:\rm{km\:s^{-1}}$|⁠, and whole W3(OH) cloud, respectively. We find that the |$-50\:\rm{km\:s^{-1}}$| cloud and the |$-43\:\rm{km\:s^{-1}}$| cloud are overlapping with each other at |$l = 133.^{\!\!\!\circ} 90$|–|$133.^{\!\!\!\circ} 95$|⁠, and suggest it is possible that the two clouds are merging via collision there. In sub-subsection 4.3.2, we discuss the detailed scenario of CCC in W3(OH).

4.3 A possible CCC scenario

Based on the CCC signatures in subsection 4.2, we assume that CCCs are operating in the W3 Main and W3(OH) regions and discuss the high-mass star formation of IC 1795, W3 Main, and W3(OH).

Figure 13 summarises a star formation scenario based on cloud–cloud collisions. The |$-43\:\rm{km\:s^{-1}}$| cloud, the most massive among the three, is associated with three clusters W3 Main, IC 1795, and W3(OH), while the gas around IC 1795 has already dispersed due to stellar feedback. The two clusters, IC 1795 and W3 Main, are located along the path of the |$-39\:\rm{km\:s^{-1}}$| cloud estimated by the CO distribution and radial velocity, which are independent of the cluster information. According to the optical and infrared observations, the IC 1795 cluster is older than that of the W3 Main cluster. This is consistent with a scenario that the |$-39\:\rm{km\:s^{-1}}$| cloud collided with |$-43\:\rm{km\:s^{-1}}$| at two different epochs, where the first collision triggered IC 1795 and the second collision triggered W3 Main. The other cluster, W3(OH), is located at the eastern edge of the |$-43\:\rm{km\:s^{-1}}$| cloud, separated by more than |$10\:$|pc from the two clusters above and not along the path of the |$-39\:\rm{km\:s^{-1}}$| cloud. Hence, it is hard to consider that the |$-39\:\rm{km\:s^{-1}}$| cloud affects the star formation in W3(OH). On the other hand, and the eastern part of the |$-43\:\rm{km\:s^{-1}}$| cloud shows signatures of a cloud–cloud collision with the |$-50\:\rm{km\:s^{-1}}$| cloud. Hence, we suggest that the W3(OH) cluster was formed by the collision between the |$-50\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds recently.

4.3.1 Multiple episodes of star formation triggered by the |$-43\:\rm{km\:s^{-1}}$| and |$-39\:\rm{km\:s^{-1}}$| clouds

IC 1795 and W3 Main have different ages, as shown by the previous works. IC 1795 is associated with an |${\small{H ii}}$| region, and most of its members are visible at optical wavelengths. The age of the cluster have been studied using the HR diagram (Ogura & Ishida 1976; Oey et al. 2005; Kiminki et al. 2015), and the stellar ages are usually suggested to be 3–|$5\:$|Myr. However, the age determination based on the HR diagram has uncertainties, mainly because of the assumption of extinction law and stellar evolution model. According to the J-, H-, and K-band observations made using the Calar Alto Observatory 3.5|$\:$|m telescope, IC 1795 still hosts a number of young sources that have circumstellar disks, indicating that star formation was active at least in the recent |$2\:$|Myr (Román-Zúñiga et al. 2015). These optical and infrared studies suggest that the star formation in IC 1795 continued until |$2\:$|Myr ago, indicating a cluster age younger than |$3\:$|Myr. On the other hand, W3 Main includes very young objects, as evidenced by the molecular outflow sources having a dynamical age of |$10^4\:$|yr, and the formation of W3 Main is very recent, within |$10^5\:$|yr. The two clusters were, therefore, formed in two different epochs separated by |$2\:$|Myr.

Based on the age separation above, we present a scenario in which the two clusters were formed by two trigger events separated by |$2\:$|Myr. Figure 13 shows a schematic illustration of the possible cloud motion and three-dimensional cloud structure in the past |$4\:$|Myr. The |$-39\:\rm{km\:s^{-1}}$| clouds collided with the |$-43\:\rm{km\:s^{-1}}$| cloud |$2\:$|Myr ago and continued to penetrate into the |$-43\:\rm{km\:s^{-1}}$| cloud until now. Because we estimated the projected displacement of |$4.1\:$|pc by the velocity difference of |$4\:\rm{km\:s^{-1}}$| (figure 11), the collision timescale is given as follows:

where |$\theta$| is the angle between the sightline and the cloud velocity vector. If we assume |$\theta$| to be less than |$30\:$|deg, the collision timescale becomes |$\sim\! 2\:$|Myr as is consistent with the age of the IC 1795 cluster. Although the exact mass of the IC 1795 cluster is not precisely determined, the most massive star has a spectral type of O6.5 V((f)), with a mass calculated to be around |$30\, \rm{M_\odot }$| according to the calibration by Martins, Schaerer, and Hillier (2005). The mass distribution of the IC 1795 cluster is consistent with Kroupa’s initial mass function (IMF) as shown by Román-Zúñiga et al. (2015). By assuming the IMF, the cluster mass is estimated to be around |$1000\, \rm{M_\odot }$|⁠. The star formation efficiency (SFE) is derived as SFE = (cluster mass)|$/$|(cluster mass |$+$| molecular cloud mass) |$=1000 / (1000+4900) = 17\%$|⁠, where molecular mass corresponds to the mass of the |$-39\:\rm{km\:s^{-1}}$| cloud in the present scenario. The SFE is likely an upper limit because the mass of the |$-43\:\rm{km\:s^{-1}}$| cloud at the position of IC 1795 was likely dissipated due to the formation of IC 1795 and the ionization, implying that the |$-43\:\rm{km\:s^{-1}}$| cloud was more massive prior to the collision than it is at present.

We suggest that the collision is still ongoing and is triggering high-mass star formation in W3 Main. The |$-39\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds overlap toward W3 Main (figure 7), corresponding to phase 3 in figure 1 of Fukui et al. (2021a), and the compressed gas has a total column density of over |$10^{23}\:$|cm|$^{-2}$|⁠. The gas distribution indicates that W3 Main corresponds to the shock-compressed merged gas in the Habe–Ohta model. This idea is supported by the presence of molecular outflows indicating star formation with a timescale of |$10^4\:$|yr. In addition to outflows, various stages of high-mass star formation—including the diffuse |${\small{H ii}}$| region W3 H, J, K, the compact |${\small{H ii}}$| region W3 A, B, and D, the ultra-compact |${\small{H ii}}$| region W3 C, E, F, and G, and the hyper-compact |${\small{H ii}}$| region W3 Mag and Ca, which were identified previously (Tieftrunk et al. 1997)—are embedded in around |$2\:$|pc from the CO peak toward W3 Main. Moreover, Troland et al. (1989) measured the magnetic field strength of W3 Main to be |$\sim\! 100\, \mu$|G using the Zeeman splitting method based on the |${\small{H\,i}}$| observation by the Very Large Array. Such a high magnetic field strength is consistent with the MHD simulations of Inoue and Fukui (2013), in which the collision can compress the gas to enhance the magnetic field up to |$\sim\! 100$|–|$600\, \mu$|G, leading to larger Alfvénic velocity and effective Jeans mass. Because the total stellar mass of the W3 Main region was estimated to be |$4000\, \rm{M_\odot }$|⁠, the SFE is calculated to be |$25\%$|⁠, by taking the molecular cloud mass to be |$1.17\times 10^4\, \rm{M_\odot }$| (⁠|$-43\:\rm{km\:s^{-1}}$| cloud and |$-39\:\rm{km\:s^{-1}}$| cloud). Another small cluster, NGC 896, is located in the south of W3 Main. The age of the cluster is estimated to be 1–|$2\:$|Myr by Román-Zúñiga et al. (2015) and is likely formed between IC 1795 and W3 Main. We infer that the formation of NGC 896 was triggered by a collision between the |$-43\:\rm{km\:s^{-1}}$| cloud and the western part of the |$-39\:\rm{km\:s^{-1}}$| cloud |$\sim\! 1\:$|Myr ago, nearly continuously following the first collision which triggered IC 1795 (see figure 13).

4.3.2 The collision between the |$-50\:\rm{km\:s^{-1}}$| and |$-43\:\rm{km\:s^{-1}}$| clouds in the W3(OH) region

Star formation in W3(OH) seems less active than that in W3 Main. We next argue that the high mass stars W3(OH) were formed |$0.7\:$|Myr ago by the collision between the |$-43\:\rm{km\:s^{-1}}$| cloud and the |$-50\:\rm{km\:s^{-1}}$| cloud. The molecular clouds in the W3(OH) region are elongated along the Galactic plane. Figure 12 shows that the |$-43\:\rm{km\:s^{-1}}$| and |$-50\:\rm{km\:s^{-1}}$| clouds have a similar size, which suggests that the two clouds collided with each other to form the elongated cloud as observed. Instead of the picture by Habe and Ohta (1992) where the small cloud compresses the large cloud to create a cavity in it, as in figure 12, the two clouds with similar extents perpendicular to the collision direction collided to compress gas into an elongated structure along the Galactic latitude. Such a mode of CCC was reported in the Sh2-233 region (see figure 6 of Yamada et al. 2022).

We estimate the timescale using the crossing time from |$3\:\rm{pc}4\:\rm{km\:s^{-1}}= 0.7\:$|Myr because there is no hint of a displacement between the two clouds. Numerical simulations of CCCs (Habe & Ohta 1992; Anathpindika 2010; Takahira et al. 2014) show that star formation does not take place just after the collision onset but some time after the merging begins. Therefore, the real star formation happened well after the timescale. The ages of the maser sources, W3(OH) and W3(H|$_2$|O), are roughly consistent with the timescale of the collision. The driving sources of OH maser are stars of the zero-age main sequence (ZAMS), the age of which is |$\sim\! 0.1\:$|Myr. Further, the driving sources of H|$_2$|O masses with ages of a few |$10^3\:$|yr are hot cores (Qin et al. 2016). The W3(OH) region star formation is ongoing with merging clouds. The short lifetimes do not contradict the CCC model.

Considering the above, we frame a scenario as follows: in W3(OH), the |$-50\:\rm{km\:s^{-1}}$| and the |$-43\:\rm{km\:s^{-1}}$| clouds began to collide about |$0.7\:$|Myr ago along the Galactic plane. The two clouds have a column density of |$\sim\! 10^{22}\:$|cm|$^{-2}$|⁠. This filamentary molecular cloud became gravitationally unstable in the last |$10^5\:$|yr and triggered the formation of the OH maser and H|$_2$|O maser. The W3 (OH) region has a number of B stars which have ages of 2–|$3\:$|Myr (Román-Zúñiga et al. 2015). They are unrelated to the collision of |$-43\:\rm{km\:s^{-1}}$| and |$-50\:\rm{km\:s^{-1}}$| clouds.

Up to this point, we have discussed the potential scenarios of CCC in both the W3 Main region and the W3(OH) region. As illustrated in figure 13, both regions are associated with the same |$-43\:\rm{km\:s^{-1}}$| cloud. In the case of the W3 Main region, star formation could be induced by the collision with the |$-39\:\rm{km\:s^{-1}}$| cloud, while in the W3(OH) region, it could be triggered by the collision with the |$-50\:\rm{km\:s^{-1}}$| cloud. Furthermore, the formation of IC 1795 can also be explained depending on the assumed collision angles.

The W3 GMC has a molecular mass of |$10^6\, \rm{M_\odot }$| along with the associated stellar mass of over |$5000\, \rm{M_\odot }$|⁠. The molecular mass is outstanding in the outer solar circle. The GMC consists of three velocity components. The mass of the |$-43\:\rm{km\:s^{-1}}$| cloud, the most massive among the three, is |$6800\, \rm{M_\odot }$|⁠, and its collision with the |$-39\:\rm{km\:s^{-1}}$| cloud is a standard CCC according to the simulations of the collisions in the Galactic plane (Kobayashi et al. 2017; see also figure 9d of Fukui et al. 2021a).

4.4 Comparison with the other CCC candidates

It is known that W3 Main has a Trapezium-like cluster (Abt & Corbally 2000). Table 2 compares the Orion Nebula Cluster (ONC) and W3 Main and indicates that the star formation in W3 Main shares similar molecular column density and age to the ONC (for a review of the ONC, see Muench et al. 2008 and references therein).

In the ONC, Fukui et al. (2018) identified two clouds with a velocity difference of |$\sim\! 4 \:\rm{km\:s^{-1}}$| that are shown to have complementary distribution which is consistent with a CCC that triggered the OB stars in the ONC. These authors presented a scenario that the ONC consists of two populations, one formed by the CCC in the last |$0.1\:$|Myr and the other of low-mass members which have been continuously formed over the last |$1.5\:$|Myr. The SFE in W3 Main was estimated to be |$\sim\! 25\%$|⁠, which is consistent with an SFE of |$\sim\! 20\%$| in the ONC (e.g., Fukui et al. 2021a). Fukui et al. (2021b) showed that SFE is not particularly enhanced in a compressed layer of CCC, and a few percent to a few times |$10\%$| are typical values. This suggestion is also consistent with the present result when we consider the larger stellar ages.

The present study revealed that W3 shows evidence for triggered high-mass star formation by CCCs, where sufficiently high column density gas with |$\sim\! 10^{23}\:$|cm|$^{-2}$| is colliding. Enokiya, Torii, and Fukui (2021b) compiled |$\sim\! 50$| CCC candidates and made a statistical study, and have shown that the number of O and early B stars are correlated with the molecular column density; i.e., the formation of a single O star requires |$10^{22}\:$|cm|$^{-2}$| and more than 10 O stars requires |$10^{23}\:$|cm|$^{-2}$|⁠. W3 Main has a column density of |$\sim\! 10^{23}\:$|cm|$^{-2}$|⁠, and the formation of more than 10 O stars is consistent with the results of Enokiya, Torii, and Fukui (2021b).

The molecular column density in W3(OH) is derived to be |$4.1\times 10^{22}\:$|cm|$^{-2}$|⁠. On the other hand, the number of OB stars formed by the CCC in W3(OH) is 1, smaller than that in W3 Main. Nonetheless, the H|$_2$|O masers are associated with two cloud cores of |$10\, \rm{M_\odot }$| (Ahmadi et al. 2018) and they are potential OB stars. This is consistent with the conclusion by Enokiya, Torii, and Fukui (2021b) that the column density in W3(OH) is not enough to form 10 OB stars.

W3 is an exceptionally active star formation site, while it is located in the outer solar circle where a marked decrease in the high-mass star formation rate is observed (e.g., Djordjevic et al. 2019). According to Fukui et al. (2021a), among |$\sim\! 50$| Galactic CCC candidates, the number of objects in the outer solar circle is limited to less than 10. This prevents us from concluding that CCCs are common phenomena in the outer solar circle. However, in the past few years, attempts to search for CCC objects in the outer solar circle have been made, and the number of CCCs is increasing (e.g., Sh2-233: Yamada et al. 2022, Sh2-235: Dewangan & Ojha 2017, W5: Issac et al. 2024, AFGL 333: Liang et al. 2021, IRAS 01123+6430: Koide et al. 2019). The present work provides further evidence of the CCCs in the active star formation site W3, lending support for the importance of CCCs not only in the inner solar circle but also in the outer solar circle.

5 Conclusions

We analyzed the |${^{12}\rm{CO}(J = 2-1)}$| and |${^{13}{\rm CO}(J = 2-1)}$| data of the W3 region (Bieging & Peters 2011). It has been discussed as a possible scenario for three decades that the stars in the W3 Main and W3(OH) region have been formed by the feedback effect of an |${\small{H ii}}$| region driven by IC 1795 (e.g., Oey et al. 2005). It was generally thought that, on a large scale of |$10\:$|pc or more, the |${\small{H ii}}$| region W4 compressed the gas in the HDL and triggered star formation in the HDL. The present data cover a smaller area than the whole W4 and W3 region and are not suited to test the star formation on a |$20\:$|pc scale. Instead, the present results have a reasonable resolution to resolve details relevant to pc-scale star formation in W3, where we made a detailed kinematic study and obtained the following results:

• The maximum gas column densities of the W3 Main and W3(OH) regions are |$1.1\times 10^{23}\:$|cm|$^{-2}$| and |$4.1\times 10^{22}\:$|cm|$^{-2}$|⁠, respectively. The first moment distribution revealed that the W3 region consists of at least three clouds. The |$-43\:\rm{km\:s^{-1}}$| cloud is the most extended, and it is distributed in both the W3 Main and W3(OH) regions. The |$-39\:\rm{km\:s^{-1}}$| component is localized in W3 Main region, while the |$-50\:\rm{km\:s^{-1}}$| cloud overlaps the |$-43\:\rm{km\:s^{-1}}$| cloud in W3(OH). The total gas mass of the region analysed by the present study amounts to |$21000\, \rm{M_\odot }$|⁠, while three clouds have masses of |$4900\, \rm{M_\odot }$| (⁠|$-39\:\rm{km\:s^{-1}}$| cloud), |$6800\, \rm{M_\odot }$| (⁠|$-43\:\rm{km\:s^{-1}}$| cloud), and |$3000\, \rm{M_\odot }$| (⁠|$-50\:\rm{km\:s^{-1}}$| cloud).

• In W3 Main, we tested if the feedback is important in the cloud kinematics by comparing the stellar feedback energy with the kinetic energy of the clouds. The most energetic source near W3 Main is IC 1795, which includes 10 high-mass stars and an |${\small{H ii}}$| region. We estimated that the total kinetic energy of these stars/|${\small{H ii}}$| region is not large enough to affect the gas kinematics of the two clouds, nor does the local velocity distribution at the boundary of the |${\small{H ii}}$| region show any velocity shift. We suggest that any feedback by the |${\small{H ii}}$| region or IC 1795 or the molecular outflow is not significant in altering the cloud morphology or kinematics. Accordingly, we suggest that stellar feedback does not play a role in W3.

• In W3 Main, the |$-39\:\rm{km\:s^{-1}}$| cloud has a diameter of |$\sim\! 5 \:$|pc, while the |$-43\:\rm{km\:s^{-1}}$| cloud is extended along the Galactic plane by more than |$25\:$|pc with a “cavity” of |$\sim\! 5\:$|pc diameter with significantly decreased CO intensity in the eastern edge. We find that the two clouds show spatially complementary distribution with a displacement of |$4.1\:$|pc, where the |$-39\:\rm{km\:s^{-1}}$| cloud fits the cavity of the |$-43\:\rm{km\:s^{-1}}$| cloud. We also find that the clouds show a V-shape in a position–velocity diagram. These signatures are consistent with the fact that the two clouds are colliding with each other to deform their original distribution and kinematics into a merging cloud. The displacement indicates that the |$-39\:\rm{km\:s^{-1}}$| cloud has moved in the northwestern direction in the past. The location of W3 Main, which is in the northwest of the cavity, is consistent with W3 Main, where 10 OB stars are localized and correspond to the collision-compressed layer as modelled by Habe and Ohta (1992).

• The collision in W3 Main explains the formation of the most massive star IRS 2 and 10 OB stars. The W3 Main region also includes several outflows, indicating star formation activity with a timescale of |$10^4\:$|yr. This short timescale is consistent with the scenario that the W3 Main is now at the collision-compressed layer, and currently triggered star formation is ongoing. On the other hand, we estimate the typical timescale of the collision to be 1–|$2\:$|Myr by dividing the displacement |$4.1\:$|pc by the relative velocity of the clouds |$\sim\! 4 \:\rm{km\:s^{-1}}$|⁠, depending on the assumption of the angle between collision direction and line-of-sight. This collision to form the cavity toward IC 1795 may explain the formation of the IC 1795 cluster because the age of the IC 1795 may be as young as |$2\:$|Myr, which is consistent with the stellar age.

• The |$-50$| and |$-43\:\rm{km\:s^{-1}}$| clouds in W3(OH) are also complementary in the spatial distribution in the sense that the |$-50\:\rm{km\:s^{-1}}$| cloud is located on the east of the |$-43\:\rm{km\:s^{-1}}$| cloud on a scale of 3–|$5\:$|pc. The spatial distribution seems to be simpler than in W3 Main, and the total cloud mass involved is less than a factor of 2 smaller than the W3 Main cloud. We suggest a possible scenario in which the two clouds are colliding with each other, where the timescale of the collision is roughly estimated to be |$0.7\:$|Myr, shorter than in W3 Main. We conservatively note that the evidence for the collision is not as strong as in W3 Main, for which the complicated CO distribution lends firmer support for the complementary distribution typical to a CCC.

• W3 is experiencing a CCC in two places now. In W3 Main, the maximum column density is |$1.1\times 10^{23}\:$|cm|$^{-2}$| for a projected velocity difference of |$\sim\! 4\:\rm{km\:s^{-1}}$| and more than 10 O stars are formed. These regions are the sites of high-mass star formation relatively close to the Sun. The physical parameters are similar to the ONC. W3(OH) has a somewhat smaller maximum column density for the projected velocity difference of |$\sim\! 4\:\rm{km\:s^{-1}}$| and a few high-mass star candidates for O star are formed. These are well consistent with the 50 samples of CCC candidates (Enokiya et al. 2021b; Fukui et al. 2021a).

The W3 region has attracted keen interest in the last few decades, whereas there has been no unified picture of star formation, including the effects of triggering. This would be due to the paucity of investigations of molecular gas, where the most direct and recent traces of star formation are carved. We, therefore, studied the CO gas in detail. As a result, clear signatures of CCCs have been revealed. Our model frames a scenario which offers a unified view of the star formation over a few Myr. The method naturally has no direct explanation for the cluster, which has no associated molecular gas, whereas it is still possible that the cluster was formed by a past event whose relic has already been dispersed. A stellar system with age spread and better statistics is essential.

Acknowledgements

We are grateful to Professor Philippe André for kindly providing Herschel data. We also acknowledge Akio Taniguchi, Keisuke Sakasai, Kazuki Shiotani for their valuable support during data analysis. The Heinrich Hertz Submillimeter Telescope is operated by the Arizona Radio Observatory, a part of Steward Observatory at The University of Arizona. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAF-IFSI/OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). SPIRE has been developed by a consortium of institutes led by Cardiff University (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). This research made use of Astropy,² a community-developed core Python package for Astronomy (Astropy Collaboration 2013, 2018). This research made use of APLpy, an open-source plotting package for Python hosted at |$\langle$|http://aplpy.github.com|$\rangle$|⁠. This work was supported by JSPS KAKENHI Grant Numbers JP15H05694, JP18K13580, JP19K14758, JP19H05075, JP20K14520, JP20H01945, and 22KJ1604. R.Y. is a Research Fellow of JSPS.

Appendix 1 Calculations of column densities and masses

We assume the local thermodynamic equilibrium (LTE) and calculate the molecular column density and mass of each cloud. We used only the pixels having physical parameters of more than |$6\sigma$|⁠. By assuming that the |${^{12}\rm{CO}(J = 2-1)}$| emission is optically thick, the excitation temperature |$T_\mathrm{ex}$| is given as follows:

From this equation, we derived |$T_{\mathrm{ex}}$| for every pixel. The equivalent brightness temperature |$J(T)$| is expressed as below for Planck constant h, Boltzmann constant |$k_\mathrm{B}$|⁠, and the observed frequency |$\nu$|⁠:

The radiation transfer equation gives the |${^{13}{\rm CO}(J = 2-1)}$| optical depth |$\tau (\nu )$| to be

The |${^{13}{\rm CO}(J = 2-1)}$| column density is given as follows:

where we used |$k_\mathrm{B} = 1.38 \times 10^{-16}$| (erg|$\:$|K|$^{-1}$|⁠), |$\nu = 2.20\times 10^{11}\:$|(Hz), |$\mu = 1.10 \times 10^{-19}$| (esu|$\:$|cm), |$h = 6.63 \times 10^{-27}$| (erg|$\:$|s), |$J = 1$|⁠, and |$T_\mathrm{ex}$| was adopted from each pixel. By assuming that the ratio |$N_\mathrm{H_2}/N_{^{13}\mathrm{CO}}$| is |$7.1\times 10^5$| (Frerking et al. 1982), the column density can be calculated. The molecular mass is given by

where |$\mu _{\rm m}$|⁠, |$m_\mathrm{p}$|⁠, D, |$\Omega$|⁠, and |$N_{i}(\mathrm{H_2})$| are the mean molecular weight, the proton mass, the distance, solid angle, and column density of the ith pixel. If the helium abundance is assumed to be |$20\%$|⁠, |$\mu _{\rm m}$| is 2.8. The distances of W3 Main and W3(OH) are |$2.00\:$|kpc (e.g., Navarete et al. 2019). The derived parameters are listed in table 1.

Appendix 2 Comparison of CO-derived and dust-derived molecular hydrogen column density

In this study, we utilize the physical parameters of molecular clouds derived from CO using the procedure outlined in appendix  1. The column densities derived from CO and Herschel data are consistent. Figures 14a and 14b depict maps of hydrogen column density obtained from Herschel and CO, respectively. These figures are displayed with aligned color scales, revealing a similarity in spatial distribution between the two datasets. Figure 15 presents an enlarged view of W3 Main. While regions with high hydrogen column densities generally exhibit optical thickness in |$^{13}$|CO, the differences with column densities derived from Herschel are within a factor of approximately 2, suggesting that the impact of optical thickness is not significant.

Footnotes

References