Investigation of Rocket Effect in Bright-Rimmed Clouds using Gaia EDR3

The methodology adopted here to affirm the coupling between young sources with their parental clouds is similar to our previous studies (Saha et al., 2020; Saha et al., 2021, 2022). Based on the literature, out of 89 BRCs, candidate YSOs have been identified towards 52 of them using various methods till date (as described in section 2). Among the 52 BRCs, we selected 29 of them, which are associated with at least 4 candidate YSOs satisfying our selection criteria. The median absolute deviation (MAD) was used to compute the statistical dispersion in $d$, $\mu_{\alpha\star}$, and $\mu_{\delta}$. Only those candidate YSOs, which are lying within 5$\times$MAD with respect to the median values of the $d$, $\mu_{\alpha\star}$, and $\mu_{\delta}$, are selected as the members of each of their respective BRCs. The adoption of 5$\times$MAD was made because the majority of the candidate YSOs in the BRCs are distributed within this boundary. We recomputed the median and the MAD of $d$, $\mu_{\alpha\star}$, and $\mu_{\delta}$ of the selected candidate YSOs to estimate the final astrometric results of the BRCs (also see Paper I).

Of the 29 BRCs, we first excluded BRCs 15, 24, and 30, where the candidate YSOs are distributed far from the cloud-ionizing star vicinities. Also, we excluded BRC 51 due to its high MAD in $\mu_{\delta}$ (-2.187$\pm$6.657 mas yr^-1, obtained from Gaia EDR3 measurements of the candidate YSOs) from further study. Also, ionizing stars of this BRC ($\zeta$ Pup and $\gamma^{2}$ Vel; Thompson et al., 2004) do not have astrometric measurements in Gaia EDR3. Additionally, we set a numerical limit $z=(d-d_{\star})/(\Delta d+\Delta d_{\star})$ for the consistency of distance between the BRC (or the candidate YSOs residing in the BRC) and the respective ionizing sources, where, $d_{\star}$ and $\Delta d_{\star}$ are the distance for the ionizing source and its corresponding uncertainty, respectively. In our study, we select only those BRCs, for which $z\leq 1$. Thus, BRCs 34, 68, and 76 were eliminated. Therefore, out of 29 BRCs, seven were excluded from our further analysis. In Tables 1 and 2 (available as supplementary material), we present the details of candidate YSOs in the BRCs along with the $\theta_{pm}$ and $\theta_{ip}$ found in the analysis. The strategies followed to obtain the $\theta_{pm}$ of the candidate YSOs in the remaining 22 BRCs are discussed below:

BRC 2: The massive source responsible for ionization of BRC 2 is BD+66 1675, which does not fulfill our selection criteria. We used the median PM obtained from the members of the Hii region Sh2-171, which are associated with BD+66 1675 (Getman et al., 2018; Panwar et al., 2018), as the reference to obtain the $\theta_{pm}$.

BRCs 5 and 7: Three early type sources, BD+60 502, BD+60 504, and BD+60 507, are considered to influence BRCs 5 and 7 (Ishida, 1970; Morgan et al., 2004). BD+60 504, and BD+60 507 both have good astrometric measurements and reside at 2122${}_{-81}^{121}$ and 1960${}_{-68}^{65}$ pc, respectively. We used the PMs of BD+60 504 as the reference as its $d$ is more consistent with the BRCs.

BRCs 17 and 18: BRCs 17 and 18 reside at the $\lambda$ Ori Hii region and considered to be ionized by $\lambda$-Ori (Sugitani et al., 1991). The methodology adopted to find the relative PM of the candidate YSOs in these BRCs is described in Paper I.

BRC 25: The massive source considered to ionize BRC 25 is HD 47839, which has a higher RUWE making its astrometric measurements unreliable. Therefore, we obtained the reference PM values of NGC 2264 from Buckner et al. (2020) to estimate the $\theta_{pm}$.

BRCs 36 to 39: BRCs 36-39, located in the Hii region IC 1396, are considered to be ionized by the central ionizing source HD 206267 (Sugitani et al., 1991), which fails our selection criteria. Therefore, we used median PM values of the cluster members of IC 1396 provided in the literature (Contreras et al., 2002; Sicilia-Aguilar et al., 2005; Mercer et al., 2009; Sicilia-Aguilar et al., 2019) as the reference to compute the $\theta_{pm}$ of the candidate YSOs in the BRCs.

BRC 55: For BRC 55, in the Hii region RCW 27, the massive source responsible for ionizing BRC 55 is HD 73882, which has RUWE = 2.068. Therefore, we obtained the astrometric parameters of the members of RCW 27 (Prisinzano et al., 2018) from Gaia EDR3 and used the median PM of the cluster members as the reference PM to estimate $\theta_{pm}$.

BRC 64: The star responsible for ionizing BRC 64 is LSS2231, located at 3145${}_{-437}^{400}$ pc, while BRC 64 resides at 2968$\pm$225 pc. Thus the lower limit of $d$ of LSS2231 lies within the distance range of BRC 64. Though the RUWE of LSS2231 is 1.819, this is to note that it satisfies all of our other selection criteria. Due to lack of information of any other members of the Hii region BBW 347 where BRC 64 resides, we used the PM values of LSS2231 to estimate the $\theta_{pm}$.

BRC 65: There are three early type sources considered to ionize BRC 65, which are, HD 101131, HD 101205, and HD 101436 (Thompson et al., 2004), located in the Hii region RCW 62. As only HD 101205 satisfies our selection criteria, we used its PM values as the reference to compute the $\theta_{pm}$.

BRC 79: BRC 79 is found to be located in the Hii region RCW 108. Two massive sources are found to be responsible for the ionization of this region, HD 150136 (O5III) and HD 150135 (O6.5V) (Thompson et al., 2004). As $d$ of HD 150136 (1428${}_{-96}^{93}$ pc) is more consistent than HD 150135 (1242${}_{-39}^{37}$ pc) with the same for BRC 79, and the spectral type of HD 150136 is earlier than the later, we considered the PM of HD 150136 as the reference PM.

BRC 82: Three early type sources, HD 152233 (O6III), HD 326286 (B0), and HD 152245 (B0Ib) are considered to be responsible for the ionization of BRC 82 (Yamaguchi et al., 1999; Thompson et al., 2004). The earliest type ionizing source, HD 152233, is a member of the cluster NGC 6231. As there is a high possibility of the influence of other massive stars of NGC 6231, we obtained median PM of the cluster members from Kuhn et al. (2017) and considered those as reference PM.

The rest BRCs, i.e., 11, 26, 27, 31, 54, 75, and 89 are associated with Hii regions having reliable astrometric measurements of the ionizing sources in the Gaia EDR3 catalogue. Therefore, the PMs of these ionizing sources were used as the reference PMs in order to investigate the RE taking place in the respective BRCs.

Our study finally focuses on 22 BRCs (including BRC 18), which consist of a considerable number of candidate YSOs with reliable astrometric measurements in Gaia EDR3. Mostly the YSOs are embedded deep in the natal cloud, so the optical emission from many of them are highly obscured by the circumstellar and interstelllar dust resulting in unreliable or no detection in Gaia EDR3. In Fig. 2 (a) we present the distribution of $\theta_{ip}$ versus $\theta_{pm}$ of 22 BRCs. BRCs 54 and 89 show distinctively higher $\mid$$\theta_{ip}-\theta_{pm}$$\mid$ compared to other BRCs. We marked them using open circles. Other 20 BRCs are shown using filled grey circles. We made two cases A and B, which indicate inclusion and exclusion of both BRCs 54 and 89, respectively. The solid black line shows the best-fitted line for case A. The slope of this line is estimated as 1.011$\pm$0.103. We again show the best-fitted line in case B using solid grey line, of which the slope is estimated as 1.148$\pm$0.071. Error in $\theta_{pm}$ is estimated using the error propagation method. The error in $\theta_{ip}$ is negligible because the positional errors of the sources are in milli arcsecond order. To obtain the correlation between $\theta_{ip}$ and $\theta_{pm}$, we computed the Pearson’s correlation coefficient. For case A, the value is found to be 0.909 with pnull 4.641$\times$10^-9. The Spearman’s correlation coefficient is estimated as 0.899, with pnull as 1.247$\times$10^-8. We also performed Kolmogorov-Smirnov (K$-$S) test on these angles. The computed statistic is 0.182, and the pvalue is 0.821. For case B, the Pearson’s and Spearman’s correlation coefficients for 20 BRCs are estimated as 0.967 and 0.964 with pnull 3.444$\times$10^-12 and 8.654$\times$10^-12, respectively. The K$-$S test provides statistic of 0.200, and the pvalue is 0.771 for the 20 BRCs. All these statistical analyses indicate a strong correlation between $\theta_{ip}$ and $\theta_{pm}$. The distribution of $\mid$$\theta_{ip}-\theta_{pm}$$\mid$ as a form of histogram with binsize $20\degr$ is shown in Fig. 2 (b), using white- and grey-colored bins, for cases A and B, respectively. A maximum in the lowest of $\mid$$\theta_{ip}-\theta_{pm}$$\mid$ and a decrease in the number of BRCs with higher $\mid$$\theta_{ip}-\theta_{pm}$$\mid$ is clearly noticeable. In Fig. 2 (c), we show the cumulative histogram of $\mid$$\theta_{ip}-\theta_{pm}$$\mid$, using white- and grey-colored bins, for cases A and B, respectively. It is apparent from both Figs. 2 (b) and (c), that almost $\sim 80$% of the BRCs show $\mid$$\theta_{ip}-\theta_{pm}$$\mid\leq 60\degr$.

This is to note that because of the lack of information of the radial velocities of the sources, in Paper I as well as in this study too, we consider only the PMs of the sources, which is on the sky plane. In an Hii region, where the ionizing star and the BRC both are not located at the sky plane, but have a significant distance along the line-of-sight, the $\mid$$\theta_{ip}-\theta_{pm}$$\mid\sim 0\degr$ might not always be satisfied because of the possible presence of a significant radial component of motion of the BRC/ionizing source. Apparently, $180\degr>\mid$$\theta_{ip}-\theta_{pm}$$\mid>90\degr$ might seem as a phenomenon opposite to RE in 2D, i.e. PMs of the YSOs towards the ionizing star, but these sources may have significant components of motions in the radial direction, which might make their total motions in 3D away from the ionizing star, satisfying the RE scenario. Thus, the $\mid$$\theta_{ip}-\theta_{pm}$$\mid\sim 0\degr$ condition does not signify the RE scenario completely in 2D, but in 3D.

A higher $\mid$$\theta_{ip}-\theta_{pm}$$\mid$ for BRCs 54 and 89 signifies that the relative PM of the candidate YSOs direct towards their respective ionizing sources. For BRC 54, we initially suspected that the presence of another massive star, HD 73882 (also considered to ionize BRC 55), might have influenced the motion of the candidate YSOs. But due to higher distance ($\sim$13 pc), the probability of HD 73882 influencing BRC 54 is low. Prisinzano et al. (2018) detected second generation of stars around BRC 54, which indicates that the kinematic coupling between the candidate YSOs and BRC 54 might have been lost. Therefore, the $\theta_{pm}$ of the candidate YSOs might not indicate the PM of BRC 54.

The massive star considered to ionize BRC 89 is HD 165921, with respect to which $\theta_{pm}$ of the candidate YSOs is estimated. Based on the 2MASS all-sky survey, Bica et al. (2003) discovered a stellar cluster encircling an ionizing source HD 166056, a B2Ve star (Herbst et al., 1982) in BRC 89. It is embedded in a cavity, surrounded by a prominent shell-like structure indicative of expanding ionization front (Santos et al., 2014). The pressure of HD 166056 might have affected the motion of the surrounding YSOs which is why $\theta_{pm}$ of the candidate YSOs show significantly different direction in BRC 89.