Unveiling the Physical Conditions in NGC 6910

The initial stellar distribution in star clusters may be governed by the structure of the parental molecular cloud and also how star formation proceeds in the cloud. Later evolution of the cluster may be governed by the internal gravitational interaction among member stars and external tidal forces due to the Galactic disk or giant molecular clouds (Chen et al. 2004; Sharma et al. 2006). The structure and radius of the NGC 6910 cluster (core and corona regions) can be studied by means of density estimations. Since the distribution of stars in a cluster follows a systematic distribution from the cluster to the field region, the center of the cluster is estimated by involving a Gaussian kernel with the stellar distribution and taking the point of maximum density as the center. This was performed for both axes to get the center coordinates of the cluster, i.e., ${\alpha }_{{\rm{J}}2000}$ = 20^h23^m18^s, ${\delta }_{{\rm{J}}2000}$ = +40°46' 12''. To determine the radial stellar surface density, the cluster was divided into a number of concentric rings. The projected radial stellar density in each concentric circle was obtained by dividing the number of stars in each annulus by its area, and this is plotted in Figure 5 for various magnitude levels. The error bars are derived assuming that the number of stars in each annulus follows Poisson statistics. The point where the radial density becomes nearly constant and merges with the contaminating field star density (indicated by horizontal dashed lines in the plot) is defined as the radius of the cluster, r_cl (see also Sharma et al. 2006). For almost all magnitude levels, we can determine the r_cl of this cluster as 55. The observed radial density profile (RDP) of the cluster was parameterized following the approach by Kaluzny & Udalski (1992), in which the projected radial density ρ(r) is described as

$$\begin{eqnarray}&&\rho (r)\propto \displaystyle \frac{{f}_{\circ }}{1+{\left(\tfrac{r}{{r}_{c}}\right)}^{2}},\end{eqnarray} \tag{ 6 }$$

where the cluster's core radius, r_c, is the radial distance at which the value of the projected radial density, ρ(r), becomes half of the central density, f₀. Within the uncertainties, the King model (King 1962) well reproduces the RDP of the cluster at different magnitude levels, except for V < 21 mag. This might be due to the apparent contamination in the cluster region from the field stars at fainter magnitudes. By fitting the King model surface density profile to the observed RDP of stars with V ≃ 19 mag having a least-fitting error, we have found that the core radius of this cluster comes out as 14.

Zoom In Zoom Out Reset image size

To further study the structure of the cluster and stellar density distribution in the region, we generated stellar surface density maps using the nearest-neighbor method as described by Gutermuth et al. (2005). We have taken the radial distance necessary to encompass the 20th-nearest star detected in the optical band (V < 16 mag) and computed the local surface density in a grid size of ∼20''. Surface density contours in the NGC 6910 region are shown in Figure 2 as red contours, whereas the cluster region as determined by RDP is shown as a green circle. The lowest contour is 1σ above the mean of the stellar density (i.e., 1.3 + 2.2 stars pc⁻² at 1720 pc), and the step size is equal to 1σ (2.2 stars pc⁻² at 1720 pc). Figure 2 reveals that stellar surface density contours correspond to the cluster size (55) determined by the RDP. The core region of this cluster seems to be elongated.

Membership determination based on proper-motion (PM) studies will be useful to carry out astrophysical studies in the region of the cluster. To determine the membership probability, we adopted the method described in Balaguer-Núnez et al. (1998) by using Gaia PM data (see Table 2). This method was previously used for ω Centauri (Bellini et al. 2009), NGC 6809 (Sariya et al. 2012), NGC 6366 (Sariya & Yadav 2015), and NGC 3201 (Sariya et al. 2017). In Figure 6 (left panel), we show the PM μ_αcos(δ) and μ_δ vector point diagrams (VPDs; top panels) and the corresponding G versus $({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})$ color–magnitude diagrams (CMDs; bottom panels) for the stars located within the radius of the cluster, i.e., ${r}_{\mathrm{cl}}\lt 5\buildrel{\,\prime}\over{.} 5$. The left subpanel shows all stars, while the middle and right subpanels show the probable cluster members and field stars, respectively. A tight circular clump can be seen visually at μ_xc = −3.4, μ_yc = −5.4 mas yr⁻¹ having a radius of 0.8 mas yr⁻¹ in the top left subpanel of Figure 6. As we know that the cluster stars have more or less similar PMs, this group most probably represents the PMs of cluster stars. The chosen radius is a compromise between losing cluster members with poor PMs and including field stars sharing the cluster mean PM. The corresponding well-defined CMD of these most probable cluster members can be seen in the bottom middle subpanel. The remaining stars in the VPD are assigned as field stars, which is further demonstrated by the broad distribution in their CMD (bottom right subpanel). Few cluster members might be visible in this CMD because of their wrong estimation of PMs due to large errors in their values. Assuming a distance of 1.74 kpc (Delgado & Alfaro 2000) and a radial velocity dispersion of 1 km s⁻¹ for open clusters (Girard et al. 1989), the expected dispersion (σ_c) in PMs would be ∼0.12 mas yr⁻¹. For the remaining field stars, we have calculated μ_xf = −2.2, σ_xf = 3.9 mas yr⁻¹ and μ_yf = −4.6, σ_yf = 4.3 mas yr⁻¹ as the mean and standard deviation of their PM values in the R.A. and decl. axes, respectively. These values are further used to construct the frequency distributions of cluster stars (${\phi }_{c}^{\nu }$) and field stars (${\phi }_{f}^{\nu }$) by using the equations given in Yadav et al. (2013) and then the value of membership probability (ratio of distribution of cluster stars with all stars) by using the following equation:

$$\begin{eqnarray}&&{P}_{\mu }(i)=\displaystyle \frac{{n}_{c}\times {\phi }_{c}^{\nu }(i)}{{n}_{c}\times {\phi }_{c}^{\nu }(i)+{n}_{f}\times {\phi }_{f}^{\nu }(i)},\end{eqnarray} \tag{ 7 }$$

where n_c (=0.16) and n_f (=0.84) are the normalized numbers of stars for the cluster and field region (n_c + n_f = 1).

Zoom In Zoom Out Reset image size

The estimated membership probability of the Gaia sources located within the radius of the NGC 6910 cluster region is plotted as a function of G magnitude in Figure 6 (right panel). As can be seen in this plot, a high membership probability (P_μ >  80%) extends down to G ∼ 20 mag. At fainter magnitudes, the probability gradually decreases. In Figure 6 (right panel), we have also plotted the parallax of the same stars as a function of G magnitude. Except for a few outliers, most of the stars with high membership probability (P_μ >  80% and G < 20 mag) are following a tight distribution. Finally, from the above analysis, we calculate the membership probability of 916 stars in the NGC 6910 cluster region, and 128 stars were assigned as cluster members based on their high membership probability (P_μ >80% and G < 20 mag). The details of these cluster members are given in Table 3.

Table 3.  Sample of the 128 Cluster Members Identified through Their Gaia PM Data

ID	αJ2000	δJ2000	V	B	I	R	U	Parallax	μαcos(δ)	μδ	G	$({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})$	Pμ
	(deg)	(deg)	(mag)	(mag)	(mag)	(mag)	(mag)	(mas)	(mas yr−1)	(mas yr−1)	(mag)	(mag)	(%)
1	305.888133	40.693244	18.376 ± 0.011	19.838 ± 0.015	16.211 ± 0.010	⋯	⋯	0.753 ± 0.131	−2.706 ± 0.148	−5.341 ± 0.197	17.450	2.080	98
2	305.898745	40.707285	19.526 ± 0.014	21.124 ± 0.033	17.243 ± 0.010	⋯	⋯	0.374 ± 0.216	−2.408 ± 0.225	−5.536 ± 0.323	18.504	2.145	96
3	305.875944	40.712293	19.277 ± 0.013	20.818 ± 0.023	16.937 ± 0.013	⋯	⋯	0.453 ± 0.161	−2.974 ± 0.183	−5.727 ± 0.247	18.245	2.167	81
4	305.797771	40.716103	19.653 ± 0.013	21.479 ± 0.052	17.105 ± 0.060	18.307 ± 0.027	⋯	0.389 ± 0.205	−2.527 ± 0.306	−5.285 ± 0.314	18.427	2.377	96

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

The nature of the diffuse interstellar medium (ISM) is often characterized by the ratio of total-to-selective extinction, represented by R_V = A_V/E(B − V). The normal reddening law for the solar vicinity gives the value R_V = 3.1 ± 0.2 (Guetter & Vrba 1989; Whittet 2003; Lim et al. 2011), but in the case of several star-forming regions having an unusual distribution of dust sizes, it is found to be abruptly high (see, e.g., Pandey et al. 2000, Pandey et al. 2008; Hur et al. 2012; Pandey et al. 2013; Kumar et al. 2014). To separate the influence of normal extinction produced by the general ISM from that of abnormal extinction arising within regions, we used (V − λ) versus $(B-V)$ two-color diagrams (TCDs; see Chini et al. 1990; Pandey et al. 2000, 2003), where λ indicates one of the wavelengths of the broadband filters ($J,H,K,{I}_{C}$). Figure 7 shows the (V − λ) versus $(B-V)$ TCDs of all cluster member stars having optical and NIR observations. The slopes of the least-squares fit to the distribution of stars in the $(V-{I}_{c}),(V-J),(V-H)$, and $(V-K)$ versus $(B-V)$ TCDs are found to be 1.35 ± 0.10, 2.33 ± 0.12, 2.94 ± 0.11, and 3.10 ± 0.09, respectively, which are higher by a factor of m ∼ 1.21 ± 0.01 than those found for the general ISM (1.10, 1.96, 2.42, and 2.60; see Pandey et al. 2003). This concedes a higher value for R_V (∼3.75 ± 0.02; please refer Pandey et al. 2003 for a detailed description of reddening law estimation), indicating larger grain sizes of the material in this region as compared to the general ISM. We have also calculated the R_V value for the stars that are not cluster members (i.e., Pμ <  20% and V < 20 mag) and found a similar value of R_V (∼3.75 ± 0.02) as for cluster member stars. This means that, in general, the R_V value is higher in this region. Inside dense dark clouds, the coagulation due to grain collision and accretion of ice mantles on grains can change the size distribution leading to higher R_V values (Cardelli et al. 1989). In many star-forming regions, R_V values tend to diverge from the normal value toward the higher ones; for example, R_V = 3.7 (Kumar et al. 2014; the Carina region), 3.3 (Pandey et al. 2013; NGC 1931), 3.5 (Sharma et al. 2012; NGC 281), and 3.7 (Pandey et al. 2008; Be 59).

Zoom In Zoom Out Reset image size

The extinction toward the cluster NGC 6910 can be estimated by using the $(U-B)$ versus $(B-V)$ TCD, as shown in Figure 8 (left panel). In this figure, stars inside the cluster region (r_cl < 55; black dots), along with the intrinsic zero-age main sequence (ZAMS; blue dotted curve) taken from Pecaut & Mamajek (2013), are shown. We have also overplotted the probable cluster member stars identified by using the PM data (see Section 4.1.2) as red circles. The distribution of the stars shows a large spread along the reddening vector, indicating heavy differential reddening in this region. It reveals two different populations, one (mostly black dots) distributed along the ZAMS and another (mostly red circles) showing a large spread in reddening value. The former, having negligible reddening, must be the foreground population, and the latter could be member stars. If we look at the MIR images of this region (Figure 1), we see several dust lanes, along with enhancements of nebular emission at many places. Both of them are likely responsible for the large spread of reddening in the NGC 6910 region. The ZAMS is shifted along the reddening vector with a slope of $E(U-B)/E(B-V)$ =0.72 × 1.21 (corresponding to R_V ∼3.75; see Section 4.1.3) to match the distribution of stars showing minimum reddening among the member population. Only those stars were chosen for reddening analysis if their position in the TCD indicated that their spectral type is A or earlier. This choice was dictated by several factors, such as metallicity, distribution of binary stars, rotation, PMS stars, and error in photometry (for more details, see Golay 1974; Phelps & Janes 1994). The cluster foreground reddening value, $E{(B-V)}_{\min }$, thus comes out to be ∼0.95 mag, and the ZAMS reddened by this amount is shown by a red solid curve. The other stars may be embedded in the nebulosity of this region, and the maximum reddening value, $E{(B-V)}_{\max }$, for them comes out to be 1.35 mag (red dashed curve). The approximate error in the reddening measurement $E(B-V)$ is ∼0.1 mag and has been determined by the procedure outlined in Phelps & Janes (1994).

Zoom In Zoom Out Reset image size

The photometric distance (∼1.5 kpc) of this cluster has been estimated previously in the literature (Shevchenko et al. 1991; Vansevicius 1992). Recent distance estimates put this cluster at a distance of 1.6 (Kolaczkowski et al. 2004) to 1.74 (Delgado & Alfaro 2000) kpc. Delgado & Alfaro (2000) quoted the distance and age of this cluster as 1740 pc and 6.8 Myr, respectively. However, as the extinction in the NGC 6910 region is high and apparently anomalous, these distance measurements will be sensitive to the adopted R_V values. We calculated the distance of the member stars of this cluster by using their parallax values with good accuracy (error <0.05 mas) from Bailer-Jones et al. (2018). The mean distance value comes out to be 1.72 ± 0.08 kpc. The distance and age of a cluster can also be derived quite accurately by using the CMD of their MS member stars (see Phelps & Janes 1994; Sharma et al. 2006; Friel et al. 2014; Perren et al. 2015; Sharma et al. 2017; Bossini et al. 2019; Pandey et al. 2020a, 2020b). The V versus $(V-I)$ CMD for stars lying within the cluster region is shown in the right panel of Figure 8. The probable cluster member stars (see Section 4.1.2) are also plotted in the figure with red circles. Here also, the CMD reveals two different populations, one (mostly black dots) for foreground stars having almost zero reddening value (near the dotted curve) and another (mostly red circles) for the cluster members at higher reddening values and larger distances. The CMD of cluster members displays a few MS stars up to V = 16 mag and PMS stars at the fainter end. The blue dotted curve in the right panel of Figure 8 denotes a ZAMS from Pecaut & Mamajek (2013), randomly corrected for a distance of 0.8 kpc, matching well with the distribution of foreground stars. We have further visually fitted the post-MS isochrone for an age of 4.5 Myr from Pastorelli et al. (2019) to the lower envelope of the distribution of member stars where the bend occurs in the MS. This choice of visual fitting was imposed by several factors, such as distribution of binary stars, rotation, and evolutionary effects (for details, see Golay 1974; Phelps & Janes 1994). The isochrone, when corrected for exinction, is matching nicely to the lower envelop of the MS stars. The locations of massive stars such as HD 194279 (B2Ia C, blue supergiant; Adelman & Yüce 2007), BD+40 4148 (O9.5V; Hoag & Applequist 1965), BD+40 4146 (B1 D; Walker & Hodge 1968), and LS III +40 12 (B0.5V; Comerón & Pasquali 2012) are also matching well with the isochrone. Therefore, from both parallax and CMD analyses, we have derived the distance and post-MS age of this cluster as 1.72 kpc and 4.5 Myr, respectively. The approximate error in the age estimation is ∼2.5 Myr, as has been determined by the procedure outlined in Phelps & Janes (1994). A summary of the physical parameters of the cluster is given in Table 4.

Table 4.  A Summary of the Physical Parameters of the Cluster

Reference	Rcl	Age	Distance Modulus	RV	$E(B-V)$
	(arcmin)	(Myr)	(mag)		(mag)
Present study $({UBVRI})$	5.5	4.5 ± 2.5	11.18 ± 0.12	3.75 ± 0.02	0.95 ± 0.10
Delgado & Alfaro (2000; UBV)	⋯	6.5 ± 3.0	11.2 ± 0.2	3.1 ± 0.1	1.02 ± 0.13
Kolaczkowski et al. (2004; VI)	⋯	6.0 ± 2.0	11.0 ± 0.3	⋯	1.19 ± 0.21

Download table as:  ASCIITypeset image

The distribution of stellar masses that form in one star formation event in a given volume of space is called IMF, and together with star formation rate, it is one of the important statistical tools to study star formation. The MF is often expressed by a power law, $N(\mathrm{log}m)\propto {m}^{{\rm{\Gamma }}}$, and the slope of the MF is given as

$$\begin{eqnarray}&&{\rm{\Gamma }}=d\mathrm{log}N(\mathrm{log}m)/d\mathrm{log}m,\end{eqnarray} \tag{ 8 }$$

where $N(\mathrm{log}m)$ is the number of stars per unit logarithmic mass interval. We have used our deep optical data to generate the MF of different regions of the NGC 6910 cluster as it reaches to the fainter end as compared to the Gaia DR2 data. For this, we have utilized the optical CMDs of the sources in the target region and that of the nearby field region of equal area, decontaminated the former sources from foreground/background stars, and corrected for data incompleteness using a statistical subtraction method already described in detail in our previous papers (see Sharma et al. 2007; Pandey et al. 2008; Chauhan et al. 2011; Sharma et al. 2012; Pandey et al. 2013; Jose et al. 2013; Sharma et al. 2017).

As an example, in Figure 9 (top left panel), we show V versus $(V-{I}_{c})$ CMDs for the stars lying within the cluster region in subpanel (a) and for those in the reference field region (taken as an annular area outside the cluster region having radius $5\buildrel{\,\prime}\over{.} 5\lt {r}_{\mathrm{field}}\lt 7\buildrel{\,\prime}\over{.} 65$) in subpanel (b). In subpanel (c), we plot the statistically cleaned V versus $(V-{I}_{c})$ CMD for the cluster region that is showing the presence of PMS stars. Since, at the age of 4.5 Myr, the stars having V ≤ 16 mag are considered to be still on the MS, for these stars, the luminosity function was converted into MF using theoretical models by Pastorelli et al. (2019). The MF for the PMS stars was obtained by counting the number of stars in various mass bins (shown as evolutionary tracks) having ages ≤7 Myr (age of cluster, i.e., 4.5 Myr + error in age) in Figure 9, subpanel (c). The resulting MFs of the cluster region using MS ($2.3\lt M/{M}_{\odot }\lt 24.86$) and MS+PMS ($0.8\lt M/{M}_{\odot }\lt 24.86$) stars are plotted in Figure 9 (top right) in the top and bottom subpanels, respectively. Similarly, we have also derived MF slopes Γ for the core and corona regions of the cluster using both MS and MS+PMS stars, and their values are given in Table 5.

Zoom In Zoom Out Reset image size

As the NGC 6910 cluster region contains several massive stars, we shall study the environmental effects due to the presence of high-mass stars on the lower-mass end of the present-day MF. In Figure 9 (top right panel), we can observe that the MF for the cluster region shows a turnoff at 1.58 M_⊙, and the distribution up to this mass limit can be represented by a single power law. The MF slopes of different regions of the cluster NGC 6910 are generally shallower than the Salpeter value −1.35, which indicates the abundance of massive stars in this cluster. It has been shown (see, e.g., Scalo 1986, 1998; Kroupa 2002; Chabrier 2003; Corbelli et al. 2005) that, for masses above ∼1 M_⊙, the MF can generally be approximated by a declining power law with a slope similar to that found by Salpeter (1955). To investigate further, we look for the signature of mass segregation in this cluster by checking the change of MF slope from the core region to the outer corona region of this cluster, which is in fact getting steeper in the outer corona region. To evaluate the degree of mass segregation in the cluster, we subdivided the samples of cluster stars into two mass groups and plotted their cumulative distribution with respect to radial distance from the cluster center as shown in Figure 9 (bottom panels) for both MS (left) and MS+PMS (right) stars. Figure 9 (bottom panels) also reveals the effect of mass segregation in the sense that relatively massive stars tend to lie near the cluster center. The Kolmogorov–Smirnov test confirms the abovementioned mass segregation at a confidence level better than ∼99%.

Dynamical relaxation is one of the possible reasons for the segregation of massive stars in the central region of this cluster. At the time of formation, the cluster may have a uniform spatial stellar mass distribution; however, the spatial stellar mass distribution would change with time as the cluster evolves dynamically. Low-mass stars in a cluster may possess high random velocities because of dynamical relaxation; consequently, they will try to occupy a larger volume than the high-mass stars and move away from the cluster center (Mathieu 1985; McNamara & Sekiguchi 1986). To check whether mass segregation is primordial or due to dynamical relaxation, we have estimated the dynamical relaxation time, T_E, the time in which individual stars exchange sufficient energy so that their velocity distribution approaches that of a Maxwellian equilibrium. The dynamical relaxation time is given by

$$\begin{eqnarray}&&{T}_{E}=\displaystyle \frac{8.9\times {10}^{5}{N}^{1/2}{R}_{h}^{3/2}}{{m}^{1/2}\mathrm{log}(0.4N)},\end{eqnarray} \tag{ 9 }$$

where N = 215 is the number of cluster members, R_h = 1.6 pc is the radius containing half of the cluster mass, and m = 4.31 M_⊙ is the average mass of the cluster stars (Spitzer & Hart 1971). The total number of MS stars and the total mass of MS stars (775 ${M}_{\odot }$) in the given mass range are obtained with the help of the MF. This total mass of MS stars should be considered as a lower limit to the total mass of the cluster. The half-mass–radius R_h as half of the cluster radius appears to be a tenable approximation. We used half of the cluster radius (r_cl) obtained from the optical data as the half-mass–radius. The dynamical age of this cluster comes out to be 6.5 Myr, which is more than the age of this cluster (i.e., 4.5 Myr), suggesting that the dynamics is not fully responsible for the observed mass segregation, and it may be the imprint of the star formation process itself.

Recently available high-resolution radio/infrared/submillimeter observations have helped us to probe deeply embedded star-forming regions and provided a wealth of new information to probe young stars, gas and dust distribution, ionized gas distribution, etc., which are very good indicators/tools for star formation studies (e.g., Deharveng et al. 2010; Watson et al. 2010; Dewangan et al. 2016, 2017).

In Figures 10(a) and (b), the large-scale environment of the cluster NGC 6910 is shown using the CGPS 480 and 1420 MHz continuum images, respectively. These radio continuum images reveal an extended spherical-like structure, which is related to the γ Cygni SNR. Our selected target area is highlighted by a white box in both of the radio continuum images, indicating the location of the NGC 6910 cluster at the border of the SNR. Uchiyama et al. (2002) reported the age of SNR G78.2+2.1 to be 6600 yr. No molecular ¹³CO emission is observed toward the NGC 6910 cluster (see positions at l = 7869, b = 196 in Figure 8 in Piano et al. 2019). It is likely that the SNR might have influenced its surrounding environment. However, the impact of the young SNR G78.2+2.1 on the formation of the relatively old cluster NGC 6910 (∼4.5 Myr; Section 4.1.4) is unlikely. Figure 10(c) displays the NRAO VLA Sky Survey (NVSS) 1.4 GHz continuum map. The NVSS map indicates the presence of the extended diffuse radio continuum emission (1σ ∼ 0.45 mJy beam⁻¹) showing the existence of radio continuum clumps toward the cluster, which is not seen in the CGPS continuum images having lower sensitivity (see the white box in Figures 10(a)–(c)). The presence of the radio clumps suggests the existence of embedded massive OB stars, implying the ongoing massive star formation in the region. Using the Planck image at 850 μm (or 353 GHz), a tracer of the cold dust emission, we show a field hosting the SNR and the cluster NGC 6910 in Figure 10(d). It seems that the cluster area is not associated with any noticeable cold dust emission.

Zoom In Zoom Out Reset image size

Figures 11(a) and (b) present the Spitzer 24 μm and Herschel 70 μm images of the area selected in this paper, respectively. Both infrared images are overlaid with the NVSS 1.4 GHz continuum emission contours. The extension of the stellar cluster is also marked in both infrared images. The images at 24 and 70 μm allow one to qualitatively trace the warm dust emission present in the cluster NGC 6910. In Figures 11(c)–(f), we present a zoomed-in view of the central part of the cluster (see the dashed boxed in Figure 7(b)) using the 3.6, 8.0, 24, and 70 μm images, respectively. These images are also overlaid with the NVSS 1.4 GHz radio continuum emission contours. Diffuse emission is seen in all of these infrared images except at 3.6 μm. We find that the warm dust emission depicted in the 24 and 70 μm images is surrounded by the Spitzer 8.0 μm emission. Note that the Spitzer band at 8.0 μm hosts PAH features at 7.7 and 8.6 μm. Considering the inclusion of PAH features in the 8.0 μm band, the existence of PDRs is evident in the NGC 6910 region, suggesting the impact of massive OB stars present in the stellar cluster.

Zoom In Zoom Out Reset image size

Figure 12(a) shows the submillimeter image at 350 μm (resolution ∼25''), where the extension of the stellar cluster is also marked. In the east direction of the cluster, the submillimeter emission is observed and is not spatially coincident with the 24 and 70 μm emission (see Figures 11(a) and (b)). In Figure 12(b), we plot the stellar surface density contours against the distribution of the warm dust emission and ionized emission in the cluster area. In Figure 12(b), the warm dust emission is traced using the Spitzer 24 μm image (see filled area), while the NVSS 1.4 GHz continuum emission depicts the ionized emission (see black contours). We find that the radio continuum peaks (ionized clumps or H ii regions) are located away from the center of the cluster (see arrows in Figure 12(b)). Based on the analysis of the NVSS radio continuum data, we calculate that these ionized clumps are powered by B1V–B0.5V stars (see Table 2 in Panagia 1973, for a theoretical value), and their dynamical ages are estimated to be ∼0.07–0.12 Myr. In this calculation, we have employed the same procedures as carried out in Dewangan et al. (2017). Using the integrated radio continuum flux density and radius (R_{H ii}) of each ionized clump, the number of Lyman continuum photons (N_uv) was estimated following the equation given in Matsakis et al. (1976). Then, with knowledge of the N_uv and R_{H ii} values, the age of each ionized clump or H ii region has been estimated using the equation given in Dyson & Williams (1980).

Zoom In Zoom Out Reset image size

The Herschel temperature and column density maps can be used to deduce the physical conditions present in a given star-forming region (see Dewangan 2019; Dewangan et al. 2019a, 2019b). Figures 12(c) and (d) show the Herschel temperature and column density maps (resolution ∼12''), respectively. These Herschel maps are also overlaid with the NVSS radio continuum emission contours. In Figure 12(c), we have traced a feature in the temperature map using a contour of T_d = 17.5 K ($\approx \mathrm{average}\,\mathrm{dust}\,\mathrm{temperature}$). Using a black broken contour, this feature is also highlighted in both Herschel maps. The ionized clumps distributed within the cluster are associated with emission at T_d = 17.5–18.0 K. In Figure 12(d), we do not find high column density materials in the direction of the cluster except in the east direction, where radio peaks are seen harboring the very young stellar sources.

Our careful analysis of various observational data sets suggests that the MF slope of the cluster region is shallower than the Salpeter value (i.e., Γ = −1.35). It shows a signature of the presence of more massive stars compared to the low-mass stars in the cluster region. This argument suggests the effect of mass segregation. A comparison between the cluster age (i.e., ∼4.5 Myr) and its dynamical relaxation time (i.e., ∼6.5 Myr) indicates that the cluster is not relaxed yet. Furthermore, the observed mass segregation seen in this cluster may be the imprint of their formation processes. These properties make the NGC 6910 cluster a special target to study the feedback effect of massive star(s) on its environment.

Massive stars can provide positive feedback affecting star formation by accumulating neutral material at the periphery of H ii regions via the "collect-and-collapse" mechanism (Elmegreen & Lada 1977; Whitworth et al. 1994) or by the compression of preexisting dense condensations via the "radiation-driven implosion" (RDI) mechanism (Bertoldi 1989; Lefloch & Lazareff 1994). Star formation induced in a region by these processes is also called "triggered" star formation, and observational signposts usually include the age sequence of the stellar sources and the distribution of cool, warm, and ionized gas in the region (see also Samal et al. 2007; Sharma et al. 2007; Jose et al. 2011; Sharma et al. 2012, Sharma et al. 2017). Observational studies of bubbles associated with H ii regions created by massive stars suggest that their expansion probably triggers 14%–30% of star formation in our Galaxy (e.g., Deharveng et al. 2010; Kendrew et al. 2012; Thompson et al. 2012), thus implying the importance of massive OB stars on the star formation activities in our Galaxy.

The cluster NGC 6910 contains several massive OB stars, and the most massive of them is an O9.5V star known as BD+40 4148 (Hoag & Applequist 1965). The position of this massive star is marked by a diamond in Figure 2. In general, a massive star can influence its surroundings through its different feedback pressure components (such as pressure of an H ii region $({P}_{{\rm{H}}{\rm{II}}})$, radiation pressure (P_rad), and stellar wind ram pressure (P_wind); see, e.g., Bressert et al. 2012; Dewangan et al. 2017). These pressure components can be expressed as (see, e.g., Bressert et al. 2012)

$$\begin{eqnarray}&&{P}_{{\rm{H}}{\rm{II}}}=\mu {m}_{{\rm{H}}}{c}_{s}^{2}\left(\sqrt{\displaystyle \frac{3{N}_{\mathrm{uv}}}{4\pi \,{\alpha }_{B}\,{D}_{s}^{3}}}\right),\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{P}_{\mathrm{rad}}={L}_{\mathrm{bol}}/4\pi {{cD}}_{s}^{2},\end{eqnarray} \tag{ 11 }$$

and

$$\begin{eqnarray}&&{P}_{\mathrm{wind}}={\dot{M}}_{w}{V}_{w}/4\pi {D}_{s}^{2}.\end{eqnarray} \tag{ 12 }$$

In the equations above, N_uv is the number of Lyman continuum photons, c_s is the sound speed in the photoionized region (=11 km s⁻¹; Bisbas et al. 2009), α_B is the radiative recombination coefficient (=2.6 × 10⁻¹³ × (10⁴ K/T_e)^0.7 cm³ s⁻¹; Kwan 1997), μ is the mean molecular weight in the ionized gas (=0.678; Bisbas et al. 2009), m_H is the hydrogen atom mass, ${\dot{M}}_{w}$ is the mass-loss rate, V_w is the wind velocity of the ionizing source, L_bol is the bolometric luminosity of the ionizing source, and D_s is the projected distance from the location of the O9.5V-type star to the ionized clumps, which is adopted to be 1.0 pc (see Figure 12(b)).

We have used L_bol = 66,070 L_⊙ (Panagia 1973), ${\dot{M}}_{w}\approx 1.58$ × 10⁻⁹ M_⊙ yr⁻¹ (Marcolino et al. 2009), V_w ≈ 1500 km s⁻¹ (Marcolino et al. 2009), and N_uv = 1.2 × 10⁴⁸ photons per second (Panagia 1973) for a star of O9.5V spectral type to estimate different pressure components, which comes out to be P_{H ii} ≈ 2.6 × 10⁻¹⁰, P_rad ≈ 7.1 × 10⁻¹¹, and P_wind ≈ 1.3 × 10⁻¹³ dyne cm⁻². It gives the total pressure (i.e., P_total = P_{H ii} + P_rad + P_wind) driven by a massive star as ∼3.4 × 10⁻¹⁰ dyne cm⁻². It appears that the P_{H ii} component is relatively higher than other two pressure components. Furthermore, we find that the value of P_total is also higher than the pressure of a typical cool molecular cloud (P_MC ∼ 10⁻¹¹–10⁻¹² dyne cm⁻² for a temperature ∼20 K and particle density ∼10³–10⁴ cm⁻³; see Table 7.3 of Dyson & Williams 1980). It suggests that the massive star seems to have significantly influenced its environment. Additionally, the photoionized gas associated with the cluster appears to be responsible for the feedback mechanism.

We also find the existence of young ionized clumps, located along the edge of the NGC 6910 cluster containing massive stars, in a high column density region. The center of the cluster is associated with warm dust emission, and the ionized clumps are distributed in the PDRs. Hence, it is likely that these massive stars might have influenced the birth of the youngest massive B-type stars (age range ∼0.07–0.12 Myr) powering the ionized clumps. In the triggered star-forming region Sh 2-294, Samal et al. (2007) also found ionized clumps away from the exciting source. We did not find any ring/arc of gas and dust surrounding the NGC 6910 cluster, as has been found in the regions showing the collect-and-collapse mechanism (for details, see Deharveng et al. 2005). Therefore, the age difference between the young B-type stars and the central massive star (O9.5V), and the distribution of PDRs/warm and cold gas and dust/ionized gas in the region, indicate that the star formation at the border of NGC 6910 is maybe due to the RDI process. However, with the currently available observations and data, it is too early to establish or rule out either of the scenarios.