Census of young stellar population in the Galactic H ii region Sh2-242

As a complementary data set to the observed optical photometry (Section 2.1.1), we used optical/NIR imaging from the Panoramic Survey Telescope and Rapid Response System 1 (Pan-STARRS 1, or PS1; Chambers et al. 2019). The PS1 camera consists of a mosaic of 60 edge-abutted 4846$\times$4868 pixel detectors, with 10 $\mu$m pixels subtending 0$\farcs$258. The PS1 provides homogeneous and deeper coverage photometry in five broad passbands g_P1, r_P1, i_P1, z_P1, and y_P1, ranging from 400 nm to 1000 nm (Stubbs et al., 2010). The effective wavelengths for the five filters are roughly 480, 620, 750, 870, and 960 nm, respectively, similar to those used by the SDSS (York et al., 2000), with most significant difference being the replacement of the Sloan u band with a NIR band y_P1. The PS1 image processing, astrometry, and photometry are detailed in Magnier et al. (2016a, b) and the relative and absolute calibration survey are reported in Schlafly et al. (2012) and Tonry et al. (2012). The typical single-epoch 5$\sigma$ photometric depths in the corresponding five passbands are 22.0, 21.8, 21.5, 20.9, and 19.7 mag (AB), respectively (Chambers et al., 2019). The empirical components of the adopted extinction vector are taken from Schlafly et al. (2016) and given in Table 3.

The Gaia Data Release 2 (Gaia DR2; Gaia Collaboration et al. 2018) provides five parameter (position, proper motion, and parallax) astrometric results for over 1.3 billion sources from the observations of the European Space Agency Gaia satellite (Gaia Collaboration et al., 2016). The parallaxes of the sources toward the S242 cluster are collected from the Gaia DR2 archive²²2https://gea.esac.esa.int/archive/. The distance and membership status of the sources are estimated by restricting the data to only positive parallaxes. The positive parallaxes with relative uncertainties typically below 20% are primarily considered as reliable astrometry (Luri et al., 2018).

The INT/WFC Photometric H$\alpha$ Survey of the Northern Galactic Plane (IPHAS; Drew et al. 2005) is an imaging survey covering an 1800 deg² sky in broadband Sloan $r$ (624 nm) and $i$ (774.3 nm), and narrowband H$\alpha$ (656.8 nm) filters using the Wide Field Camera (WFC) on the 2.5 m Isaac Newton Telescope (INT) in La Palma. The WFC generates a mosaic of four CCDs at a pixel scale of 0$\farcs$33 pixel^-1. This survey offers an unique facility to detect H$\alpha$ emission line objects by comprehensive CCD photometry of point sources at visible wavelengths. The photometric data for $r$, $i$, and H$\alpha$ bands were obtained from the IPHAS DR2 catalog (Barentsen et al., 2014) for the S242 cluster.

The final catalog was generated by matching different optical to infrared data sets in stages. The $BVI$ catalog was built by cross-matching all the sources detected from optical photometry (Section 2.1.1) with a radial tolerance of 2$\arcsec$. As the seeing ($\sim$ 2$\arcsec$) was not sufficiently good, we used a matching radius of 2$\arcsec$ to match the sources detected in optical photometry. We performed several test matches by increasing the radial distance from 1$\arcsec$ to 3$\arcsec$ in steps of 0$\farcs$1 to pick up the suitable matching radius for each catalog data. In case of multiple sources matched within a given matching radius, we have taken the nearest one as the preferred match. To match the sources detected from WIRCam $JHK$ bands, a matching radius of 1$\arcsec$ was used. $JHK$, IRAC, and IPHAS catalogs were matched within a matching radius of 1$\arcsec$. We have adopted the matching radius of 1$\arcsec$ to match the sources selected from optical and infrared catalog data.

We have used histogram turn over method to estimate the completeness of our utilized data sets. In general, the completeness limits are calculated from histograms, where the logarithmic distribution of the sources deviates from the linear distribution. The completeness limits for different data sets for the S242 region are $V$ = 17.8 mag, $J$ = 18.4 mag, $H$ = 17.6 mag, $K$ = 17.2 mag, [3.6] = 16.8 mag, and [4.5] = 16.4 mag, respectively. However, there may be several additional factors, such as saturation caused by bright luminous sources, variable reddening, stellar crowding, telescope detection sensitivity, etc., that can constrain the completeness of different data sets (Jose et al., 2013).

The target stars for spectroscopic observations were selected based on their brightness ($J$ < 11 mag) within the cluster region. The details of observations for each star are listed in Table 1. The flux-calibrated normalized spectra of the observed stars obtained with Grism 7 and 8 are presented in Fig. 3.

Spectral classifications were done by comparison to the spectral indices of Danks & Dennefeld (1994), Kobulnicky et al. (2012), and Hernández et al. (2004), and comparison with the spectral atlas of Jacoby et al. (1984), Walborn & Fitzpatrick (1990), and Torres-Dodgen & Weaver (1993). The classification scheme relied on the marking and utilizing of strong conspicuous features for any spectral range. For early-type stars (B, A, and F), we compared the strength of atomic absorption lines, such as hydrogen Balmer series (H$\delta$ $\lambda$4102 Å, H$\gamma$ $\lambda$4340 Å, H$\beta$ $\lambda$4861 Å, H$\alpha$ $\lambda$6563 Å), He i ($\lambda\lambda$5876, 6678, 7065 Å), and He ii ($\lambda\lambda$4200, 4541, 4686, 5411, 5720 Å) lines. Whereas for cooler stars like G-type or later than that, different metallic line features such as Mg i triplet ($\lambda\lambda$5167, 5172, 5183 Å), Mg ii ($\lambda\lambda$4481, 6347 Å), Ca i ($\lambda\lambda$6122, 6162 Å), and Fe i ($\lambda\lambda$6495, 7749, 7834 Å) are used. We also adopted certain constraints on the specific line features. The absence of He ii $\lambda$5411 Å line in any spectra limits the spectral type to B0.5 or later (Kobulnicky et al., 2012), while the absence of He i $\lambda$5876 Å constrains the spectral type to later than A0 (Lundquist et al., 2014). Si iii $\lambda$4552 Å and O ii $\lambda$4650 Å show maximum strength at spectral type B0.5 V, and He ii $\lambda$4686 Å is last seen up to types B0.5$-$B0.7 V (Walborn & Fitzpatrick, 1990). The declining strength of C iii $\lambda$4070 Å and O ii $\lambda$4650 Å blends are used as an additional criteria to classify the stars in the spectral range B1$-$B2 V. He i line strength is maximum for B2 type stars, whereas for later than that Si ii $\lambda\lambda$4128$-$4130 Å and Mg ii $\lambda$4481 Å increase distinctly (Walborn & Fitzpatrick, 1990). He i $\lambda$6678 Å appears strongest at O9 V, before disappearing at B8 V (Danks & Dennefeld, 1994). The weak presence of O i $\lambda$7776 Å is notable at B2 V, strengthens to maximum at A5 V and disappears at G0 V. The appearance of Fe i $\lambda$6495 Å is evident at A2 V and grows in strength to K0 V (Danks & Dennefeld, 1994). The presence of Fe i $\lambda\lambda$7749, 7937 Å in any spectrum is an indication of K dwarfs (Allen & Storm, 1995). We also compared the equivalent widths of He ii $\lambda$5411 Å, He i $\lambda$5876 Å and H$\alpha$ $\lambda$6563 Å for B-type stars, and Na i ($\lambda\lambda$5890$-$5896 Å), H$\alpha$ and Ca ii triplet ($\lambda\lambda$8498, 8542, 8662 Å) for later-type stars with the spectral indices of Danks & Dennefeld (1994), Kobulnicky et al. (2012), and Lundquist et al. (2014).

The spectroscopic analysis of the observed sources produced only one massive and early-type star (B0.5 V). Other spectroscopically observed sources were found to be late-type (either G or K) stars. The star ID 1 shows weaker H$\alpha$ $\lambda$6563 Å and Na i $\lambda\lambda$5893, 8195 Å absorption features, presence of Fe i $\lambda\lambda$6495, 7747, 7834 Å and Ca ii triplet $\lambda\lambda$8498, 8542, 8662 Å indicative of an early-K type star (K1 V-III). The star ID 2 is classified as K0 V-III, from similar diagnostic as ID 1. The spectrum of star ID 3 shows strong He i $\lambda$5876 Å and H$\alpha$ absorption feature along with the presence of He ii $\lambda$4200 Å and He i $\lambda\lambda$6678, 7065 Å lines. As no signature of He ii $\lambda$5411 Å was detected from the spectrum, we categorized the star as B0.5 V spectral type. The stars ID 4 and 5 were classified as G9 V and G0 V type, respectively, for showing weak and narrow H$\alpha$ absorption features and presence of Mg i triplet at $\lambda\lambda$5167, 5172, 5183 Å. We designated the stars with luminosity class V/III, as their spectral resemblance with the main-sequence/giants are better than super-giants. Also in some cases it was difficult to properly distinguish between the main-sequence and the giant stars. Based on the low-resolution spectroscopy, an uncertainty of $\pm$1 spectral subtype for early-type stars up to F- and $\pm$3 subtype for G-type and later stars is expected. The photometric and spectroscopic details of the five observed stars are tabulated in Table 4.

Membership estimation of the observed stars toward a cluster region is a crucial step to quantify the essential cluster parameters. The relevant parameters used to ascertain the spectrophotometric distances for each star are listed in Table 4. We used the spectral types and infrared photometry ($J$, $H$, and $K$) to determine the distances of the spectroscopically observed bright sources (Dutta et al., 2015). We have estimated the spectroscopic $A_{V}$ of individual sources, using the relation $E(J-H)=(J-H)-(J-H)_{0}$, and similar relations simultaneously for other two bands, where $(J-H)$ is the observed color and $(J-H)_{0}$ being the intrinsic color. The intrinsic distance modulus ($J_{0}-M_{J}$), ($H_{0}-M_{H}$), and ($K_{0}-M_{K}$) were calculated from reddening $A_{V}$, absolute ($M_{J},M_{H},M_{K}$) and observed ($J,H,K$) magnitudes. The intrinsic values of magnitudes and colors were taken from Pecaut & Mamajek (2013). The intrinsic distance modulus of star ID 3 was calculated as 11.58 $\pm$ 0.05 mag, which corresponds to a distance of 2.08 $\pm$ 0.24 kpc. Additionally from the Gaia DR2 catalog, the distance of the source is derived as 2.08 $\pm$ 0.19 kpc, which is in close agreement with our estimated spectrophotometric distance. Out of the five spectroscopically observed stars, we assigned BD+26 980 (star ID 3) of spectral type B0.5 V, a massive member of the cluster. Others are either foreground or background stars as mentioned in Table 4.

Fig. 4 shows the distribution of sources detected from the observed optical photometry toward S242 in the $V/(B-V)$ and $V/(V-I)$ color-magnitude (CM) diagrams. The black filled circles represent the sources with photometric uncertainty $<$ 0.1 mag and gray filled circles are those with photometric uncertainty higher than this. The spectroscopically observed stars are numbered and marked with red circles. The blue solid lines represent the locus of the zero-age main sequence (ZAMS) taken from Girardi et al. (2002) and corrected for the cluster distance of 2.08 kpc, and reddening $E(B-V)$ = 0.56 and $E(V-I)$ = 0.70 mag [$E(B-V)/E(V-I)=0.794$ ; Cohen et al. 1981]. In order to shift the ZAMS, we used the extinction $A_{V}=1.8$ mag (Table 4) of the main illuminating source BD+26 980 of the region. The photometric catalog of optically observed point sources toward the S242 region is tabulated in Table 5. A total of 503 sources was detected at least in $B$, $V$, or $I$ band with a limiting magnitude of $V\sim$ 19.4 mag. We obtained a total of 291 sources having counterparts in all the three $B$, $V$, and $I$ bands, within a 18$\arcmin\times$18$\arcmin$ sky area. Although the spatial variation of extinction can be non-uniform throughout the region. There may be several causes for the broad distribution of sources in the CM diagrams, such as variable reddening, presence of field stars, binaries, and peculiar stars. However it is difficult to differentiate the cluster members and field stars from these diagrams.

Discriminating embedded young stars in clusters from field stars is a salient feature in the study of young stellar distributions of interest. Young cluster environments are rich with dust, reducing the density of background stellar contamination (Gutermuth et al., 2005). Often the nonuniform distribution of dust in these environments makes it far more challenging to get a proper census of detectable background stars (Gutermuth et al., 2005). In general, the distribution of dust in a cloud can be traced by measurements of the extinction of background starlight produced by the cloud (Lada et al., 1994). In order to map the extinction throughout the S242 region, we used $H$ and $K$ photometry from the 2MASS catalog with photometric uncertainty $<$ 0.1 mag. Since our target area is not completely covered with WIRCam photometry, we used 2MASS catalog to generate the map. The $A_{K}$ values were derived from ($H-K$) colors, following the method outlined in more detail by Gutermuth et al. (2005). In brief, we divided the region of our interest into uniform grids of size 15$\arcsec\times$15$\arcsec$. We have taken 20 nearest neighbor sources from the center of each grid to calculate the mean and standard deviation of ($H-K$) color for each grid, excluding the sources whose ($H-K$) values deviated 3$\sigma$ from the mean value. The mean ($H-K$) color for each grid were converted to $A_{K}$, using the reddening law $A_{K}=1.82\times[(H-K)_{obs}-(H-K)_{int}]$ from Flaherty et al. (2007). The average intrinsic color $(H-K)_{int}$ of the background population was taken into account to accurately characterize the distribution of extinction toward the region. The $(H-K)_{int}$ color was measured to be 0.2 mag using a nearby unextincted region ($\alpha_{(2000)}$ = 05^h51^m54^s, $\delta_{(2000)}$ = +28$\arcdeg$01$\arcmin$54$\arcsec$) of the sky from 2MASS catalog. The control field was chosen $\sim$ 1$\arcdeg$ away toward the north of S242. In an attempt to reduce the contribution from embedded young stars, only nonexcess infrared sources were used to generate the extinction map. The final extinction map has an angular resolution of 15$\arcsec$ and is sensitive down to $A_{V}\sim$ 17.8 mag. It is to be noted that the resolution and sensitivity of the map are a function of grid size and number of nearest neighbor sources used. To select the suitable grid size and number of nearest neighbor sources, we performed a series of iterations and found the grid size of $\sim$ 15$\arcsec$ and nearest neighbor source $\sim$ 20 are a good compromise between the sensitivity and signal-to-noise ratio of the extinction map. If the grid size was doubled (30$\arcsec$), the sensitivity dropped to $A_{V}\sim$ 1 mag.

The variation of extinction ($A_{K}$) throughout the S242 region is shown in the Fig. 5. The extinction shows a highly nonuniform structure throughout the region. In the map, three distinct and isolated extinction peaks are prominent. They are categorized into three subregions ‘A’, ‘B’ and ‘C’ and their zoomed-in distributions are shown in Fig. 5. The subregion ‘C’ suffers with highest value of extinction $A_{V}$ = 17.2 mag ($A_{K}$ = 1.5 mag); (Cohen et al., 1981), while the subregion ‘A’ has a maximum extinction of $A_{V}$ = 16.1 mag ($A_{K}$ = 1.4 mag). The subregion ‘B’ shows a modest distribution of extinction, with a maximum value of $A_{V}$ = 7.4 mag ($A_{K}$ = 0.7 mag). Among the three extinction complexes, subregions ‘A’ and ‘C’ are the highly extincted regions. These two regions are supposed to be the dominant sites for the next generation star formation. Subregion ‘B’ is supposed to be relatively evolved or its association with molecular clouds is significantly less compared with ‘A’ and ‘C’. Throughout the region the extinction varies from $A_{V}$ = 1.3–17.2 mag ($A_{K}$ = 0.1–1.5 mag), and the average value of extinction is $A_{V}$ = 3.1 mag ($A_{K}$ = 0.3 mag) with a standard deviation of $A_{V}$ $\sim$ 0.8 mag ($A_{K}\sim$ 0.07 mag). Although, this analysis is limited by sensitivity of the 2MASS survey. The derived extinction can also be underestimated due to the lack of detection of a sufficient number of background stars in the heavily extincted areas.

The infrared color-color (CC) space analysis is an efficient tool to identify and characterize the YSOs (Lada & Adams, 1992). The YSOs show excess infrared emission due to the presence of circumstellar disks and envelopes and thus occupy certain locations in the infrared CC diagrams. We used IRAC and $JHK$ colors to classify the young sources toward the S242 region. We adopted the IRAC [3.6] and [4.5] $\mu$m along with the WIRCam $H$ and $K$ bands photometry to categorize the pre-main-sequence (PMS) populations using the methods described in Gutermuth et al. (2009). Though the infrared excess emission is an essential and powerful membership diagnostic for young and embedded sources, this method also suffers from many potential contaminants. The dominant limitations arise from the extragalactic sources like star-forming galaxies, narrow- and broad-line active galactic nuclei (AGNs), as well as polycyclic aromatic hydrocarbon (PAH) emission excited by young and high-mass stars (Gutermuth et al., 2008). We used $JHK$ photometry from the WIRCam and the 2MASS catalog as an additional tool for further classification of sources that lack higher wavelength IRAC data. Since a majority of the H$\alpha$ emitters toward H ii regions are considered as classical T Tauri stars (CTTs; Meyer et al. 1997), due to the presence of hot and infalling gas accreting from circumstellar disks (Barentsen et al., 2011), we used the IPHAS photometry as an additional criteria to detect the young stars showing H$\alpha$ emission.

Using the slitless spectroscopic data from the HCT, we have visually identified a total of three sources that show counterparts in H$\alpha$ emission. All the three sources are depicted as blue crosses in the CC diagram (Fig. 8) and were also detected from IPHAS photometry. No extra sources were found from the slitless spectroscopy.

The IPHAS survey provides photometry of fainter emission line objects up to $r$ = 20.5, and $i$ and H$\alpha$ = 19.5 mag with photometric uncertainty limited to 0.1 mag (Barentsen et al., 2014). Fig. 8 shows the ($r-i$/$r-$H$\alpha$) CC diagram for the sources detected in the IPHAS catalog toward the S242 region. The solid and dashed blue lines represent the unreddened main-sequence and the expected position of unreddened main-sequence stars with H$\alpha$ emission line strengths of equivalent width (EW) = $-$10 Å. The nearly vertical solid black and green lines show the trend for an unreddened Rayleigh-Jeans continuum and an unreddened optically thick disk continuum (Barentsen et al., 2014; Dutta et al., 2015), respectively. Whereas the black broken lines are predicted lines of constant net emission EW. The reliable sources are selected by applying the quality criteria of $r$ < 20 mag and photometric uncertainty < 0.1 mag in all three bands in IPHAS DR2. A total of 36 H$\alpha$ emission line stars was selected as lying above the dashed blue line at the level of 3$\sigma$, i.e. the distance between the selected objects and the dashed blue line is larger than three times the average uncertainty in their ($r-$H$\alpha$) color (Barentsen et al., 2014). These candidate H$\alpha$ emitters are represented by magenta boxes in the CC diagram. The majority of the H$\alpha$ emitters toward a H ii region are likely to be CTTs (Barentsen et al., 2011, 2014). Among the 36 H$\alpha$ emitting objects, 5 sources show infrared counterparts and are classified as Class II sources either from IRAC or $JHK$ colors. The photometric catalog of the H$\alpha$ emitting sources is detailed in Table 7.

The NIR CM ($H-K$ versus $K$) space serves as a practical tool to estimate the spectral nature of YSOs by incorporating their distribution in the diagram. Fig. 9 depicts the YSOs identified from the WIRCam, 2MASS, and IRAC catalogs; H$\alpha$ emitters from the IPHAS photometry, and field population distribution, respectively. The locus of ZAMS (Pecaut & Mamajek, 2013), reddened by $A_{V}=$ 0, 5, 10, 20, and 30 mag and corrected for the cluster distance of 2.08 kpc (taken from Table 4) are represented by nearly vertical lines. The slanting horizontal lines are the reddening vectors corresponding to different spectral types. All the symbols in the figure are same as in Fig. 7. From the diagram, it is apparent that the YSOs show a large variation in spectral type from K6 to B0, with a majority concentrated within G0 to B2. The main illuminating source of the S242 cluster is located toward the reddening vector corresponding to B0 spectral type, as marked by a black star symbol. Earlier the spectral nature of this star was mentioned as B0 V, which is quite consistent with our results, and the spectroscopic analysis also reveals it as a B0.5 V type star. It is prominent that a reasonable amount of YSOs suffer large reddening of about 20 to 30 mag, possibly caused due to the presence of dusty circumstellar envelopes and gaseous environments. So, S242 is a rich stellar cluster, evolving with considerable number of young members and showing wide span in their spectral variation. The gray dots, representing the sources having no or less infrared excess emission, are primarily field population. A majority of them are concentrated within ($H-K$) $<$ 0.6 mag.

We used Pan-STARRS 1 photometry to diagnose the age spread of the YSOs within the S242 region. Since our observed optical data are not deep enough to detect most of the young sources, we used Pan-STARRS 1 photometry. The magnitude depth of the observed optical photometry is down to $V\sim$ 19.4 mag, whereas Pan-STARRS 1 provides photometry deeper down to g_P1 $\sim$ 22.5 mag and y_P1 $\sim$ 20.2 mag for this region. The distribution of YSOs and H$\alpha$ emitting sources in the (g_P1$-$ y_P1) versus g_P1 CM diagram is shown in Fig. 10. The ZAMS and PMS isochrones from Marigo et al. (2017), corrected for the cluster distance of 2.08 kpc, reddening $E(B-V)$ = 0.56 mag (taken from Table 4), and $E({\large g\textsubscript{P1}}-{\large y\textsubscript{P1}})$ = 1.26 mag (Schlafly et al., 2016) are overplotted. The evolutionary tracks for various masses are also shown to characterize the mass spectrum of the YSOs. A notable scatter in the age distribution of the YSO population is observed in Fig. 10. The ages vary between 0.1 Myr and 10 Myr, with a majority indicating an age around 1 Myr. However, our age determination method can be subject to a few limitations: the use of different PMS evolutionary models can yield different ages (Sung, Chun & Bessel, 2000), the presence of variable extinction, binaries, and variables may also introduce systematic errors (Herbst et al., 1994; Herbst & Shevchenko, 1999). We ascertained an average age of the YSOs as 1 Myr. Most of the H$\alpha$ emitting sources are relatively evolved compared to the YSOs, as seen from their distribution in the CM diagram. As a larger fraction of the low-mass YSOs lack the reliable photometry, this diagram cannot be used as a suitable tool to estimate mass ranges of the region.

We used the NIR CM ($J-H$ versus $J$) diagram to estimate the mass ranges of candidate YSOs toward the S242 region. Since the YSOs show excess emission at longer wavelengths, we used ($J-H$) versus $J$ diagram in an attempt to reduce the effect of excess emission (Ojha et al., 2004, 2011; Dutta et al., 2015). The NIR CM diagrams allow us to manipulate two fundamental parameters of a cluster, the distance and reddening. The change in distance shifts the isochrones vertically, while the parallel slanting lines trace the reddening zones for each extincted mass vector. Masses were estimated by comparing the distribution of young objects with theoretical PMS isochrones in the diagram. In Fig. 11, the blue solid line presents the loci of ZAMS taken from Girardi et al. (2002) and shifted for the cluster distance of 2.08 kpc. The evolutionary models of PMS isochrones of age 0.1, 1, and 10 Myr are taken from Marigo et al. (2017) and indicated by green, black, and red solid lines. The black dashed lines are the reddening vectors corresponding to different mass tracks, respectively. We used the same symbols as in Fig. 7 to represent the YSOs identified from infrared CC diagrams and H$\alpha$ emitters from IPHAS photometry. We used an average age of 1 Myr (Section 4.2) to estimate the mass ranges of YSOs. The YSOs show a wide range of variation in their masses with a majority having masses between 0.1 and 3.0 $M_{\sun}$, as indicated in the figure. It is also observed that the YSOs show larger variation in their color, probably an indication of the combined effect of spatially variable extinction and a weak contribution of excess emission in the $J$ and $H$ bands (Ojha et al., 2011). Few of the candidate YSOs are seen to be more massive ($>$ 3.0 $M_{\sun}$) and also located in highly extincted ($A_{V}$ $\sim$ 10-30 mag) regions. It is to be noted that estimating the stellar masses from the infrared CM diagrams relies on uncertain ages and different distances to the objects. The ambiguity is even more severe among the massive members (early B-type stars). Because the stellar mass can vary significantly when estimated from a 1 Myr PMS isochrone compared to the main-sequence isochrones of a younger age. Therefore, estimating the parameters for the massive members was difficult. Also, there can be several other causes which put constraints on this method, such as the use of separate PMS isochrones, binarity, and variable extinction (Hillenbrand et al., 2008).

The spatial variation of the embedded young stellar population is a footprint of how star formation has progressed throughout space and time in a given region. Fig. 12 manifests the distribution of Class I (red circles), Class II (blue triangles), and H$\alpha$ emission line (green boxes) sources, overlaid on the WISE W1 3.4 $\mu$m mosaic image. The location of the main ionizing star BD+26 980 is marked by a black star symbol. The FOV of DFOT optical (18$\arcmin\times$18$\arcmin$), WIRCam NIR (29$\arcmin\times$26$\arcmin$), and other archival photometric catalogs (2MASS, Spitzer, Gaia DR2, IPHAS) for a radius of 25$\arcmin$ are indicated in the figure. A noticeable number of the PMS populations are preferentially concentrated around the central core region. A majority of the YSOs are seen to be spatially aligned along an elongated filamentary structure (EFS). From the distribution of young stellar candidates, the spatial extent of the elongated structure is estimated as $\sim$ 43$\arcmin$ (26 pc). Using the ¹³CO molecular line data, Dewangan et al. (2017) also reported the presence of an EFS of length $\sim$ 25 pc and average width $\sim$ 1.3 pc. A significant number of the Class I sources have formed two discrete groups, one at the central region and another at the northern end of the long scale structure. While Class II type sources also show a similar grouping as Class I sources along with a nice positional coincidence with the long scale feature. The three peak extinction complexes, marked by ‘A’, ‘B’ and ‘C’ (see Section 3.3 for details) are shown by red dashed boxes in the diagram. The prominent clustering of the young populations are nicely match the extinction complexes. The spatial distribution of YSOs along the filamentary-like extinction structure indicates that ongoing star formation is likely occurring toward the cluster.

The number of YSOs in each class is useful to estimate the relative age of the subclusters in a young region (Hatchell et al., 2007; Gutermuth et al., 2009; Saral et al., 2015). We used the ratio of number of Class I sources to the number of Class II sources to interpret the evolutionary status of the star-forming region. Since Class I objects represent the earlier phase of star formation compared to Class II sources, the Class I/II ratio serves as a proxy to estimate the relative age of the subclusters (Chavarría et al., 2008). The ratio of Class I/II for the subregions ‘A’ and ‘C’ are obtained as 0.31 in both the cases. Whereas, for subregion ‘B’, the ratio is quite low: 0.08. Using a MIR survey of 36 young and active star-forming clusters, Gutermuth et al. (2009) estimated the median ratio of Class I/II to be 0.27. For the overall S242 region, the ratio is obtained as $\sim$ 0.25, which is in close proximity to the value derived by Gutermuth et al. (2009). Studying a nearby star forming complex, Chavarría et al. (2008) has shown the ratio of Class I/II to vary between 0.31 and 0.78. Beerer et al. (2010) presented the Class I/II ratio to range from 0.05 to 0.78 for 13 young clusters. Jose et al. (2013) evaluated the ratio to vary between 0.13 and 0.54 for the different subregions of a large H ii region. The Class I/II ratio is a function of the evolutionary stage of the complex, where the higher ratio indicates a younger cluster (Chavarría et al., 2008; Beerer et al., 2010). The ratio of Class I/II suggests that the subregions ‘A’ and ‘C’ are the locations of the youngest population for the region and the sources in these groups are evolving almost on a similar timescale. In general, it is predicted from the spatial distribution of the YSOs and the Class I/II ratio that the S242 region is in its early stage of star formation. Comparing the ratio of Class I/II with the earlier reports (Chavarría et al., 2008; Beerer et al., 2010; Jose et al., 2013; Saral et al., 2017), the average age of the young members in the S242 region is estimated around 1 Myr. Although, as the subregions ‘A’ and ‘C’ suffer the highest extinction, it may cause undercounting due to the undetectable background stars. Also limitations may occur with distance of the sources and detection sensitivity of the instruments.