OPTICAL PHOTOMETRIC AND POLARIMETRIC INVESTIGATION OF NGC 1931

The photometric data were acquired on 2005 December 31, 2006 January 22, 23, and 2006 February 24 using the 2048 × 2048 pixel CCD camera mounted on the f/13 Cassegrain focus of the 104 cm Sampurnanand Telescope at the Aryabhatta Research Institute of Observational Sciences (ARIES) in Nainital, India. In this setup, the entire chip covers a field of ∼13 × 13 arcmin² on the sky. The readout noise and gain of the CCD are 5.3e⁻ and 10e⁻ ADU⁻¹, respectively. The observations were carried out in the binning mode of 2 × 2 pixels to improve the signal-to-noise ratio (S/N). The FWHM of the star images was ∼2''–3''. The sky flat frames and bias frames were also taken frequently during the observing runs. A number of short exposures in all the filters were also taken to avoid saturation of bright stars. The observations were standardized using the stars in the SA98 field (Landolt 1992) observed on 2006 January 23. The log of the observations is given in Table 1. To estimate the contamination due to the foreground/background field stars, a reference field of ∼13 × 13 arcmin² located at about 40' away, was also observed.

The CCD data frames were reduced using the computing facilities available at ARIES, Nainital. Initial processing of the data frames was done using the IRAF (Image Reduction and Analysis Facility)⁷ and ESO-MIDAS (European Southern Observatory Munich Image Data Analysis System)⁸ data reduction packages. The details of the data reduction can be found in our earlier works (e.g., Pandey et al. 2007; Jose et al. 2008).

To translate the instrumental magnitudes to the standard magnitudes, the following calibration equations, derived using a least-squares linear regression, were used:

$$\begin{eqnarray*} u &=& U + (6.670 \pm 0.011) + (0.044 \pm 0.008)(U-B)\nonumber\\ && + (0.582 \pm 0.013)X, \\ b &=& B + (4.519 \pm 0.006) + (-0.026 \pm 0.004)(B-V)\nonumber\\ && + (0.332 \pm 0.006)X, \\ v &=& V + (4.096 \pm 0.004) + (-0.029 \pm 0.003)(V-I)\nonumber\\ && + (0.224 \pm 0.004)X, \\ r &=& R_{c} + (4.018 \pm 0.006) + (-0.012 \pm 0.007)(V-R)\nonumber\\ && + (0.165 \pm 0.006)X, \\ i &=& I_{c} +(4.559 \pm 0.006) + (-0.055 \pm 0.003)(V-I)\nonumber\\ && + (0.117 \pm 0.006)X, \\ \end{eqnarray*}$$

where U, B, V, R_c, and I_c are the standard magnitudes, u, b, v, r, and i are the instrumental aperture magnitudes normalized for 1 s of exposure time, and X is the airmass. The second-order color correction terms were ignored as they are generally small in comparison to other errors present in the photometric data reduction. The standard deviations of the standardization residuals, Δ, between standard and transformed V magnitude and (U − B), (B − V), (V − R), and (V − I) colors of the standard stars are 0.02, 0.04, 0.02, 0.02, and 0.01 mag, respectively. The typical DAOPHOT errors in magnitude as a function of corresponding magnitude in different passbands are found to increase with the magnitude and become large (⩾0.1 mag) for stars fainter than V ≃ 21 mag. The measurements beyond this magnitude limit were not considered in the analysis. The photometric data along with positions of the stars are given in Table 2. A sample and the format of the table is shown here. The complete table is available only in the online journal.

Table 2. UBV(RI)_c Photometric Data

Star ID	R.A. (J2000)	Decl. (J2000)	U ± σU	B ± σB	V ± σV	$R_{c} \pm \sigma _{R_{c}}$	$I_{c} \pm \sigma _{I_{c}}$
	(h m s)	(° ' '')	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
1	5 30 59.954	34 15 31.95	13.085 ± 0.007	12.063 ± 0.005	10.759 ± 0.006	10.050 ± 0.008	9.398 ± 0.013
2	5 31 57.547	34 10 47.45	11.520 ± 0.007	11.449 ± 0.008	10.872 ± 0.009	10.520 ± 0.002	10.161 ± 0.009
3	5 31 26.307	34 11 9.94	11.036 ± 0.005	11.411 ± 0.009	11.136 ± 0.010	10.918 ± 0.005	10.643 ± 0.005
4	5 31 40.582	34 10 52.00	11.694 ± 0.006	11.599 ± 0.009	11.193 ± 0.011	10.948 ± 0.005	10.676 ± 0.007
5	5 31 40.243	34 14 26.25	11.966 ± 0.008	11.643 ± 0.006	11.252 ± 0.012	11.017 ± 0.006	10.718 ± 0.010
...	...	...	...	...	...	...	...
...	...	...	...	...	...	...	...
...	...	...	...	...	...	...	...

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.

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2.1.1. Completeness of the Data

The study of the luminosity functions (LFs)/MFs requires necessary corrections in the data sample to take into account incompleteness that may occur for various reasons (e.g., crowding of the stars). We used the ADDSTAR routine of DAOPHOT II to determine the completeness factor (CF). The procedures have been outlined in detail in our earlier works (Pandey et al. 2001, 2005). The CF as a function of V magnitude is given in Table 3, which indicates that present optical data have ∼90% completeness at V ∼ 20 mag. As expected, the incompleteness increases with the magnitude.

Table 3. Completeness Factor (CF) of the Optical Photometric Data in the Cluster and Field Regions

V Range	Cluster Region	Field Region
(mag)	r ⩽ 35
10–11	1.00	1.00
11–12	1.00	1.00
12–13	1.00	1.00
13–14	1.00	1.00
14–15	1.00	1.00
15–16	1.00	1.00
16–17	1.00	0.98
17–18	0.97	0.97
18–19	0.94	0.96
19–20	0.92	0.92
20–21	0.88	0.86

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2.1.2. Comparison with Previous Studies

A comparison of the present photometric data with those available in the literature has been carried out and the difference Δ (literature − present data) as a function of V magnitude is plotted in Figure 2. The comparison indicates that the present V mag and colors are in good agreement with the CCD and photoelectric photometry by Pandey & Mahra (1986) and Bhatt et al. (1994), respectively.

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Polarimetric observations were carried out on two nights (2010 November 12 and December 13) using the ARIES Imaging Polarimeter (AIMPOL; Rautela et al. 2004) mounted on the Cassegrain focus of the 104 cm Sampurnanand Telescope at ARIES in Nainital, India. The details of the AIMPOL are given in our earlier works (E11; E12). The observations were carried out in the V, R_c, and I_c photometric bands. The detailed procedures used to estimate the polarization and position angles for the program stars are given in E11 and E12.

The instrumental polarization of the AIMPOL is estimated to be less than 0.1% in all the bands (E11; E12). The polarization measurements were corrected for both the null polarization (∼0.1%), which is independent of the passbands, and the zero-point polarization angle by observing several unpolarized and polarized standard stars from Schmidt et al. (1992, hereafter S92). The results for the polarized standard stars are given in Table 4. The values of θ are in an equatorial coordinate system measured eastward from the north. Both the observed degree of polarization (P(%)) and the polarization angle (θ(°)) for the polarized standards are in good agreement with those given by S92.

Table 4. Observed Polarized Standard Stars

	P ± P(%)	θ ± θ(°)	P ± P(%)	θ ± θ(°)
Our Work			Schmidt et al. (1992)
Polarized Standard Stars
2010 Nov 12
HD 19820
B	4.54 ± 0.11	116.3 ± 0.7	4.70 ± 0.04	115.7 ± 0.2
V	4.74 ± 0.10	115.1 ± 0.6	4.79 ± 0.03	114.9 ± 0.2
Rc	4.57 ± 0.07	114.4 ± 0.4	4.53 ± 0.03	114.5 ± 0.2
Ic	3.97 ± 0.07	115.4 ± 0.5	4.08 ± 0.02	114.5 ± 0.2
HD 204827
B	5.75 ± 0.14	57.6 ± 0.7	5.65 ± 0.02	58.2 ± 0.1
V	5.47 ± 0.10	63.3 ± 0.5	5.32 ± 0.01	58.7 ± 0.1
Rc	4.93 ± 0.09	59.2 ± 0.5	4.89 ± 0.03	59.1 ± 0.2
Ic	4.07 ± 0.09	59.1 ± 0.6	4.19 ± 0.03	59.9 ± 0.2
2010 Dec 13
HD 19820
B	4.47 ± 0.11	115.3 ± 0.7	4.70 ± 0.04	115.7 ± 0.2
V	4.78 ± 0.09	115.6 ± 0.5	4.79 ± 0.03	114.9 ± 0.2
Rc	4.60 ± 0.07	114.2 ± 0.4	4.53 ± 0.03	114.5 ± 0.2
Ic	3.99 ± 0.07	114.3 ± 0.5	4.08 ± 0.02	114.5 ± 0.2
HD 25443
B	5.17 ± 0.11	134.7 ± 0.6	5.23 ± 0.09	134.3 ± 0.5
V	5.24 ± 0.09	134.7 ± 0.5	5.13 ± 0.06	134.2 ± 0.3
Rc	4.97 ± 0.09	134.3 ± 0.5	4.73 ± 0.05	133.6 ± 0.3
Ic	4.27 ± 0.10	134.6 ± 0.6	4.25 ± 0.04	134.2 ± 0.3

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NIR JHK_s data for point sources in the NGC 1931 region have been obtained from 2MASS (Cutri et al. 2003). The 2MASS data reported to be 99% complete up to ∼15.7, 15.1, and 14.3 mag in J, H, and K_s bands, respectively.⁹ To ensure photometric accuracy, we used only those photometric data that have quality flag ph-qual = AAA, which endorses an S/N ⩾ 10 and photometric uncertainty <0.10 mag. The NIR data are used to identify the classical T Tauri stars (CTTSs) and weak line T Tauri stars (WTTSs).

The archived MIR data observed with the Spitzer/IRAC have also been used in the present study. We obtained basic calibrated data (BCD) using the software Leopard. The exposure time of each BCD was 10.4 s and for each mosaic, 169 and 139 BCDs, respectively, in Ch1 (3.6 μm) and Ch2 (4.5 μm) have been used. Mosaicking was performed using the MOPEX software provided by the Spitzer Science Center (SSC). All of the mosaics were built at the native instrument resolution of 12 pixel⁻¹ with the standard BCDs. In order to avoid source confusion due to crowding, point-spread function (PSF) photometry for all the sources was carried out using the DAOPHOT package available with the IRAF photometry routine. The detections are also examined visually in each band to remove non-stellar objects or false detections. The sources with photometric uncertainties <0.2 mag in each band were considered as good detections. A total of 3950 and 2793 sources were detected in the 3.6 and 4.5 μm bands. Aperture photometry for well-isolated sources was done using an aperture radius of 36 with a concentric sky annulus of the inner and outer radii of 36 and 84, respectively. For a standard aperture radius (12'') and background annulus of 12''–224, we adopted zero-point magnitude as 19.670 and 18.921 for the 3.6 and 4.5 μm bands, respectively. Aperture corrections were also made using the values described in the IRAC Data Handbook (Reach et al. 2006). The necessary aperture correction for the PSF photometry was then calculated from the selected isolated sources and was applied to the PSF magnitudes of all the sources.

Table 6 lists the polarization measurements for 62 stars toward the cluster region. The star identification numbers for 59 stars are taken from Column 1 of Table 2, whereas three stars, 2001, 2002, and 2003, do not have optical data. The degree of polarization P (in percent), polarization angles θ (in degrees) measured in V, (R, I)_c bands, and their corresponding standard errors are given in Columns 4–9. The black vectors (Figure 5) show the sky projection of the V-band polarization measurements. In the case of a few stars for which the V-band polarization measurements are not available, we plotted the polarization measurements of either the R_c band (red) or the I_c band (magenta). The length of each polarization vector is proportional to the degree of polarization. The dash-dotted line represents the orientation of the projection of the Galactic plane (GP) at b = 030, which corresponds to a position angle of 142°. Interestingly, all the polarization vectors except those near the cluster center (enclosed by a square box) are roughly parallel to the GP. The enlarged view of the central region is shown in a separate panel at the top right part of the figure. The polarization measurements of stars 7 and 11 could be affected by their close companions as well as by nebulosity. Hence, the polarization measurements of these stars could be less reliable.

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The distribution of P and θ in the V and (R, I)_c bands is shown in Figure 6. A Gaussian fit to each distribution yields a mean and a standard deviation of P_V = 2.4%  ±  0.6%, P_R = 2.2%  ±  0.5%, and P_I = 2.0%  ±  0.6%, and θ_V = 155°  ±  7°, θ_R = 154°  ±  6°, and θ_I = 156°  ±  12°. The values of P_V(2.4%  ±  0.6%) and θ_V(155°  ±  7°) toward NGC 1931 are comparable to those (P_V = 2.3%  ±  0.1% and θ_V = 160°  ±  3°; E11) for Stock 8 (l = 17337, b = −018, and distance = 2.05 kpc), which is spatially located near the NGC 1931.

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The identification of probable cluster members and the foreground/background stars toward the direction of the cluster is necessary to study the nature of the dust properties of the ICM/ISM and the magnetic field associated with the foreground and the ICM. Our earlier studies (E11; E12) have shown that the polarimetry in combination with the (U − B) − (B − V) two-color diagram (TCD) can be efficiently used to identify the probable members in the cluster region. This section describes the determination of membership using the polarization properties in combination with the (U − B) − (B − V) TCD.

The individual Stokes parameters of the polarization vectors of the V/R/I band, $P_{V/R_{c}/I_{c}}$, given by $Q_{V/R_{c}/I_{c}} = P_{V/R_{c}/I_{c}} \cos (2\theta _{V/R_{c}/I_{c}})$ and $U_{V/R_{c}/I_{c}} = P_{V/R_{c}/I_{c}} \sin (2\theta _{V/R_{c}/I_{c}})$ have been estimated and are presented in the $U_{V/R_{c}/I_{c}}$ versus $Q_{V/R_{c}/I_{c}}$ plot as shown in Figure 7. Since the polarization of light from a star depends on the column density of aligned dust grains that lie in front of the star, the cluster members are expected to group together in the U versus Q plot, whereas non-members are expected to show a scattered distribution. Similarly, the polarization angles of cluster members would be similar but could be different for foreground or background non-member stars as light from them could be affected in a different manner because of contributions from different/additional dust components. Therefore, the U–Q plot is a useful tool to segregate the members from non-members in the cluster region. However, the stars with intrinsic polarization, e.g., due to an asymmetric distribution of matter around young stellar objects (YSOs) and/or rotation in their polarization angles (see, e.g., E11; E12), may also create scattered distribution in the U–Q plane.

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The probable members of the cluster should have a similar location in all three U–Q diagrams. The Stokes parameters for the stars lying within the square box as shown in Figure 5 and embedded in the nebulosity are shown with filled squares. The box with a dashed line in the U–Q plots shows the boundary of the area with mean P ± σ (P_V = 2.4% ± 0.6%, P_R = 2.3% ± 0.5%, and P_I = 2.0% ± 0.6%) and mean θ ± σ (θ_V = 155° ± 7°, θ_R = 155° ± 6°, θ_I = 156° ± 12°) obtained from the distribution shown in Figure 6. The stars lying within or near the 1σ box in all three U–Q plots may be probable members associated with the cluster.

It is expected that the members of a cluster should exhibit comparable E(B − V) values, whereas the foreground (background) population is expected to be less (highly) extincted as compared to the cluster members. Figure 8 shows the (U − B) − (B − V) TCD for only 58 stars as U−B color is not available for three stars. The symbols of the stars are the same as in Figure 7. All the stars shown in Figure 8 have polarimetric data. In Figure 8, the zero-age main sequence (ZAMS) from Schmidt-Kaler (1982) is shifted along a normal reddening vector with a slope of E(U − B)/E(B − V) = 0.72. The TCD shows a variable reddening in the cluster region with E(B − V)_min ∼ 0.5 mag and E(B − V)_max ∼ 0.9 mag. It is also apparent from Figure 8 that sources located in the northern nebulous region (lying within the box in Figure 5) reveals the presence of a parent molecular cloud and show a variable extinction of E(B − V) ∼ 0.5–0.9 mag. The polarimetric observations in combination with the (U − B) − (B − V) TCD are used to identify members of the NGC 1931 cluster (cf. E11; E12). The probable members thus identified are given in Table 5. The stars 7, 11, 14, 35, 49, 88, and 99 are embedded in the northern nebulosity, and hence the polarization measurements may be affected by the nebulosity, and consequently may show scattered distribution in the U versus Q diagram. Out of 22 probable members, 11 stars (stars 3, 7, 11, 14, 21, 22, 35, 49, 79, 88, and 93) have either σ₁ > 1.5 and/or $\overline{\epsilon }> 2.3$, indicating the presence of intrinsic polarization and/or rotation in their polarization angles (cf. Section 5.4).

In our previous studies (E11; E12) we have shown that the Stokes plane can be used to study the distribution of dust layers, the role of dust layers in polarization, the associated magnetic field orientation, etc. The vector connecting two points in the Stokes plane represents the amount of polarization, whereas the change in the direction of vectors indicates a change in the polarization angle. In the case of uniformly aligned dust grains (i.e., uniform magnetic field orientation), the degree of polarization is expected to increase with distance, but the direction of polarization (the polarization angle) should remain the same and hence the Stokes vector should not change its direction with increasing distance. For example, in the case of NGC 1893 (E11), the degree of polarization was found to increase with distance, whereas the direction of polarization remained almost constant (cf. their Figure 5). In contrast, the magnetic field orientation shows systematic rotation with distance toward the direction of Berkeley 59 (E12, see their Figure 7) as the radiation from the cluster members might have a depolarization effect due to the systematic change in the dust grain alignment in the foreground medium. NGC 1931 is located toward the direction of NGC 1893, hence a similar behavior is also expected for the cluster NGC 1931. Figure 9 shows the U_V–Q_V distribution for probable members of NGC 1931 along with the data for other clusters, NGC 2281 (∼0.6 kpc), NGC 1664 (∼1.2 kpc), NGC 1960 (∼1.3 kpc), Stock 8 (∼2.0 kpc), and NGC 1893 (∼3.2 kpc), located toward the direction of NGC 1931. The data for other clusters have been taken from E11. Out of 22 probable members (cf. Table 5) of NGC 1931, we have used only 10 stars (stars 5, 9, 12, 13, 32, 45, 47, 51, 53, and 55) in Figure 9 that are free from intrinsic polarization and/or rotation in their polarization angles and are also free from background nebulosity. The polarization data for NGC 1931 is consistent with the fact that the degree of polarization increases with the column density of dust grains lying in front of the stars that are relatively well aligned.

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The various dust layers located between the star and the observer can cause a sudden increase in the degree of polarization. The number of these sudden increases has been used by E11 to characterize the dust layers encountered by the radiation along its path and the relative magnetic field orientations of the dust layers toward the direction of NGC 1893, which is spatially located near the cluster NGC 1931. The polarimetric observations for NGC 1931 obtained in the present study follow the general trend revealed by the stars and clusters located toward the anticenter direction of the Galaxy as described by E11.

The wavelength dependence of polarization in the Galaxy can be represented by the following relation (Serkowski 1973; Coyne et al. 1974; Wilking et al. 1982):

$$\begin{eqnarray} &&P_{\lambda } = P_{{\rm max}} \exp [-K \ln ^{2} (\lambda _{{\rm max}}/\lambda )], \end{eqnarray} \tag{ 1 }$$

where P_λ and λ_max are the polarization percentage at wavelength λ and the peak polarization occurring at wavelength λ_max. The λ_max depends on the optical properties and characteristic particle size distribution of aligned grains (Serkowski et al. 1975; McMillan 1978), whereas the value of P_max is dictated by the chemical composition, shape, size, column density, and alignment efficiency of the dust grains. The Serkowski's relation with K = 1.15 provides a reasonable representation of the observations of interstellar polarization between wavelengths 0.36 and 1.0 μm. The P_max and λ_max are obtained using the weighted least-squares fitting to the measured polarization in V(RI)_c bands to Equation (1) by adopting K = 1.15. The parameters σ₁ (the unit weight error of the fit for each star),¹⁰ which quantifies the departure of the data from the standard Serkowski's law, and $\overline{\epsilon }$, the dispersion of the polarization angle for each star normalized by the average of the polarization angle errors (cf. Marraco et al. 1993), were also estimated. The estimated values of P_max, λ_max, σ₁, and $\overline{\epsilon }$ for each star are given in Table 6.

Figure 10 shows σ₁ versus P_max (upper panel) and $\overline{\epsilon }$ versus λ_max (lower panel) plots. The criteria mentioned above indicate that the majority of the stars do not show evidence of intrinsic polarization. However, a few stars (15) show an indication of either intrinsic polarization and/or rotation in their polarization angles. Ten stars (stars 3, 14, 15, 21, 22, 26, 35, 88, 93, and 139) are found to exhibit an indication of intrinsic polarization as they have σ₁ > 1.5, and eight stars (7, 11, 15, 35, 49, 79, 88, and 139) are found to show rotation in their polarization angles whose $\overline{\epsilon }$ values are higher (>2.3) than that for the rest of the stars. Four stars (15, 35, 88, and 139) are found to show both indication of intrinsic polarization and also rotation in their polarization angles.

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The weighted mean values of P_max and λ_max using all of the 22 probable members are found to be 2.51% ± 0.03% and 0.57 ± 0.01 μm, respectively. The exclusion of stars showing intrinsic polarization does not change the mean values of P_max and λ_max significantly. The estimated λ_max is slightly higher than the value corresponding to the diffuse ISM (0.545 μm; Serkowski et al. 1975). Using the relation R_V = (5.6 ± 0.3)× λ_max (Whittet & van Breda 1978), the value of R_V, the total-to-selective extinction, comes out to be 3.20 ± 0.05.

However, the λ_max value (0.55 ± 0.01 μm; E11) toward cluster NGC 1893, which is spatially close to NGC 1931, is found to be comparable to the value of the diffuse ISM (0.545 μm; Serkowski et al. 1975), and the reddening law toward NGC 1893 is found to be average (Sharma et al. 2007). This indicates that the size of the dust grains toward NGC 1893 is comparable to those in the diffuse ISM. Jose et al. (2008) have also found the presence of the average reddening law toward the cluster region of Stock 8, which is also located near the NGC 1931. The indication of slightly bigger dust grains toward NGC 1931 could be due to relatively bigger dust grains within the "ICM." The extinction law in the cluster region is further discussed in the following section.

The (V − λ) versus (B − V) TCDs, where λ is one of the wavelengths of the broadband filters R, I, J, H, K, or L, have been used to separate the influence of the extinction produced by the diffuse ISM from that of the extinction due to the ICM (cf. Chini & Wargau 1990; Pandey et al. 2000). The (V − λ) versus (B−V) TCDs for the probable members (selected on the basis of polarimetric analysis and optical color–color diagrams; cf. Section 5.2) and probable pre-main-sequence (PMS) stars (cf. Section 6.2.3) of the cluster region are shown in Figure 11. The open circles are the stars with V(RI)_c polarimetric data and the triangles are those with either single or double band polarimetric data. The slope for the general distribution of the majority of the stars (excluding the stars in the nebulous region (filled square symbols) and two (stars 88 and 236) PMS stars)) is found to be 1.17 ± 0.05, 2.10 ± 0.12, 2.63 ± 0.14, and 2.76 ± 0.16 for (V − I), (V − J), (V − H), (V − K) versus (B − V) TCDs, respectively. These slopes are higher in comparison to those obtained for diffuse ISM, which indicates a differing reddening law in the cluster region. The stars associated with the nebulous region of the northern cluster, shown with filled square symbols, seem to deviate from the distribution of the majority of the stars.

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To have a general view of the reddening law in the cluster region (r ⩽ 35), we used TCDs for all the sources detected in the region. Figure 12 shows (V − I) versus (B − V) TCD, which indicates a combination of distributions for the field stars and the cluster members. We selected probable field stars, which are shown by gray filled circles, by visually assuming that stars following the slope of the diffuse ISM are contaminating field stars in the cluster region. The slopes for the diffuse ISM have been taken from Pandey et al. (2003). The remaining sources, shown by open circles, may be members of the cluster. The probable members associated with the nebulous region are shown by filled squares. The slopes of the distributions for probable cluster members (i.e., open circles + filled squares), m_cluster, are found to be 1.22 ± 0.04, 2.20 ± 0.08, 2.67 ± 0.10, and 2.81 ± 0.12, for the (V − I), (V − J), (V − H), and (V − K) versus (B − V) TCDs, respectively. The ratios E(V − λ)/E(B − V) and the ratio of total-to-selective extinction for the general distribution of probable cluster members in the cluster region, R_cluster, are derived using the procedure given by Pandey et al. (2003). Assuming the value of R_V for the diffuse foreground ISM as 3.1, the ratios E(V − λ)/E(B − V) yield R_cluster = 3.3 ± 0.1, which is in fair agreement with the value derived using polarimetric data (cf. Section 5.4) and indicate a differing reddening law in the cluster region. The probable members associated with the nebulous region, shown by filled squares, indicate a relatively higher R_V value for the nebulous region. Several studies, e.g., Pandey et al. (2003), Pandey et al. (2008), and references therein, have pointed out high R_V values in the vicinity of star-forming regions, which is attributed to the presence of larger dust grains in the region.

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The polarization efficiency (P_max/E(B − V)) of the medium depends mainly on the magnetic field strength, the grain alignment efficiency, and the amount of depolarization due to the radiation passing through various mediums having different magnetic field directions (see, e.g., Feinstein et al. 2003; E11; E12, and references therein). Figure 13 displays the polarization efficiency diagram for the stars toward NGC 1931. The empirical upper limit relation for the polarization efficiency of the diffuse ISM, given by P_max = 3A_V ≃ 3R_VE(B − V) ≃ 9.3E(B − V) (assuming R_V = 3.1; Hiltner & Johnson 1956; Serkowski et al. 1975), is shown by a continuous line in Figure 13. Serkowski et al. (1975) have shown that the polarization efficiency of the ISM in general follows the mean relation P_max ≃ 5E(B − V) and the same is shown by a dashed line. The dash-dotted line represents the average polarization efficiency for the general diffuse ISM by Fosalba et al. (2002), which is valid for E(B − V) < 1.0 mag. The majority of the cluster members are distributed below the dashed line, indicating that the polarization efficiency of the ICM is less than the polarization efficiency of the diffuse ISM (∼5% per mag) and seems to follow the relation for the general diffuse ISM by Fosalba et al. (2002). Four stars, 35, 79, 88, and 99, have relatively high polarization (P_max ∼ 5%–8%) and a polarization efficiency greater than 5% per mag. Interestingly, stars 35 and 88 have σ₁ and $\overline{\epsilon }$ values >1.5 and >2.3, respectively, thereby indicating the presence of intrinsic polarization and rotation in their polarization angles. It is worthwhile to mention that these two stars are associated with the nebulosity of the northern region. Star 79 has $\overline{\epsilon }> 2.3$, which indicates a rotation in the polarization angle. Stars 7 and 11 show significantly smaller polarization efficiency (∼1% per mag). The $\overline{\epsilon }$ values for these stars are >2.3, and hence there could be a rotation in the polarization angle. As we have already mentioned (cf. Section 5.1), the polarization measurements of these two stars (stars 7 and 11) are less reliable. Interestingly, all the stars deviating from the mean polarization efficiency behavior of the region are located in the northern region.

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Here it is interesting to mention that the dust grains toward NGC 1893 (l = 1736, b = −17), which is spatially close to NGC 1931, show higher polarization efficiency (cf. Figure 9, E11) whereas the dust grains toward NGC 1931 exhibit less polarization efficiency in comparison to mean polarization efficiency for the general diffuse ISM. This could be due to the average extinction law in the foreground medium and a differing reddening law in the ICM.

The V₀/(B − V)₀ color–magnitude diagram (CMD; Figure 14) of the 22 identified probable members (Section 5.2) has been used to estimate the distance to the cluster. Reddening of individual probable members having spectral types earlier than A0 has been estimated using the reddening free index Q (Johnson & Morgan 1953), which is defined as Q = (U − B) − 0.72(B − V). The reddening law was assumed to be normal. The intrinsic (B − V)₀ color and color excess for the MS stars can be obtained from the relation (B − V)₀ = 0.332 × Q (Johnson 1966; Hillenbrand et al. 1993) and E(B − V) = (B − V) − (B − V)₀, respectively. A visual fit of the isochrone for 1 Myr and Z = 0.02 by Marigo et al. (2008) to the observations yields a distance modulus of V₀ − M_V = 11.81 ± 0.3, which corresponds to a distance of 2.3 ± 0.3 kpc. The distance estimate is in agreement with that obtained by Pandey & Mahra (1986), Bhatt et al. (1994), and Bonatto & Bica (2009).

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Stars 7 (E(B − V) = 0.61) and 11 (E(B − V) = 0.79) are located in the northern nebulous region and could be the ionizing source(s) of the region (cf. Section 8). Star 3 is located in the southern region and has E(B − V) = 0.47. The present photometric data for star 3 are in agreement with that reported by Moffat et al. (1979). The E(B − V) value for star 3 is comparable to the E(B − V)_min. Moffat et al. (1979) concluded that either this star is a foreground star or could be a binary star. Since polarimetric observations suggest that it could be a member, we presume that this star could be a binary star and a member of the cluster.

The V/(V − I) CMDs of all the stars within the cluster region (i.e., r_cl ⩽ 35) and the nearby field region are shown in the left and middle panels of Figure 15. As discussed in our earlier works (e.g., Pandey et al. 2008; Jose et al. 2008), the removal of field star contamination from the sample of stars in the cluster region is necessary as both PMS and dwarf foreground stars occupy similar positions above the ZAMS in the CMDs. Since proper-motion data are not available for the region, the statistical criterion was used to estimate the number of probable member stars in the cluster region. To remove contamination from field stars, we statistically subtracted their contribution from the CMD of the cluster region using the following procedure. The CMDs of the cluster as well as of the reference region were divided into grids of ΔV = 1 mag and Δ(V − I) = 0.4 mag. The number of stars in each grid of the CMDs was counted. After applying the completeness corrections using the CF (cf. Table 3) to both data samples, the probable number of cluster members in each grid was estimated by subtracting the corrected reference star counts from the corrected counts in the cluster region. The estimated numbers of contaminating field stars were removed from the cluster CMD in the following manner. For a randomly selected star in the CMD of the reference region, the nearest star in the cluster CMD within V  ±  0.25 and (V − I)  ±  0.125 of the field was removed. Although the statistically cleaned V/(V − I) CMD of the cluster region shown in the right panel of Figure 15 clearly shows the presence of PMS stars in the cluster, the contamination due to field stars near V ∼ 20 mag and (V − I) ∼ 2.0 can still be seen (cf. Figure 16). This field population could be due to the background population as discussed by Pandey et al. (2006).

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The statistically cleaned V/(V − I) CMD (SCMD) of the cluster region with PMS isochrones by Siess et al. (2000) for ages 1, 2, 5, and 10 Myr (dashed curves) and 1 Myr (continuous curve) by Marigo et al. (2008) is shown in Figure 16, which manifests the presence of the PMS population with an age spread of ∼5 Myr. The statistics of PMS sources obtained from the SCMD can be used to study the IMF of the PMS population of NGC 1931. Here we would like to point out that the points shown by the filled circles in Figure 16 may not represent the actual members of the clusters. However, the filled circles should represent the statistics of PMS stars in the region and it has been used to study the MF of the cluster region.

6.2.1. On the Basis of (J − H)/(H − K) TCD

NIR imaging surveys are important tools to detect YSOs in star-forming regions. The locations of YSOs on (J − H)/(H − K) TCD (NIR TCD) are determined to a large extent by their evolutionary state. The NIR TCD, using the 2MASS data for all the sources lying in the NGC 1931 region and having photometric errors less than 0.1 mag, is shown in the left panel of Figure 17. All the 2MASS magnitudes and colors have been converted into the California Institute of Technology (CIT) system. The solid and thick dashed curves represent the unreddened MS and giant branch (Bessell & Brett 1988), respectively. The dotted line indicates the locus of unreddened TTSs (Meyer et al. 1997). All the curves and lines are also in the CIT system. The parallel dashed lines are the reddening vectors drawn from the tip (spectral type M4) of the giant branch (left reddening line), from the base (spectral type A0) of the MS branch (middle reddening line), and from the tip of the intrinsic TTS line (right reddening line). The extinction ratios A_J/A_V = 0.265, A_H/A_V = 0.155, and A_K/A_V = 0.090 have been taken from Cohen et al. (1981). The sources located in the "F" region (cf. the left panel of Figure 17) could be either field stars (MS stars, giants) or Class III and Class II sources with small NIR excesses, whereas the sources distributed in the "T" and "P" regions are considered to be mostly CTTSs (or Class II objects) with relatively large NIR excesses and likely Class I objects, respectively (for details see Pandey et al. 2008; Chauhan et al. 2011a, 2011b). It is worthwhile to mention also that Robitaille et al. (2006) have shown that there is a significant overlap between protostars and CTTSs. The NIR TCD of the NGC 1931 region (the left panel of Figure 17) indicates that a few sources show (H − K) excess, which are shown by open circles. A comparison of the TCD of the NGC 1931 region with the NIR TCD of the nearby reference region (the right panel of Figure 17) suggests that the sources lying in the "T" region could be CTTSs/Class II sources.

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6.2.2. On the Basis of MIR Data

The Spitzer MIR observations (3.6 and 4.5 μm) for the NGC 1931 region are also available. Since young stars in the NGC 1931 could be deeply embedded, the MIR observations can provide a deeper insight into the embedded YSOs. YSOs occupy distinct regions in the IRAC color plane according to their nature; this makes MIR TCDs a very useful tool for the classification of YSOs. Since 8.0 μm data are not available for the region, we used [[K] − [3.6]]₀ and [[3.6] − [4.5]]₀ TCDs (cf. Gutermuth et al. 2009) to identify the deeply embedded YSOs. Figure 18 presents a [[K] − [3.6]]₀ versus [[3.6] − [4.5]]₀ TCD for the observed sources. The identified Class I and Class II sources along with photometric data (optical: present work; JHK_s: 2MASS; 3.6 μm and 4.5 μm: Spitzer; 3.4 μm, 4.6 μm, and 12 μm: WISE) are given in Tables 7 and 8. The 3.4, 4.6, and 12 μm data have been taken from the WISE database (http://irsa.ipac.caltech.edu/).

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Table 6. Observed Polarization, Polarization Angles, and Estimated Serkowski Parameters

Star ID	R.A. (J2000)	Decl. (J2000)	PV ±	θV ±	$P_{R_c} \pm \epsilon$	$\theta _{R_c} \pm \epsilon$	$P_{I_c} \pm \epsilon$	$\theta _{I_c} \pm \epsilon$	Pmax ±	λmax ±	σ1	$\overline{\epsilon }$
	(h m s)	(° ' '')	(%)	(°)	(%)	(°)	(%)	(°)	(%)	(μm)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
Stars with V(RI)c passband data
3	5 31 26.304	34 11 9.838	2.11 ± 0.09	153.1 ± 1.1	2.25 ± 0.08	151.7 ± 0.9	1.83 ± 0.09	150.3 ± 1.4	2.19 ± 0.06	0.58 ± 0.04	1.98	1.22
5	5 31 40.241	34 14 26.232	2.29 ± 0.10	156.3 ± 1.1	2.39 ± 0.08	156.1 ± 1.0	2.16 ± 0.09	156.2 ± 1.1	2.37 ± 0.06	0.61 ± 0.04	0.61	0.10
8	5 31 9.989	34 11 13.049	0.38 ± 0.11	6.1 ± 6.4	0.41 ± 0.09	2.7 ± 5.2	0.33 ± 0.11	0.3 ± 7.3	0.40 ± 0.08	0.57 ± 0.25	0.34	0.50
9	5 31 21.278	34 11 17.927	2.82 ± 0.12	155.6 ± 1.2	2.71 ± 0.11	155.8 ± 1.2	2.57 ± 0.14	156.7 ± 1.4	2.82 ± 0.09	0.58 ± 0.04	0.67	0.37
10	5 31 43.544	34 16 30.803	0.65 ± 0.16	172.0 ± 5.8	0.35 ± 0.14	163.0 ± 8.8	0.66 ± 0.13	4.7 ± 5.0	...	...	...	...
12	5 31 20.102	34 13 40.692	2.91 ± 0.16	154.3 ± 1.5	2.78 ± 0.14	151.7 ± 1.4	2.38 ± 0.17	156.1 ± 1.9	2.93 ± 0.15	0.53 ± 0.05	0.32	0.91
13	5 31 16.265	34 11 51.515	1.95 ± 0.20	151.9 ± 2.9	1.84 ± 0.18	151.6 ± 2.6	2.18 ± 0.21	159.7 ± 2.6	2.05 ± 0.13	0.73 ± 0.12	1.43	1.00
15	5 31 27.834	34 18 13.799	2.19 ± 0.25	160.5 ± 3.0	2.57 ± 0.22	148.3 ± 2.4	1.79 ± 0.24	141.4 ± 3.7	2.36 ± 0.20	0.56 ± 0.09	1.81	3.43
16	5 31 0.899	34 11 39.829	2.07 ± 0.24	158.2 ± 3.2	2.30 ± 0.17	152.3 ± 2.0	2.07 ± 0.16	152.6 ± 2.1	2.23 ± 0.12	0.64 ± 0.09	0.60	1.58
20	5 31 6.557	34 8 44.956	2.29 ± 0.25	151.8 ± 3.1	2.18 ± 0.17	151.1 ± 2.2	1.85 ± 0.17	149.6 ± 2.5	2.31 ± 0.24	0.52 ± 0.08	0.20	0.38
21	5 31 11.433	34 12 42.754	1.85 ± 0.25	154.6 ± 3.8	2.08 ± 0.23	154.7 ± 3.0	1.30 ± 0.28	153.9 ± 5.7	1.98 ± 0.27	0.51 ± 0.11	1.59	0.06
22	5 31 25.078	34 11 36.672	1.52 ± 0.24	166.6 ± 4.3	2.20 ± 0.21	161.1 ± 2.6	1.12 ± 0.24	160.5 ± 5.6	1.79 ± 0.19	0.56 ± 0.12	3.13	0.94
23	5 31 44.304	34 12 2.462	1.80 ± 0.30	159.5 ± 4.4	2.03 ± 0.21	164.7 ± 2.8	1.82 ± 0.18	168.5 ± 2.7	1.96 ± 0.15	0.64 ± 0.12	0.46	1.45
26	5 31 24.496	34 9 52.686	2.32 ± 0.29	163.7 ± 3.4	1.89 ± 0.21	156.4 ± 3.0	2.25 ± 0.23	168.1 ± 2.7	2.18 ± 0.15	0.64 ± 0.12	1.81	1.27
30	5 31 40.680	34 13 48.137	1.80 ± 0.36	159.8 ± 5.3	2.03 ± 0.30	165.3 ± 4.0	1.90 ± 0.30	163.3 ± 4.4	1.98 ± 0.19	0.69 ± 0.18	0.20	0.67
32	5 31 18.638	34 11 17.844	2.64 ± 0.30	155.5 ± 3.1	1.86 ± 0.24	148.4 ± 3.5	1.82 ± 0.26	154.0 ± 3.8	2.70 ± 0.56	0.42 ± 0.08	1.18	0.83
37	5 30 54.507	34 10 49.141	3.50 ± 0.33	150.9 ± 2.6	2.90 ± 0.23	148.6 ± 2.2	2.58 ± 0.21	152.6 ± 2.3	3.47 ± 0.41	0.47 ± 0.06	0.61	0.56
41	5 31 45.626	34 13 31.739	3.32 ± 0.44	166.4 ± 3.5	2.62 ± 0.25	163.4 ± 2.6	2.68 ± 0.17	164.0 ± 1.8	2.99 ± 0.31	0.56 ± 0.09	1.41	0.67
45	5 31 7.708	34 14 16.768	2.53 ± 0.40	153.5 ± 4.4	2.13 ± 0.33	146.2 ± 4.2	1.45 ± 0.37	153.9 ± 6.8	2.94 ± 1.00	0.38 ± 0.11	0.43	0.50
46	5 31 43.463	34 15 59.080	2.10 ± 0.44	149.6 ± 5.7	2.44 ± 0.31	158.9 ± 3.4	1.94 ± 0.27	151.8 ± 3.9	2.30 ± 0.30	0.58 ± 0.14	0.84	0.88
47	5 30 53.075	34 11 45.953	2.28 ± 0.40	149.2 ± 4.8	2.49 ± 0.34	155.9 ± 3.8	2.63 ± 0.40	159.1 ± 4.2	2.59 ± 0.29	0.76 ± 0.19	0.23	1.30
48	5 31 46.759	34 14 11.717	2.44 ± 0.45	145.7 ± 5.1	2.19 ± 0.30	160.6 ± 3.8	1.57 ± 0.25	148.1 ± 4.3	2.73 ± 0.80	0.41 ± 0.10	0.52	1.31
51	5 31 20.036	34 10 7.406	2.16 ± 0.41	149.5 ± 5.1	1.77 ± 0.35	152.0 ± 5.4	1.49 ± 0.42	165.8 ± 7.6	2.25 ± 0.71	0.43 ± 0.15	0.14	1.04
52	5 30 59.940	34 12 44.003	1.17 ± 0.44	158.3 ± 10.1	1.52 ± 0.35	157.7 ± 6.3	2.44 ± 0.39	163.9 ± 4.4	...	...
53	5 30 59.192	34 8 31.110	2.34 ± 0.43	152.3 ± 5.0	1.72 ± 0.35	143.3 ± 5.5	1.94 ± 0.40	153.8 ± 5.5	2.19 ± 0.47	0.50 ± 0.16	1.04	0.65
55	5 30 59.360	34 14 20.011	2.25 ± 0.47	155.5 ± 5.7	2.45 ± 0.41	158.8 ± 4.7	2.21 ± 0.49	158.3 ± 6.1	2.39 ± 0.27	0.64 ± 0.20	0.21	0.37
57	5 31 20.978	34 13 47.093	3.18 ± 0.43	155.7 ± 3.8	2.47 ± 0.34	152.9 ± 3.8	2.51 ± 0.37	141.6 ± 4.1	3.04 ± 0.51	0.49 ± 0.11	0.97	1.44
58	5 30 53.382	34 12 17.334	2.67 ± 0.47	155.0 ± 4.9	2.52 ± 0.33	151.7 ± 3.6	2.47 ± 0.31	149.1 ± 3.4	2.64 ± 0.27	0.61 ± 0.14	0.37	0.77
71	5 31 1.710	34 8 26.826	2.88 ± 0.60	156.6 ± 5.8	2.13 ± 0.47	155.1 ± 6.0	2.60 ± 0.56	−3.3 ± 5.9	2.63 ± 0.48	0.56 ± 0.20	1.12	9.12
73	5 31 37.341	34 16 48.904	2.28 ± 0.64	153.5 ± 7.6	2.49 ± 0.52	159.6 ± 5.7	2.32 ± 0.50	162.3 ± 5.9	2.45 ± 0.33	0.66 ± 0.24	0.11	0.78
79	5 31 3.560	34 15 20.297	4.76 ± 0.55	151.8 ± 3.3	5.05 ± 0.47	135.2 ± 2.6	4.81 ± 0.53	167.0 ± 3.1	5.04 ± 0.31	0.66 ± 0.11	0.05	3.53
84	5 31 17.663	34 13 27.548	2.30 ± 0.57	157.1 ± 6.8	2.89 ± 0.48	158.1 ± 4.6	1.79 ± 0.57	148.9 ± 8.7	2.56 ± 0.47	0.55 ± 0.20	1.23	0.46
92	5 31 20.749	34 11 53.851	1.98 ± 0.61	167.9 ± 8.5	2.45 ± 0.47	156.0 ± 5.2	1.55 ± 0.49	136.9 ± 8.6	2.23 ± 0.58	0.53 ± 0.21	1.04	1.92
93	5 31 37.064	34 14 15.670	2.28 ± 0.69	146.6 ± 8.4	4.05 ± 0.58	158.8 ± 4.0	3.02 ± 0.56	160.9 ± 5.1	3.40 ± 0.50	0.79 ± 0.25	1.65	1.51
103	5 31 13.736	34 13 26.782	3.14 ± 0.70	154.0 ± 6.2	3.36 ± 0.57	147.1 ± 4.7	2.08 ± 0.66	142.9 ± 8.5	3.43 ± 0.97	0.47 ± 0.16	0.97	0.93
Stars embedded in the nebulosity
7	5 31 27.071	34 14 49.520	0.82 ± 0.11	148.9 ± 3.3	0.73 ± 0.09	131.8 ± 3.1	0.55 ± 0.09	99.4 ± 3.9	0.88 ± 0.18	0.43 ± 0.09	0.36	6.47
11	5 31 26.523	34 14 45.071	0.62 ± 0.13	162.9 ± 5.0	0.86 ± 0.10	170.6 ± 2.9	0.87 ± 0.10	26.7 ± 2.8	0.90 ± 0.13	0.89 ± 0.20	0.56	13.42
14	5 31 26.434	34 14 56.224	2.11 ± 0.22	140.4 ± 2.9	2.10 ± 0.12	143.6 ± 1.5	1.30 ± 0.19	127.8 ± 3.9	2.40 ± 0.36	0.44 ± 0.07	2.18	1.89
34	5 31 27.504	34 15 3.132	2.11 ± 0.37	156.0 ± 4.6	1.11 ± 0.29	135.0 ± 7.0	1.04 ± 0.29	175.0 ± 7.4	...	...	...	...
35	5 31 25.024	34 14 40.484	6.51 ± 0.32	159.1 ± 1.3	6.23 ± 0.23	163.3 ± 1.1	6.82 ± 0.20	163.4 ± 0.8	6.73 ± 0.14	0.71 ± 0.04	2.59	2.64
49	5 31 25.012	34 14 17.387	1.61 ± 0.49	158.2 ± 8.0	1.58 ± 0.40	135.6 ± 7.0	1.73 ± 0.41	130.0 ± 6.4	1.69 ± 0.27	0.71 ± 0.30	0.35	2.39
68	5 31 31.881	34 13 57.500	2.03 ± 0.57	152.1 ± 7.6	1.70 ± 0.42	149.6 ± 6.8	1.52 ± 0.41	156.9 ± 7.3	2.01 ± 0.71	0.48 ± 0.20	0.20	0.34
70	5 31 26.662	34 14 21.656	2.21 ± 0.60	142.5 ± 7.6	3.25 ± 0.49	145.9 ± 4.2	2.32 ± 0.50	141.4 ± 5.9	2.74 ± 0.31	0.67 ± 0.21	1.37	0.25
72	5 31 20.975	34 14 22.715	2.08 ± 0.60	163.3 ± 7.5	2.67 ± 0.40	152.8 ± 4.1	2.82 ± 0.33	142.4 ± 3.2	2.86 ± 0.45	0.88 ± 0.26	0.14	2.12
88	5 31 25.693	34 14 41.104	8.66 ± 0.47	164.7 ± 1.5	6.36 ± 0.35	153.0 ± 1.6	6.42 ± 0.33	147.8 ± 1.4	8.26 ± 0.61	0.47 ± 0.04	2.88	6.41
99	5 31 25.777	34 14 33.565	4.77 ± 0.64	164.3 ± 3.6	4.80 ± 0.52	154.7 ± 3.0	5.39 ± 0.53	162.9 ± 2.7	5.22 ± 0.40	0.76 ± 0.14	0.84	1.17
139	5 31 20.503	34 15 17.975	4.51 ± 1.01	127.6 ± 6.8	3.18 ± 0.60	146.4 ± 5.3	4.26 ± 0.44	143.3 ± 2.8	4.05 ± 0.37	0.77 ± 0.22	1.74	2.32
Stars with either single or double band data
1	5 30 59.954	34 15 32.065	1.97 ± 0.08	150.7 ± 1.1	...	...	1.61 ± 0.05	151.5 ± 0.9	...	...	...	...
60	5 31 44.919	34 12 17.676	2.16 ± 0.52	156.5 ± 6.4	2.11 ± 0.40	164.9 ± 5.2	...	...	...	...	...	...
65	5 31 25.097	34 10 24.942	2.70 ± 0.48	161.1 ± 4.9	1.88 ± 0.41	163.9 ± 5.9	...	...	...	...	...	...
66	5 31 12.905	34 13 54.822	2.06 ± 0.54	162.4 ± 7.2	1.83 ± 0.47	154.5 ± 7.0	...	...	...	...	...	...
76	5 31 23.673	34 10 40.710	3.04 ± 0.56	159.7 ± 5.1	2.06 ± 0.49	154.3 ± 6.5	...	...	...	...	...	...
85	5 31 27.167	34 18 19.141	...	...	...	...	2.99 ± 0.28	143.9 ± 2.5	...	...	...	...
86	5 31 36.690	34 16 58.282	...	...	...	...	1.51 ± 0.45	167.0 ± 7.9	...	...	...	...
102	5 31 35.799	34 13 22.894	...	...	2.87 ± 0.59	179.1 ± 5.7	2.79 ± 0.59	154.8 ± 5.8	...	...	...	...
115	5 31 26.544	34 16 0.836	3.11 ± 0.90	168.7 ± 7.7	2.60 ± 0.45	171.3 ± 4.7	...	...	...	...	...	...
128	5 31 23.382	34 12 11.347	...	...	2.23 ± 0.72	154.4 ± 8.9	...	...	...	...	...	...
133	5 31 30.090	34 16 47.089	3.30 ± 0.95	147.1 ± 8.1	...	...	...	...	...	...	...	...
236	5 31 23.741	34 13 47.338	6.52 ± 0.55	130.1 ± 2.5	3.59 ± 0.41	129.4 ± 3.2	...	...	...	...	...	...
2001a	5 30 47.429	34 11 47.864	...	...	1.96 ± 0.61	158.3 ± 8.4	2.58 ± 0.70	169.6 ± 7.5	...	...	...	...
2002a	5 30 49.688	34 11 28.666	3.10 ± 0.59	147.1 ± 5.3	3.54 ± 0.51	147.8 ± 4.1	...	...	...	...	...	...
2003a	5 31 24.224	34 14 0.139	3.16 ± 0.79	172.6 ± 6.6	...	...	...	...	...	...	...	...

Notes. ^aOptical data are not available for the three stars, namely, 2001, 2002, and 2003. Their IDs are given arbitrarily.

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Table 7. The Optical (Present Work), JHK_s (2MASS) Data for the Identified YSOs

ID	R.A. (J2000)	Decl. (J2000)	U ± σU	B ± σB	V ± σV	$R_{c}\pm \sigma _{R_{c}}$	$I_{c}\pm \sigma _{I_{c}}$	J ± σJ	H ± σH	K ± σK
	(h m s)	(° ' '')	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
46	5 31 43.461	34 15 59.011	16.689 ± 0.007	15.684 ± 0.004	14.436 ± 0.002	13.719 ± 0.002	13.071 ± 0.003	12.087 ± 0.022	11.500 ± 0.021	11.331 ± 0.019
58	5 30 53.386	34 12 17.417	16.964 ± 0.014	16.098 ± 0.004	14.784 ± 0.004	13.998 ± 0.003	13.241 ± 0.003	12.060 ± 0.019	11.433 ± 0.022	11.237 ± 0.018
72	5 31 20.999	34 14 23.129	16.685 ± 0.008	16.223 ± 0.004	15.027 ± 0.003	14.237 ± 0.003	13.432 ± 0.003	12.119 ± 0.023	11.449 ± 0.023	11.220 ± 0.019
85	5 31 27.171	34 18 19.087	18.808 ± 0.020	17.055 ± 0.009	15.183 ± 0.010	14.016 ± 0.004	12.940 ± 0.009	11.192 ± 0.022	10.203 ± 0.021	9.897 ± 0.018
88	5 31 36.688	34 16 57.950	15.893 ± 0.093	15.916 ± 0.090	15.274 ± 0.026	14.662 ± 0.060	13.748 ± 0.150	13.406 ± 0.037	12.924 ± 0.035	12.818 ± 0.033
129	5 31 32.081	34 9 26.896	17.474 ± 0.009	16.924 ± 0.018	15.965 ± 0.004	15.268 ± 0.011	14.551 ± 0.009	13.252 ± 0.022	12.688 ± 0.025	12.172 ± 0.021
139	5 31 20.503	34 15 17.975	18.715 ± 0.018	17.715 ± 0.011	16.094 ± 0.005	15.016 ± 0.012	13.943 ± 0.005	12.120 ± 0.022	11.221 ± 0.021	10.919 ± 0.018
236	5 31 23.731	34 13 47.352	18.290 ± 0.026	18.168 ± 0.022	16.980 ± 0.029	16.140 ± 0.015	15.032 ± 0.236	12.805 ± 0.023	12.057 ± 0.024	11.269 ± 0.018
544	5 31 19.522	34 14 41.392	...	20.354 ± 0.018	18.623 ± 0.022	17.524 ± 0.015	16.420 ± 0.111	14.665 ± 0.034	13.699 ± 0.033	13.267 ± 0.029
589	5 31 23.966	34 12 21.672	...	20.661 ± 0.021	18.776 ± 0.011	17.694 ± 0.012	16.618 ± 0.048	14.877 ± 0.040	13.947 ± 0.046	13.636 ± 0.044
609	5 31 24.859	34 13 34.457	...	20.444 ± 0.044	18.876 ± 0.012	17.583 ± 0.021	16.401 ± 0.070	14.489 ± 0.034	13.549 ± 0.037	13.135 ± 0.034
1493	5 31 4.709	34 17 7.112	...	...	21.161 ± 0.048	19.845 ± 0.029	18.253 ± 0.021	16.274 ± 0.096	15.404 ± 0.102	14.799 ± 0.089
a	5 31 23.926	34 9 56.668	...	...	...	...	...	14.737 ± 0.041	13.021 ± 0.049	11.750 ± 0.021
b	5 30 50.131	34 12 57.532	...	...	...	...	...	13.392 ± 0.017	12.800 ± 0.022	12.541 ± 0.021
c	5 31 38.609	34 14 24.760	...	...	...	...	...	15.171 ± 0.042	14.112 ± 0.035	13.482 ± 0.033
d	5 30 47.194	34 7 0.048	...	...	...	...	...	16.188 ± 0.106	15.204 ± 0.096	14.597 ± 0.091

Note. The stars (a, b, c, d) are not covered by optical photometric observations.

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6.2.3. On the Basis of Optical and NIR CMDs and NIR TCD

Figure 19 shows V/(V − I) and J/(J − H) CMDs as well as (J − H)/(H − K) TCD for the remaining stars that have polarimetric data but are not classified as probable members in Section 5.2. We found a few stars located near 1 Myr isochrone in both the CMDs. These are shown by star symbols. Four stars, 46, 58, 72, and 88, are located near the extension of TTSs locus by Meyer et al. (1997) in (J − H)/(H − K) TCD. The disk accretion rates $\dot{M}_{{\rm disk}}$, estimated using the spectral energy distribution (SED; cf. Section 6.4) for stars 46 and 72, are of the order of 10⁻⁹ and 10⁻⁷ M_☉ yr⁻¹, which are comparable to the Class II sources. We presume that these could be WTTSs with a small NIR excess. Star 139 could also be a reddened WTTS, whereas star 236 could be an HAe/Be star. Star 236 is identified as a Class II source on the basis of NIR and MIR data (cf. Section 6.2.2). The $\dot{M}_{{\rm disk}}$ for stars 236 and 139 is estimated to be 0.8 × 10⁻⁸ and 0.8 × 10⁻⁷ M_☉ yr⁻¹, respectively.

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The V/(V − I) CMD for the YSOs identified in Section 6.2 is shown in Figure 20. PMS isochrones by Siess et al. (2000) for 1, 2, 5, and 10 Myr (dashed lines) and the post-main-sequence isochrone for 1 Myr by Marigo et al. (2008, continuous curve) corrected for cluster distance (2.3 kpc) and minimum reddening (E(B − V) = 0.5) are also shown. Figure 20 reveals that a majority of the sources have ages <5 Myr with a possible age spread of ∼5 Myr. Since the reddening vector in V/(V − I) CMD is nearly parallel to the PMS isochrone, the presence of variable extinction in the region will not affect the age estimation significantly. The age and mass of each YSO have been estimated using the V/(V − I) CMD, as discussed by Pandey et al. (2008) and Chauhan et al. (2009) and are given in Table 9. It is worthwhile to point out that the estimation of the ages and masses of the PMS stars by comparing their locations in the CMDs with theoretical isochrones is prone to random as well as systematic errors (see, e.g., Hillenbrand 2005; Hillenbrand et al. 2008; Chauhan et al. 2009, 2011b). The effect of random errors due to photometric errors and reddening estimation in the determination of ages and masses has been estimated by propagating the random errors to their observed estimation by assuming normal error distribution and using the Monte Carlo simulations (cf. Chauhan et al. 2009). The systematic errors could be due to the use of different PMS evolutionary models and the error in distance estimation, etc. Since we are using evolutionary models by Siess et al. (2000) to estimate the age of all the YSOs in the region, we presume that the age estimation is affected only by random errors. The presence of binaries may also introduce errors in the age determination. Binarity will brighten the star, consequently the CMD will yield a lower age estimate. In the case of an equal-mass binary, we expect an error of ∼50%–60% in the PMS age estimation. However, it is difficult to estimate the influence of binaries/variables on the mean age estimation as the fraction of binaries/variables is not known. In the study of TTSs in the H ii region IC 1396, Barentsen et al. (2011) pointed out that the number of binaries in their sample of TTSs could be very low as close binaries lose their disk significantly faster than single stars (cf. Bouwman et al. 2006). Estimated ages and masses of the YSOs range from ∼0.1 to 5 Myr and ∼0.3 to 3.5 M_☉, respectively, which are comparable with the lifetime and masses of TTSs. The age spread indicates a non-coeval star formation in this region.

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To characterize the circumstellar disk properties of YSOs, we analyzed the SEDs using the fitting tool of Robitaille et al. (2007). The SED fitting tool fits thousands of models to the observed SED simultaneously. This SED fitting tool determines their physical parameters like mass (M_⋆), age, interstellar extinction (A_V), temperature (T_⋆), disk mass, disk mass accretion rate ($\dot{M}_{{\rm acc}}$), etc. The SED fitting tool fits each of the models to the data, allowing both the distance and foreground extinction to be free parameters. Since we do not have spectral type information for the identified YSOs, we estimated A_V by tracing back sources along the reddening vector to the intrinsic locus of TTS (Meyer et al. 1997) in (J − H)/(H − K) TCD. Thus the estimated value of A_V is considered as the maximum A_V, whereas the foreground extinction for the YSOs toward NGC 1931 is considered as the minimum A_V. The distance range is adopted as 2.1–2.5 kpc. The error in NIR and MIR flux estimates due to possible uncertainties in the calibration, extinction, and intrinsic object variability was set as 10%–20%. Figure 21 shows an example of SED of the resulting model for a Class II source 236. We obtained physical parameters for all the sources, adopting an approach similar to that of Robitaille et al. (2007), by considering those models that satisfy χ² − χ²_min < 2N_data, where χ²_min is the goodness-of-fit parameter for the best-fit model and N_data is the number of observational input data points. The relevant parameters are obtained from the weighted mean and the standard deviation of these models, weighted by e$^{({{-\chi }^2}/2)}$ of each model, and are shown in Table 10, which reveals that the majority of the Class II sources have a disk accretion rate of the order of ∼10⁻⁷ to 10⁻⁸ M_☉ yr⁻¹. The parameters support the classification of YSOs obtained on the basis of CMDs and NIR/MIR TCDs. We would like to mention that the stellar ages given in Table 10 are only approximate, and in the absence of far-infrared (FIR) to millimeter data the disk parameters should be taken with a caution; however, these parameters can still be used as a quantitative indicator of stellar youth.

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Table 10. The Physical Parameters of the YSOs Estimated from the SED Fits

ID	M*	T*	Age	$\dot{M}_{\rm acc}$	AV
	(M☉)	(103 K)	(106 yr)	(10−7 M☉ yr−1)	(mag)
46	3.44 ± 0.20	5.30 ± 0.45	0.980 ± 0.352	0.011 ± 0.000	1.4 ± 0.4
58	3.65 ± 0.17	5.33 ± 0.05	0.901 ± 0.099	0.000 ± 0.000	1.8 ± 0.1
72	3.07 ± 0.44	6.02 ± 1.05	1.532 ± 0.588	1.036 ± 0.028	2.1 ± 0.6
85	3.74 ± 0.00	5.35 ± 0.00	0.852 ± 0.000	0.000 ± 0.000	2.9 ± 0.0
88	3.45 ± 0.49	12.81 ± 1.82	4.307 ± 2.346	0.000 ± 0.000	2.8 ± 0.4
129	4.34 ± 0.66	14.89 ± 1.91	3.667 ± 0.514	0.006 ± 0.001	4.0 ± 0.4
139	3.56 ± 0.51	5.70 ± 0.57	1.035 ± 0.408	0.821 ± 0.032	3.1 ± 1.0
236	3.76 ± 0.43	13.70 ± 1.10	5.052 ± 2.050	0.082 ± 0.007	4.1 ± 0.4
544	2.07 ± 0.71	6.61 ± 2.80	4.171 ± 2.903	0.206 ± 0.006	3.9 ± 1.4
589	2.23 ± 0.27	7.73 ± 1.83	5.755 ± 2.119	0.046 ± 0.002	4.8 ± 1.3
609	1.76 ± 0.76	5.56 ± 2.20	2.994 ± 2.648	0.177 ± 0.006	3.5 ± 1.3
1493	2.07 ± 0.60	5.20 ± 0.61	3.261 ± 1.230	0.155 ± 0.003	3.1 ± 0.6
a	3.95 ± 1.25	13.07 ± 3.67	4.526 ± 2.497	0.265 ± 0.005	10.0 ± 1.7
b	2.47 ± 0.64	7.27 ± 2.93	4.330 ± 1.314	0.024 ± 0.002	3.4 ± 0.5
c	2.85 ± 1.30	9.97 ± 4.24	4.202 ± 2.264	0.107 ± 0.004	8.7 ± 2.3
d	2.02 ± 0.67	8.09 ± 2.73	5.991 ± 2.842	0.070 ± 0.002	8.8 ± 2.8

Note. The stars (a, b, c, d) are not covered by optical photometric observations.

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