UOCS-XI. Study of blue straggler stars in open cluster NGC 7142 using UVIT/AstroSat

The observations of NGC 7142 were carried out using UVIT in one FUV filter, F148W, on 13^th June 2018 under the proposal ID A04-075 with the exposure time of 2280.717 sec. UVIT is an imaging instrument onboard AstroSat, which is made up of two Ritchey-Chrétien telescopes with 38 cm apertures. In UVIT, one telescope observes in FUV (130$-$180 nm), and the other in NUV (200$-$300 nm) and visible wavelengths (320$-$550 nm). However, the NUV channel developed a technical issue in 2018 and has not been functional since then. UVIT produces images with a Full Width Half Maximum of $\sim$1.5″and a circular field of view of 28′in diameter. There are various filters available in the FUV, NUV, and visible bands. The UV detectors operate in photon counting mode, whereas the visible detectors operate in integration mode. For the details on the effective area curves of UVIT filters and other instrument-related information, readers are referred to Kumar et al. (2012); Subramaniam et al. (2016b); Tandon et al. (2017). We use CCDLAB (Postma & Leahy, 2017, 2021), a customised software package, to correct for geometric distortion, flat field, spacecraft drift, astrometry and create images for each orbit. The orbit-wise images were then co-aligned and combined to generate science-ready images.

TESS is an all-sky broad-band photometric survey mission covering upto 85$\%$ of the sky in its first two years. Each hemisphere is divided into thirteen sectors, with one sector being observed for 27.4 days. It provided the data in two cadences, 2 minutes and 30 minutes, in the 2-year nominal mission, but was later augmented to 20 seconds and 200 seconds, in the extended mission. It has four identical cameras, each with a field of view of 24 $\times$ 24 degrees. Each of the four cameras is equipped with a 2K $\times$ 2K CCD, with each pixel covering 21″. The cameras are arranged so that all four can cover a 24 $\times$ 96 square degree strip of sky. The detectors are sensitive from 600 to 1000 nm, i.e., within blue to the near-IR wavelengths.

TESS light curves (LCs) of all our BSS samples are observed using different data projects. These include Quick Look Pipeline (QLP; Huang et al. 2020; Kunimoto et al. 2022), Cluster Difference Imaging Photometric Survey (CDIPS; Bouma et al. 2019), and a PSF-based Approach to TESS High-Quality Data Of Stellar Clusters (PATHOS; Nardiello et al. 2019, 2021). The QLP project generates LCs from a group of stars and other stationary luminous objects with a limited G magnitude of 13.5. For the details on the data reduction process, readers are referred to Huang et al. (2020). On the other hand, the CDIPS project creates the LCs for stars that are candidate members of OCs and moving groups. Each LC corresponds to 20 to 25 days of observations of a star brighter than 16 in G magnitude. The PATHOS project generates a library of high-precision LCs for cluster members using photometry extracted from TESS Full Frame Pictures. The PSF-based technique reduces dilution effects in crowded situations, allowing for the extraction of high-precision photometry for faint stars. The PATHOS data release X has 770 LCs of 168 star clusters, including NGC 7142 (Messina et al., 2022).

In the case of OCs, the contamination due to field stars is a big challenge. Hence, obtaining secure membership is of utmost importance to do any further analysis. We used ML-MOC algorithm (Agarwal et al., 2021) on Gaia DR3 (Vallenari et al., 2022) data in order to determine the cluster members. This is a machine-learning-based algorithm that does not require any prior knowledge of a cluster and employs the k-Nearest Neighbour (kNN, Cover & Hart 1967) and the Gaussian mixture model (GMM, Peel & McLachlan 2000) algorithms. The steps that we followed to determine cluster members using ML-MOC are described briefly here. First, we downloaded the sources within 30$\arcmin$ radius of the cluster center that have five astrometric parameters (positions, proper motions, and parallax), appropriate measurements in three Gaia photometric passbands G, G_BP, and G_BP, non-negative parallaxes, and error in G-mag less than 0.005. These are called All sources. Then, we estimated the mean proper motions and mean parallaxes of the cluster using the kNN algorithm to determine the ranges of proper motions and parallaxes that enclose all of the likely cluster members. These are termed as Sample sources. Next, we apply the GMM, an unsupervised clustering algorithm, to the Sample sources in order to separate the likely cluster members from the field stars by fitting two Gaussian distributions in the proper motions and parallax space of the Sample sources. The fitting of GMM is done by maximizing the likelihood of the distribution parameters using the expectation maximization algorithm (Dempster et al., 1977). The K-component GMM, for N data points in an M-dimensional parameter space, is defined as

where P(x) represents the probability distribution of data points x and $\omega_{i}$ is the mixture weight of the i^th Gaussian component, G(x| $\mu_{i},\Sigma_{i}$). This Gaussian component is defined as

In both the above equations, $\mu_{i}$ is the mean vector, and $\Sigma_{i}$ is the full covariance matrix of the i^th Gaussian component. The GMM calculates a probability that designates the likelihood of each data point belonging to the cluster. We use a two-component, i.e., cluster and field, GMM on the normalized three-dimensional parameter space ($\mu\alpha$, $\mu\delta$, $\omega$) assuming that the proper motions and parallaxes of the Sample sources follow a two-component Gaussian distribution. Our member selection criteria considers sources with high membership probabilities exceeding 0.6 as members. Subsequently, we expand this list to include Sample sources whose parallax values lie within the range of parallaxes of even higher probability members ($>$ 0.8). The members added later are low-probability members with probabilities ranging between 0.2 and 0.6. Out of the 546 sources identified as cluster members, only six are with probabilities ranging between 0.2 and 0.6; the rest are high probability members. The proper motion, spatial, and parallax distributions of sample sources and the identified cluster members are shown in Figure 1.

We used the DAOPHOT package of IRAF (Stetson, 1987) in order to perform the point-spread function (PSF) photometry and obtained the magnitudes of the detected stars in FUV image, F148W. To accomplish this task, we employed the following steps. First, we estimated the background counts and mean FWHM of the image using imexamine task. Then, we detected the sources above a certain threshold limit using daofind task in IRAF. We performed the aperture photometry of the sources using the phot task. In order to perform PSF photometry, we selected the bright and isolated sources using pstselect and created a PSF model using psf task. Finally, PSF magnitudes of all the stars were estimated simultaneously using multiple iterations of PSF fitting to the group of stars using allstar task. We also applied the PSF corrections in order to eliminate the systematic difference between allstar magnitudes and phot magnitudes, followed by the aperture correction, which was determined using the curve-of-growth technique. Moreover, since the FUV detector of UVIT works in photon counting mode, it may be subjected to counts more than one photon per frame. In order to eliminate this issue, we applied the saturation corrections following Tandon et al. (2020).

To quantify the differential reddening and correct it, we used the method adopted in Della Croce et al. (2023). First, we select the likely main sequence stars (G $>$ 15 mag or G_BP $-$ G_RP $<$ 1.5 mag) from the members determined using ML-MOC. Then we find counterparts of these members in Pan-STARRS (Chambers et al., 2016) photometric bands r, i, and z by searching within 1″of the Gaia coordinates. Next, we plot a color-color diagram, G$-$r vs i$-$z. This diagram is a suitable choice as the evolutionary sequences are generally orthogonal to the reddening vector in these colors (Della Croce et al., 2023). We refer to the median of this color-color distribution as our reference point. Afterward we obtain the median colors of the closest 50 stars of each main sequence star and estimated the distance of this median value to the reference system along the reddening vector using the coefficients given in Cardelli et al. (1989). For the remaining stars which are not in the main-sequence, we assign the median reddening of the closest 50 neighbors (Della Croce et al., 2023). At last, we apply the extinction value corresponding to the derived distance to member stars and plotted the reddening map, as shown in the left panel of Figure 2. It is noteworthy that the reddening is more severe in the northwest field; however in the center as well as in the southern regions, the reddening is low and does not vary significantly. The significantly high reddening in the northwest direction can be attributed to the presence of the NGC 7129 nebula in the same direction. The right panel of Figure 2 shows the optical CMD of the cluster members determined using ML-MOC before and after the differential reddening and extinction corrections.

Figure 3 shows the differential reddening and extinction corrected optical CMD of the cluster. The cluster members determined using the machine-learning-based algorithm, ML-MOC, are shown in red dots along with their membership probabilities. The 10 BSSs identified as members and with counterparts in the UVIT/F148W are shown as blue open circles, labeled according to the coordinates given in Table LABEL:Table1. There are four additional BSSs candidates which are cluster members but have no UV counterparts. We only study the 10 BSSs, which are members of the cluster and detected in the UVIT filter in this work. It is noteworthy that all the BSSs are highly probable cluster members with a membership probability of $\sim$0.8 - 0.9. Furthermore, the variable stars identified in a study by Sandquist et al. (2011), which are cluster members as per our criteria, are shown as green-filled circles. BSS 7 is one of the five variable stars from their study. The remaining four variables do not show variable nature using Gaia or TESS data. A PARSEC isochrone (Bressan et al., 2012) of age = 4.0 Gyr, distance = 2368 pc, and [Fe/H] = 0 (Sun et al., 2020) is plotted after applying the extinction correction of A${}_{\text{G}}$ = 0.09 and reddening of E(B${}_{\text{P}}$ $-$ R${}_{\text{P}}$) = 0.03. Furthermore, we have also shown a binary sequence isochrone as the blue dashed curve for equal-mass binaries that have a G-band magnitude brighter than 0.75 mag than the MS stars. It is evident from the CMD that G-band magnitudes of BSSs range from $\sim$0.4 to $\sim$1.4 above the MSTO.

Variable stars can provide a wealth of new information, allowing us to confirm current theories that seek to predict cluster stellar properties from basic principles (Sandquist et al., 2011). For example, pulsating stars can reveal information about stellar interior structure and mass. Short-period semi-detached and contact binaries may carry encoded information about the dynamical history of the cluster. Detached eclipsing binaries can be particularly valuable since they can offer high-precision measurements of masses and radii for individual stars with minimal theoretical interpretation. In order to check if any of the BSS is variable in nature, we used the TESS (Ricker et al., 2015) data. We searched for the TESS LCs of all our BSS samples in different data releases, as mentioned above. In this work, we have presented the LCs of PATHOS data release. We used Lightkurve (Lightkurve Collaboration et al., 2018), a python based package, to construct and analyse the LC of the BSSs. We found that two of our ten BSSs candidates (BSS 1 and BSS 7) showed some signatures of variability in sectors 16, 18, and 24, using all the three pipelines mentioned above. The LCs of these BSSs of sector 16, generated using the PATHOS pipeline, are shown in Figure 4. Then, we computed the power spectrum using Fourier transform (FT) from the LC in order to determine the period as shown in Figure 5. We take all the significant frequencies from the periodogram. A frequency is considered significant if the amplitude or power of that frequency is four times the noise (Breger et al., 1993). After doing it for all the frequencies, the orbital frequency will give a phase folded curve with two dips resembling two eclipses, whereas all others will give sinusoidal variations as shown in Figure 6. It can be noted that the orbital period of BSS 1 is $\sim$1 day, whereas the period of BSS 7 is $\sim$0.5 days. Sandquist et al. (2011) categorised BSS 7 as an eclipsing contact or near-contact binary with an orbital period of $\sim$ 0.58 days, using high -resolution spectrograph at Hobby-Eberly Telescope. However, none of their other variables were found to be variable in our analysis.

Stars emit electromagnetic radiation across the entire frequency or wavelength range. The Spectral Energy Distribution (SED) describes the distribution of this radiation over wavelengths. Analyzing the SEDs of stars allows us to estimate their fundamental parameters and thus gain a better understanding of their formation and evolution. Furthermore, the excess in UV fluxes can indicate the likelihood of a hotter companion of BSSs, hence constraining their formation mechanism. We used the virtual observatory SED analyser (VOSA, Bayo et al. 2008) to create the SEDs. We found that three of the ten BSS candidates (BSS 4, BSS 9, and BSS 10) in this cluster have a nearby source within 3″, and hence we did not construct their SEDs.

We obtained photometric fluxes of sources in NUV from GALEX (Martin et al., 2005), optical from Gaia DR3 (Babusiaux et al., 2022) and PAN-STARRS (Chambers et al., 2016), near-IR from Two Micron All Sky Survey (2MASS, Cohen et al. 2003), and far-IR from Wide-field Infrared Survey (WISE, Wright et al. 2010), using VOSA. The photometric fluxes were corrected for extinction by VOSA according to the extinction law by Fitzpatrick (1999) and Indebetouw et al. (2005) using the value of extinction A_v = 1.04$\pm$0.09 provided by us, which is taken from Sun et al. (2020). Table LABEL:Table1 shows the values of the BSS fluxes in various filters.

VOSA calculates synthetic photometry for selected theoretical models using filter transmission curves and performs a $\chi^{2}$ minimization test by comparing the synthetic photometry with the extinction-corrected observed fluxes to determine the best-fitting SED parameters. The following formula is used to calculate the reduced $\chi^{2}_{r}$:

where N is the number of photometric data points used and N_f is the number of model-free parameters. The observed and model fluxes of the star are denoted by F_o,i and F_m,i respectively. M_d is the scaling factor that must be multiplied by the model to obtain the fit, and it is given by (R/D)², where R is the radius of the star, D is the distance to the star, and $\sigma_{o,i}$ is the error in the observed flux. We used Kurucz stellar models (Castelli et al., 1997) to fit the SEDs to the BSSs. We kept T_eff and log g as free parameters, with ranges of 3500 – 50000 K and 3 – 5, respectively. We set the metallicity ([Fe/H]) value to zero, which is the cluster metallicity reported by Sun et al. (2020). We first removed the UV data points from the SEDs and checked whether the optical and IR data points fit satisfactorily with the model flux. We carefully examined each UV filter to see if there was any excess to the UV and/or IR data points. We consider sources with UV excess greater than 50$\%$ with respect to the single component model for the binary component SED fits. It is interesting to note that all the seven BSSs showed the excess in UV fluxes greater than 50$\%$, and therefore, we attempted the binary-component SED fits to them. Since we select stars based on a 50$\%$ flux excess, it is not surprising that we find that all candidates have excess larger than this threshold. BSS 6 could not be fitted with the binary component SED since all the models fitting the data points showed the highest temperatures and hence were unreliable. The single-component SED of BSS 6 is shown in Figure 7.

In order to fit the binary component SEDs, we used a python code Binary SED Fitting¹¹1https://github.com/jikrant3/Binary SED Fitting, which is based on $\chi^{2}_{r}$ minimization technique (Jadhav et al., 2021b). We used the Koester model (Koester, 2010) for this purpose, as this gives a temperature range of 5000 – 80000 K and log g range of 6.5 – 9.5, thus making it suitable to fit a compact hotter companion. The double component SEDs for all the BSSs are shown in Figure 8. The top panel for each BSSs shows the fitted SED and the bottom panel shows the residual for single and composite fit in each filter. We note that the residuals come out to be nearly zero on fitting the binary component SED since the excess in UV fluxes have reduced significantly. The parameters of all the BSSs are listed in Table LABEL:Table2, where the parameters of the cooler components are taken from VOSA, and that of the hotter companions are taken from the python code mentioned above. The errors in the parameters are determined by following the statistical approach mentioned in Jadhav et al. (2021a). The $\chi^{2}$ of the fits are found to be large even when the SED fits are visually good, mostly due to very small observational flux errors (Rebassa-Mansergas et al., 2021). We estimate modified reduced $\chi^{2}$, visual goodness of fit (vgf_b), determined by VOSA by forcing the observational errors to be at least 10$\%$ of the observed flux. The vgf_b values $<$ 15 implies that the fits are good (Jiménez-Esteban et al., 2018; Rebassa-Mansergas et al., 2021).

Binary modelling is an excellent technique to obtain constraints on the stellar orbital parameters of a binary system. The additional constraints help us to understand the possible formation mechanism of the BSSs. In this study, we used PHysics Of Eclipsing BinariEs (PHOEBE) v0.32 (Prša & Zwitter, 2005) to model the two BSSs (BSS 1 and BSS 7) systems. This software package is an open-source eclipsing binary modelling code that theoretically calculates the stellar and orbital parameters of an eclipsing binary system using a synthetic light curve and a radial velocity curve. This is based on the Wilson-Devinney code (Wilson & Devinney, 1971) and accepts an observed light curve and radial velocity measurements as inputs, as well as initial guesses for parameters such as effective temperature, surface gravity, inclination, semi-major axis, luminosity, and surface potential.

The modelling of the two systems was performed in the following steps. Initially, we manually changed the parameters to obtain a close solution to the light curve. However, due to the unavailability of the radial velocity data for both systems, we used the Q-search method to determine the mass ratios. In the Q-search method, we performed multiple modelling runs for the same system with different values of the mass ratio. The value corresponding to the lowest sum of the squared deviations is taken as the mass ratio of the system. Once the mass ratio and an initial reasonable LC are obtained, we carry out iterative minimisation to find the best-fit model. The differential correction routine, available in PHOEBE, is performed repeatedly, where the next iteration is performed using the values of the previous cycle. This process is continued till the convergence of the cost function of the fitting. The parameters of BSS 1 and BSS 7 derived by fitting the binary model to the LCs using PHOEBE are listed in Table LABEL:Table3.

It is noteworthy that only two BSSs showed the variability signature in TESS, despite the fact that many may also be binary systems with hot companions and variables found in the literature. This could be due to several reasons. A binary system becomes an eclipsing binary only if the star is able to occult the light of the other, which is possible either if the system has high inclination or the radii of the companions are large. The BSSs in this cluster are found to have compact objects like white dwarfs as companions, which have a low probability of exhibiting eclipses. A similar system is shown in Vernekar et al. (2023). Furthermore, even if many more systems are eclipsing, their detection is limited by the amount of data available using TESS. Therefore, the BSSs system with longer periods cannot be probed using this method.

On fitting the SED of the BSSs using the method described above, we found that the temperatures of the BSSs vary from 6500 K to 8000 K, which is consistent with the age of the cluster. Furthermore, the luminosities vary from 8.72 to 26.91 L_⊙, and radii vary from 2.04 R_⊙ to 4.09 R_⊙. Upon comparing temperatures derived from fitting the SED with the temperatures based on BP/RP spectra-based from Gaia DR3 (Babusiaux et al., 2022), we found that the SED-based temperatures are within 400 K with the low-resolution spectra-based temperatures. We also find the rough estimation of masses of the BSSs by comparing it with the ZAMS of age 8.5 Gyr. The masses of the BSSs vary from 1.60 M_⊙ to 2.15 M_⊙. Since the turn-off mass of the cluster is 1.55 M_⊙, we suggest that the BSSs are likely to have gained $\sim$0.05 M_⊙ to 0.60 M_⊙ via MT/merger channel.

We performed binary modelling of the LCs by fixing the temperatures of the BSSs generated from the SED. The binary LCs of BSS 1 and BSS 7 fitted with the model using PHOEBE are shown in Figure 9. The observed and synthetic LCs are in agreement with each other, which is well conveyed by the residuals shown in the lower panels. This implies that the temperatures determined by constructing the SED are much accurate. In the case of BSS 1, the radius derived using SED fitting is 4.09 $\pm$ 0.01 R_⊙ and that from binary modelling of LC is 3.55 $\pm$ 0.12 R_⊙, which are consistent with each other. However, in the case of BSS 7, the radius of the BSSs derived by constructing the SED is 2.04 $\pm$ 0.04 R_⊙ and that from the binary modelling of LC is 5.69 $\pm$ 0.29 R_⊙. The parameters of both the BSSs derived from fitting the LC are listed in Table LABEL:Table3. Figure 10 shows the mesh plot of both the BSSs systems in different phases. The deformation of the blue straggler is indeed dominating the entire light curve with a small effect from eclipses.

We also checked for the information on the variability of BSSs in Gaia DR3 (Eyer et al., 2023), where BSS 1 and BSS 7 are reported as eclipsing binaries with the period of $\sim$1.07 and 0.58 days. On the other hand, BSS 3 and BSS 8 are found to be short time-scale ($<$ 0.5–1 d) MS-type oscillators (GDOR | DSCTU | SXPHE). However, for BSS 3 and BSS 8, we did not find any signatures of variability using TESS data.

In order to gain a complete understanding of how the BSSs have formed, examining the nature of their hotter companions is crucial. In order to achieve this, we constructed the Hertzsprung-Russell (H-R) diagram as shown in Figure 11. The locations of the hotter companions of BSS 1 and BSS 8 in the left panel of this figure indicate that they are ELM WDs (Althaus et al., 2013) of mass 0.18 M_⊙. The stellar remnants known as ELM WDs do not ignite helium in their cores (Brown et al., 2011). The hotter companion of BSS 7, on the other hand, lies on the WD cooling curve with a mass of 0.20 M_⊙ (Panei et al., 2007), indicating that it is an LM WD. The discovery of ELM/LM WD companions supports the Case-A/Case-B MT formation mechanism of BSS because ELM WDs and LM WDs cannot form from a single star evolution within Hubble time (Brown et al., 2011). This implies that these WDs must have lost mass during their evolution. Furthermore, the hotter companions of BSS 3 and BSS 5 are likely to be normal-mass WDs, suggesting Case-C MT as the possible formation channel. The hotter companion of BSS 2 is lying on the WD cooling curve of a high-mass WD, suggesting merger in a hierarchical triple system as the formation mechanism of this BSS. Moreover, the radii of the hotter companions of BSS 1 and BSS 7 derived from fitting the SED and fitting the LCs are in good agreement. In the case of BSS 1, the SED-based radius of the hotter companion is 0.04 $\pm$ 0.00 R_⊙, whereas the LC-based radius is 0.038 $\pm$ 0.011 R_⊙. Similarly, in the case of BSS 7, the SED-based radius is 0.03 $\pm$ 0.00 R_⊙ and that derived from LC fitting is 0.037 $\pm$ 0.013 R_⊙. The reason for such a large error in the parameters of the secondary companion is that the whole LC is dominated by the luminosity variation of the deformed primary. Only a small portion of the light variation arises due to eclipse. Since the parameters such as T_eff and radius are measured from the width and depth of the eclipses, the ability to obtain good constraints is not possible, leading to large errors.

It is evident from the right panel of Figure 11, that the log age of hot companions of BSS 1 and BSS 8 are $\sim$ 8.3, implying that these BSSs are formed via MT almost 0.2 Gyr ago. Moreover, the log age of BSS 3 and BSS 7 WDs are $\sim$7.6, which suggests that these objects were formed 30 Myr ago. On the other hand, the hot companions of BSS 2 and BSS 5 are lying on the WD cooling curves of log age $\sim$7.9, which suggests that these BSSs were formed $\sim$ 70 Myr ago.

This is the first-ever OC studied using AstroSat/ UVIT data that has hotter companions of BSSs with masses varying from 0.18 M_⊙ to 1.0 M_⊙. The most comprehensive study of a BSSs population in an OC is NGC 188, where 80$\%$ of the BSS are found to be SB1s with typical orbital periods, P $\sim$ 1000 days(Mathieu & Geller, 2009; Gosnell et al., 2015). Additionally, Geller & Mathieu (2011) found that the statistical mass distribution of the companions to these BSSs peaks around 0.5 M_⊙, strongly indicating the presence of WD secondary stars. Subsequent to that, Hubble Space Telescope UV photometry further confirmed that seven out of the 20 BSSs in NGC 188 possess hot WD companions with an age less than 400 Myr. This suggests recent MT events from RGB or AGB companions (Gosnell et al., 2014, 2015). Various studies based on UVIT/AstroSat mentioned in Section 1, including this work, also suggest MT as the predominant mechanism for the formation of BSSs in OCs. Even in the case of GCs, the absence of a correlation between cluster density and BSSs frequency implies that internal binary evolution, including MT, is the primary formation pathway, as opposed to dynamical collisions (Knigge et al., 2009). Furthermore, the presence of a significant population of BSs and other AFG-type post-MT binaries in the field suggests that MT is likely a prevalent formation mechanism across various environments (Carney et al., 2001; Murphy et al., 2018; Escorza et al., 2019; Panthi et al., 2023). Collectively, these populations provide valuable insights into the outcomes of post-MT events in solar-type binaries. However, detailed investigations of BSSs populations, particularly across diverse populations encompassing different cluster ages, densities, and metallicities, remain highly relevant.