BVRI polarization of stars in the direction of Stock 19

Abstract

We present BVRI polarimetric measurements of nine bright stars in a 15′-square region centered on Stock 19. Seven of them satisfy the Serkowski equation for star light polarization due to interstellar dust. This allowed us to estimate the degree of maximum polarization (p_max) and the wavelength of maximum polarization (λ_max). Along this line of sight, p_max ranges from 0.332% to 0.948%, and the average λ_max of 0.542 ± 0.018 μm yields a total-to-selective extinction ratio R_V = 3.04 ± 0.11. Four of the observed stars were previously listed as high-probability members of Stock 19. However, based on their Gaia distances, they are spread out along the line of sight and show a correlation between polarization and distance that is typical for the diffuse interstellar medium. The extinction, as obtained from dust maps, and the Planck 353 GHz polarization are low for this line of sight, additionally suggesting that these stars might not represent an actual cluster. The polarization parameters of three of the observed stars indicate the possible presence of an intrinsic polarization component, likely due to circumstellar material.

1 Introduction

In a search for dispersed clusters in the Milky Way, Stock (1954) listed 21 candidates, including Stock 19 (OCL 274, C0001+557). The study utilized the Warner and Swasey Observatory objective-prism plates, and the selection was based on spectral classes and apparent magnitudes. At present, Stock 19 is poorly investigated. It is located slightly below the Galactic plane, at ICRS (J2000.0) coordinates |$\alpha , \delta = {00^{\rm h}04^{\rm m}41{_{.}^{\rm s}}00}, +56^{\circ }{05^{\prime }00^{{\prime \prime}_{.}}0}$| and galactic coordinates l, b = 116|${_{.}^{\circ}} $|40280, −06|${_{.}^{\circ}} $|19457. This is about 6° below the classical Cassiopeia OB5 association, in a region free of any significant Hα emission.

Stock 19 was included in the catalog for optically visible open clusters by Dias et al. (2014a). The authors used the UCAC4 catalog and applied a global optimization statistical procedure to the observed proper motion distribution to obtain the mean proper motion of each of the included clusters, as well as membership probabilities of the stars in the region of each cluster. Within a 3′ radius centered at Stock 19, the number of members is estimated as 42, and the mean proper motion as μ_αcos δ = 1.43 ± 3.77 mas yr⁻¹ and μ_δ = −2.04 ± 1.25 mas yr⁻¹. Stock 19 was included in the catalog by Sampedro et al. (2017), also utilizing UCAC4 data. These authors considered three different criteria that used a Bayesian approach to obtain cluster membership: a parametric method, a completely non-parametric algorithm, and a combination of both. Sampedro et al. (2017) analyzed 31 stars in the field of Stock 19. Of these, only two stars are members according to all three membership criteria just mentioned; seven additional stars satisfy two of the criteria, and seven more satisfy only one membership criterion. However, Stock 19 was not included in the recent catalog by Dias et al. (2021) that utilizes Gaia DR2 proper motions and parallaxes.

In this paper we present multi-wavelength BVRI polarization measurements of nine bright stars in a 15′-square region in the direction of Stock 19. Four of these stars have a membership probability of 100%, according to Dias et al. (2014a). They also satisfy at least one membership criterion from the Sampedro et al. (2017) catalog. The rest of the stars are foreground, projected around the center of the observed field. Using Gaia-based distance estimates and polarimetry extracted from the literature for additional stars in the vicinity of the studied area, we examine the extinction and the magnetic field orientation in this region.

2 Polarization observations and analysis

The broadband BVRI polarization measurements were obtained on 2021 November 9, using the polarimeter on the 0.5 m f/13.5 Cassegrain telescope at the Virginia Military Institute Observatory. The acquisition and reduction of polarization data, along with the design and construction of the polarimeter, are described in Topasna, Topasna, and Popko (2013). This is an imaging polarimeter using an achromatic half-waveplate at positions 0°, 22|${_{.}^{\circ}} $|5, 45°, and 67|${_{.}^{\circ}} $|5 as the analyzer, and a Wollaston prism to separate the light of a star into its ordinary and extraordinary rays. The normalized Stokes parameters q and u are determined from successive measurements of stellar fluxes that are imaged on a charge-coupled device. The method used to calculate the Stokes and polarization parameters and their uncertainties was described most recently in Topasna, Gibson, and Kaltcheva (2022).

The unpolarized standard star HD 188512 from the list by Serkowski (1974) was observed to determine the instrumental polarization. The instrumental polarization percentages for each band are as follows: 0.053% in B, 0.045% in V, 0.069% in R, and 0.024% in I. The Stokes parameters of this star were vectorially subtracted from the target stars. The polarized standard star HD 187929, also from the list of Serkowski (1974), was used to determine the offset of the half-waveplate in order to calibrate the position angle. Its known polarization wavelength dependence was used to verify the data reduction procedure. The best fit of the Serkowski curve to the measurements of HD 187929 is shown in figure 1, along with the position angle for each of the broadband filters. The V-band polarization and equatorial position angle were found to be |$p_V = 1.94\% \pm 0.03$|% and θ_V = 93|${_{.}^{\circ}} $|8 ± 0|${_{.}^{\circ}} $|2, respectively. The maximum degree of polarization was determined to be |$p_{\rm max} = 1.92\%\pm 0.02\%$| at a wavelength of λ_max = 0.544 ± 0.035 μm. To compare, the polarization parameters for HD 187929 listed by Serkowski (1974) are |$\lambda _{\rm max} = 0.56 \, \mu \rm {m}$|⁠, |$p(\lambda _{\rm max}) = 1.8\%$|⁠, and θ(λ_max) = 93°. A later analysis by Hsu and Breger (1982) yielded similar results: |$\lambda _{\rm max} = 0.562\pm 0.014 \, \mu \rm {m}$| and |$p_{\rm max} = 1.73\%\pm 0.03\%$|⁠, with θ_V = 93|${_{.}^{\circ}} $|8 ± 0|${_{.}^{\circ}} $|3. We find good agreement with the published values.

The BVRI polarization measurements for the program stars are presented in table 1. Throughout the paper we use the Tycho catalog (TYC) identifications listed in the first column. We added, however, a running number (N) from one to nine in order to more easily specify the location of the stars on the plots, if needed. The table provides the degree of polarization p (in percent) and the equatorial position angle θ (in degrees), and their associated uncertainties. The last column lists the Galactic position angle that corresponds to the equatorial position angle in the V band. Stars 1, 4, 8, and 9 (running numbers indicated in bold) are located at the center of the observed field and are listed as probable members of Stock 19 by both Dias et al. (2014b) and Sampedro et al. (2017). The other five stars are farther from the Stock 19 center and appear foreground based on their Gaia distances.

Figure 2 presents the plots of the multi-wavelength polarization measurements. The empirical relationship from Serkowski, Mathewson, and Ford (1975), |$p(\lambda )/p_{\rm max}=\rm {exp}[-{\it K} \rm {ln}^2(\lambda _{\rm max}/\lambda )]$|⁠, was fitted to the BVRI data to determine the maximum degree of polarization (p_max) and the wavelength at maximum polarization (λ_max). The parameter K can be related to grain size, distribution, and growth in the interstellar medium (ISM), as noted by Wilking, Lebofsky, and Rieke (1982), Aannestad (1982), and Aannestad and Greenberg (1983). Wilking, Lebofsky, and Rieke (1982) suggested that K displayed a linear dependence on λ_max over the UBVRIJHK wavelength range. However, Clarke and Al-Roubaie (1983, 1984) and Bagnulo et al. (2017) later concluded that K should also depend on the signal-to-noise ratio, bandpass, and the presence of clouds along the line of sight. An analysis of the K parameter over the BVRI wavelength range for the polarimeter used here was performed by Topasna, Gibson, and Kaltcheva (2022), and it was found that no significance can be attached to the value of K using this type of design. We therefore consider K as a free-fit parameter, which results in better nonlinear fits to the Serkowski equation. These fits are included in figure 2. It should be noted that other expressions that approximate the wavelength dependence of polarization (e.g., Wolstencroft & Smith 1984; Efimov 2009) also incorporate a free-fit parameter similar to K.

Seven stars have reliable fits to the Serkowski equation. Their fitted parameters, p_max and λ_max, and the corresponding uncertainties are listed in table 2, along with the fitting parameter K and the r² goodness of fit. The maximum degree of polarization ranges from |$0.332\%$| to |$0.948\%$|⁠, with an average of |$0.622\% \pm 0.084\%$| (⁠|$\mathrm{median} = 0.623\%$|⁠). The wavelength of maximum polarization is between 0.491 μm and 0.610 μm, with an average value of 0.542 ± 0.018 μm (median = 0.545 μm). The average and median values of λ_max are in agreement with the estimated value of 0.545 μm that is expected for this region based on the empirical relationship λ_max = 0.545 + 0.03sin (l + 175°) (Whittet 1977). Using the average λ_max and the expression for the ratio of total-to-selective extinction for normal stars, (5.6 ± 0.3)λ_max (Whittet & van Breda 1978), yields R_V = 3.04 ± 0.11. This value is consistent with the nominal value of 3.1 that is typically assumed for the ISM (Whittet 2003). Table 2 also presents the membership probability as listed in the catalogs by Sampedro et al. (2017), denoted in the table as MP1, and Dias et al. (2014a), denoted in the table as MP2. MP1 shows the membership classifications based on the three procedures adopted by Sampedro et al. (2017), where 0 is used for non-members and 1 is used for members. MP2 expresses the membership probability in percent. The last column includes the Gaia-based distances used here.

The upper plot in figure 3 displays in equatorial coordinates the V-band polarization measurements for the nine stars listed in table 1. The geometric distances (in parsecs) from Bailer-Jones et al. (2021) are shown next to the stars. Currently, only TYC 3656-465-1 does not have a Gaia measurement for parallax or distance. The high-probability members of Stock 19 are labeled with the numbers we assigned here.

The average equatorial position angle for these nine stars is 49° ± 18°—the error is the standard deviation (s.d.)— with a median value of 44°. The corresponding average and median Galactic position angles are 60° and 55°, respectively. These values in general match the position angle presented by Makarov and Andreassian (1990). However, the different scales used do not allow a precise comparison.

Very little star light polarization data exists in the literature for this region. Between 108° < l < 120° and −7|${_{.}^{\circ}} $|5 < b < −4|${_{.}^{\circ}} $|0, data for only 25 stars are included in the Heiles (2000) catalog, and more recent polarization studies of this field are not available. These 25 stars are plotted (red filled symbols) in galactic coordinates in the second panel of figure 3, with their Gaia distances indicated. For the majority the polarization is less than 2%, and the average of their galactic position angles is 72° (s.d. 21°, median 78°). The stars observed here are also included, represented by their polarization vectors (black color). Within the errors, there is no statistically significant difference between the average polarization parameters of the stars that we observed and the stars located up to several degrees away from Stock 19. The third panel of figure 3 presents an overview of the field in galactic coordinates utilizing the Aladin interactive sky map (Boch & Fernique 2014). A Planck 353 GHz image with overlaid contours is used as a background. Stock 19 is located in a region of low intensity, just to the west of a tiny feature of slightly enhanced dust emission.

For the 15′-square region observed here, we constructed histograms based on the Planck 353 GHz dust emission data using cutouts from the IRSA website.¹ These histograms are shown in figure 4. The upper panel is the submillimeter polarization yielding a mean value of |$5.9\% \pm 0.25$|% (s.d. ±3%) and a median value of 5.6%. This is a polarized emission integrated along the line of sight, and therefore sampling a larger column density of dust in comparison to the optical polarization that we measured. This presumably accounts for the overall larger value of the dust emission polarization compared to the stellar polarization, which is caused by selective extinction due to dust grains foreground to the stars. The second panel in figure 4 presents the Galactic position angle as measured eastward from the North Galactic Pole. We expect that the optical star light polarization is perpendicular to the polarization of the emission by dust (Planck Collaboration 2015). Based on the median value of the galactic position angle of the stars that we observed (55° ± 18°), as well the stars in the vicinity of the studied area that we extracted from the Heiles (2000) catalog (78° ± 21°), the expected galactic polarization position angle of emission by dust should be in the 145°–168° range. Indeed, this is where the peak of the Planck position angle histogram is located.

Figure 5 provides several comparisons of the color excesses of the stars considered here obtained using different methods. For the nine stars we observed, very limited UBV photometry or Gaia-based color excess exists. For the majority of the stars extracted from Heiles (2000), both UBV photometry (General Catalog of Photometric Data: Mermilliod et al. 1997) and Gaia color excesses E(BP − RP) are available. Their spectral classification and the (U − B) vs. (B − V) diagram (not shown here) both indicate that these stars are in the B-type spectral range. We used the Pecaut and Mamajek (2013) calibration for luminosity class V, supplemented by the Deutschman, Davis, and Schild (1976) calibration to estimate E(B − V). The upper plot of figure 5 presents comparisons of E(BP − RP) from Gaia DR2 and Gaia DR3 with the UBV-based E(B − V) and the E(B − V) values collated in the Heiles (2000) catalog (which provides the largest color excess dataset for this sample). All three datasets show a reasonable agreement with the E(B − V) data in Heiles (2000). The lower panel in figure 5 is a plot of polarization vs. extinction using the four sets of extinction data just mentioned. The majority of the stars are confined below the Serkowski limit on this diagram, but no correlation is present for any of the datasets.

The top panel of figure 6 presents the V-band polarization plotted vs. the Gaia EDR3 distances for all the stars considered here. The distribution of the color excess E(g − r) with distance (not to scale), as obtained from the latest interactive three-dimensional dust map of the Milky Way (Green et al. 2019) is also shown on this panel. The E(g − r) data suggest that the interstellar extinction increases sharply at 250 pc and stays constant after 1500 pc. The fractional polarization and the color excess (lower panel of figure 6) also increase similarly at around 250 pc. For the interactive dust map, the relation E(B − V) = 0.884E(g − r)_P1 between the color excesses E(B − V) and E(g − r) is provided, which yields E(B − V) = 0.24 mag for the plateau of the E(g − r) line.

Interestingly, the four stars toward Stock 19 that have high membership probabilities based on UCAC4 data (Dias et al. 2014a; Sampedro et al. 2017) show a tight correlation of their V-band polarization with distance. They are labeled in the top panel of figure 6 with the numbers assigned here (1, 4, 8, and 9). Their V-band polarization–distance relation indicates a slope of |$0.76\%\pm 0.043$|% fractional polarization per kiloparsec (intercept −0.17 ± 0.052). This slope is consistent with the one estimated based on the Heiles (2000) catalog for distances of less than 2 kpc, showing an increase of about 1% per kiloparsec (see Fosalba et al. 2002). The B, R, and I polarization data for these four stars also indicate a dependence of polarization on distance, and the slopes are decreasing with increasing wavelength between 1.1% per kiloparsec in B and 0.6% per kiloparsec in R and I. Since this line of sight seems free of clumpy interstellar matter, expanding the multi-wave polarimetric sample to fainter stars could be used to investigate the polarization–distance relation at low galactic latitudes, probing in this way the diffuse component of the ISM.

3 Notes on individual stars

In the literature, no peculiarities have been noted for any of the stars observed here. Those with available spectral classification (Nos. 3, 4, and 8) are included in the catalog of stellar diameters and fluxes for mid-infrared interferometry by Cruzalèbes et al. (2019), and for the rest no specific references discussing their properties are available. The polarization data of two of the target stars, Nos. 1 (TYC 3656-19-1) and 7 (TYC 3656-465-1), do not satisfy the characteristic Serkowski curve of polarization by selective extinction due to dust grains in the ISM. For both stars the polarization is higher at shorter wavelengths and decreases towards longer wavelengths. TYC 3656-19-1 has the highest polarization of the nine stars observed here, but it is also located at the largest distance. In their study of the polarization of Be, HAeBe, or T Tauri stars, Bastien (2015) noted that there is no typical wavelength dependence of the fractional polarization for such objects: some display a rise at longer wavelengths, others at shorter wavelengths, and some have a wavelength dependence that is essentially flat. The polarization behavior of TYC 3656-19-1 and TYC 3656-465-1 is also similar to that of some of the carbon stars studied by Raveendran (1991), López and Hiriart (2011), and Goswami and Karinkuzhi (2013). This polarimetric behavior may be indicative of the presence of an intrinsic polarization component. Additional observations are needed to better evaluate possible peculiarities for these two stars.

While the absence of a Serkowski curve may be an indicator of an intrinsic polarization component, this is not always the case. Dispersion in the position angles could also imply peculiarities. For example, the carbon star HE 0310+0059, observed by Goswami and Karinkuzhi (2013), has a Serkowski-type curve, but it also has dispersion in its position angle that ranges from 130|${_{.}^{\circ}} $|1 in the B band to 147|${_{.}^{\circ}} $|4 in the I band. López and Hiriart (2011) observed large night-to-night variations of the position angle with wavelength in carbon stars along the Galactic equator. While some of the stars that we observed show a particular position angle away from a general equilibrium, the position angles for others could indicate a systematic rotation. Rotation in position angle could also be due to mixing of the star’s intrinsic polarization with polarization that is caused by clouds of different grain sizes and alignments along the line, and it is generally expected at distances greater than 600 pc, as suggested by Clarke (2010). Both TYC 3656-19-1 (1950 pc) and TYC 3656-465-1 (no distance data) display a decrease of the position angle in the V band followed by a systematic increase in the R and I bands.

A significant change in the position angle may further indicate the onset of a polarization reversal. For example, Bastien (1996) found that for some young stellar objects and emission-line stars the position angle changes by 90° when going from the visible to the near-infrared, with the transition happening in the near-infrared. The reversal has been replicated in models where polarization is caused by scattering from circumstellar material (Daniel 1980a, 1980b; Bastien & Menard 1988). The polarization data of TYC 3656-77-1 show similar behavior. Its position angle ranges from 90° ± 2° in the B band to 135° ± 4° in the I band, reaching a low of 80|${_{.}^{\circ}} $|0 ± 1|${_{.}^{\circ}} $|5 in the V band. It is possible that TYC 3656-77-1 has a circumstellar envelope that affects the position angle, but the intrinsic component does not overwhelm polarization by selective extinction in the ISM (as indicated by its excellent Serkowski fit). The Gaia E(BP − RP) color excess for this star is 0.35 mag, indicating that this is one of the most reddened stars in our sample. The existing B and V magnitudes combined with this reddening yield an estimate of (B − V)₀ that is consistent with the available spectral type A2. In the catalog by Cruzalèbes et al. (2019), indications are included of an infrared excess for this star as well. Additional observations are needed to better evaluate its nature.

4 Concluding remarks

We obtained multi-wavelength polarization measurements for nine stars located in a 15′-square region centered on Stock 19. This region is poorly investigated and UBV photometry is not available even for the brightest stars. With two exceptions (TYC 3656-19-1 and TYC 3656-465-1), the observed stars display a wavelength dependence in their fractional polarization that is consistent with the Serkowski, Mathewson, and Ford (1975) equation. The calculated average λ_max yields an average of R_V = 3.04 ± 0.11 along this line of sight, a value consistent with that typically assumed for the ISM (Whittet 2003). Four of the observed stars are listed in the literature as high-probability members of Stock 19, and the rest are foreground. These high-probability members display a tight dependence of their V-band polarization on distance. Similar dependence is present in the rest of the filters as well, and is consistent with the expected behavior of polarization in terms of distance for the diffuse ISM (Fosalba et al. 2002). This finding, and the significant spread in distance for these four members of Stock 19, warrants further investigation of whether these stars represent an actual cluster.

Both the Planck 353 GHz map and the Milky Way dust map by Green et al. (2019) indicate that the extinction is low along the Stock 19 line of sight. Additional information based on stars in a several-degree vicinity around Stock 19 implies that E(B − V) does not exceed 0.3 mag up to 2 kpc. However, the increase of the extinction is steep and takes place at 200–300 pc, delineating the extent of the ISM that is causing the observed polarization. The fact that some of the stars discussed here that are closer than 500e pc have a relatively high polarization suggests a non-uniform distribution of the ISM clouds around 200–300 pc. Based on the available data, we did not find a statistically significant correlation between polarization and extinction for a several-degree vicinity around Stock 19. The available stars are, however, too few and spread out over a large area.

The polarization behavior of TYC 3656-19-1, TYC 3656-465-1, and TYC 3656-77-1 indicates peculiarities. Since the angular separation between the studied stars is very small, it is more likely that the peculiar wavelength dependence of the fractional polarization and the position angle is due to scattering from circumstellar gas and dust (Zellner & Serkowski 1972; Bastien & Menard 1988; Clarke 2010) rather than to foreground clouds of ISM.

Acknowledgements

This work is supported by a Jackson–Hope Foundation Grant-in-aid of research at the Virginia Military Institute. This research has made use of NASA’s Astrophysics Data System² and the SIMBAD database, operated at CDS, Strasbourg, France.³ This work has made use of data from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is 〈https://www.cosmos.esa.int/gaia〉. The Gaia archive website is 〈https://archives.esac.esa.int/gaia〉. This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. This research has made use of the “Aladin sky atlas” developed at CDS, Strasbourg Observatory, France. We are grateful to the referee for the useful comments that improved this paper.

Footnotes

References