1. MOTIVATION

The study of open clusters provides many possibilities for the investigation of different astronomical topics. For example, establishing membership of the stars to the cluster throws light on the initial mass function; determining their ages gives clues on stellar evolution; and fixing their distances and chemical compositions helps to accurately establish the chemical enrichment of the galaxy as a function of the galactocentric distance. This line of research began long ago with the work of ^{Villa Vargas (1999)} and the purpose of the present study is to complement the previous one with higher precision data, since Strömgren photometry provides both an accurate determination of the distance to the cluster and, through the observation of stars of spectral type F, of their metallicity.

The open cluster NGC 1528 has been a subject of much research since its discovery in 1907 by Ho-letschek.

According to the compilation of data of open clusters in ^{Paunzen and Mermilliod (2007)}, WEBDA, NGC 1528 has a distance [pc] of 776; a reddening [mag] of 0.258; a distance modulus [mag] of 10.25; a log age of 8.568 and no reported value for the metallicity.

In this paper, the distances to each one of the stars are determined using uvby − β photoelectric photometry with an already tested method, (See for example ^{Peña & Sareyan, 2006}).

2. OBSERVATIONS

The observations were carried out at the Observatorio Astronómico Nacional de San Pedro Mártir, México. The 0.84 m telescope, to which a spectrophotometer was attached, was used. The observing season lasted for six nights in December, 2017. NGC 1528 was observed only on one night, that of December 8, 2017. The cluster was also observed in December, 2016 by one of us (DSP). The ID charts used were those of WEBDA, selected for a limiting magnitude around 12 mag, which is the reasonably reachable limit given by the telescope-spectrophotometer system used during both seasons. A sample of sixty-five stars is presented.

3. COMPARISON WITH OTHER PHOTOMETRIES

Since the cluster was observed in 2016 and 2017, the first and obvious step was to compare both seasons. This was done and the results were awkward. Hence, our first problem was to elucidate which season was correct, if any.

Since no uvby − β data had been obtained previously for this cluster, a comparison of our values was done with the available U BV photometry reported in WEBDA. However, the intersection of both sets uvby − β vs. U BV was very limited (eighteen entries) despite the fact that our sample was significant (sixty-five observed stars). In view of this we com-pared our photometry from 2016 and 2017 with the much larger sample of WEBDA CCD data. The intersection of both sets was forty-one entries.

The comparison with the 2016 season showed that the data of this season were inaccurate due to bad weather conditions, whereas the 2017 season gave more accurate results. A linear fit between both sets, 2017 uvby − β vs. U BV (CCD) yielded the equation V_{W EBDA} = 0.056 + 0.9994 V_PP with a correlation coefficient of 0.9974 and a standard deviation of 0.050. The color relationship yielded (B−V) 0.027 + 0.6176 (b−y) with a correlation coefficient R of 0.9954 and a standard deviation of 0.024.

4. METHODOLOGY

Once we were sure of the quality of our uvby − β data set, further analysis was necessary in order to determine the physical characteristics of the stars in the cluster.

The main problem was, of course, to determine which stars belong to the cluster. To do this, the distance to each star had to be fixed. To evaluate the reddening we first established to which spectral class the stars belonged: early (B and early A) or late (late A and F stars) types; the later class stars (G or later) were not considered in the analysis since there is no reddening calibration for these stars. We determined each star’s spectral type through its location in the [m₁] − [c₁] diagram (Figure 1).

Fig. 1 Position of the stars in the [m ₁] − [c ₁] diagram of Alpha Per (^{Peña & Sareyan, 2006})) for NGC 1528. Small crosses are points for Alpha Per; black squares are points for NGC 1528. The color figure can be viewed online. 

The application of the calibrations for each spectral type (^{Balona & Shobbrook 1984}; ^{Shobbrook 1984}) for O and early A type and ^{Nissen (1988)} for late A and F stars, respectively allowed us to deter-mine their reddening, and hence their unreddened color indexes. The procedure has been extensively described in ^{Peña & Martínez (2014)}.

5. RESULTS

Figure 1 shows the position in the [m ₁] − [c ₁] diagram for stars in the direction of NGC 1528, along with that of the stars with well-determined spectral types in the open cluster Alpha Per (^{Peña & Sareyan 2006}). In Table 3 the photometrically determined spectral class is shown. Only a few stars have photometrically determined spectral types in WEBDA and the agreement between both classifications is ad-equate.

The physical parameters can be determined using the uvby − β photometry data and adequate empirical calibrations. These calibrations were proposed by ^{Nissen (1988)} for A and F type stars and ^{Balona Shobbrook (1984)} and ^{Shobbrook (1984)} for the O and early A types.

he application of these numerical packages gave the results shown in Table 4, where the ID, reddening, unreddened indexes, absolute magnitude, DM and distance (in parsecs), are listed. The last two columns present the membership probabilities described below.

To establish membership of the stars to the cluster the distance modulus or distance histograms (in pc) are built. The goodness of the method has been tested in the past by comparing results to the proper motion studies for a well-studied cluster like α Per (^{Peña & Sareyan 2006}).

When the histogram of distance modulii for NGC 1528 was built (Figure 2), the distances of the stars showed a clear accumulation at a distance mod-ulus of 9.8 ± 0.6, a peak determined by a Gaussian fit to the distribution.

Fig. 2 Histogram of the DM of the stars in the direction of NGC 1528. The peak is at 9.8 ± 0.6. 

To determine membership to the cluster we assumed that to be a member, the distance to the star should be within one sigma of the mean average distance. The mean distance modulus value of these stars is 9.87 ± 0.35. For the accumulation of stars, membership is indicated by an M in the twelfth column of Table 4. There are some stars close to these limits and they are indicated by M. Those beyond the membership limits are denoted by N, non-members.

We compared our membership assignation with that reported in WEBDA for NGC1528. The membership probabilities reported are listed in the last column of Table 4. It is remarkable that out of the thirty-four stars we found to be members, twenty-seven have a high membership probability and only nine have low membership probabilities in WEBDA. However, some stars that we classified as non-members have high membership probabilities in WEBDA.

The effective temperature of the hottest stars was fixed by plotting the location of all stars on the theoretical grids of ^{Lester, Gray & Kurucz} (hereinafter LGK86), after calculating the unreddened colors (Figure 3) for the correct chemical composition of the model considered. The metallicity of NGC 1528 was not reported by WEBDA but it is reported by Linga (1987) as −0.10. We found two F type stars to be cluster members for which metallicity can be evaluated. The metallicities of these stars, W206 and W1613 are −0.25 and −0.37, respectively. However, the membership probability assigned in WEBDA is, in both cases, 0.0. In view of this, we will consider models of solar metallicity.

Fig. 3 Location of the unreddened points (filled squares) in the LGK86 grids. Values of the effective temperature and surface gravity are indicated. 

We used the (b − y) vs. Hβ diagram of LGK86 which allows the determination of the temperatures of the hottest stars with an accuracy of a few hundredths of degrees. The temperature for the hottest star, W211, is around 16200 K. W211 has a membership probability of 0.70 according to WEBDA and is a member of the cluster according to our results. The second hottest star is W209 with a T e of 15500 K; according to WEBDA it is a non-member star although it belongs to the cluster in our findings. However, both W211 and W209 have log g values of 3.0 and 3.5 respectively. Furthermore, W197 has log g of 4 and an effective temperature of 13500 K (log T e of 4.13). Once the membership and effective temperature of the hottest star are established, an age for NGC 1528 can be determined through the calibrations of ^{Meynet, Mermilliod & Maeder (1993)} from the relation log(age) = −3.611 × (log T e) + 22.956 valid in the range log T e within the limits [3.98, 4.25]. The results is log(age) = 8.04. All these quantities are summarized in Table 5.

6. DISCUSSION

With the procedures we have described we obtained distances for stars of spectral types B, A and F. Membership was assigned in the histogram for those stars within one sigma of the distance mean value. Out of our sample of sixty-five stars, thirty-four were considered to be members in this fashion, six to be marginally members and nine non-members. Eleven were late type stars and no distance was determined for them. A mean reddening value was calculated for the member stars. The age was fixed from the temperature of the hottest star which, by the way, is considered to be a member of the cluster both in the literature and in our findings. This age is in agreement with its spectral type, B5V.

7. CONCLUSIONS

The physical characteristics we determined in the present study coarsely agree with the previously determined ones. As was mentioned at the beginning, the distance was fixed at 776 pc. Our value is 954 ± 154 pc. Of the 65 stars studied 14 are early type stars, 16 A type stars, and only two are of spectral type F with a mean [Fe/H] of −0.310 ± 0.079; the reddening E(B − V ) was 0.258 mag, whereas our value for E(b − y) of 0.196 ± 0.054 gives an E(B − V ) of 0.251 ± 0.069 if the well-known relation of E(b − y) = 0.78E(B − V ) is applied. The reported age is log(age) = 8.568, whereas our de-termined value is 8.04. However, the values from the uvby − β photoelectric photometry were deter-mined on a star-by-star basis whereas the literature values were determined by the main sequence fitting method, which does not consider the membership probability of each star, but rather the overall behavior of the all stars in a coarse statistical manner.