Zwicky Transient Facility and Globular Clusters: Calibration of the gr-band Absolute Magnitudes for the Yellow Post-asymptotic-giant-branch Stars

Post-asymptotic-giant-branch (hereafter PAGB) stars are the low- to intermediate-mass stars at their final and short-lived stage of stellar evolution before entering the planetary nebulae phase. PAGB stars evolve with nearly constant luminosity but with increasing effective temperature on the Hertzsprung–Russell (H-R) diagram. During such evolution, these PAGB stars become Type II Cepheids, or more specifically the RV Tauri (RV Tau) stars (for example, see Jura 1986; Alcock et al. 1998), ⁵ when they cross the instability strip on the H-R diagram.

The idea of using PAGB stars as Population II distance indicators has been proposed in the past (Bond 1997). This is because PAGB stars have the largest luminosity for the low- to intermediate-mass stars throughout their lifetime, with M_bol ∼ −3.38 mag based on ten yellow, or intermediate-temperature, PAGB stars located in seven globular clusters (Ciardullo et al. 2022). Since half of them are Type II Cepheids, Ciardullo et al. (2022) calibrated the Johnson V-band absolute magnitude of yellow PAGB stars using the nonvariable stars with colors in the range of 0.0 ≲ (B − V) ≲ 0.5 mag, i.e., blueward of the instability strip, and obtained M_V =−3.37 ± 0.05 mag. The reasons, or advantages, for choosing the blue colors have been extensively discussed in Ciardullo et al. (2022). Obviously, selecting the nonvarying yellow PAGB stars (blueward of instability strip) has an advantage on reducing the observing time, because in general RV Tau stars have pulsation periods longer than ∼20 days. As pulsating stars, RV Tau stars also obey a period–luminosity color relation, implying a color–magnitude relation (at fixed period) on the color–magnitude diagram (CMD).

Given that the ugrizy filters, or a subset of them, are increasingly popular among various synoptic sky surveys, with a representative example of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST; Ivezić et al. 2019), it is desirable to calibrate the absolute magnitudes of the yellow PAGB stars in these filters in addition to the V band. Similar to the work of Ciardullo et al. (2022) in the V band, our goal is to calibrate the gr-band absolute magnitudes for the yellow PAGB stars located in the globular clusters by using the photometric data obtained from the Zwicky Transient Facility (ZTF; Bellm et al. 2019; Graham et al. 2019; Masci et al. 2019; Dekany et al. 2020). Out of the ten yellow PAGB stars listed in Ciardullo et al. (2022), four of them are located in the southern globular clusters (ω Centauri and NGC 5986), which are outside the footprint of ZTF. Hence, our calibration was done on the remaining nonvariable yellow PAGB stars and the Type II Cepheids.

ZTF is a 47 squared-degree wide-field synoptic northern sky survey utilizing the Palomar 48 inch Samuel Oschin Telescope located in southern California, USA. The majority of the ZTF observations were conducted with the customized g and r filters, with additional i-band observations from the partner surveys. ⁶ All of the ZTF images were processed through a dedicated reduction pipeline (Masci et al. 2019), and the ZTF photometry was calibrated to the Pan-STARRS1 (Chambers et al. 2016; Magnier et al. 2020) AB magnitude system.

As in Ngeow et al. (2022), ZTF gr-band light curves for the two nonvariable yellow PAGB stars, M19 ZNG4 and M79 PAGB, were extracted from the ZTF PSF (point-spread function) catalogs. No ZTF i-band data were available for these two targets in the ZTF Public Data Release 10 and the partner surveys data until 2022 March 31. After excluding data points with non-zero flags and infobits, ⁷ ZTF light curves for these two targets are presented in Figure 1. As in Bond et al. (2016), we do not detect obvious variability for M79 PAGB at ∼0.03 mag level (the dispersion of the light curves). In case of M19 ZNG4, Bond et al. (2021) suspected this star does not exhibit variability based on two observations separated by one night (plus earlier low-quality data). The ZTF light curves confirmed this target does not exhibit obvious variability at ∼0.05 mag level. Hence, we obtained straight weighted mean magnitudes in the gr band for these two yellow PAGB stars, as reported in Table 1. ⁸

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Among the four Type II Cepheids listed in Ciardullo et al. (2022) that are observable with ZTF, three of them (V11 in M2, V42, and V84 in M5) have gr-band mean magnitudes derived in Ngeow et al. (2022), and they are given in Table 1. The Type II Cepheid V17 in M28 was excluded in Ngeow et al. (2022) due to blending.

Apparent mean magnitudes of the five targets listed in Table 1 were converted to absolute magnitudes by adopting the distances to their host globular clusters from Baumgardt & Vasiliev (2021), with extinction corrections based on the the Bayerstar2019 3D reddening map (Green et al. 2019). For more details on the extinction corrections, see Ngeow et al. (2022). Errors on the absolute magnitudes were based on the propagated errors on the apparent mean magnitudes (ranging from ∼0.002 mag to ∼0.008 mag), the errors on the distance, and the errors returned from the Bayerstar2019 3D reddening map. The final gr-band absolute magnitudes are listed in the last two columns of Table 1.

The absolute magnitudes for M19 ZNG4 seem to be brighter than other targets listed in Table 1, which hints at an issue of blending. Indeed, if we transformed the gr-band apparent magnitudes to the V band via the transformation provided in Tonry et al. (2012), we obtained V = 12.333 ± 0.014 mag. This V-band magnitude is brighter than the value of 12.512 ± 0.006 mag given in Bond et al. (2021), suggesting additional fluxes were included presumably due to blending. In contrast, the transformed V-band apparent magnitude for M79 PAGB is 12.197 ± 0.012 mag, in good agreement with the value found in (Bond et al. 2016, 12.203 ± 0.008 mag). Hence, we discarded M19 ZNG4 for the calibration of the gr-band absolute magnitudes for the yellow PAGB stars.

Based on M79 PAGB and the three Type II Cepheids, the weighted means of the gr-band absolute magnitudes are

$$\begin{eqnarray}\begin{array}{rcl}{M}_{g} & = & -3.19\pm 0.14\,\mathrm{mag},\\ {M}_{r} & = & -3.44\pm 0.04\,\mathrm{mag}.\end{array}\end{eqnarray} \tag{ 1 }$$

Errors on these absolute magnitudes were calculated based on small number statistics (Dean & Dixon 1951; Keeping 1962, p. 202), as there are only four stars in the sample. These mean absolute magnitudes are marked as solid lines in Figure 2. The g-band absolute magnitude exhibits a larger error due to its larger color-dependency as shown in the left panel of Figure 2. We have overlaid a PAGB evolutionary track, selected from models constructed in Miller Bertolami (2016) and Moehler et al. (2019), in Figure 2. The theoretical luminosities and effective temperatures along this track have been converted to the gr-band absolute magnitudes using an online tool PARSEC Bolometric Correction (Chen et al. 2019). ⁹ The PAGB evolution track shows a larger gradient on the g-band CMD than the r-band CMD, explaining the larger error on Equation (1). Therefore, we fit a linear regression to these four stars and yields: ¹⁰

$$\begin{eqnarray}\begin{array}{rcl}{M}_{g} & = & 1.30[\pm 0.15](g-r)-3.53[\pm 0.04],\\ {M}_{r} & = & 0.30[\pm 0.15](g-r)-3.53[\pm 0.04].\end{array}\end{eqnarray} \tag{ 2 }$$

Both linear regressions give the same standard deviation of 0.03 mag. As demonstrated in Figure 2, in the g band these four stars are better described with a linear regression than adopting a mean value. In contrast, the PAGB evolutionary track is almost a constant in the r band, explaining the much smaller error in the r-band mean absolute magnitude, i.e., Equation (1), than the g band.

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We tested our results using the four yellow PAGB stars located in the southern globular clusters ω Centauri and NGC 5986. The BV-band photometry of these four stars, adopted from Braga et al. (2020; for V1 in ω Centauri) and Davis et al. (2022; for HD 116745 in ω Centauri and the two PAGB stars in NGC 5986), were transformed to gr band using the relations given in Tonry et al. (2012). Since the Bayerstar2019 3D reddening map did not cover the sky south of −30° decl., we queried the Schlegel et al. (1998) extinction map to correct the extinctions for these four southern yellow PAGB stars (see Ngeow et al. 2022 on the procedure of extinction corrections). Figure 3 shows the positions of these four southern yellow PAGB stars on the extinction-corrected CMD as open circles. Except for HD 116745 in ω Centauri, other three southern yellow PAGB stars are closer to the linear regressions given in Equation (2) extrapolated to bluer colors, supporting the use of linear regressions for calibrating the absolute magnitudes of yellow PAGB stars, especially in the g band.

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A Type II Cepheid, V6 in M56, appears to be located near the extrapolated linear regressions given in Equation (2) to the redder colors. This Type II Cepheid is indeed a PAGB star (Davis et al. 2022) with a redder color of (g − r) = 0.710 mag. Its M_V = −2.95 mag is marginally fainter than the M_V = −3.0 mag cut when selecting the PAGB stars as calibrators for the distance indicators (Ciardullo et al. 2022). This star has a larger deviation from the mean gr-band absolute magnitudes (the solid lines in Figure 2), and would be treated as outlier. Nevertheless, this Type II Cepheid is located redward of the instability strip, hence it is not preferable to be included as a calibrator (Ciardullo et al. 2022).

In this work, we have derived the gr-band absolute magnitudes for yellow PAGB stars that can be used as Population II distance indicators. Both the mean absolute magnitudes and color-dependent linear regressions were derived based on four yellow PAGB stars located in the globular clusters, by using the homogeneous ZTF data and adopting the same sources for the distance to the globular clusters and reddening corrections. In this way, we minimize the possible systematic errors arising from inhomogeneous data sets.

Since there are only four stars (one nonvarying star and three Type II Cepheids) in our sample as calibrators, we were forced to include the variable Type II Cepheids in the calibration processes (in contrast to Ciardullo et al. 2022). Nevertheless, Figure 2 demonstrates that the Type II Cepheids can be included together with the nonvarying yellow PAGB star to increase the sample size. Certainly, searching for the nonvarying yellow PAGB stars in distant galaxies only requires single-shot observations, which is advantageous for expensive or competitive observations such as using the Hubble Space Telescope (Ciardullo et al. 2022). On the other hand, long-term synoptic sky surveys such as LSST will naturally provide time-series data to search for the long period Type II Cepheids, as long as these Type II Cepheids or RV Tau stars could be identified as the low-surface-gravity yellow PAGB stars. ¹¹ This would increase the number of suitable yellow PAGB stars to serve as distance indicators, hence reducing the statistical errors when deriving the distances to their host galaxies.

We thank M. M. Miller Bertolami for sharing the theoretical evolutionary tracks, and the useful comments from an anonymous referee that improved the manuscript. We are thankful for funding from the Ministry of Science and Technology (Taiwan) under the contracts 107-2119-M-008-014-MY2, 107-2119-M-008-012, 108-2628-M-007-005-RSP, and 109-2112-M-008-014-MY3.

Based on observations obtained with the Samuel Oschin Telescope 48 inch Telescope at the Palomar Observatory as part of the Zwicky Transient Facility project. Z.T.F. is supported by the National Science Foundation under grant Nos. AST-1440341 and AST-2034437 and a collaboration including current partners Caltech, IPAC, the Weizmann Institute of Science, the Oskar Klein Center at Stockholm University, the University of Maryland, Deutsches Elektronen-Synchrotron and Humboldt University, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee, Trinity College Dublin, Lawrence Livermore National Laboratories, IN2P3, University of Warwick, Ruhr University Bochum, Northwestern University and former partners the University of Washington, Los Alamos National Laboratories, and Lawrence Berkeley National Laboratories. Operations are conducted by COO, IPAC, and UW.

This research has made use of the SIMBAD database and the VizieR catalog access tool, operated at CDS, Strasbourg, France. This research made use of Astropy, ¹² a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013, 2018).

Facility: PO:1.2 m. Software: astropy (Astropy Collaboration et al. 2013, 2018), dustmaps (Green 2018), Matplotlib (Hunter 2007), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020).