HD 166620: Portrait of a Star Entering a Grand Magnetic Minimum

We primarily use the time series given in B22 that initially identified HD 166620 as a Maunder minimum candidate. These data span a 50+ yr baseline. The majority of the data come from the Mount Wilson (MW) program, courtesy of the "HK_Project_v1995_NSO" data set (Radick & Pevtsov 2018), which obtained 107 observations of this star using the "HKP-1" photometer from 1966 to 1977, and continued to obtain 1547 observations with the upgraded "HKP-2" photometer from 1977 to 1995. The California Planet Search later picked up this target, obtaining 9 observations in June–September of 1997 with Keck HIRES ("HIRES-1"), and again after the 2004 detector upgrade ("HIRES-2"), obtaining 103 spectra between 2004 and 2020 March. S_HK values were measured following Isaacson & Fischer (2010). There is no guarantee that the S_HK values across all four instruments (MW HKP-1, MW HKP-2, HIRES-1, and HIRES-2) have absolute agreement. B22 investigated the need for offsets between the various instruments and found that the Mount Wilson data (HKP-1 and HKP-2) appeared to agree without needing any offset. For the Keck HIRES data, the S_HK values from HIRES-1 in 1997 do appear to be higher than the later HIRES-2 S_HK values. However, the HIRES-1 data fail to establish a long enough time baseline for any conclusive evidence of an offset. Further inspection by eye hints that the higher HIRES-1 S_HK values could be consistent with both the Mount Wilson and HIRES-2 values, occurring during a transition from higher cycling activity in Mount Wilson to lower flat activity in Keck HIRES. Thus, no offsets were applied to the reported S_HK values in any of the four instruments in B22. This time series can be seen in the top panel of Figure 1.

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Upon investigating this star further, we were made aware of additional observations from the Mount Wilson program that took place between 1995 and 2002. A nightly binned version of the full Mount Wilson data (from 1966 to 2002) were published in a figure in Oláh et al. (2016) and we have acquired this data courtesy of K. Oláh and W. Soon. After binning the B22 data, we compared them to the the Oláh et al. (2016) data during the overlapping time (1966–1995) and in general found very good agreement in both the timestamp and S_HK. We do note, however, that the timestamps do not agree to within 0.5 days. The cause for this discrepancy is not fully understood, as both data sets contain observations at times of day when the star would not have been visible from Mount Wilson. We notice that applying a 0.5 day offset to the B22 data prior to JD 2,444,000.5 and a −0.5 day offset to the Oláh et al. (2016) data after this date removes a first-order discrepancy. We attribute this discrepancy to previous MJD/JD conversion errors. Plotting the time of day versus the time of year for the observations in Oláh et al. (2016) after JD 2444000.5 reveals an additional perplexing structure that repeats on a 4 yr timescale and includes times when the star would not have been observable. We therefore choose to retain the B22 data for observations prior to 1995 June 4 (the final MW observation in that data set). We use the MW data in Oláh et al. (2016) for observations after that date. Since our results are insensitive to these small timestamp differences, we do not apply any adjustments to the timestamps in either data set and report the values as we inherited them to avoid creating yet another time series that may add future confusion. The new MW data therefore span from 1995 June to 2002 June and contain 158 observations. The additional MW data from Oláh et al. (2016) can be seen in the second panel of Figure 1. All activity data are presented in Table 2.

We acquired 1278 photometric observations of HD 166620 covering 17 observing seasons from 1993 to 2020 (we did not observe the star during the 2005 through 2015 observing seasons). The observations were all obtained with the T4 0.75 m automatic photoelectric telescope (APT) at Fairborn Observatory in southern Arizona. The T4 APT is equipped with a single channel photometer that uses an EMI 9124QB bi-alkali photomultiplier tube to measure stellar brightness successively in the Strömgren b and y passbands.

The observations of HD 166620 (star d) were made differentially with respect to three nearby comparison stars (a, b, and c). Intercomparison of the six combinations of differential magnitudes (d–a, d–b, d–c, c–a, c–b, and b–a) reveals that only comparison star b (HD 166640) appears to be constant to the limit of our precision. Therefore, we present our results as differential magnitudes in the sense of star d minus star b, which we designate as d–b.

To improve the photometric precision of the individual nightly observations, we combine the differential b and y magnitudes into a single (b + y)/2 "passband." The precision of a single observation with T4, as measured from pairs of constant comparison stars, typically ranges between 0.0015 mag and 0.0020 mag on good photometric nights. The T4 APT is described in Henry (1999), where further details of the telescope, precision photometer, and observing and data reduction procedures can be found.

We compute the standard deviations of the nightly observations for each observing season, which range from 0.0009 to 0.002 mag, indicating little or no short-term variability within each observing season. We also compute the seasonal means and perform a frequency analysis of each individual observing season using the method of Vaníček (1971), which confirms the lack of any periodic variability. Henry et al. (2022) show extensive examples of this method of period analysis.

The APT photometry can be seen in the third panel of Figure 1 and are given in Table 3.

Considering only the S_HK time series from the combined B22 and Oláh et al. (2016) data, we see excellent agreement between all data sets and instruments. These data paint a picture of a star fully transitioning from cycling behavior to flat behavior, indicative of the beginning of a Maunder minimum–like phase.

As a result, we can conclude that the HIRES-1 data (the pre-upgrade Keck HIRES data in 1997) are consistently calibrated with both the HIRES-2 observations and all Mount Wilson observations, thus dispelling any doubts about potential offset errors between the Mount Wilson and Keck-HIRES data, while also confirming that these are observations of the same star.

We can then examine the activity level during its grand magnetic minimum as compared to the activity minima during cycling behavior. We identify two cycle minima prior to the transition period: the minimum occurring from 1971 to 1975 and the minimum occurring from 1986 to 1990. The mean activity level during the first minimum (1971.0–1975.0) is S_HK = 0.181 ± 0.004. The second minimum (1987.0–1991.0) has a mean activity level of S_HK = 0.172 ± 0.006. The period of flat activity (2004 onwards) has a mean activity level of S_HK = 0.171 ± 0.002. Thus, the period of flat activity associated with the grand magnetic minimum is not significantly lower than what the star exhibits during regular cycling behavior. However, these values also suggest that the cycle minima decayed in the final cycles before the transition into grand magnetic minimum (and this is also suggested by the decaying cycle maxima in 1980 and 1995). Thus, it may be the case that we have caught this star at the end of a much larger interval of decaying cycles. ⁸ Without a longer time baseline prior to 1966, it is impossible to tell whether that is part of a larger trend. Either way, these results imply that the grand magnetic minimum is not the result of a qualitatively different surface magnetic field than is present during regular activity cycles. We do note, however, that the variability in the grand minimum is significantly lower than during either preceding cycle minimum. In the Sun, S_HK in cycle minima are dominated by the roughly spatially uniform network, with occasional small active regions providing limited variability (e.g., Milbourne et al. 2019). If we assume that cycle minima in HD 166620 are similarly dominated by the network, the lower S_HK variability observed during the grand minimum is consistent with the hypothesis that there were even fewer active regions during this time.

We need to be careful though, as the S_HK data from the Mount Wilson and Keck programs have different average noise levels. Baliunas et al. (1995) give σ_S ≈ 1.2% from observations of their least variable stars. Wright et al. (2004) give a similar value for their differential S_HK; when looking on the timescale of a single season, however, it seems this is an overestimate. The calculated σ_S is less than this in six of the nine seasons with more than one S_HK(Keck) measurement. The lowest seasonal σ_S values approach 0.3%; we adopt this as an upper limit to the seasonal noise for Keck. If we subtract these estimates of the random noise on S_HK in quadrature from the observed values, we have σ_S (min. 1) = 0.0027, σ_S (min. 2) = 0.0054, and σ_S (grand) = 0.0019. Even when corrected for intrinsic noise differences, the variability in the grand minimum is still significantly lower than preceding minima; for example, an F-test gives 8.78 × 10⁻⁶ chance that σ_S (grand) is drawn from the same distribution as σ_S (min. 1).

We combined the APT photometry and S_HK onto a common scale in the bottom panel of Figure 1. To do so, we subtracted off the median of each data set prior to 2004, choosing to center the data on the cycling portion of the time series. We then multiplied the APT photometry by a scale factor of 10 to cover a similar range to S_HK, chosen arbitrarily by eye (scale factors of 8–12 all looked similarly consistent). The resulting combined time series show excellent agreement between activity and brightness, showing that when the star transitioned from cycling to flat behavior, the star also became slightly fainter. Its mean brightness varied for the first several years over a range of 2–3 mmag. After 2004, the scatter in the mean magnitudes is only 0.35 mmag. Combined with the scarcity of strong rotationally modulated signals in either the activity or photometry, we see this as evidence that the star is not dominated during active periods by spots, but rather by faculae and a network of bright magnetic regions (as seen on the Sun, e.g., Milbourne et al. 2019) that lead to the star dimming as it decreases in activity. Similar correlations and interpretations have been made for other stars, e.g., Lockwood et al. (2007).

We computed a floating-mean Lomb–Scargle periodogram for each season of data containing more than 10 observations. We searched for significant (false alarm probability (FAP) ≤ 5 × 10⁻⁵) periodogram peaks near (within ± ≈ 20%) the previously reported mean period (P_rot = 42.4 days; Donahue et al. 1996). Since double active longitudes are common, especially in less active stars (Basri & Nguyen 2018), we also searched for significant periods within ±20% of P_rot/2 = 21.2 days. We compared the results with computed harmonics and the data window function to discard aliases. We found a total of nine seasons with significant periods, yielding an unweighted average (including doubled P_rot/2 detections) of 〈P_rot〉 = 45.06 ± 4.07 days. The full range of detections spanned from 37.96 days to 50.99 days. The scatter of P_rot values likely reflects a complex combination of surface differential rotation, plus activity growth and decay. This updated P_rot and range should improve on the value given in Donahue et al. (1996), as it includes more seasons (nine versus seven), while discarding some less certain previous P_rot values by using a more stringent FAP threshold.