HD 4915: A Maunder Minimum Candidate

It has been almost 175 years since Heinrich Schwabe discovered the 11-year sunspot cycle in 1843. With the development of solar dynamo theory as the mechanism responsible for creating the Sun's magnetic field, the sunspot cycle was realized to be a manifestation of the Sun's magnetic cycle (see Charbonneau 2014 for a review). About 140 years after the discovery of sunspot cycle, Eddy (1976) compiled strong historical evidence spanning centuries to show that the "prolonged sunspot minimum" period from 1645 to 1715, as speculated by Gustav Spörer in 1889 and E. W Maunder in 1894, was real. Eddy called this period the Maunder Minimum (MM). Two other such periods, although less dramatic, were identified by the community (e.g., Siscoe 1980), the Dalton (1796–1820) and Spörer Minima (1460–1550).⁶ Such periods are now more generally termed Magnetic Grand Minima (MGM; e.g., Saar & Testa 2012) and are characterized by repressed magnetic activity that lasts longer than at least the typical cycle of the star.

Learning more about MGM periods has been of interest because it addresses one of the many elusive characteristics of the solar dynamo, thereby contributing to our understanding of the Sun's magnetic field, especially its evolution in the past and future. To maximize this learning, several surveys of Sun-like stars have been conducted, with the goal of collecting a large sample of stars in MGM states.

Today, the standard metric for sunspot coverage is group sunspot number (GSN), which uses the number of groups of sunspots to provide a more self-consistent and less noisy data set than the previous calibrations (Hoyt & Schatten 1998). Because it is challenging to observe sunspots on Sun-like stars on decade timescales, it is necessary to use a proxy for global magnetic field strength instead, such as chromospheric line emission. In this regard, the most common proxy has been the emission cores of the Ca ii H and K lines at 3968 Å and 3934 Å, respectively.

A drawback of using this proxy is the absence of chromospheric line emission data from the MGM periods of the Sun, specifically the MM, preventing an absolute comparison in the activity of the Sun and other stars. This compels the use of sunspots instead; however, it is important to note that although the sunspots have shown an almost flat activity during the MM period, other solar proxies, including the cosmogenic isotopes (Kocharov 1986), have in fact indicated a weakly cycling activity.

1.1. Searching for MGM in Other Stars

1.2. HD 3651

One such attempt to identify a MM analog via chromospheric time series is that of Donahue et al. (1995), who identified HD 3651 as star that might be "entering a Maunder minimum phase" using the S-Index values from the Mount Wilson Observatory HK Project (see Figure 1). Subsequent monitoring at Keck Observatory as part of the California Planet Survey shows that the star has continued to cycle, although apparently at a much lower amplitude and about a mean significantly higher than the 1987 magnetic minimum.

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So in this case, Donahue et al. (1995)'s prediction that a star that appeared to have a strongly decaying activity cycle was entering a Maunder minimum state does not seem to have been validated, although the star does seem to be in a more weakly cycling state.

In order to compare results with the seminal Mt. Wilson survey, HK emission is usually expressed in the instrumental unit used by that survey, the S-Index, which essentially tracks the equivalent width of the emission in the HK line cores (Vaughan et al. 1978). The strength of these Ca ii emission lines is proportional to the heating of the Sun's chromosphere by the magnetic fields on the surface and has a direct correspondence with the strength of the magnetic activity and the area covered (Leighton 1959; Skumanich et al. 1975). Another commonly used index is ${R}_{\mathrm{HK}}^{{\prime} }$, which is the ratio of the chromospheric emission in HK lines to the total bolometric emission from the star so that it is independent of temperature and photospheric component of the star (Noyes et al. 1984).

For our analysis, we have used the HD 4915 spectra from 2006 until present, collected as a part of the California Planet Search (CPS) Radial Velocity Survey (Howard et al. 2010) using Keck/High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994). The spectra are publicly available on Keck Observatory Archive.⁷  For data prior to 2010 we have taken data directly from the tables of Isaacson & Fischer (2010) and the calculated the rest (post-2010) from CPS spectra using the same methodology used to generate those tables.

Because the Butler et al. (2017) analysis of these same spectra find a slightly different S-Index time series that does not as obviously show evidence of entry into an MGM state, we have examined the spectra themselves to confirm that our S-Index measurements accurately reflect the emission in the HK lines. The top panel of Figure 2 shows the S-Index time series color coded by value, and the bottom panel shows the corresponding Ca ii H line core spectra. We show this color-coded correspondence to confirm a faithful tracking of the total emission in the line core by our S-Indices.

HD 4915 is a G5V star with an effective temperature of 5668 K, log g = 4.57, vsini of 1.4 ${\text{km s}}^{-1}$, [M/H] of −0.2 dex, and an isochrone derived age in the range of 0.6–4.4 Gyrs (Brewer et al. 2016). These spectroscopic properties of HD 4915 differ from that of the Sun's by −104 K, 0.132 dex (Prša et al. 2016), and 0.2 km s⁻¹ (Pavlenko et al. 2012), respectively, classifying it as a dwarf and also Sun-like.

Over its last cycle, which we suspect to be its transition period into an MGM state, it has an average S-Index of 0.184 and and HK variation of 2.28%. Following the analysis done by Noyes et al. (1984) for transforming S-Index to ${R}_{\mathrm{HK}}^{{\prime} }$, and using B − V = 0.66 (Soubiran et al. 2016), we compute $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ = −4.872.

We might use the star's activity level to deduce an estimate of its age using the activity–rotation–age relation formulated by Mamajek & Hillenbrand (2008), but the star's apparent entry into an MGM state confuses this, because that relation is based on the mean activity of (presumably) non-MGM stars, and we do not know how the activity level during the transition to an MGM state relates to its mean out-of-MGM activity level.

Using the data we have, we would determine the age of the star to be between 4.3 Gyr (at the global minimum, S = 0.176) and 2.7 Gyr (at the global maximum, S = 0.22). We would calculate an age of 3.8 Gyrs using the mean of the data from just the last full cycle. This range of ages is consistent with the isochrone age, confirming that the star is likely to be younger than the Sun.

With $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ = −4.877 and [M/H] = −0.2, we note that it does not satisfy Saar & Testa (2012)'s criteria of lying near the minimum $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$–[M/H] trend-line yet. This could be explained if HD 4915 is younger than the Sun, which would cause its average activity levels to be higher or because it is still entering an MGM state, and thus shows depressed, but not yet MGM-level, activity. On the other hand, it is a bona fide dwarf as classified by its temperature and gravity, and its HK variation of 2.28% is close to the 2% limit set down by Saar & Testa (2012).

In this section, we analyze the S-Index time series of HD 4915 to categorize it as an MM candidate. As the top panel of Figure 2 shows, we see a decrease in the amplitude of the activity cycle over the three apparent maxima until the amplitude is almost negligible. By examining the first two cycles and assuming that the first measurements just capture the first cycle maximum, we estimate the period of the cycle to be four years and note the striking delay in the occurrence of the third maxima by almost two years. We also note that the second minimum appears to be significantly lower than the first minimum. These features of the S-Index time series strongly suggest a decreasing magnetic activity in the star.

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To compare these features to that of the Sun, we look at the Sun's transitions into and out of MGM using its historical GSN record (reconstructed by Hoyt & Schatten 1998). Figure 3 shows entry into MM (first panel), the Dalton Minimum (middle panel) and exit from the MM (last panel). The black symbols represent the section of the GSN trend that we are comparing with the past activity of HD 4915, and the red symbols represent the potential futures of the HD 4915 activity record if it were in an analogous state.

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The transition of the Sun into MM is characterized by a steep and sudden drop in GSN across two normal cycles (Figure 3, top panel). GSNs then remains close to zero until toward the end of the MM at around 1700 CE, when it emerges from the MM over the course of two cycles and returns to its normal 11 year cycling state.

To date, the S-Index time series of HD 4915 most resembles the transition of the Sun into the Dalton Minimum in Figure 3 (middle panel, solid black dots). This transition is characterized by the decreasing amplitude of maxima over three cycles, with the third minimum occurring lower than the previous two (Figure 2).

Finally, we compare the HD 4915 S-Index time series to the exit of the Sun from the MM. This comparison is possible if we hypothesize that the entry and exit of the Sun's magnetic activity from a grand magnetic state are time symmetric.⁸ In the case of the MM event, the transition from MGM to a normal cycle as seen in Figure 3 (bottom panel) is characterized by the increasing amplitude of the magnetic activity (note the time reversed x-axis). This, too, bears some resemblance to the activity history of HD 4915.

The decline in the magnetic activity strength of HD 4915 is exciting because it renews the discussion of ways to identify MM candidates. As discussed in Section 1.2, there have been numerous attempts over the last few decades to set down the criteria for an MGM candidate using S-Indices; however, these criteria have been of uncertain utility because we lack directly comparable data of the Sun's chromospheric activity during its MGM episodes.

As indicated by Saar & Testa (2012), the surest way to characterize a star in MGM would be by observing it enter a long period (at least longer than its typical cycle period) of flat activity or low cycling activity and transition out of this period into a normal activity cycle. Alternatively, we could also make such a characterization by observing a star transition into a normal cyclic state from an anomalously low state.

The discovery of a true MM analog would help us understand whether the state of the Sun's field during its MGM was a state of extraordinarily low global magnetic field strength, or just an extraordinarily weak and long series of magnetic maxima. Such an understanding would greatly inform searches for other MM analogs.

HD 4915 may, in fact, not be a star with a single, strong cycle period like the Sun. Indeed, we have inferred that it has a 4 years period under the assumption that our data capture the first partial cycle's maximum and what appears to be around two full "cycles" of varying morphology. As has been shown by Metcalfe et al. (2016), many stars with cycle periods <5 years show stochastic or multi-period behavior that might be a better analogy to HD 4915 (see, for instance, HD 76151 in Figures 4.5 and B.10 of Egeland 2017, as well as HD 190406 in Figure 7, left column, second from top; Hall et al. 2007). This underscores the need for future observations of this star to determine its magnetic behavior.

We recommend immediate and future observations of chromospheric and coronal cooling indicators (such as the H & K emission lines and X rays) for at least the next decade (two cycles of the star), especially as there is strong evidence that HD 4915 is entering a state of MGM right now. The Transiting Exoplanet Survey Satellite (TESS) or other future space-based photometric missions might be able to determine if the star indeed has a spot-free photosphere.

We thank the referee for a constructive report that improved this Letter, and for pointing us to the Donahue et al. identification of HD 3651 as an MGM candidate.

We thank Eric Mamajek for useful discussions and for hunting down the early use of the term "Dalton Minimum."⁹ We also thank Thomas Beatty, Fabienne Bastien, Mark Giampapa, David Soderblom, and Larry Ramsey for useful discussions that improved the Letter.

The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium.

The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.

This research has made use of NASA's Astrophysics Data System Bibliographic Services, the SIMBAD database, operated at CDS, Strasbourg, France, and the AstroBetter blog and wiki.

This material is based upon work supported by the NSF Postdoctoral Research Fellowship in Biology under grant No. AST-1602662.

Facility: Keck:I (HIRES). -