The Sun is less active than other solar-like stars

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Science  01 May 2020:
Vol. 368, Issue 6490, pp. 518-521
DOI: 10.1126/science.aay3821

Activity levels of Sun-like stars

Magnetic activity on the Sun leads to solar flares, coronal mass ejections, and other space weather that affects Earth. Similar activity on other stars may determine the habitability of any orbiting exoplanets. Reinhold et al. analyzed brightness variations of stars observed with the Kepler and Gaia space telescopes to infer their activity levels (see the Perspective by Santos and Mathur). They found that the Sun was less active than most of the 369 solar-type stars in their sample (those with the most similar physical properties). It remains unclear whether the Sun is permanently less active than other stars of its type or if its activity levels vary over many thousands or millions of years.

Science, this issue p. 518; see also p. 466


The magnetic activity of the Sun and other stars causes their brightness to vary. We investigated how typical the Sun’s variability is compared with other solar-like stars, i.e., those with near-solar effective temperatures and rotation periods. By combining 4 years of photometric observations from the Kepler space telescope with astrometric data from the Gaia spacecraft, we were able to measure photometric variabilities of 369 solar-like stars. Most of those with well-determined rotation periods showed higher variability than the Sun and are therefore considerably more active. These stars appear nearly identical to the Sun except for their higher variability. Therefore, we speculate that the Sun could potentially also go through epochs of such high variability.

Stars like the Sun have a magnetic field in their interiors, which is driven by a self-sustaining dynamo process (1). When the magnetic field becomes unstable, it can emerge from the stellar surface, leading to the appearance of magnetic features such as bright faculae and dark star spots. As stars rotate, the transits of these magnetic features across their visible surface, and the temporal evolution of these features, lead to stellar brightness variations. Such variations have been extensively studied for the Sun (2), where they have an amplitude of up to 0.3% of the sunlight integrated over the entire spectrum, i.e., the total solar irradiance (TSI). Solar variability affects Earth’s climate on decadal and longer time scales (3) and Earth’s atmospheric chemistry on daily and monthly time scales (4). Sufficiently precise solar brightness measurements have only been available since the advent of dedicated spaceborne missions in 1978 (5). Records of sunspot areas and positions can be used to reconstruct brightness variations back to 1878 (6). Sunspot counts, the longest record of regular observations of solar magnetic activity, extend back to the onset of telescopic observations around the year 1610 (7). Solar activity can be reconstructed over longer periods, up to 9000 years, from cosmogenic isotopes (8).

We took an alternative approach by comparing the Sun’s activity with other solar-like stars (9, 10). Stellar magnetic activity and photometric variability are strongly correlated [e.g., (11)]. The same applies to the Sun, for which there is a close correlation between proxies for solar magnetic activity and photometric variability (12, 13). There is an ongoing debate about whether solar photometric variability is smaller than the variability of other stars with near-solar effective temperatures and a similar level of magnetic activity (10, 14, 15). With the advent of planet-hunting missions, particularly the Kepler space telescope (16), this topic has received renewed attention. For example, the Sun has been found to be photometrically quieter (i.e., less variable) than most of the stars observed by Kepler (17). By contrast, the TSI has a similar level of variability compared with a sample of main-sequence stars with near-solar (and lower) effective temperatures in the Kepler field (9). Those studies could not constrain their samples to near-solar rotation periods because of the lack of available measurements. This may have affected their results, because the stellar rotation period and effective temperature are related to the action of the dynamo and therefore the level of magnetic activity (1).

To compare solar photometric variability with other stars, we focused on Kepler observations of main-sequence stars with near-solar fundamental parameters and rotation periods. The stellar fundamental parameters that we considered are the effective temperature Teff, surface gravity log g, and metallicity [Fe/H] (18, 19). We adopted a parameter catalog (19) that is based on Kepler data release 25 (DR25). Rotation period measurements are available for thousands of stars observed during the Kepler mission (20, 21). We adopted a catalog of 34,030 stars with determined rotational periods and 99,000 stars for which no rotation periods were detected [(21), their tables 1 and 2]; we refer to these as the “periodic” and the “nonperiodic” samples, respectively. From both samples, we selected stars with Teff in the range of 5500 to 6000 K (the value for the Sun, indicated with subscript ⨀, is Teff,⨀ = 5780 K) and surface gravity log g > 4.2 (Sun: log g = 4.44) to focus on solar-like main-sequence stars. The surface gravity cut removes evolved stars, which are inactive, so may have diluted the variability of solar-like stars found in previous analyses (21). For the periodic sample, we selected rotation periods in the range of 20 to 30 days (Sun: Prot,⨀ = 24.47 days sidereal rotation period).

We further restricted the samples using astrometric data from the Gaia spacecraft (22). Using the sample stars’ apparent magnitudes, distance measurements (23), and interstellar extinctions from Gaia data release 2 [Gaia DR2 (24)], we constructed a Hertzsprung–Russell diagram (HRD) by computing the absolute Gaia G-band magnitude MG (Fig. 1). The absolute magnitudes of our samples were restricted by selecting stars from the HRD with near-solar ages between 4 and 5 gigayears (Gyr) (Sun: 4.57 Gyr) and metallicities in the range of –0.8 to 0.3 decimal exponents (dex). This was realized by fitting isochrones [i.e., evolutionary tracks of constant age (13)] to the HRD and then selecting periodic and nonperiodic stars between a lower isochrone of 4 Gyr and metallicity of [Fe/H] = −0.8 and an upper isochrone of 5 Gyr and metallicity of [Fe/H] = 0.3 (Fig. 1, A and B). Stellar variability depends only weakly on metallicity (13), so a stricter metallicity constraint does not affect our results; therefore, we used this broad range to improve the statistics. The Sun is slightly more luminous than most of the selected periodic and nonperiodic stars (Fig. 1), because 79% of these stars have metallicities lower than the solar value.

Fig. 1 HRDs of our samples.

The periodic (A) and nonperiodic (B) samples (21) are shown in dark green (McQ14 in the legend), and the stars that meet our selection criteria are overplotted in blue. The solid black line is a 4-Gyr isochrone (13) with a metallicity [Fe/H] of −0.8, and the dashed black line is a 5-Gyr isochrone with a metallicity [Fe/H] of 0.3. The Sun is indicated by the small black star.

We considered stars in our periodic sample to be solar like, i.e., they had near-solar fundamental parameters and rotation periods. The nonperiodic stars are considered only pseudosolar because their rotation periods are not known. Furthermore, we discarded stars fainter than 15th magnitude (in the Kepler band) because of their high noise level, which could mask the stellar variability. After applying all of these selection criteria, our final samples contained 369 solar-like stars with determined rotation periods and 2529 pseudosolar stars without a detected period.

To quantify the magnetic activity of the Sun and the selected stars, we computed their photometric variability using the variability range Rvar. This quantity is defined as the difference between the 95th and 5th percentile of the sorted flux values (normalized by its median) in a light curve, i.e., the temporal record of the stellar flux (25). Our Rvar values are based on the Kepler Presearch Data Conditioning (PDC) and maximum a priori (MAP) detrended data (26). We selected the PDC-MAP data after considering how the different Kepler data products may affect our results (13).

We found that Rvar in the periodic sample showed a weak dependence on effective temperature, rotational period, and metallicity (fig. S8) even though these were constrained to narrow ranges by our selection criteria. We therefore corrected the Rvar measurements of the periodic stars for these dependencies and normalized them to the values of the solar fundamental parameters using a multivariate analysis (13). For four of the 369 periodic stars, this process returned negative Rvar values, indicating an overcorrection. Those four stars were discarded. For the nonperiodic sample, Rvar did not correlate with the fundamental parameters (fig. S9), so no correction was applied.

Figure 2 shows three example stellar light curves and solar TSI data (13) taken at the same epoch as the Kepler observations. TSI data have been demonstrated to be suitable for direct comparison with the variability observed in the Kepler passband (9, 13). Although the star KIC 10449768 exhibits variability that is similar to the maximum observed solar variability (13), the other two stars in Fig. 2 have much higher variability.

Fig. 2 Light curves of the Sun (A) and three stars from the periodic sample [(B to D)].

(A) Solar TSI data taken at the same epoch as the Kepler observations. The TSI data were detrended by cutting the 4-year time series into 90-day segments, dividing by the median flux, and then subtracting unity. (B to D) Three examples of stars (identified above each plot) with different variabilities. The variability ranges Rvar are indicated by the differences between the horizontal red lines before (dashed) and after (solid) correction for the variability dependence on the fundamental parameters. The solid orange lines in (A) mark the maximum solar variability range [Fig. 3 and (13)]. The panels have different y-scales.

Figure 3 shows the distribution of Rvar for the Sun, the periodic stars, and a composite sample of the periodic and nonperiodic samples combined. To compare the Sun with the stars observed by Kepler, we simulated how it would have appeared in the Kepler data by adding noise to the TSI time series (fig. S7). The variability range was then computed for 10,000 randomly selected 4-year segments from ~140 years of reconstructed TSI data (13).

Fig. 3 Solar and stellar variability distributions on a logarithmic scale.

The distributions of the variability range Rvar are plotted for the composite sample (black), the periodic sample (blue), and the Sun over the last 140 years (green). Error bars indicate the Poisson uncertainties N, where N is the number of stars in each bin, for the composite and the periodic samples. The yellow line shows an exponential model a010a1Rvar fitted to the variability distribution of the (corrected) composite sample (Rvar > 0.2%, solid line) and its extrapolation to low variabilities (Rvar < 0.2%, dashed line). The solar distribution was normalized to the maximum of the composite sample. The first and last bins of the solar distribution were reduced in width to stop at the minimum and maximum values of solar variability over the last 140 years, respectively.

The activity distribution of the composite sample (Fig. 3) does not separate into distributions of periodic and nonperiodic stars, but rather appears to represent a single physical population of stars. Fitting an exponential function y=a010a1Rvar to the variability distribution of the (corrected) composite sample with Rvar > 0.2% yields a0 = 0.14 ± 0.02 and a1 = –2.27 ± 0.17. The subsample of periodic stars mostly populates the high-variability portion of the full distribution in Fig. 3, whereas the low-variability portion mostly contains stars from the nonperiodic sample. The solar Rvar distribution is consistent with most of the low-variability stars, which is consistent with previous studies (9).

Determining the solar rotation period from photometric observations alone is challenging (2729). The Sun would probably belong to the nonperiodic sample if it were observed by Kepler, and we found that the level of solar variability is typical for stars with undetected periods (Fig. 3). However, our composite sample contains stars that might have quite different rotation periods even though they have near-solar fundamental parameters.

By contrast, the variability of stars in the periodic sample has a different distribution. Although there are some periodic stars with variabilities within the observed range covered by the Sun, the variability amplitude for most periodic stars lies well above the solar maximum value of the last 140 years. Therefore, most of the solar-like stars that have measured near-solar rotation periods appear to be more active than the Sun. The variability of the periodic stars at the solar effective temperature, rotation period, and metallicity is Rvar = 0.36% (fig. S8), which is ~5 times higher than the median solar variability Rvar,⨀ = 0.07% and 1.8 times higher than the maximum solar value Rvar,⨀ ≲ 0.20%. All of these stars have near-solar fundamental parameters and rotational periods, suggesting that their values do not uniquely determine the level of any star’s magnetic activity. This result is consistent with the detection of flares with energies several orders of magnitude higher than solar flares (i.e., superflares) on other solar-type stars (30, 31).

We suggest two interpretations of our results. First, there could be unidentified differences between the periodic stars and nonperiodic stars (such as the Sun). For example, it has been proposed that the solar dynamo is in transition to a lower activity regime (32, 33) because of a change in the differential rotation inside the Sun. According to this interpretation, the periodic stars are in the high-activity regime, whereas the stars without known periods are either also in transition or are in the low-activity regime. The second possible interpretation is that the composite sample in Fig. 3 represents the distribution of possible activity values that the Sun (and other stars with near solar fundamental parameters and rotational periods) can exhibit. In this case, the measured solar distribution is different only because the Sun did not exhibit its full range of activity over the last 140 years. Solar cosmogenic isotope data indicate that in the last 9000 years, the Sun has not been substantially more active than in the last 140 years (8). There are several ways for this constraint to be reconciled with such an interpretation. For example, the Sun could alternate between epochs of low and high activity on time scales longer than 9000 years. Our analysis does not allow us to distinguish between these two interpretations.

Supplementary Materials

Materials and Methods

Figs. S1 to S10

Data S1

References (3461)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We thank the three anonymous referees for constructive criticism and useful advice, which helped to greatly improve the paper. We also thank the International Space Science Institute, Bern, for their support of science team 446 and the resulting helpful discussions. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. This work has made use of data from the European Space Agency (ESA) mission Gaia (, which were processed by the Gaia Data Processing and Analysis Consortium (DPAC; Funding for DPAC has been provided by national institutions, especially the institutions participating in the Gaia Multilateral Agreement. Funding: T.R. and A.I.S. were funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715947). S.K.S. acknowledges support from the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea. E.M.A.-G. acknowledges support from the International Max-Planck Research School (IMPRS) for Solar System Science at the University of Göttingen. Author contributions: T.R., A.I.S., and S.K.S. conceived the study. A.I.S. and S.K.S. supervised the project. T.R. analyzed the Kepler data. B.T.M. investigated instrumental effects and cross-matched the Kepler and Gaia catalogs. A.I.S., S.K.S., N.A.K., R.H.C, and E.M.A.-G. contributed to the analysis of the data. T.R., A.I.S., S.K.S., and B.T.M. wrote the paper. All authors reviewed the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: The PDC-MAP Kepler data are available at Kepler data reduced with the PDC-msMAP pipeline are available at the Mikulski Archive for Space Telescopes at Sunspot data were taken from SATIRE-T2 data can be found at VIRGO level 2 1-min data were taken from Our machine-readable catalog and software scripts are provided in data S1 in the supplementary materials.

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