Revisiting the impact of stellar magnetic activity on the detectability of solar-like oscillations by Kepler

Over 2,000 stars were observed for one month with a high enough cadence in order to look for acoustic modes during the survey phase of the Kepler mission. Solar-like oscillations have been detected in about 540 stars. The question of why no oscillations were detected in the remaining stars is still open. Previous works explained the non-detection of modes with the high level of magnetic activity. However, the studied stars contained some classical pulsators and red giants that could have biased the results. In this work, we revisit this analysis on a cleaner sample of 1,014 main-sequence solar-like stars. First we compute the predicted amplitude of the modes. We find that the stars with detected modes have an amplitude to noise ratio larger than 0.94. We measure reliable rotation periods and the associated photometric magnetic index for 684 stars and in particular for 323 stars where the mode amplitude is predicted to be high enough to be detected. We find that among these 323 stars 32% have a magnetic activity level larger than the Sun at maximum activity, explaining the non-detection of p modes. Interestingly, magnetic activity cannot be the primary reason responsible for the absence of detectable modes in the remaining 68% of the stars without p modes detected and with reliable rotation periods. Thus, we investigate metallicity, inclination angle, and binarity as possible causes of low mode amplitudes. Using spectroscopic observations for a subsample, we find that a low metallicity could be the reason for suppressed modes. No clear correlation with binarity nor inclination is found. We also derive the lower limit for our photometric activity index (of 20-30 ppm) below which rotation and magnetic activity are not detected. Finally with our analysis we conclude that stars with a photometric activity index larger than 2,000 ppm have 98.3% probability of not having oscillations detected.

where the effective temperature and the surface gravity come from the DR 25 Kepler stellar properties 126 catalog (Mathur et al., 2017). The grey symbols represent the KASC WG1 stars observed in short cadence 127 during the survey phase. The stars without oscillations detected are represented by black circles. We 128 superimposed the stars with p-mode detections (red circles) and the new detection candidates (blue crosses). 129 We will focus on the stars without detection of oscillations (or the non-oscillating stars) in the following 130 sections. We also represent the HR Diagram of each sample in different panels for a better clarity. amplitudes. We computed the predicted maximum amplitude of the modes for the 1,014 stars without 139 detection of acoustic modes and for the 529 stars with detected oscillations using the following relation: where T eff is the effective temperature, R is the stellar radius, and denotes the solar values (T eff, = 5777 K; R = 6.955 × 10 10 cm). A max, is the root-mean-square maximum amplitude for defined as: with T red = 8907(L/L ) −0.093 K. 146 Here, we used the temperatures from the DR25 Kepler star properties catalog (Mathur et al., 2017) 147 and radii from Berger et al. (2018)) that incorporated DR1 Gaia parallaxes to the previous catalog. We 148 then computed the noise level for each star by taking the mean value of the power spectrum density in 149 the frequency range 5,000 µHz to the Nyquist frequency for the short cadence (∼ 8300 µHz). there is no systematic behaviour. We also compared the predicted amplitudes with the observed amplitudes 155 for that sample of stars. We found that in average, the predicted amplitudes are slightly overestimated 156 compared to the observed ones. However, two of the most studied stars (KIC 8006161 and KIC 10644253) In addition, for the comparison with the stars where we detected modes, we select stars that are in the 165 same region of the HR Diagram with: and This yields a sample of 470 non-oscillating stars and 397 oscillating stars that are represented in Figure 3.

DATA ANALYSIS
In this section, we present the methodology used to measure the surface rotation of the stars and how we determine the level of magnetic activity using the photometric data of Kepler.  in the PDC-msMAP lightcurves, either the signal has been filtered out in these time series or the signal 198 detected in the KADACS lightcurves could originate from a polluting star. Therefore, we discard this star. parameters that affect the spectroscopic observations for other classical proxies of stellar magnetic activity.

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So the S ph is as good as a proxy as the Mount Wilson S-index. We just note that given the limitations listed 218 above, it should be considered as a lower limit of the stellar photospheric activity.

RESULTS OF THE ANALYSIS
We performed the analysis of the rotation as described in the previous section for the full sample of 1,014 220 stars. The comparison of the different filters provided a list of reliable rotation periods for 412 stars. We stars that we checked visually. We found that 6 could be due to pollution and discarded them. We end 227 up with a list of 684 stars with rotation periods measured. surface gravity, and metallicity). Table 2 gives the list of stars without detection of rotation periods. panel shows the hot stars and we clearly see that they are mostly rapid rotators as seen in García et al.

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(2014a). This is in agreement with the theory as hot stars (i.e massive stars) have thinner outer convection 240 zones leading to a smaller braking due to stellar winds. The mass limit between the hot stars and the cool 241 stars is set to 1.3 M that is also called the Kraft break (Kraft, 1967). So around the subgiant phase, stars 242 with higher masses than 1.3M will not undergo braking while cooler stars with lower masses will slow 243 down. However in the middle panel of Figure 5, we observe many dwarfs with small rotation periods.

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One explanation is that the fundamental stellar parameters (temperature and gravity) are less reliable and 245 some stars in the dwarf sample might actually be hotter stars. Another plausible explanation is that these 246 fast rotating cool stars are younger and have not yet slowed down. Comparing the rotation period of the 247 subgiants (right panel of Figure 5) to the ones from the hot stars and the dwarfs, we find that the number of 248 subgiants is much smaller. Indeed, stellar evolution theory predicts that when a star evolves on the subgiant 249 branch, it slows down and its magnetic activity decreases, i.e. less spots are present at their surfaces. Since 250 our measurements depend on the passage of spots on the stellar surfaces, we do not expect to measure the 251 surface rotation in many of these more evolved stars. Our results corroborate this theory. We also notice 252 that the subgiants with a measured rotation period are rather fast rotators ( shorter than 30 days).
In Figure 6, we can see a histogram representation of the photospheric magnetic proxy, < S ph >, 254 where the black dashed lines represent the range of the magnetic index of the Sun between minimum 255 and maximum activity ( < S ph, ,min >=67.4 ppm and < S ph, ,max >=314.5 ppm respectively). The hot 256 stars (left panel of Figure 6) have in general a similar level of magnetic activity to the Sun, while the 257 dwarfs appear to be more active (middle panel of Figure 6), which is not what we expected. For these two 258 categories, we see that the distribution peaks very close to the maximum activity of the Sun. Given the 259 uncertainties on the magnetic index, we could say that stars where no acoustic modes have been detected 260 have slightly larger magnetic activity levels than the Sun. As the sample of subgiants is very small we 261 cannot conclude on their magnetic activity. Here again, this can be explained by the fact that subgiants are 262 less active than main-sequence stars. 263 We then represent the distribution of the rotation periods ( Figure 7) and the magnetic activity proxy which could suggest that these are young subgiants.

DISCUSSION
In Figure 9, we show the magnetic index, S ph , as a function of the rotation period, P rot . We compare the    so the amplitudes could still be large enough to be detected even for stars with a < S ph > value above 298 < S ph, ,max >. 299 We see that below the S ph at minimum solar activity, there are around 100 stars with rotation and 300 magnetic activity detection whether they have detected p modes or not. We can consider that the threshold 301 of rotation and magnetic activity detectability is ∼ 20-30 ppm. We can also derive a threshold on < S ph > 302 of 2,000 ppm above which the probability of non detection of p modes is of 98.3%.

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Regarding the stars without oscillations detected, as expected they have larger magnetic indexes compared 304 to the oscillating sample. We find that 47.7% of the non-oscillating stars have an < S ph > larger than Since we find a large number of stars without detection of p modes and with magnetic indexes in the 323 same range as the oscillating stars, we propose to investigate three explanations for these stars:

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• the inclination angle affects the measurement of < S ph > as with a low inclination angle not all the 325 active regions are observed. As a consequence, the value we measure is just a lower limit of the real 326 magnetic activity proxy of the star;

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• correlation between the acoustic-mode amplitudes and the metallicity. Indeed it has been shown that In Figure 13, we also represented the S ph as a function of effective temperature. We do not see any correlation between the magnetic activity level and the T eff . From Figure 1, the non-oscillating stars had 337 a temperature range between 3,800 K and 7,500 K. We note that stars with very low levels of magnetic 338 activity are rather hot stars with temperatures above 6,000 K. low-resolution spectroscopic data from LAMOST. We note that there could be an overlap between these two 347 samples. Figure 14

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We then focus on the least active stars (with S ph smaller than the maximum activity value for the Sun) 358 that are represented with the blue dot-dash line while the stars more active are represented with a red line.

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In the LAMOST sample, we clearly see that the average metallicity of the stars is close to the solar one metallicity will lead to a less opaque convection zone and hence less energy for the excitation of the modes.

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As a consequence metal-poor stars are expected to have smaller acoustic-mode amplitudes.

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However for the stars with APOGEE metallicity, it seems that the very active stars have both super and 365 sub-solar metallicity. We find that 24 stars have sub-solar metallicity while 52 have super-solar metallicity.

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So the low metallicity only confirms the non detection of the modes in a smaller sample of stars. As

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More high-resolution spectroscopic observations would be needed to better study that effect.
classical pulsator. According to the literature, that star is actually listed as an eruptive variable star, agreeing 417 with the peculiar flag of FliPer Class . However being included in the preliminary work and still a candidate 418 of a fast rotator without detection of oscillations, we will discuss the spectroscopic analysis of that star.

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For the other two stars we have computed that the predicted amplitude of the modes is much larger than the 420 noise.  Currently, these are only first diagnostics from a small sample of stars. We plan to have a final sample of 429 several dozens of stars, all obtained with the same spectrograph, which will then be consistently analyzed. have a ratio between the predicted amplitude and the noise above 1, with only 16 stars below. We 441 found that for 394 non-oscillating stars, that ratio is below 1.

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• We can provide a lower limit of detection of magnetic activity of 20-30 ppm below which we do not 443 detect any rotation periods.

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• If we discard the stars for which the predicted amplitude of the modes is smaller than the noise, we