Low-amplitude Solar-like Oscillations in the K5 V Star ϵ Indi A

We have detected solar-like oscillations in the mid-K-dwarf ϵ Indi A, making it the coolest dwarf to have measured oscillations. The star is noteworthy for harboring a pair of brown dwarf companions and a Jupiter-type planet. We observed ϵ Indi A during two radial velocity campaigns, using the high-resolution spectrographs HARPS (2011) and UVES (2021). Weighting the time series, we computed the power spectra and established the detection of solar-like oscillations with a power excess located at 5265 ± 110 μHz—the highest frequency solar-like oscillations so far measured in any star. The measurement of the center of the power excess allows us to compute a stellar mass of 0.782 ± 0.023 M ⊙ based on scaling relations and a known radius from interferometry. We also determine the amplitude of the peak power and note that there is a slight difference between the two observing campaigns, indicating a varying activity level. Overall, this work confirms that low-amplitude solar-like oscillations can be detected in mid-K-type stars in radial velocity measurements obtained with high-precision spectrographs.


INTRODUCTION
Asteroseismology, the study of stellar oscillations, has flourished in recent years thanks largely to the success of the space missions CoRoT (Convection, Rotation and planetary Transits, Baglin et al. 2006b,a;Auvergne et al. 2009), Kepler (Borucki et al. 2010;Koch et al. 2010;Gilliland et al. 2010;Chaplin et al. 2011a) and TESS (Transiting Exoplanet Survey Satellite Ricker et al. 2015).These satellites delivered high-quality photometric times series that are excellent for asteroseismology.However, for bright Sun-like stars, radial velocity observations with a ground-based telescope can deliver better signal-to-noise, due to the much lower stellar granulation background.This is particularly true for cool main-sequence stars, where the oscillation amplitudes are very low (Kjeldsen et al. 2008;Huber et al. 2011).
In the case of solar-like oscillations, the overall frequency pattern is governed by two socalled global asteroseismic parameters namely the large frequency separation (∆ν) and the frequency of maximum power (ν max ).These two parameters describe the overall regularity in the frequency comb and the location of the stellar oscillations, respectively, and they are often used to determine fundamental parameters of main-sequence and red-giant stars (see reviews by Chaplin & Miglio 2013;Hekker & Christensen-Dalsgaard 2017;García & Ballot 2019;Jackiewicz 2021).* Now at Met Office, UK Here, we report the detection of solar-like oscillations in the K5 V star ε Indi A (HD 209100).ε Indi A is orbited every ∼45 yr by a jovian mass exoplanet, ε Indi Ab, which has been detected in both RV and astrometry (Feng et al. 2019).ε Indi Ab is the nearest cold Jupiter-type planet to Earth and its infrared emission is expected to be sufficiently high to be measured by JWST (Feng et al. 2023).
In addition, ε Indi A is part of a hierarchical triple system with the brown dwarfs ε Indi Ba and ε Indi Bb, which have been extensively studied (see, for example, Scholz et al. 2003;Smith et al. 2003;McCaughrean et al. 2004;Roellig et al. 2004;Mainzer et al. 2007;Reiners et al. 2007;Kasper et al. 2009;King et al. 2010;Cardoso et al. 2010;Chen et al. 2022).With the current determined dynamical masses of 66.92 ± 0.36 M Jup and 53.25 ± 0.29 M Jup for the brown dwarfs (Chen et al. 2022), as well as an accurate distance, these are among the best-characterised brown dwarfs (Chen et al. 2022).Thereby, the ε Indi system is highly valuable to put constraints on formation and evolution in the substellar regime (Joergens & Reffert 2014;Feng et al. 2019).However, there is disagreement over the age of the system, with estimates spanning a range 0.39-5 Gyr (Cannon 1970;Lachaume et al. 1999;Rocha-Pinto et al. 2002;Barnes 2007;Kasper et al. 2009;King et al. 2010;Dieterich et al. 2018;Feng et al. 2019;Viswanath et al. 2021;Pathak et al. 2021;Chen et al. 2022), leaving the age to be firmly pinned down.
In Sec. 2 we present our radial velocity observations and the spectroscopic analysis.The analysis of the time series with respect to asteroseismology is the topic of Sec. 3, while the results are presented and discussed in Sec. 4. The conclusion follows in Sec. 5.

OBSERVATIONAL DATA
We observed ε Indi A in two intensive radial velocity (RV) campaigns separated in time by about 10 years.The first campaign was carried out with HARPS in 2011, while a UVES campaign followed in 2021.It should be noted that ε Indi A fell in the TESS field in Sectors 1 and 27 and was observed photometrically in the 2-minute-cadence mode for ∼27 d each.It was also observed by TESS with 20-s cadence in Sector 68.However, the oscillations are not visible in any of these data, which is to be expected given their small amplitudes.

HARPS RV data
The data were collected over 12 nights in August 2011 with HARPS on the ESO 3.6 m telescope at La Silla Observatory, Chile.Around 40% of the time was lost due to bad weather.The median exposure time was 30 s, sometimes increased to 35 s or 40 s in poorer conditions.The exposure time was kept short due to the high expected frequency of the oscillations.The readout time between each exposure was 32 s, and hence the median sampling time was 62 s (which corresponds to a Nyquist frequency of about 8000 µHz).
For this work we used the RVs derived by Trifonov et al. ( 2020) as part of the correction of public HARPS data for systematic errors.A plot of the RV time series can be found in the top panel of Fig. 1.

UVES RV data
In August 2021 we observed ε Indi A during 6 non-consecutive (5+1) nights with UVES on the VLT, using the iodine cell as a wavelength reference.Again, some time was lost due to the weather (around 25%), including all of night Table 1.Atmospheric parameters derived from the spectroscopic analysis.Note that the quoted uncertainties are internal only (for the abundances; the spread ± the sensitivity to the other parameters), and g is measured in cm/s 2 .
To obtain the RV time series, all the individual spectra were reduced following the method described in Butler et al. (1996Butler et al. ( , 2004)).The RV time series is shown in the bottom panel of Fig. 1.

Spectroscopic analysis
Some spectra taken as part of the UVES campaign were also used for a spectroscopic analysis.Based on the high signal-to-noise iodine-free template spectrum of ε Indi A, we were able to derive spectroscopic values of the effective temperature, surface gravity, [Fe/H], and the alpha enhancement using a classical equivalent-width spectral analysis with the line list from Slumstrup et al. (2019).The results are presented in Table 1, with uncertainties internal to the analysis only.The auxiliary program abundance within the spectrum software (Gray & Corbally 1994) was used to determine the atmospheric parameters under the assumption of LTE, using ATLAS9 models (Castelli & Kurucz 2003) and solar abundances from Grevesse & Sauval (1998).We used astrophysical oscillator strengths, with the log gf values for each absorption line adjusted to yield the solar elemental abundances of Grevesse & Sauval (1998).The [α/Fe] in this paper is defined as The orange points show the smoothed uncertainties that were measured from the scatter and used for weights when calculating the power spectra (see Sec. 3.1).
ε Indi A has been the subject of several previous spectroscopic analyses, dating as far back as 1980 (for an overview, visit for instance Simbad).The star is reported to be metal-poor, with a median [Fe/H] = −0.16dex, which is in excellent agreement with our determination from the UVES spectrum.Median values of the effective temperature (T eff = 4649 K) and surface gravity (log g = 4.54) are also in agreement with our determined values.Based on abundances from the literature (Kollatschny 1980;Adibekyan et al. 2012;Delgado Mena et al. 2017;Luck 2018;Soto & Jenkins 2018;Hojjatpanah et al. 2019), it is possible to compute values of the alpha enhancement that can be compared to our value.The median value computed from the literature is [α/Fe] = 0.12 which, in combination with our value, indicates little to no alpha enhancement.

Calculation of the power spectrum
We calculated weighted power spectra using a standard sine-wave fitting technique (see, e.g.Kjeldsen 1992;Frandsen et al. 1995;Handberg & Lund 2014).The weights were taken as the inverse of the measurement uncertainties, which we estimated as the smoothed scatter in the time series (orange points in Fig. 1).The median scatter was 76 cm/s for UVES and 78 cm/s for HARPS.The slightly smoothed weighted power spectra for the HARPS and UVES observing runs are shown in the top two panels of Fig. 2 (blue lines).
To calculate the power spectrum of the combined HARPS and UVES data we merged them in the time domain, rather than averaging the power spectra, because this allowed us to estimate the spectral window of the combined data (see also Bedding & Kjeldsen 2022).This combined weighted power spectrum, shown in the bottom panel of Fig. 2, comprises around 70% power from HARPS and 30% power from UVES.

Location of the power envelope and mode amplitude
To determine the frequency of maximum oscillation power, ν max , and to estimate the amplitude of the oscillations, we followed the method described by Kjeldsen et al. (2005Kjeldsen et al. ( , 2008)).This involves the following steps: (i) remove the structure from individual p modes in the power spectrum by heavily smoothing with a Gaussian with a full-width at half maximum of 800 µHz (∼ 4∆ν, with ∆ν being the expected large frequency separation; orange curves in Fig. 2); (ii) convert to power density by multiplying by the effective length of the observing run (calculated as the reciprocal of the area under the spectral window in power); and (iii) fit and subtract the background noise using a linear fit to the area surrounding the power envelope (orange curves in Fig. 2).From this, ν max can be found as the peak position.
A last step is needed to extract the mode amplitude, namely (iv) multiply by 4.09 (the effective number of modes per order) and take the square root, in order to convert to amplitude per oscillation mode.

Measurement of ν max
The determined center of the power excess (ν max ) as well as the amplitude of the central radial mode (having degree ℓ = 0) can be found for the HARPS, UVES and combined power In each panel, the blue curve is the power spectrum smoothed over a width of 2 µHz, the orange curve is smoothed by a width of 800 µHz, and the green curve shows the power excess after subtracting the noise (expanded vertically by a factor of 20 for visibility).
spectra in Table 2.The main source of uncertainty for ν max and the peak amplitude is the noise background.We estimated the error bars for the three excess power estimates by making simple simulations with a known input, using the same spectral window and signal-to-noise ratio as the real data.In the following, we chose to use the ν max from the combined power spectrum as this is based on the most data, which is a choice in line with our previous multi-site campaigns to detect solar-like oscillations (e.g.Kjeldsen et al. 2005;Bedding et al. 2006Bedding et al. , 2007;;Arentoft et al. 2008).
As an effect of the non-zero exposure time, the mode amplitudes will decrease slightly and the frequency of maximum power will shift to lower frequencies; an effect sometimes referred to as apodization (for the effect on mode amplitudes see, e.g., Chaplin et al. 2011b;Kallinger et al. 2014).To understand this effect, all three data sets (HARPS, UVES and the combined) were simulated 100 times with the actual exposure times and using the individual statistical weights.The effect for the three data sets-based on simulating a p-mode excess power envelope at 5250 microHz-is that, to account for the non-zero exposure times, the measured peak amplitudes should be increased by 4.2% (HARPS), 12.2% (UVES) and 6.8% (combined), while the ν max values should be increased by 0.1% (HARPS), 0.4% (UVES) and 0.2% (combined).While the shift of ν max is well below the uncertainty, the effect on the amplitude is relatively larger, although still below the uncertainty of the amplitude estimate.These corrections have been applied in Table 2.

Mass of ε Indi A
As mentioned in the Introduction, it is common to estimate the mass of a star with solarlike oscillations from ν max and ∆ν using the asteroseismic scaling relations.However, if a reliable luminosity or radius is available, the mass can be estimated from ν max without requiring ∆ν, as has been done in studies of red giants (Stello et al. 2008;Hon et al. 2021).Based on the frequency of maximum power (Table 2), the effective temperature (Table 1) as well as the computed radius from combining the distance with the measured angular diameter, we can calculate the mass of ε Indi A using the scaling relations (see e.g. Brown et al. 1991;Kjeldsen & Bedding 1995).Specifically, the mass can be found as (Stello et al. 2008;Kallinger et al. 2010): with suitable solar reference values.In this work we adopt ν max,⊙ = 3090 ± 30 µHz (Huber et al. 2011) and T eff,⊙ = 5772.0± 0.8 K (Prša et al. 2016).To obtain the radius of ε Indi A we used the distance from the astrophysical parameters table of Gaia DR3 (Creevey et al. 2023): d = 3.648 +0.022 −0.009 pc (distance gspphot).Combining this with the limb-darkened angular diameter of θ LD = 1.817 ± 0.013 mas (Rains et al. 2020) gives a radius of 0.713 ± 0.006 R ⊙ , in excellent agreement with the value found by Rains et al. (2020).Using Eq. 1 yields a stellar mass of 0.782 ± 0.023 M ⊙ .This is in agreement with the mass of 0.762 ± 0.038 found by Demory et al. (2009) using the interferometric radius and mass-luminosity relationship from Xia et al. (2008).

Mode amplitude variation with the activity cycle
We see indications of a difference between the mode amplitudes observed in the HARPS and UVES time series (see Table 2).This is not surprising as the two time series are separated by a time period of a decade, and the mode amplitudes in the Sun are known to vary over its 11-yr activity cycle (Chaplin et al. 2000;Kjeldsen et al. 2008;Kim & Chang 2022).
In fact, making use of 4293 HARPS archival data obtained for ε Indi A between 2003 and A(ℓ = 0 at peak) UVES 3.1 ± 0.9 cm/s HARPS 3.6 ± 0.7 cm/s Combined 3.4 ± 0.6 cm/s 2016, binned to 112 nights, we can place our observations in the context of the activity cycle of ε Indi A. From the HARPS archival data, we obtained the log R ′ HK values (following Gomes da Silva et al. 2018Silva et al. , 2021) ) and used those to model the activity cycle of ε Indi A. Figure 3 shows the variation of log R ′ HK phase-folded onto the estimated cycle period of ∼ 2600 days.The scatter of the HARPS observations about the sinusoidal model is caused by rotational activity variations.
As can be seen from the figure, we happened to observe ε Indi A both near the minimum (HARPS) and near the maximum (UVES) of activity.The difference between our two measurements of the oscillation amplitude is only marginally significant (Table 2) but it is noteworthy that it is consistent with expectations of an inverse correlation with activity.

CONCLUSIONS
We have detected solar-like oscillations in the K5 dwarf ε Indi A. Our measured value of ν max of 5265 ± 110 µHz is the highest so far found for solar-like oscillations, surpassing Kepler-444 (K0 V; 4540 µHz; Campante et al. 2015), τ Ceti (G8 V; 4490 µHz; Teixeira et al. 2009) and α Cen B (K1 V; 4090 µHz; Kjeldsen et al. 2005).Combining this detection with a known distance and angular diameter, we estimate the mass of ε Indi A to be 0.782 ± 0.023 M ⊙ , in agreement with literature values.In addition, we see indications of the expected inverse correlation between the activity cycle and the observed mode amplitudes.This result paves the way for detections of solar-like oscillations in more earlyto-mid K-dwarfs.

Figure 1 .
Figure 1.Radial velocity time series of ε Indi A from HARPS (August 2011) and UVES (August 2021).The orange points show the smoothed uncertainties that were measured from the scatter and used for weights when calculating the power spectra (see Sec. 3.1).

Figure 2 .
Figure2.Power spectra of ε Indi A from HARPS (top), UVES (middle), and the combined data (bottom; note the different vertical scale).In each panel, the blue curve is the power spectrum smoothed over a width of 2 µHz, the orange curve is smoothed by a width of 800 µHz, and the green curve shows the power excess after subtracting the noise (expanded vertically by a factor of 20 for visibility).

Figure 3 .
Figure 3. Phase-folded activity cycle of ε Indi A from log R ′HK .The black dots show the HARPS observations with our seismic campaign marked in yellow (error bar given by the standard deviation of the observations taken during the campaign).The red dotted line indicates the time of our UVES seismic observations, where the Ca-II H&K lines were not measured, and the solid black line represent a simple sinusoidal variation of log R ′ HK with a period of 2600 days.

Table 2 .
Frequency of maximum oscillation power (ν max ) and amplitudes of the central ℓ = 0 mode of ε Indi A (corrected for apodization).