Constraining the asteroseismic scaling relations with interferometric measurements from the CHARA Array

Introduction Scaling relations are fundamental to determine the radius and mass of stars with asteroseismology. However, recent studies have shown that those relations tend to break down at high radius when compared to other measurements such as dynamical radii (Gaulme et al. 2016) or fundamental radii (Zinn et al. 2019). We need independent measurement methods in order to understand and correct those failings. In this work, we have the objective to strengthen the asteroseismic scaling relations by the use of interferometric radius measurements. For this, we are presenting a comparison between the stellar Radius that was measured from asteroseismology and interferometry for 15 stars: 5 main-sequence and 10 red giants (Fig 1). Method We are using the first results of the new SPICA (Stellar Parameters and Images with a Cophased Array, Mourard et al. 2022) beam combiner in R-band situated at the CHARA Array for the interferometric observations. Simultaneously, we also took data from the two infrared beam combiner at CHARA Array: MIRCX (Anugu et al. 2020) in H-band and MYSTIC (Setterholm et al. 2023) in K-band. The interferometric Radius was obtained with the interferometric observations fit (Fig 2) and Gaia parallax. The asteroseismic observations were taken from previous data treatment based on the Kepler (Guzik et al. 2016), K2 (Pope et al. 2019, Schofield et al. 2019) and TESS (Hon et al. 2022) observations as well as ground-based radial velocity observations for 2 stars (Teixeira et al. 2009, Grundahl et al. 2017). Results We present the first results of the CHARA Array on three bands (R, H and K) and compare them to the results from asteroseismic observations. We found that, at first approximation, the radius from the two approaches give similar results within the 1-σ uncertainties (Fig 4), even at high Radius (> 20 R☉). However, descrepancies are still present between the visible R band and the results in H and K bands (Fig 3) and between the asteroseismic results and the R band. That is certainly due to the fact that SPICA is currently still in test phase. We also found some descrepancies between H, K band interferometric radius and asteroseismic radius, probably due to the quality of asteroseismic data, the higher discrepancies being with K2 targets but it stays in the 2-σ error bars. Conclusion We present here the biggest sample comparing asteroseismic and interferometric radius estimation. Our results show that both measurements are consistent with each other, most descrepancies can be attributed to lowquality asteroseismic data or peculiar objects. This work point towards the reliability of scaling relations even at high Radius but need to be confirmed by further observations. Finally, these results show the potentiality of the SPICA instrument, allowing precise measurements even for small objects. Constraining the asteroseismic scaling relations with interferometric measurements from the CHARA Array M. Vrard1, D. Mourard1, O. Creevey1, S. Deheuvels2 & ISSP team Interferometry confirms asteroseismic scaling relations -We present the current results of the interferometric survey of asteroseismic targets with the Interferometry Survey of Stellar Parameters (ISSP) -15 stars with asteroseismic data were observed during 2023 and 2024 with the SPICA, MIRCX and MYSTIC instruments at the CHARA interferometer -Our results show statistically good agreement with asteroseismic radii, allowing to say that scaling relations are reliable with the precision of our measurements -As SPICA is operating in the visible, the identified difficulties of CHARA (adaptive optics and delay lines) for 2023 and 2024 lead to a lower quality level for these data. We expect much better results in 2025, as already demonstrated by the first observations. -The dispersion of the results are mostly coming from low-quality asteroseismic data, like K2 data, at the exception of HD185395 that has Kepler data -The interferometric survey will continue during the following year, we plan to observe a few supplementary dozen targets Figure 1: Relative Magnitude in V band as a function of the effective temperature (in K). The red diamonds correspond to stars observed with SPICA, MIRCX and MYSTIC, the black diamonds are the stars that were observed with MIRCX and MYSTIC only. In total, we observed 5 mainsequence and 10 red giant targets. Some of those stars were observed several times. Figure 2: Squared visibilities for the star HD161797 (red dots) from the interferometric observations that was obtained during the night of the 4th of July 2024 with the MYSTIC instrument (top) and the SPICA instrument (bottom). The blue line correspond to an angular diameter (θ) fit with root-squared LD and fixed Claret coefficients. Figure 3: MYSTIC (infrared) interferometric radius as a function of the SPICA (visible) interferometric Radius for the 7 stars with exploitable SPICA data. The SPICA results have larger uncertainties due to noisier visibilities. This noise comes from problems in the CHARA infrastructure (adaptative optics and delay lines) that were resolved in 2025. The next batch of data are not exhibiting this behavior. We have a good agreement between the different interferometric measurements even if 2 SPICA fit had to take into account MIRCX/MYSTIC results. Figure 4: Asteroseismic radius as a function of MIRCX (infrared) interferometric Radius. The blue points correspond to stars with K2 asteroseismic data. The agreement between the two sets of data is very good. Most of the dispersion can be explained by the low quality of asteroseismic data, like with K2 data. The only exception is the star HD185395 that were already identified as a possible binary (White et al. 2013). Key points Anugu et al. 2020, Aj, 160, 158 Gaulme et al. 2016, ApJ, 832, 121 Grundahl et al. 2017, ApJ, 836, 142 Guzik et al. 2016, ApJ, 831, 17 Hon et al. 2022, Aj, 164, 135 Mourard et al. 2022, Optical and Infrared Interferometry and Imaging VIII, 1218308 Pope et al. 2019, ApJs, 245, 8 References: 1: Université Côte d'Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France 2: IRAP, Université de Toulouse, CNRS, CNES, UPS, 14 avenue Edouard Belin, 31400 Toulouse, France e-mail: [email protected] MIRCX/MYSTIC observations only SPICA + MIRCX/MYSTIC observations θ = 1.929+/-0.010 mas Stars with K2 data Stars with other asteroseismic observations HD185395 Schofield et al. 2019, ApJs, 241, 12 Setterholm et al. 2023, JATIS, 9, 025006 Teixeira et al. 2009, A&A, 494, 237-242 Zinn et al. 2019, ApJ, 885, 166 θ = 1.797+/-0.053 mas