A Dataset for Exploring Stellar Activity in Astrometric Measurements from SDO Images of the Sun

We present a dataset for investigating the impact of stellar activity on astrometric measurements using NASA's Solar Dynamics Observatory (SDO) images of the Sun. The sensitivity of astrometry for detecting exoplanets is limited by stellar activity (e.g. starspots), which causes the measured"center of flux"of the star to deviate from the true, geometric, center, producing false positive detections. We analyze Helioseismic and Magnetic Imager continuum image data obtained from SDO between July 2015 and December 2022 to examine this"astrometric jitter"phenomenon for the Sun. We employ data processing procedures to clean the images and compute the time series of the sunspot-induced shift between the center of flux and the geometric center. The resulting time series show quasiperiodic variations up to 0.05% of the Sun's radius at its rotation period.


INTRODUCTION
Astrometric planet detection relies on measuring the location of stars in the sky and searching for wobbles due to the gravitational pull of a planet.The ongoing Gaia mission is expected to detect thousands of exoplanets using astrometry (Perryman et al. 2014;Yahalomi et al. 2023), and several proposed missions hope to launch in the coming decades (The Theia Collaboration et al. 2017;Ji et al. 2022).Due to high precision requirements, small perturbations in the measurement may lead to false-positive detections, such as those caused by stellar activity in the form of starspots.Starspots cause the star's flux-based measured position to shift from its geometric center, and will also move with the star's surface as it rotates, creating a quasi-periodic pseudo-wobble motion (e.g.Eriksson & Lindegren 2007;Morris et al. 2018;Shapiro et al. 2021;Sowmya et al. 2021;Kaplan-Lipkin et al. 2022;Sowmya et al. 2022) called "astrometric jitter".We measure this phenomenon for the Sun using the HMI continuum image data from NASA's SDO satellite, which covers a small range of wavelengths near the 6173 Å Fe I line.We computed the time series of the shift between the Sun's center of flux and its geometric center due to sunspots in data from July 2015 to December 2022.

METHODS
To measure the Sun's center of flux and geometric center from SDO images, we took the following steps: • We downloaded the HMI Continuum images of the Sun, taken at 12:00 AM UTC daily from 1 July 2015 to 31 December 2022, in fits files from the SDO archive using sunpy.net.Fido (The SunPy Community et al. 2020).
• To compute the geometric center of the Sun, we modeled the solar images by calculating the radial intensity profile, I(r), of the Sun's disk as a function of the distance, r, from its geometric center using the following function: where I 0 represents the central intensity, R is the disk radius, u 1 and u 2 are linear and quadratic limb darkening coefficients, µ ≡ 1 − r 2 R 2 , k is the background intensity, s is a "smear" coefficient, and m is a "slope" coefficient.All length parameters are in pixels.The function was initially computed in steps of 1 pixel in the first part, s pixels in the second part, and 10 pixels in the third part.
We then calculated r of each pixel and used scipy.interpolate.interp1d(Virtanen et al. 2020) to interpolate the function over these distances.This produced a simulated image of the Sun with an intensity profile and center location defined by inputs to our function.
We performed a fit to this intensity profile, the Sun's radius, and the Sun's geometric center coordinates in each image, using mpfit (Markwardt 2009 1 ).First, we fitted the function to an entire image, minimizing the residual I image − I model .From this fit, we measured u 1 = 0.74 and u 2 = 0.34.Then, for every other image, we minimized the residual over the range 0.95R ≤ r ≤ 1.05R, holding limb darkening parameters fixed at those values, but varying other parameters (center coordinates x fit and y fit , R, I 0 , k, s, and m).We evaluated each fit by visual inspection.
• Next, we measured the "center of flux" -a good proxy for the location measured by telescopes like Gaia.However, we needed to perform additional steps to "clean" the images of artifacts as follows: ) arXiv:2310.12196v1 [astro-ph.SR] 18 Oct 2023

Figure 1 .
Figure 1.a) Time series of xcen −x fit as a percentage of rsun b) Time series of ycen −y fit as a percentage of rsun c) Autocorrelation value of xcen − x fit vs Time Lag d) Autocorrelation value of ycen − y fit vs Time Lag. Red vertical lines in c) and d) indicate the Sun's Carrington rotation period of 27.2753 days.