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Dynamics of photospheric magnetic flux distribution and variations in solar RVs -- a study using HARPS-N solar and SDO observations
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Abstract
The distribution and evolution of photospheric magnetic field in sunspots, plages and network, and variations in their relative flux content, play key roles in radial velocity (RV) fluctuations observed in Sun-as-a-star spectra. Differentiating and disentangling such magnetic contributions to RVs help in building models to account for stellar activity signals in high precision RV exoplanet searches. In this work, as earlier authors, we employ high-resolution images of the solar magnetic field and continuum intensities from SDO/HMI to understand the activity contributions to RVs from HARPS-N solar observations. Using well observed physical relationships between strengths and fluxes of photospheric magnetic fields, we show that the strong fields (spots, plages and network) and the weak internetwork fields leave distinguishing features in their contributions to the RV variability. We also find that the fill-factors and average unsigned magnetic fluxes of different features correlate differently with the RVs and hence warrant care in employing either of them as a proxy for RV variations. In addition, we examine disk averaged UV intensities at 1600 \r{A} and 1700 \r{A} wavelength bands imaged by SDO/AIA and their performances as proxies for variations in different magnetic features. We find that the UV intensities provide a better measure of contributions of plage fields to RVs than the Ca II H-K emission indices, especially during high activity levels when the latter tend to saturate.
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In this article we review small-scale dynamo processes that are responsible for magnetic field generation on scales comparable to and smaller than the energy carrying scales of turbulence. We provide a review of critical observation of quiet Sun magnetism, which have provided strong support for the operation of a small-scale dynamo in the solar photosphere and convection zone. After a review of basic concepts we focus on numerical studies of kinematic growth and non-linear saturation in idealized setups, with special emphasis on the role of the magnetic Prandtl number for dynamo onset and saturation. Moving towards astrophysical applications we review convective dynamo setups that focus on the deep convection zone and the photospheres of solar-like stars. We review the critical ingredients for stellar convection setups and discuss their application to the Sun and solar-like stars including comparison against available observations.
Magnetic fields on small scales are ubiquitous in the Universe. Although they can often be observed in detail, their generation mechanisms are not fully understood. One possibility is the so-called small-scale dynamo (SSD). Prevailing numerical evidence, however, appears to indicate that an SSD is unlikely to exist at very low magnetic Prandtl numbers (PrM) such as those that are present in the Sun and other cool stars. Here we have performed high-resolution simulations of isothermal forced turbulence using the lowest PrM values achieved so far. Contrary to earlier findings, the SSD not only turns out to be possible for PrM down to 0.0031 but also becomes increasingly easier to excite for PrM below about 0.05. We relate this behaviour to the known hydrodynamic phenomenon referred to as the bottleneck effect. Extrapolating our results to solar values of PrM indicates that an SSD would be possible under such conditions.
Future direct imaging missions similar to the HabEx and LUVOIR mission concepts aim to catalog and characterize Earth-mass analogs around nearby stars. The exoplanet yield of these missions will be dependent on the frequency of Earth-like planets, and potentially the a priori knowledge of which stars specifically host suitable planetary systems. Ground- or space-based radial velocity surveys can potentially perform the pre-selection of targets and assist in the optimization of observation times, as opposed to an uninformed direct imaging survey. In this paper, we present our framework for simulating future radial velocity surveys of nearby stars in support of direct imaging missions. We generate lists of exposure times, observation time-series, and radial velocity time-series given a direct imaging target list. We generate simulated surveys for a proposed set of telescopes and precise radial velocity spectrographs spanning a set of plausible global-network architectures that may be considered for next-generation extremely precise radial velocity surveys. We also develop figures of merit for observation frequency and planet detection sensitivity, and compare these across architectures. From these, we draw conclusions, given our stated assumptions and caveats, to optimize the yield of future radial velocity surveys supporting direct imaging missions. We find that all of our considered surveys obtain sufficient numbers of precise observations to meet the minimum theoretical white noise detection sensitivity for Earth-mass habitable-zone planets. While our detection rates and mass-sensitivity are optimistic, we have margin to explore systematic effects due to stellar activity and correlated noise in future work.
Characterizing the masses and orbits of near-Earth-mass planets is crucial for interpreting observations from future direct imaging missions (e.g., HabEx, LUVOIR). Therefore, the Exoplanet Science Strategy report recommended further research so future extremely precise radial velocity surveys could contribute to the discovery and/or characterization of near-Earth-mass planets in the habitable zones of nearby stars prior to the launch of these future imaging missions. Newman et al. (2023) simulated such 10 yr surveys under various telescope architectures, demonstrating they can precisely measure the masses of potentially habitable Earth-mass planets in the absence of stellar variability. Here, we investigate the effect of stellar variability on the signal-to-noise ratio (S/N) of the planet mass measurements in these simulations. We find that correlated noise due to active regions has the largest effect on the observed mass S/N, reducing the S/N by a factor of ∼5.5 relative to the no-variability scenario; granulation reduces by a factor of ∼3, while p-mode oscillations has little impact on the proposed survey strategies. We show that in the presence of correlated noise, 5 cm s ⁻¹ instrumental precision offers little improvement over 10 cm s ⁻¹ precision, highlighting the need to mitigate astrophysical variability. With our noise models, extending the survey to 15 yr doubles the number of Earth-analogs with mass S/N > 10, and reaching this threshold for any Earth-analog orbiting a star >0.76 M ⊙ in a 10 yr survey would require an increase in the number of observations per star from that in Newman et al. (2023).
A major obstacle to detecting and characterizing long-period, low-mass exoplanets is the intrinsic radial-velocity (RV) variability of host stars. To better understand RV variability, we estimate disk-averaged RV variations of the Sun over its magnetic cycle, from the Fe i line observed by SDO/HMI, using a physical model for rotationally modulated magnetic activity that was previously validated against HARPS-N solar observations. We estimate the unsigned magnetic flux and show that a linear fit to it reduces the rms of RV variations by 62%, i.e., a factor of 2.6. We additionally apply the FF ′ method, which predicts RV variations based on a star’s photometric variations. At cycle maximum, we find that additional processes must be at play beyond suppression of convective blueshift and velocity imbalances resulting from brightness inhomogeneities, in agreement with recent studies of RV variations. By modeling RV variations over the magnetic cycle using a linear fit to the unsigned magnetic flux, we recover injected planets at a period of ≈300 days with RV semi-amplitudes down to 0.3 m s ⁻¹ . To reach 0.1 m s ⁻¹ , we will need to identify and model additional phenomena that are not well traced by ∣ B ˆ obs ∣ or FF ′. This study motivates ongoing and future efforts to develop observation and analysis techniques to measure the unsigned magnetic flux at high precision in slowly rotating, relatively inactive stars like the Sun. We conclude that the unsigned magnetic flux is an excellent proxy for rotationally modulated, activity-induced RV variations, and could become key to confirming and characterizing Earth analogs.
Context. While the longitudinal field that dominates in photospheric network regions has been studied extensively, small-scale transverse fields have recently been found to be ubiquitous in the quiet internetwork photosphere and this merits further study. Furthermore, few observations have been able to capture how this field evolves.
Aims. We aim to statistically characterize the magnetic vector in a quiet Sun internetwork region and observe the temporal evolution of specific small-scale magnetic features.
Methods. We present two high spatio-temporal resolution observations that reveal the dynamics of two disk-centre internetwork regions taken by the new GREGOR Infrared Spectrograph Integral Field Unit with the highly magnetically sensitive photospheric Fe I line pair at 15648.52 Å and 15652.87 Å. We record the full Stokes vector and apply inversions with the Stokes inversions based on response functions code to retrieve the parameters characterizing the atmosphere. We consider two inversion schemes: scheme 1 (S1), where a magnetic atmosphere is embedded in a field free medium, and scheme 2 (S2), with two magnetic models and a fixed 30% stray light component.
Results. The magnetic properties produced from S1 inversions returned a median magnetic field strength of 200 and 240 G for the two datasets, respectively. We consider the median transverse (horizontal) component, among pixels with Stokes Q or U , and the median unsigned longitudinal (vertical) component, among pixels with Stokes V , above a noise threshold. We determined the former to be 263 G and 267 G, and the latter to be 131 G and 145 G, for the two datasets, respectively. Finally, we present three regions of interest, tracking the dynamics of small-scale magnetic features. We apply S1 and S2 inversions to specific profiles of interest and find that the latter produces better approximations when there is evidence of mixed polarities. We find patches of linear polarization with magnetic flux density of the order of 130−150 G and find that linear polarization appears preferentially at granule-intergranular lane boundaries. The weak magnetic field appears to be organized in terms of complex ‘loop-like’ structures, with transverse fields often flanked by opposite polarity longitudinal fields.
Context. Polar magnetic fields play a key role in the solar magnetic cycle and they are the source of a significant portion of the interplanetary magnetic field. However, observations of the poles are challenging and hence our understanding of the polar magnetic environment is incomplete.
Aims. We deduce properties of small-scale magnetic features in the polar region using high-resolution data and specifically aim to determine the flux per patch above which one magnetic polarity starts to dominate over the other.
Methods. We study the high spatial resolution, seeing-free observations of the north solar polar region, obtained with the IMaX instrument on-board the balloon-borne S UNRISE observatory during June 2009, at the solar activity minimum. We performed inversions of the full Stokes vector recorded by IMaX to retrieve atmospheric parameters of the Sun’s polar region, mainly the temperature stratification and the magnetic field vector.
Results. We infer kilo-Gauss (kG) magnetic fields in patches harbouring polar faculae, without resorting to a magnetic filling factor. Within these patches we find the maxima of the magnetic field to be near the dark narrow lanes, which are shifted towards the disc centre side in comparison to the maxima in continuum intensity. In contrast, we did not find any fields parallel to the solar surface with kG strengths. In addition to the kG patches, we found the polar region to be covered in patches of both polarities, which have a range of sizes. We find the field strength of these patches to increase with increasing size and flux, with the smaller patches showing a significant dispersion in field strength. The dominating polarity of the north pole during this phase of the solar cycle is found to be maintained by the larger patches with fluxes above 2.3 × 10 ¹⁷ Mx.
Context. How global faculae and network coverage relates to that of sunspots is relevant to the brightness variations of the Sun and Sun-like stars.
Aims. We aim to extend and improve on earlier studies that established that the facular-to-sunspot-area ratio diminishes with total sunspot coverage.
Methods. Chromospheric indices and the total magnetic flux enclosed in network and faculae, referred to here as “facular indices”, are modulated by the amount of facular and network present. We probed the relationship between various facular and sunspot indices through an empirical model, taking into account how active regions evolve and the possible non-linear relationship between plage emission, facular magnetic flux, and sunspot area. This model was incorporated into a model of total solar irradiance (TSI) to elucidate the implications for solar and stellar brightness variations.
Results. The reconstruction of the facular indices from the sunspot indices with the model presented here replicates most of the observed variability, and is better at doing so than earlier models. Contrary to recent studies, we found the relationship between the facular and sunspot indices to be stable over the past four decades. The model indicates that, like the facular-to-sunspot-area ratio, the ratio of the variation in chromospheric emission and total network and facular magnetic flux to sunspot area decreases with the latter. The TSI model indicates the ratio of the TSI excess from faculae and network to the deficit from sunspots also declines with sunspot area, with the consequence being that TSI rises with sunspot area more slowly than if the two quantities were linearly proportional to one another. This explains why even though solar cycle 23 is significantly weaker than cycle 22, TSI rose to comparable levels over both cycles. The extrapolation of the TSI model to higher activity levels indicates that in the activity range where Sun-like stars are observed to switch from growing brighter with increasing activity to becoming dimmer instead, the activity-dependence of TSI exhibits a similar transition. This happens as sunspot darkening starts to rise more rapidly with activity than facular and network brightening. This bolsters the interpretation of this behaviour of Sun-like stars as the transition from a faculae-dominated to a spot-dominated regime.
Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. As a key to understanding stellar dynamos, empirical relations between stellar parameters and magnetic fields are required for comparison to ab initio predictions from dynamo models. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15 000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, ⟨ B ⟩, and Rossby number, Ro , resembling the well-studied rotation–activity relation. Among the slowly rotating stars, we find that magnetic flux, Φ B , is proportional to rotation period, P , and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric H α and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation–activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of ⟨ B ⟩≈800 G while H α and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.
The time-variable velocity fields of solar-type stars limit the precision of radial-velocity determinations of their planets’ masses, obstructing detection of Earth twins. Since 2015 July, we have been monitoring disc-integrated sunlight in daytime using a purpose-built solar telescope and fibre feed to the HARPS-N stellar radial-velocity spectrometer. We present and analyse the solar radial-velocity measurements and cross-correlation function (CCF) parameters obtained in the first 3 yr of observation, interpreting them in the context of spatially resolved solar observations. We describe a Bayesian mixture-model approach to automated data-quality monitoring. We provide dynamical and daily differential-extinction corrections to place the radial velocities in the heliocentric reference frame, and the CCF shape parameters in the sidereal frame. We achieve a photon-noise-limited radial-velocity precision better than 0.43 m s−1 per 5-min observation. The day-to-day precision is limited by zero-point calibration uncertainty with an RMS scatter of about 0.4 m s−1. We find significant signals from granulation and solar activity. Within a day, granulation noise dominates, with an amplitude of about 0.4 m s−1 and an autocorrelation half-life of 15 min. On longer time-scales, activity dominates. Sunspot groups broaden the CCF as they cross the solar disc. Facular regions temporarily reduce the intrinsic asymmetry of the CCF. The radial-velocity increase that accompanies an active-region passage has a typical amplitude of 5 m s−1 and is correlated with the line asymmetry, but leads it by 3 d. Spectral line-shape variability thus shows promise as a proxy for recovering the true radial velocity.