Equatorially trapped Rossby waves in radiative stars

Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This paper aims to study the theoretical dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near-surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained. The solutions were found to be confined around the equator leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes

Long-period oscillations of active region patterns: least-squares mapping on second-order curves

Active regions (ARs) are the main sources of variety in solar dynamic events. Automated detection and identification tools need to be developed for solar features for a deeper understanding of the solar cycle. Of particular interest here are the dynamical properties of the ARs, regardless of their internal structure and sunspot distribution. We studied the oscillatory dynamics of two ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern recognition. We developed a novel method of automated AR border detection and compared it to an existing method for the proof-of-concept. The first method uses least-squares fitting on the smallest ellipse enclosing the AR, while the second method applies regression on the convex hull.} After processing the data, we found that the axes and the inclination angle of the ellipse and the convex hull oscillate in time. These oscillations are interpreted as the second harmonic of the standing long-period kink oscillations (with the node at the apex) of the magnetic flux tube connecting the two main sunspots of the ARs. In both ARs we have estimated the distribution of the phase speed magnitude along the magnetic tubes (along the two main spots) by interpreting the obtained oscillation of the inclination angle as the standing second harmonic kink mode. After comparing the obtained results for fast and slow kink modes, we conclude that both of these modes are good candidates to explain the observed oscillations of the AR inclination angles, as in the high plasma $\beta$ regime the phase speeds of these modes are comparable and on the order of the Alfv\'{e}n speed. Based on the properties of the observed oscillations, we detected the appropriate depth of the sunspot patterns, which coincides with estimations made by helioseismic methods. The latter analysis can be used as a basis for developing a magneto-seismological tool for ARs.Comment: 10 pages, 6 figures, Accepted for publication in A&

Rieger-type cycles on the solar-like star KIC 2852336

Context. A Rieger-type periodicity of 150–180 days (six to seven times the solar rotation period) has been observed in the Sun’s magnetic activity and is probably connected with the internal dynamo layer. Observations of Rieger cycles in other solar-like stars may give us information about the dynamo action throughout stellar evolution. Aims. We aim to use the Sun as a star analogue to find Rieger cycles on other solar-like stars using Kepler data. Methods. We analyse the light curve of the Sun-like star KIC 2852336 (with a rotation period of 9.5 days) using wavelet and generalised Lomb-Scargle methods to find periodicities over rotation and Rieger timescales. Results. Besides the rotation period of 9.5 days, the power spectrum shows a pronounced peak at a period of 61 days (about six times the stellar rotation period) and a less pronounced peak at 40–44 days. These two periods may correspond to Rieger-type cycles and can be explained by the harmonics of magneto-Rossby waves in the stellar dynamo layer. The observed periods and theoretical properties of magneto-Rossby waves lead to the estimation of the dynamo magnetic field strength of 40 kG inside the star. Conclusions. Rieger-type cycles can be used to probe the dynamo magnetic field in solar-type stars at different phases of evolution. Comparing the rotation period and estimated dynamo field strength of the star KIC 2852336 with the corresponding solar values, we conclude that the ratio Ω/BD, where Ω is the angular velocity and BD is the dynamo magnetic field, is the same for the star and the Sun. Therefore, the ratio can be conserved during stellar evolution, which is consistent with earlier observations that younger stars are more active

Rieger-type periodicity in the total irradiance of the Sun as a star during solar cycles 23-24

Context. Total solar irradiance allows for the use of the Sun as a star for studying observations of stellar light curves from recent space missions. Aims. We aim to study how the mid-range periodicity observed in solar activity indices influences the total solar irradiance. Methods. We studied periodic variations of total solar irradiance based on SATIRE-S and SOHO/VIRGO data during solar cycles 23–24 on timescales of Rieger-type periodicity. Then we compared the power spectrum of oscillations in the total solar irradiance to those of sunspot and faculae data to determine their contributions. Results. Wavelet analyses of TSI data reveal strong peaks at 180 days and 115 days in cycle 23, while cycle 24 showed periods of 170 days and 145 days. There are several periods in the sunspot and faculae data that are not seen in total solar irradiance as they probably cancel each other out through simultaneous brightening (in faculae) and darkening (in sunspots). Rieger-type periodicity is probably caused by magneto-Rossby waves in the internal dynamo layer, where the solar cyclic magnetic field is generated. Therefore, the observed periods in the total solar irradiance and the wave dispersion relation allow us to estimate the dynamo magnetic field strength as 10–15 kG. Conclusions. Total solar irradiance can be used to estimate the magnetic field strength in the dynamo layer. This tool can be of importance in estimating the dynamo magnetic field strength of solar-like stars using light curves obtained by space missions

Rossby Waves in Astrophysics

Rossby waves are a pervasive feature of the large-scale motions of the Earth's atmosphere and oceans. These waves (also known as planetary waves and r-modes) also play an important role in the large-scale dynamics of different astrophysical objects such as the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and exoplanetary atmospheres. This paper provides a review of theoretical and observational aspects of Rossby waves on different spatial and temporal scales in various astrophysical settings. The physical role played by Rossby-type waves and associated instabilities is discussed in the context of solar and stellar magnetic activity, angular momentum transport in astrophysical discs, planet formation, and other astrophysical processes. Possible directions of future research in theoretical and observational aspects of astrophysical Rossby waves are outlined