Chromospheric Radiative Losses Research Articles

Phase Mixing of Propagating Alfvén Waves in a Single-fluid Partially Ionized Solar Plasma

The phase mixing of Alfvén waves is one of the most promising mechanisms for the heating of the solar atmosphere. The damping of waves in this case requires small transversal scales, relative to the magnetic field direction; this requirement is achieved by considering a transversal inhomogeneity in the equilibrium plasma density profile. Using a single-fluid approximation of a partially ionized chromospheric plasma, we study the effectiveness of the damping of phase-mixed shear Alfvén waves and investigate the effect of varying the ionization degree on the dissipation of waves. Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionization degree of the plasma, but more importantly, in a partially ionized plasma, the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case of a fully ionized plasma, providing evidence that phase mixing could be a large contributor to heating the solar chromosphere. The effectiveness of phase mixing is investigated for various ionization degrees, ranging from very weakly to very strongly ionized plasmas. Our results show that phase-mixed propagating Alfvén waves in a partially ionized plasma with ionization degrees in the range μ = 0.518–0.657, corresponding to heights of 1916–2150 km above the solar surface, can provide sufficient heating to balance chromospheric radiative losses in the quiet Sun.

An evaluation of different recipes for chromospheric radiative losses in solar flares

Context. Radiative losses are an indispensable part of the numerical simulation of flares. Detailed calculations could be computationally expensive, especially in the chromosphere. There have been some approximate recipes for chromospheric radiative losses in flares, yet their feasibility in flare simulations needs further evaluation. Aims We aim to evaluate the performance of different recipes for chromospheric radiative losses in flare simulations. Methods. We compared the atmospheric structure and the line profiles in beam-heated flares calculated with detailed radiative losses and the approximate recipes. Results. Both the Gan & Fang (1990, ApJ, 358, 328; hereafter GF90) and Hong, J., et al. (2022, A&A, 661, A77) recipes provide acceptable total radiative losses compared with the detailed treatment, but there are discrepancies in the different atmospheric layers during the different evolutionary phases, which lead to misestimations of temperature and line intensity. The recipe of GF90 overestimates the coolings in the upper chromosphere greatly when the temperature exceeds 105 K, which also affects the flare evolution and the line asymmetries. Radiative heating in the middle chromosphere only functions in the initial stage and could be safely neglected. However, radiative heating from the Lyman continuum could dominate near the transition region.

Spatio-temporal analysis of chromospheric heating in a plage region

Context. Our knowledge of the heating mechanisms that are at work in the chromosphere of plage regions remains highly unconstrained from observational studies. While many heating candidates have been proposed in theoretical studies, the exact contribution from each of them is still unknown. The problem is rather difficult because there is no direct way of estimating the heating terms from chromospheric observations. Aims. The purpose of our study is to estimate the chromospheric heating terms from a multi-line high-spatial-resolution plage dataset, characterize their spatio-temporal distribution and set constraints on the heating processes that are at work in the chromosphere. Methods. We used nonlocal thermodynamical equilibrium inversions in order to infer a model of the photosphere and chromosphere of a plage dataset acquired with the Swedish 1-m Solar Telescope (SST). We used this model atmosphere to calculate the chromospheric radiative losses from the main chromospheric cooler from H I, Ca II, and Mg II atoms. In this study, we approximate the chromospheric heating terms by the net radiative losses predicted by the inverted model. In order to make the analysis of time-series over a large field of view computationally tractable, we made use of a neural network which is trained from the inverted models of two non-consecutive time-steps. We have divided the chromosphere in three regions (lower, middle, and upper) and analyzed how the distribution of the radiative losses is correlated with the physical parameters of the model. Results. In the lower chromosphere, the contribution from the Ca II lines is dominant and predominantly located in the surroundings of the photospheric footpoints. In the upper chromosphere, the H I contribution is dominant. Radiative losses in the upper chromosphere form a relatively homogeneous patch that covers the entire plage region. The Mg II also peaks in the upper chromosphere. Our time analysis shows that in all pixels, the net radiative losses can be split in a periodic component with an average amplitude of amp̅Q = 7.6 kW m−2 and a static (or very slowly evolving) component with a mean value of −26.1 kW m−2. The period of the modulation present in the net radiative losses matches that of the line-of-sight velocity of the model. Conclusions. Our interpretation is that in the lower chromosphere, the radiative losses are tracing the sharp lower edge of the hot magnetic canopy that is formed above the photosphere, where the electric current is expected to be large. Therefore, Ohmic current dissipation could explain the observed distribution. In the upper chromosphere, both the magnetic field and the distribution of net radiative losses are room-filling and relatively smooth, whereas the amplitude of the periodic component is largest. Our results suggest that acoustic wave heating may be responsible for one-third of the energy deposition in the upper chromosphere, whereas other heating mechanisms must be responsible for the rest: turbulent Alfvén wave dissipation or ambipolar diffusion could be among them. Given the smooth nature of the magnetic field in the upper chromosphere, we are inclined to rule out Ohmic dissipation of current sheets in the upper chromosphere.

An approximate recipe of chromospheric radiative losses for solar flares

Context. Radiative losses in the chromosphere are very important for the energy balance of the Sun. There have been efforts to make simple lookup tables for chromospheric radiative losses in the quiet Sun. During solar flares, the atmospheric conditions are quite different, and the currently available recipe is constructed from semi-empirical models. How these recipes work in flare conditions remains to be evaluated. Aims. We aim to construct an approximate recipe of chromospheric radiative losses for solar flares. Methods. We tabulate the optically thin radiative loss, escape probability, and ionization fraction using a grid of flare models from radiative hydrodynamic simulations as our dataset. Results. We provide new lookup tables to calculate chromospheric radiative losses for flares. Compared with previous recipes, our recipe provides a better approximation of the detailed radiative losses for flares.

IRIS observations of chromospheric heating by acoustic waves in solar quiet and active regions

Aims. To study the heating of solar chromospheric magnetic and nonmagnetic regions by acoustic and magnetoacoustic waves, the deposited acoustic-energy flux derived from observations of strong chromospheric lines is compared with the total integrated radiative losses. Methods. A set of 23 quiet-Sun and weak-plage regions were observed in the Mg II k and h lines with the Interface Region Imaging Spectrograph (IRIS). The deposited acoustic-energy flux was derived from Doppler velocities observed at two different geometrical heights corresponding to the middle and upper chromosphere. A set of scaled nonlocal thermodynamic equilibrium 1D hydrostatic semi-empirical models – obtained by fitting synthetic to observed line profiles – was applied to compute the radiative losses. The characteristics of observed waves were studied by means of a wavelet analysis. Results. Observed waves propagate upward at supersonic speed. In the quiet chromosphere, the deposited acoustic flux is sufficient to balance the radiative losses and maintain the semi-empirical temperatures in the layers under study. In the active-region chromosphere, the comparison shows that the contribution of acoustic-energy flux to the radiative losses is only 10−30%. Conclusions. Acoustic and magnetoacoustic waves play an important role in the chromospheric heating, depositing a main part of their energy in the chromosphere. Acoustic waves compensate for a substantial fraction of the chromospheric radiative losses in quiet regions. In active regions, their contribution is too small to balance the radiative losses and the chromosphere has to be heated by other mechanisms.

An observationally constrained model of strong magnetic reconnection in the solar chromosphere

Context.The evolution of the photospheric magnetic field plays a key role in the energy transport into the chromosphere and the corona. In active regions, newly emerging magnetic flux interacts with the pre-existent magnetic field, which can lead to reconnection events that convert magnetic energy into thermal energy.Aims.We aim to study the heating caused by a strong reconnection event that was triggered by magnetic flux cancelation.Methods.We use imaging and spectropolarimetric data in the Fe I6301& 6302 Å, Ca II8542 Å, and Ca IIK spectral lines obtained with the CRISP and CHROMIS instruments at the Swedish 1-m Solar Telescope. These data were inverted with the STiC code by performing multi-atom, multi-line, non-local thermodynamic equilibrium inversions. These inversions yielded a three-dimensional model of the reconnection event and surrounding atmosphere, including temperature, velocity, microturbulence, magnetic field, and radiative loss rate.Results.The model atmosphere shows the emergence of magnetic loops with a size of several arcseconds into a pre-existing predominantly unipolar field. Where the reconnection region is expected to be, we see an increase in the chromospheric temperature of roughly 2000 K as well as bidirectional flows of the order of 10 km s−1emanating from there. We see bright blobs of roughly 0.2 arcsec in diameter in the Ca IIK, moving at a plane-of-the-sky velocity of the order of 100 km s−1and a blueshift of 100 km s−1, which we interpret as ejected plasmoids from the same region. This scenario is consistent with theoretical reconnection models, and therefore provides evidence of a reconnection event taking place. The chromospheric radiative losses at the reconnection site are as high as 160 kW m−2, providing a quantitative constraint on theoretical models that aim to simulate reconnection caused by flux emergence in the chromosphere.

Transient brightenings in the quiet Sun detected by ALMA at 3 mm

Aims. We investigate transient brightenings, that is, weak, small-scale episodes of energy release, in the quiet solar chromosphere; these episodes can provide insights into the heating mechanism of the outer layers of the solar atmosphere. Methods. Using Atacama Large Millimeter/submillimeter Array (ALMA) observations, we performed the first systematic survey for quiet Sun transient brightenings at 3 mm. Our dataset included images of six 87″ × 87″ fields of view of the quiet Sun obtained with angular resolution of a few arcsec at a cadence of 2 s. The transient brightenings were detected as weak enhancements above the average intensity after we removed the effect of the p-mode oscillations. A similar analysis, over the same fields of view, was performed for simultaneous 304 and 1600 Å data obtained with the Atmospheric Imaging Assembly. Results. We detected 184 3 mm transient brightening events with brightness temperatures from 70 K to more than 500 K above backgrounds of ∼7200 − 7450 K. All events showed light curves with a gradual rise and fall, strongly suggesting a thermal origin. Their mean duration and maximum area were 51.1 s and 12.3 Mm2, respectively, with a weak preference of appearing at network boundaries rather than in cell interiors. Both parameters exhibited power-law behavior with indices of 2.35 and 2.71, respectively. Only a small fraction of ALMA events had either 304 or 1600 Å counterparts but the properties of these events were not significantly different from those of the general population except that they lacked their low-end energy values. The total thermal energies of the ALMA transient brightenings were between 1.5 × 1024 and 9.9 × 1025 erg and their frequency distribution versus energy was a power law with an index of 1.67 ± 0.05. We found that the power per unit area provided by the ALMA events could account for only 1% of the chromospheric radiative losses (10% of the coronal ones). Conclusions. We were able to detect, for the first time, a significant number of weak 3 mm quiet Sun transient brightenings. However, their energy budget falls short of meeting the requirements for the heating of the upper layers of the solar atmosphere and this conclusion does not change even if we use the least restrictive criteria possible for the detection of transient brightenings.

Energy Transport and Heating by Torsional Alfvén Waves Propagating from the Photosphere to the Corona in the Quiet Sun

Abstract In the solar atmosphere, Alfvén waves are believed to play an important role in the transfer of energy from the photosphere to the corona and solar wind, and in the heating of the chromosphere. We perform numerical computations to investigate the energy transport and dissipation associated with torsional Alfvén waves propagating in magnetic flux tubes that expand from the photosphere to the corona in quiet-Sun conditions. We place a broadband driver at the photosphere that injects a wave energy flux of 107 erg cm−2 s−1 and consider Ohm’s magnetic diffusion and ion–neutral collisions as dissipation mechanisms. We find that only a small fraction of the driven flux, ∼105 erg cm−2 s−1, is able to reach coronal heights, but it may be sufficient to partly compensate the total coronal energy loss. The frequency of maximal transmittance is ∼5 mHz for a photospheric field strength of 1 kG and is shifted to smaller/larger frequencies for weaker/stronger fields. Lower frequencies are reflected at the transition region, while higher frequencies are dissipated, producing enough heat to balance chromospheric radiative losses. Heating in the low and middle chromosphere is due to Ohmic dissipation, while ion–neutral friction dominates in the high chromosphere. Ohmic diffusion is enhanced by phase mixing because of the expansion of the magnetic field. This effect has the important consequence of increasing the chromospheric dissipation and, therefore, reducing the energy flux that reaches the corona. We provide empirical fits of the transmission coefficient that could be used as input for coronal models.

Chromospheric heating during flux emergence in the solar atmosphere

Context. The radiative losses in the solar chromosphere vary from 4 kW m−2 in the quiet Sun, to 20 kW m−2 in active regions. The mechanisms that transport non-thermal energy to and deposit it in the chromosphere are still not understood. Aim. We aim to investigate the atmospheric structure and heating of the solar chromosphere in an emerging flux region. Methods. We have used observations taken with the CHROMIS and CRISP instruments on the Swedish 1-m Solar Telescope in the Ca II K , Ca II 854.2 nm, Hα, and Fe I 630.1 nm and 630.2 nm lines. We analysed the various line profiles and in addition perform multi-line, multi-species, non-local thermodynamic equilibrium (non-LTE) inversions to estimate the spatial and temporal variation of the chromospheric structure. Results. We investigate which spectral features of Ca II K contribute to the frequency-integrated Ca II K brightness, which we use as a tracer of chromospheric radiative losses. The majority of the radiative losses are not associated with localised high-Ca II K-brightness events, but instead with a more gentle, spatially extended, and persistent heating. The frequency-integrated Ca II K brightness correlates strongly with the total linear polarization in the Ca II 854.2 nm, while the Ca II K profile shapes indicate that the bulk of the radiative losses occur in the lower chromosphere. Non-LTE inversions indicate a transition from heating concentrated around photospheric magnetic elements below log τ500 = −3 to a more space-filling and time-persistent heating above log τ500 = −4. The inferred gas temperature at log τ500 = −3.8 correlates strongly with the total linear polarization in the Ca II 854.2 nm line, suggesting that that the heating rate correlates with the strength of the horizontal magnetic field in the low chromosphere.

Carrington cycle 24: the solar chromospheric emission in a historical and stellar perspective

We present the solar S-index record of cycle 24, obtained by the TIGRE robotic telescope facility and its high-resolution spectrograph HEROS (R$\approx$20,000), which measures the solar chromospheric Ca II H&K line emission by using moonlight. Our calibration process uses the same set of standard stars as introduced by the Mt. Wilson team, thus giving us a direct comparison with their huge body of observations taken between 1966 and 1992, as well as with other cool stars. Carrington cycle 24 activity started from the unusually deep and long minimum 2008/09, with an S-index average of only 0.154, by 0.015 deeper than the one of 1986 (<S>=0.169). In this respect,the chromospheric radiative losses differ remarkably from the variation of the coronal radio flux F10.7cm and the sunspot numbers. In addition, the cycle 24 S-amplitude remained small, 0.022 (cycles 21 and 22 averaged: 0.024), and so resulted a very low 2014 maximum of <S>=0.176 (cycles 21 and 22 averaged: 0.193). We argue that this find is significant, since the Ca II H&K line emission is a good proxy for the solar far-UV flux, which plays an important role in the heating of the Earth's stratosphere, and we further argue that the solar far-UV flux changes change s with solar activity much more strongly than the total solar output.

12 years of stellar activity observations in Argentina

AbstractWe present an observational program we started in 1999, to systematically obtain mid-resolution spectra of late-type stars, to study in particular chromospheric activity. In particular, we found cyclic activity in four dM stars, including Prox-Cen. We directly derived the conversion factor that translates the known S index to flux in the Ca II cores, and extend its calibration to a wider spectral range. We investigated the relation between the activity measurements in the calcium and hydrogen lines, and found that the usual correlation observed is the product of the dependence of each flux on stellar color, and it is not always preserved when simultaneous observations of a particular star are considered. We also used our observations to model the chromospheres of stars of different spectral types and activity levels, and found that the integrated chromospheric radiative losses, normalized to the surface luminosity, show a unique trend for G and K dwarfs when plotted against the S index.

MAGNETOACOUSTIC WAVE ENERGY FROM NUMERICAL SIMULATIONS OF AN OBSERVED SUNSPOT UMBRA

We aim at reproducing the height dependence of sunspot wave signatures obtained from spectropolarimetric observations through 3D MHD numerical simulations. A magneto-static sunspot model based on the properties of the observed sunspot is constructed and perturbed at the photosphere introducing the fluctuations measured with the \SiI\ $\lambda$ 10827 \AA\ line. The results of the simulations are compared with the oscillations observed simultaneously at different heights from the \HeI\ $\lambda$ 10830 \AA\ line, the \CaIIH\ core and the \FeI\ blends in the wings of the \CaIIH\ line. The simulations show a remarkable agreement with the observations. They reproduce the velocity maps and power spectra at the formation heights of the observed lines, as well as the phase and amplification spectra between several pair of lines. We find that the stronger shocks at the chromosphere are accompanied with a delay between the observed signal and the simulated one at the corresponding height, indicating that shocks shift the formation height of the chromospheric lines to higher layers. Since the simulated wave propagation matches very well the properties of the observed one, we are able to use the numerical calculations to quantify the energy contribution of the magneto-acoustic waves to the chromospheric heating in sunspots. Our findings indicate that the energy supplied by these waves is too low to balance the chromospheric radiative losses. The energy contained at the formation height of the lowermost \SiI\ $\lambda$ 10827 \AA\ line in the form of slow magneto-acoustic waves is already insufficient to heat the higher layers, and the acoustic energy which reaches the chromosphere is around 3-9 times lower than the required amount of energy. The contribution of the magnetic energy is even lower.

Heating of solar chromosphere by electromagnetic wave absorption in a plasma slab model

The heating of solar chromospheric internetwork regions by means of the absorption of electromagnetic (EM) waves that originate from the photospheric blackbody radiation is studied in the framework of a plasma slab model. The absorption is provided by the electron-neutral collisions in which electrons oscillate in the EM wave field and electron-neutral collisions damp the EM wave. Given the uncertain nature of the collision cross-section due to the plasma microturbulence, it is shown that for plausible physical parameters, the heating flux produced by the absorption of EM waves in the chromosphere is between 20% and 45% of the chromospheric radiative loss flux requirement. It is also established that there is an optimal value for the collision cross-section, 5×10-18 m2, which produces the maximal heating flux of 1990 W m−2.

The basal chromospheric Mg ii h+k flux of evolved stars: probing the energy dissipation of giant chromospheres

Of a total of 177 cool G, K, and M giants and supergiants, we measured the Mg II h+k line emission of extended chromospheres in high-resolution (LWR) IUE spectra by using the IUE final data archive at STScI, and derived the respective stellar surface fluxes. They represent the chromospheric radiative energy losses presumably related to basal heating by the dissipation of acoustic waves, plus a highly variable contribution due to magnetic activity. Thanks to the large sample size, we find a very well defined lower limit, the basal chromospheric Mg II h+k line flux of cool giant chromospheres, as a function of T_eff. A total of 16 giants were observed several times, over a period of up to 20 years. Their respective minimal Mg II h+k line fluxes confirm the basal flux limit very well because none of their emissions dip beneath the empirically deduced basal flux line representative for the overall sample. Based on a total of 15 to 22 objects with very low Mg II h+k emission, we find as limit: log F_Mg_h+k = 7.33 log T_eff - 21.75 (cgs units; based on B-V). Within its uncertainties, this is almost the same relation as has been found in the past for the geometrically much thinner chromospheres of main sequence stars. Concerning any residual dependence of the basal flux on the surface gravity it can be stated that over a gravity range of more than four orders of magnitude (main-sequence stars to supergiants), the basal flux does not appear to vary by more than a factor of 2. These findings are in good agreement with the predictions by previous hydrodynamic models of acoustic wave propagation and energy dissipation, as well as with earlier empirical determinations. Finally, we discuss the idea that the ample energy flux of the chromospheric acoustic waves in a cool giant may yield, as a by-product, the energy flux required by its cool wind (i.e., non-dust-driven, "Reimers-type" mass-loss).

Reflection and conversion of magnetogravity waves in the solar chromosphere: windows to the upper atmosphere

The detection of upward propagating internal gravity waves at the base of the Sun's chromosphere has recently been reported by Straus et al., who postulated that these may efficiently couple to Alfven waves in magnetic regions. This may be important in transporting energy to higher levels. Here we explore the propagation, reflection and mode conversion of linear gravity waves in a VAL C atmosphere, and find that even weak magnetic fields usually reflect gravity waves back downward as slow magnetoacoustic waves well before they reach the Alfven/acoustic equipartition height at which mode conversion might occur. However, for certain highly inclined magnetic field orientations in which the gravity waves manage to penetrate near or through the equipartition level, there can be substantial conversion to either or both upgoing Alfven and acoustic waves. Wave energy fluxes comparable to the chromospheric radiative losses are expected.

Wave propagation and energy transport in the magnetic network of the Sun

We investigate wave propagation and energy transport in magnetic elements, which are representatives of small scale magnetic flux concentrations in the magnetic network on the Sun. This is a continuation of earlier work by Hasan et al. (2005). The new features in the present investigation include a quantitative evaluation of the energy transport in the various modes and for different field strengths, as well as the effect of the boundary-layer thickness on wave propagation. We carry out 2-D MHD numerical simulations of magnetic flux concentrations for strong and moderate magnetic fields. Waves are excited in the tube and ambient medium by a transverse impulsive motion of the lower boundary. The nature of the modes excited depends on the value of beta. Mode conversion occurs in the moderate field case when the fast mode crosses the beta=1 contour. In the strong field case the fast mode undergoes conversion from predominantly magnetic to predominantly acoustic when waves are leaking from the interior of the flux concentration to the ambient medium. We also estimate the energy fluxes in the acoustic and magnetic modes. The main conclusions of our work are twofold: firstly, for transverse, impulsive excitation, flux tubes/sheets with strong fields are more efficient than those with weak fields in providing acoustic flux to the chromosphere. However, there is insufficient energy in the acoustic flux to balance the chromospheric radiative losses in the network, even for the strong field case. Secondly, the acoustic emission from the interface between the flux concentration and the ambient medium decreases with the width of the boundary layer.

Chromospheric heating by the Farley-Buneman instability

Context. Chromospheric heating produces UV emissions that can only occur in an enhanced electron temperature medium. In the quiet Sun the radiative losses are orders of magnitude larger than those in the much hotter corona. Chromospheric heating mechanisms considered previously (e.g. shock waves and nanoflares) have failed to account for the observed persistency and uniformity of UV lines and continua. Also, resistive magnetic free-energy dissipation is not efficient enough in the highly electrically conductive solar atmosphere. Aims. In this paper we consider plasma effects in the low chromosphere and propose that the Farley-Buneman (hereafter FB) plasma-instability mechanism provides the mechanism for dissipating the energy of convectively driven motions of neutral atoms into chromospheric heating in the Sun and other cool stars that have a partially ionized chromosphere. Methods. Analysis of the ion acoustic sound speed and consideration of recent measurements of magnetic field in the quiet, internetwork, solar low chromosphere are carried out in the context of understanding the characteristics and onset of chromospheric heating. The FB instability is triggered by the cross-field motion of the partially ionized gas at velocities in excess of the ion acoustic velocity. The ions acquire their cross-field velocities through collisions with the much denser chromospheric neutral atoms. Estimates of cross-field velocities are obtained from consideration of both spectral line widths and convection numerical simulations that indicate values from a few to several km s -1 at the top of the practically radiative-equilibrium low chromosphere. Results. The FB instability is triggered by the cross-field motion of the neutral component of the partially ionized gas at velocities in excess of the ion acoustic velocity. This instability occurs in the solar chromosphere because electrons become strongly magnetized just above the photosphere, while heavy ions and protons remain unmagnetized, and only at the very top of the chromosphere do they become magnetized. Conclusions. We find that convective overshoot motions are drivers of the FB instability and provide enough energy to account for the upper chromospheric radiative losses in the quiet-Sun internetwork and network lanes.

The Energy of High-Frequency Waves in the Low Solar Chromosphere

High-frequency acoustic waves have been suggested as a source of mechanical heating in the chromosphere. In this work the radial component of waves in the frequency interval 22 to 1 mHz are investigated. Observations were performed using 2D spectroscopy in the spectral lines of Fe i 543.45 nm and Fe i 543.29 nm at the Vacuum Tower Telescope, Tenerife, Spain. Speckle reconstruction has been applied to the observations. We have used Fourier and wavelet techniques to identify oscillatory power. The energy flux is estimated by assuming that all observed oscillations are acoustic running waves. We find that the estimated energy flux is not sufficient to cover the chromospheric radiative losses.

Mg II chromospheric radiative loss rates in cool active and quiet stars

The Mg  k emission line is a good indicator of the level of chromospheric activity in late-type stars. We investigate the dependence of this activity indicator on fundamental stellar parameters. To this purpose we use IUE observations of the Mg  k line in 225 late-type stars of luminosity classes I-V, with different levels of chromospheric activity. We first re-analyse the relation between Mg  k line luminosity and stellar absolute magnitude, performing linear fits to the points. The ratio of Mg  surface flux to total surface flux is found to be independent of stellar luminosity for evolved stars and to increase with decreasing luminosity for dwarfs. We also analyse the Mg  k line surface flux-metallicity connection. The Mg  k emission level turns out to be not dependent on metallicity. Finally, the Mg  k line surface flux-temperature relation is investigated by treating separately, for the first time, a large sample of very active and normal stars. The stellar surface fluxes in the k line of normal stars are found to be strongly dependent on the temperature and slightly dependent on the gravity, thus confirming the validity of recently proposed models. In contrast, data relative to RS CVn binaries and BY Dra stars, which show very strong chromospheric activity, are not justified in the framework of a description based only on acoustic waves and uniformly distributed magnetic flux tubes so that they require more detailed models.

Evidence for short-period acoustic waves in the solar atmosphere

Short-period acoustic waves are thought to supply the energy for the radiative losses of the non-magnetic chromo- sphere of the Sun and, in general, of late-type stars. Here, we present evidence for the existence of waves in the solar atmosphere with periods in the range of 50 s< P< 100 s. Two-dimensional time sequences with a cadence of 25 s were obtained from quiet Sun disk center in Fei 5434 A. The observations were performed with the Gottingen Fabry-Perot spectrometer in the Vacuum Tower Telescope at the Observatorio del Teide/Tenerife. They are subjected to speckle reconstruction and to a wavelet analysis. The atmospheric ranges forming the velocity signals are narrowed by linear combinations of Doppler maps from wavelengths near line center. The power in the short-period range is concentrated above intergranular spaces. We estimate an acoustic flux into the chromosphere of approximately 310 6 erg cm 2 s 1 , as needed for the chromospheric radiative losses.