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The Atacama Large Millimeter/submillimeter Array (ALMA) allows for solar observations in the wavelength range of 0.3$-$10 mm, giving us a new view of the chromosphere. The measured brightness temperature at various frequencies can be fitted with theoretical models of density and temperature versus height. We use the available ALMA and Mets\"ahovi measurements of selected solar structures (quiet sun (QS), active regions (AR) devoid of sunspots, and coronal holes (CH)). The measured QS brightness temperature in the ALMA wavelength range agrees well with the predictions of the semiempirical Avrett$-$Tian$-$Landi$-$Curdt$-$W\"ulser (ATLCW) model, better than previous models such as the Avrett$-$Loeser (AL) or Fontenla$-$Avrett$-$Loeser model (FAL). We scaled the ATLCW model in density and temperature to fit the observations of the other structures. For ARs, the fitted models require 9%$-$13% higher electron densities and 9%$-$10% higher electron temperatures, consistent with expectations. The CH fitted models require electron densities 2%$-$40% lower than the QS level, while the predicted electron temperatures, although somewhat lower, do not deviate significantly from the QS model. Despite the limitations of the one-dimensional ATLCW model, we confirm that this model and its appropriate adaptations are sufficient for describing the basic physical properties of the solar structures., Comment: 11 pages, 3 figures, 2 tables, accepted and published in Astronomische Nachrichten/Astronomical Notes

This study investigates and compares brightness and area of coronal bright points (CBPs) inside and outside of coronal holes (CHs) using the single-dish Band 6 observations by the Atacama Large Millimeter/submillimeter Array (ALMA), combined with extreme-ultraviolet (EUV) 193 $\overset{\circ}{\mathrm{A}}$ filtergrams obtained by the Atmospheric Imaging Assembly (AIA) and magnetograms obtained by the Helioseismic and Magnetic Imager (HMI), both on board Solar Dynamics Observatory (SDO). The CH boundaries were extracted from the SDO/AIA images using the Collection of Analysis Tools for Coronal Holes (CATCH) and CBPs were identified in the SDO/AIA, SDO/HMI, and ALMA data. Measurements of brightness and areas in both ALMA and SDO/AIA images were conducted for CBPs within CHs and quiet Sun regions outside CHs. A statistical analysis of the measured physical properties resulted in a lower average CBP brightness in both ALMA and SDO/AIA data for CBPs within the CHs. Depending on the CBP sample size, the difference in intensity for the SDO/AIA data, and brightness temperature for the ALMA data, between the CBPs inside and outside CHs ranged from between 2$\sigma$ and 4.5$\sigma$, showing a statistically significant difference between those two CBP groups. For CBP areas, CBPs within the CH boundaries showed smaller areas on average, with the observed difference between the two CBP groups between 1$\sigma$ and 2$\sigma$ for the SDO/AIA data, and up to 3.5$\sigma$ for the ALMA data, indicating that CBP areas are also significantly different. Given the measured properties, we conclude that the CBPs inside CHs tend to be less bright on average, but also smaller in comparison to those outside of CHs. This conclusion might point to the specific physical conditions and properties of the local CH region around a CBP limiting the maximum achievable intensity (temperature) and size of a CBP., Comment: 27 pages, 28 figures, accepted in Astronomy and Astrophysics

The (sub)millimeter radiation of solar flares is poorly understood. Without spatial resolution, it cannot be compared easily to flare emissions in other wavelengths. The Atacama Large Millimeter-submillimeter Array (ALMA) offers sufficient resolution for the first time. However, used as an interferometer, its field of view is smaller than an active region and ALMA cannot observe on demand when a flare occurs. We use readily available large scale single-dish ALMA observations of solar millimeter flares and compare them to well-known features observed in other wavelengths. The properties of these other flare emissions, correlating in space and time, may then be used to interpret the millimeter brightenings and vice versa. The aim is to obtain reliable associations, limited by the time and space resolution of single-dish observations. We collected ALMA observations at 3 mm and 1 mm and searched for millimeter brightenings during times given in a flare catalog. We found five events with 9 or more images that can be used for comparison in time and space. The millimeter brightenings are associated with a variety of flare features in cool (H$\alpha$, 30.4 nm), intermediate (17.1 nm), and hot (9.4 nm) lines. In several cases, the millimeter brightening peaked at the footpoint of a hot flare loop. In other cases the peak coincided with the top or footpoint of an active H{\alpha} filament. We found correlations also with post-flare loops and tops of a hot loop, and in some cases to no features at all. The wide field of view provided by the single-dish observations allowed for completely overviewing the flare activity in millimeter waves for the first time. The associated phenomena often changed during the flare in type and location, and may explain the sometimes bewildering behavior of millimeter flare emissions observed previously without spatial resolution., Comment: 13 pages, 10 figures, accepted in Astronomy and Astrophysics

We determined the differential rotation (DR) parameters $A$ and $B$ (corresponding to the equatorial rotation velocity and the gradient of the solar DR) by tracing sunspot groups in sunspot drawings of the Kanzelh\"ohe Observatory for Solar and Environmental Research (KSO; 1964-2008, for solar cycles (SC) 20-23) and KSO white-light images (2009-2016, for SC 24). We used different statistical methods and approaches to analyse cycle related variations, solar cycle phase-related variations and long-term variations of the DR. $A$ and $B$ show statistically significant periodic variability. The changes in $A$ related to solar cycle phase are in accordance with previously reported theoretical and experimental results (higher $A$ during solar minimum, lower $A$ during the maximum of activity), while changes in $B$ differ from the theoretical predictions as we observe more negative values of $B$, that is, a more pronounced DR during activity maximum. The main result of this paper for the long-term variations in $A$ is the detection of a phase shift between the activity flip (in the 1970s) and the equatorial rotation velocity flip (in the early 1990s). During this time period both $A$ and activity show a secular decreasing trend, indicating their correlation. Therefore, the theoretical model fails in the phase-shift time period that occurs after the modern Gleissberg maximum, while in the time period thereafter (after the 1990s), theoretical and experimental results are consistent. The long-term variations in $B$ in general yield an anticorrelation of $B$ and activity, as a rise of $B$ is observed during the entire time period (1964-2016) we analysed, during which activity decreased. We study for the first time the variation in solar DR and activity based on 53 years of KSO data. Our results agree well with the results related to the solar cycle phase from corona observations.

Images of the Sun at millimeter wavelengths obtained by ALMA show a significant correspondence with the magnetograms. In this paper, we investigate this correspondence by comparing ALMA full-disk solar image taken at 1.2 mm with a SDO/HMI magnetogram and analyze their correlation. It is found that chromospheric network and active regions show a positive correlation where brightness temperature is increasing with the line-of-sight magnetic field strength, while sunspots have a negative correlation. Quiet Sun regions do not show any dependence of the brightness temperature with the magnetic field. Thermal bremsstrahlung is given as the best explanation for the observed correlations., Comment: 11 pages, 4 figures, published in Central European Astrophysical Bulletin, 2020

Ru{\dj}er Bo\v{s}kovi\'c developed methods for determination of solar rotation elements: the solar equator inclination i, the longitude of the node {\Omega} and the period of solar rotation. In his last work Opera pertinentia ad opticam et astronomiam, published in 1785, in the chapter Opuscule II he described his methods, the formulae with figure descriptions and an example for calculation of the solar rotation elements with detailed numerical explanation using his own observations performed in September 1777. The original numerical procedure was performed using logarithmic formulae. In present work we give a description of the original results of R. Bo\v{s}kovi\'c and compare them with our recalculated values., Comment: 7 pages, 2 figures, published Contributed paper (oral presentation) at the International Advent Workshop 17th - 18th December 2020, Zagreb - Graz, Hvar Observatory, Faculty of Geodesy, University of Zagreb, Croatia and IGAM, Institute of Physics, Karl-Franzens University Graz, Austria

The minimum - maximum method, belonging to the precursor class of the solar activity forecasting methods, is based on a linear relationship between relative sunspot number in the minimum and maximum epochs of solar cycles. In the present analysis we apply a modified version of this method using data not only from the minimum year, but also from a couple of years before and after the minimum. The revised 13-month smoothed monthly total sunspot number data set from SILSO/SIDC is used. Using data for solar cycle nos. 1-24 the largest correlation coefficient (CC) is obtained when correlating activity level 3 years before solar cycle minimum with the subsequent maximum (CC = 0.82), independent of inclusion or exclusion of the solar cycle no. 19. For the next solar maximum of the cycle no. 25 we predict: Rmax = 121 +- 33. Our results indicate that the next solar maximum (of the cycle no. 25) will be of the similar amplitude as the previous one, or even something lower. This is in accordance with the general middle-term lowering of the solar activity after the secular maximum in the 20th century and consistent with the Gleissberg period of the solar activity. The reliability of the 3 years before the minimum predictor is experimentally justified by the largest correlation coefficient and verified with the Student t-test. It is satisfactorily explained with the two empirical well-known findings: the extended solar cycle and the Waldmeier effect. Finally, we successfully reproduced the maxima of the last four solar cycles, nos. 21-25, using the 3 years before the minimum method., Comment: 10 pages, 4 figures, accepted by Astronomische Nachrichten / Astronomical Notes

This paper focuses on the observations of sunspots made by Ru{\dj}er Bo\v{s}kovi\'c in 1777. We derived the expressions needed to calculate the elements of the Sun's rotation and period from observations. We used modern ephemeris data in the processing of the observation results. Obtained results are very similar to Bo\v{s}kovi\'c's original calculations. In addition to historical significance, they also provide scientifically valuable data on the Sun's differential rotation, which plays a significant role in generating and maintaining solar magnetic activity., Comment: 6 pages, 3 figures, Proceedings of Thirteenth Workshop "Solar Influences on the Magnetosphere, Ionosphere and Atmosphere" Primorsko, Bulgaria, September, 2021

Aims. The main aim of the present analysis is to decipher (i) the small-scale bright features in solar images of the quiet Sun and active regions obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) and (ii) the ALMA correspondence of various known chromospheric structures visible in the H-alpha images of the Sun. Methods. Small-scale ALMA bright features in the quiet Sun region were analyzed using single-dish ALMA observations (1.21 mm, 248 GHz) and in an active region using interferometric ALMA measurements (3 mm, 100 GHz). With the single-dish observations, a full-disk solar image is produced, while interferometric measurements enable the high-resolution reconstruction of part of the solar disk, including the active region. The selected quiet Sun and active regions are compared with the H-alpha (core and wing sum), EUV, and soft X-ray images and with the magnetograms. Results. In the quiet Sun region, enhanced emission seen in the ALMA is almost always associated with a strong line-of-sight (LOS) magnetic field. Four coronal bright points were identified, while other small-scale ALMA bright features are most likely associated with magnetic network elements and plages. In the active region, in 14 small-scale ALMA bright features randomly selected and compared with other images, we found five good candidates for coronal bright points, two for plages, and five for fibrils. Two unclear cases remain: a fibril or a jet, and a coronal bright point or a plage. A comparison of the H-alpha core image and the 3 mm ALMA image of the analyzed active region showed that the sunspot appears dark in both images (with a local ALMA radiation enhancement in sunspot umbra), the four plage areas are bright in both images and dark small H-alpha filaments are clearly recognized as dark structures of the same shape also in ALMA., Comment: 12 pages, 4 figures, to be published in Astronomy and Astrophysics

An online software tool for the easy preparation of ephemerides of the solar surface features is presented. It was developed as a helper tool for the preparation of observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), but it can be used at other observatories as well. The tool features an easy to use point-and-click graphical user interface with the possibility to enter or adjust input parameters, while the result is a table of predicted positions in the celestial equatorial coordinate system, suitable for import into the ALMA Observing Tool software. The tool has been successfully used for the preparation and execution of solar observations with ALMA., Comment: Submitted to The Mining Geological Petroleum Engineering Bulletin (see https://www.scopus.com/sourceid/101730), 7 pages, 2 figures

In this work we use solar observations with the ALMA radio telescope at the wavelength of 1.21 mm. The aim of the analysis is to improve understanding of the solar chromosphere, a dynamic layer in the solar atmosphere between the photosphere and corona. The study has an observational and a modeling part. In the observational part full-disc solar images are analyzed. Based on a modified FAL atmospheric model, radiation models for various observed solar structures are developed. Finally, the observational and modeling results are compared and discussed., Comment: 4 pages, presented at The 20th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, July 29 - Aug 3 2018, Boston / Cambridge, USA

Various solar features can be seen on maps of the Sun in the mm and sub-mm wavelength range. The recently installed Atacama Large Millimeter/submillimeter Array (ALMA) is capable of observing the Sun in that wavelength range with an unprecedented spatial, temporal and spectral resolution. To interpret solar observations with ALMA the first important step is to compare ALMA maps with simultaneous images of the Sun recorded in other spectral ranges. First we identify different structures in the solar atmosphere seen in the optical, IR and EUV parts of the spectrum (quiet Sun (QS), active regions (AR), prominences on the disc, magnetic inversion lines (IL), coronal holes (CH) and coronal bright points (CBPs)) in a full disc solar ALMA image. The second aim is to measure the intensities (brightness temperatures) of those structures and compare them with the corresponding QS level. A full disc solar image at 1.21 mm obtained on December 18, 2015 during a CSV-EOC campaign with ALMA is calibrated and compared with full disc solar images from the same day in H\alpha, in He I 1083 nm core, and with SDO images (AIA at 170 nm, 30.4 nm, 21.1 nm, 19.3 nm, and 17.1 nm and HMI magnetogram). The brightness temperatures of various structures are determined by averaging over corresponding regions of interest in the ALMA image. Positions of the QS, ARs, prominences on the disc, ILs, CHs and CBPs are identified in the ALMA image. At 1.21 mm ARs appear as bright areas (but sunspots are dark), while prominences on the disc and CHs are not discernible from the QS background, although having slightly less intensity than surrounding QS regions. ILs appear as large, elongated dark structures and CBPs correspond to ALMA bright points. These results are in general agreement with sparse earlier measurements at similar wavelengths. The identification of CBPs represents the most important new result., Comment: 9 pages, 3 figures

The main aim of this work is to determine the solar differential rotation by tracing sunspot groups during the period 1964-2016, using the Kanzelh\"ohe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images. Two procedures for the determination of the heliographic positions were applied: an interactive procedure on the KSO sunspot drawings (1964 - 2008, solar cycles nos. 20 - 23) and an automatic procedure on the KSO white light images (2009 - 2016, solar cycle no. 24). For the determination of the synodic angular rotation velocities two different methods have been used: a daily shift (DS) method and a robust linear least-squares fit (rLSQ) method. Afterwards, the rotation velocities had to be converted from synodic to sidereal, which were then used in the least-squares fitting for the solar differential rotation law. For the test data from 2014, we found the rLSQ method for calculating rotational velocities to be more reliable than the DS method. The best fit solar differential rotation profile for the whole time period is $\omega(b)$ = (14.47 $\pm$ 0.01) - (2.66 $\pm$ 0.10) $\sin^2b$ (deg/day) for the DS method and $\omega(b)$ = (14.50 $\pm$ 0.01) - (2.87 $\pm$ 0.12) $\sin^2b$ (deg/day) for the rLSQ method. A barely noticeable north - south asymmetry is observed for the whole time period 1964 - 2016 in the present paper. Rotation profiles, using different data sets (e.g. Debrecen Photoheliographic Data, Greenwich Photoheliographic Results), presented by other authors for the same time periods and the same tracer types, are in good agreement with our results. Therefore, the KSO data set is suitable for the investigation of the long-term variabilities in the solar rotation profile.

The Atacama Large Millimeter-submillimeter Array (ALMA) radio telescope has commenced science observations of the Sun starting in late 2016. Since the Sun is much larger than the field of view of individual ALMA dishes, the ALMA interferometer is unable to measure the background level of solar emission when observing the solar disk. The absolute temperature scale is a critical measurement for much of ALMA solar science, including the understanding of energy transfer through the solar atmosphere, the properties of prominences, and the study of shock heating in the chromosphere. In order to provide an absolute temperature scale, ALMA solar observing will take advantage of the remarkable fast-scanning capabilities of the ALMA 12m dishes to make single-dish maps of the full Sun. This article reports on the results of an extensive commissioning effort to optimize the mapping procedure, and it describes the nature of the resulting data. Amplitude calibration is discussed in detail: a path that utilizes the two loads in the ALMA calibration system as well as sky measurements is described and applied to commissioning data. Inspection of a large number of single-dish datasets shows significant variation in the resulting temperatures, and based on the temperature distributions we derive quiet-Sun values at disk center of 7300 K at lambda=3 mm and 5900 K at lambda=1.3 mm. These values have statistical uncertainties of order 100 K, but systematic uncertainties in the temperature scale that may be significantly larger. Example images are presented from two periods with very different levels of solar activity. At a resolution of order 25 arcsec, the 1.3 mm wavelength images show temperatures on the disk that vary over about a 2000 K range., Comment: Solar Physics, accepted: 24 pages, 13 figures

Observations of the Sun at millimeter and submillimeter wavelengths offer a unique probe into the structure, dynamics, and heating of the chromosphere; the structure of sunspots; the formation and eruption of prominences and filaments; and energetic phenomena such as jets and flares. High-resolution observations of the Sun at millimeter and submillimeter wavelengths are challenging due to the intense, extended, low- contrast, and dynamic nature of emission from the quiet Sun, and the extremely intense and variable nature of emissions associated with energetic phenomena. The Atacama Large Millimeter/submillimeter Array (ALMA) was designed with solar observations in mind. The requirements for solar observations are significantly different from observations of sidereal sources and special measures are necessary to successfully carry out this type of observations. We describe the commissioning efforts that enable the use of two frequency bands, the 3 mm band (Band 3) and the 1.25 mm band (Band 6), for continuum interferometric-imaging observations of the Sun with ALMA. Examples of high-resolution synthesized images obtained using the newly commissioned modes during the solar commissioning campaign held in December 2015 are presented. Although only 30 of the eventual 66 ALMA antennas were used for the campaign, the solar images synthesized from the ALMA commissioning data reveal new features of the solar atmosphere that demonstrate the potential power of ALMA solar observations. The ongoing expansion of ALMA and solar-commissioning efforts will continue to enable new and unique solar observing capabilities., Comment: 22 pages, 12 figures, accepted for publication in Solar Physics

This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) in preparation of the first regular observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), which are anticipated to start in ALMA Cycle 4 in October 2016. The science cases presented here demonstrate that a large number of scientifically highly interesting observations could be made already with the still limited solar observing modes foreseen for Cycle 4 and that ALMA has the potential to make important contributions to answering long-standing scientific questions in solar physics. With the proposal deadline for ALMA Cycle 4 in April 2016 and the Commissioning and Science Verification campaign in December 2015 in sight, several of the SSALMON Expert Teams composed strategic documents in which they outlined potential solar observations that could be feasible given the anticipated technical capabilities in Cycle 4. These documents have been combined and supplemented with an analysis, resulting in recommendations for solar observing with ALMA in Cycle 4. In addition, the detailed science cases also demonstrate the scientific priorities of the solar physics community and which capabilities are wanted for the next observing cycles. The work on this White Paper effort was coordinated in close cooperation with the two international solar ALMA development studies led by T. Bastian (NRAO, USA) and R. Brajsa, (ESO). This document will be further updated until the beginning of Cycle 4 in October 2016. In particular, we plan to adjust the technical capabilities of the solar observing modes once finally decided and to further demonstrate the feasibility and scientific potential of the included science cases by means of numerical simulations of the solar atmosphere and corresponding simulated ALMA observations., Comment: SSALMON White Paper with focus on potential solar science with ALMA in Cycle 4; 54 pages. Version 1.2, March 29th, 2016 (updated technical capabilities and observing plans)

The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere - a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases., Comment: 73 pages, 21 figures ; Space Science Reviews (accepted December 10th, 2015); accepted version

The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere - a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA., Comment: 15 pages, 3 figures, to appear in Advances in Solar Physics (special issue of Advances in Space Research, AdSR), proceedings of the 14th European Solar Physics Meeting (ESPM-14, Dublin, Ireland, September 2014); (resubmitted version after minor revision)

Very long baseline interferometry at millimetre/submillimetre wavelengths (mmVLBI) offers the highest achievable spatial resolution at any wavelength in astronomy. The anticipated inclusion of ALMA as a phased array into a global VLBI network will bring unprecedented sensitivity and a transformational leap in capabilities for mmVLBI. Building on years of pioneering efforts in the US and Europe the ongoing ALMA Phasing Project (APP), a US-led international collaboration with MPIfR-led European contributions, is expected to deliver a beamformer and VLBI capability to ALMA by the end of 2014 (APP: Fish et al. 2013, arXiv:1309.3519). This report focuses on the future use of mmVLBI by the international users community from a European viewpoint. Firstly, it highlights the intense science interest in Europe in future mmVLBI observations as compiled from the responses to a general call to the European community for future research projects. A wide range of research is presented that includes, amongst others: - Imaging the event horizon of the black hole at the centre of the Galaxy - Testing the theory of General Relativity an/or searching for alternative theories - Studying the origin of AGN jets and jet formation - Cosmological evolution of galaxies and BHs, AGN feedback - Masers in the Milky Way (in stars and star-forming regions) - Extragalactic emission lines and astro-chemistry - Redshifted absorption lines in distant galaxies and study of the ISM and circumnuclear gas - Pulsars, neutron stars, X-ray binaries - Testing cosmology - Testing fundamental physical constants, Comment: Replaced figures 2 and 3: corrected position SRT. Corrected minor typo in 5.1

Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide 10Be measured in polar ice cores are studied. Methods. By applying methods of nonlinear dynamics, the solar activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years. The complexity of the system is expressed by several parameters of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series. We also fit a damped random walk model, which accurately describes the variability of quasars, to the solar 10Be data and investigate the corresponding power spectral distribution. The periods in the data series were searched by the Fourier and wavelet analyses. The solar activity on the long-term scale is found to be on the edge of chaotic behavior. This can explain the observed intermittent period of longer lasting solar activity minima. Filtering the data by eliminating variations below a certain period (the periods of 380 yr and 57 yr were used) yields a far more regular behavior of solar activity. A comparison between the results for the 10Be data with the 14C data shows many similarities. Both cosmogenic isotopes are strongly correlated mutually and with solar activity. Finally, we find that a series of damped random walk models provides a good fit to the 10Be data with a fixed characteristic time scale of 1000 years, which is roughly consistent with the quasi-periods found by the Fourier and wavelet analyses., Comment: 8 pages, 11 figures

The goal of this paper is to investigate Reynolds stresses and to check if it is plausible that they are responsible for angular momentum transfer toward the solar equator. We also analysed meridional velocity, rotation velocity residuals and correlation between the velocities. We used sunspot groups position measurements from GPR (Greenwich Photographic Result) and SOON/USAF/NOAA (Solar Observing Optical Network/United States Air Force/National Oceanic and Atmospheric Administration) databases covering the period from 1878 until 2011. In order to calculate velocities we used daily motion of sunspot groups. The sample was also limited to $\pm$58\degr in Central Meridian Distance (CMD) in order to avoid solar limb effects. We mainly investigated velocity patterns depending on solar cycle phase and latitude. We found that meridional motion of sunspot groups is toward the centre of activity from all available latitudes and in all phases of the solar cycle. The range of meridional velocities is $\pm10$ m s$^{-1}$. Horizontal Reynolds stress is negative at all available latitudes and indicates that there is a minimum value ($q\approx$ - 3000 m$^2$ s$^{-2}$) located at $b\approx\pm$30$^{0}$. In our convention this means that angular momentum is transported toward the solar equator in agreement with the observed rotational profile of the Sun.

Existing methods for conversion between synodic and sidereal rotation velocities of the Sun are tested for validity using state of the art ephemeris data. It is found that some of them are in good agreement with ephemeris calculations, while the other ones show a discrepancy of almost 0.01 deg per day. The discrepancy is attributed to a missing factor and a new corrected relation is given., Comment: Accepted for publication in Sol. Phys., 7 pages, 3 figures