We study the evolution of the eccentricity and inclination of protoplanetary embryos and low-mass protoplanets (from a fraction of an Earth mass to a few Earth masses) embedded in a protoplanetary disc, by means of three dimensional hydrodynamics calculations with radiative transfer in the diffusion limit. When the protoplanets radiate in the surrounding disc the energy released by the accretion of solids, their eccentricity and inclination experience a growth toward values which depend on the luminosity to mass ratio of the planet, which are comparable to the disc's aspect ratio and which are reached over timescales of a few thousand years. This growth is triggered by the appearance of a hot, under-dense region in the vicinity of the planet. The growth rate of the eccentricity is typically three times larger than that of the inclination. In long term calculations, we find that the excitation of eccentricity and the excitation of inclination are not independent. In the particular case in which a planet has initially a very small eccentricity and inclination, the eccentricity largely overruns the inclination. When the eccentricity reaches its asymptotic value, the growth of inclination is quenched, yielding an eccentric orbit with a very low inclination.As a side result, we find that the eccentricity and inclination of non-luminous planets are damped more vigorously in radiative discs than in isothermal discs.

Context. The Atacama Large Millimeter/submillimeter Array (ALMA) started regular observations of the Sun in 2016, first offering receiver Band 3 at wavelengths near 3 mm (100 GHz) and Band 6 at wavelengths around 1.25 mm (239 GHz). Aims. Here we present an initial study of one of the first ALMA Band 3 observations of the Sun. Our aim is to characterise the diagnostic potential of brightness temperatures measured with ALMA on the Sun. Methods. The observation covers a duration of 48 min at a cadence of 2 s targeting a quiet Sun region at disc-centre. Corresponding time series of brightness temperature maps are constructed with the first version of the Solar ALMA Pipeline and compared to simultaneous observations with the Solar Dynamics Observatory (SDO). Results. The angular resolution of the observations is set by the synthesised beam, an elliptical Gaussian that is approximately 1.4″ × 2.1″ in size. The ALMA maps exhibit network patches, internetwork regions, and elongated thin features that are connected to large-scale magnetic loops, as confirmed by a comparison with SDO maps. The ALMA Band 3 maps correlate best with the SDO/AIA 171 Å, 131 Å, and 304 Å channels in that they exhibit network features and, although very weak in the ALMA maps, imprints of large-scale loops. A group of compact magnetic loops is very clearly visible in ALMA Band 3. The brightness temperatures in the loop tops reach values of about 8000−9000 K and in extreme moments up to 10 000 K. Conclusions. ALMA Band 3 interferometric observations from early observing cycles already reveal temperature differences in the solar chromosphere. The weak imprint of magnetic loops and the correlation with the 171, 131, and 304 SDO channels suggests, however, that the radiation mapped in ALMA Band 3 might have contributions from a wider range of atmospheric heights than previously assumed, but the exact formation height of Band 3 needs to be investigated in more detail. The absolute brightness temperature scale as set by total power measurements remains less certain and must be improved in the future. Despite these complications and the limited angular resolution, ALMA Band 3 observations have a large potential for quantitative studies of the small-scale structure and dynamics of the solar chromosphere.

Context. Solar observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) facilitate studies of the atmosphere of the Sun at chromospheric heights at high spatial and temporal resolution at millimeter wavelengths. Aims. ALMA intensity data at millimeter(mm)-wavelengths are used for a first detailed systematic assessment of the occurrence and properties of small-scale dynamical features in the quiet Sun. Methods. We analyzed ALMA Band 3 data (∼3 mm/100 GHz) with a spatial resolution of ∼1.4–2.1 arcsec and a duration of ∼40 min together with SDO/HMI magnetograms. The temporal evolution of the mm maps is studied to detect pronounced dynamical features, which then are connected to dynamical events via a k-means clustering algorithm. We studied the physical properties of the resulting events and explored whether or not they show properties consistent with propagating shock waves. For this purpose, we calculated observable shock wave signatures at mm wavelengths from one- and three-dimensional model atmospheres. Results. We detect 552 dynamical events with an excess in brightness temperature (ΔTb) of at least ≥400 K. The events show a large variety in size up to ∼9″, amplitude ΔTb up to ∼1200 K with typical values in the range ∼450–750 K, and lifetime at full width at half maximum of ΔTb of between ∼43 and 360 s, with typical values between ∼55 and 125 s. Furthermore, many of the events show signature properties suggesting that they are likely produced by propagating shock waves. Conclusions. There are a lot of small-scale dynamic structures detected in the Band 3 data, even though the spatial resolution sets limitations on the size of events that can be detected. The number of dynamic signatures in the ALMA mm data is very low in areas with photospheric footpoints with stronger magnetic fields, which is consistent with the expectation for propagating shock waves.

Context. Interferometric observations of the Sun with the Atacama Large Millimeter/sub-millimeter Array (ALMA) provide valuable diagnostic tools for studying the small-scale dynamics of the solar atmosphere. Aims. The aims are to perform estimations of the observability of the small-scale dynamics as a function of spatial resolution for regions with different characteristic magnetic field topology facilitate a more robust analysis of ALMA observations of the Sun. Methods. A three-dimensional model of the solar atmosphere from the radiation-magnetohydrodynamic code Bifrost was used to produce high-cadence observables at millimeter and submillimeter wavelengths. The synthetic observables for receiver bands 3–10 were degraded to the angular resolution corresponding to ALMA observations with different configurations of the interferometric array from the most compact, C1, to the more extended, C7. The observability of the small-scale dynamics was analyzed in each case. The analysis was thus also performed for receiver bands and resolutions that are not commissioned so far for solar observations as a means for predicting the potential of future capabilities. Results. The minimum resolution required to study the typical small spatial scales in the solar chromosphere depends on the characteristic properties of the target region. Here, a range from quiet Sun to enhanced network loops is considered. Limited spatial resolution affects the observable signatures of dynamic small-scale brightening events in the form of reduced brightness temperature amplitudes, potentially leaving them undetectable, and even shifts in the times at which the peaks occur of up to tens of seconds. Conversion factors between the observable brightness amplitude and the original amplitude in the fully resolved simulation are provided that can be applied to observational data in principle, but are subject to wavelength-dependent uncertainties. Predictions of the typical appearance at the different combinations of receiver band, array configuration, and properties of the target region are conducted. Conclusions. The simulation results demonstrate the high scientific potential that ALMA already has with the currently offered capabilities for solar observations. For the study of small-scale dynamic events, however, the spatial resolution is still crucial, and wide array configurations are preferable. In any case, it is essential to take the effects due to limited spatial resolution into account in the analysis of observational data. Finally, the further development of observing capabilities including wider array configurations and advanced imaging procedures yields a high potential for future ALMA observations of the Sun.

Observations at millimetre wavelengths provide a valuable tool to study the small-scale dynamics in the solar chromosphere. We evaluate the physical conditions of the atmosphere in the presence of a propagating shock wave and link that to the observable signatures in mm-wavelength radiation, providing valuable insights into the underlying physics of mm-wavelength observations. A realistic numerical simulation from the three-dimensional radiative magnetohydrodynamic code Bifrost is used to interpret changes in the atmosphere caused by shock wave propagation. High-cadence (1 s) time series of brightness temperature ( T b ) maps are calculated with the Advanced Radiative Transfer code at the wavelengths 1.309 mm and 1.204 mm, which represents opposite sides of spectral band 6 of the Atacama Large Millimeter/submillimeter Array (ALMA). An example of shock wave propagation is presented. The brightness temperatures show a strong shock wave signature with large variation in formation height between approximately 0.7 and 1.4 Mm. The results demonstrate that millimetre brightness temperatures efficiently track upwardly propagating shock waves in the middle chromosphere. In addition, we show that the gradient of the brightness temperature between wavelengths within ALMA band 6 can potentially be used as a diagnostics tool in understanding the small-scale dynamics at the sampled layers. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.