Mapping the subsurface structure and flow field of sunspots has been a challenging task for helioseismology. In this work, we investigate the propagation of acoustic waves in a sunspot in NOAA active region 11312 using time-distance helioseismology. Travel times of waves traveling into and out of the sunspot are measured as functions of travel distance and azimuthal angle relative to the local radial direction. The same time-distance analysis is also applied to a simulated data based on a magnetohydrostatic (MHS) model of sunspot, and forward modeling of travel times is performed using ray tracing based on both the MHS sunspot model and a magnetohydrodynamic (MHD) simulation. We find that both ingoing (traveling from the quiet area into the sunspot) and outgoing waves (traveling from the sunspot into the quiet area) have shorter travel times than in the quiet Sun, with travel-time reductions of up to 40 s. The magnitude of the mean time shift is largest for waves traveling along the radial direction at small travel distances. A clear asymmetry is detected between ingoing and outgoing waves: outgoing waves generally exhibit shorter travel times. This asymmetry is strongest for radial direction and small travel distances, with differences exceeding 1 min for 3.5 mHz and 4.5 mHz waves. From the results of both observations and models, our analysis indicates that the overall reduction in travel time could be primarily caused by the combined effects of Wilson depression, magnetic field, and wave-speed perturbations, while the ingoing-outgoing asymmetry could be partly attributable to subsurface flows. Although the forward-modeling results reproduce several qualitative features of the observations, quantitative discrepancies remain, highlighting limitations of current sunspot models and ray-theoretical approximations.

Solar vortices are fundamental components of solar atmospheric dynamics, serving as natural laboratories for magnetic field twisting, energy concentration and transport, wave guidance, and plasma coupling across atmospheric layers. Numerical and observational studies show that solar vortices are intimately connected to key physical processes including magnetic reconnection, atmospheric heating, turbulence, and wave generation. This white paper, prepared for the UK Space Frontiers 2035 call, outline five high-priority scientific questions addressing vortex generation mechanisms, cross-layer coupling, magnetic restructuring, collective wave-guidance structures, and their role in triggering explosive events and modulating the solar wind. Key observations and capabilities required to make significant advancements over the coming decade are identified. The UK solar physics community has established world-leading expertise in vortex dynamics, combining strengths in high-resolution observations, MHD turbulence theory, numerical modelling, and space instrumentation. UK researchers have made foundational contributions to Solar Orbiter, delivered critical systems for DKIST, and maintain active involvement in MUSE and SOLAR-C EUVST missions. Our technical approach centres on developing next-generation instrumentation: a multi-band, space-qualified system employing four tunable Fabry-Pérot Interferometers providing diffraction-limited, high-cadence spectropolarimetric coverage from the deep photosphere to the low corona. This capability will be validated through a staged mission architecture beginning with balloon-borne demonstrators. Continuing this effort over the coming decade is vital to maintain UK leadership in this field and achieve the goals of roadmap for solar system research.

This Primer provides an overview of a fundamental set of analysis methods for studying waves, vibrations and related oscillatory phenomena — including instabilities, turbulence and shocks — across diverse scientific fields. These phenomena are ubiquitous, from astrophysics to complex systems in terrestrial environments, and understanding them requires careful selection of techniques. Misapplication of analysis tools can introduce misleading results. In this Primer, the fundamental principles of various wave analysis methods are first reviewed, along with adaptations to address complexities such as nonlinear, non-stationary and transient signal behaviour. These techniques are applied to identical synthetic datasets to provide a quantitative comparison of their strengths and limitations. Details are provided to help select the most appropriate analysis tools based on specific data characteristics and scientific goals, promoting reliable interpretations and ensuring reproducibility. Additionally, the Primer highlights best ethical practices for data deposition and the importance of open-code sharing. Finally, the broad applications of these techniques are explored in various research fields, current challenges in wave analysis are discussed, and an outlook on future directions is provided, with an emphasis on potential transformative discoveries that could be made by optimizing and developing cutting-edge analysis methods. Waves are ubiquitous in nature and occur across various scales and settings. In this Primer, Jafarzadeh et al. discuss techniques for preprocessing and analysing waves, including information on choosing the appropriate methods based on wave properties, and present worked examples using synthetic datasets.

Sunspots are intense regions of magnetic flux that are rooted deep below the photosphere. It is well established that sunspots host magnetohydrodynamic waves, with numerous observations showing a connection to the internal acoustic (or p- )modes of the Sun. The p- modes are fast waves below the equipartition layer and are thought to undergo a double mode conversion as they propagate upward into the atmosphere of sunspots, which can generate Alfvénic modes in the upper atmosphere. We employ 2.5D magnetohydrodynamic numerical simulations to investigate the adiabatic wave propagation and examine the resulting power spectra of coronal Alfvénic waves. A broadband wave source is used, which has a 1D power spectrum mimicking aspects of the observed p- mode power spectrum. We examine magnetoacoustic wave propagation and mode conversion from the photosphere to the corona. Frequency filtering of the upwardly propagating acoustic waves is a natural consequence of a gravitationally stratified atmosphere and plays a key role in shaping the power spectra of mode-converted waves. We demonstrate that the slow and fast magnetoacoustic waves and Alfvén waves above the equipartition layer have similarly shaped power spectra, which are modified versions of the driver spectrum. Notably, the results reveal that the coronal wave power spectra have a peak at a higher frequency than that of the underlying p -mode driver. This matches observations of coronal Alfvénic waves and further supports the role of the mode conversion process as a mechanism for Alfvénic wave generation in the Sun's atmosphere.

In sunspot umbrae, the core of some chromospheric lines exhibits periodic brightness enhancements known as umbral flashes. The consensus is that they are produced by the upward propagation of shock waves. This view has recently been challenged by the detection of downflowing umbral flashes and the confirmation of the existence of a resonant cavity above sunspots. We aim to determine waves' propagating or standing nature in the low umbral chromosphere and confirm or refute the existence of downflowing umbral flashes. Spectroscopic temporal series of Ca II 8542 Å, Ca II H, and Halpha in a sunspot were acquired with the Swedish Solar Telescope. The Halpha velocity was inferred using bisectors. Simultaneous inversions of the Ca II 8542 Å line and the Ca II H core were performed using the NICOLE code. The nature of the oscillations and insights into the resonant oscillatory pattern were determined by analyzing the phase shift between the velocity signals and examining the temporal evolution. Propagating waves in the low chromosphere are more common in regions with frequent umbral flashes, where the transition region is shifted upward, making resonant cavity signatures less noticeable. In contrast, areas with fewer umbral flashes show velocity fluctuations that align with standing oscillations. Evidence suggests dynamic changes in the location of velocity resonant nodes due to variations in transition region height. Downflowing profiles appear at the onset of some umbral flashes, but upflowing motion dominates during most of the flash. These downflowing flashes are more common in standing umbral flashes. We confirm the existence of a chromospheric resonant cavity above sunspot umbrae produced by wave reflections at the transition region. The oscillatory pattern depends on the transition region height, which exhibits spatial and temporal variations due to the impact of the waves.

Our aim is to characterize the effects of the local magnetic fields in quiet regions of stellar atmospheres. We compute magneto-hydrodynamic and purely hydrodynamic simulations of G2V, K0V and M2V star. The magnetic simulations are started from the hydrodynamical ones, adding the Biermann battery term in the induction equation to produce a magnetic seed, that is enhanced by the action of the small-scale dynamo. Once the magnetic field is saturated, we compare the simulations with and without magnetic fields and characterize the differences in statistics of velocities, appearance of granulation, and the mean stratification of a number of relevant parameters. These differences are also compared with the deviations produced by different treatments of the opacity in the simulations. The saturation values of the magnetic fields are ∼ 100 G for the three stars in their surface, consistent with the recent results for cool stars, and other results for the Sun in the literature. The local magnetic fields have a negligible effect on the velocities of the plasma or the mean stratifications of the simulated stars. In contrast, they produce changes in the bolometric intensity of the intergranular lanes and the power spectrum at small scales of the temperature and vertical velocity of downflows. Significant differences between the hydrodynamic and magneto-hydrodynamic simulations are also found for the kinetic energy. This difference in energy can be explained by the transformation of kinetic into magnetic energy, which is consistent with the action of the small-scale dynamo.

Solar partially ionized plasma is frequently modeled using single-fluid (1F) or two-fluid (2F) approaches. In the 1F case, charge-neutral interactions are often described through ambipolar diffusion, while the 2F model fully considers charge-neutral drifts. Here, we expand the definition of the ambipolar diffusion coefficient to include inelastic collisions (ion/rec) in two cases: a VAL3C 1D model and a 2F simulations of the Rayleigh-Taylor instability (RTI) in a solar prominence thread based on \cite{PopLukKho2021aa, PopLukKho2021ab}. On one side, we evaluate the relative importance of the inelastic contribution, compared to elastic and charge-exchange collisions. On the other side, we compare the contributions of ion/rec, thermal pressure, viscosity, and magnetic forces to the charge-neutral drift velocity of the turbulent flow of the RTI. Our analysis reveals that the contribution of inelastic collisions to the ambipolar diffusion coefficient is negligible across the chromosphere, allowing the classical definition of this coefficient to be safely used in 1F modeling. However, in the transition region, the contribution of inelastic collisions can become as significant as that of elastic collisions. Furthermore, we ascertain that the thermal pressure force predominantly influences the charge-neutral drifts in the RTI model, surpassing the impact of the magnetic force.

The Mancha3D code is a versatile tool for numerical simulations of magnetohydrodynamic (MHD) processes in solar/stellar atmospheres. The code includes nonideal physics derived from plasma partial ionization, a realistic equation of state and radiative transfer, which allows performing high-quality realistic simulations of magnetoconvection, as well as idealized simulations of particular processes, such as wave propagation, instabilities or energetic events. The paper summarizes the equations and methods used in the Mancha3D (Multifluid (-purpose -physics -dimensional) Advanced Non-ideal MHD Code for High resolution simulations in Astrophysics 3D) code. It also describes its numerical stability and parallel performance and efficiency. The code is based on a finite difference discretization and a memory-saving Runge–Kutta (RK) scheme. It handles nonideal effects through super-time-stepping and Hall diffusion schemes, and takes into account thermal conduction by solving an additional hyperbolic equation for the heat flux. The code is easily configurable to perform different kinds of simulations. Several examples of the code usage are given. It is demonstrated that splitting variables into equilibrium and perturbation parts is essential for simulations of wave propagation in a static background. A perfectly matched layer (PML) boundary condition built into the code greatly facilitates a nonreflective open boundary implementation. Spatial filtering is an important numerical remedy to eliminate grid-size perturbations enhancing the code stability. Parallel performance analysis reveals that the code is strongly memory bound, which is a natural consequence of the numerical techniques used, such as split variables and PML boundary conditions. Both strong and weak scalings show adequate performance up to several thousands of processors (CPUs).

Context . Three-dimensional time-dependent simulations of stellar atmospheres are essential to study the surface of stars other than the Sun. These simulations require the opacity binning method to reduce the computational cost of solving the radiative transfer equation down to viable limits. The method depends on a series of free parameters, among which the location and number of bins are key to set the accuracy of the resulting opacity. Aims . Our aim is to test how different binning strategies previously studied in one-dimensional models perform in three-dimensional radiative hydrodynamic simulations of stellar atmospheres. Methods . Realistic box-in-a-star simulations of the near-surface convection and photosphere of three spectral types (G2V, K0V, and M2V) were run with the MANCHA code with grey opacity. After reaching the stationary state, one snapshot of each of the three stellar simulations was used to compute the radiative energy exchange rate with grey opacity, opacity binned in four τ -bins, and opacity binned in 18 { τ , λ }-bins. These rates were compared with the ones computed with opacity distribution functions. Then, stellar simulations were run with grey, four-bin, and 18-bin opacities to see the impact of the opacity setup on the mean stratification of the temperature and its gradient after time evolution. Results . The simulations of main sequence cool stars with the MANCHA code are consistent with those in the literature. For the three stars, the radiative energy exchange rates computed with 18 bins are remarkably close to the ones computed with the opacity distribution functions. The rates computed with four bins are similar to the rates computed with 18 bins, and present a significant improvement with respect to the rates computed with the Rosseland opacity, especially above the stellar surface. The Rosseland mean can reproduce the proper rates in sub-surface layers, but produces large errors for the atmospheric layers of the G2V and K0V stars. In the case of the M2V star, the Rosseland mean fails even in sub-surface layers, owing to the importance of the contribution from molecular lines in the opacity, underestimated by the harmonic mean. Similar conclusions are reached studying the mean stratification of the temperature and its gradient after time evolution.

Aims. Solar prominences contain a significant number of neutral species. The dynamics of the ionised and neutral fluids composing the prominence plasma can be slightly different if the collisional coupling is not strong enough. The differential dynamics can be discerned by tracing line-of-sight velocities using observational techniques. Large-scale velocities can be quantified by measuring the global local and instantaneous displacement of spectral lines by the Doppler effect. Small-scale velocities leave their imprint on the width of spectral lines. In addition, these small-scale velocities can have a thermal (pure stochastic motion) nature or a non-thermal (small-scale unresolved instabilities, high-frequency waves, etc.) origin. For this work, we used one spectral line of ionised and two spectral lines of neutral elements to measure the resolved and unresolved velocities in a prominence with the aim to investigate the possible decoupling of the observed charged and neutral species. Methods. A faint prominence was observed with the German Vacuum Tower Telescope (VTT) on June 17, 2017. Time series consisting of repeated ten-position scans over the prominence were performed while simultaneously recording the intensity spectra of the Ca II IR 854.2 nm, H α 656.28 nm, and He I D 3 587.56 nm lines. The line-of-sight velocities and the Doppler width of the three spectral lines were determined at every spatial position and temporal moment. To make sure all spectral lines were sampling the same plasma volume, we applied selection criteria to identify locations with optically thin plasma. In addition, asymmetric or double-peaked profiles were also excluded for the analysis, since (even in an optically thin regime) they are indicative of the presence of strong velocity gradients or multiple components in the line of sight. Thus, only optically thin, symmetric, single-lobed profiles were retained for this study. As an additional reliability test of the selection criteria, we have also compared our results with optical thickness calculations. Results. After the application of all the selection criteria, only a region close to the prominence border met all requirements. The velocities of the three spectral lines turned out to be very similar over this region, with the ionised Ca II IR showing velocity excursions systematically larger compared to those of the neutral lines of H α and He I at some moments. The latter was found to be much closer to each other. Most of the velocity differences were below 1 km s −1 . The analysis of the Doppler widths indicated that the Ca II IR line shows an excess of unresolved motions. We cannot establish whether these velocities are related to a different temperature of the ions or to unresolved small-scale motions due to any non-thermal mechanism. Conclusions. The dynamics of the ionised and neutral plasma components in the observed prominence were very close to one another. The differences found may indicate that a localised decoupling between ions and neutrals may appear at particular spatial locations or instants of time. Indications of different unresolved motions between those species have also been obtained.

We report on results of high resolution two fluid non-linear simulations of the Rayleigh Taylor Instability (RTI) at the interface between a solar prominence and the corona. These follow results reported earlier by Popescu Braileanu et al. (2021a,b) on linear and early non-linear RTI dynamics in this environment. The simulations use a two fluid model that includes collisions between neutrals and charges, including ionization/recombination, energy and momentum transfer, and frictional heating. High resolution 2.5D magnetized RTI simulations with the magnetic field dominantly normal to and slightly sheared with respect to the prominence plane demonstrate that in a fully developed state of RTI a large fraction of the gravitational energy of a prominence thread can be converted into quasi-turbulent energy of the magnetic field. RTI magnetic energy generation is further accompanied by magnetic and plasma density structure formation, including dynamic formation, break-up, and merging of current sheets and plasmoid sub-structures. The simulations show the role of flow decoupling and ionization/recombination reactions between the neutrals and charges on the structure formation in magnetized RTI. We provide a careful examination of sources and form of numerical dissipation of the evolving magnetic field structures.

Aims. Our aim is to test how different binning strategies previously studied in one-dimensional models perform in three-dimensional radiative hydrodynamic simulations of stellar atmospheres. Methods. Realistic box-in-a-star simulations of the near-surface convection and photosphere of three spectral types (G2V, K0V, and M2V) were run with the MANCHA code with grey opacity. After reaching the stationary state, one snapshot of each of the three stellar simulations was used to compute the radiative energy exchange rate with grey opacity, opacity binned in four τ-bins, and opacity binned in 18 {τ, λ}-bins. These rates were compared with the ones computed with opacity distribution functions. Then, stellar simulations were run with grey, four-bin, and 18-bin opacities to see the impact of the opacity setup on the mean stratification of the temperature and its gradient after time evolution. Results. The simulations of main sequence cool stars with the MANCHA code are consistent with those in the literature. For the three stars, the radiative energy exchange rates computed with 18 bins are remarkably close to the ones computed with the opacity distribution functions. The rates computed with four bins are similar to the rates computed with 18 bins, and present a significant improvement with respect to the rates computed with the Rosseland opacity, especially above the stellar surface. The Rosseland mean can reproduce the proper rates in sub-surface layers, but produces large errors for the atmospheric layers of the G2V and K0V stars. In the case of the M2V star, the Rosseland mean fails even in sub-surface layers, owing to the importance of the contribution from molecular lines in the opacity, underestimated by the harmonic mean. Similar conclusions are reached studying the mean stratification of the temperature and its gradient after time evolution.

This Chapter outlines the basic properties of waves in solar partially ionized plasmas. It provides a summary of the main sets of equations, from the single-fluid formalism, to the multi-fluid one, giving examples for purely hydrogen, and for hydrogen-helium plasmas. It then discusses the solutions for waves under the single-fluid frame: the influence of the ambipolar diffusion, diamagnetic effect, and the Hall effect on the propagation, dissipation, and mode conversion of the magnetohydrodynamic waves. The Chapter continues by outlining the wave solutions in the multi-fluid formalism: the influence of the elastic inter-particle collisions into the propagation, damping and dissipation of different magnetohydrodynamic modes. Both parts discuss linear and non-linear wave solutions, and the effects of the gravitational stratification of the solar atmosphere.

Using Swedish 1 m Solar Telescope Crisp Imaging Spectro-Polarimeter 6563 & Aring; (H alpha) observations and Mancha3D simulations, we analyze the formation and evolution of falling knots beneath a hedgerow prominence. By comparing the observed knot widths and kinematics to those of a parametric survey of simulations, we estimate the range of magnetic field values and characteristic wavelengths to test if the magnetic Rayleigh-Taylor instability (MRTI) can provide a physically meaningful explanation. We recover observational parameters using a novel semiautomated method and find knot velocities with a mean of -9.68 km s-1 and a mean width of 614 km. Our simulations survey a range of critical wavelengths, lambda c , of 100 to 500 km, and magnetic field strengths, B 0, of 1 to 20 G, finding the closest match to observations around lambda c = 300 km, and B 0 = 2 to 6 G. As both the observational and simulated values match expected values, we conclude that the MRTI can provide a physically meaningful explanation of this observation. Additionally, we also predict that the Daniel K. Inouye Solar Telescope will be able to observationally recover secondary instabilities on the leading edge of the falling mass through applying a point-spread function to an example from the simulated results.

This study explores non-linear development of the magnetized Rayleigh-Taylor instability (RTI) in a prominence-corona transition region. Using a two-fluid model of a partially ionized plasma, we compare RTI simulations for several different magnetic field configurations. We follow prior descriptions of the numerical prominence model [Popescu Braileanu et al., 2021a,b, 2023] and explore the charged-neutral fluid coupling and plasma heating in a two-dimensional mixing layer for different magnetic field configurations. We also investigate how the shear in magnetic field surrounding a prominence may impact the release of the gravitational potential energy of the prominence material. We show that the flow decoupling is strongest in the plane normal to the direction of the magnetic field, where neutral pressure gradients drive ion-neutral drifts and frictional heating is balanced by adiabatic cooling of the expanding prominence material. We also show that magnetic field within the mixing plane can lead to faster non-linear release of the gravitational energy driving the RTI, while more efficiently heating the plasma via viscous dissipation of associated plasma flows. We relate the computational results to potential observables by highlighting how integrating over under-resolved two-fluid sub-structure may lead to misinterpretation of observational data.

Context. Realistic three-dimensional time-dependent simulations of stellar near-surface convection employ the opacity binning method for the efficient and accurate computation of the radiative energy exchange. The method provides several orders of magnitude of speedup, but its implementation includes a number of free parameters. Aims. Our aim is to evaluate the accuracy of the opacity binning method as a function of the choice of these free parameters. Methods. The monochromatic opacities computed with the SYNSPEC code were used to construct opacity distribution function (ODF) that was then verified through detailed comparison with the results of the ATLAS code. The opacity binning method was implemented with the SYNSPEC opacities for four representative cool main-sequence stellar spectral types (F3V, G2V, K0V, and M2V). Results. The ODFs from SYNSPEC and ATLAS show consistent results for the opacity and bolometric radiative energy exchange rate Q in the case of the F-, G-, and K-type stars. Significant differences, coming mainly from the molecular line lists, are found for the M-type star. It is possible to optimise a small number of bins to reduce the deviation of the results coming from the opacity grouping with respect to the ODF for the F-, G-, and K-type stars. In the case of the M-type star, the inclusion of splitting in wavelength is needed in the grouping to get similar results, with a subsequent increase in computing time. In the limit of a large number of bins, the deviation for all the binning configurations tested saturates and the results do not converge to the ODF solution. Due to this saturation, the Q rate cannot be improved by increasing the number of bins to more than about 20 bins. The more effective strategy is to select the optimal location of fewer bins.

photosphere to the chromosphere Multi-height observations will also able to estimate and correct the center-to-limb variation which is crucial for the measurement of meridional flow in the deeper convection zone including the tachocline region.These measurements will further help to reduce the convective background noise in the power spectra resulting in a more accurate determination of the oscillation frequencies.

In this work, we study the accuracy that can be achieved when inferring the atmospheric information from realistic numerical magneto-hydrodynamic simulations that reproduce the spatial resolution we will obtain with future observations made by the 4m class telescopes DKIST and EST. We first study multiple inversion configurations using the SIR code and the Fe I transitions at 630 nm until we obtain minor differences between the input and the inferred atmosphere in a wide range of heights. Also, we examine how the inversion accuracy depends on the noise level of the Stokes profiles. The results indicate that when the majority of the inverted pixels come from strongly magnetised areas, there are almost no restrictions in terms of the noise, obtaining good results for noise amplitudes up to 1 × 10 −3 of I c . At the same time, the situation is different for observations where the dominant magnetic structures are weak, and noise restraints are more demanding. Moreover, we find that the accuracy of the fits is almost the same as that obtained without noise when the noise levels are on the order of 1 × 10 −4 of I c . We, therefore, advise aiming for noise values on the order of or lower than 5 × 10 −4 of I c if observers seek reliable interpretations of the results for the magnetic field vector reliably. We expect those noise levels to be achievable by next-generation 4m class telescopes thanks to an optimised polarisation calibration and the large collecting area of the primary mirror.

Vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above. Their presence is revealed in high-resolution and high-cadence solar observations from the ground and from space and with state-of-the-art magnetoconvection simulations. Vortical flows exhibit complex characteristics and dynamics, excite a wide range of different waves, and couple different layers of the solar atmosphere, which facilitates the channeling and transfer of mass, momentum and energy from the solar surface up to the low corona. Here we provide a comprehensive review of documented research and new developments in theory, observations, and modelling of vortices over the past couple of decades after their observational discovery, including recent observations in Hα , innovative detection techniques, diverse hydrostatic modelling of waves and forefront magnetohydrodynamic simulations incorporating effects of a non-ideal plasma. It is the first systematic overview of solar vortex flows at granular scales, a field with a plethora of names for phenomena that exhibit similarities and differences and often interconnect and rely on the same physics. With the advent of the 4-m Daniel K. Inouye Solar Telescope and the forthcoming European Solar Telescope, the ongoing Solar Orbiter mission, and the development of cutting-edge simulations, this review timely addresses the state-of-the-art on vortex flows and outlines both theoretical and observational future research directions.

Context. Several energetic disturbances have been identified as triggers of large-amplitude oscillations (LAOs) in prominences. Observations show that Moreton or extreme ultraviolet waves excite prominence oscillations of the longitudinal, transverse, or mixed polarities. However, the mechanisms for the excitation of LAOs by these waves are not well understood.Aims. In this study, we aim to investigate mechanisms behind the triggering of LAOs via self-consistent perturbation produced by an eruption and via energetic waves coming from a distant energy source.Methods. We performed time-dependent numerical simulations in 2.5D and 2D setups, using the magnetohydrodynamic code MANCHA3D, involving a flux rope and dipped arcade magnetic configurations with an artificially loaded prominence mass in the magnetic dips. Two types of disturbances were applied to excite prominence oscillations. The first type involves perturbations produced self-consistently by an eruption, while the second type of perturbation is associated with the waves caused by an artificial energy release.Results. In the simulations of the eruption, we find that this eruption by itself does not produce LAOs in the prominence located in its vicinity. Its only effect is in inclining the magnetic configuration of the prominence. While the erupting flux rope rises, an elongated current sheet forms behind it. This current sheet becomes unstable and breaks into plasmoids. The downward-moving plasmoids cause perturbations in the velocity field by merging with the post-reconnection loops. This velocity perturbation propagates in the surroundings and enters the flux rope, causing the disturbance of the prominence mass. The analysis of the oscillatory motions of the prominence plasma reveals the excitation of small-amplitude oscillations (SAOs), which are a mixture of longitudinal and vertical oscillations with short and long periods. In the simulations with a distant artificial perturbation, a fast-mode shock wave is produced and it gradually reaches two flux rope prominences at different distances. This shock wave excites vertical LAOs as well as longitudinal SAOs with similar amplitudes, periods, and damping times in both prominences. Finally, in the experiment with the external triggering of LAOs of solar prominences by an artificial perturbation in a dipped arcade prominence model, we find that although the vector normal to the front of a fast-mode shock wave is parallel to the spine of the dipped arcade well before the contact, this wave does not excite longitudinal LAOs. When the wave front approaches the prominence, it pushes the dense plasma down, establishing vertical LAOs and motions due to compression and rarefaction along the magnetic field.Conclusions. The external triggering of prominence oscillations is a complex process that excites LAOs or SAOs of the longitudinal or transverse polarizations or a mix of both types. It is not an easy task to produce LAOs in prominences because the triggering event requires a sufficient amount of energy. The orientation of the prominence axis with respect to the driving event may play a crucial role in triggering a certain type of LAOs.