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We present an interpretation of the recent Daniel K. Inouye Solar Telescope (DKIST) observations of propagating wavefronts in the lower solar atmosphere. Using MPS/University of Chicago MHD (MURaM) radiative magnetohydrodynamic simulations spanning solar photosphere, overshoot region, and lower chromosphere, we identify three acoustic-wave source mechanisms, each occurring at a different atmospheric height. We synthesize the DKIST Visible Broadband Imager (VBI) G-band, blue-continuum, and CaIIK signatures of these waves at high spatial and temporal resolution, and conclude that the wavefronts observed by DKIST likely originate from acoustic sources at the top of the solar photosphere overshoot region and in the chromosphere proper. The overall importance of these local sources to the atmospheric energy and momentum budget of the solar atmosphere is unknown, but one of the excitation mechanism identified (upward propagating shock interaction with down-welling chromospheric plasma resulting in acoustic radiation) appears to be an important shock dissipation mechanism. Additionally, the observed wavefronts may prove useful for ultra-local helioseismological inversions and promise to play an important diagnostic role at multiple atmospheric heights., Comment: For associated video (mp4) files see https://drive.google.com/file/d/1vWrXVsaazyk--0WSaFXp_shNrZug0cu7/view?usp=drive_link, https://drive.google.com/file/d/12VL2O2O5QztxUVxyB0HqNeGdnKH-ti2Y/view?usp=drive_link, and https://drive.google.com/file/d/1ARmq-m7UTHofPAuQf-p4_9yooRFaJUe9/view?usp=drive_link

The Sun's axisymmetric large-scale flows, differential rotation and meridional circulation, are thought to be maintained by the influence of rotation on the thermal-convective motions in the solar convection zone. These large-scale flows are crucial for maintaining the Sun's global magnetic field. Over the last several decades, our understanding of large-scale motions in the Sun has significantly improved, both through observational and theoretical efforts. Helioseismology has constrained the flow topology in the solar interior, and the growth of supercomputers has enabled simulations that can self-consistently generate large scale flows in rotating spherical convective shells. In this chapter, we review our current understanding of solar convection and the large-scale flows present in the Sun, including those associated with the recently discovered inertial modes of oscillation. We discuss some issues still outstanding, and provide an outline of future efforts needed to address these.

In this paper we refine a previously developed acoustic-source filter (Bahauddin & Rast 2021), improving its reliability and extending its capabilities. We demonstrate how to fine-tune the filter to meet observational constraints and to focus on specific wavefront speeds. This refinement enables discrimination of acoustic-source depths and tracking of local-source wavefronts, thereby facilitating ultra-local helioseismology on very small scales. By utilizing the photospheric Doppler signal from a subsurface source in a MURaM simulation, we demonstrate that robust ultra-local three-dimensional helioseismic inversions for the granular flows and sound speed to depths of at least 80 km below the photosphere are possible. The capabilities of the National Science Foundation's new Daniel K. Inouye Solar Telescope (DKIST) will enable such measurements of the real Sun., Comment: One mp4 video file included

This paper describes an adaptation of the Optimal Localized Averaging (OLA) inversion technique, originally developed for geo- and helioseismological applications, to the interpretation of solar spectroscopic data. It focuses on inverting the thermodynamical properties of the solar atmosphere assuming that the atmosphere and radiation field are in Local Thermodynamic Equilibrium (LTE). We leave inversions for magnetic field and non-LTE inversions for future work. The advantage with the OLA method is that it computes solutions that are optimally resolved (in depth) with minimal cross-talk error between variables. Additionally, the method allows for direct assessment of the vertical resolution of the inverted solutions. The primary challenges faced when adapting the method to spectroscopic inversions originate with the possible large amplitude differences between the atmospheric model used to initiate the inversion and the underlying atmosphere it aims to recover, necessitating the development of an iterative scheme. Here we describe the iterative OLA method we have developed for both single and multi-variable inversions and demonstrate its performance on simulated data and synthesized spectra. We note that when carrying out multi-variable inversions, employing response function amplification factors can address the inherent spectral-sensitivity bias that makes it hard to invert for less spectrally-sensitive variables. The OLA method can, in most cases, reliably invert as well as or better than the frequently employed Stokes Inversion based on Response functions (SIR) scheme, however some difficulties remain. In particular, the method struggles to recover large-scale offsets in the atmospheric stratification. We propose future strategies to improve this aspect., Comment: 18 pages, 9 figures. Submitted to ApJ

The interaction between individuals in biological populations, dilute components of chemical systems, or particles transported by turbulent flows depends critically on their contact statistics. This work clarifies those statistics under the simplifying assumptions that the underlying motions approximate a Brownian random walk and that the particles can be treated as noninteracting. We measure the contact-interval (also called the waiting-time or inter-arrival-time), contact-count, and contact-duration distributions in populations of individuals undergoing noninteracting continuous-space-time random walks on a periodic two-dimensional plane (a torus), as functions of the population number density, walker radius, and random-walk step size. The contact-interval is exponentially distributed for times longer than the mean-free-collision time but not for times shorter than that, and the contact duration distribution is strongly peak at the ballistic-crossing time for head-on collisions, when the ballistic-crossing time is short compared to the mean step duration. While successive contacts between individuals are independent, the probability of repeat contact decreases with time after a previous contact. This leads to a negative duration dependence of the waiting-time interval and over dispersion of the contact-count probability density function for all time intervals. The paper demonstrates that for populations of small particles (walker radius small compared to the mean-separation or random-walk step size) the mean-free-collision interval, the ballistic-crossing time, and the random-walk-step duration can be used to construct temporal scalings which allow for common waiting-time, contact-count, and contact-duration distributions across different populations. Semi-analytic approximations for both the waiting-time and contact-duration distributions are also presented.

The solar acoustic oscillations are likely stochastically excited by convective dynamics in the solar photosphere, though few direct observations of individual source events have been made and their detailed characteristics are still unknown. Wave source identification requires measurements that can reliably discriminate the local wave signal from the background convective motions and resonant modal power. This is quite challenging as these 'noise' contributions have amplitudes several orders of magnitude greater than the sources and the propagating wave fields they induce. In this paper, we employ a high-temporal-frequency filter to identify sites of acoustic emission in a radiative magnetohydrodynamic simulation. The properties of the filter were determined from a convolutional neural network trained to identify the two-dimensional acoustic Green's function response of the atmosphere, but once defined, it can be directly applied to an image time series to extract the signal of local wave excitation, bypassing the need for the original neural network. Using the filter developed, we have uncovered previously unknown properties of the acoustic emission process. In the simulation, acoustic events are found to be clustered at mesogranular scales, with peak emission quite deep, about 500 km below the photosphere, and sites of very strong emission can result from the interaction of two supersonic downflows that merge at that depth. We suggest that the method developed, when applied to high-resolution high-cadence observations, such as those forthcoming with Daniel K. Inouye Solar Telescope (DKIST), will have important applications in chromospheric wave-studies and may lead to new investigations in high-resolution local-helioseismology., Comment: 19 Pages, 9 Figures

The Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities which will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the Daniel K. Inouye Solar Telescope hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members, who generously shared their experiences, plans, knowledge and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute.

Observations of the solar photosphere show spatially-compact large-amplitude Doppler velocity events with short lifetimes. In data from the Imaging Magnetograph eXperiment (IMaX) on the first flight of the Sunrise balloon in 2009, events with velocities in excess of 4{\sigma} from the mean can be identified in both intergranular downflow lanes and granular upflows. We show that the statistics of such events are consistent with the random superposition of strong convective flows and p-mode coherence patches. Such coincident superposition has implications for the interpretation of acoustic wave sources in the solar photosphere, and may be important to the interpretation of spectral line profiles formed in solar photosphere., Comment: 10 pages, 6 figures, 1 table

The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfven wave excitation spectrum for coronal heating models. We examine the motions of internetwork flux elements in a 24 hour long Hinode/NFI magnetogram sequence with 90 second cadence, and study both the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 seconds, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short temporal increments is a consequence of random changes in the barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in the distribution can be modeled analytically by accounting for supergranular advection along with motions due to granulation. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive trace motions in measured photospheric flows may yield more robust transport statistics., Comment: submitted to ApJ

Radiative transfer coupled with highly realistic simulations of the solar atmosphere is routinely used to infer the physical properties underlying solar observations. Due to its computational efficiency, the method of short-characteristics is often employed, despite it introducing numerical diffusion as an interpolation artifact. In this paper, we quantify the effect of the numerical diffusion on the spatial resolution of synthesize emergent intensity images, and derive a closed form analytical model of the diffusion error as a function of viewing angle when using linear interpolation. We demonstrate that the image degradation adversely affects the comparison between simulated data and observations, for observations away from disk-center, unless the simulations are computed at much higher intrinsic resolution than the observations. We also show that the diffusion error is readily avoided by interpolating the simulation solution on a viewing-angle aligned grid prior to computing the radiative transfer. Doing this will be critical for comparisons with observations using the upcoming large aperture telescopes --- the Daniel K. Inouye Solar Telescope and the European Solar Telescope., Comment: Accepted in ApJ on October 3, 2017. 12 pages, 8 figures

We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuous-time eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbulence, for which single-particle dispersion differs from the well studied case of homogeneous and isotropic turbulence.

Supergranulation is characterized by horizontally divergent flows with typical length scales of 32 Mm in the solar photosphere. Unlike granulation, the size of which is comparable to both the thickness of the radiative boundary layer and local scale height of the plasma in the photosphere, supergranulation does not reflect any obvious length scale of the solar convection zone. Early suggestions that the depth of second helium ionization is important are not supported by numerical simulations. Thus the origin of the solar supergranulation remains largely a mystery. Moreover, observations of flows in the photosphere using either Doppler imaging or correlation or feature tracking show a monotonic decrease in power at scales larger than supergranulation. Both local area and global spherical shell simulations of solar convection by contrast show the opposite, a power law increase in horizontal flow amplitudes to low wavenumber. Here we examine this disparity, and investigate how the solar supergranulation may arise as a consequence of strong photospheric driving and non-local heat transport by cool diving plumes. Using three dimensional anelastic simulations with surface driving, we show that the kinetic energy of largest convective scales in the upper layers of a stratified domain reflects the depth of transition from strong buoyant driving to adiabatic stratification below. We interpret the observed monotonic decrease in solar convective power at scales larger than supergranulation to be a consequence of this rapid transition, and show how the supergranular scale can be understood as the largest buoyantly driven mode of convection in the Sun.

Solar irradiance variations over solar rotational time-scales are largely determined by the passage of magnetic structures across the visible solar disk. Variations on solar cycle time scales are thought to be similarly due to changes in surface magnetism with activity. Understanding the contribution of magnetic structures to total solar irradiance and solar spectral irradiance requires assessing their contributions as a function of disk position. Since only relative photometry is possible from the ground, the contrasts of image pixels are measured with respect to a center-to-limb intensity profile. Using nine years of full-disk red and blue continuum images from the Precision Solar Photometric Telescope at the Mauna Loa Solar Observatory (PSPT/MLSO), we examine the sensitivity of continuum contrast measurements to the center-to-limb profile definition. Profiles which differ only by the amount of magnetic activity allowed in the pixels used to determine them yield oppositely signed solar cycle length continuum contrast trends; either agreeing with the result of Preminger et al. (2011) showing negative correlation with solar cycle or disagreeing and showing positive correlation with solar cycle. Changes in the center-to-limb profile shape over the solar cycle are responsible for the contradictory contrast results, and we demonstrate that the lowest contrast structures, internetwork and network, are most sensitive to these. Thus the strengths of the full-disk, internetwork, and network photometric trends depend critically on the magnetic flux density used in the quiet-sun definition. We conclude that the contributions of low contrast magnetic structures to variations in the solar continuum output, particularly to long-term variations, are difficult, if not impossible, to determine without the use of radiometric imaging., Comment: Accepted to ApJ. 11 pages, 5 figures

We present the initial results of an observational study into the variation of the dominant length-scale of quiet solar emission: supergranulation. This length-scale reflects the radiative energy in the plasma of the upper solar chromosphere and transition region at the magnetic network boundaries forming as a result of the relentless interaction of magnetic fields and convective motions of the Sun's interior. We demonstrate that a net difference of ~0.5Mm in the supergranular emission length-scale occurs when comparing observations cycle 22/23 and cycle 23/24 minima. This variation in scale is reproduced in the datasets of multiple space- and ground-based instruments and using different diagnostic measures. By means of extension, we consider the variation of the supergranular length-scale over multiple solar minima by analyzing a subset of the Mt Wilson Solar Observatory (MWO) Ca II K image record. The observations and analysis presented provide a tantalizing look at solar activity in the absence of large-scale flux emergence, offering insight into times of "extreme" solar minimum and general behavior such as the phasing and cross-dependence of different components of the spectral irradiance. Given that the modulation of the supergranular scale imprints itself in variations of the Sun's spectral irradiance, as well as in the mass and energy transport into the entire outer atmosphere, this preliminary investigation is an important step in understanding the impact of the quiet sun on the heliospheric system., Comment: 6 pages, 5 figures - ApJL. We thank Frank Eparvier, Tom Woods, Stan Solomon, Anna Malanushenko, and Rachel Hauser for useful discussions and help with the text, SOHO, STEREO, and the Canadian Space Agency for making their data publicly available

As we approach solar convection simulations that seek to model the interaction of small-scale granulation and supergranulation and even larger scales of convection within the near-surface shear layer (NSSL), the treatment of the boundary conditions and minimization of sub-grid scale diffusive processes become increasingly crucial. We here assess changes in the dynamics and the energy flux balance of the flows established in rotating spherical shell segments that capture much of the NSSL with the Curved Spherical Segment (CSS) code using two different diffusion schemes. The CSS code is a new massively parallel modeling tool capable of simulating 3-D compressible MHD convection with a realistic solar stratification in rotating spherical shell segments., Comment: 4 pages, 2 figures, SOHO/GONG 2010 conference proceedings

We investigate the photometric signature of magnetic flux tubes in the solar photosphere. We developed two dimensional, static numerical models of isolated and clustered magnetic flux tubes. We investigated the emergent intensity profiles at different lines-of-sight for various spatial resolutions and opacity models. We found that both geometric and photometric properties of bright magnetic features are determined not only by the physical properties of the tube and its surroundings, but also by the particularities of the observations, including the line/continuum formation height, the spatial resolution and the image analyses techniques applied. We show that some observational results presented in the literature can be interpreted by considering bright magnetic features to be clusters of smaller elements, rather than a monolithic flux tube., Comment: 12 pages

We have examined images from the Precision Solar Photometric Telescope (PSPT) at the Mauna Loa Solar Observatory (MLSO) in search of latitudinal variation in the solar photospheric intensity. Along with the expected brightening of the solar activity belts, we have found a weak enhancement of the mean continuum intensity at polar latitudes (continuum intensity enhancement $\sim0.1 - 0.2%$ corresponding to a brightness temperature enhancement of $\sim2.5{\rm K}$). This appears to be thermal in origin and not due to a polar accumulation of weak magnetic elements, with both the continuum and CaIIK intensity distributions shifted towards higher values with little change in shape from their mid-latitude distributions. Since the enhancement is of low spatial frequency and of very small amplitude it is difficult to separate from systematic instrumental and processing errors. We provide a thorough discussion of these and conclude that the measurement captures real solar latitudinal intensity variations., Comment: 24 pages, 8 figs, accepted in ApJ

Several studies have investigated the fractal and multifractal nature of magnetic features in the solar photosphere and its variation with the solar magnetic activity cycle. Here we extend those studies by examining the fractal geometry of bright magnetic features at higher atmospheric levels, specifically in the solar chromosphere. We analyze structures identified in CaIIK images obtained with the Precision Solar Photometric Telescopes (PSPTs) at Osservatorio Astronomico di Roma (OAR) and Mauna Loa Solar Observatory (MLSO). Fractal dimension estimates depend on the estimator employed, the quality of the images, and the structure identification techniques used. We examine both real and simulated data and employ two different perimeter-area estimators in order to understand the sensitivity of the deduced fractal properties to pixelization and image quality. The fractal dimension of bright 'magnetic' features in CaIIK images ranges between values of 1.2 and 1.7 for small and large structures respectively. This size dependency largely reflects the importance of image pixelization in the measurement of small objects. The fractal dimension of chromospheric features does not show any clear systematic variation with time over the period examined, the descending phase of solar cycle 23. These conclusions, and the analysis of both real and synthetic images on which they are based, are important in the interpretation of previously reported results., Comment: 11 pages

These numerical studies show that ionization influences both the transport and dynamical properties of compressible convection near the surface of the Sun. About two-thirds of the enthalpy transported by convective motions in the region of partial hydrogen ionization is carried as latent heat. The role of fast downflow plumes in total convective transport is substantially elevated by this contribution. Instability of the thermal boundary layer is strongly enhanced by temperature sensitive variations in the radiative properties of the fluid, and this provides a mechanism for plume initiation and cell fragmentation in the surface layers. As the plumes descend, temperature fluctuations and associated buoyancy forces are maintained because of the increased specific heat of the partially ionized material. This can result is supersonic vertical flows. At greater depths, ionization effects diminish, and the plumes are decelerated by significant entrainment of surrounding fluid.