One of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - is connected to one of the most powerful equations in all of physics - Ampere's law. In doing so, the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.

We propose to use a deterministically-driven class of self-organized criticality sandpile models to carry out predictions of the largest, most dangerous, and hardest to predict solar flares.

The concept of “self-organized criticality” (SOC) was originally proposed as an explanation of 1/f-noise by Bak, Tang, and Wiesenfeld (1987), but turned out to have a far broader significance for scale-free nonlinear energy dissipation processes occurring in the entire universe. Over the last 30 years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into numerical SOC toy models. The novel applications stimulated also vigorous debates about the discrimination between SOC-related and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC models applied to astrophysical observations, attempt to describe what physics can be captured by SOC models, and offer a critique of weaknesses and strengths in existing SOC models.

The superbubble (SB) 30 Dor C with the strong non-thermal X-ray emission is one of the best targets for study of the cosmic-ray (CR) acceleration. We investigated X-ray spectral properties of the SB with a high spatial resolution of ~10 pc. Consequently, the spectra in the east regions can be described with a combination of absorbed thermal and non-thermal models while the spectra in the west regions can be fitted with an absorbed non-thermal model. We found that the observed photon index and intensity in 2-10 keV show variations of 2.0-3.5 and (0.6-8.0) × 10−7 erg s−1 cm−2 str−1, respectively. The results are possibly caused by the spatial variation of the CR acceleration efficiency and/or the circumstellar environment.

There is an ongoing argument regarding galaxies, like there is regarding children, of whether the final outcome is driven primarily by nature or nurture. In the case of galaxies, the total mass plays the role of genetics (nature) and the number of nearby galaxies plays the role of family life (nurture). Untangling the role of each has been particularly difficult for galaxies because the mass of a galaxy is closely tied to its environment.

We show that as equilibrium is approached in deep gravity wells, such as those of galactic halos, gravitational quantum theory predicts that radial particle densities ρ(r) tend toward 1/r2 profiles, and photon-baryon scattering cross sections are significantly reduced.

We develop a new star formation (SF) law based on the density PDF of turbulence and on the multi-freefall concept of gas collapse. We derive a relation where the star formation rate (SFR) correlates with the molecular gas mass per multi-freefall time, whereas previous models had used the average, single-freefall time. We define a new quantity called maximum (multi-freefall) gas consumption rate (MGCR) and show that the actual SFR is only about 0.4% of this maximum possible SFR, confirming the observed low efficiency of star formation.

We study fundamental properties of transonic galactic outflows in the gravitational potential of a cold dark matter halo (DMH) with a central super-massive black hole (SMBH) assuming an isothermal, steady and spherically symmetric state. Transonic solutions of galactic outflows are classified according to their topological features. As result, we find two types of transonic solutions distinguished by a magnitude relationship between the gravity of DMH and that of SMBH. The loci of transonic points for two types are different; one transonic point is formed at a central region (< 0.01kpc) and another is at a very distant region (> 100kpc). Also, mass fluxes and outflow velocities are different for two solutions. Thus, these solutions may differently influence the evolution of galaxies and the release of metals into the intergalactic space.

Furthermore, we apply our model to the Sombrero galaxy. In this galaxy, the wide-spread hot gas is detected as the trace of galactic outflows while the star-formation rate is low, and the observed gas density distribution is similar to the hydrostatic state (Li et al. 2011). To solve this discrepancy, we propose a solution that this galaxy has a slowly accelerating outflow; the transonic point forms in a very distant region (~ 120 kpc) and the wide subsonic region spreads across the stellar distribution. Thus, the gas density distribution in the observed region is similar to the hydrostatic state. Such slowly accelerating outflows are different from high-velocity outflows conventionally studied (Igarashi et al. 2014).

However, this isothermal model requires an unrealistically large mass flux. Then, we apply the polytropic model to this galaxy incorporating mass flux supplied by stellar components. We find that it can reproduce the observed gas density and the temperature distributions with the realistic mass flux. Thus, our polytropic model successfully demonstrates the existence of the slowly accelerating outflow in the Sombrero galaxy (Igarashi et al. 2015).

The smallest dark matter halos are formed first in the early universe (e.g., Hofmann et al. 2001; Berezinsky et al. 2003; Ishiyama et al. 2010). We present results of very large cosmological N-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. In the largest simulation, the motions of 40963 particles in comoving boxes of side lengths 400 pc and 200 pc were followed. The particle masses were 3.4 × 10−11M⊙ and 4.3 × 10−12M⊙, ensuring that halos at the cutoff scale were represented by 30,000 and 230,000 particles, respectively. We found that the central density cusp is much steeper in these halos than in larger halos (dwarf-galaxy-sized to cluster-sized halos), and scales as ρ ∝ r-(1.5–1.3). The cusp slope gradually becomes shallower as the halo mass increases.The slope of halos 50 times more massive than the smallest halo is approximately −1.3. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the cutoff scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be 60–70, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Such halos could still exist in the present universe with the same steep density profiles. Strongly depending on the subhalo mass function and the adopted concentration model, the steeper inner cusps of halos near the cutoff scale enhance the annihilation luminosity of a Milky Way sized halo between 12 to 67 (Ishiyama 2014).

A self-gravitating system usually shows a quasi-universal density profile, such as the NFW profile of a simulated dark matter halo, the flat rotation curve of a spiral galaxy, the Sérsic profile of an elliptical galaxy, the King profile of a globular cluster and the exponential law of the stellar disk. It will be interesting if all of the above can be obtained from first principles. Based on the original work of White & Narayan (1987), we propose that if the self-bounded system is divided into infinite infinitesimal subsystems, the entropy of each subsystem can be maximized, but the whole system's gravity may just play the role of the wall, which may not increase the whole system's entropy St, and finally St may be the minimum among all of the locally maximized entropies (He & Kang 2010). For spherical systems with isotropic velocity dispersion, the form of the equation of state will be a hybrid of isothermal and adiabatic (Kang & He 2011). Hence this density profile can be approximated by a truncated isothermal sphere, which means that the total mass must be finite and our results can be consistent with observations (Kang & He 2011b). Our method requires that the mass and energy should be conserved, so we only compare our results with simulations of mild relaxation (i.e. the virial ratio is close to -1) of dissipationless collapse (Kang 2014), and the fitting also is well. The capacity can be calculated and is found not to be always negative as in previous works, and combining with calculations of the second order variation of the entropy, we find that the thermodynamical stability still can be true (Kang 2012) if the temperature tends to be zero. However, the cusp in the center of dark matter halos can not be explained, and more works will continue.

The above work can be generalized to study the radial distribution of the disk (Kang 2015). The energy constraint automatically disappears in our variation, because angular momentum is much more important than energy for the disk-shape system. To simplify this issue, a toy model is taken: 2D gravity is adopted, then at large scale it will be consistent with a flat rotation curve; the bulge and the stellar disk are studied together. Then with constraints of mass and angular momentum, the calculated surface density can be consistent with the truncated, up-bended or standard exponential law. Therefore the radial distribution of the stellar disk may be determined by both the random and orbital motions of stars. In our fittings the central gravity is set to be nonzero to include the effect of asymmetric components.

Cosmic ray (CR) is an important component of the interstellar medium. It interacts with plasma via embedded magnetic irregularities. We study the magneto-rotational instability (MRI) in the presence of CRs. We analyse the effect of CRs including their diffusion using both linear stability analysis and MHD simulations. Two models are studied. (1) In the shearing box model, uniform initial state is adopted. Linear analysis shows that the growth rate of MRI is not sensitive to the value of CR diffusion coefficient. (2) In the differentially rotating cylinder model, the initial state is taken as a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both linear results are confirmed by MHD simulations.

The Planck satellite (Planck 2015 Results I) has mapped the polarized microwave sky (from 30 GHz to 353 GHz) with unprecedented sensitivity and angular resolution. This wealth of data yields the first complete map of polarized thermal emission from dust in our own Galaxy (Planck Intermediate Results XIX),, shedding new light on the formation of dense cold structures within which new stars and planetary systems are born, under the combined effects of gravity, turbulence and magnetic fields. We present a statistical analysis of this polarized emission from nearby molecular clouds, with an emphasis on the evolution of the maximum polarization fraction observed as a function of column density, and on the anti-correlation between the polarization fraction and the local dispersion of polarization angles. To interpret this data, numerical simulations of anisotropic MHD turbulence (Fromang, Hennebelle, & Teyssier 2006, Hennebelle et al. 2008) underline the essential role played by the topology of the interstellar magnetic field, in particular its large-scale component (Planck Intermediate Results XX). Indeed, the polarization of dust thermal emission at the scales observed by Planck is essentially related to the geometry of the magnetic field. Polarization fractions anti-correlate with column densities, which may be due to a succession of variously polarized structures on the line of sight. They also anti-correlate with the local dispersion of polarization angles. These features are well reproduced by MHD simulations of the diffuse ISM, with comparable correlation coefficients. As an extension to this work published in Planck Intermediate Results XX, the statistical properties of the random component of the interstellar magnetic field are explored using a toy model of the turbulent magnetized ISM based on fractional Brownian motion (fBm) fields. A least-squares analysis to retrieve the statistical properties of the interstellar magnetic field from Planck observations is pursued. Application of this method on the toy model shows good promise, and we are currently working towards its application on Planck data.

Following the discovery of quantum phenomena at laboratory scale (Couder & Fort 2006), de Broglie pilot wave theory (De Broglie 1962) has been revived under a hydrodynamic guise (Bush 2015). Theoretically, it boils down to solving the transport equations for the energy and linear momentum densities of a postulated fundamental fluid in terms of classical wave equations, which inherently are Lorentz-invariant and scale-invariant. Instead of the conventional harmonic solutions, for astronomical and gravitational problems the novel solutions for the homogeneous wave equation in spherical coordinates are more suitable (Munera et al. 1995, Munera & Guzman 1997, and Munera 2000). Two groups of solutions are particularly relevant: (a) The inherently-quantized helicoidal solutions that may be applicable to describe spiral galaxies, and (b) The non-harmonic solutions with time (t) and distance (r) entangled in the single variable q = Ct/r (C is the two-way local electromagnetic speed). When these functions are plotted against 1/q they manifestly depict quantum effects in the near field, and Newtonian-like gravity in the far-field. The near-field predicts quantized effects similar to ring structures and to Titius-Bode structures, both in our own solar system and in exoplanets, the correlation between predicted and observed structures being typically larger than 99 per cent. In the far-field, some non-harmonic functions have a rate of decrement with distance slower than inverse-square thus explaining the flat rotation rate of galaxies. Additional implications for Trojan orbits, and quantized effects in photon deflection were also noted.

Convection is one of the fundamental mechanisms to transport energy, e.g., in planetology, oceanography, as well as in astrophysics where stellar structure is customarily described by the mixing-length theory, which makes use of the mixing-length scale parameter to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height of the star, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to claim that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty. In a recent paper (Pasetto et al. 2014) we presented the first fully analytical scale-free theory of convection that does not require the mixing-length parameter. Our self-consistent analytical formulation of convection determines all the properties of convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium (be it a star, an ocean, or a primordial planet). The new theory of convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time dependent formalism. We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory in astrophysical environment are compared with those from the standard mixing-length paradigm in stars with exceptional results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

Exceptionally deep observations of the distant universe with the Hubble Space Telescope have consistently pushed the frontiers of human knowledge. How deep can we go? What are the faintest and most distant galaxies we can see with the Hubble Space Telescope now, before the launch of the James Webb Space Telescope? This is the challenge taken up by the Frontier Fields, a director's discretionary time campaign with HST and the Spitzer Space Telescope to see deeper into the universe than ever before. The Frontier Fields combines the power of HST with the natural gravitational telescopes of high-magnification clusters of galaxies to produce the deepest observations of clusters and their lensed galaxies ever obtained. I will review the original goals of the Frontier Fields program and its progress over the last several years. In addition to pushing forward the study of the most distant galaxies, the Frontier Fields have been transformative in the study of galaxy clusters and their lensing properties. Finally, I will discuss the prospects for studying galaxies at cosmic dawn with JWST, extremely large ground-based telescopes, and future space missions over the next decade and beyond.

While the identification of a worthy topic or challenge is fundamental to the goal of conducting cutting-edge research, another ingredient is indispensable in the field of observational astronomy: the best possible target. Indeed, the ability to choose from a significant number of extremely powerful gravitational lenses was central to the success of the Frontier Fields project. We here briefly review the surveys that provided this crucial pool of targets, before focusing on the results of ongoing work to identify similarly extreme (if not more extreme) systems at higher redshift for the exploration of a yet more distant extragalactic frontier – with JWST and other, evermore ambitious missions.

Chandra has deeply observed the clusters and parallel fields in four Frontier Fields. These observations allow us to dramatically improve our understanding of cluster mergers by comparing the detailed mapping of the hot cluster gas with high resolution mass maps and by identifying merger shocks and cold fronts. In merging clusters, relativistic particles can be re-accelerated to produce radio relics. A comparison of lensing maps and Chandra images allows us to determine the cluster morphology and dynamical state and if there are offsets between the dark matter and the hot gas.

Abell 2744 was the first HFF cluster completed. It displays a fascinating complexity in its distribution of dark and luminous matter, which led to its nickname of the Pandora cluster. In late 2014 we obtained a deep (110 ks) observation of this cluster with XMM-Newton, with the aim of making a detailed comparison between the optical, X-ray and lensing properties of this system. The new X-ray observation unveiled the presence of three hot gas filaments extending on scales of several Mpc and connected to the cluster core. The X-ray structures coincide spatially with the distribution of galaxies and dark matter and provide strong evidence for the existence of the elusive warm-hot intergalactic medium (WHIM). The new observation also reveals the complexity of the thermodynamic structure of the cluster core and a probable shock front associated with the radio relic located 1 Mpc NW of the cluster core.

Strong gravitational magnification in the core of lensing clusters allows to probe the faint-end of the galaxy luminosity function up to very high redshift. In particular, the Frontier Fields have allowed us to identify a large number of faint dropouts and constrain the Lyman-break luminosity function at z~5-7. I present here the results of an ongoing program with MUSE, a new integral field spectrograph on the Very Large Telescope having a large field of view (1 arcmin2), to confirm these candidate high redshift dropouts through Lyman-α emission and identify additional emitters with high equivalent width, fainter than the depth of the Frontier Fields Hubble images. Combined with similar deep exposures taken with MUSE in blank fields, this gives us the best opportunity to probe the Lyman-α luminosity function over a wide range in luminosity.

The Grism Lens-Amplified Survey From Space (GLASS) is a 140 orbit spectroscopic survey of 10 massive galaxy clusters, including the six Hubble Frontier Fields. GLASS has observed the cluster cores with the HST-WFC3 G102 and G141 grisms providing a wide wavelength coverage in the near-infrared from roughly 0.8–1.7μm. The parallel fields were observed through the optical ACS G800L grism. Taking advantage of the lensing magnification of the clusters, GLASS reaches intrinsic spectroscopic 1σ flux limits of roughly 10-18erg/s/cm2 and improved spatial resolution for lensed sources behind the clusters. These features are particularly useful for the three main science drivers of GLASS which are, I) exploring the universe at the epoch of reionization, II) describe how metals cycle in and out of galaxies, and III) asses the environmental dependence of galaxy evolution. The former two benefit highly from the improved depth and increased resolution provided by the cluster lensing. Apart from the main science drivers, a slew of ancillary science has been enabled by the survey, including improving cluster lens modeling and searches for supernovae. Here we present the survey and the GLASS data releases, which are continuously being made available to the community through https://archive.stsci.edu/prepds/glass/. For further information we refer to Schmidt et al. (2014), Treu et al. (2015), and http://glass.physics.ucsb.edu.