In my talk I reviewed observations of the dark matter and total mass profiles in massive ETGs and clusters and their implications for ΛCDM. In this brief proceedings, I have extracted just a subset of material from my talk due to space limitations.

According to the ΛCDM paradigm of cosmology, galaxies form at the centers of dark matter (DM) halos. While galaxy formation involves complex baryonic physics, the formation of DM halos is governed solely by gravity and cosmology. As a result, many of their properties exhibit a near scale-free behaviour, self-similar in either halo mass, cosmic time or both. This is especially true in the Einstein-de Sitter (EdS) regime, valid at redshifts z ≳ 1, when cosmological scaling relations become particularly simple, and in the narrow mass range of normal galaxies, where the fluctuation power spectrum can be approximated by a power law. Since many galaxy properties are strongly correlated with halo mass, they tend to exhibit a self-similar behaviour as well. A partial list of self-similar properties include the mass function of DM halos, the structure of the cosmic web, the accretion/merger rate of matter onto halos, the density profiles of DM halos and their angular momentum, which eventually determines the galaxy structure. We briefly review these below, and comment on how they can be used in conjunction with simple toy models to gain insight into galaxy formation.

Using the MHD version of Gadget3 (Stasyszyn, Dolag & Beck 2013) and a model for the seeding of magnetic fields by supernovae (SN), we performed simulations of the evolution of the magnetic fields in galaxy clusters and study their effects on the heat transport within the intra cluster medium (ICM). This mechanism – where SN explosions during the assembly of galaxies provide magnetic seed fields – has been shown to reproduce the magnetic field in Milky Way-like galactic halos (Beck et al. 2013). The build up of the magnetic field at redshifts before z = 5 and the accordingly predicted rotation measure evolution are also in good agreement with current observations. Such magnetic fields present at high redshift are then transported out of the forming protogalaxies into the large-scale structure and pollute the ICM (in a similar fashion to metals transport). Here, complex velocity patterns, driven by the formation process of cosmic structures are further amplifying and distributing the magnetic fields. In galaxy clusters, the magnetic fields therefore get amplified to the observed μG level and produce the observed amplitude of rotation measures of several hundreds of rad/m2. We also demonstrate that heat conduction in such turbulent fields on average is equivalent to a suppression factor around 1/20th of the classical Spitzer value and in contrast to classical, isotropic heat transport leads to temperature structures within the ICM compatible with observations (Arth et al. 2014).

Massive galaxy clusters (GC) are filled with a hot, turbulent and magnetised intra-cluster medium (ICM). They are still forming under the action of gravitational instability, which drives supersonic mass accretion flows. These partially dissipate into heat through a complex network of large scale shocks, and partly excite giant turbulent eddies and cascade. Turbulence dissipation not only contributes to heating of the ICM but also amplifies magnetic energy by way of dynamo action. The pattern of gravitational energy turning into kinetic, thermal, turbulent and magnetic is a fundamental feature of GC hydrodynamics but quantitative modelling has remained a challenge. In this contribution we present results from a recent high resolution, fully cosmological numerical simulation of a massive Coma-like galaxy cluster in which the time dependent turbulent motions of the ICM are resolved (Miniati 2014) and their statistical properties are quantified for the first time (Miniati 2015, Beresnyak & Miniati 2015). We combine these results with independent state-of-the art numerical simulations of MHD turbulence (Beresnyak 2012), which shows that in the nonlinear regime of turbulent dynamo (for magnetic Prandtl numbers≳ 1) the growth rate of the magnetic energy corresponds to a fraction CE ≃ 4 − 5 × 10−2 of the turbulent dissipation rate. We thus determine without adjustable parameters the thermal, turbulent and magnetic history of giant GC (Miniati & Beresnyak 2015). We find that the energy components of the ICM are ordered according to a permanent hierarchy, in which the sonic Mach number at the turbulent injection scale is of order unity, the beta of the plasma of order forty and the ratio of turbulent injection scale to Alfvén scale is of order one hundred. These dimensionless numbers remain virtually unaltered throughout the cluster's history, despite evolution of each individual component and the drive towards equipartition of the turbulent dynamo, thus revealing a new type of self-similarity in cosmology. Their specific values, while consistent with current data, indicate that thermal energy dominates the ICM energetics and the turbulent dynamo is always far from saturation, unlike the condition in other familiar astrophysical fluids (stars, interstellar medium of galaxies, compact objects, etc.). In addition, they have important physical meaning as their specific values encodes information about the efficiency of turbulent heating (the fraction of ICM thermal energy produced by turbulent dissipation) and the efficiency of dynamo action in the ICM (CE).

What is a galaxy group?

Using the largest and most accurate ever catalog of galaxy peculiar velocities Cosmicflows-2, the large scale structure has been reconstructed by means of the Wiener filter and constrained realizations assuming as a Bayesian prior model the LCDM standard model of cosmology. Our main result is that the estimated bulk flow is consistent with the LCDM model with the WMAP inferred cosmological parameters. At R=50 (150)Mpc/h the estimated bulk velocity is 250 ± 21 (239 ± 38) km/s. The SGX and SGY components of the CMB dipole velocity are recovered by the Wiener Filter (WF) velocity field down to a very few km/s. The SGZ component of the estimated velocity, the one that is most affected by the Zone of Avoidance, is off by 126 km/s (an almost 2 sigma discrepancy).

Like the Bode-Titius Law before it, the Schmidt Law is not properly understood, given that it has never been reduced to, or predicted from first principles. Star formation is complicated. And, it is almost certainly a multi-scale process that has multiple immediate causes (quiescent, periodic and impulsive in their time dependence; local, global and cosmic/external in their origin) resulting in the same end product: stars. Philosophers of science would say that the theory of star formation is “massively underdetermined by the observations” of stars alone.

Contrary to common belief, the column density PDFs of molecular clouds are not described well by log-normal functions, but are instead power-laws with exponents close to two. We argue that the intrinsic functional form of the PDF cannot be securely determined below AK ~ 0.1-0.2 mag, limiting our ability to investigate more complex models for the shape of the cloud PDF.

The origin of the stellar initial mass function (IMF) is one of the most debated issues in astrophysics. Two major features of the IMF are 1) a fairly robust power-law slope at the high-mass end (Salpeter 1955), and 2) a broad peak around ~ 0.3 M⊙ corresponding to a characteristic stellar mass scale (cf. Elmegreen et al. 2008). In recent years, the dominant theoretical model proposed to account for these features has been the “gravo-turbulent fragmentation” picture (e.g., Hennebelle & Chabrier 2008; Hopkins 2012) whereby the properties of interstellar turbulence lead to the Salpeter power law and gravity sets the characteristic mass scale (Jeans mass). We discuss modifications to this picture based on extensive submillimeter continuum imaging observations of nearby molecular clouds with the Herschel Space Observatory which emphasize the importance of filamentary geometry (André et al. 2010; Könyves et al. 2015). The Herschel results point to the key role of the quasi-universal filamentary structure pervading the cold interstellar medium and support a scenario in which star formation occurs in two main steps (cf. André et al. 2014): first, the dissipation of kinetic energy in large-scale turbulent MHD flows generates ~ 0.1 pc-wide filaments (Arzoumanian et al. 2011) in the cold ISM; second, the densest filaments grow and fragment into prestellar cores (and ultimately protostars) by gravitational instability above a critical threshold ~ 16 M⊙/pc in mass per unit length or ~ 160 M⊙/pc2 in gas surface density (AV ∼ 8). In our observationally-driven scenario, the dense cores making up the peak of the prestellar core mass function (CMF) - likely responsible for the peak of the IMF - result from gravitational fragmentation of filaments near the critical threshold for global gravitational instability. The power-law tail of the CMF/IMF arises from the growth of the Kolmogorov-like power spectrum of initial density fluctuations [P(k) ∝ k−1.6±0.3] measured along Herschel filaments (Roy et al. 2015), in agreement with the model by Inutsuka (2001), and from the power-law distribution of line masses observed for supercritical filaments.

We discuss the formation of filaments in molecular clouds (MCs) as the result of large-scale collapse in the clouds. We first give arguments suggesting that self-gravity dominates the nonthermal motions, and then briefly describe the resulting structure, similar to that found in molecular-line and dust observations of the filaments in the clouds. The filaments exhibit a hierarchical structure in both density and velocity, suggesting a scale-free nature, similar to that of the cosmic web, resulting from the domination of self-gravity from the MC down to the core scale.

The newly discovered Massive Molecular Filament (MMF) G32.02+0.05 (~ 70 pc long, 105 M⊙) has been shaped and compressed by older generations of massive stars. The similarity of this filament in physical structure (density profile, temperature) to much smaller star-forming filaments, suggests that the mechanism to form such filaments may be a universal process. The densest portion of the filament, apparent as an Infrared Dark Cloud (IRDC) shows a range of massive star formation signatures throughout. We investigate the kinematics in this filament and find widespread inverse P cygni asymmetric line profiles. These line asymmetries are interpreted as a signature of large-scale radial collapse. Using line asymmetries observed with optically thick HCO+ (1-0) and optically thin H13CO+ (1-0) across a range of massive star forming regions in the filament, we estimate the global radial infall rate of the filament to range from a few 100 to a few 1000 M⊙ Myr−1 pc−1. At its current infall rate the densest portions of the cloud will more than double their current mass within a Myr.

The origin of the linewidth-size (LWS) scaling law, first noticed by Larson three decades ago and ascribed to turbulence, is still a highly debated issue. Not unexpectedly, its properties depend on the environment and on the line tracer used. When the optically thick 12CO (J=1-0) line is used, a specific medium is sampled: the translucent molecular gas of moderate density that builds up the bulk of the molecular interstellar medium in galaxies like the Milky Way. The sensitivity of the 12CO line to this gas is such that the LWS is found to hold over almost five orders of magnitude in lengthscale, although with a considerable scatter (± 0.5 dex). It also appears to split into two regimes, depending on the gas mass surface density: below a given threshold that is proposed to be linked to the galactic structure, it bears the signature of a turbulent cascade, while above it, the scaling law is ascribed to virial balance. Large deviations from the LWS scaling law are observed at small scales where signatures of turbulent intermittency appear. The mass-size scaling law built with the 12CO (J=1-0) line also splits into two regimes. The mass surface density is uniform (also with a large scatter) above lengthscales ~ 10pc and increases with size at smaller scales, following turbulence predictions. The two thresholds define an average gas density nH ~ 300 cm−3.

The so-called Larson (1981) scaling laws found empirically in molecular clouds have been generally interpreted as evidence that the clouds are turbulent and fractal. In the present contribution we discussed how recent observations and models of cloud formation suggest that:

1. (a) these relations are the result of strong observational biases due to the cloud definition itself: since the filling factor of the dense structures is small, by thresholding the column density the computed mean density between clouds is nearly constant, and nearly the same as the threshold (Ballesteros-Paredes et al. 2012).

2. (b) When accounting for column density variations, the velocity dispersion-size relation does not appears anymore. Instead, dense cores populate the upper-left corner of the δ v-R diagram (Ballesteros-Paredes et al. 2011a).

3. (c) Instead of a δ v-R relation, a more appropriate relation seems to be δ v2 / R = 2 GMΣ, which suggest that clouds are in collapse, rather than supported by turbulence (Ballesteros-Paredes et al. 2011a).

4. (d) These results, along with the shapes of the star formation histories (Hartmann, Ballesteros-Paredes & Heitsch 2012), line profiles of collapsing clouds in numerical simulations (Heitsch, Ballesteros-Paredes & Hartmann 2009), core-to-core velocity dispersions (Heitsch, Ballesteros-Paredes & Hartmann 2009), time-evolution of the column density PDFs (Ballesteros-Paredes et al. 2011b), etc., strongly suggest that the actual source of the non-thermal motions is gravitational collapse of the clouds, so that the turbulent, chaotic component of the motions is only a by-product of the collapse, with no significant “support" role for the clouds. This result calls into question if the scale-free nature of the motions has a turbulent, origin (Ballesteros-Paredes et al. 2011a; Ballesteros-Paredes et al. 2011b, Ballesteros-Paredes et al. 2012).

We review some of the basic population properties of stellar clusters, as well as how they relate to star-formation more broadly within their host galaxies. Despite the common assertion, the vast majority of stars do not form within stellar clusters. For typical galaxies (including the solar neighbourhood), the fraction of stars forming in clusters is ~10%. There are indications however that this fraction increases as a function of increasing star-formation rate surface density, in agreement with model predictions (based on a turbulent ISM and relatively straight-forward prescriptions of star-formation).

The formation of stars is a “social” process. It leads to the assembly of young stars at various length-scales into structures of diverse degrees of self-binding, from gravitationally-bound star clusters to unbound stellar associations, and beyond (e.g., Elmegreen 2000). These different young stellar systems are, however, not independent to each other. In nearby star-forming regions compact clusters appear at few 1-pc scales as the nested centers of star formation within loose stellar aggregations of few 10-pc sizes (e.g., Schmeja et al. 2009). Resolved populations across whole galaxies show that these structures are themselves components of larger stellar complexes with typical sizes of few 100-pc, and this structural behavior seems to extend to kpc scales in galactic super-structures and spiral arms (e.g., Gouliermis et al. 2015). From the stellar clustering point-of-view, star formation behaves as a scale-free process, expressed by power-laws in size distributions and correlation functions (e.g., Elmegreen et al. 2014). The origins of the self-similar stellar structural morphology, the scales where it changes behavior, and how these scales are determined, are fundamental questions to our understanding of star formation.

Turbulence in the interstellar medium is ubiquitous. The turbulent energy density in the gas is significant, and comparable to energy densities of magnetic fields and cosmic rays. Studies of the turbulent interstellar gas in the Milky Way have mostly focused on the neutral gas component, since various spectral lines can give velocity information. Probing turbulent properties in the ionized gas, let alone in magnetic fields, is observationally more difficult. A number of observational methods are discussed below which provide estimates of the maximum scale of fluctuations, the Mach number and other turbulence characteristics.

It has long been recognized that magnetic fields play an important role in many astrophysical environments, yet the strength and structure of magnetic fields beyond our solar system have been at best only qualitatively constrained. The Galactic magnetic field in particular is crucial for modeling the transport of Galactic CRs, for calculating the background to dark matter and CMB-cosmology studies, and for determining the sources of UHECRs. This report gives a brief overview of recent major advances in our understanding of the Galactic magnetic field (GMF) and its lensing of Galactic and ultrahigh energy cosmic rays.

Astrophysical dynamos are usually characterised by huge values of the magnetic Reynolds number (Rm). This reflects the short turn-over time compared to the resistive time. The extreme values of Rm relevant to astrophysical objects cannot be tackled with today's numerical resources and this number is always under-estimated by several orders of magnitudes in numerical models.

Here we chose to focus on an extremely simplified problem (dynamo action from a periodic steady flow) and take advantage of this simplicity to numerically investigate the limit of very large magnetic Reynolds number. We present results recently published in physics journals, which highlight the difficulty of approaching the limit in which dynamo action is independent of the value of the ohmic resistivity (measured by 1/Rm), known as the “fast dynamo” limit. Using state of the art high performance computing, we present high resolution simulations (up to (40963) and extend the value of (Rm) up to (5⋅105).

Turbulent flows exhibit scale-free regimes, for which information on the statistical properties of the dynamics exists for many length-scales. The simulation of turbulent systems can benefit from the inclusion of such information on sub-grid process. How can statistical information about the flow on small scales be optimally incorporated into simulation schemes? Information field dynamics (IFD) is a novel information theoretical framework to design schemes that exploit such statistical knowledge on sub-grid flow fluctuations.

We decribe direct numerical simulations of turbulent astrophysical media exposed to the redshift zero metagalactic background. The simulations assume solar composition and explicitly track ionizations, recombinations, and ion-by-ion radiative cooling for hydrogen, helium, carbon, nitrogen, oxygen, neon, sodium, magnesium, silicon, and iron. Each run reaches a global steady state that not only depends on the ionization parameter, U, and mass-weighted average temperature, TMW, but also on the the one-dimensional turbulent velocity dispersion, σ1D.

We carry out runs that span a grid of models with U ranging from 0 to 10−2 and σ1D ranging from 12 to 58 km s−1, and we vary the product of the mean density and the driving scale of the turbulence, nL, which determines the average temperature of the medium, from nL =1016 to nL =1020 cm−2. The turbulent Mach numbers of our simulations vary from M ≈ 0.5 for the lowest velocity dispersions cases to M ≈ 20 for the largest velocity dispersion cases. When M ≲1, turbulent effects are minimal, and the species abundances are reasonably described as those of a uniform photoionized medium at a fixed temperature. On the other hand, when M ≳ 1, dynamical simulations such as the ones carried out here, are required to accurately predict the species abundances.

We gather our results into a set of tables, to allow future redshift zero studies of the intergalactic medium to account for turbulent effects. They are available at http://zofia.sese.asu.edu/~evan/turbspecies/ and will be updated as we increase our parameter study. These results are explained in more detailed in Gray, Scannapieco, & Kasen (2015), and Gray and Scannapieco (2015)