Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques

The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison, and study the effects of varying the disk radius. Adopting a marginally stable disk profile (Q_init=1), we validate the numerical robustness of our model for different spatial extensions, from compact to larger, extended disks (R_disk = 10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combining our findings from the resolution and parameter studies we find a lower limit of the resolution to be able to resolve GI induced fragmentation features and distinct, turbulence inducing clumps. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells, which holds as a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures.Comment: 12 pages, 12 figures; accepted for publication in A&A; for associated movie files, see http://timlichtenberg.net/publications/gi1

The far-infrared - radio correlation in dwarf galaxies

The far-infrared - radio correlation connects star formation and magnetic fields in galaxies, and has been confirmed over a large range of far-infrared luminosities. Recent investigations indicate that it may even hold in the regime of local dwarf galaxies, and we explore here the expected behavior in the regime of star formation surface densities below 0.1 M_sun kpc^{-2} yr^{-1}. We derive two conditions that can be particularly relevant for inducing a change in the expected correlation: a critical star formation surface density to maintain the correlation between star formation rate and the magnetic field, and a critical star formation surface density below which cosmic ray diffusion losses dominate over their injection via supernova explosions. For rotation periods shorter than 1.5x10^7 (H/kpc)^2 yrs, with H the scale height of the disk, the first correlation will break down before diffusion losses are relevant, as higher star formation rates are required to maintain the correlation between star formation rate and magnetic field strength. For high star formation surface densities Sigma_SFR, we derive a characteristic scaling of the non-thermal radio to the far-infrared / infrared emission with Sigma_SFR^{1/3}, corresponding to a scaling of the non-thermal radio luminosity L_s with the infrared luminosity L_{th} as L_{th}^{4/3}. The latter is expected to change when the above processes are no longer steadily maintained. In the regime of long rotation periods, we expect a transition towards a steeper scaling with Sigma_SFR^{2/3}, implying L_s~L_th^{5/3}, while the regime of fast rotation is expected to show a considerably enhanced scatter. These scaling relations explain the increasing thermal fraction of the radio emission observed within local dwarfs, and can be tested with future observations by the SKA and its precursor radio telescopes.Comment: 16 pages, 11 figures, accepted at A&

Planet formation from the ejecta of common envelopes

The close binary system NN Serpentis must have gone through a common envelope phase before the formation of its white dwarf. During this phase, a substantial amount of mass was lost from the envelope. The recently detected orbits of circumbinary planets are likely inconsistent with planet formation before the mass loss.We explore whether new planets may have formed from the ejecta of the common envelope and derive the expected planetary mass as a function of radius.We employed the Kashi & Soker model to estimate the amount of mass that is retained during the ejection event and inferred the properties of the resulting disk from the conservation of mass and angular momentum. The resulting planetary masses were estimated from models with and without radiative feedback. We show that the observed planetary masses can be reproduced for appropriate model parameters. Photoheating can stabilize the disks in the interior, potentially explaining the observed planetary orbits on scales of a few AU. We compare the expected mass scale of planets for 11 additional systems with observational results and find hints of two populations, one consistent with planet formation from the ejecta of common envelopes and the other a separate population that may have formed earlier. The formation of the observed planets from the ejecta of common envelopes seems feasible. The model proposed here can be tested through refined observations of additional post-common envelope systems. While it appears observationally challenging to distinguish between the accretion on pre-existing planets and their growth from new fragments, it may be possible to further constrain the properties of the protoplanetary disk through additional observations of current planetary candidates and post-common envelope binary systems.Comment: 12 pages, 8 figures, 3 tables. Accepted at A&

Rational Parameter Rays of The Multibrot Sets

We prove a structure theorem for the multibrot sets, which are the higher degree analogues of the Mandelbrot set, and give a complete picture of the landing behavior of the rational parameter rays and the bifurcation phenomenon. Our proof is inspired by previous works of Schleicher and Milnor on the combinatorics of the Mandelbrot set; in particular, we make essential use of combinatorial tools such as orbit portraits and kneading sequences. However, we avoid the standard global counting arguments in our proof and replace them by local analytic arguments to show that the parabolic and the Misiurewicz parameters are landing points of rational parameter rays

A new interpretation of the far-infrared - radio correlation and the expected breakdown at high redshift

(Abrigded) Observations of galaxies up to z 2 show a tight correlation between far-infrared and radio continuum emission. We explain the far-infrared - radio continuum correlation by relating star formation and magnetic field strength in terms of turbulent magnetic field amplification, where turbulence is injected by supernova explosions from massive stars. We calculate the expected amount of turbulence in galaxies based on their star formation rates, and infer the expected magnetic field strength due to turbulent dynamo amplification. We estimate the timescales for cosmic ray energy losses via synchrotron emission, inverse Compton scattering, ionization and bremsstrahlung emission, probing up to which redshift strong synchrotron emission can be maintained. We find that the correlation between star formation rate and magnetic field strength in the local Universe can be understood as a result of turbulent magnetic field amplification. If the typical gas density in the interstellar medium increases at high z, we expect an increase of the magnetic field strength and the radio emission, as indicated by current observations. Such an increase would imply a modification of the far-infrared - radio correlation. We expect a breakdown when inverse Compton losses start dominating over synchrotron emission. For a given star formation surface density, we calculate the redshift where the breakdown occurs, yielding z (Sigma_SFR/0.0045 M_solar kpc^{-2} yr^{-1})^{1/(6-alpha/2)}. In this relation, the parameter \alpha describes the evolution of the characteristic ISM density in galaxies as (1+z)^\alpha. Both the possible raise of the radio emission at high redshift and the final breakdown of the far-infrared -- radio correlation at a critical redshift will be probed by the Square Kilometre Array (SKA) and its pathfinders, while the typical ISM density in galaxies will be probed with ALMA.Comment: 13 pages, 14 figures, 1 table, accepted at A&A (proof corrections included

Magnetic fields in primordial accretion disks

Magnetic fields are considered as a vital ingredient of contemporary star formation, and may have been important during the formation of the first stars in the presence of an efficient amplification mechanism. Initial seed fields are provided via plasma fluctuations, and are subsequently amplified by the small-scale dynamo, leading to a strong tangled magnetic field. Here we explore how the magnetic field provided by the small-scale dynamo is further amplified via the $\alpha-\Omega$ dynamo in a protostellar disk and assess its implications. For this purpose, we consider two characteristic cases, a typical Pop.~III star with $10$~M$_\odot$ and an accretion rate of $10^{-3}$~M$_\odot$~yr$^{-1}$, and a supermassive star with $10^5$~M$_\odot$ and an accretion rate of $10^{-1}$~M$_\odot$~yr$^{-1}$. For the $10$~M$_\odot$ Pop.~III star, we find that coherent magnetic fields can be produced on scales of at least $100$~AU, which are sufficient to drive a jet with a luminosity of $100$~L$_\odot$ and a mass outflow rate of $10^{-3.7}$~M$_\odot$~yr$^{-1}$. For the supermassive star, the dynamical timescales in its environment are even shorter, implying smaller orbital timescales and an efficient magnetization out to at least $1000$~AU. The jet luminosity corresponds to $\sim10^{6.0}$~L$_\odot$, and a mass outflow rate of $10^{-2.1}$~M$_\odot$~yr$^{-1}$. We expect that the feedback from the supermassive star can have a relevant impact on its host galaxy.Comment: Accepted for publication in Astronomy & Astrophysics, comments are still welcom