High-resolution Adaptive Mesh Refinement Research Articles

Growth of a Massive Black Hole in a Dense Star Cluster Via Tidal Disruption Accretion

Stars that are tidally disrupted by a massive black hole (MBH) may contribute significantly to the growth of the MBH, especially in dense nuclear star clusters. Yet, this tidal disruption accretion (TDA) of stars onto the MBH has largely been overlooked compared to the gas accretion (GA) channel in most numerical experiments until now. In this work, we implement a black hole growth channel via TDA in the high-resolution adaptive mesh refinement code Enzo to investigate its influence on an MBH seed’s early evolution. We find that an MBH seed grows rapidly from 103 to ≳106 M ⊙ in 200 Myr in some of the tested simulations. Compared to an MBH seed that grows only via GA, TDA can enhance the MBH’s growth rate by more than 1 order of magnitude. However, as predicted, TDA mainly helps the early growth of the MBH (from 103–4 to ≲105 M ⊙) while the later evolution is generally dominated by GA. We also observe that the star formation near the MBH is suppressed when TDA is the most active, sometimes with a visible cavity in gas (of size ∼ a few pc) created in the vicinity of the MBH. It is because the MBH may grow expeditiously with both GA and TDA, and the massive MBH could consume its neighboring gas faster than being replenished by gas inflows. Our study demonstrates the need to consider different channels of black hole accretion that may provide clues for the existence of supermassive black holes at high redshifts.

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) [3] to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥107) with the successful resolution of plasmoid instabilities and thin current sheets.

Numerical investigation of three deflagration-to-detonation transition conditions related to the velocity of the spontaneous reaction wave

In this work, the deflagration-to-detonation transition (DDT) process in a tube filled with quiescent and stoichiometric hydrogen/oxygen mixture is numerically simulated by a detailed chemical reaction model together with a high-resolution adaptive mesh refinement (AMR) mesh system. Then the flow field is analyzed in detail. It is found that for the onset of detonation in a DDT process there are three essential conditions related to the velocity of the spontaneous reaction wave DSpRW. The first condition is that on a hot spot the DSpRW should be slower than the speed of the Chapman–Jouguet (CJ) detonation wave DCJ to make sure that a spontaneous shock wave could arise originating from the spontaneous reaction wave. The spontaneous shock wave and the spontaneous reaction wave have conspicuous positive correlation to accelerate the spontaneous reaction wave to be faster than the local sound speed, which is the second DDT condition. With this condition the spontaneous reaction wave could catch up with its associated spontaneous shock wave and implement a coupling of the gasdynamics and the chemical energy release. This process is in line with Lee's SWACER idea, while throughout the process the spontaneous reaction wave propagates mainly through the Zel'dovich's reactivity gradients mechanism. Meanwhile, the gas velocity Vg is also essential to maintain the above two conditions and the resultant velocity meets the relation ∥DSpRW+Vg∥≥DCJ, which is the third condition. Distinctly this settles the wave speed gap between deflagration and detonation. More importantly, gas velocity plays an important role especially for the pressure build-up. The most important expressive differences between CJ deflagration and CJ detonation are the gas velocities of both the reactants and products as well as the pressure build-up. When these three relations successfully trigger a DDT and get a detonation wave, they still hold in the resulting detonation wave. They are delicately inherited as the inherent characters of the (detonation) wave. Formerly they are preconditioning-sustaining in the DDT process, and now they become self-sustaining in the detonation wave. Besides, the important role of the progress ratio of the induction period ε is emphasized for a spontaneous propagation.

Magnetized interstellar molecular clouds – II. The large-scale structure and dynamics of filamentary molecular clouds

Abstract We perform ideal magnetohydrodynamics high-resolution adaptive mesh refinement simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ∼4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fibre/web-like substructures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to L1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of the true three-dimensional physical shape, size, and velocity structure of the clouds. Helical magnetic field structures found around filamentary clouds that are interpreted from Zeeman observations can be explained by a simple bending of the magnetic field that pierces through the cloud. We demonstrate that two dark clouds form a T-shaped configuration that is strikingly similar to the infrared dark cloud SDC13, leading to the interpretation that SDC13 results from a collision of two long filamentary clouds. We show that a moderately strong magnetic field (${{\cal M}_{\rm A}}\sim 1$) is crucial for maintaining a long and slender filamentary cloud for a long period of time ∼0.5 Myr.

Rise of the first supermassive stars

We use high resolution adaptive mesh refinement simulations to model the formation of massive metal-free stars in the early Universe. By applying Lyman-Werner (LW) backgrounds of 100 J$_{21}$ and 1000 J$_{21}$ respectively we construct environments conducive to the formation of massive stars. We find that only in the case of the higher LW backgrounds are super-critical accretion rates realised that are necessary for super-massive star (SMS) formation. Mild fragmentation is observed for both backgrounds. Violent dynamical interactions between the stars that form in the more massive halo formed (1000 J$_{21}$ background) results in the eventual expulsion of the two most massive stars from the halo. In the smaller mass halo (100 J$_{21}$ background) mergers of stars occur before any multibody interactions and a single massive Pop III star is left at the centre of the halo at the end of our simulation. Feedback from the very massive Pop III stars is not effective in generating a large HII region with ionising photons absorbed within a few thousand AU of the star. In all cases a massive black hole seed is the expected final fate of the most massive objects. The seed of the massive Pop III star which remained at the centre of the less massive halo experiences steady accretion rates of almost $10^{-2}$ M$_{\odot}$/yr and if these rates continue could potentially experience super-Eddington accretion rates in the immediate aftermath of collapsing into a black hole.

Collapse in self-gravitating turbulent fluids

Motivated by the nonlinear star formation efficiency found in recent numerical simulations by a number of workers, we perform high-resolution adaptive mesh refinement simulations of star formation in self-gravitating turbulently driven gas. As we follow the collapse of this gas, we find that the character of the flow changes at two radii, the disk radius $r_d$, and the radius $r_*$ where the enclosed gas mass exceeds the stellar mass. Accretion starts at large scales and works inwards. In line with recent analytical work, we find that the density evolves to a fixed attractor, $\rho(r,t ) \rightarrow \rho(r)$, for $r_d<r<r_*$; mass flows through this structure onto a sporadically gravitationally unstable disk, and from thence onto the star. In the bulk of the simulation box we find that the random motions $v_T \sim r^p$ with $p \sim 0.5$, in agreement with Larson's size-linewidth relation. In the vicinity of massive star forming regions we find $ p \sim 0.2-0.3$, as seen in observations. For $r<r_*$, $v_T$ increases inward, with $p=-1/2$. Finally, we find that the total stellar mass $M_*(t)\sim t^2$ in line with previous numerical and analytic work that suggests a nonlinear rate of star formation.

MASS TRANSPORT AND TURBULENCE IN GRAVITATIONALLY UNSTABLE DISK GALAXIES. I. THE CASE OF PURE SELF-GRAVITY

The role of gravitational instability-driven turbulence in determining the structure and evolution of disk galaxies, and the extent to which gravity rather than feedback can explain galaxy properties, remains an open question. To address it, we present high-resolution adaptive mesh refinement simulations of Milky Way-like isolated disk galaxies, including realistic heating and cooling rates and a physically motivated prescription for star formation, but no form of star formation feedback. After an initial transient, our galaxies reach a state of fully nonlinear gravitational instability. In this state, gravity drives turbulence and radial inflow. Despite the lack of feedback, the gas in our galaxy models shows substantial turbulent velocity dispersions, indicating that gravitational instability alone may be able to power the velocity dispersions observed in nearby disk galaxies on 100 pc scales. Moreover, the rate of mass transport produced by this turbulence approaches yr−1 for Milky Way-like conditions, sufficient to fully fuel star formation in the inner disks of galaxies. In a companion paper, we add feedback to our models, and use the comparison between the two cases to understand which galaxy properties depend sensitively on feedback and which can be understood as the product of gravity alone. All of the code, initial conditions, and simulation data for our model are publicly available.

Numerical simulation of star formation in filamentary dark molecular clouds

AbstractNumerical simulations of star formation faces challenges including the huge spatial dynamic range and the presence of multiply coupled highly non-linear physics, such as magnetic field, supersonic turbulence, gravitation, radiation and protostellar outflow feedback. We present in this symposium our latest high resolution adaptive mesh refinement numerical simulations of the formation of filamentary dark molecular clouds from 4.55 pc size scale down to the formation of a protostellar cluster with maximum resolution at 28 AU. The physical properties of the long braided filamentary dark cloud formed in the simulation, the magnetic field properties of the cloud clumps, and the protostellar mass function in the simulations match well with the latest observations.

The effect of dark matter resolution on the collapse of baryons in high-redshift numerical simulations

We examine the impact of dark matter particle resolution on the formation of a baryonic core in high resolution adaptive mesh refinement simulations. We test the effect that both particle smoothing and particle splitting have on the hydrodynamic properties of a collapsing halo at high redshift (z > 20). Furthermore, we vary the background field intensity, with energy below the Lyman limit (< 13.6 eV), as may be relevant for the case of metal-free star formation and super-massive black hole seed formation. We find that using particle splitting methods greatly increases our particle resolution without introducing any numerical noise and allows us to achieve converged results over a wide range of external background fields. Additionally, we find that for lower values of the background field a lower dark matter particle mass is required. We define the radius of the core as the point at which the enclosed baryonic mass dominates over the enclosed dark matter mass. For our simulations this results in $\rm{R_{core} \sim 5\ pc}$. We find that in order to produce converged results which are not affected by dark matter particles requires that the relationship ${M_{\rm{core}} / M_{\rm{DM}}} > 100.0$ be satisfied, where ${M_{\rm{core}}}$ is the enclosed baryon mass within the core and $M_{\rm{DM}}$ is the minimum dark matter particle mass. This ratio should provide a very useful starting point for conducting convergence tests before any production run simulations. We find that dark matter particle smoothing is a useful adjunct to already highly resolved simulations.

Rayleigh–Taylor instability in magnetohydrodynamic simulations of the Crab nebula

In this paper we discuss the development of Rayleigh-Taylor filaments in axisymmetric simulations of Pulsar wind nebulae (PWN). High-resolution adaptive mesh refinement magnetohydrodynamic (MHD) simulations are used to resolve the non-linear evolution of the instability. The typical separation of filaments is mediated by the turbulent flow in the nebula and hierarchical growth of the filaments. The strong magnetic dissipation and field-randomization found in recent global three-dimensional simulations of PWN suggests that magnetic tension is not strong enough to suppress the growth of RT filaments, in agreement with the observations of prominent filaments in the Crab nebula. The long-term axisymmetric results presented here confirm this finding.

MODELING ACTIVE GALACTIC NUCLEUS FEEDBACK IN COOL-CORE CLUSTERS: THE BALANCE BETWEEN HEATING AND COOLING

We study the long-term evolution of an idealized cool-core galaxy cluster under the influence of momentum-driven AGN feedback using three-dimensional high-resolution (60 pc) adaptive mesh refinement (AMR) simulations. The momentum-driven AGN feedback is modeled with a pair of (small-angle) precessing jets, and the jet power is calculated based on the accretion rate of the cold gas in the vicinity of the Supermassive Black Hole (SMBH). The ICM first cools into clumps along the propagation direction of the AGN jets. As the jet power increases, gas condensation occurs isotropically, forming spatially extended (up to a few tens kpc) structures that resemble the observed $\rm H\alpha$ filaments in Perseus and many other cool-core cluster. Jet heating elevates the gas entropy and cooling time, halting clump formation. The cold gas that is not accreted onto the SMBH settles into a rotating disk of $\sim 10^{11}$ M$_{\odot}$. The hot gas cools directly onto the cold disk while the SMBH accretes from the innermost region of the disk, powering the AGN that maintains a thermally balanced steady state for a few Gyr. The mass cooling rate averaged over 7 Gyr is $\sim 30$ M$_{\odot}$/yr, an order of magnitude lower than the classic cooling flow value (which we obtain in runs without the AGN). Medium resolution simulations produce similar results, but when the resolution is lower than 0.5 kpc, the cluster experiences cycles of gas condensation and AGN outbursts. Owing to its self-regulating mechanism, AGN feedback can successfully balance cooling with a wide range of model parameters. Besides suppressing cooling, our model produces cold structures in early stages (up to $\sim 2$ Gyr) that are in good agreement with the observations. However, the long-lived massive cold disk is unrealistic, suggesting that additional physical processes are still needed.

HEAVY DUST OBSCURATION OFz= 7 GALAXIES IN A COSMOLOGICAL HYDRODYNAMIC SIMULATION

Hubble Space Telescope observations with Wide Field Camera 3/IR reveal that galaxies at z~7 have very blue ultraviolet (UV) colors, consistent with these systems being dominated by young stellar populations with moderate or little attenuation by dust. We investigate UV and optical properties of the high-z galaxies in the standard cold dark matter model using a high-resolution adaptive mesh refinement cosmological hydrodynamic simulation. For this purpose, we perform panchromatic three-dimensional dust radiative transfer calculations on 198 galaxies of stellar mass 5x10^8-3x10^{10} Msun with three parameters, the dust-to-metal ratio, the extinction curve, and the fraction of directly escaped light from stars (\fesc). Our stellar mass function is found to be in broad agreement with Gonzalez et al., independent of these parameters. We find that our heavily dust-attenuated galaxies (A_V~1.8) can also reasonably match modest UV-optical colors, blue UV slopes, as well as UV luminosity functions, provided that a significant fraction (~10%) of light directly escapes from them. The observed UV slope and scatter are better explained with an Small Magellanic Cloud-type extinction curve, whereas Milky Way-type dust predicts too blue UV colors due to the 2175A bump. We expect that upcoming observations by ALMA will be able to test this heavily obscured model.

HYBRID COSMOLOGICAL SIMULATIONS WITH STREAM VELOCITIES

In the early universe, substantial relative "stream" velocities between the gas and dark matter arise due to radiation pressure and persist after recombination. To asses the impact of these velocities on high-redshift structure formation, we carry out a suite of high-resolution Adaptive Mesh Refinement (AMR) cosmological simulations, which use Smoothed Particle Hydrodynamic datasets as initial conditions, converted using a new tool developed for this work. These simulations resolve structures with masses as small as a few 100 M$_\odot$, and we focus on the $10^6$ M$_\odot$ "mini-halos" in which the first stars formed. At $z \approx 17,$ the presence of stream velocities has only a minor effect on the number density of halos below $10^6$ M$_\odot$, but it greatly suppresses gas accretion onto all halos and the dark matter structures around them. Stream velocities lead to significantly lower halo gas fractions, especially for $\approx 10^5$ M$_\odot$ objects, an effect that is likely to depend on the orientation of a halo's accretion lanes. This reduction in gas density leads to colder, more compact radial profiles, and it substantially delays the redshift of collapse of the largest halos, leading to delayed star formation and possibly delayed reionization. These many differences suggest that future simulations of early cosmological structure formation should include stream velocities to properly predict gas evolution, star-formation, and the epoch of reionization.

Three-dimensional structure of relativistic jet formation

Using high-resolution adaptive mesh refinement simulations in 3D, we investigate the formation of relativistic jets from rotating magnetospheres. Here, we focus on the development of non-axisymmetric modes due to internal and external perturbations to the jet. These originate either from injection of perturbations with the flow or from a clumpy external medium. In the helical field geometry of the accelerating jet, the m = 1–5 modes are analysed and found to saturate at a height of ∼20 inner disc radii. We also discuss a means to control artificial amplification of m = 4 noise in the Cartesian simulation geometry. Strong perturbations due to an inhomogeneous ambient medium lead to flow configurations with increased magnetic pitch and thus indicate a self-stabilization of the jet formation mechanism.

SIMULATING THE COOLING FLOW OF COOL-CORE CLUSTERS

We carry out high-resolution adaptive mesh refinement simulations of a cool core cluster, resolving the flow from Mpc scales down to pc scales. We do not (yet) include any AGN heating, focusing instead on cooling in order to understand how gas gets to the supermassive black hole (SMBH) at the center of the cluster. We find that, as the gas cools, the cluster develops a very flat temperature profile, undergoing a cooling catastrophe only in the central 10-100 pc of the cluster. Outside of this region, the flow is smooth, with no local cooling instabilities, and naturally produces very little low-temperature gas (below a few keV), in agreement with observations. The gas cooling in the center of the cluster rapidly forms a thin accretion disk. The amount of cold gas produced at the very center grows rapidly until a reasonable estimate of the resulting AGN heating rate (assuming even a moderate accretion efficiency) would overwhelm cooling. We argue that this naturally produces a thermostat which links the cooling of gas out to 100 kpc with the cold gas accretion in the central 100 pc, potentially closing the loop between cooling and heating. Isotropic heat conduction does not affect the result significantly, but we show that including the potential well of the brightest cluster galaxy is necessary to obtain the correct result. Also, we found that the outcome is sensitive to resolution, requiring very high mass resolution to correctly reproduce the small transition radius.

EVOLUTION AND DISTRIBUTION OF MAGNETIC FIELDS FROM ACTIVE GALACTIC NUCLEI IN GALAXY CLUSTERS. II. THE EFFECTS OF CLUSTER SIZE AND DYNAMICAL STATE

Theory and simulations suggest that magnetic fields from radio jets and lobes powered by their central super massive black holes can be an important source of magnetic fields in the galaxy clusters. This is paper II in a series of studies where we present self-consistent high-resolution adaptive mesh refinement cosmological magnetohydrodynamic (MHD) simulations that simultaneously follow the formation of a galaxy cluster and evolution of magnetic fields ejected by an active galactic nucleus (AGN). We studied 12 different galaxy clusters with virial masses ranging from 1 $\times$ 10$^{14}$ to 2 $\times$ 10$^{15}$ M$_{\odot}$. In this work we examine the effects of the mass and merger history on the final magnetic properties. We find that the evolution of magnetic fields is qualitatively similar to those of previous studies. In most clusters, the injected magnetic fields can be transported throughout the cluster and be further amplified by the intra-cluster medium (ICM) turbulence during the cluster formation process with hierarchical mergers, while the amplification history and the magnetic field distribution depend on the cluster formation and magnetism history. This can be very different for different clusters. The total magnetic energies in these clusters are between 4 $\times$ 10$^{57}$ and $10^{61}$ erg, which is mainly decided by the cluster mass, scaling approximately with the square of the total mass. Dynamically older relaxed clusters usually have more magnetic fields in their ICM. The dynamically very young clusters may be magnetized weakly since there is not enough time for magnetic fields to be amplified.

GALAXY FORMATION WITH SELF-CONSISTENTLY MODELED STARS AND MASSIVE BLACK HOLES. I. FEEDBACK-REGULATED STAR FORMATION AND BLACK HOLE GROWTH

There is mounting evidence for the coevolution of galaxies and their embedded massive black holes (MBHs) in a hierarchical structure formation paradigm. To tackle the nonlinear processes of galaxy-MBH interaction, we describe a self-consistent numerical framework which incorporates both galaxies and MBHs. The high-resolution adaptive mesh refinement (AMR) code Enzo is modified to model the formation and feedback of molecular clouds at their characteristic scale of 15.2 pc and the accretion of gas onto a MBH. Two major channels of MBH feedback, radiative feedback (X-ray photons followed through full 3D adaptive ray tracing) and mechanical feedback (bipolar jets resolved in high-resolution AMR), are employed. We investigate the coevolution of a 9.2e11 Msun galactic halo and its 1e5 Msun embedded MBH at redshift 3 in a cosmological LCDM simulation. The MBH feedback heats the surrounding ISM up to 1e6 K through photoionization and Compton heating and locally suppresses star formation in the galactic inner core. The feedback considerably changes the stellar distribution there. This new channel of feedback from a slowly growing MBH is particularly interesting because it is only locally dominant, and does not require the heating of gas globally on the disk. The MBH also self-regulates its growth by keeping the surrounding ISM hot for an extended period of time.

CONSTRAINING INTRACLUSTER GAS MODELS WITH AMiBA13

Clusters of galaxies have been used extensively to determine cosmological parameters. A major difficulty in making best use of Sunyaev-Zel'dovich (SZ) and X-ray observations of clusters for cosmology is that using X-ray observations it is difficult to measure the temperature distribution and therefore determine the density distribution in individual clusters of galaxies out to the virial radius. Observations with the new generation of SZ instruments are a promising alternative approach. We use clusters of galaxies drawn from high-resolution adaptive mesh refinement (AMR) cosmological simulations to study how well we should be able to constrain the large-scale distribution of the intra-cluster gas (ICG) in individual massive relaxed clusters using AMiBA in its configuration with 13 1.2-m diameter dishes (AMiBA13) along with X-ray observations. We show that non-isothermal beta models provide a good description of the ICG in our simulated relaxed clusters. We use simulated X-ray observations to estimate the quality of constraints on the distribution of gas density, and simulated SZ visibilities (AMiBA13 observations) for constraints on the large-scale temperature distribution of the ICG. We find that AMiBA13 visibilities should constrain the scale radius of the temperature distribution to about 50% accuracy. We conclude that the upgraded AMiBA, AMiBA13, should be a powerful instrument to constrain the large-scale distribution of the ICG.

ACCRETION SHOCKS IN CLUSTERS OF GALAXIES AND THEIR SZ SIGNATURE FROM COSMOLOGICAL SIMULATIONS

Cold dark matter (CDM) hierarchical structure formation models predict the existence of large-scale accretion shocks between the virial and turnaround radii of clusters of galaxies. Kocsis et al. (2005) suggest that the Sunyaev-Zel'dovich (SZ) signal associated with such shocks might be observable with the next generation radio interferometer, ALMA. We study the three--dimensional distribution of accretion shocks around individual clusters of galaxies drawn from adaptive mesh refinement (AMR) and smoothed particle hydrodynamics (SPH) simulations of LCDM (dark energy dominated CDM) models. In relaxed clusters, we find two distinct sets of shocks. One set ("virial shocks"), with Mach numbers of 2.5-4, is located at radii 0.9-1.3 Rvir, where Rvir is the spherical infall estimate of the virial radius, covering about 40-50% of the total surface area around clusters at these radii. Another set of stronger shocks ("external shocks") is located farther out, at about 3 Rvir, with large Mach numbers (~100), covering about 40-60% of the surface area. We simulate SZ surface brightness maps of relaxed massive galaxy clusters drawn from high resolution AMR runs, and conclude that ALMA should be capable of detecting the virial shocks in massive clusters of galaxies. More simulations are needed to improve estimates of astrophysical noise and to determine optimal observational strategies.

Escape of Ionizing Radiation from High‐Redshift Galaxies

We model the escape of ionizing radiation from high-redshift galaxies using high-resolution Adaptive Mesh Refinement N-body + hydrodynamics simulations. Our simulations include time-dependent and spatially-resolved transfer of ionizing radiation in three dimensions, including effects of dust absorption. For galaxies of total mass M > 10^11 Msun and star formation rates SFR ~ 1-5 Msun/yr, we find angular averaged escape fractions of 0.01-0.03 over the entire redshift interval studied (3<z<9). In addition, we find that the escape fraction varies by more than an order of magnitude along different lines-of-sight within individual galaxies, from the largest values near galactic poles to the smallest along the galactic disk. The escape fraction declines steeply at lower masses and SFR. We show that the low values of escape fractions are due to a small fraction of young stars located just outside the edge of HI disk. We compare our predicted escape fraction of ionizing photons with previous results, and find a general agreement with both other simulation results and available direct detection measurements at z ~ 3. We also compare our simulations with a novel method to estimate the escape fraction in galaxies from the observed distribution of neutral hydrogen column densities along the lines of sights to long duration gamma-ray bursts. Using this method we find escape fractions of the GRB host galaxies of 2-3%, consistent with our theoretical predictions. [abridged]