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Wave (fuzzy) dark matter ($\psi$DM) consists of ultralight bosons, featuring a solitonic core within a granular halo. Here we extend $\psi$DM to two components, with distinct particle masses $m$ and coupled only through gravity, and investigate the resulting soliton-halo structure via cosmological simulations. Specifically, we assume $\psi$DM contains $75$ per cent major component and $25$ per cent minor component, fix the major-component particle mass to $m_{\rm major}=1\times10^{-22}\,{\rm eV}$, and explore two different minor-component particle masses with $m_{\rm major}:m_{\rm minor}=3:1$ and $1:3$, respectively. For $m_{\rm major}:m_{\rm minor}=3:1$, we find that (i) the major- and minor-component solitons coexist, have comparable masses, and are roughly concentric. (ii) The soliton peak density is significantly lower than the single-component counterpart, leading to a smoother soliton-to-halo transition and rotation curve. (iii) The combined soliton mass of both components follows the same single-component core-halo mass relation. In dramatic contrast, for $m_{\rm major}:m_{\rm minor}=1:3$, a minor-component soliton cannot form with the presence of a stable major-component soliton; the total density profile, for both halo and soliton, is thus dominated by the major component and closely follows the single-component case. To support this finding, we propose a toy model illustrating that it is difficult to form a soliton in a hot environment associated with a deep gravitational potential. The work demonstrates the extra flexibility added to the multi-component $\psi$DM model can resolve observational tensions over the single-component model while retaining its key features., Comment: 19 pages, 24 figures, 1 table, accepted for publication in MNRAS

Ultralight axion-like particles $m_a \sim 10^{-22}$ eV, or Fuzzy Dark Matter (FDM), behave comparably to cold dark matter (CDM) on cosmological scales and exhibit a kpc-size de Broglie wavelength capable of alleviating established (sub-)galactic-scale problems of CDM. Substructures inside an FDM halo incur gravitational potential perturbations, resulting in stellar heating sufficient to account for the Galactic disc thickening over a Hubble time, as first demonstrated by Church et al. We present a more sophisticated treatment that incorporates the full baryon and dark matter distributions of the Milky Way and adopts stellar disc kinematics inferred from recent Gaia, APOGEE, and LAMOST surveys. Ubiquitous density granulation and subhalo passages respectively drive inner disc thickening and flaring of the outer disc, resulting in an observationally consistent `U-shaped' disc vertical velocity dispersion profile with the global minimum located near the solar radius. The observed age-velocity dispersion relation in the solar vicinity can be explained by the FDM-substructure-induced heating and places an exclusion bound $m_a \gtrsim 0.4\times10^{-22}$ eV. We assess non-trivial uncertainties in the empirical core-halo relation, FDM subhalo mass function and tidal stripping, and stellar heating estimate. The mass range $m_a\simeq 0.5-0.7\times10^{-22}$ eV favoured by the observed thick disc kinematics is in tension with several exclusion bounds inferred from dwarf density profiles, stellar streams, and Milky Way satellite populations, which could be significantly relaxed due to the aforesaid uncertainties. Additionally, strongly anisotropic heating could help explain the formation of ultra-thin disc galaxies., Comment: 19 pages, 9 figures; Accepted for publication in MNRAS. Matches published version

We present a new special relativistic hydrodynamics (SRHD) code capable of handling coexisting ultra-relativistically hot and non-relativistically cold gases. We achieve this by designing a new algorithm for conversion between primitive and conserved variables in the SRHD solver, which incorporates a realistic ideal-gas equation of state covering both the relativistic and non-relativistic regimes. The code can handle problems involving a Lorentz factor as high as 106 and optimally avoid the catastrophic cancellation. In addition, we have integrated this new SRHD solver into the code gamer (https://github.com/gamer-project/gamer) to support adaptive mesh refinement and hybrid OpenMP/MPI/GPU parallelization. It achieves a peak performance of 7 × 107 cell updates per second on a single Tesla P100 GPU and scales well to 2048 GPUs. We apply this code to two interesting astrophysical applications: (a) an asymmetric explosion source on the relativistic blast wave and (b) the flow acceleration and limb brightening of relativistic jets.

Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{\rm b} \sim 10^{-22}\ \rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical simulations that solve the Schr\"odinger-Poisson (SP) equation show that FDM halos consist of a central solitonic core, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states. These excited states also interfere with the soliton, causing it to oscillate and execute a confined random walk with respect to the halo center of mass. Using high-resolution numerical simulations of a $6.6 \times 10^9 M_{\odot}$ FDM halo with $m_{\rm b} = 8 \times 10^{-23}\ \rm eV$ in isolation, we demonstrate that the wobbling, oscillating soliton gravitationally perturbs nuclear objects, such as supermassive black holes or dense star clusters, causing them to diffuse outwards. In particular, we show that, on average, objects with mass $\lesssim 0.3 \%$ of the soliton mass ($M_{\rm sol}$) are expelled from the soliton in $\sim 3\ \rm Gyr$, after which they continue their outward diffusion due to gravitational interactions with the soliton and the halo granules. More massive objects ($\gtrsim 1 \% M_{\rm sol}$), while executing a random walk, remain largely confined to the soliton due to dynamical friction. We also present an effective treatment of the diffusion, based on kinetic theory, that accurately reproduces the outward motion of low mass objects and briefly discuss how the observed displacements of star clusters and active galactic nuclei from the centers of their host galaxies can be used to constrain FDM., Comment: 20 pages, 9 figures, minor revisions, accepted for publication in ApJ

Fuzzy dark matter (FDM) has been a promising alternative to standard cold dark matter. The model consists of ultralight bosons with mass $m_b \sim 10^{-22}$ eV and features a quantum-pressure-supported solitonic core that oscillates. In this work, we show that the soliton density oscillations persist even after significant tidal stripping of the outer halo. We report two intrinsic yet distinct timescales associated, respectively, with the ground-state soliton wavefunction $\tau_{00}$ and the soliton density oscillations $\tau_\text{soliton}$, obeying $\tau_\text{soliton} /\tau_{00} \simeq 2.3$. The central star cluster (SC) in Eridanus II has a characteristic timescale $\tau_\text{soliton} / \tau_\text{SC} \sim 2$ to $3$ that deviates substantially from unity. As a result, we demonstrate, both analytically and numerically with three-dimensional self-consistent FDM simulations, that the gravitational heating of the SC owing to soliton density oscillations is negligible irrespective of $m_b$. We also show that the subhalo mass function to form Eridanus II does not place a strong constraint on $m_b$. These results are contrary to the previous findings by Marsh & Niemeyer (2019)., Comment: 19 pages, 19 figures; Accepted for publication in PRD

Extremely light bosonic wave dark matter ($\psi$DM) is an emerging dark matter candidate contesting the conventional cold dark matter paradigm and a model subject to intense scrutiny of late. This work for the first time reports testable salient features pertinent to gravitational lenses of $\psi$DM halos. $\psi$DM halos are distinctly filled with large-amplitude, small-scale density fluctuations with $\delta\rho/\rho_{\rm halo}\sim 1$ in form of density granules. This halo yields ubiquitous flux ratio anomalies of a few tens of percent, as is typically found for lensed quasars, and may also produce rare hexad and octad images, for sources located in well-defined caustic zones. We have found new critical features appearing in the highly de-magnified lens center when the halo has sufficiently high surface density near a very compact massive core., Comment: 6 pages, 4 figures

Wave dark matter ($\psi$DM) predicts a compact soliton core and a granular halo in every galaxy. This work presents the first simulation study of an elliptical galaxy by including both stars and $\psi$DM, focusing on the systematic changes of the central soliton and halo granules. With the addition of stars in the inner halo, we find the soliton core consistently becomes more prominent by absorbing mass from the host halo than that without stars, and the halo granules become "non-isothermal", "hotter" in the inner halo and "cooler" in the outer halo, as opposed to the isothermal halo in pure $\psi$DM cosmological simulations. Moreover, the composite (star+$\psi$DM) mass density is found to follow a $r^{-2}$ isothermal profile near the half-light radius in most cases. Most striking is the velocity dispersion of halo stars that increases rapidly toward the galactic center by a factor of at least 2 inside the half-light radius caused by the deepened soliton gravitational potential, a result that compares favorably with observations of elliptical galaxies and bulges in spiral galaxies. However in some rare situations we find a phase segregation turning a compact distribution of stars into two distinct populations with high and very low velocity dispersions; while the high-velocity component mostly resides in the halo, the very low-velocity component is bound to the interior of the soliton core, resembling stars in faint dwarf spheroidal galaxies., Comment: 15 pages, 11 figures

Wave dark matter ($\psi \rm{DM}$) composed of extremely light bosons ($m_{\psi} \sim 10^{-22}\,\rm eV$), with quantum pressure suppressing structures below a kpc-scale de Broglie wavelength, has become a viable dark matter candidate. Compared to the conventional free-particle $\psi {\rm DM}$ (${\rm FP} \psi {\rm DM}$), the extreme-axion $\psi \rm{DM}$ model (${\rm EA} \psi {\rm DM}$) proposed by Zhang & Chiueh (2017) features a larger cut-off wavenumber and a broad spectral bump in the matter transfer function. Here we conduct cosmological simulations to compare the halo abundances and assembly histories at $z=4-11$ between three different scenarios: ${\rm FP} \psi {\rm DM}$, ${\rm EA} \psi {\rm DM}$, and cold dark matter (CDM). We show that ${\rm EA} \psi {\rm DM}$ produces significantly more abundant low-mass haloes than ${\rm FP} \psi {\rm DM}$ with the same $m_{\psi}$, and therefore could alleviate the tension in $m_{\psi}$ required by the Ly$\alpha$ forest data and by the kpc-scale dwarf galaxy cores. We also find that, compared to the CDM counterparts, massive ${\rm EA} \psi {\rm DM}$ haloes are on average $3-4$ times more massive at $z=10-11$ due to their earlier formation, undergo a slower mass accretion at $7 \lesssim z \lesssim 11$, and then show a rapidly rising major merger rate exceeding CDM by $\sim 50\%$ at $4 \lesssim z \lesssim 7$. This fact suggests that ${\rm EA} \psi {\rm DM}$ haloes may exhibit more prominent starbursts at $z \lesssim 7$., Comment: 5 pages, 4 figures, only minor updates (accepted for publication in MNRAS letters)

Although still under debate, observations generally suggest that dwarf spheroidal (dSph) galaxies exhibit large constant-density cores in the centers, which can hardly be explained by dissipationless cold dark matter simulations without baryonic feedback. Wave dark matter (${\psi {\rm DM}}$), characterized by a single parameter, the dark matter particle mass $m_{\psi}$, predicts a central soliton core in every galaxy arising from quantum pressure against gravity. Here we apply Jeans analysis assuming a soliton core profile to the kinematic data of eight classical dSphs so as to constrain $m_{\psi}$, and obtain $m_{\psi}=1.18_{-0.24}^{+0.28}\times10^{-22}{\,\rm eV}$ and $m_{\psi}=1.79_{-0.33}^{+0.35}\times10^{-22}{\,\rm eV}~(2\sigma)$ using the observational data sets of Walker et al. (2007) and Walker et al. (2009b), respectively. We show that the estimate of $m_{\psi}$ is sensitive to the dSphs kinematic data sets and is robust to various models of stellar density profile. We also consider multiple stellar subpopulations in dSphs and find consistent results. This mass range of $m_{\psi}$ is in good agreement with other independent estimates, such as the high-redshift luminosity functions, the reionization history, and the Thomson optical depth to the cosmic microwave background., Comment: 12 pages, 11 figures, 2 tables, add appendix B about the joint analysis, submitted to MNRAS

Without an existing large-scale coherent magnetic field in the early universe, Population III stars would likely rotate at or near breakup speed. In this work, focusing on the accretion phase of Population III stars, we investigate the possibility of generating a coherent magnetic field through large-scale dynamo processes, as well as the corresponding field saturation level. Using results from hydrodynamic simulations performed with a cylindrical grid, we demonstrate that primordial accretion disks are turbulent with a Shakura–Sunyaev disk parameter α ss ≳ 10−3 and evidence for helical turbulence with a dynamo number ∣D αΩ∣ ≫ 10. The presence of helical turbulence at these levels allows large-scale dynamo modes to grow, and the saturation level is determined by the amount of net helicity remaining in the dynamo active regions (i.e., the quenching problem). We demonstrate that if the accretion could successfully alleviate the quenching problem, the magnetic field can reach approximate equipartition with B/B eq ∼ 3.

Simulations of ultralight, $\sim 10^{-22}\,\rm eV$, bosonic dark matter exhibit rich wave-like structure, including a soliton core within a surrounding halo that continuously self-interferes on the de Broglie scale. We show here that as an inherent consequence, the soliton undergoes a confined random walk at the base of the halo potential. This is significant for the fate of the ancient central star cluster in Eridanus II, as the agitated soliton gravitationally shakes the star cluster in and out of the soliton on a time scale of $\sim 100\,\rm Myr$, so complete tidal disruption of the star cluster can occur within $\sim 1\,\rm Gyr$. This destructive effect can be mitigated by tidal stripping of the halo of Eridanus II, thereby reducing the agitation, depending on its orbit around the Milky Way. Our simulations show the Milky Way tide affects the halo much more than the soliton, so the star cluster in Eridanus II can survive for over $5\,\rm Gyr$ within the soliton if it formed after significant halo stripping., Comment: Accepted for publication in Phys. Rev. Lett. 6 pages, 4 figures

The fuzzy dark matter model (FDM, also known as quantum wave dark matter model) argues that light bosons with a mass of $\sim10^{-22}{\;{\rm eV}}$ are a possible candidate for dark matter in the Universe. One of the most important predictions of FDM is the formation of a soliton core instead of a density cusp at the center of galaxies. If FDM is the correct theory of dark matter, then the predicted soliton core can help to form the Central Molecular Zone (CMZ) in the Milky Way. We present high-resolution hydrodynamical simulations of gas flow patterns to constrain the properties of the soliton core based on a realistic Milky Way potential. We find that a dense center is required to form a reasonable CMZ. The size and kinematics of the CMZ offer a relatively strong constraint on the inner enclosed mass profile of the Galaxy. If a soliton core is not considered, a compact nuclear bulge alone with a radially varying mass-to-light ratio can match the observed size and kinematics of the CMZ. A soliton core model with a mass of $\approx4.0\times10^8{\; {\rm M}_{\odot}}$ and a core radius of $\approx0.05{\;{\rm kpc}}$, together with a less massive nuclear bulge with a constant mass-to-light ratio, also agrees nicely with the current data. Such a FDM soliton core corresponds to a boson mass of $\sim2-7\times10^{-22}{\;{\rm eV}}$, which could be further constrained by the improved determination of the mass-to-light ratio in the Galactic center., Accepted for publication in ApJ. 14 pages, 7 figures

Using cosmological particle hydrodynamical simulations and uniform ultraviolet backgrounds, we compare Lyman-$\alpha$ forest flux spectra predicted by the conventional cold dark matter (CDM) model, the free-particle wave dark matter (FP$\psi$DM) model and extreme-axion wave dark matter (EA$\psi$DM) models of different initial axion field angles against the BOSS Lyman-$\alpha$ forest absorption spectra with a fixed boson mass $m_b\sim 10^{-22}$eV. We recover results reported previously (Ir\v{s}i\v{c} et al. 2017b; Armengaud et al. 2017) that the CDM model agrees better with the BOSS data than the FP$\psi$DM model by a large margin, and we find the difference of total $\chi^2$'s is $120$ for $420$ data bins. These previous results demand a larger boson mass by a factor $>10$ to be consistent with the date and are in tension with the favoured value determined from local satellite galaxies. We however find that such tension is removed as some EA$\psi$DM models predict Lyman-$\alpha$ flux spectra agreeing better with the BOSS data than the CDM model, and the difference of total $\chi^2$'s can be as large as $24$ for the same bin number. This finding arises with no surprise since EA$\psi$DM models have unique spectral shapes with spectral bumps in excess of the CDM power near the small-scale cutoff typical of $\psi$DM linear matter power spectra as well as more extended cutoffs than FP$\psi$DM (Zhang & Chiueh 2017a,b).

Acting as powerful gravitational lenses, the strong lensing galaxy clusters of the deep Hubble Frontier Fields (HFF) program permit access to lower-luminosity galaxies lying at higher redshifts than hitherto possible. We analyzed the HFF to measure the volume density of Lyman-break galaxies at $z > 4.75$ by identifying a complete and reliable sample up to $z \simeq 10$. A marked deficit of such galaxies was uncovered in the highly magnified regions of the clusters relative to their outskirts, implying that the magnification of the sky area dominates over additional faint galaxies magnified above the flux limit. This negative magnification bias is consistent with a slow rollover at the faint end of the UV luminosity function, and indicates a preference for Bose-Einstein condensate dark matter with a light boson mass of $m_\mathrm{B} \simeq 10^{-22} \, \mathrm{eV}$ over standard cold dark matter. We emphasize that measuring the magnification bias requires no correction for multiply lensed images (with typically three or more images per source), whereas directly reconstructing the luminosity function will lead to an overestimate unless such images can be exhaustively matched up, especially at the faint end that is accessible only in the strongly lensed regions. In addition, we detected a distinctive downward transition in galaxy number density at $z \gtrsim 8$, which may be linked to the relatively late reionization reported by Planck. Our results suggests that JWST will likely peer into an "abyss" with essentially no galaxies detected in deep NIR imaging at $z > 10$., 46 pages, 23 figures, accepted for publication in ApJ

The cold dark matter (CDM) paradigm successfully explains the cosmic structure over an enormous span of redshifts. However, it fails when probing the innermost regions of dark matter halos and the properties of the Milky Way’s dwarf galaxy satellites. Moreover, the lack of experimental detection of Weakly Interacting Massive Particle (WIMP) favors alternative candidates such as light axionic dark matter that naturally arise in string theory. Cosmological N-body simulations have shown that axionic dark matter forms a solitonic core of size of ≃150 pc in the innermost region of the galactic halos. The oscillating scalar field associated to the axionic dark matter halo produces an oscillating gravitational potential that induces a time dilation of the pulse arrival time of ≃400 ns/(m B /10 −22 eV) for pulsar within such a solitonic core. Over the whole galaxy, the averaged predicted signal may be detectable with current and forthcoming pulsar timing array telescopes. IDM acknowledges financial support from University of the Basque Country UPV/EHU under the program "Convocatoria de contratacion para la especializacion de personal investigador doctor en la UPV/EHU 2015", from the Spanish Ministerio de Economia y Competitividad through research project FIS2010-15492, and from the Basque Government through research project IT-956-16. RL is supported by the Spanish Ministry of Economy and Competitiveness through research projects FIS2010-15492 and Consolider EPI CSD2010-00064, and by the University of the Basque Country UPV/EHU under program UFI 11/55. IDM and RL also acknowledge support from the COST Action CA1511 Cosmology and Astrophysics Network for Theoretical Advances and Training Actions (CANTATA). TJB acknowledges generous hospitality from the Institute for Advanced Studies in Hong Kong and helpful conversations with Nick Kaiser and Kfir Blum. SHHT is supported by CRF Grant HKUST4/CRF/13G and GRF 16305414 issued by the Research Grants Council (RGC) of the Government of the Hong Kong SAR. Chipbond Technology Corporation is acknowledged for donating the GPU cluster with which this work was conducted. This work was supported in part by the National Science Council of Taiwan under grants NSC100-2112-M-002-018-MY3 and NSC99-2112-M-002-009-MY3

Wave dark matter ($\psi$DM), which satisfies the Schr\"odinger-Poisson equation, has recently attracted substantial attention as a possible dark matter candidate. Numerical simulations have in the past provided a powerful tool to explore this new territory of possibility. Despite their successes to reveal several key features of $\psi$DM, further progress in simulations is limited, in that cosmological simulations so far can only address formation of halos below $\sim 2\times 10^{11} M_\odot$ and substantially more massive halos have become computationally very challenging to obtain. For this reason, the present work adopts a different approach in assessing massive halos by constructing wave-halo solutions directly from the wave distribution function. This approach bears certain similarity with the analytical construction of particle-halo (cold dark matter model). Instead of many collisionless particles, one deals with one single wave that has many non-interacting eigenstates. The key ingredient in the wave-halo construction is the distribution function of the wave power, and we use several halos produced by structure formation simulations as templates to determine the wave distribution function. Among different models, we find the fermionic King model presents the best fits and we use it for our wave-halo construction. We have devised an iteration method for constructing the nonlinear halo, and demonstrate its stability by three-dimensional simulations. A Milky-Way-sized halo has also been constructed, and the inner halo is found flatter than the NFW profile. These wave-halos have small-scale interferences both in space and time producing time-dependent granules. While the spatial scale of granules varies little, the correlation time is found to increase with radius by one order of magnitude across the halo., Comment: 14 pages, 7 figures, accepted by PRD

Light Axionic Dark Matter, motivated by string theory, is increasingly favored for the "no-WIMP era". Galaxy formation is suppressed below a Jeans scale, of $\simeq 10^8 M_\odot$ by setting the axion mass to, $m_B \sim 10^{-22}$eV, and the large dark cores of dwarf galaxies are explained as solitons on the de-Broglie scale. This is persuasive, but detection of the inherent scalar field oscillation at the Compton frequency, $\omega_B= (2.5{\rm \, months})^{-1}(m_B/10^{-22}eV)$, would be definitive. By evolving the coupled Schr\"odinger-Poisson equation for a Bose-Einstein condensate, we predict the dark matter is fully modulated by de-Broglie interference, with a dense soliton core of size $\simeq 150pc$, at the Galactic center. The oscillating field pressure induces General Relativistic time dilation in proportion to the local dark matter density and pulsars within this dense core have detectably large timing residuals, of $\simeq 400nsec/(m_B/10^{-22}eV)$. This is encouraging as many new pulsars should be discovered near the Galactic center with planned radio surveys. More generally, over the whole Galaxy, differences in dark matter density between pairs of pulsars imprints a pairwise Galactocentric signature that can be distinguished from an isotropic gravitational wave background., Comment: 6 pages, 3 figures. Accepted for publication in Physics Review Letter

Radio observations suggest that 3C 75, located in the dumbbell shaped galaxy NGC 1128 at the center of Abell 400, hosts two colliding jets. Motivated by this source, we perform three-dimensional hydrodynamical simulations using a modified version of the GPU-accelerated Adaptive-MEsh-Refinement hydrodynamical parallel code ($\mathit{GAMER}$) to study colliding extragalactic jets. We find that colliding jets can be cast into two categories: 1) bouncing jets, in which case the jets bounce off each other keeping their identities, and 2) merging jets, when only one jet emerges from the collision. Under some conditions the interaction causes the jets to break up into oscillating filaments of opposite helicity, with consequences for their downstream stability. When one jet is significantly faster than the other and the impact parameter is small, the jets merge; the faster jet takes over the slower one. In the case of merging jets, the oscillations of the filaments, in projection, may show a feature which resembles a double helix, similar to the radio image of 3C 75. Thus we interpret the morphology of 3C 75 as a consequence of the collision of two jets with distinctly different speeds at a small impact parameter, with the faster jet breaking up into two oscillating filaments.

We present a time domain waveform model that describes the inspiral-merger-ringdown (IMR) of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero eccentricity limit. To improve phase accuracy, we incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced inspiral evolution prescription is combined with an analytical prescription for the merger-ringdown evolution using a catalog of numerical relativity simulations. This IMR waveform model reproduces effective-one-body waveforms for systems with mass-ratios between 1 to 15 in the zero eccentricity limit. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our eccentric model accurately reproduces the features of eccentric compact binary coalescence throughout the merger. Using this model we show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular, spin-aligned waveforms if the eccentricity $e_0$ of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies $e_0^{\rm GW150914}\leq0.15$ and $e_0^{\rm GW151226}\leq0.1$., Comment: 31 pages, 19 figures, 3 appendices. Submitted to Phys Rev D. v2: direct comparison to eccentric numerical relativity simulations, not used for calibration of the model, included. References added. Accepted to Phys Rev D

We present GAMER-2, a GPU-accelerated adaptive mesh refinement (AMR) code for astrophysics. It provides a rich set of features, including adaptive time-stepping, several hydrodynamic schemes, magnetohydrodynamics, self-gravity, particles, star formation, chemistry and radiative processes with GRACKLE, data analysis with yt, and memory pool for efficient object allocation. GAMER-2 is fully bitwise reproducible. For the performance optimization, it adopts hybrid OpenMP/MPI/GPU parallelization and utilizes overlapping CPU computation, GPU computation, and CPU-GPU communication. Load balancing is achieved using a Hilbert space-filling curve on a level-by-level basis without the need to duplicate the entire AMR hierarchy on each MPI process. To provide convincing demonstrations of the accuracy and performance of GAMER-2, we directly compare with Enzo on isolated disk galaxy simulations and with FLASH on galaxy cluster merger simulations. We show that the physical results obtained by different codes are in very good agreement, and GAMER-2 outperforms Enzo and FLASH by nearly one and two orders of magnitude, respectively, on the Blue Waters supercomputers using $1-256$ nodes. More importantly, GAMER-2 exhibits similar or even better parallel scalability compared to the other two codes. We also demonstrate good weak and strong scaling using up to 4096 GPUs and 65,536 CPU cores, and achieve a uniform resolution as high as $10{,}240^3$ cells. Furthermore, GAMER-2 can be adopted as an AMR+GPUs framework and has been extensively used for the wave dark matter ($\psi$DM) simulations. GAMER-2 is open source (available at https://github.com/gamer-project/gamer) and new contributions are welcome., Comment: 29 pages, 22 figures. MNRAS accepted. GAMER can be found at https://github.com/gamer-project/gamer

We present the implementation and performance of a class of directionally unsplit Riemann-solver-based hydrodynamic schemes on Graphic Processing Units (GPU). These schemes, including the MUSCL-Hancock method, a variant of the MUSCL-Hancock method, and the corner-transport-upwind method, are embedded into the adaptive-mesh-refinement (AMR) code GAMER. Furthermore, a hybrid MPI/OpenMP model is investigated, which enables the full exploitation of the computing power in a heterogeneous CPU/GPU cluster and significantly improves the overall performance. Performance benchmarks are conducted on the Dirac GPU cluster at NERSC/LBNL using up to 32 Tesla C2050 GPUs. A single GPU achieves speed-ups of 101(25) and 84(22) for uniform-mesh and AMR simulations, respectively, as compared with the performance using one(four) CPU core(s), and the excellent performance persists in multi-GPU tests. In addition, we make a direct comparison between GAMER and the widely-adopted CPU code Athena (Stone et al. 2008) in adiabatic hydrodynamic tests and demonstrate that, with the same accuracy, GAMER is able to achieve two orders of magnitude performance speed-up., Comment: 16 pages, 5 figures, accepted for publication in International Journal of High Performance Computing Applications (IJHPCA)

GAMER, a parallel Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement hydrodynamic code, has been extended to support magnetohydrodynamics (MHD) with both the corner-transport-upwind (CTU) and MUSCL-Hancock schemes and the constraint transport (CT) technique. The divergent preserving operator for adaptive mesh refinement (AMR) has been applied to reinforce the divergence-free constraint on the magnetic field. GAMER-MHD has fully exploited the concurrent executions between the GPU MHD solver and other CPU computation pertinent to AMR. We perform various standard tests to demonstrate that GAMER-MHD is both second-order accurate and robust, producing results as accurate as those given by high-resolution uniform-grid runs. We also explore a new 3D MHD test, where the magnetic field assumes the Arnold-Beltrami-Childress (ABC) configuration, temporarily becomes turbulent with current sheets and finally settles to a lowest-energy equilibrium state. This 3D problem is adopted for the performance test of GAMER-MHD. The single-GPU performance reaches $1.2\times 10^8$ and $5.5\times 10^7$ cell-updates/sec for the single- and double-precision calculations, respectively, on Tesla P100. We also demonstrate a parallel efficiency of $\sim 70\%$ for both weak and strong scaling using $1,024$ XK nodes on the Blue Waters supercomputers., Comment: 29 pages, 22 figures, 1 table. GAMER-MHD will soon become available at https://github.com/gamer-project/gamer

We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh Refinement code), which has adopted a novel approach to improve the performance of adaptive mesh refinement (AMR) astrophysical simulations by a large factor with the use of the graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is made to diminish by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely-baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with 8192^3 effective resolution, respectively.

Inspired by Barnard 68, a Bok globule, that undergoes stable oscillations, we perform multi-phase hydrodynamic simulations to analyze the stability of Bok globules. We show that a high-density soft molecular core, with an adiabatic index $\gamma$ = 0.7 embedded in a warm isothermal diffuse gas, must have a small density gradient to retain the stability. Despite being stable, the molecular core can still collapse spontaneously as it will relax to develop a sufficiently large density gradient after tens of oscillations, or a few $10^7$ years. However, during its relaxation, the core may abruptly collapse triggered by the impingement of small-amplitude, long-wavelength ($\sim$ 6 $-$ 36 pc) sound waves in the warm gas. This triggered collapse mechanism is similar to a sonoluminescence phenomenon, where underwater ultrasounds can drive air bubble coalescence. The collapse configuration is found to be different from both inside-out and outside-in models of low-mass star formation; nonetheless the mass flux is close to the prediction of the inside-out model. The condition and the efficiency for this core collapse mechanism are identified. Generally speaking, a broad-band resonance condition must be met, where the core oscillation frequency and the wave frequency should match each other within a factor of several. A consequence of our findings predicts the possibility of propagating low-mass star formation, for which collapse of cores, within a mass range short of one order of magnitude, takes place sequentially tracing the wave front across a region of few tens of pc over $10^7$ years., Comment: 9 pages, 8 figures

We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter ($\psi$DM), described by the Schr\"{o}dinger-Poisson (SP) equation with a particle mass $\sim 10^{-22} {\rm eV}$. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass ($M_c$) and halo mass ($M_h$), $M_c \propto a^{-1/2} M_h^{1/3}$, where $a$ is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations, and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kpc sized cores and a minimum mass of $\sim 10^8 {M_\odot}$, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of $2\times10^{12} {M_\odot}$ at $z=8$ should have massive solitonic cores of $\sim 2\times10^9 {M_\odot}$ within $\sim 60 {\rm pc}$. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars., Comment: 6 pages, 4 figures, accepted for publication in PRL

The newly established luminosity functions of high-z galaxies at 4 . z . 10 can provide a stringent check on dark matter models that aim to explain the core properties of dwarf galaxies. The cores of dwarf spheroidal galaxies are understood to be too large to be accounted for by free streaming of warm dark matter without overly suppressing the formation of such galaxies. Here we demonstrate with cosmological simulations that wave dark matter, ψDM, appropriate for light bosons such as axions, does not suffer this problem, given a boson mass of mψ ≥ 1.2 × 10−22 eV (2σ). In this case, the halo mass function is suppressed below ∼ 10M at a level that is consistent with the high-z luminosity functions, while simultaneously generating the kpc-scale cores in dwarf galaxies arising from the solitonic ground state in ψDM. We demonstrate that the reionization history in this scenario is consistent with the Thomson optical depth recently reported by Planck, assuming a reasonable ionizing photon production rate. We predict that the luminosity function should turn over slowly around an intrinsic UV luminosity of MUV & −16 at z & 4. We also show that for galaxies magnified >10× in the Hubble Frontier Fields, ψDM predicts an order of magnitude fewer detections than cold dark matter at z & 10 down to MUV ∼ −15, allowing us to distinguish between these very different interpretations for the observed coldness of dark matter. Subject headings: cosmology: theory – dark ages, reionization, first stars – dark matter – galaxies: abundances – galaxies: evolution – galaxies: high-redshift

Graphical processing units (GPUs) have become widely used to accelerate a broad range of applications, including computational physics and astrophysics, image/video processing, engineering simulations, and quantum chemistry. This chapter presents results obtained from GPU clusters with previous generations of GPU accelerators, which have no or very limited double-precision support. It provides an astrophysical N-body application for star clusters and galactic nuclei, which is currently the well-tested and heavily used application. The chapter explains exemplary implementations of parallel codes using many GPUs as accelerators, so combining message passing parallelization with many-core parallelization. It discusses their benchmarks using up to 512 Fermi Tesla GPUs in parallel on the Mole-8.5 hardware of the Institute of Process Engineering of the Chinese Academy of Sciences (IPE/CAS) in Beijing, and the Laohu Tesla C1070 cluster of the National Astronomical Observatories of CAS in Beijing and smaller clusters in Germany and in the United States. galactic nuclei; graphics processing units; star clusters

GAMER is a GPU-accelerated Adaptive-MEsh-Refinement code for astrophysical simulations. In this work, two further extensions of the code are reported. First, we have implemented the MUSCL-Hancock method with the Roe's Riemann solver for the hydrodynamic evolution, by which the accuracy, overall performance and the GPU versus CPU speed-up factor are improved. Second, we have implemented the out-of-core computation, which utilizes the large storage space of multiple hard disks as the additional run-time virtual memory and permits an extremely large problem to be solved in a relatively small-size GPU cluster. The communication overhead associated with the data transfer between the parallel hard disks and the main memory is carefully reduced by overlapping it with the CPU/GPU computations., 4 pages, 4 figures, conference proceedings of IAU Symposium 270 (eds. Alves, Elmegreen, Girart, Trimble)

In this paper, we describe the architecture and performance of the GraCCA system, a Graphic-Card Cluster for Astrophysics simulations. It consists of 16 nodes, with each node equipped with 2 modern graphic cards, the NVIDIA GeForce 8800 GTX. This computing cluster provides a theoretical performance of 16.2 TFLOPS. To demonstrate its performance in astrophysics computation, we have implemented a parallel direct N-body simulation program with shared time-step algorithm in this system. Our system achieves a measured performance of 7.1 TFLOPS and a parallel efficiency of 90% for simulating a globular cluster of 1024K particles. In comparing with the GRAPE-6A cluster at RIT (Rochester Institute of Technology), the GraCCA system achieves a more than twice higher measured speed and an even higher performance-per-dollar ratio. Moreover, our system can handle up to 320M particles and can serve as a general-purpose computing cluster for a wide range of astrophysics problems., Comment: Accepted for publication in New Astronomy

Quantum turbulence that exhibits vortex creation, annihilation and interactions is demonstrated as an exact solution of the time-dependent, free-particle Schr\"odinger equation evolved from a smooth random-phased initial condition. Relaxed quantum turbulence in 2D and 3D exhibits universal scaling in the steady-state energy spectrum as k-1 in small scales. Due to the lack of dissipation, no evidence of the Kolmogorov-type forward energy cascade in 3D or the inverse energy cascade in 2D is found, but the rotational and potential flow components do approach equi-partition in the scaling regime. In addition, the 3D vortex line-line correlation exhibits universal behaviour, scaled as \Deltar^-2, where \Deltar is the separation between any two vortex line elements, in fully developed turbulence. We also show that the quantum vortex is not frozen to the matter, nor is the vortex motion induced by other vortices via Biot-Savart's law. Thus, the quantum vortex is actually a nonlinear wave, propagating at a speed very different from a classical vortex., Comment: 9 pages, 14 figures

We present the Grackle chemistry and cooling library for astrophysical simulations and models. Grackle provides a treatment of non-equilibrium primordial chemistry and cooling for H, D, and He species, including H2 formation on dust grains; tabulated primordial and metal cooling; multiple UV background models; and support for radiation transfer and arbitrary heat sources. The library has an easily implementable interface for simulation codes written in C, C++, and Fortran as well as a Python interface with added convenience functions for semi-analytical models. As an open-source project, Grackle provides a community resource for accessing and disseminating astrochemical data and numerical methods. We present the full details of the core functionality, the simulation and Python interfaces, testing infrastructure, performance, and range of applicability. Grackle is a fully open-source project and new contributions are welcome., Comment: 20 pages, 8 figures, accepted for publication in MNRAS. For more info, visit grackle.readthedocs.io