The conventional cold-particle interpretation of dark matter (known as 'cold dark matter', or CDM) still lacks laboratory support and struggles with the basic properties of common dwarf galaxies, which have surprisingly uniform central masses and shallow density profiles 1-5 . In contrast, galaxies predicted by CDM extend to much lower masses, with steeper, singular profiles 6-9 . This tension motivates cold, wavelike dark matter (ψDM) composed of a non-relativistic Bose-Einstein condensate, so the uncertainty principle counters gravity below a Jeans scale 10-12 . Here we achieve cosmological simulations of this quantum state at unprecedentedly high resolution capable of resolving dwarf galaxies, with only one free parameter, m B , the boson mass. We demonstrate the large-scale structure is indistinguishable from CDM, as desired, but di ers radically inside galaxies where quantum interference forms solitonic cores surrounded by extended haloes of fluctuating density granules. These results allow us to determine m B = (8.0 +1.8 −2.0 ) × 10 −23 eV using stellar phase-space distributions in dwarf spheroidal galaxies. Denser, more massive solitons are predicted for Milky Way sized galaxies, providing a substantial seed to help explain early spheroid formation. The onset of galaxy formation is substantially delayed relative to CDM, appearing at redshift z 13 in our simulations.Standard, thermally generated dark matter remains firmly undetected in laboratory searches for weakly interacting massive particles (WIMPs; ref. 13). Non-thermal bosonic fields, particularly scalar fields, provide another well-motivated class of dark matter, formed in a non-relativistic, low-momentum state as a cold Bose-Einstein condensate (BEC), and increasingly motivated by extensions of the Standard Model of particle physics and to the mechanism driving the universal expansion 14 . The field in this context can be described by a coherent wave function ψ with an interference pattern determining the distribution of dark matter, which we term ψDM. Axions are long-standing CDM candidates of this form, and higher-dimensional theories motivate an 'axiverse' , where a discrete mass spectrum of axion-like particles spans many decades, possibly affecting cosmic structure 15 .The distribution of ψDM mimics particle CDM on large scales 16,17 , and hence distinguishing between CDM and cold, wavelike ψDM is best made on small scales owing to the additional quantum stress [10][11][12]17 . Dwarf spheroidal (dSph) galaxies are the smallest and most common class of galaxy with internal motions dominated by dark matter. Their basic properties are very hard to explain with standard CDM, including the surprising uniformity of their central masses, M(<300 pc) 10 7 M , where M is the solar mass, and shallow density profiles 1-5 . In contrast, galaxies ) for the same cosmological parameters, with the high-k modes of the linear power spectrum intentionally suppressed in a way similar to the ψDM model to highlight the comparison of large-scale features. This compa...

We develop and test a method for measuring the gravitational lensing induced distortion of faint background galaxies. We first describe how we locate the galaxies and measure a 2-component `polarisation' or ellipticity statistic $e_\alpha$ whose expectation value should be proportional to the gravitational shear $\gamma_\alpha$. We then show that an anisotropic instrumental psf perturbs the polarisation by $\delta e_\alpha = P^s_{\alpha\beta} p_\beta$, where $p_\alpha$ is a measure of the psf anisotropy and $P^s_{\alpha\beta}$ is the `linearised smear polarisability tensor'. By estimating $P^s_{\alpha\beta}$ for each object we can determine $p_\alpha$ from the foreground stars and apply a correction $-P^s_{\alpha\beta}p_\beta$ to the galaxies. We test this procedure using deep high-resolution images from HST which are smeared with an anisotropic psf and then have noise added to simulate ground-based observations. We find that the procedure works very well. A similar analysis yields a linear shear polarisability tensor $P^\gamma_{\alpha\beta}$ which describes the response to a gravitational shear. This calibrates the polarisation-shear relation, but only for galaxies which are well resolved. To empirically calibrate the effect of seeing on the smaller galaxies we artificially stretch HST images to simulate lensing and then degrade them as before. These experiments provide a rigorous and exacting test of the method under realistic conditions. They show that it is possible to remove the effect of instrumental psf anisotropy, and that the method provides an efficient and quantitative measurement of the gravitational shear.Comment: 39 pages, no figures, Latex, available by anonymous ftp inc figs from ftp://ftp.cita.utoronto.ca/cita/nick/methods.p

We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter (ψDM), described by the Schrödinger-Poisson (SP) equation with a particle mass ∼ 10 −22 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 (Mc) and haloh , 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 ∼ 10 8 M⊙, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of 2 × 10 12 M⊙ at z = 8 should have massive solitonic cores of ∼ 2 × 10 9 M⊙ within ∼ 60 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.PACS numbers: 03.75. Lm, 95.35.+d, 98.56.Wm, 98.62.Gq Accumulating evidences suggest that the Universe contains ∼ 26% dark matter [1] which interacts primarily through self-gravity. Dark matter comprising very light bosons with a mass m ψ ∼ 10 −22 eV has been recognized as a viable means of suppressing low mass galaxies and providing cored profiles in dark matter dominated galaxies [2,3]. Interestingly, this boson mass scale can naturally arise in a non-QCD axion model [4], lending support for the very light boson. The relative deficiency of the observed number of low-mass galaxies is a major problem for standard cold dark matter (CDM) [5][6][7], for which a steeply rising mass function is predicted [8]. Furthermore, the dwarf spheroidal galaxies [9-20] and low surface brightness galaxies [21,22] are generally inferred to have large flat cores of dark matter, at odds with the singular cores required by standard CDM [23,24]. Complicated baryonic physics such as supernova feedback is required to solve both issues in the CDM paradigm [25][26][27][28][29][30][31][32][33][34].Extremely light bosonic dark matter can be assumed to be non-thermally generated and described by a single coherent wave function [2,[35][36][37][38], which we term ψDM. Here solutions to both the missing-satellite and ...

Subaru observations of A1689 (z = 0.183) are used to derive an accurate, model-independent mass profile for the entire cluster, r < ∼ 2Mpc/h, by combining magnification bias and distortion measurements. The projected mass profile steepens quickly with increasing radius, falling away to zero at r ∼ 1.0Mpc/h, well short of the anticipated virial radius. Our profile accurately matches onto the inner profile, r < ∼ 200kpc/h, derived from deep HST/ACS images. The combined ACS and Subaru information is well fitted by an NFW profile with virial mass, (1.93 ± 0.20) × 10 15 M ⊙ , and surprisingly high concentration, c vir = 13.7 +1.4 −1.1 , significantly larger than theoretically expected (c vir ≃ 4), corresponding to a relatively steep overall profile. A slightly better fit is achieved with a steep power-law model, d logΣ(θ)/d logθ ≃ −3, with a core θ c ≃ 1. ′ 7 (r c ≃ 210kpc/h), whereas an isothermal profile is strongly rejected. These results are based on a reliable sample of background galaxies selected to be redder than the cluster E/S0 sequence. By including the faint blue galaxy population a much smaller distortion signal is found, demonstrating that blue cluster members significantly dilute the true signal for r < ∼ 400kpc/h. This contamination is likely to affect most weak lensing results to date.