We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic r −3 NFW-like profile. We find a fundamental relation of the core=to-halo mass with the dimensionless invariant Ξ ≡ |E|/M 3 /(Gm/ ) 2 or M c /M 2.6Ξ 1/3 , linking the soliton to global halo properties. For r ≥ 3.5 r c core radii, we find equipartition between potential, classical kinetic, and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behavior driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a k −1.1 power-law. This suggests the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a k −5/3 Kolmogorov power-law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying the soliton-sized granules carry most of the turbulent energy in BECDM haloes.
The early star-forming Universe is still poorly constrained, with the properties of high-redshift stars, the first heating sources, and reionization highly uncertain. This leaves observers planning 21-cm experiments with little theoretical guidance. In this work we explore the possible range of high-redshift parameters including the star formation efficiency and the minimal mass of star-forming halos; the efficiency, spectral energy distribution, and redshift evolution of the first X-ray sources; and the history of reionization. These parameters are only weakly constrained by available observations, mainly the optical depth to the cosmic microwave background. We use realistic seminumerical simulations to produce the global 21-cm signal over the redshift range z = 6 − 40 for each of 193 different combinations of the astrophysical parameters spanning the allowed range. We show that the expected signal fills a large parameter space, but with a fixed general shape for the global 21-cm curve. Even with our wide selection of models we still find clear correlations between the key features of the global 21-cm signal and underlying astrophysical properties of the high redshift Universe, namely the Lyα intensity, the X-ray heating rate, and the production rate of ionizing photons. These correlations can be used to directly link future measurements of the global 21cm signal to astrophysical quantities in a mostly model-independent way. We identify additional correlations that can be used as consistency checks.
of ionized bubbles. This is based on the assumption 5,6,7 that the cosmic gas was heated by stellar remnants -particularly X-ray binaries -to temperatures well above the cosmic microwave background at that time (∼30 K). Here we show instead that the hard spectra (that is, spectra with more high-energy photons than low-energy photons) of X-ray binaries 8,9 make such heating ineffective, resulting in a delayed and spatially uniform heating 1 that modifies the 21-cm signature of reionization. Rather than looking for a simple rise and fall of the large-scale fluctuations (peaking at several millikelvin), we must expect a more complex signal also featuring a distinct minimum (at less than a millikelvin) that marks the rise of the cosmic mean gas temperature above the microwave background.Observing this signal, possibly with radio telescopes in operation today, will demonstrate the presence of a cosmic background of hard X-rays at that early time.While stellar remnants at high redshift have been previously considered, a more reliable prediction of the radiative feedback from X-ray binaries (XRBs) is now possible due to a recent detailed population synthesis simulation of their evolution across cosmic time 8,9 . This simulation was calibrated to all available observations in the local and low redshift Universe, and it predicts the evolution of the luminosity and X-ray spectrum of XRBs with redshift. In particular, high-mass XRBs (especially black hole binaries) should dominate, with a ratio at high redshift of bolometric X-ray luminosity to star-formation rate (SFR) ofWe have allowed for an uncertainty in the X-ray efficiency with an extra parameter in eq. 1, where f X = 1 indicates our standard value. We focus on XRBs as the most natural heating source, since other observed sources should be sub-dominant at high redshift (see Methods section).Previous calculations of X-ray heating 6,10,11,12,13 have assumed power-law spectra that place most of the X-ray energy at the low-energy end, where the mean free path of the soft X-rays is relatively short. This means that most of the emitted X-rays are absorbed soon after they are emitted, before much energy is lost due to cosmological effects. The absorbed energy is then enough to heat the gas by the time of reionization to ∼ 10 times the temperature of the Cosmic Microwave Background (CMB; see Methods section). Thus, it is generally assumed 2 that reionization occurs when T gas ≫ T CMB , a limit referred to as saturated heating since the 21-cm intensity then becomes independent of T gas and mainly dependent on ionization and density. A different possibility whereby heating is delayed until reionization has only been previously considered as a fringe case of having an unusually low X-ray luminosity to SFR ratio 10,11 .However, the average radiation from XRBs is expected to have a much harder spectrum ( Fig. 1) whose energy content (per logarithmic frequency interval) peaks at ∼ 3 keV. Photons above a (roughly redshift-independent) critical energy of ∼ 1 keV have such a long me...
Dark and baryonic matter moved at different velocities in the earlyThe relative velocity between the dark matter and baryons also reduces the gas content of each halo. Previous work 2 assumed that this reduces star formation, but it mainly affects smaller halos that do not form stars 13,14 . Another critical issue for observations of early stars is timing, since on the one hand, early times bring us closer to the primeval era of the very first stars 9,10,15,14 , but on the other hand, the cosmological 21-cm signal is obscured by the foreground (mainly Galactic synchrotron), which is brighter at longer wavelengths (corresponding to higher redshifts). Unlike the fluctuations at z ∼ 20 from inhomogeneous gas heating, previously considered sources 2 produce smaller fluctuations and are likely to be effective only at z ∼ 30 16 .We use a hybrid method to produce realistic, three-dimensional images of the expected global distribution of the first stars. We use the known statistical properties of the initial perturbations of density and of the relative dark matter to baryon velocity to generate a realistic sample universe on large, linear scales. Then, we calculate the stellar content of each pixel using analytical models and the results of small-scale numerical simulations. In this approach we build upon previous hybrid methods used for high-redshift galaxy formation 1,2,17 , and include a fit 14 to recent simulation results on the effect of the relative velocity 7,8 (for further details, seeSupplementary Information section S1). Note that numerical simulations (even if limited to following gravity) cannot on their own cover the full range of scales needed to find the large-scale distribution of high-redshift galaxies 18 . 2We assume standard initial perturbations (e.g., from a period of inflation), where the density and velocity components are Gaussian random fields. Velocities are coherent on larger scales than the density, due to the extra factor of 1/k in the velocity from the continuity equation that relates the two fields (where k is the wavenumber). Indeed, velocity fluctuations have significant power over the range k ∼ 0.01 − 0.5 Mpc −1 , with prominent BAOs 1 .We find a remarkable cosmic web (Fig. 1), reminiscent of that seen in the distribution of massive galaxies in the present universe 19,20,21 . The large coherence length of the velocity makes it the dominant factor (relative to density) in the large-scale pattern. The resulting enhanced structure on 100 Mpc scales becomes especially notable at the highest redshifts (Fig. 2).This large-scale structure has momentous implications for cosmology at high redshift and for observational prospects. As the first stars formed, their radiation (plus emission from stellar remnants) produced feedback that radically affected both the intergalactic medium and the character of newly-forming stars. Prior to reionization, three major transitions are expected due to energetic photons. Lyman-α photons couple the hyperfine levels of hydrogen to the kinetic temperature and thu...
Recently the initial supersonic relative velocity between the dark matter and baryons was shown to have an important effect on galaxy formation at high redshift. We study the impact of this relative motion on the distribution of the star‐forming haloes and on the formation redshift of the very first star. We include a new aspect of the relative velocity effect found in recent simulations by fitting their results to obtain the spatially varying minimum halo mass needed for molecular cooling. Thus, the relative velocities have three separate effects: suppression of the halo abundance, suppression of the gas content within each halo and boosting of the minimum cooling mass. We show that the two suppressions (of gas content and of halo abundance) are the primary effects on the small minihaloes that cannot form stars, while the cooling mass boost combines with the abundance suppression to produce order unity fluctuations in stellar density. We quantify the large‐scale inhomogeneity of galaxies, finding that 68 per cent of the star formation (averaged on a 3 Mpc scale) is confined to 35 per cent of the volume at z= 20 (and just 18 per cent at z= 40). In addition, we estimate the first observable star to be formed at redshift z= 65 (t∼ 33 Myr) which includes a delay of Δz∼ 5 (Δt∼ 3.6 Myr) due to the relative velocity.
The formation of the first stars is an exciting frontier area in astronomy. Early redshifts (z ∼ 20) have become observationally promising as a result of a recently recognized effect (Tseliakhovich & Hirata 2010) of a supersonic relative velocity between the dark matter and gas. This effect produces prominent structure on 100 comoving Mpc scales, which makes it much more feasible to detect 21-cm fluctuations from the epoch of first heating (Visbal et al. 2012). We use semi-numerical hybrid methods to follow for the first time the joint evolution of the X-ray and Lyman-Werner radiative backgrounds, including the effect of the supersonic streaming velocity on the cosmic distribution of stars. We incorporate self-consistently the negative feedback on star formation induced by the Lyman-Werner radiation, which dissociates molecular hydrogen and thus suppresses gas cooling. We find that the feedback delays the X-ray heating transition by a ∆z ∼ 2, but leaves a promisingly large fluctuation signal over a broad redshift range. The large-scale power spectrum is predicted to reach a maximal signal-to-noise ratio of S/N∼ 3 − 4 at z ∼ 18 (for a projected first-generation instrument), with S/N> 1 out to z ∼ 22 − 23. We hope to stimulate additional numerical simulations as well as observational efforts focused on the epoch prior to cosmic reionization.
The Schrödinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As /m → 0, m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as /m → 0 due to interference and the uncertainty principle, the potential field converges to the classical answer as ( /m) 2 . Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as /m → 0. The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrödinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultra-light axions, which in the classical limit ( /m → 0) is expected to manifest itself as collisionless cold dark matter.
The Herschel Multi-tiered Extragalactic Survey (HerMES) has identified large numbers of dusty star-forming galaxies (DSFGs) over a wide range in redshift. A detailed understanding of these DSFGs is hampered by the limited spatial resolution of Herschel. We present 870 μm 0 45 resolution imaging obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) of a sample of 29 HerMES DSFGs that have far-infrared (FIR) flux densities that lie between the brightest of sources found by Herschel and fainter DSFGs found via groundbased surveys in the submillimeter region. The ALMA imaging reveals that these DSFGs comprise a total of 62 sources (down to the 5s point-source sensitivity limit in our ALMA sample; 0.2 mJy s » ). Optical or nearinfrared imaging indicates that 36 of the ALMA sources experience a significant flux boost from gravitational lensing ( 1.1 m > ), but only six are strongly lensed and show multiple images. We introduce and make use of UVMCMCFIT, a general-purpose and publicly available Markov chain Monte Carlo visibility-plane analysis tool to analyze the source properties. Combined with our previous work on brighter Herschel sources, the lens models presented here tentatively favor intrinsic number counts for DSFGs with a break near 8 mJy at 880 m m and a steep fall-off at higher flux densities. Nearly 70% of the Herschel sources break down into multiple ALMA counterparts, consistent with previous research indicating that the multiplicity rate is high in bright sources discovered in singledish submillimeter or FIR surveys. The ALMA counterparts to our Herschel targets are located significantly closer to each other than ALMA counterparts to sources found in the LABOCA ECDFS Submillimeter Survey. Theoretical models underpredict the excess number of sources with small separations seen in our ALMA sample. The high multiplicity rate and small projected separations between sources seen in our sample argue in favor of interactions and mergers plausibly driving both the prodigious emission from the brightest DSFGs as well as the sharp downturn above S 8 mJy 880 = .
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