• #### Radiative Transfer in a Clumpy Universe: III. The Nature of Cosmological Ionizing Sources

The history of the transition from a neutral intergalactic medium (IGM) to one that is almost fully ionized can reveal the character of cosmological ionizing sources. We study the evolution of the volume filling factor of HII and HeIII regions in a clumpy IGM, and discuss the implications for rival reionization scenarios of the rapid decline in the space density of radio-loud quasars and of the large population of star-forming galaxies recently observed at z>3. The hydrogen component in a highly inhomogeneous universe is completely reionized when the number of photons emitted above 1 ryd in one recombination time equals the mean number of hydrogen atoms. If stellar sources are responsible for keeping the IGM ionized at z=5, the rate of star formation at this epoch must be comparable or greater than the one inferred from optical observations of galaxies at z=3, and the mean metallicity per baryon in the universe of order 1/500 solar. An early generation of stars in dark matter halos with circular velocities v_circ=50 km/s, possibly one of the main source of UV photons at high-z, could be detectable with the Next Generation Space Telescope. Models in which the quasar emissivity declines rapidly at z>3 predict a late HeII reionization epoch, a feature that could explain the recent detection of patchy HeII Lyman-alpha at z=2.9 by Reimers et al. (1997) and the abrupt change observed by Songaila (1998) at about the same epoch of the SiIV/CIV ratio, but appear unable to provide the required number of hydrogen-ionizing photons at z=5.
QuasarIntergalactic mediumIonizing radiationReionizationOf starsRecombinationLuminosity functionLyman recombination continuaStar formationLuminosity...
• #### Gas Clumping in Self-Consistent Reionisation Models

We use a suite of cosmological hydrodynamic simulations including a self-consistent treatment for inhomogeneous reionisation to study the impact of galactic outflows and photoionisation heating on the volume-averaged recombination rate of the intergalactic medium (IGM). By incorporating an evolving ionising escape fraction and a treatment for self-shielding within Lyman limit systems, we have run the first simulations of "photon-starved" reionisation scenarios that simultaneously reproduce observations of the abundance of galaxies, the optical depth to electron scattering of cosmic microwave background photons \tau, and the effective optical depth to Lyman\alpha absorption at z=5. We confirm that an ionising background reduces the clumping factor C by more than 50% by smoothing moderately-overdense (\Delta=1--100) regions. Meanwhile, outflows increase clumping only modestly. The clumping factor of ionised gas is much lower than the overall baryonic clumping factor because the most overdense gas is self-shielded. Photoionisation heating further suppresses recombinations if reionisation heats gas above the canonical 10,000 K. Accounting for both effects within our most realistic simulation, C rises from <1 at z>10 to 3.3 at z=6. We show that incorporating temperature- and ionisation-corrected clumping factors into an analytical reionisation model reproduces the numerical simulation's \tau to within 10%. Finally, we explore how many ionising photons are absorbed during the process of heating filaments by considering the overall photon cost of reionisation in analytical models that assume that the IGM is heated at different redshifts. For reionisation redshifts of 9--10, cold filaments boost the reionisation photon budget by ~1 photon per hydrogen atom.
ReionizationIntergalactic mediumRecombination rateGalaxyStar formationGalaxy filamentAbundanceFluid dynamicsAbsorbanceIonizing radiation...
• #### Interpreting the evolution of galaxy colours from $z = 8$ to $z = 5$ver. 2

We attempt to interpret existing data on the evolution of the UV luminosity function and UV colours, $\beta$, of galaxies at $5 \leq z \leq 8$, to improve our understanding of their dust content and ISM properties. To this aim, we post-process the results of a cosmological hydrodynamical simulation with a chemical evolution model, which includes dust formation by supernovae and intermediate mass stars, dust destruction in supernova shocks, and grain growth by accretion of gas-phase elements in dense gas. We find that observations require a steep, Small Magellanic Cloud-like extinction curve and a clumpy dust distribution, where stellar populations younger than 15 Myr are still embedded in their dusty natal clouds. Investigating the scatter in the colour distribution and stellar mass, we find that the observed trends can be explained by the presence of two populations: younger, less massive galaxies where dust enrichment is mainly due to stellar sources, and massive, more chemically evolved ones, where efficient grain growth provides the dominant contribution to the total dust mass. Computing the IR-excess - UV color relation we find that all but the dustiest model galaxies follow a relation shallower than the Meurer et al. (1999) one, usually adopted to correct the observed UV luminosities of high-$z$ galaxies for the effects of dust extinction. As a result, their total star formation rates might have been over-estimated. Our study illustrates the importance to incorporate a proper treatment of dust in simulations of high-$z$ galaxies, and that massive, dusty, UV-faint galaxies might have already appeared at $z \lesssim 7$.
LuminosityInterstellar mediumExtinctionLuminosity functionDust extinctionStarSupernovaMilky WayStellar populationsMolecular cloud...
• #### Acceleration in Modified Gravity (MOG) and the Mass-Discrepancy Baryonic Relation

The equation of motion in the generally covariant modified gravity (MOG) theory leads for weak gravitational fields and the non-relativistic limit to a modification of the Newtonian gravitational acceleration law, expressed in terms of two parameters $\alpha$ and $\mu$. The parameter $\alpha$ determines the strength of the gravitational field and $\mu$ is the effective mass of the vector field $\phi_\mu$, coupled with gravitational strength to baryonic matter. The MOG acceleration law for weak field gravitation and non-relativistic particles has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. We demonstrate that the MOG acceleration law for a point mass source is in agreement with the McGaugh et al., correlation between the radial acceleration traced by galaxy rotation curves and the distribution of baryonic matter for the SPARC sample of 153 rotationally supported spiral and irregular galaxies.
Modified gravityRotation CurveDark matterModified Newtonian DynamicsWeak gravitational fieldGravitational fieldsMass discrepancyGeneral relativityBullet ClusterTheory...
• #### Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect

Due to cosmic variance we cannot learn any more about large-scale inhomogeneities from the primary cosmic microwave background (CMB) alone. More information on large scales is essential for resolving large angular scale anomalies in the CMB. Here we consider cross correlating the large-scale kinetic Sunyaev Zel'dovich (kSZ) effect and probes of large-scale structure, a technique known as kSZ tomography. The statistically anisotropic component of the cross correlation encodes the CMB dipole as seen by free electrons throughout the observable Universe, providing information about long wavelength inhomogeneities. We compute the large angular scale power asymmetry, constructing the appropriate transfer functions, and estimate the cosmic variance limited signal to noise for a variety of redshift bin configurations. The signal to noise is significant over a large range of power multipoles and numbers of bins. We present a simple mode counting argument indicating that kSZ tomography can be used to estimate more modes than the primary CMB on comparable scales. This paper motivates a more systematic investigation of how close to the cosmic variance limit it will be possible to get with future observations.
Cosmic microwave backgroundKinetic Sunyaev-Zel'dovich effectCosmic varianceRedshift binsLarge scale structureCross-correlationIntegrated Sachs-WolfeTheoryTransfer functionAnisotropy...
• #### Weak-lensing mass calibration of redMaPPer galaxy clusters in Dark Energy Survey Science Verification data

We use weak-lensing shear measurements to determine the mean mass of optically selected galaxy clusters in Dark Energy Survey Science Verification data. In a blinded analysis, we split the sample of more than 8,000 redMaPPer clusters into 15 subsets, spanning ranges in the richness parameter $5 \leq \lambda \leq 180$ and redshift $0.2 \leq z \leq 0.8$, and fit the averaged mass density contrast profiles with a model that accounts for seven distinct sources of systematic uncertainty: shear measurement and photometric redshift errors; cluster-member contamination; miscentering; deviations from the NFW halo profile; halo triaxiality; and line-of-sight projections. We combine the inferred cluster masses to estimate the joint scaling relation between mass, richness and redshift, $\mathcal{M}(\lambda,z) \varpropto M_0 \lambda^{F} (1+z)^{G}$. We find $M_0 \equiv \langle M_{200\mathrm{m}}\,|\,\lambda=30,z=0.5\rangle=\left[ 2.35 \pm 0.22\ \rm{(stat)} \pm 0.12\ \rm{(sys)} \right] \cdot 10^{14}\ M_\odot$, with $F = 1.12\,\pm\,0.20\ \rm{(stat)}\, \pm\, 0.06\ \rm{(sys)}$ and $G = 0.18\,\pm\, 0.75\ \rm{(stat)}\, \pm\, 0.24\ \rm{(sys)}$. The amplitude of the mass-richness relation is in excellent agreement with the weak-lensing calibration of redMaPPer clusters in SDSS by Simet et al. (2016) and with the Saro et al. (2015) calibration based on abundance matching of SPT-detected clusters. Our results extend the redshift range over which the mass-richness relation of redMaPPer clusters has been calibrated with weak lensing from $z\leq 0.3$ to $z\leq0.8$. Calibration uncertainties of shear measurements and photometric redshift estimates dominate our systematic error budget and require substantial improvements for forthcoming studies.
Cluster of galaxiesCalibrationSystematic errorPhotometric redshiftWeak lensingWeak lensing mass estimateVirial cluster massStatistical estimatorSloan Digital Sky SurveyCovariance matrix...
• #### Bose-Einstein Condensate Dark Matter Halos confronted with galactic rotation curvesver. 2

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We conclude that the BEC model fits better the dwarf galaxy dark matter distribution, but suffers from sharp cut-off in larger galaxies, where the NFW model performs better. In more detail, we employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB) and 7 dwarf galaxies with rotation curves falling into two classes, based on their shapes. In the first class the rotational velocities increase with radius over the whole observed range, the BEC and NFW models giving comparable fits for both HSB and LSB galaxies, while significantly improving over the NFW fit for dwarf galaxies. This improvement is due to the central density cusp avoidance property of the BEC model. The rotational velocity of HSB and LSB galaxies falling into the second class exhibit long flat plateaus, resulting in a better fit of the NFW model for HSB galaxies, and comparable fits for LSB galaxies. The weaker performance of the BEC model for the HSB type II galaxies is due to the BEC density profiles dropping rapidly to zero outside a nearly constant density core.
Bose-Einstein condensateGalaxyNavarro-Frenk-White profileRotation CurveDark matterDwarf galaxyLow surface brightness galaxyLow surface brightnessDark matter haloGalactic rotation...
• #### Electrical Conductivity of Quark-Gluon Plasma in Strong Magnetic Fields

We compute the electrical conductivity of quark-gluon plasma in a strong magnetic field $B$ with quantum field theory at finite temperature using the lowest Landau level approximation. We provide the one-loop result arising from 1-to-2 scattering processes whose kinematics are satisfied by the (1+1) dimensional fermion dispersion relation. Due to the chirality conservation, the conductivity diverges in the massless limit, and is sensitive to the value of the current quark mass. As a result, we find that the conductivity along the direction of the magnetic field is quite large compared with the value at $B=0$, mainly because of the small value of the current quark mass. We show that the resummation of the ladder diagrams for the current-current correlator gives rise to only sub-leading contributions beyond the leading-log order, and thus verify our one-loop result at the leading-log accuracy. We also discuss possible implications for the relativistic heavy-ion collisions.
Strong magnetic fieldLowest Landau LevelCurrent quark massLLL approximationQuark-gluon plasmaHeavy ion collisionPinch singularityElectrical Conductivity of Quark-Gluon PlasmaPropagatorChirality...
• #### The Skeleton of the Milky Wayver. 4

Recently, Goodman et al. (2014) argued that the very long, very thin infrared dark cloud "Nessie" lies directly in the Galactic mid-plane and runs along the Scutum-Centaurus arm in position-position-velocity ($p-p-v$) space as traced by lower density $\rm {CO}$ and higher density ${\rm NH}_3$ gas. Nessie was presented as the first "bone" of the Milky Way, an extraordinarily long, thin, high-contrast filament that can be used to map our Galaxy's "skeleton." Here, we present evidence for additional bones in the Milky Way Galaxy, arguing that Nessie is not a curiosity but one of several filaments that could potentially trace Galactic structure. Our ten bone candidates are all long, filamentary, mid-infrared extinction features which lie parallel to, and no more than 20 pc from, the physical Galactic mid-plane. We use $\rm {CO}$, ${\rm N}_2{\rm H}^+$, $\rm {HCO}^+$, and ${\rm NH}_3$ radial velocity data to establish the three-dimensional location of the candidates in ${\it p-p-v}$ space. Of the ten candidates, six also: have a projected aspect ratio of $\geqq$50:1; run along, or extremely close to, the Scutum-Centaurus arm in ${\it p-p-v}$ space; and exhibit no abrupt shifts in velocity. The evidence presented here suggests that these candidates are marking the locations of significant spiral features, with the bone called filament 5 ("BC_18.88-0.09") being a close analog to Nessie in the Northern Sky. As molecular spectral-line and extinction maps cover more of the sky at increasing resolution and sensitivity, it should be possible to find more bones in future studies.
Galaxy filamentMilky WayExtinctionSpiral armScutum-Centaurus ArmGalactic structureRadial velocityBolocam Galactic Plane SurveySpiral structureStar formation...
• #### Diffuse Interstellar Bands and the Ultraviolet Extinction Curves: The Missing Link Revisited

A large number of interstellar absorption features at ~ 4000\AA\ -- 1.8 {\mu}m, known as the "diffuse interstellar bands" (DIBs), remains unidentified. Most recent works relate them to large polycyclic aromatic hydrocarbon (PAH) molecules or ultrasmall carbonaceous grains which are also thought to be responsible for the 2175 \AA\ extinction bump and/or the far ultraviolet (UV) extinction rise at $\lambda^{-1} > 5.9\ {\mu}m^{-1}$. Therefore, one might expect some relation between the UV extinction and DIBs. Such a relationship, if established, could put important constraints on the carrier of DIBs. Over the past four decades, whether DIBs are related to the shape of the UV extinction curves has been extensively investigated. However, the results are often inconsistent, partly due to the inconsistencies in characterizing the UV extinction. Here we re-examine the connection between the UV extinction curve and DIBs. We compile the extinction curves and the equivalent widths of 40 DIBs along 97 slightlines. We decompose the extinction curve into three Drude-like functions composed of the visible/near-infrared component, the 2175 \AA\ bump, and the far-UV extinction at $\lambda^{-1} > 5.9\ {\mu}m^{-1}$. We argue that the wavelength-integrated far-UV extinction derived from this decomposition technique best measures the strength of the far-UV extinction. No correlation is found between the far-UV extinction and most (~90\%) of the DIBs. We have also shown that the color excess E(1300-1700), the extinction difference at 1300 \AA\ and 1700 \AA\ often used to measure the strength of the far-UV extinction, does not correlate with DIBs. Finally, we confirm the earlier findings of no correlation between the 2175 \AA\ bump and DIBs or between the 2175 \AA\ bump and the far-UV extinction.
ExtinctionBumpingLine of sightColor excessInterstellar extinctionDiffuse interstellar bandSilicateInterstellar mediumUltraviolet extinctionEquivalent width...
• #### Not that long time ago in the nearest galaxy: 3D slice of molecular gas revealed by a 110 years old flare of Sgr A*

A powerful outburst of X-ray radiation from the supermassive black hole Sgr A* at the center of the Milky Way is believed to be responsible for the illumination of molecular clouds in the central ~100 pc of the Galaxy (Sunyaev et al., 1993, Koyama et al., 1996). The reflected/reprocessed radiation comes to us with a delay corresponding to the light propagation time that depends on the 3D position of molecular clouds with respect to Sgr A*. We suggest a novel way of determining the age of the outburst and positions of the clouds by studying characteristic imprints left by the outburst in the spatial and time variations of the reflected emission. We estimated the age of the outburst that illuminates the Sgr A molecular complex to be ~110 yr. This estimate implies that we see the gas located ~10 pc further away from us than Sgr A*. If the Sgr B2 complex is also illuminated by the same outburst, then it is located ~130 pc closer than our Galactic Center. The outburst was short (less than a few years) and the total amount of emitted energy in X-rays is $\displaystyle \sim 10^{48}\rho_3^{-1}$ erg, where $\rho_3$ is the mean hydrogen density of the cloud complex in units of $10^3 {\rm cm^{-3}}$. Energetically, such fluence can be provided by a partial tidal disruption event or even by a capture of a planet. Further progress in more accurate positioning and timing of the outburst should be possible with future X-ray polarimetric observations and long-term systematic observations with Chandra and XMM-Newton. A few hundred-years long X-ray observations would provide a detailed 3D map of the gas density distribution in the central $\sim 100$ pc region.
Optical burstsXMM-NewtonSagittarius A*Chandra X-ray ObservatoryMolecular cloudGalactic CenterSurface brightnessLine of sightLuminosityLight curve...
• #### The turbulent life of dust grains in the supernova-driven, multi-phase interstellar medium

Dust grains are an important component of the interstellar medium (ISM) of galaxies. We present the first direct measurement of the residence times of interstellar dust in the different ISM phases, and of the transition rates between these phases, in realistic hydrodynamical simulations of the multi-phase ISM. Our simulations include a time-dependent chemical network that follows the abundances of H^+, H, H_2, C^+ and CO and take into account self-shielding by gas and dust using a tree-based radiation transfer method. Supernova explosions are injected either at random locations, at density peaks, or as a mixture of the two. For each simulation, we investigate how matter circulates between the ISM phases and find more sizeable transitions than considered in simple mass exchange schemes in the literature. The derived residence times in the ISM phases are characterised by broad distributions, in particular for the molecular, warm and hot medium. The most realistic simulations with random and mixed driving have median residence times in the molecular, cold, warm and hot phase around 17, 7, 44 and 1 Myr, respectively. The transition rates measured in the random driving run are in good agreement with observations of Ti gas-phase depletion in the warm and cold phases in a simple depletion model, although the depletion in the molecular phase is under-predicted. ISM phase definitions based on chemical abundance rather than temperature cuts are physically more meaningful, but lead to significantly different transition rates and residence times because there is no direct correspondence between the two definitions.
SupernovaMolecular cloudMass exchangeSupernova explosionInterstellar dustAbundanceDust grainGas-to-dust ratioChemical abundanceAccretion...
• #### Revealing a spiral-shaped molecular cloud in our galaxy - Cloud fragmentation under rotation and gravity

The dynamical processes that control star formation in molecular clouds are not well understood, and in particular, it is unclear if rotation plays a major role in cloud evolution. We investigate the importance of rotation in cloud evolution by studying the kinematic structure of a spiral-shaped Galactic molecular cloud G052.24+00.74. The cloud belongs to a large filament, and is stretching over ~ 100 pc above the Galactic disk midplane. The spiral-shaped morphology of the cloud suggests that the cloud is rotating. We have analysed the kinematic structure of the cloud, and study the fragmentation and star formation. We find that the cloud exhibits a regular velocity pattern along west-east direction - a velocity shift of ~ 10 km/s at a scale of ~ 30 pc. The kinematic structure of the cloud can be reasonably explained by a model that assumes rotational support. Similarly to our Galaxy, the cloud rotates with a prograde motion. We use the formalism of Toomre (1964) to study the cloud's stability, and find that it is unstable and should fragment. The separation of clumps can be consistently reproduced assuming gravitational instability, suggesting that fragmentation is determined by the interplay between rotation and gravity. Star formation occurs in massive, gravitational bound clumps.
FragmentationMolecular cloudStar formationMilky WayKinematicsSpiral armJeans instabilityTurbulenceGalaxy cloudInclination...
• #### Quantized chiral magnetic current from reconnections of magnetic fluxver. 2

We introduce a new mechanism for the chiral magnetic effect that does not require an initial chirality imbalance. The chiral magnetic current is generated by reconnections of magnetic flux that change the magnetic helicity of the system. The resulting current is entirely determined by the change of magnetic helicity, and it is quantized.
Chiral magnetic effectMagnetic helicityChirality imbalanceLowest Landau LevelHelicityChiralityMagnetic reconnectionQuantizationAntiparticleMagnetic effects...
• #### Frobenius integrability and Finsler metrizability for $2$-dimensional sprays

For a $2$-dimensional non-flat spray we associate a Berwald frame and a $3$-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of the given spray. In the integrable case, the sought after Finsler function is provided by a closed, homogeneous $1$-form from the annihilator of the Berwald distribution. We discuss both the degenerate and non-degenerate cases using the fact that the regularity of the Finsler function is encoded into a regularity condition of a $2$-form, canonically associated to the give spray. The integrability of the Berwald distribution and the regularity of the $2$-form have simple and useful expressions in terms of the Berwald frame.
GeodesicEndomorphismRankManifoldCovariant derivativeCurvatureScalar curvatureEuler-Lagrange equationHomogeneous functionRiemannian metric...
• #### Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature

In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.
CurvatureEndomorphismGeodesicHomogenizationTangent bundleScalar curvatureCurvature tensorOrdinary differential equationsManifoldSymplectic form...
• #### Funk functions and projective deformations of sprays and Finsler spaces of scalar flag curvaturever. 2

In 2001, Zhongmin Shen asked if it is possible for two projectively related Finsler metrics to have the same Riemann curvature tensor, [14, page 184]. In this paper, we provide an answer to this question, within the class of Finsler metrics of scalar flag curvature. In Theorem 3.1, we show that the answer is negative, for non-vanishing scalar flag curvature. The answer is known to be positive when the scalar flag curvature vanishes, [12, 14] and this positive answer is related to the existence of many solutions to Hilbert's Fourth Problem. As a generalisation of this problem, we can ask if it is possible for a given spray, with non-vanishing scalar flag curvature, to represent, after reparametrisation, the geodesic spray of a Finsler metric. In Proposition 3.3, we show how to construct sprays whose projective class does not contain any Finsler metrizable spray with the same Riemann curvature tensor.
CurvatureEndomorphismGeodesicCurvature tensorHomogenizationScalar curvatureTangent spaceFrölicher-Nijenhuis bracketOrdinary differential equationsManifold...
• #### A universal pair of genus-two curves

Let $\mathfrak{p}$ be any point in the moduli space of genus-two curves $\mathcal{M}_2$ and $K$ its field of moduli. We provide a universal pair of genus-two curves over its minimal field of definition $K[d]$ where $d^2$ is given in terms of $\mathfrak{p}$. Furthermore, $K$ is a field of definition if and only if $d^2$ is a complete square in $K$.
Modular formAutomorphismIsomorphismEisenstein seriesElliptic curveEndomorphism ringRamificationQuaternionsAsymptotic expansionModular transformation...
• #### The arithmetic of genus two curvesver. 3

Genus 2 curves have been an object of much mathematical interest since eighteenth century and continued interest to date. They have become an important tool in many algorithms in cryptographic applications, such as factoring large numbers, hyperelliptic curve cryptography, etc. Choosing genus 2 curves suitable for such applications is an important step of such algorithms. In existing algorithms often such curves are chosen using equations of moduli spaces of curves with decomposable Jacobians or Humbert surfaces. In these lectures we will cover basic properties of genus 2 curves, moduli spaces of (n,n)-decomposable Jacobians and Humbert surfaces, modular polynomials of genus 2, Kummer surfaces, theta-functions and the arithmetic on the Jacobians of genus 2, and their applications to cryptography. The lectures are intended for graduate students in algebra, cryptography, and related areas.
AutomorphismElliptic curveTheta functionCryptographyArithmeticRamificationIsomorphismBranch pointHomogeneous polynomialMorphism...
• #### Quasi-classical generalized CRF structures

In an earlier paper, we studied manifolds $M$ endowed with a generalized F structure $\Phi\in End(TM\oplus T^*M)$, skew-symmetric with respect to the pairing metric, such that $\Phi^3+\Phi=0$. Furthermore, if $\Phi$ is integrable (in some well-defined sense), $\Phi$ is a generalized CRF structure. In the present paper we study quasi-classical generalized F and CRF structures, which may be seen as a generalization of the holomorphic Poisson structures (it is well known that the latter may also be defined via generalized geometry). The structures that we study are equivalent to a pair of tensor fields $(A\in End(TM),\pi\in\wedge^2TM)$ where $A^3+A=0$ and some relations between $A$ and $\pi$ hold. We establish the integrability conditions in terms of $(A,\pi)$. They include the facts that $A$ is a classical CRF structure, $\pi$ is a Poisson bivector field and $im\,A$ is a (non)holonomic Poisson submanifold of $(M,\pi)$. We discuss the case where either $ker\,A$ or $im\,A$ is tangent to a foliation and, in particular, the case of almost contact manifolds. Finally, we show that the dual bundle of $im\,A$ inherits a Lie algebroid structure and we briefly discuss the Poisson cohomology of $\pi$, including an associated spectral sequence and a Dolbeault type grading.
HolomorphFoliationSpectral sequenceCohomologyLuminosity functionTensor fieldSubbundleManifoldEndomorphismContact manifold...
• #### Dirac and Maxwell equations in Split Octonions

The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of split octonions.
Zero divisorCauchy-Riemann equationsQuaternionsKeyphraseDegree of freedomCauchy-RiemannDivision algebraGamma matricesComplex numberWavefunction...
• #### A machine-learning approach to measuring the escape of ionizing radiation from galaxies in the reionization epochver. 2

Recent observations of galaxies at $z \gtrsim 7$, along with the low value of the electron scattering optical depth measured by the Planck mission, make galaxies plausible as dominant sources of ionizing photons during the epoch of reionization. However, scenarios of galaxy-driven reionization hinge on the assumption that the average escape fraction of ionizing photons is significantly higher for galaxies in the reionization epoch than in the local Universe. The NIRSpec instrument on the James Webb Space Telescope (JWST) will enable spectroscopic observations of large samples of reionization-epoch galaxies. While the leakage of ionizing photons will not be directly measurable from these spectra, the leakage is predicted to have an indirect effect on the spectral slope and the strength of nebular emission lines in the rest-frame ultraviolet and optical. Here, we apply a machine learning technique known as lasso regression on mock JWST/NIRSpec observations of simulated $z=7$ galaxies in order to obtain a model that can predict the escape fraction from JWST/NIRSpec data. Barring systematic biases in the simulated spectra, our method is able to retrieve the escape fraction with a mean absolute error of $\Delta f_{\mathrm{esc}} \approx 0.12$ for spectra with $S/N\approx 5$ at a rest-frame wavelength of 1500 {\AA} for our fiducial simulation. This prediction accuracy represents a significant improvement over previous similar approaches.
Epoch of reionizationLyman recombination continuaIonizing radiationSignal to noise ratioRegressionJames Webb Space TelescopeDust attenuation curveTraining setStellar evolutionMachine learning...
• #### The Evolution of the Galaxy Stellar Mass Function at z= 4-8: A Steepening Low-mass-end Slope with Increasing Redshiftver. 2

We present galaxy stellar mass functions (GSMFs) at $z=$ 4-8 from a rest-frame ultraviolet (UV) selected sample of $\sim$4500 galaxies, found via photometric redshifts over an area of $\sim$280 arcmin$^2$ in the CANDELS/GOODS fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data yet-to-date and the relatively large volume allow us to place a better constraint at both the low- and high-mass ends of the GSMFs compared to previous space-based studies from pre-CANDELS observations. Supplemented by a stacking analysis, we find a linear correlation between the rest-frame UV absolute magnitude at 1500 \AA\ ($M_{\rm UV}$) and logarithmic stellar mass ($\log M_*$) that holds for galaxies with $\log(M_*/M_{\odot}) \lesssim 10$. We use simulations to validate our method of measuring the slope of the $\log M_*$-$M_{\rm UV}$ relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over $z=$ 4-8, while the normalization of the trend exhibits a weak evolution toward lower masses at higher redshift. We combine the $\log M_*$-$M_{\rm UV}$ distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs, finding that the low-mass-end slope becomes steeper with increasing redshift from $\alpha=-1.55^{+0.08}_{-0.07}$ at $z=4$ to $\alpha=-2.25^{+0.72}_{-0.35}$ at $z=8$. The inferred stellar mass density, when integrated over $M_*=10^8$-$10^{13} M_{\odot}$, increases by a factor of $10^{+30}_{-2}$ between $z=7$ and $z=4$ and is in good agreement with the time integral of the cosmic star formation rate density.
Galactic stellar mass functionGalactic evolutionStellar mass functionPhotometryStellar massUV luminosity functionHigh massFaint galaxiesBright galaxiesAbsolute magnitude...
• #### Extremely Small Sizes for Faint z~2-8 Galaxies in the Hubble Frontier Fields: A Key Input For Establishing their Volume Density and UV Emissivityver. 2

We provide the first observational constraints on the sizes of the faintest galaxies lensed by the Hubble Frontier Fields (HFF) clusters. Ionizing radiation from faint galaxies likely drives cosmic reionization, and the HFF initiative provides a key opportunity to find such galaxies. Yet, we cannot really assess their ionizing emissivity without a robust measurement of their sizes, since this is key to quantifying both their prevalence and the faint-end slope to the UV luminosity function. Here we provide the first such size constraints with 2 new techniques. The first utilizes the fact that the detectability of highly-magnified galaxies as a function of shear is very dependent on a galaxy's size. Only the most compact galaxies will remain detectable in regions of high shear (vs. a larger detectable size range for low shear), a phenomenon we carefully quantify using simulations. Remarkably, however, no correlation is found between the surface density of faint galaxies and the predicted shear, using 87 faint high-magnification mu>10 z~2-8 galaxies seen behind the first 4 HFF clusters. This can only be the case if such faint (~-15 mag) galaxies have significantly smaller sizes than luminous galaxies. We constrain their half-light radii to be <~30 mas (<160-240 pc). As a 2nd size probe, we rotate and stack 26 faint high-magnification sources along the major shear axis. Less elongation is found than even for objects with an intrinsic half-light radius of 10 mas. Together these results indicate that extremely faint z~2-8 galaxies have near point-source profiles in the HFF dataset (half-light radii conservatively <30 mas and likely 5-10 mas). These results suggest smaller completeness corrections and hence much lower volume densities for faint z~2-8 galaxies and shallower faint-end slopes than have been derived in many recent studies (by factors of ~2-3 and by dalpha>~0.1-0.3).
Hubble Frontier FieldsHalf-light radiusFaint galaxiesCompletenessLuminosityPoint sourceThe Hubble Space Telescope "Ultra Deep Field" ViewReionizationVisual magnitudeParsec...
• #### Constraining SN feedback: a tug of war between reionization and the Milky Way satellitesver. 2

Theoretical models of galaxy formation based on the cold dark matter cosmogony typically require strong feedback from supernova (SN) explosions in order to reproduce the Milky Way satellite galaxy luminosity function and the faint end of the field galaxy luminosity function. However, too strong a SN feedback also leads to the universe reionizing too late, and the metallicities of Milky Way satellites being too low. The combination of these four observations therefore places tight constraints on SN feedback. We investigate these constraints using the semi-analytical galaxy formation model galform. We find that these observations favour a SN feedback model in which the feedback strength evolves with redshift. We find that, for our best fit model, half of the ionizing photons are emitted by galaxies with rest-frame far-UV absolute magnitudes $M_{\rm AB}(1500{\rm \AA})<-17.5$, which implies that already observed galaxy populations contribute about half of the photons responsible for reionization. The $z=0$ descendants of these galaxies are mainly galaxies with stellar mass $M_*>10^{10}\,{\rm M}_{\odot}$ and preferentially inhabit halos with mass $M_{\rm halo}>10^{13}\,{\rm M}_{\odot}$.
ReionizationLuminosity functionMilky WayIonizing radiationMilky Way satelliteStar formationActive Galactic NucleiStellar massMerger treeStar...
• #### Substructure of fuzzy dark matter halos

We derive the halo mass function (HMF) for fuzzy dark matter (FDM) by solving the excursion set problem explicitly with a mass-dependent barrier function, which has not been done before. We find that compared to the naive approach of the Sheth-Tormen HMF for FDM the one we obtain has a higher cut off mass and the cut off mass change less strongly with redshifts. Using merger trees constructed with a modified version of the Lacey & Cole formalism that accounts for suppressed small scale power and the scale-dependent growth of FDM halos and the semi-analytic Galacticus code, we study the statistics of halo substructure including the effects from dynamical friction and tidal stripping. We find that if the dark matter is a mixture of cold dark matter (CDM) and FDM, there will be a suppression on the halo substructure on small scales which may be able to solve the Missing Satellites Problem faced by the pure CDM model. The suppression becomes stronger with increasing FDM fraction or decreasing FDM mass. Thus it may be used to constrain the FDM model.
Halo mass functionCold dark matterMerger treeTidal strippingDark matter subhaloDark matterDynamical frictionMixed dark matterDark matter haloTransfer function...
• #### Evolution of cosmic star formation in the SCUBA-2 Cosmology Legacy Survey

We present a new exploration of the cosmic star-formation history and dust obscuration in massive galaxies at redshifts $0.5< z<6$. We utilize the deepest 450 and 850$\mu$m imaging from SCUBA-2 CLS, covering 230arcmin$^2$ in the AEGIS, COSMOS and UDS fields, together with 100-250$\mu$m imaging from Herschel. We demonstrate the capability of the T-PHOT deconfusion code to reach below the confusion limit, using multi-wavelength prior catalogues from CANDELS/3D-HST. By combining IR and UV data, we measure the relationship between total star-formation rate (SFR) and stellar mass up to $z\sim5$, indicating that UV-derived dust corrections underestimate the SFR in massive galaxies. We investigate the relationship between obscuration and the UV slope (the IRX-$\beta$ relation) in our sample, which is similar to that of low-redshift starburst galaxies, although it deviates at high stellar masses. Our data provide new measurements of the total SFR density (SFRD) in $M_\ast>10^{10}M_\odot$ galaxies at $0.5<z<6$. This is dominated by obscured star formation by a factor of $>10$. One third of this is accounted for by 450$\mu$m-detected sources, while one fifth is attributed to UV-luminous sources (brighter than $L^\ast_{UV}$), although even these are largely obscured. By extrapolating our results to include all stellar masses, we estimate a total SFRD that is in good agreement with previous results from IR and UV data at $z\lesssim3$, and from UV-only data at $z\sim5$. The cosmic star-formation history undergoes a transition at $z\sim3-4$, as predominantly unobscured growth in the early Universe is overtaken by obscured star formation, driven by the build-up of the most massive galaxies during the peak of cosmic assembly.
Star formation rateStellar massStar formationSpectral energy distributionLuminosityMassive galaxiesStar-forming galaxyHubble Space TelescopeLuminosity functionLyman break galaxy...
• #### The Minimum Halo Mass for Star Formation at z = 6 - 8

Recent analysis of strongly-lensed sources in the Hubble Frontier Fields indicates that the rest-frame UV luminosity function of galaxies at $z=$6--8 rises as a power law down to $M_\mathrm{UV}=-15$, and possibly as faint as -12.5. We use predictions from a cosmological radiation hydrodynamic simulation to map these luminosities onto physical space, constraining the minimum dark matter halo mass and stellar mass that the Frontier Fields probe. While previously-published theoretical studies have suggested or assumed that early star formation was suppressed in halos less massive than $10^9$--$10^{11} M_\odot$, we find that recent observations demand vigorous star formation in halos at least as massive as (3.1, 5.6, 10.5)$\times10^9 M_\odot$ at $z=(6,7,8)$. Likewise, we find that Frontier Fields observations probe down to stellar masses of (8.1, 18, 32)$\times10^6 M_\odot$; that is, they are observing the likely progenitors of analogues to Local Group dwarfs such as Pegasus and M32. Our simulations yield somewhat different constraints than two complementary models that have been invoked in similar analyses, emphasizing the need for further observational constraints on the galaxy-halo connection.
Star formationVirial massLuminosity functionLuminosityStellar massDark matter haloLocal Group dwarf galaxyStarFluid dynamicsAccretion...
• #### The Stellar Initial Mass Function at the Epoch of Reionizationver. 2

I provide estimates of the ultraviolet and visible light luminosity density at z~6 after accounting for the contribution from faint galaxies below the detection limit of deep Hubble and Spitzer surveys. I find the rest-frame V-band luminosity density is a factor of ~2-3 below the ultraviolet luminosity density at z~6. This implies that the maximal age of the stellar population at z~6, for a Salpeter initial mass function, and a single, passively evolving burst, must be <100 Myr. If the stars in z~6 galaxies are remnants of the star-formation that was responsible for ionizing the intergalactic medium, reionization must have been a brief process that was completed at z<7. This assumes the most current estimates of the clumping factor and escape fraction and a Salpeter slope extending up to 200 M_{\sun} for the stellar initial mass function (IMF; dN/dM \propto M^{\alpha}, \alpha=-2.3). Unless the ratio of the clumping factor to escape fraction is less than 60, a Salpeter slope for the stellar IMF and reionization redshift higher than 7 is ruled out. In order to maintain an ionized intergalactic medium from redshift 9 onwards, the stellar IMF must have a slope of \alpha=-1.65 even if stars as massive as ~200 M_{\sun} are formed. Correspondingly, if the intergalactic medium was ionized from redshift 11 onwards, the IMF must have \alpha~-1.5. The range of stellar mass densities at z~6 straddled by IMFs which result in reionization at z>7 is 1.3+/-0.4\times10^{7} Msun/Mpc^3.
LuminosityIonizing radiationStellar massIntergalactic mediumReionizationStar formationSalpeter Initial Mass FunctionMetallicityStarStellar populations...
• #### Physical Properties of Galaxies from z=2-4ver. 2

The epoch of galaxy assembly from 2<=z<=4 marks a critical stage during the evolution of today's galaxy population. During this period the star-formation activity in the Universe was at its peak level, and the structural patterns observed among galaxies in the local Universe were not yet in place. A variety of novel techniques have been employed over the past decade to assemble multiwavelength observations of galaxies during this important epoch. In this primarily observational review, I present a census of the methods used to find distant galaxies and the empirical constraints on their multiwavelength luminosities and colors. I then discuss what is known about the stellar content and past histories of star formation in high-redshift galaxies; their interstellar contents including dust, gas, and heavy elements; and their structural and dynamical properties. I conclude by considering some of the most pressing and open questions regarding the physics of high-redshift galaxies, which are to be addressed with future facilities.
LuminosityStar formationStar formation rateStellar massOf starsStar-forming galaxySubmillimeter galaxyHigh-redshift galaxyStellar populationsLuminosity function...
• #### The Bright End of the z~9 and z~10 UV Luminosity Functions using all five CANDELS Fieldsver. 4

The deep, wide-area (~800-900 arcmin**2) near-infrared/WFC3/IR + Spitzer/IRAC observations over the CANDELS fields have been a remarkable resource for constraining the bright end of high redshift UV luminosity functions (LFs). However, the lack of HST 1.05-micron observations over the CANDELS fields has made it difficult to identify z~9-10 sources robustly, since such data are needed to confirm the presence of an abrupt Lyman break at 1.2 microns. We report here on the successful identification of many such z~9-10 sources from a new HST program (z9-CANDELS) that targets the highest-probability z~9-10 galaxy candidates with observations at 1.05 microns, to search for a robust Lyman-break at 1.2 microns. The potential z~9-10 candidates are preselected from the full HST, Spitzer/IRAC S-CANDELS observations, and the deepest-available ground-based optical+near-infrared observations. We identified 15 credible z~9-10 galaxies over the CANDELS fields. Nine of these galaxies lie at z~9 and 5 are new identifications. Our targeted follow-up strategy has proven to be very efficient in making use of scarce HST time to secure a reliable sample of z~9-10 galaxies. Through extensive simulations, we replicate the selection process for our sample (both the preselection and follow-up) and use it to improve current estimates for the volume density of bright z~9 and z~10 galaxies. The volume densities we find are 5(-2)(+3)x and 8(-3)(+9)x lower, respectively, than found at z~8. When compared with the best-fit evolution (i.e., dlog_{10} rho(UV)/dz=-0.29+/-0.02) in the UV luminosities densities from z~8 to z~4 integrated to 0.3L*(z=3) (-20 mag), these luminosity densities are 2.6(-0.9)(+1.5)x and 2.2(-1.1)(+2.0)x lower, respectively, than the extrapolated trends. Our new results are broadly consistent with the "accelerated evolution" scenario at z>8, as seen in many theoretical models.
GalaxyCosmic Assembly Near-IR Deep Extragalactic Legacy SurveyGOODS surveyLuminosity functionCOSMOS surveyCANDELS fieldLuminositySpectral energy distributionPhotometryUV luminosity function...
• #### Detection of an oxygen emission line from a high redshift galaxy in the reionization epoch

The physical properties and elemental abundances of the interstellar medium in galaxies during cosmic reionization are important for understanding the role of galaxies in this process. We report the Atacama Large Millimeter/submillimeter Array detection of an oxygen emission line at a wavelength of 88 micrometers from a galaxy at an epoch about 700 million years after the Big Bang. The oxygen abundance of this galaxy is estimated at about one-tenth that of the Sun. The non-detection of far-infrared continuum emission indicates a deficiency of interstellar dust in the galaxy. A carbon emission line at a wavelength of 158 micrometers is also not detected, implying an unusually small amount of neutral gas. These properties might allow ionizing photons to escape into the intergalactic medium.
LuminosityIonizing radiationStar formation rateInterstellar mediumIntergalactic mediumAtacama Large Millimeter ArrayStar formationSpectral energy distributionFull width at half maximumCalibration...
• #### The Star Formation Rate Function for Redshift z~4-7 Galaxies: Evidence for a Uniform Build-Up of Star-Forming Galaxies During the First 3 Gyr of Cosmic Timever. 2

We combine recent estimates of dust extinction at z~4-7 with UV luminosity function (LF) determinations to derive star formation rate (SFR) functions at z~4, 5, 6 and 7. SFR functions provide a more physical description of galaxy build-up at high redshift and allow for direct comparisons to SFRs at lower redshifts determined by a variety of techniques. Our SFR functions are derived from well-established z~4-7 UV LFs, UV-continuum slope trends with redshift and luminosity, and IRX-beta relations. They are well-described by Schechter relations. We extend the comparison baseline for SFR functions to z~2 by considering recent determinations of the H{\alpha} and mid-IR luminosity functions. The low-end slopes of the SFR functions are flatter than for the UV LFs, \Delta\alpha\sim+0.13, and show no clear evolution with cosmic time (z~0-7). In addition, we find that the characteristic value SFR* from the Schechter fit to SFR function exhibits consistent, and substantial, linear growth as a function of redshift from ~5 M_sun/yr at z~8, 650 Myr after the Big Bang, to ~100 M_sun/yr at z~2, ~2.5 Gyr later. Recent results at z~10, close to the onset of galaxy formation, are consistent with this trend. The uniformity of this evolution is even greater than seen in the UV LF over the redshift range z~2-8, providing validation for our dust corrections. These results provide strong evidence that galaxies build up uniformly over the first 3 Gyr of cosmic time.
Star formation rateLuminosity functionLuminosityGalaxyDust extinctionStar-forming galaxyOf starsBolometric luminosityUV luminosity functionStar formation...
• #### Clustering of Ly-alpha emitters around luminous quasars at z = 2-3: an alternative probe of reionization on galaxy formation

Narrowband observations have detected no Ly-alpha emission within a 70 pMpc^3 volume centered on the z = 2.168 quasar PKS 0424-131. This is in contrast to surveys of Ly-alpha emitters in the field at similar redshifts and flux limits, which indicate that tens of sources should be visible within the same volume. The observed difference indicates that the quasar environment has a significant influence on the observed density of Ly-alpha emitters. To quantify this effect we have constructed a semi-analytic model to simulate the effect of a luminous quasar on nearby Ly-alpha emitters. We find the null detection around PKS 0424-131 implies that the minimum isothermal temperature of Ly-alpha emitter host halos is greater than 3.4 x 10^6 K (68% level), corresponding to a virial mass of ~1.2 x 10^12 M_solar. This indicates that the intense UV emission of the quasar may be suppressing the star formation in nearby galaxies. Our study illustrates that low redshift quasar environments may serve as a surrogate for studying the radiative suppression of galaxy formation during the epoch of reionization.
QuasarLuminosityMilky WayGalaxy FormationLyman alpha emitterReionizationVirial massUV luminosity functionVirial radiusLuminosity function...
• #### Spatially adaptive radiation-hydrodynamical simulations of galaxy formation during cosmological reionizationver. 2

We present a suite of cosmological radiation-hydrodynamical simulations of the assembly of galaxies driving the reionization of the intergalactic medium (IGM) at z >~ 6. The simulations account for the hydrodynamical feedback from photoionization heating and the explosion of massive stars as supernovae (SNe). Our reference simulation, which was carried out in a box of size 25 comoving Mpc/h using 2 x 512^3 particles, produces a reasonable reionization history and matches the observed UV luminosity function of galaxies. Simulations with different box sizes and resolutions are used to investigate numerical convergence, and simulations in which either SNe or photoionization heating or both are turned off, are used to investigate the role of feedback from star formation. Ionizing radiation is treated using accurate radiative transfer at the high spatially adaptive resolution at which the hydrodynamics is carried out. SN feedback strongly reduces the star formation rates (SFRs) over nearly the full mass range of simulated galaxies and is required to yield SFRs in agreement with observations. Photoheating helps to suppress star formation in low-mass galaxies, but its impact on the cosmic SFR is small. Because the effect of photoheating is masked by the strong SN feedback, it does not imprint a signature on the UV galaxy luminosity function, although we note that our resolution is insufficient to model star-forming minihaloes cooling through molecular hydrogen transitions. Photoheating does provide a strong positive feedback on reionization because it smooths density fluctuations in the IGM, which lowers the IGM recombination rate substantially. Our simulations demonstrate a tight non-linear coupling of galaxy formation and reionization, motivating the need for the accurate and simultaneous inclusion of photoheating and SN feedback in models of the early Universe.
ReionizationStar formation rateSupernovaIntergalactic mediumStar formationIonizing radiationStarGalaxy FormationHistory of the reionizationLuminosity function...
• #### The evolution of the star formation rate function and cosmic star formation rate density of galaxies at $z \sim 1-4$

We investigate the evolution of the galaxy Star Formation Rate Function (SFRF) and Cosmic Star Formation Rate Density (CSFRD) of $z\sim 1-4$ galaxies, using cosmological Smoothed Particle Hydrodynamic (SPH) simulations and a compilation of UV, IR and H$\alpha$ observations. These tracers represent different populations of galaxies with the IR light being a probe of objects with high star formation rates and dust contents, while UV and H$\alpha$ observations provide a census of low star formation galaxies where mild obscuration occurs. We compare the above SFRFs with the results of SPH simulations run with the code {\small{P-GADGET3(XXL)}}. We focus on the role of feedback from Active Galactic Nuclei (AGN) and supernovae in form of galactic winds. The AGN feedback prescription that we use decreases the simulated CSFRD at $z < 3$ but is not sufficient to reproduce the observed evolution at higher redshifts. We explore different wind models and find that the key factor for reproducing the evolution of the observed SFRF and CSFRD at $z \sim1-4$ is the presence of a feedback prescription that is prominent at high redshifts ($z \ge 4$) and becomes less efficient with time. We show that variable galactic winds which are efficient at decreasing the SFRs of low mass objects are quite successful in reproducing the observables.
Star formation rateLuminosity functionLuminosityStar formationGalactic windUV luminosity functionAGN feedbackDust attenuation curveActive Galactic NucleiSmoothed-particle hydrodynamics...
• #### Mapping mobility patterns to public spaces in a medium-sized city using geolocated tweets

This research evidences the usefulness of open big data to map mobility patterns in a medium-sized city. Motivated by the novel analysis that big data allow worldwide and in large metropolitan areas, we developed a methodology aiming to complement origin-destination surveys with \a la carte spatial boundaries and updated data at a minimum cost. This paper validates the use of Twitter data to map the impact of public spaces on the different parts of the metropolitan area of Concepci\'on, Chile. Results have been validated by local experts and evidence the main mobility patterns towards spaces of social interaction like malls, leisure areas, parks and so on. The map represents the mobility patterns from census districts to different categories of public spaces with schematic lines at the metropolitan scale and it is centred in the city of Concepci\'on (Chile) and its surroundings (~10 kilometres).
• #### MOND Prediction for the Velocity Dispersion of the Feeble Giant' Crater II

Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime ($g_{in} \approx 34\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1} \ll a_0 = 3700\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$). Despite its great distance ($\approx 120$ kpc) from the Milky Way, the external field of the host ($g_{ex} \approx 282\; \mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$) comfortably exceeds the internal field. Consequently, Crater II should be subject to the external field effect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: $\sigma_{efe} = 2.1^{+0.9}_{-0.6}\;\mathrm{km}\,\mathrm{s}^{-1}$.
Modified Newtonian DynamicsVelocity dispersionLuminosityDark matterHalf-light radiusStarMilky WayRotation CurveScaling lawSatellite galaxy...
• #### The number and size of subhalo-induced gaps in stellar streamsver. 2

Ample observational capabilities exist today to detect the small density perturbations that low-mass dark matter subhaloes impart on stellar streams from disrupting Galactic satellites. In anticipation of these observations, we investigate the expected number and size of gaps by combining an analytic prescription for gap evolution on circular orbits with the flux of subhaloes near the stream. We explore the distribution of gap sizes and depths for a typical cold stream around the Milky Way and find that for a given stream age and gap depth, each subhalo mass produces a characteristic gap size. For a stream with an age of a few Gyr, orbiting at a distance of 10-20 kpc from the Galactic center, even modest subhaloes with a mass of $10^6-10^7 M_\odot$ produce gaps with sizes that are on the order of several degrees. We consider the number and distribution of gap sizes created by subhaloes with masses $10^5-10^9 M_\odot$, accounting for the expected depletion of subhaloes by the Milky Way disk, and present predictions for six cold streams around the Milky Way. For Pal 5, we forecast 0.7 gaps with a density depletion of at least 25\% and a typical gap size of $8^\circ$. Thus, there appears to be {\it no tension} between the recent non-detection of density depletions in the Pal 5 tidal tails and $\Lambda$CDM expectations. These predictions can be used to guide the scale of future gap searches.
Dark matter subhaloGiant Molecular CloudMilky WayCircular orbitVelocity dispersionStellar streamCircular velocityN-body simulationRadial velocityATLAS Experiment at CERN...
• #### The Velocity Distribution Function of Galaxy Clusters as a Cosmological Probever. 2

We present a new approach for quantifying the abundance of galaxy clusters and constraining cosmological parameters using dynamical measurements. In the standard method, galaxy line-of-sight (LOS) velocities, $v$, or velocity dispersions are used to infer cluster masses, $M$, in order to quantify the halo mass function (HMF), $dn(M)/d\log(M)$, which is strongly affected by mass measurement errors. In our new method, the probability distribution of velocities for each cluster in the sample are summed to create a new statistic called the velocity distribution function (VDF), $dn(v)/dv$. The VDF can be measured more directly and precisely than the HMF and it can also be robustly predicted with cosmological simulations which capture the dynamics of subhalos or galaxies. We apply these two methods to mock cluster catalogs and forecast the bias and constraints on the matter density parameter $\Omega_m$ and the amplitude of matter fluctuations $\sigma_8$ in flat $\Lambda$CDM cosmologies. For an example observation of 200 massive clusters, the VDF with (without) velocity errors constrains the parameter combination $\sigma_8\Omega_m^{0.29\ (0.29)} = 0.587 \pm 0.011\ (0.583 \pm 0.011)$ and shows only minor bias. However, the HMF with dynamical mass errors is biased to low $\Omega_m$ and high $\sigma_8$ and the fiducial model lies well outside of the forecast constraints, prior to accounting for Eddington bias. When the VDF is combined with constraints from the cosmic microwave background (CMB), the degeneracy between cosmological parameters can be significantly reduced. Upcoming spectroscopic surveys that probe larger volumes and fainter magnitudes will provide a larger number of clusters for applying the VDF as a cosmological probe.
Halo mass functionVelocity distribution functionVirial cluster massCluster of galaxiesCosmological parametersLine of sightObservational errorCosmologyDark matter subhaloAbundance...
• #### The trouble with $H_0$ver. 2

We perform a comprehensive cosmological study of the $H_0$ tension between the direct local measurement and the model-dependent value inferred from the Cosmic Microwave Background. With the recent measurement of $H_0$ this tension has raised to more than $3\sigma$. We consider changes in the early time physics without modifying the late time cosmology. We also reconstruct the late time expansion history in a model independent way with minimal assumptions using distances measures from Baryon Acoustic Oscillations and Type Ia Supernovae, finding that at $z<0.6$ the recovered shape of the expansion history is less than 5 % different than that of a standard LCDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination $r_s h$ where $H_0=h \times 100$ km/s/Mpc and $r_s$ is the sound horizon at radiation drag (the standard ruler), traditionally constrained by CMB observations. Thus $r_s$ and $H_0$ provide absolute scales for distance measurements (anchors) at opposite ends of the observable Universe. We calibrate the cosmic distance ladder and obtain a model-independent determination of the standard ruler for acoustic scale, $r_s$. The tension in $H_0$ reflects a mismatch between our determination of $r_s$ and its standard, CMB-inferred value. Without including high-l Planck CMB polarization data (i.e., only considering the "recommended baseline" low-l polarisation and temperature and the high l temperature data), a modification of the early-time physics to include a component of dark radiation with an effective number of species around 0.4 would reconcile the CMB-inferred constraints, and the local $H_0$ and standard ruler determinations. The inclusion of the "preliminary" high-l Planck CMB polarisation data disfavours this solution.
Planck missionBaryon acoustic oscillationsCold dark matterStandard rulerLambda-CDM modelCosmologyThe early UniverseSound horizonNeutrinoDark Radiation...
• #### NIHAO XII: galactic uniformity in a $\Lambda$CDM universe

We use a sample of 83 high-resolution cosmological zoom-in simulations and a semi-analytic model to study the stocasticity of galaxy formation in haloes ranging from dwarf ($M_{200} \sim 10^{10} M_{\odot}$) to Milky Way ($M_{200}\sim 10^{12}M_{\odot}$) masses. Our simulated galaxies reproduce the observed inefficiency of galaxy formation as expressed through the stellar, gas and baryonic Tully-Fisher (TF) relations. The scatter in our simulated TF relations is very small, and velocity dependent. For HI velocities in the range ($70 < V < 220$ km/s), the scatter is just 0.08 to 0.14 dex, consistent with the observed intrinsic scatter. At low velocities ($20 < V < 70$ km/s), the simulated scatter is 0.20-0.25 dex, which could be tested with future observations. The scatter in the stellar mass vs dark halo velocity relation is constant for $30 < V < 200$ km/s, and smaller ($\simeq 0.17$ dex) when using the maximum circular velocity of the dark matter only simulation, $V_{max}^{DMO}$, compared to the virial velocity ($V_{200}$ or $V_{200}^{DMO}$). The scatter in stellar mass is correlated with halo concentration, and is minimized when using a circular velocity at a fixed fraction of the virial radius $\simeq 0.4 R_{200}$ or with $V_{\alpha}=V_{200}^{DMO} (V_{max}^{DMO}/V_{200}^{DMO})^\alpha$ with $\alpha\simeq 0.7$, consistent with constraints from halo clustering. This uniformity in galaxy formation efficiency we see in our hydrodynamical simulations and a semi-analytic model proves the simplicity and self-regulating nature of galaxy formation in a $\Lambda$CDM universe.
Stellar massCircular velocityGalaxy FormationVirial massVirial velocityTully-Fisher relationN-body simulationMaximum circular velocityVirial radiusStar...
• #### La Fin du MOND? {\Lambda} CDM is Fully Consistent with SPARC Acceleration Law

Recent analysis (McGaugh et al. 2016) of the SPARC galaxy sample found a surprisingly tight relation between the radial acceleration inferred from the rotation curves, and the acceleration due to the baryonic components of the disc. It has been suggested that this relation may be evidence for new physics, beyond {\Lambda}CDM . In this letter we show that the 18 galaxies from the MUGS2 match the SPARC acceleration relation. These cosmological simulations of star forming, rotationally supported discs were simulated with a WMAP3 {\Lambda}CDM cosmology, and match the SPARC acceleration relation with less scatter than the observational data. These results show that this acceleration law is a consequence of dissipative collapse of baryons, rather than being evidence for exotic dark-sector physics or new dynamical laws.
• #### The Cosmic Evolution of the Metallicity Distribution of Ionized Gas Traced by Lyman Limit Systemsver. 2

We present the first results from our KODIAQ Z survey aimed to determine the metallicity distribution and physical properties of the z>2 partial and full Lyman limit systems (pLLSs and LLSs; 16.2<log N(HI)<19), which are probed of the interface regions between the intergalactic medium (IGM) and galaxies. We study 31 HI-selected pLLSs and LLSs at 2.3<z<3.3 observed with Keck/HIRES in absorption against background QSOs. We compare the column densities of metal-ions to HI and use photoionization models to assess the metallicity. The metallicity distribution of the pLLSs/LLSs at 2.3<z<3.3 is consistent with a unimodal distribution peaking at [X/H]=-2. The metallicity distribution of these absorbers therefore evolves markedly with z since at z<1 it is bimodal with peaks at [X/H]=-1.8 and -0.3. There is a substantial fraction (25-41%) of pLLSs/LLSs with metallicities well below those of damped Lya absorbers (DLAs) at any studied z from z<1 to z~2-4, implying reservoirs of metal-poor cool, dense gas in the IGM/galaxy interface at all z. However, the gas probed by pLLSs and LLSs is rarely pristine, with a fraction 3-18% for pLLSs/LLSs with [X/H]<-3. We find C/alpha enhancement in several pLLSs and LLSs in the metallicity range -2<[X/H]<-0.5, where C/alpha is 2-5 times larger than observed in Galactic metal-poor stars or high redshift DLAs at similar metallicities. This is likely caused by preferential ejection of carbon from metal-poor galaxies into their surroundings.
Lyman Limit SystemMetallicityIonizationCircumgalactic mediumPhotoionizationStarPopulation IIIStar formationMilky WayCooling...
• #### An observer's guide to the (Local Group) dwarf galaxies: predictions for their own dwarf satellite populationsver. 2

A recent surge in the discovery of new ultrafaint dwarf satellites of the Milky Way has inspired the idea of searching for faint satellites, $10^3\, \mathrm{M_{\odot}}< M_* < 10^6 \, \mathrm{M_{\odot}}$, around less massive field galaxies in the Local Group. Such satellites would be subject to weaker environmental influences than Milky Way satellites, and could lead to new insights on low mass galaxy formation. In this paper, we predict the number of luminous satellites expected around field dwarf galaxies by applying several abundance matching models and a reionization model to the dark-matter only Caterpillar simulation suite. For three of the four abundance matching models used, we find a $>99\%$ chance that at least one satellite with stellar mass $M_*> 10^5 \, \mathrm{M_{\odot}}$ exists around the combined five Local Group field dwarf galaxies with the largest stellar mass. When considering satellites with $M_*> 10^4 \, \mathrm{M_{\odot}}$, we predict a combined $5-25$ satellites for the five largest field dwarfs, and $10-50$ for the whole Local Group field dwarf population. Because of the relatively small number of predicted dwarfs, and their extended spatial distribution, a large fraction each Local Group dwarf's virial volume will need to be surveyed to guarantee discoveries. We compute the predicted number of satellites in a given field of view of specific Local Group galaxies, as a function of minimum satellite luminosity, and explicitly obtain such values for the Solitary Local dwarfs survey. Uncertainties in abundance matching and reionization models are large, implying that comprehensive searches could lead to refinements of both models.
ReionizationStellar massMilky WayDwarf galaxyVirial massHalo abundance matchingDark matter subhaloLocal groupField galaxyUltra-faint dwarf spheroidal galaxy...
• #### Bootstrapping Pure Quantum Gravity in AdS3

The three-dimensional pure quantum gravity with negative cosmological constant is supposed to be dual to the extremal conformal field theory of central charge $c=24k$ in two dimensions. We employ the conformal bootstrap method to analyze the extremal CFTs, and find numerical evidence for the non-existence of the extremal CFTs for sufficiently large central charge ($k \ge 20$). We also explore near-extremal CFTs, a small modification of extremal ones, and find similar evidence for their non-existence for large central charge. This indicates, under the assumption of holomorphic factorization, the pure gravity in the weakly curved AdS$_3$ do not exist as a consistent quantum theory.
Conformal field theoryCentral chargeQuantum gravityAnti de Sitter spaceScaling dimensionOperator product expansionHolomorphic CFTPartition functionTwo-point correlation functionCosmological constant...
• #### The nature and evolution of the highly ionized near-zones in the absorption spectra of z~6 quasarsver. 2

We use state-of-the-art hydrodynamical simulations combined with a 1D radiative transfer code to assess the extent to which the highly ionized regions observed close to z~6 quasars, which we refer to as near-zones, can constrain the ionization state of the surrounding IGM. We find the appearance in Lya absorption of a quasar HII ionization front expanding into a neutral IGM can be very similar to a classical proximity zone, produced by the enhancement in ionizing flux close to a quasar embedded in a highly ionized IGM. The observed sizes of these highly ionized near-zones and their redshift evolution can be reproduced for a wide range of IGM neutral hydrogen fractions for plausible values of the luminosity and lifetime of the quasars. The observed near-zone sizes at the highest observed redshifts are equally consistent with a significantly neutral and a highly ionized surrounding IGM. Stronger constraints on the IGM neutral hydrogen fraction can be obtained by considering the relative size of the near-zones in the Lya and Lyb regions of a quasar spectrum. A large sample of high quality quasar absorption spectra with accurate determinations of near-zone sizes and their redshift evolution in both the Lya and Lyb regions should confirm or exclude the possibility that the Universe is predominantly neutral at the highest observed redshifts. The width of the discrete absorption features in these near-zones will contain important additional information on the ionization state and the previous thermal history of the IGM at these redshifts.
• #### The Habitability of Planets Orbiting M-dwarf Stars

The prospects for the habitability of M-dwarf planets have long been debated, due to key differences between the unique stellar and planetary environments around these low-mass stars, as compared to hotter, more luminous Sun-like stars. Over the past decade, significant progress has been made by both space- and ground-based observatories to measure the likelihood of small planets to orbit in the habitable zones of M-dwarf stars. We now know that most M dwarfs are hosts to closely-packed planetary systems characterized by a paucity of Jupiter-mass planets and the presence of multiple rocky planets, with roughly a third of these rocky M-dwarf planets orbiting within the habitable zone, where they have the potential to support liquid water on their surfaces. Theoretical studies have also quantified the effect on climate and habitability of the interaction between the spectral energy distribution of M-dwarf stars and the atmospheres and surfaces of their planets. These and other recent results fill in knowledge gaps that existed at the time of the previous overview papers published nearly a decade ago by Tarter et al. (2007) and Scalo et al. (2007). In this review we provide a comprehensive picture of the current knowledge of M-dwarf planet occurrence and habitability based on work done in this area over the past decade, and summarize future directions planned in this quickly evolving field.
M dwarfsPlanetDwarf starDwarf planetHabitable zoneRocky planetsClimateLow-mass starsObservatoriesJupiter...
• #### Random matrix approaches to open quantum systems

Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic Processes and Random Matrices" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how the different features are interlinked. The notes mainly focus on elastic scattering but also include a short detour to interacting systems, which we motivate by the overarching question of ergodicity. The first chapters introduce general notions from random matrix theory, such as the ten universality classes and ensembles of hermitian, unitary, positive-definite and non-hermitian matrices. We then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics and transport. The last chapter briefly touches on Anderson localization and localization in interacting systems.
HamiltonianScattering matrixRandom matrixTime-reversal symmetryC-symmetryZero modeStatisticsChiral symmetryQuaternionsDecay rate...