Twisted Linnik implies optimal covering exponent for S3 - Browning, Timothy D; Kumaraswamy, Vinay; Steiner, Rapael (International Mathematics Research Notices)
We show that a twisted variant of Linnik’s conjecture on sums of Kloosterman sums leads to an optimal covering exponent for S3.

Strong approximation and a conjecture of Harpaz and Wittenberg - Browning, Timothy D; Schindler, Damaris (International Mathematics Research Notices)
We study strong approximation for some algebraic varieties over ℚ which are defined using norm forms. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.

Lighthouse in the dust: infrared echoes of periodic emission from massive black hole binaries★ - D'Orazio, Daniel J.; Haiman, Zoltán (Monthly Notices of the Royal Astronomical Society)
The optical and UV emission from sub-parsec massive black hole binaries (MBHBs) in active galactic nuclei (AGNs) is believed to vary periodically, on time-scales comparable to the binary's orbital time. If driven by accretion rate fluctuations, the variability could be isotropic. If dominated by relativistic Doppler modulation, the variability should instead be anisotropic, resembling a rotating forward-beamed lighthouse. We consider the infrared (IR) reverberation of either type of periodic emission by pc-scale circumbinary dust tori. We predict the phase and amplitude of IR variability as a function of the ratio of dust light crossing time to the source variability period, and of the torus inclination and opening angle. We enumerate several differences between the isotropic and anisotropic cases. Interestingly, for a nearly face-on binary with an inclined dust torus, the Doppler boost can produce IR variability without any observable optical/UV variability. Such orphan-IR variability would have been missed in optical searches for periodic AGNs. We apply our models to time-domain WISE IR data from the MBHB candidate PG 1302−102 and find consistency with dust reverberation by both isotropically emitting and Doppler-boosted sources in the shorter wavelength W1–W2 (2.8 → 5.3 μm) bands. We constrain the dust torus to be thin (aspect ratio ∼ 0.1), with an inner radius at 1–5 pc. More generally, our dust-echo models will aid in identifying new MBHB candidates, determining their nature and constraining the physical properties of MBHBs and their dust tori.

A statistical method for detecting gravitational recoils of supermassive black holes in active galactic nuclei - Raffai, P.; Bécsy, B.; Haiman, Zoltán; Frei, Z. (Proceedings of the International Astronomical Union)
We propose an observational test for gravitationally recoiling supermassive black holes in active galactic nuclei, based on a positive correlation between the velocities of black holes relative to their host galaxies, |Δv|, and their obscuring dust column densities, Σdust, both measured along the line of sight. Our findings using a set of toy models implemented to a Monte Carlo simulation imply that models of the galactic centre and of recoil dynamics can be tested by future observations of the potential Σdust–|Δv| correlation. We have also found that the fraction of obscured quasars decreases with |Δv|, for which the predicted trend can be compared to the observed fraction of type II quasars, and can further test combinations of models we may implement.

A drop in the pond: The effect of rapid mass-loss on the dynamics and interaction rate of collisionless particles - Penoyre, Zephyr; Haiman, Zoltán (Monthly Notices of the Royal Astronomical Society)
In symmetric gravitating systems experiencing rapid mass-loss, particle orbits change almost instantaneously, which can lead to the development of a sharply contoured density profile, including singular caustics for collisionless systems. This framework can be used to model a variety of dynamical systems, such as accretion discs following a massive black hole merger and dwarf galaxies following violent early star formation feedback. Particle interactions in the high-density peaks seem a promising source of observable signatures of these mass-loss events (i.e. a possible EM counterpart for black hole mergers or strong gamma-ray emission from dark matter annihilation around young galaxies), because the interaction rate depends on the square of the density. We study post-mass-loss density profiles, both analytic and numerical, in idealized cases and present arguments and methods to extend to any general system. An analytic derivation is presented for particles on Keplerian orbits responding to a drop in the central mass. We argue that this case, with initially circular orbits, gives the most sharply contoured profile possible. We find that despite the presence of a set of singular caustics, the total particle interaction rate is reduced compared to the unperturbed system; this is a result of the overall expansion of the system dominating over the steep caustics. Finally, we argue that this result holds more generally, and the loss of central mass decreases the particle interaction rate in any physical system.

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening - Leigh, N W C; Geller, A M; McKernan, B; Ford, K E S; Mac Low, M-M; Bellovary, J; Haiman, Zoltán; Lyra, W; Samsing, J; O'Dowd, M; Kocsis, B; Endlich, S (Monthly Notices of the Royal Astronomical Society)
We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disc components hosting a super-massive black hole (SMBH). We determine the total number of encounters NGW needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disc components. Using a Monte Carlo approach, we refine our calculations for NGW to include gravitational wave emission between scattering events. For astrophysically plausible models, we find that typically NGW ≲ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low-velocity dispersions, and no significant Keplerian component and (2) migration traps in discs around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disc. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because discs enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.

Interactions between multiple supermassive black holes in galactic nuclei: A solution to the final parsec problem - Ryu, Taeho; Perna, Rosalba; Haiman, Zoltán; Ostriker, Jeremiah P.; Stone, Nicholas C. (Monthly Notices of the Royal Astronomical Society)
Using few-body simulations, we investigate the evolution of supermassive black holes (SMBHs) in galaxies (M* = 1010–1012 M⊙ at z = 0) at 0 < z < 4. Following galaxy merger trees from the Millennium simulation, we model BH mergers with two extreme binary decay scenarios for the ‘hard binary’ stage: a full or an empty loss cone. These two models should bracket the true evolution, and allow us to separately explore the role of dynamical friction and that of multibody BH interactions on BH mergers. Using the computed merger rates, we infer the stochastic gravitational wave background (GWB). Our dynamical approach is a first attempt to study the dynamical evolution of multiple SMBHs in the host galaxies undergoing mergers with various mass ratios (10−4 < q* < 1). Our main result demonstrates that SMBH binaries are able to merge in both scenarios. In the empty loss cone case, we find that BHs merge via multibody interactions, avoiding the ‘final parsec’ problem, and entering the pulsar timing arrays band with substantial orbital eccentricity. Our full loss cone treatment, albeit more approximate, suggests that the eccentricity becomes even higher when GWs become dominant, leading to rapid coalescences (binary lifetime ≲1 Gyr). Despite the lower merger rates in the empty loss cone case, due to their higher mass ratios and lower redshifts, the GWB in the full/empty loss cone models are comparable (0.70 × 10−15 and 0.53 × 10−15 at a frequency of 1 yr−1, respectively). Finally, we compute the effects of high eccentricities on the GWB spectrum.

Rapid formation of massive black holes in close proximity to embryonic protogalaxies - Regan, John A.; Visbal, Eli; Wise, John H.; Haiman, Zoltán; Johansson, Peter H.; Bryan, Greg L. (Nature Astronomy)
The Direct Collapse Black Hole (DCBH) scenario provides a solution for forming the massive black holes powering bright quasars observed in the early Universe. A prerequisite for forming a DCBH is that the formation of (much less massive) Population III stars be avoided - this can be achieved by destroying H2 via Lyman-Werner (LW) radiation (ELW = 12.6 eV). We find that two conditions must be met in the proto-galaxy that will host the DCBH. First, prior star formation must be delayed; this can be achieved with a background LW flux of JBG≳100 J21. Second, an intense burst of LW radiation from a neighbouring star-bursting proto-galaxy is required, just before the gas cloud undergoes gravitational collapse, to finally suppress star formation completely. We show here for the first time using high-resolution hydrodynamical simulations, including full radiative transfer, that this low-level background, combined with tight synchronisation and irradiation of a secondary proto-galaxy by a primary proto-galaxy, inevitably moves the secondary proto-galaxy onto the isothermal atomic cooling track, without the deleterious effects of either photo-evaporating the gas or polluting it by heavy elements. These, atomically cooled, massive proto-galaxies are expected to ultimately form a DCBH of mass 104−105M⊙.

Beyond Jcrit: A critical curve for suppression of H2-cooling in protogalaxies - Wolcott-Green, J.; Haiman, Zoltán; Bryan, G. L. (Monthly Notices of the Royal Astronomical Society)
Suppression of H2-cooling in early protogalaxies has important implications for the formation of supermassive black holes seeds, the first generation of stars, and the epoch of reionization. This suppression can occur via photodissociation of H2 (by ultraviolet Lyman-Werner [LW] photons) or by photodetachment of H-, a precursor in H2 formation (by infrared [IR] photons). Previous studies have typically adopted idealised spectra, with a blackbody or a power-law shape, in modeling the chemistry of metal-free protogalaxies, and utilised a single parameter, the critical UV flux, or Jcrit, to determine whether H2-cooling is prevented. This can be misleading, and that independent of the spectral shape, there is a critical curve in the (kLW , kH^- ) plane, where kLW and kH^- are the H2-dissocation rates by LW and IR photons, which determines whether a protogalaxy can cool below ~1000 Kelvin. We use a one-zone model to follow the chemical and thermal evolution of gravitationally collapsing protogalactic gas, to compute this critical curve, and provide an accurate analytical fit for it. We improve on previous works by considering a variety of more realistic Pop III or Pop II-type spectra from population synthesis models and perform fully frequency-dependent calculations of the H2-photodissociation rates for each spectrum. We compute the ratio kLW/kH^- for each spectrum, as well as the minimum stellar mass M_star, for various IMFs and metallicities, required to prevent cooling in a neighboring halo a distance d away. We provide critical M_star/d2 values for suppression of H2-cooling, with analytic fits, which can be used in future studies.

Validity of the Born approximation for beyond Gaussian weak lensing observables - Petri, Andrea; Haiman, Zoltán; May, Morgan (Physical Review D)
Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the non-linear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray-tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray--traced counterparts are consistent with the smallest non-trivial O(Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born approximated power spectrum is negligible even for an LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray-tracing in reconstructing the convergence.

What is the maximum mass of a Population III galaxy? - Visbal, Eli; Bryan, Greg L.; Haiman, Zoltán (Monthly Notices of the Royal Astronomical Society)
We utilize cosmological hydrodynamic simulations to study the formation of Population III (Pop III) stars in dark matter halos exposed to strong ionizing radiation. We simulate the formation of three halos subjected to a wide range of ionizing fluxes, and find that for high flux, ionization and photoheating can delay gas collapse and star formation up to halo masses significantly larger than the atomic cooling threshold. The threshold halo mass at which gas first collapses and cools increases with ionizing flux for intermediate values, and saturates at a value approximately an order of magnitude above the atomic cooling threshold for extremely high flux (e.g. ≈5×108 M⊙ at z≈6). This behavior can be understood in terms of photoheating, ionization/recombination, and Lyα cooling in the pressure-supported, self-shielded gas core at the center of the growing dark matter halo. We examine the spherically-averaged radial velocity profiles of collapsing gas and find that a gas mass of up to ≈106 M⊙ can reach the central regions within 3 Myr, providing an upper limit on the amount of massive Pop III stars that can form. The ionizing radiation increases this limit by a factor of a few compared to strong Lyman-Werner (LW) radiation alone. We conclude that the bright HeII 1640 Å emission recently observed from the high-redshift galaxy CR7 cannot be explained by Pop III stars alone. However, in some halos, a sufficient number of Pop III stars may form to be detectable with future telescopes such as the James Webb Space Telescope (JWST).

On the orbital evolution of supermassive black hole binaries with circumbinary accretion discs - Tang, Yike; MacFadyen, Andrew; Haiman, Zoltán (Monthly Notices of the Royal Astronomical Society)
Gaseous circumbinary accretion discs provide a promising mechanism to facilitate the mergers of supermassive black holes (SMBHs) in galactic nuclei. We measure the torques exerted on accreting SMBH binaries, using 2D, isothermal, moving-mesh, viscous hydrodynamical simulations of circumbinary accretion discs. Our computational domain includes the entire inner region of the circumbinary disk with the individual black holes (BHs) included as point masses on the grid and a sink prescription to model accretion onto each BH. The BHs each acquire their own well-resolved accretion discs ("minidiscs"). We explore a range of mass removal rates for the sink prescription removing gas from the central regions of the minidiscs. We find that the torque exerted on the binary is primarily gravitational, and dominated by the gas orbiting close behind and ahead of the individual BHs. The torques from the distorted circumbinary disc farther out and from the direct accretion of angular momentum are subdominant. The torques are sensitive to the sink prescription: slower sinks result in more gas accumulating near the BHs and more negative torques, driving the binary to merger more rapidly. For faster sinks, the torques are less negative and eventually turn positive (for unphysically fast sinks). When the minidiscs are modeled as standard alpha discs, our results are insensitive to the choice of sink radius. Scaling the simulations to a binary orbital period tbin = 1yr and background disc accretion rate Mdot = 0.3MEdd in Eddington units, the binary inspirals on a timescale of 3X10^6 years, irrespective of the SMBH masses. For binaries with total mass <10^7Msun, this is shorter than the inspiral time due to gravitational wave (GW) emission alone, implying that gas discs will have a significant impact on the SMBH binary population and can affect the GW signal for Pulsar Timing Arrays.

Rapid and bright stellar-mass binary black hole mergers in active galactic nuclei - Bartos, Imre; Kocsis, Bence; Haiman, Zoltán; Márka, Szabolcs (The Astrophysical Journal)
The Laser Interferometer Gravitational-Wave Observatory, LIGO, found direct evidence for double black hole binaries emitting gravitational waves. Galactic nuclei are expected to harbor the densest population of stellar-mass black holes. A significant fraction (∼30%) of these black holes can reside in binaries. We examine the fate of the black hole binaries in active galactic nuclei, which get trapped in the inner region of the accretion disk around the central supermassive black hole. We show that binary black holes can migrate into and then rapidly merge within the disk well within a Salpeter time. The binaries may also accrete a significant amount of gas from the disk, well above the Eddington rate. This could lead to detectable X-ray or gamma-ray emission, but would require hyper-Eddington accretion with a few percent radiative efficiency, comparable to thin disks. We discuss implications for gravitational wave observations and black hole population studies. We estimate that Advanced LIGO may detect ∼20 such, gas-induced binary mergers per year.

Electromagnetic chirp of a compact binary black hole: A phase template for the gravitational wave inspiral - Haiman, Zoltán (Physical Review D)
The gravitational waves (GWs) from a binary black hole (BBH) with masses between 10^4 and 10^7 Msun can be detected with the Laser Interferometer Space Antenna (LISA) once their orbital frequency exceeds 10^-4 - 10^-5 Hz. The binary separation at this stage is approximately a=100 R_g (gravitational radius), and the orbital speed is of order v/c=0.1. We argue that at this stage, the binary will be producing bright electromagnetic (EM) radiation via gas bound to the individual BHs. Both BHs will have their own photospheres in X-ray and possibly also in optical bands. Relativistic Doppler modulations and lensing effects will inevitably imprint periodic variability in the EM light-curve, tracking the phase of the orbital motion, and serving as a template for the GW inspiral waveform. Advanced localization of the source by LISA weeks to months prior to merger will enable a measurement of this EM chirp by wide-field X-ray or optical instruments. A comparison of the phases of the GW and EM chirp signals will help break degeneracies between system parameters, and probe a fractional difference difference Delta v in the propagation speed of photons and gravitons as low as Delta v/c = O(10^-17).

Geometry and growth contributions to cosmic shear observables - Matilla, José Manuel Zorrilla; Haiman, Zoltán; Petri, Andrea; Namikawa, Toshiya (Physical Review D)
We explore the sensitivity of weak lensing observables to the expansion history of the universe and to the growth of cosmic structures, as well as the relative contribution of both effects to constraining cosmological parameters. We utilize ray-tracing dark-matter-only N-body simulations and validate our technique by comparing our results for the convergence power spectrum with analytic results from past studies. We then extend our analysis to non-Gaussian observables which cannot be easily treated analytically. We study the convergence (equilateral) bispectrum and two topological observables, lensing peaks and Minkowski functionals, focusing on their sensitivity to the matter density Ωm and the dark energy equation of state w. We find that a cancelation between the geometry and growth effects is a common feature for all observables, and exists at the map level. It weakens the overall sensitivity by up to a factor of 3 and 1.5 for w and Ωm, respectively, with the bispectrum worst affected. However, combining geometry and growth information alleviates the degeneracy between Ωm and w from either effect alone. As a result, the magnitude of marginalized errors remain similar to those obtained from growth-only effects, but with the correlation between the two parameters switching sign. These results shed light on the origin of cosmology-sensitivity of non-Gaussian statistics, and should be useful in optimizing combinations of observables.

Gravitational-wave localization alone can probe origin of stellar-mass black hole mergers - Bartos, I.; Haiman, Zoltán; Marka, Z.; Metzger, B. D.; Stone, N. C.; Marka, S. (Nature Communications)
The recent discovery of gravitational waves from stellar-mass binary black hole mergers by the Laser Interferometer Gravitational-wave Observatory opened the door to alternative probes of stellar and galactic evolution, cosmology and fundamental physics. Probing the origin of binary black hole mergers will be difficult due to the expected lack of electromagnetic emission and limited localization accuracy. Associations with rare host galaxy types—such as active galactic nuclei—can nevertheless be identified statistically through spatial correlation. Here we establish the feasibility of statistically proving the connection between binary black hole mergers and active galactic nuclei as hosts, even if only a sub-population of mergers originate from active galactic nuclei. Our results are the demonstration that the limited localization of gravitational waves, previously written off as not useful to distinguish progenitor channels, can in fact contribute key information, broadening the range of astrophysical questions probed by binary black hole observations.

Probing stellar binary black hole formation in galactic nuclei via the imprint of their center of mass acceleration on their gravitational wave signal - Inayoshi, Kohei; Tamanini, Nicola; Caprini, Chiara; Haiman, Zoltán (Physical Review D)
Multi-frequency gravitational wave (GW) observations are useful probes of the formation processes of coalescing stellar-mass binary black holes (BBHs). We discuss the phase drift in the GW inspiral waveform of the merging BBH caused by its center-of-mass acceleration. The acceleration strongly depends on the location where a BBH forms within a galaxy, allowing observations of the early inspiral phase of LIGO-like BBH mergers by the Laser Interferometer Space Antenna (LISA) to test the formation mechanism. In particular, BBHs formed in dense nuclear star clusters or via compact accretion disks around a nuclear supermassive black hole in active galactic nuclei would suffer strong acceleration, and produce large phase drifts measurable by LISA. The host galaxies of the coalescing BBHs in these scenarios can also be uniquely identified in the LISA error volume, without electromagnetic counterparts. A non-detection of phase drifts would rule out or constrain the contribution of the nuclear formation channels to the stellar-mass BBH population.

Predation drives local adaptation of phenotypic plasticity - Reger, Julia; Lind, Martin I.; Robinson, Matthew Richard; Beckerman, Andrew P. (Nature Ecology & Evolution)
Phenotypic plasticity is the ability of an individual genotype to alter aspects of its phenotype depending on the current environment. It is central to the persistence, resistance and resilience of populations facing variation in physical or biological factors. Genetic variation in plasticity is pervasive, which suggests its local adaptation is plausible. Existing studies on the adaptation of plasticity typically focus on single traits and a few populations, while theory about interactions among genes (for example, pleiotropy) suggests that a multi-trait, landscape scale (for example, multiple populations) perspective is required. We present data from a landscape scale, replicated, multi-trait experiment using a classic predator–prey system centred on the water flea Daphnia pulex. We find predator regime-driven differences in genetic variation of multivariate plasticity. These differences are associated with strong divergent selection linked to a predation regime. Our findings are evidence for local adaptation of plasticity, suggesting that responses of populations to environmental variation depend on the conditions in which they evolved in the past.

Major histocompatibility complex-linked social signalling affects female fertility - Burger, D.; Thomas, S.; Aepli, H.; Dreyer, M.; Fabre, G.; Marti, E.; Sieme, H.; Robinson, Matthew Richard; Wedekind, C. (Proceedings of the Royal Society B: Biological Sciences)
Genes of the major histocompatibility complex (MHC) have been shown to influence social signalling and mate preferences in many species, including humans. First observations suggest that MHC signalling may also affect female fertility. To test this hypothesis, we exposed 191 female horses (Equus caballus) to either an MHC-similar or an MHC-dissimilar stimulus male around the time of ovulation and conception. A within-subject experimental design controlled for non-MHC-linked male characteristics, and instrumental insemination with semen of other males (n = 106) controlled for potential confounding effects of semen or embryo characteristics. We found that females were more likely to become pregnant if exposed to an MHC-dissimilar than to an MHC-similar male, while overall genetic distance to the stimulus males (based on microsatellite markers on 20 chromosomes) had no effect. Our results demonstrate that early pregnancy failures can be due to maternal life-history decisions (cryptic female choice) influenced by MHC-linked social signalling.

Hidden heritability due to heterogeneity across seven populations - Tropf, Felix C.; Lee, S. Hong; Verweij, Renske M.; Stulp, Gert; van der Most, Peter J.; de Vlaming, Ronald; Bakshi, Andrew; Briley, Daniel A.; Rahal, Charles; Hellpap, Robert; Iliadou, Anastasia N.; Esko, Tõnu; et al. (Nature Human Behaviour)
Meta-analyses of genome-wide association studies, which dominate genetic discovery, are based on data from diverse historical time periods and populations. Genetic scores derived from genome-wide association studies explain only a fraction of the heritability estimates obtained from whole-genome studies on single populations, known as the ‘hidden heritability’ puzzle. Using seven sampling populations (n = 35,062), we test whether hidden heritability is attributed to heterogeneity across sampling populations and time, showing that estimates are substantially smaller across populations compared with within populations. We show that the hidden heritability varies substantially: from zero for height to 20% for body mass index, 37% for education, 40% for age at first birth and up to 75% for number of children. Simulations demonstrate that our results are more likely to reflect heterogeneity in phenotypic measurement or gene–environment interactions than genetic heterogeneity. These findings have substantial implications for genetic discovery, suggesting that large homogenous datasets are required for behavioural phenotypes and that gene–environment interaction may be a central challenge for genetic discovery.