Where did the globular clusters of the Milky Way form? Insights from the E-MOSAICS simulations

Globular clusters (GCs) are typically old, with most having formed at z >~ 2. This makes understanding their birth environments difficult, as they are typically too distant to observe with sufficient angular resolution to resolve GC birth sites. Using 25 cosmological zoom-in simulations of Milky Way-like galaxies from the E-MOSAICS project, with physically-motivated models for star formation, feedback, and the formation, evolution, and disruption of GCs, we identify the birth environments of present-day GCs. We find roughly half of GCs in these galaxies formed in-situ (52.0 +/- 1.0 per cent) between z ~ 2 - 4, in turbulent, high-pressure discs fed by gas that was accreted without ever being strongly heated through a virial shock or feedback. A minority of GCs form during mergers (12.6 +/- 0.6 per cent in major mergers, and 7.2 +/- 0.5 per cent in minor mergers), but we find that mergers are important for preserving the GCs seen today by ejecting them from their natal, high density interstellar medium (ISM), where proto-GCs are rapidly destroyed due to tidal shocks from ISM substructure. This chaotic history of hierarchical galaxy assembly acts to mix the spatial and kinematic distribution of GCs formed through different channels, making it difficult to use observable GC properties to distinguish GCs formed in mergers from ones formed by smooth accretion, and similarly GCs formed in-situ from those formed ex-situ. These results suggest a simple picture of GC formation, in which GCs are a natural outcome of normal star formation in the typical, gas-rich galaxies that are the progenitors of present-day galaxies

Constraining the shape of dark matter haloes with globular clusters and diffuse stellar light in the E-MOSAICS simulations

We explore how diffuse stellar light and globular clusters (GCs) can be used to trace the matter distribution of their host halo using an observational methodology. For this, we use 117 simulated dark matter (DM) haloes from the periodic volume of the E-MOSAICS project. For each halo, we compare the stellar surface brightness and GC projected number density maps to the surface density of DM. We find that the dominant structures identified in the stellar light and GCs correspond closely with those from the DM. Our method is unaffected by the presence of satellites and its precision improves with fainter GC samples. We recover tight relations between the dimensionless profiles of stellar-to-DM surface density and GC-to-DM surface density, suggesting that the profile of DM can be accurately recovered from the stars and GCs (σ ≤ 0.5 dex). We quantify the projected morphology of DM, stars, and GCs and find that the stars and GCs are more flattened than the DM. Additionally, the semimajor axes of the distribution of stars and GCs are typically misaligned by ∼10 degrees from that of DM. We demonstrate that deep imaging of diffuse stellar light and GCs can place constraints on the shape, profile, and orientation of their host halo. These results extend down to haloes with central galaxies M⋆ ≥ 1010 M⊙, and the analysis will be applicable to future data from the Euclid, Roman, and the Rubin observatorie

The globular cluster system mass-halo mass relation in the E-MOSAICS simulations

Linking globular clusters (GCs) to the assembly of their host galaxies is an overarching goal in GC studies. The inference of tight scaling relations between GC system properties and the mass of both the stellar and dark halo components of their host galaxies are indicative of an intimate physical connection, yet have also raised fundamental questions about how and when GCs form. Specifically, the inferred correlation between the mass of a GC system (Mgc) and the dark matter halo mass (Mhalo) of a galaxy has been posited as a consequence of a causal relation between the formation of dark matter mini-haloes and GC formation during the early epochs of galaxy assembly. We present the first results from a new simulation of a cosmological volume ($L=34.4$~cMpc on a side) from the E-MOSAICS suite, which includes treatments of the formation and evolution of GCs within the framework of a detailed galaxy formation model. The simulated Mgc-Mhalo relation is linear for halo masses $>5\times10^{11}~Msun$, and is driven by the hierarchical assembly of galaxies. Below this halo mass, the simulated relation features a downturn, which we show is consistent with observations, and is driven by the underlying stellar mass-halo mass relation of galaxies. Our fiducial model reproduces the observed Mgc-Mstar relation across the full mass range, which we argue is more physically relevant than the Mgc-Mhalo relation. We also explore the physical processes driving the observed constant value of $Mgc / Mhalo \sim 5\times10^{-5}$ and find that it is the result of a combination of cluster formation physics and cluster disruption

Stamp transferred suspended graphene mechanical resonators for radio-frequency electrical readout

We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio-frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f=5-6 GHz producing modulation sidebands at f +/- fm. A mechanical resonance frequency up to fm=178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples, and obtain a critical amplitude of ~40 pm for the onset of nonlinearity in graphene mechanical resonators. Measurements of the quality factor of the mechanical resonance as a function of DC bias voltage Vdc indicate that dissipation due to motion-induced displacement currents in graphene electrode is important at high frequencies and large Vdc

Quantum spin coverings and statistics

SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.Comment: 15 page

An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the noncommutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the noncommutative KP hierarchy. Relations with Rota-Baxter algebras are established.Comment: 59 pages, relative to the second version a few minor corrections, but quite a lot of amendments, to appear in J. Phys.

Higgs Boson Masses in the Complex NMSSM at One-Loop Level

The Next-to-Minimal Supersymmetric Extension of the Standard Model (NMSSM) with a Higgs sector containing five neutral and two charged Higgs bosons allows for a rich phenomenology. In addition, the plethora of parameters provides many sources of CP violation. In contrast to the Minimal Supersymmetric Extension, CP violation in the Higgs sector is already possible at tree-level. For a reliable understanding and interpretation of the experimental results of the Higgs boson search, and for a proper distinction of Higgs sectors provided by the Standard Model or possible extensions, the Higgs boson masses have to be known as precisely as possible including higher-order corrections. In this paper we calculate the one-loop corrections to the neutral Higgs boson masses in the complex NMSSM in a Feynman diagrammatic approach adopting a mixed renormalization scheme based on on-shell and $\bar{DR}$ conditions. We study various scenarios where we allow for tree-level CP-violating phases in the Higgs sector and where we also study radiatively induced CP violation due to a non-vanishing phase of the trilinear coupling $A_t$ in the stop sector. The effects on the Higgs boson phenomenology are found to be significant. We furthermore estimate the theoretical error due to unknown higher-order corrections by both varying the renormalization scheme of the top and bottom quark masses and by adopting different renormalization scales. The residual theoretical error can be estimated to about 10%