A grounded L-graph is the intersection graph of a collection of L shapes whose topmost points belong to a common horizontal line. We prove that every grounded L-graph with clique number $omega$ has chromatic number at most $17omega^4$. This improves
the doubly-exponential bound of McGuinness and generalizes the recent result that the class of circle graphs is polynomially $chi$-bounded. We also survey $chi$-boundedness problems for grounded geometric intersection graphs and give a high-level overview of recent techniques to obtain polynomial bounds.
Axions and axion-like particles (ALPs) are hypothetical particles that occur in extensions of the Standard Model and are candidates for cold dark matter. They could be detected through their oscillations into photons in the presence of external elect
romagnetic fields. gammaALPs is an open-source python framework that computes the oscillation probability between photons and axions/ALPs. In addition to solving the photon-ALP equations of motion, gammaALPs includes models for magnetic fields in different astrophysical environments such as jets of active galactic nuclei, intra-cluster and intergalactic media, and the Milky Way. Users are also able to easily incorporate their own custom magnetic-field models. We review the basic functionality and features of gammaALPs, which is heavily based on other open-source scientific packages such as numpy and scipy. Although focused on gamma-ray energies, gammaALPs can be easily extended to arbitrary photon energies.
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number $omega$ has chromatic number at most $3cdot 4^{omega-1}
$. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.
Many theories beyond the Standard Model of particle physics predict the existence of axionlike particles (ALPs) that mix with photons in the presence of a magnetic field. One prominent indirect method of searching for ALPs is to look for irregulariti
es in blazar gamma-ray spectra caused by ALP-photon mixing in astrophysical magnetic fields. This requires the modelling of magnetic fields between Earth and the blazar. So far, only very simple models for the magnetic field in the blazar jet have been used. Here we investigate the effects of more complicated jet magnetic field configurations on these spectral irregularities, by imposing a magnetic field structure model onto the jet model proposed by Potter & Cotter. We simulate gamma-ray spectra of Mrk 501 with ALPs and fit them to no-ALP spectra, scanning the ALP and B-field configuration parameter space and show that the jet can be an important mixing region, able to probe new ALP parameter space around $m_asim$ 1-1000 neV and $g_{agamma}gtrsim$ $5times10^{-12}$ GeV$^{-1}$. However, reasonable (i.e. consistent with observation) changes of the magnetic field structure can have a large effect on the mixing. For jets in highly magnetized clusters, mixing in the cluster can overpower mixing in the jet. This means that the current constraints using mixing in the Perseus cluster are still valid.
The globular cluster (GC) system of our Galaxy contains four planetary nebulae (PNe): K 648 (or Ps 1) in M15, IRAS 18333-2357 in M22, JaFu 1 in Pal 6, and JaFu 2 in NGC 6441. Because single-star evolution at the low stellar mass of present-epoch GCs
was considered incapable of producing visible PNe, their origin presented a puzzle. We imaged the PN JaFu 1 with the Hubble Space Telescope (HST) to obtain photometry of its central star (CS) and high-resolution morphological information. We imaged IRAS 18333-2357 with better depth and resolution, and we analyzed its archival HST spectra to constrain its CS temperature and luminosity. All PNe in Galactic GCs now have high-quality HST data, allowing us to improve CS mass estimates. We find reasonably consistent masses between 0.53 and 0.58 Msun for all four objects, though estimates vary when adopting different stellar evolutionary calculations. The CS mass of IRAS 18333-2357, though, depends strongly on its temperature, which remains elusive due to reddening uncertainties. For all four objects, we consider their CS and nebular masses, their morphologies, and other incongruities to assess the likelihood that these objects formed from binary stars. Although generally limited by uncertainties (~0.02 Msun) in post-AGB tracks and core mass vs. luminosity relations, the high-mass CS in K 648 indicates a binary origin. The CS of JaFu 1 exhibits compact bright [O III] and Halpha emission, like EGB 6, suggesting a binary companion or disk. Evidence is weaker for a binary origin of JaFu 2.
