ALBERT

Description: We present CO observations towards a sample of six H i-rich Ultradiffuse galaxies (UDGs) as well as one UDG (VLSB-A) in the Virgo Cluster with the Institut de RadioAstronomie Millimétrique (IRAM) 30-m telescope. CO J = 1–0 is marginally detected at 4σ level in AGC 122966, as the first detection of CO emission in UDGs. We estimate upper limits of molecular mass in other galaxies from the non-detection of CO lines. These upper limits and the marginal CO detection in AGC 122966 indicate low mass ratios between molecular and atomic gas masses. With the star formation efficiency derived from the molecular gas, we suggest that the inefficiency of star formation in such H i-rich UDGs is likely caused by the low efficiency in converting molecules from atomic gas, instead of low efficiency in forming stars from molecular gas.

Description: We find that the minor axes of the ultra-diffuse galaxies (UDGs) in Abell 2634 tend to be aligned with the major axis of the central dominant galaxy, at a $gtrsim 95{{ m per cent}}$ confidence level. This alignment is produced by the bright UDGs with the absolute magnitudes Mr 〈 −15.3 mag, and outer-region UDGs with R 〉 0.5R200. The alignment signal implies that these bright, outer-region UDGs are very likely to acquire their angular momenta from the vortices around the large-scale filament before they were accreted into A2634, and form their extended stellar bodies outside of the cluster; in this scenario, the orientations of their primordial angular momenta, which are roughly shown by their minor axes on the images, should tend to be parallel to the elongation of the large-scale filament. When these UDGs fell into the unrelaxed cluster A2634 along the filament, they could still preserve their primordial alignment signal before violent relaxation and encounters. These bright, outer-region UDGs in A2634 are very unlikely to be the descendants of the high-surface-brightness dwarf progenitors under tidal interactions with the central dominant galaxy in the cluster environment. Our results indicate that the primordial alignment could be a useful probe of the origin of UDGs in large-scale structures.

Description: We present a detailed analysis of the gaseous component of the Si K edge using high-resolution Chandra spectra of low-mass X-ray binaries. We fit the spectra with a modified version of the ISMabs model, including new photoabsorption cross-sections computed for all Si ionic species. We estimate column densities for Si i, Si ii, Si iii, Si xii, and Si xiii, which trace the warm, intermediate temperature, and hot phases of the Galactic interstellar medium. We find that the ionic fractions of the first two phases are similar. This may be due to the physical state of the plasma determined by the temperature or due to the presence of absorber material in the close vicinity of the sources. Our findings highlight the need for accurate modelling of the gaseous component before attempting to address the solid component.

Description: Using state-of-the-art high-resolution fully GPU N-body simulations, we demonstrate for the first time that the infall of a dark matter-rich satellite naturally explains a present black hole offset by subparsecs in M31. Observational data of the tidal features provide stringent constraints on the initial conditions of our simulations. The heating of the central region of M31 by the satellite via dynamical friction entails a significant black hole offset after the first pericentric passage. After having reached its maximum offset, the massive black hole sinks towards the M31 centre due to dynamical friction and it is determined to be offset by subparsecs as derived by observations.

Description: In two recent papers published in MNRAS, Namouni and Morais claimed evidence for the interstellar origin of some small Solar system bodies, including: (i) objects in retrograde co-orbital motion with the giant planets and (ii) the highly inclined Centaurs. Here, we discuss the flaws of those papers that invalidate the authors’ conclusions. Numerical simulations backwards in time are not representative of the past evolution of real bodies. Instead, these simulations are only useful as a means to quantify the short dynamical lifetime of the considered bodies and the fast decay of their population. In light of this fast decay, if the observed bodies were the survivors of populations of objects captured from interstellar space in the early Solar system, these populations should have been implausibly large (e.g. about 10 times the current main asteroid belt population for the retrograde co-orbital of Jupiter). More likely, the observed objects are just transient members of a population that is maintained in quasi-steady state by a continuous flux of objects from some parent reservoir in the distant Solar system. We identify in the Halley-type comets and the Oort cloud the most likely sources of retrograde co-orbitals and highly inclined Centaurs.

Description: Strong gravitational lensing has been a powerful probe of cosmological models and gravity. To date, constraints in either domain have been obtained separately. We propose a new methodology through which the cosmological model, specifically the Hubble constant, and post-Newtonian parameter can be simultaneously constrained. Using the time-delay cosmography from strong lensing combined with the stellar kinematics of the deflector lens, we demonstrate that the Hubble constant and post-Newtonian parameter are incorporated in two distance ratios that reflect the lensing mass and dynamical mass, respectively. Through the re-analysis of the four publicly released lenses distance posteriors from the H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring) collaboration, the simultaneous constraints of Hubble constant and post-Newtonian parameter are obtained. Our results suggest no deviation from the general relativity; $gamma _{t {PPN}}=0.87^{+0.19}_{-0.17}$ with a Hubble constant that favours the local Universe value, $H_0=73.65^{+1.95}_{-2.26}$ km s−1 Mpc−1. Finally, we forecast the robustness of gravity tests by using the time-delay strong lensing for constraints we expect in the next few years. We find that the joint constraint from 40 lenses is able to reach the order of $7.7{{ m per cent}}$ for the post-Newtonian parameter and $1.4{{ m per cent}}$ for the Hubble constant.

Description: One of the proposed channels of binary black hole mergers involves dynamical interactions of three black holes. In such scenarios, it is possible that all three black holes merge in a so-called hierarchical merger chain, where two of the black holes merge first and then their remnant subsequently merges with the remaining single black hole. Depending on the dynamical environment, it is possible that both mergers will appear within the observable time window. Here, we perform a search for such merger pairs in the public available LIGO and Virgo data from the O1/O2 runs. Using a frequentist p-value assignment statistics, we do not find any significant merger pair candidates, the most significant being GW170809-GW151012 pair. Assuming no observed candidates in O3/O4, we derive upper limits on merger pairs to be ∼11–110 yr−1 Gpc−3, corresponding to a rate that relative to the total merger rate is ∼0.1−1.0. From this, we argue that both a detection and a non-detection within the next few years can be used to put useful constraints on some dynamical progenitor models.

Description: We present extremely deep upper limits on the radio emission from 4U 1957+11, an X-ray binary that is generally believed to be a persistently accreting black hole that is almost always in the soft state. We discuss a more comprehensive search for Type I bursts than in past work, revealing a stringent upper limit on the burst rate, bolstering the case for a black hole accretor. The lack of detection of this source at the 1.07 μJy/beam noise level indicates jet suppression that is stronger than expected even in the most extreme thin disc models for radio jet production – the radio power here is 1500–3700 times lower than the extrapolation of the hard state radio/X-ray correlation, with the uncertainties depending primarily on the poorly constrained source distance. We also discuss the location and velocity of the source and show that it must have either formed in the halo or with a strong asymmetric natal kick.

Description: Swift J004427.3−734801 is an X-ray source in the Small Magellanic Cloud (SMC) that was first discovered as part of the Swift S-CUBED programme in 2020 January. It was not detected in any of the previous 3 yr worth of observations. The accurate positional determination from the X-ray data has permitted an optical counterpart to be identified that has the characteristics of an O9V−B2III star. Evidence for the presence of an infrared excess and significant I-band variability strongly suggests that this is an OBe-type star. Over 17 yr worth of optical monitoring by the OGLE (Optical Gravitational Lensing Experiment) project reveals periods of time in which quasi-periodic optical flares occur at intervals of ∼21.5 d. The X-ray data obtained from the S-CUBED project reveal a very soft spectrum, too soft to be that from accretion on to a neutron star or black hole. It is suggested here that this is a rarely identified Be star–white dwarf binary in the SMC.

Description: Gravitational microlensing can detect isolated stellar-mass black holes (BHs), which are believed to be the dominant form of Galactic BHs according to population synthesis models. Previous searches for BH events in microlensing data focused on long time-scale events with significant microlensing parallax detections. Here we show that, although BH events preferentially have long time-scales, the microlensing parallax amplitudes are so small that in most cases the parallax signals cannot be detected statistically significantly. We then identify OGLE-2006-BLG-044 to be a candidate BH event because of its long time-scale and small microlensing parallax. Our findings have implications to future BH searches in microlensing data.

Description: We present a sub-100 pc-scale analysis of the CO molecular gas emission and kinematics of the gravitational lens system SDP.81 at redshift 3.042 using Atacama Large Millimetre/submillimetre Array (ALMA) science verification data and a visibility-plane lens reconstruction technique. We find clear evidence for an excitation-dependent structure in the unlensed molecular gas distribution, with emission in CO (5–4) being significantly more diffuse and structured than in CO (8–7). The intrinsic line luminosity ratio is r 8–7/5–4  = 0.30 ± 0.04, which is consistent with other low-excitation starbursts at z  ~ 3. An analysis of the velocity fields shows evidence for a star-forming disc with multiple velocity components that is consistent with a merger/post-coalescence merger scenario, and a dynamical mass of M (〈1.56 kpc) = 1.6 ± 0.6  x  10 10 M . Source reconstructions from ALMA and the Hubble Space Telescope show that the stellar component is offset from the molecular gas and dust components. Together with Karl G. Jansky Very Large Array CO (1–0) data, they provide corroborative evidence for a complex ~2 kpc-scale starburst that is embedded within a larger ~15 kpc structure.

Description: We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of non-autonomous Hamiltonian vector fields.

Description: We consider the Schur–Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$ . We show that the infinite-dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I $_\infty$ , II, and III. A key result is an approximation theorem that can be seen as an approximate multivariate analogue of Kadison's Carpenter Theorem.

Description: We study the rate of convergence to zero of the tail entropy of $C^\infty$ maps. We give an upper bound of this rate in terms of the growth in $k$ of the derivative of order $k$ and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to $C^r$ $(r\geqslant 2)$ robustly non- $h$ -expansive dynamical systems.

Description: Let ${{\mathscr {C}}}^0_{{{\mathfrak {g}}}}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'({{\mathfrak {g}}})$ and let $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of type $A_{\infty }$ . In this paper, we investigate the relationship between the categories ${{\mathscr {C}}}^0_{A_{N-1}^{(1)}}$ and ${{\mathscr {C}}}^0_{A_{N-1}^{(2)}}$ by constructing the generalized quantum affine Schur–Weyl duality functors ${\mathcal {F}}^{(t)}$ from $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ to ${{\mathscr {C}}}^0_{A_{N-1}^{(t)}}\ (t=1,2)$ .

Description: We present new constructions of complex and $p$ -adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.

Description: Regardless of the physical origin of stellar magnetic fields – fossil or dynamo induced - an inclination angle between the magnetic and rotation axes is very often observed. Absence of observational evidence in this direction in the solar case has led to generally assume that its global magnetic field and rotation axes are well aligned. We present the detection of a monthly periodic signal of the photospheric solar magnetic field at all latitudes, and especially near the poles, revealing that the main axis of the Sun's magnetic field is not aligned with the surface rotation axis. This result reinforces the view of our Sun as a common intermediate-mass star. Furthermore, this detection challenges and imposes a strong observational constraint to modern solar dynamo theories.

Description: We use the ‘Evolution and Assembly of GaLaxies and their Environments’ ( eagle ) suite of hydrodynamical cosmological simulations to measure offsets between the centres of stellar and dark matter components of galaxies. We find that the vast majority (〉95 per cent) of the simulated galaxies display an offset smaller than the gravitational softening length of the simulations (Plummer-equivalent  = 700 pc), both for field galaxies and satellites in clusters and groups. We also find no systematic trailing or leading of the dark matter along a galaxy's direction of motion. The offsets are consistent with being randomly drawn from a Maxwellian distribution with  ≤ 196 pc. Since astrophysical effects produce no feasible analogues for the $1.62^{+0.47}_{-0.49}$  kpc offset recently observed in Abell 3827, the observational result is in tension with the collisionless cold dark matter model assumed in our simulations.

Description: The solar wind magnetic field contains rotations at a broad range of scales, which have been extensively studied in the magnetohydrodynamics range. Here, we present an extension of this analysis to the range between ion and electron kinetic scales. The distribution of rotation angles was found to be approximately lognormal, shifting to smaller angles at smaller scales almost self-similarly, but with small, statistically significant changes of shape. The fraction of energy in fluctuations with angles larger than α was found to drop approximately exponentially with α, with e-folding angle 9.8° at ion scales and 0 $_{.}^{\circ}$ 66 at electron scales, showing that large angles (α 〉 30°) do not contain a significant amount of energy at kinetic scales. Implications for kinetic turbulence theory and the dissipation of solar wind turbulence are discussed.

Description: We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross–Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton with zero speed.

Description: Let $k$ and $n$ be positive even integers. For a cuspidal Hecke eigenform $h$ in the Kohnen plus space of weight $k-n/2+1/2$ for $\varGamma _0(4),$ let $I_n(h)$ be the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift of $h$ in the space of cusp forms of weight $k$ for ${\rm Sp}_n({{\bf{Z}}}),$ and $f$ be the primitive form of weight $2k-n$ for ${\rm SL}_2({{\bf{Z}}})$ corresponding to $h$ under the Shimura correspondence. We then express the ratio $\displaystyle {\langle I_n(h), I_n(h) \rangle / \langle h, h \rangle }$ of the period of $I_n(h)$ to that of $h$ in terms of special values of certain $L$ -functions of $f$ . This proves the conjecture proposed by Ikeda concerning the period of the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift.

Description: We report the broad-band spectral properties of the X-ray pulsar Cep X-4 by using a Suzaku observation in 2014 July. The 0.8–70 keV spectrum was found to be well described by three continuum models – Negative and Positive power-law with Exponential cut-off (NPEX), high-energy cut-off power-law and CompTT models. Additional components such as a cyclotron line at ~28 keV and two Gaussian components for iron lines at 6.4 and 6.9 keV were required in the spectral fitting. Apart from these, an additional absorption feature at ~45 keV was clearly detected in residuals obtained from the spectral fitting. This additional feature at ~45 keV was clearly seen in phase-resolved spectra of the pulsar. We identified this feature as the first harmonic of the fundamental cyclotron line at ~28 keV. The ratio between the first harmonic and fundamental line energies (1.7) was found to be in disagreement with the conventional factor of 2, indicating that the heights of line-forming regions are different or viewed at larger angles. The phase-resolved spectroscopy of the fundamental and first harmonic cyclotron lines shows significant pulse-phase variation of the line parameters. This can be interpreted as the effect of viewing angle or the role of complicated magnetic field of the pulsar.

Description: The spin-down of a neutron star, e.g. due to magneto-dipole losses, results in compression of the stellar matter and induces nuclear reactions at phase transitions between different nuclear species in the crust. We show that this mechanism is effective in heating recycled pulsars, in which the previous accretion process has already been compressing the crust, so it is not in nuclear equilibrium. We calculate the corresponding emissivity and confront it with available observations, showing that it might account for the likely thermal ultraviolet emission of PSR J0437–4715.

Description: New insights into the formation of interstellar formamide, a species of great relevance in prebiotic chemistry, are provided by electronic structure and kinetic calculations for the reaction NH 2 + H 2 CO -〉 NH 2 CHO + H. Contrarily to what previously suggested, this reaction is essentially barrierless and can, therefore, occur under the low temperature conditions of intestellar objects thus providing a facile formation route of formamide. The rate coefficient parameters for the reaction channel leading to NH 2 CHO + H have been calculated to be A = 2.6 x 10 –12  cm 3  s –1 , β = –2.1 and = 26.9 K in the range of temperatures 10–300 K. Including these new kinetic data in a refined astrochemical model, we show that the proposed mechanism can well reproduce the abundances of formamide observed in two very different interstellar objects: the cold envelope of the Sun-like protostar IRAS16293–2422 and the molecular shock L1157-B2. Therefore, the major conclusion of this Letter is that there is no need to invoke grain-surface chemistry to explain the presence of formamide provided that its precursors, NH 2 and H 2 CO, are available in the gas phase.

Description: Recent Low-Frequency Array (LOFAR) observations at 115–175 MHz of a field at medium Galactic latitudes (centred at the bright quasar 3C196) have shown striking filamentary structures in polarization that extend over more than 4° across the sky. In addition, the Planck satellite has released full sky maps of the dust emission in polarization at 353 GHz. The LOFAR data resolve Faraday structures along the line of sight, whereas the Planck dust polarization maps probe the orientation of the sky projected magnetic field component. Hence, no apparent correlation between the two is expected. Here we report a surprising, yet clear, correlation between the filamentary structures, detected with LOFAR, and the magnetic field orientation, probed by the Planck satellite. This finding points to a common, yet unclear, physical origin of the two measurements in this specific area in the sky. A number of follow-up multifrequency studies are proposed to shed light on this unexpected finding.

Description: Protoplanetary discs are now routinely observed and exoplanets, after the numerous indirect discoveries, are starting to be directly imaged. To better understand the planet formation process, the next step is the detection of forming planets or of signposts of young planets still in their disc, such as gaps. A spectacular example is the Atacama Large Millimeter/submillimeter Array (ALMA) science verification image of HL Tau showing numerous gaps and rings in its disc. To study the observability of planet gaps, we ran 3D hydrodynamical simulations of a gas and dust disc containing a 5 M J gap-opening planet and characterized the spatial distribution of migrating, growing and fragmenting dust grains. We then computed the corresponding synthetic images for ALMA. For a value of the dust fragmentation threshold of 15 m s –1 for the collisional velocity, we identify for the first time a self-induced dust pile-up in simulations taking fragmentation into account. This feature, in addition to the easily detected planet gap, causes a second apparent gap that could be mistaken for the signature of a second planet. It is therefore essential to be cautious in the interpretation of gap detections.

Description: Recent observations have discovered a number of extremely gas-rich very faint dwarf galaxies possibly embedded in low-mass dark matter haloes. We investigate star formation histories of these gas-rich dwarf (‘almost dark’) galaxies both for isolated and interacting/merging cases. We find that although star formation rates (SFRs) are very low (〈10 –5 M  yr –1 ) in the simulated dwarfs in isolation for the total halo masses ( M h ) of 10 8 -10 9 M , they can be dramatically increased to be ~10 –4 M  yr –1 when they interact or merge with other dwarfs. These interacting faint dwarfs with central compact H ii regions can be identified as isolated emission line dots (‘ELdots’) owing to their very low surface brightness envelopes of old stars. The remnant of these interacting and merging dwarfs can finally develop central compact stellar systems with very low metallicities ( Z /Z  〈 0.1), which can be identified as extremely metal-deficient (‘XMD’) dwarfs. These results imply that although there would exist many faint dwarfs that can be hardly detected in the current optical observations, they can be detected as isolated ELdots or XMD dwarfs, when they interact with other galaxies and their host environments. We predict that nucleated ultrafaint dwarfs formed from the darkest dwarf merging can be identified as low-mass globular clusters owing to the very low surface brightness stellar envelopes.

Description: The BRITE ( BRIght Target Explorer ) constellation of nanosatellites performs seismology of bright stars via high-precision photometry. In this context, we initiated a high-resolution, high signal-to-noise, high-sensitivity, spectropolarimetric survey of all stars brighter than V = 4. The goal of this survey is to detect new bright magnetic stars and provide prime targets for both detailed magnetic studies and asteroseismology with BRITE . Circularly polarized spectra were acquired with Narval at TBL (Bernard Lyot Telescope, France) and HARPSpol at ESO (European Southern Observatory) in La Silla (Chile). We discovered two new magnetic B stars: the B3V star i Car and the B8V component of the binary star Atlas. Each star was observed twice to confirm the magnetic detections and check for variability. These bright magnetic B stars are prime targets for asteroseismology and for flux-demanding techniques, such as interferometry.

Description: Accreting neutron stars exhibit Type I X-ray bursts from both frequent hydrogen/helium flashes as well as rare carbon flashes. The latter (superbursts) ignite in the ashes of the former. Hydrogen/helium bursts, however, are thought to produce insufficient carbon to power superbursts. Stable burning could create the required carbon, but this was predicted to only occur at much larger accretion rates than where superbursts are observed. We present models of a new steady-state regime of stable hydrogen and helium burning that produces pure carbon ashes. Hot CNO burning of hydrogen heats the neutron star envelope and causes helium to burn before the conditions of a helium flash are reached. This takes place when the mass accretion rate is around 10 per cent of the Eddington limit: close to the rate where most superbursts occur. We find that increased heating at the base of the envelope sustains steady-state burning by steepening the temperature profile, which increases the amount of helium that burns before a runaway can ensue.

Description: We present new late-time near-infrared imaging of the site of the nearby core-collapse supernova SN 2012aw, confirming the disappearance of the point source identified by Fraser et al. and Van Dyk et al. as a candidate progenitor in both J and Ks filters. We remeasure the progenitor photometry, and find that both the J and Ks magnitudes of the source are consistent with those quoted in the literature. We also recover a marginal detection of the progenitor in H -band, for which we measure H = 19.67 ± 0.40 mag. Comparing the luminosity of the progenitor to stellar evolutionary models, SN 2012aw appears to have resulted from the explosion of a 12.5 ± 1.5 M red supergiant.

Description: We derive the carbon monoxide (CO) luminosity function (LF) for different rotational transitions [i.e. (1–0), (3–2), (5–4)] starting from the Herschel LF by Gruppioni et al. and using appropriate L CO – L IR conversions for different galaxy classes. Our predicted LFs fit the data so far available at z 0 and 2. We compare our results with those obtained by semi-analytical models (SAMs): while we find a good agreement over the whole range of luminosities at z 0, at z 1 and z 2, the tension between our LFs and SAMs in the faint and bright ends increases. We finally discuss the contribution of luminous active galactic nucleus ( L X 〉 10 44 erg s – 1 ) to the bright end of the CO LF concluding that they are too rare to reproduce the actual CO LF at z 2.

Description: The formation of the Milky Way stellar halo is thought to be the result of merging and accretion of building blocks such as dwarf galaxies and massive globular clusters. Recently, Deason et al. suggested that the Milky Way outer halo formed mostly from big building blocks, such as dwarf spheroidal galaxies, based on the similar number ratio of blue straggler (BS) stars to blue horizontal branch (BHB) stars. Here we demonstrate, however, that this result is seriously biased by not taking into detailed consideration on the formation mechanism of BHB stars from helium-enhanced second-generation population. In particular, the high BS-to-BHB ratio observed in the outer halo fields is most likely due to a small number of BHB stars provided by globular clusters (GCs) rather than to a large number of BS stars. This is supported by our dynamical evolution model of GCs which shows preferential removal of first-generation stars in GCs. Moreover, there are a sufficient number of outer halo GCs which show very high BS-to-BHB ratio. Therefore, the BS-to-BHB number ratio is not a good indicator to use in arguing that more massive dwarf galaxies are the main building blocks of the Milky Way outer halo. Several lines of evidence still suggest that GCs can contribute a significant fraction of the outer halo stars.

Description: Nuclear star clusters (NCs) are found to exist in the centres of many galaxies and appear to follow scaling relations similar to those of supermassive black holes. Previous analytical work has suggested that such relations are a consequence of feedback-regulated growth. We explore this idea using high-resolution hydrodynamical simulations, focusing on the validity of the simplifying assumptions made in analytical models. In particular, we investigate feedback emanating from multiple stellar sources rather than from a single source, as is usually assumed, and show that collisions between shells of gas swept up by feedback leads to momentum cancellation and the formation of high-density clumps and filaments. This high-density material is resistant both to expulsion from the galaxy potential and to disruption by feedback; if it falls back on to the NC, we expect the gas to be available for further star formation or for feeding a central black hole. We also note that our results may have implications for the evolution of globular clusters and stellar clusters in high-redshift dark matter haloes.

Description: We explain the axisymmetric gaps seen in recent long-baseline observations of the HL Tau protoplanetary disc with the Atacama Large Millimetre/Submillimetre Array (ALMA) as being due to the different response of gas and dust to embedded planets in protoplanetary discs. We perform global, three-dimensional dusty smoothed particle hydrodynamics calculations of multiple planets embedded in dust/gas discs which successfully reproduce most of the structures seen in the ALMA image. We find a best match to the observations using three embedded planets with masses of 0.2, 0.27 and 0.55 M J in the three main gaps observed by ALMA, though there remain uncertainties in the exact planet masses from the disc model.

Description: Using deep Herschel and ALMA observations, we investigate the star formation rate (SFR) distributions of X-ray-selected active galactic nucleus (AGN) host galaxies at 0.5 〈  z  〈 1.5 and 1.5 〈  z  〈 4, comparing them to that of normal, star-forming (i.e. ‘main-sequence’, or MS) galaxies. We find that 34–55 per cent of AGNs in our sample have SFRs at least a factor of 2 below that of the average MS galaxy, compared to 15 per cent of all MS galaxies, suggesting significantly different SFR distributions. Indeed, when both are modelled as lognormal distributions, the mass and redshift-normalized SFR distributions of X-ray AGNs are roughly twice as broad, and peak 0.4 dex lower, than that of MS galaxies. However, like MS galaxies, the normalized SFR distribution of AGNs in our sample appears not to evolve with redshift. Despite X-ray AGNs and MS galaxies having different SFR distributions, the linear-mean SFR of AGNs derived from our distributions is remarkably consistent with that of MS galaxies, and thus with previous results derived from stacked Herschel data. This apparent contradiction is due to the linear-mean SFR being biased by bright outliers, and thus does not necessarily represent a true characterization of the typical SFR of X-ray AGNs.

Description: We investigate the density–shear instability in Hall-magnetohydrodynamics (Hall-MHD) via numerical simulation of the full non-linear problem in the context of magnetar activity. We confirm the development of the instability of a plane-parallel magnetic field with an appropriate intensity and electron density profile, in accordance with analytic theory. We find that the instability also appears for a monotonically decreasing electron number density and magnetic field, a plane-parallel analogue of an azimuthal or meridional magnetic field in the crust of a magnetar. The growth rate of the instability depends on the Hall properties of the field (magnetic field intensity, electron number density and the corresponding scaleheights), while being insensitive to weak resistivity. Since the Hall effect is the driving process for the evolution of the crustal magnetic field of magnetars, we argue that this instability is critical for systems containing strong meridional or azimuthal fields. We find that this process mediates the formation of localized structures with much stronger magnetic field than the average, which can lead to magnetar activity and accelerate the dissipation of the field and consequently the production of Ohmic heating. Assuming a 5  x  10 14  G magnetic field at the base of crust, we anticipate that magnetic field as strong as 10 15  G will easily develop in regions of typical size of a few hundred metres, containing magnetic energy of 10 43  erg, sufficient to power magnetar bursts. These active regions are more likely to appear in the magnetic equator where the tangential magnetic field is stronger.

Description: Long expected transition states between the rotation powered and accretion powered non-thermal emission in the millisecond pulsar binary systems have been recently observed in the case of three objects PSR J1023+0038, PSR J1824–2452, and PSR J1227–4859. Surprisingly, the transition is related to the significant change in the -ray flux being a factor of a few higher with the presence of an accretion disc. The origin of this enhanced emission seems to be related to the penetration of the inner pulsar magnetosphere by the accretion disc. We propose that the radiation processes, characteristic for the rotation powered pulsar, can co-exist with the presence of an accretion disc in the inner pulsar magnetosphere. In our scenario additional -ray emission is produced by secondary leptons, originated close to the acceleration gap, which Compton up-scatter thermal radiation from the accretion disc to GeV energies. The accretion disc penetrates deep into the pulsar magnetosphere allowing the matter to fall on to the neutron star surface producing pulsed X-ray emission. We show that the sum of the rotation powered pulsar -ray emission, produced by the primary electrons in the curvature process, and the -ray emission, produced by secondary leptons, can explain the observed high-energy radiation from the redback binary pulsar PSR J1227–4853 in the state with evidences of the accretion disc.

Description: In the context of the ASAI (Astrochemical Surveys At IRAM) project, we carried out an unbiased spectral survey in the millimetre window towards the well known low-mass Class I source SVS13-A. The high sensitivity reached (3–12 mK) allowed us to detect at least six HDO broad (full width at half-maximum ~4–5 km s –1 ) emission lines with upper level energies up to E u = 837 K. A non-local thermodynamic equilibrium Large Velocity Gradient (LVG) analysis implies the presence of very hot (150–260 K) and dense (≥3  x  10 7  cm –3 ) gas inside a small radius (~25 au) around the star, supporting, for the first time, the occurrence of a hot corino around a Class I protostar. The temperature is higher than expected for water molecules are sublimated from the icy dust mantles (~100 K). Although we cannot exclude we are observing the effects of shocks and/or winds at such small scales, this could imply that the observed HDO emission is tracing the water abundance jump expected at temperatures ~220–250 K, when the activation barrier of the gas phase reactions leading to the formation of water can be overcome. We derive X ( HDO ) ~ 3  x  10 –6 , and a H 2 O deuteration ≥1.5  x  10 –2 , suggesting that water deuteration does not decrease as the protostar evolves from the Class 0 to the Class I stage.

Description: Evidence for the presence of quasi-periodic oscillations (QPOs) in the optical polarization of the blazar PKS 2155–304, during a period of enhanced gamma-ray brightness, is presented. The periodogram of the polarized flux revealed the existence of a prominent peak at T ~ 13 min, detected at 〉99.7 per cent significance, and T ~ 30 min, which was nominally significant at 〉99 per cent. This is the first evidence of QPOs in the polarization of an active galactic nucleus, potentially opening up a new avenue of studying this phenomenon.

Description: The spectrum and morphology of the diffuse Galactic -ray emission carries valuable information on cosmic ray (CR) propagation. Recent results obtained by analyzing Fermi -LAT data accumulated over 7 yr of observation show a substantial variation of the CR spectrum as a function of the distance from the Galactic Centre. The spatial distribution of the CR density in the outer Galaxy appears to be weakly dependent upon the galactocentric distance, as found in previous studies as well, while the density in the central region of the Galaxy was found to exceed the value measured in the outer Galaxy. At the same time, Fermi -LAT data suggest a gradual spectral softening while moving outwards from the centre of the Galaxy to its outskirts. These findings represent a challenge for standard calculations of CR propagation based on assuming a uniform diffusion coefficient within the Galactic volume. Here, we present a model of non-linear CR propagation in which transport is due to particle scattering and advection off self-generated turbulence. We find that for a realistic distribution of CR sources following the spatial distribution of supernova remnants and the space dependence of the magnetic field on galactocentric distance, both the spatial profile of CR density and the spectral softening can easily be accounted for.

Description: The correlation between the frequency and the absolute value of the frequency derivative of the kilohertz quasi-periodic oscillations (QPOs) observed for the first time from 4U 1636-53 is a simple consequence and indicator of the existence of a non-Keplerian rotation rate in the accretion disc boundary layer. This Letter interprets the observed correlation, showing that the observations provide strong evidence in support of the fundamental assumption of disc accretion models around slow rotators, that the boundary layer matches the Keplerian disc to the neutron star magnetosphere.

Description: During their formation phase, stars gain most of their mass in violent episodic accretion events, such as observed in FU Orionis (FUor) and EXor stars. V346 Normae is a well-studied FUor that underwent a strong outburst beginning around 1980. Here, we report on photometric and spectroscopic observations, which show that the visual/near-infrared brightness has decreased dramatically between the 1990s and 2010 ( R 10.9 mag, J 7.8 mag and K 5.8 mag). The spectral properties of this fading event cannot be explained by variable extinction alone, but indicate a drop in accretion rate by two to three orders of magnitude. This is the first time that a member of the FUor class has been observed to switch to a very low accretion phase. Remarkably, in the last few years (2011–2015) V346 Nor has brightened again at all near-infrared wavelengths, indicating the onset of a new outburst event. The observed behaviour might be consistent with the clustered luminosity bursts that have been predicted by recent gravitational instability and fragmentation models for the early stages of protostellar evolution. Given V346 Nor's unique characteristics (concerning outburst duration, repetition frequency and spectroscopic diagnostics), our results also highlight the need to revisit the FUor/EXor classification scheme.

Description: Approximately 0.2 ± 0.2 of white dwarfs (WDs) show signs of pollution by metals, which is likely due to the accretion of tidally disrupted planetary material. Models invoking planet–planet interactions after WD formation generally cannot explain pollution at cooling times of several Gyr. We consider a scenario in which a planet is perturbed by Lidov–Kozai oscillations induced by a binary companion and exacerbated by stellar mass-loss, explaining pollution at long cooling times. Our computed accretion rates are consistent with observations assuming planetary masses between ~0.01 and 1 M Mars , although non-gravitational effects may already be important for masses 0.3 M Mars . The fraction of polluted WDs in our simulations, ~0.05, is consistent with observations of WDs with intermediate cooling times between ~0.1 and 1 Gyr. For cooling times 0.1 Gyr and 1 Gyr, our scenario cannot explain the high observed pollution fractions of up to 0.7. Nevertheless, our results motivate searches for companions around polluted WDs.

Description: We present high resolution observations of fine structures at pore boundaries. The inner part of granules towards umbra show dark striations which evolve into a filamentary structure with dark core and ‘Y’ shape at the head of the filaments. These filaments migrate into the umbra similar to penumbral filaments. These filaments show higher temperature, lower magnetic field strength and more inclined field compared to the background umbra. The optical depth stratification of physical quantities suggests their similarity with penumbral filaments. However, line-of-sight velocity pattern is different from penumbral filaments where they show downflows in the deeper layers of the atmosphere while the higher layers show upflows. These observations show filamentation in a simple magnetic configuration.

Description: A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product $\mathcal S^2\times \mathcal S^2$ of two copies of the Hilbert–Schmidt classes into the trace class $\mathcal S^1$ is established in terms of linear Schur multipliers acting on the space $\mathcal S^\infty $ of all compact operators. Using this formula, we resolve Peller's problem on Koplienko–Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function $f$ with a bounded second derivative, a self-adjoint (unbounded) operator $A$ and a self-adjoint operator $B\in \mathcal S^2$ such that \[ f(A+B)-f(A)-\left.\frac{d}{dt}(f(A+tB))\right\vert_{t=0}\notin \mathcal S^1. \]

Description: Let $\mu $ be a probability measure on $ \mathbb R^n$ with a bounded density $f$ . We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann–Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu $ , any marginal $\pi _E(\mu )$ , or a small perturbation thereof, satisfies a nearly optimal small-ball probability.

Description: Let $\pi :X\to \mathbb {P}^1_{\mathbb {Q}}$ be a non-singular conic bundle over $\mathbb {Q}$ having $n$ non-split fibres and denote by $N(\pi ,B)$ the cardinality of the fibres of Weil height at most $B$ that possess a rational point. Serre showed in 1990 that a direct application of the large sieve yields \[ N(\pi,B)\ll B^2(\log B)^{-n/2} \] and raised the problem of proving that this is the true order of magnitude of $N(\pi ,B)$ under the necessary assumption that there exists at least one smooth fibre with a rational point. We solve this problem for all non-singular conic bundles of rank at most 3. Our method comprises the use of Hooley neutralisers, estimating divisor sums over values of binary forms, and an application of the Rosser–Iwaniec sieve.

Description: We associate a dimer algebra $A$ to a Postnikov diagram $D$ (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian ${\rm Gr}(k,n)$ . We show that $A$ is isomorphic to the endomorphism algebra of a corresponding Cohen–Macaulay module $T$ over the algebra $B$ used to categorify the cluster structure of ${\rm Gr}(k,n)$ by Jensen–King–Su. It follows that $B$ can be realised as the boundary algebra of $A$ , that is, the subalgebra $eAe$ for an idempotent $e$ corresponding to the boundary of the disc. The construction and proof uses an interpretation of the diagram $D$ , with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus.

Description: We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$ -planes in $n$ -space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective–injective object is Geiss–Leclerc–Schröer's category Sub $Q_k$ , which categorifies the coordinate ring of the big cell in this Grassmannian.

Description: We develop a way of seeing a complete orientable hyperbolic 4-manifold $ {\mathcal {M}}$ as an orbifold cover of a Coxeter polytope $ {\mathcal {P}} \subset \mathbb {H}^4$ that has a facet colouring. We also develop a way of finding a totally geodesic sub-manifold $ {\mathcal {N}}$ in $ {\mathcal {M}}$ , and describing the result of mutations along $ {\mathcal {N}}$ . As an application of our method, we construct an example of a complete orientable hyperbolic 4-manifold $ {\mathcal {X}}$ with a single non-toric cusp and a complete orientable hyperbolic 4-manifold ${\mathcal {Y}}$ with a single toric cusp. Both $ {\mathcal {X}}$ and $ {\mathcal {Y}}$ have twice the minimal volume among all complete orientable hyperbolic 4-manifolds.

Description: A large number of supernova remnants (SNRs) in our Galaxy and galaxies nearby have been resolved in various radio bands. This radio emission is thought to be produced via synchrotron emission from electrons accelerated by the shock that the supernova ejecta drives into the external medium. Here we consider the sample of radio SNRs in the Magellanic Clouds. Given the size and radio flux of an SNR, we seek to constrain the fraction of shocked fluid energy in non-thermal electrons ( e ) and magnetic field ( B ), and find e B ~ 10 –3 . These estimates do not depend on the largely uncertain values of the external density and the age of the SNR. We develop a Monte Carlo scheme that reproduces the observed distribution of radio fluxes and sizes of the population of radio SNRs in the Magellanic Clouds. This simple model provides a framework that could potentially be applied to other galaxies with complete radio SNRs samples.

Description: We present a line survey of the ultraluminous infrared galaxy Arp 220, taken with the newly installed SEPIA (Swedish-European Southern Observatory PI receiver for APEX) Band 5 instrument on APEX (Atacama Pathfinder Experiment). We illustrate the capacity of SEPIA to detect the 183.3 GHz H 2 O 3 1,3 –2 2,0 line against the atmospheric H 2 O absorption feature. We confirm the previous detection of the HCN(2–1) line, and detect new transitions of standard dense gas tracers such as HNC(2–1), HCO + (2–1), CS(4–3), C 34 S(4–3) and HC 3 N(20–19). We also detect HCN(2–1) v 2 = 1 and the 193.5 GHz methanol (4–3) group for the first time. The absence of time variations in the megamaser water line compared to previous observations seems to rule out an AGN nuclear origin for the line. It could, on the contrary, favour a thermal origin instead, but also possibly be a sign that the megamaser emission is associated with star-forming cores washed out in the beam. We finally discuss how the new transitions of HCN, HNC and HCO + refine our knowledge of the interstellar medium physical conditions in Arp 220.

Description: We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial Fourier mode amplitudes are fixed to the ensemble average power spectrum) and paired (with initial modes exactly out of phase). We measure the power spectrum, monopole and quadrupole redshift-space correlation functions, halo mass function and reduced bispectrum at z  = 1. By these measures, predictions from a fixed pair can be as precise on non-linear scales as an average over 50 traditional simulations. The fixing procedure introduces a non-Gaussian correction to the initial conditions; we give an analytic argument showing why the simulations are still able to predict the mean properties of the Gaussian ensemble. We anticipate that the method will drive down the computational time requirements for accurate large-scale explorations of galaxy bias and clustering statistics, and facilitating the use of numerical simulations in cosmological data interpretation.

Description: The covariogram $g_{K}$ of a convex body $K$ in $ \mathbb {R}^n$ is the function that associates to each $x\in \mathbb {R}^n$ the volume of the intersection of $K$ with $K+x$ . Determining $K$ from the knowledge of $g_K$ is known as the Covariogram Problem. It is equivalent to determining the characteristic function $1_K$ of $K$ from the modulus of its Fourier transform $\widehat {{1_K}}$ in $ \mathbb {R}^n$ , a particular instance of the Phase Retrieval Problem. We connect the Covariogram Problem to two aspects of the Fourier transform $\widehat {{1_K}}$ seen as a function in $\mathbb {C}^n$ . The first connection is with the problem of determining $K$ from the knowledge of the zero set of $\widehat {{1_K}}$ in $\mathbb {C}^n$ . To attack this problem T. Kobayashi studied the asymptotic behavior at infinity of this zero set. We obtain this asymptotic behavior assuming less regularity on $K$ and we use this result as an essential ingredient for proving that when $K$ is sufficiently smooth and in any dimension $n$ , $K$ is determined by $g_K$ in the class of sufficiently smooth bodies. The second connection is with the irreducibility of the entire function $\widehat {{1_K}}$ . This connection also shows a link between the Covariogram Problem and the Pompeiu Problem in integral geometry.

Description: Using a specialized technique sensitive to the presence of expanding ionized gas, we have detected a set of three concentric expanding shells in an H ii region in the nearby spiral galaxy M33. After mapping the kinematics in Hα with Fabry–Perot spectroscopy, we used slit spectra to measure the intensities of the [S ii ] doublet at 671.9, 673.1 nm and the [N ii ] doublet at 645.8, 658.3 nm to corroborate the kinematics and apply diagnostic tests using line ratios. These showed that the expanding shells are shock dominated as would be the case if they had originated with supernova explosions. Estimating their kinetic energies, we find fairly low values, indicating a fairly advanced stage of evolution. We obtain density, mass and parent star mass estimates, which, along with the kinetic energies, are inconsistent with the simplest models of shock–interstellar medium interaction. We propose that the presence and properties of an inhomogeneous medium offer a scenario which can account for these observations, and discuss the implications. Comparing our results with data from the literature supports the combined presence of an H ii region and supernova remnant material at the observed position.

Description: We study the origin of the stellar α-element-to-iron abundance ratio, [α/Fe] * , of present-day central galaxies, using cosmological, hydrodynamical simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project. For galaxies with stellar masses of M * 〉 10 10.5 M , [α/Fe] * increases with increasing galaxy stellar mass and age. These trends are in good agreement with observations of early-type galaxies, and are consistent with a ‘downsizing’ galaxy formation scenario: more massive galaxies have formed the bulk of their stars earlier and more rapidly, hence from an interstellar medium that was mostly α-enriched by massive stars. In the absence of feedback from active galactic nuclei (AGNs), however, [α/Fe] * in M * 〉 10 10.5 M galaxies is roughly constant with stellar mass and decreases with mean stellar age, extending the trends found for lower mass galaxies in both simulations with and without AGN. We conclude that AGN feedback can account for the α-enhancement of massive galaxies, as it suppresses their star formation, quenching more massive galaxies at earlier times, thereby preventing the iron from longer lived intermediate-mass stars (supernova Type Ia) from being incorporated into younger stars.

Description: We report broad-band spectral properties of the high-mass X-ray binary pulsar SMC X-2 by using three simultaneous Nuclear Spectroscopy Telescope Array and Swift /XRT observations during its 2015 outburst. The pulsar was significantly bright, reaching a luminosity up to as high as ~5.5 x 10 38 erg s –1 in 1–70 keV range. Spin period of the pulsar was estimated to be 2.37 s. Pulse profiles were found to be strongly luminosity dependent. The 1–70 keV energy spectrum of the pulsar was well described with three different continuum models such as (i) negative and positive power law with exponential cutoff, (ii) Fermi -Dirac cutoff power law and (iii) cutoff power-law models. Apart from the presence of an iron line at ~6.4 keV, a model independent absorption like feature at ~27 keV was detected in the pulsar spectrum. This feature was identified as a cyclotron absorption line and detected for the first time in this pulsar. Corresponding magnetic field of the neutron star was estimated to be ~2.3 x 10 12  G. The cyclotron line energy showed a marginal negative dependence on the luminosity. The cyclotron line parameters were found to be variable with pulse phase and interpreted as due to the effect of emission geometry or complicated structure of the pulsar magnetic field.

Description: We analyse structural decompositions of 500 late-type galaxies (Hubble T -type ≥6) from the Spitzer Survey of Stellar Structure in Galaxies ( S 4 G ; Salo et al.), spanning stellar mass range of about 10 7 to a few times 10 10 M . Their decomposition parameters are compared with those of the early-type dwarfs in the Virgo cluster from Janz et al. They have morphological similarities, including the fact that the fraction of simple one-component galaxies in both samples increases towards lower galaxy masses. We find that in the late-type two-component galaxies both the inner and outer structures are by a factor of 2 larger than in the early-type dwarfs, for the same stellar mass of the component. While dividing the late-type galaxies to low- and high-density environmental bins, it is noticeable that both the inner and outer components of late types in the high local density galaxies are smaller, and lie closer in size to those of the early-type dwarfs. This suggests that, although structural differences between the late- and early-type dwarfs are observed, environmental processes can plausibly transform their sizes sufficiently, thus linking them evolutionarily.

Description: We calculate the microlensing event rate and typical time-scales for the free-floating planet (FFP) population that is predicted by the core accretion theory of planet formation. The event rate is found to be ~1.8  x  10 –3 of that for the stellar population. While the stellar microlensing event time-scale peaks at around 20 d, the median time-scale for FFP events (~0.1 d) is much shorter. Our values for the event rate and the median time-scale are significantly smaller than those required to explain the Sumi et al. result, by factors of ~13 and ~16, respectively. The inclusion of planets at wide separations does not change the results significantly. This discrepancy may be too significant for standard versions of both the core accretion theory and the gravitational instability model to explain satisfactorily. Therefore, either a modification to the planet formation theory is required or other explanations to the excess of short-time-scale microlensing events are needed. Our predictions can be tested by ongoing microlensing experiment such as Korean Microlensing Telescope Network, and by future satellite missions such as WFIRST and Euclid .

Description: The recent discovery of three Earth-sized, potentially habitable planets around a nearby cool star, TRAPPIST-1, has provided three key targets for the upcoming James Webb Space Telescope (JWST) . Depending on their atmospheric characteristics and precise orbit configurations, it is possible that any of the three planets may be in the liquid water habitable zone, meaning that they may be capable of supporting life. We find that present-day Earth levels of ozone, if present, would be detectable if JWST observes 60 transits for innermost planet 1b and 30 transits for 1c and 1d.

Description: The Advanced Laser Interferometer Gravitational-Wave Observatory (ALIGO) observatory recently reported the first direct detection of gravitational waves (GW) which triggered ALIGO on 2015 September 14. We report on observations taken with the Swift satellite two days after the trigger. No new X-ray, optical, UV or hard X-ray sources were detected in our observations, which were focused on nearby galaxies in the GW error region and covered 4.7 deg 2 (~2 per cent of the probability in the rapidly available GW error region; 0.3 per cent of the probability from the final GW error region, which was produced several months after the trigger). We describe the rapid Swift response and automated analysis of the X-ray telescope and UV/Optical telescope data, and note the importance to electromagnetic follow-up of early notification of the progenitor details inferred from GW analysis.

Description: Superluminous supernovae (SLSNe) have been suggested to be powered by strongly magnetized, rapidly rotating neutron stars which are often called magnetars. In this process, rotational energy of the magnetar is radiated via magnetic dipole radiation and heats the supernova ejecta. However, if magnetars are highly distorted in their geometric shape, rotational energy is mainly lost as gravitational wave radiation and thus such magnetars cannot power SLSNe. By simply comparing electromagnetic and gravitational wave emission time-scales, we constrain upper limits to the ellipticity of magnetars by assuming that they power the observed SLSNe. We find that their ellipticity typically needs to be less than about a few 10 –3 . This indicates that the toroidal magnetic field strengths in these magnetars are typically less than a few 10 16 G so that their distortions remain small. Because light-curve modelling of SLSNe shows that their dipole magnetic field strengths are of the order of 10 14 G, the ratio of poloidal to toroidal magnetic field strengths is found to be larger than ~0.01 in magnetars powering SLSNe.

Description: Let $\varphi :X\to S$ be a morphism between smooth complex analytic spaces and let $f=0$ define a free divisor on $S$ . We prove that if the deformation space $T^1_{X/S}$ of $\varphi $ is a Cohen–Macaulay $\mathcal {O}_X$ -module of codimension 2, and all of the logarithmic vector fields for $f=0$ lift via $\varphi $ , then $f\circ \varphi =0$ defines a free divisor on $X$ ; this is generalized in several directions. Among applications we recover a result of Mond–van Straten, generalize a construction of Buchweitz–Conca, and show that a map $\varphi :\mathbb {C}^{n+1}\to \mathbb {C}^n$ with critical set of codimension 2 has a $T^1_{X/S}$ with the desired properties. Finally, if $X$ is a representation of a reductive complex algebraic group $G$ and $\varphi $ is the algebraic quotient $X\to S=X\!{/\!/} G$ with $X\!{/\!/} G$ smooth, then we describe sufficient conditions for $T^1_{X/S}$ to be Cohen–Macaulay of codimension 2. In one such case, a free divisor on $\mathbb {C}^{n+1}$ lifts under the operation of ‘castling’ to a free divisor on $\mathbb {C}^{n(n+1)}$ , partially generalizing work of Granger–Mond–Schulze on linear free divisors. We give several other examples of such representations.

Description: Let $M^n$ be a compact manifold of dimension $n$ with free $T^k$ -action. We consider collapsings of $M$ on $N=M/T^k$ such that the sectional curvature and diameter of $M$ satisfy $|K(M)|\leq a$ and $ {\rm diam}(M) 〈 d$ , and give examples of collapsings for all $k$ such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of $M$ are bounded above by $c(M)\cdot \hbox {inj}(M)^{2k}$ . Moreover, we prove that the first non-zero eigenvalue of Laplacian acting on 1-forms of all principal $T^k$ -bundle $M$ over $N$ is bounded below by $c(n,a,d,N)\cdot {\rm Vol}(M)^2$ and $c\cdot \hbox {inj}(M)^{2k}$ when $M$ collapses on $N$ .

Description: We present Gemini Multi-Object Spectrograph (GMOS) imaging of 12 candidate intergalactic globular clusters (IGCs) in the Local Group, identified in a recent survey of the Sloan Digital Sky Survey (SDSS) footprint by di Tullio Zinn & Zinn. Our image quality is sufficiently high, at ~0.4–0.7 arcsec, that we are able to unambiguously classify all 12 targets as distant galaxies. To reinforce this conclusion we use GMOS images of globular clusters in the M31 halo, taken under very similar conditions, to show that any genuine clusters in the putative IGC sample would be straightforward to distinguish. Based on the stated sensitivity of the di Tullio Zinn & Zinn search algorithm, we conclude that there cannot be a significant number of IGCs with M V ≤ –6 lying unseen in the SDSS area if their properties mirror those of globular clusters in the outskirts of M31 – even a population of 4 would have only a 1 per cent chance of non-detection.

Description: The R h  =  ct cosmological model has received considerable attention in recent years owing to claims that it is favoured over the standard cold dark mater (CDM) model by most observational data. A key feature of the R h  =  ct model is that the zero active mass condition  + 3 p  = 0 holds at all epochs. Most recently, Melia has claimed that this condition is a requirement of the symmetries of the Friedmann–Robertson–Walker spacetime. We demonstrate that this claim is false and results from a flaw in the logic of Melia's argument.

Description: We investigate the prospects for the capture of the proposed Planet 9 from other stars in the Sun's birth cluster. Any capture scenario must satisfy three conditions: the encounter must be more distant than ~150 au to avoid perturbing the Kuiper belt; the other star must have a wide-orbit planet ( a 100 au); the planet must be captured on to an appropriate orbit to sculpt the orbital distribution of wide-orbit Solar system bodies. Here we use N -body simulations to show that these criteria may be simultaneously satisfied. In a few per cent of slow close encounters in a cluster, bodies are captured on to heliocentric, Planet 9-like orbits. During the ~100 Myr cluster phase, many stars are likely to host planets on highly eccentric orbits with apastron distances beyond 100 au if Neptune-sized planets are common and susceptible to planet–planet scattering. While the existence of Planet 9 remains unproven, we consider capture from one of the Sun's young brethren a plausible route to explain such an object's orbit. Capture appears to predict a large population of trans-Neptunian objects (TNOs) whose orbits are aligned with the captured planet, and we propose that different formation mechanisms will be distinguishable based on their imprint on the distribution of TNOs.

Description: We explore the formation of massive high-redshift Population III (Pop III) galaxies through photoionization feedback. We consider dark matter haloes formed from progenitors that have undergone no star formation as a result of early reionization and photoevaporation caused by a nearby galaxy. Once such a halo reaches 10 9 M , corresponding to the Jeans mass of the photoheated intergalactic medium at z 7, pristine gas is able to collapse into the halo, potentially producing a massive Pop III starburst. We suggest that this scenario may explain the recent observation of strong He  ii 1640 Å line emission in CR 7, which is consistent with ~10 7 M of young Pop III stars. Such a large mass of Pop III stars is unlikely without the photoionization feedback scenario, because star formation is expected to inject metals into haloes above the atomic cooling threshold (~10 8 M at z 7). We use merger trees to analytically estimate the abundance of observable Pop III galaxies formed through this channel, and find a number density of 10 –7 Mpc –3 at z  = 6.6 (the redshift of CR 7). This is approximately a factor of 10 lower than the density of Ly α emitters as bright as CR 7.

Description: In this Letter we investigate the effect of boxy/peanut (b/p) bulges on bar-induced gas inflow to the central kiloparsec, which plays a crucial role on the evolution of disc galaxies. We carry out hydrodynamic gas response simulations in realistic barred galaxy potentials, including or not the geometry of a b/p bulge, to investigate the amount of gas inflow induced in the different models. We find that b/p bulges can reduce the gas inflow rate to the central kiloparsec by more than an order of magnitude, which leads to a reduction in the amount of gas available in the central regions. We also investigate the effect of the dark matter halo concentration on these results, and find that for maximal discs, the effect of b/p bulges on gas inflow remains significant. The reduced amount of gas reaching the central regions due to the presence of b/p bulges could have significant repercussions on the formation of discy- (pseudo-) bulges, on the amount of nuclear star formation and feedback, on the fuel reservoir for AGN activity, and on the overall secular evolution of the galaxy.

Description: We present a proof-of-concept study of a method to estimate the inclination angle of compact high velocity clouds (CHVCs), i.e. the angle between a CHVC's trajectory and the line of sight. The inclination angle is derived from the CHVC's morphology and kinematics. We calibrate the method with numerical simulations, and we apply it to a sample of CHVCs drawn from HIPASS (Putman et al.). Implications for CHVC distances are discussed.

Description: The optical/ultraviolet (UV) variability of quasars has been discovered to be correlated with other quasar properties, such as luminosity, black hole mass and rest-frame wavelength. However, the origin of variability has been a puzzle so far. In this work, we upgrade the accretion disc model, which assumed the variability is caused by the change of global mass accretion rate, by constraining the disc size to match the viscous time-scale of accretion disc to the variability time-scale observed and by including the irradiation/X-ray reprocessing to make the emitted spectrum become steeper. We find this hybrid model can reproduce the observed bluer-when-brighter trend quite well, which is used to validate the theoretical model by several works recently. The traditional correlation between the variability amplitude and rest-frame wavelength can also be well fitted by our model. In addition, a weak positive correlation between variability amplitude and black hole mass is present, qualitatively consistent with recent observations.

Description: The first-known tidal disruption event (TDE) with strong evidence for a relativistic jet – based on extensive multiwavelength campaigns – is Swift J1644+5734. In order to directly measure the apparent speed of the radio jet, we performed very long baseline interferometry (VLBI) observations with the European VLBI network (EVN) at 5 GHz. Our observing strategy was to identify a very nearby and compact radio source with the real-time e-EVN, and then utilize this source as a stationary astrometry reference point in the later five deep EVN observations. With respect to the in-beam source FIRST J1644+5736, we have achieved a statistical astrometric precision about 12 μas (68 per cent confidence level) per epoch. This is one of the best phase-referencing measurements available to date. No proper motion has been detected in the Swift J1644+5734 radio ejecta. We conclude that the apparent average ejection speed between 2012.2 and 2015.2 was less than 0.3 c with a confidence level of 99 per cent. This tight limit is direct observational evidence for either a very small viewing angle or a strong jet deceleration due to interactions with a dense circum-nuclear medium, in agreement with some recent theoretical studies.

Description: Near-field cosmology – using detailed observations of the Local Group and its environs to study wide-ranging questions in galaxy formation and dark matter physics – has become a mature and rich field over the past decade. There are lingering concerns, however, that the relatively small size of the present-day Local Group (~2 Mpc diameter) imposes insurmountable sample-variance uncertainties, limiting its broader utility. We consider the region spanned by the Local Group's progenitors at earlier times and show that it reaches 3 arcmin 7 comoving Mpc in linear size (a volume of 350 Mpc 3 ) at z  = 7. This size at early cosmic epochs is large enough to be representative in terms of the matter density and counts of dark matter haloes with M vir ( z = 7) 2 x 10 9 M . The Local Group's stellar fossil record traces the cosmic evolution of galaxies with 10 3 M * ( z = 0)/M 10 9 (reaching M 1500  〉 –9 at z  ~ 7) over a region that is comparable to or larger than the Hubble Ultra-Deep Field (HUDF) for the entire history of the Universe. In the JWST era, resolved stellar populations will probe regions larger than the HUDF and any deep JWST fields, further enhancing the value of near-field cosmology.

Description: The presence or lack of eclipses in the X-ray light curves of ultraluminous X-ray sources (ULXs) can be directly linked to the accreting system geometry. In the case where the compact object is stellar mass and radiates isotropically, we should expect eclipses by a main-sequence to sub-giant secondary star on the recurrence time-scale of hours to days. X-ray light curves are now available for large numbers of ULXs as a result of the latest XMM–Newton catalogue. We determine the amount of fractional variability that should be injected into an otherwise featureless light curve for a given set of system parameters as a result of eclipses and compare this to the available data. We find that the vast majority of sources for which the variability has been measured to be non-zero and for which available observations meet the criteria for eclipse searches, have fractional variabilities which are too low to derive from eclipses and so must be viewed such that ≤ cos – 1 ( R * / a ). This would require that the disc subtends a larger angle than that of the secondary star and is therefore consistent with a conical outflow formed from super-critical accretion rates and implies some level of geometrical beaming in ULXs.

Description: We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types A and à . This entails showing that the minimal elements of the positive semiring of these cluster algebras form a linear basis over the integers for the cluster algebra.

Description: We prove that strongly F -regular and F -pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F -injective singularities fail to satisfy even the most basic Bertini-type results.

Description: This is the second of a pair of papers on the Delta-group structure on the braid and mapping class groups of a surface. We obtain a description of the homotopy groups of these Delta-groups and generalize to an arbitrary surface the Berrick–Cohen–Wong–Wu exact sequence relating the Brunnian braid groups of the 2-sphere to its homotopy groups. We prove a similar result for Brunnian mapping class groups.

Description: We construct a geometric realization of the Khovanov–Lauda–Rouquier algebra R associated with a symmetric Borcherds–Cartan matrix A = ( a ij ) i , j I via quiver varieties. As an application, if a ii != 0 for any i I , we prove that there exists a one-to-one correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of U A – (g) (respectively, V A ( )) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, R ).

Description: The purpose of this paper is to study the nature of quasi-invariant measures for finitely generated non-discrete subgroups of Diff ( S 1 ). For this, we apply ideas involving the closure of these groups to find out that the regularity of the measure depends on a ‘measurable version’ of well-known problems concerning stable self-intersection of Cantor sets. As applications, we prove that every d -quasiconformal probability measure for a non-solvable and non-discrete group must be absolutely continuous. Concerning singular quasi-invariant measures, it is also proved that their associated Hausdorff measures must either be zero or of infinite mass, a result contrasting with the case of dynamically defined Cantor sets and also applicable to the examples of singular stationary measures constructed by Kaimanovich and Le Prince. As a further application of our methods, a theorem of rigidity for measurable conjugations between groups as above is obtained.

Description: We study the space of period polynomials associated with modular forms of integral weight for finite-index subgroups of the modular group. For the modular group, this space is endowed with a pairing, corresponding to the Petersson inner product on modular forms via a formula of Haberland, and with an action of Hecke operators, defined algebraically by Zagier. We generalize Haberland's formula to (not necessarily cuspidal) modular forms for finite-index subgroups, and we show that it conceals two stronger formulas. We extend the action of Hecke operators to period polynomials of modular forms, we show that the pairing on period polynomials appearing in Haberland's formula is nondegenerate, and we determine the adjoints of Hecke operators with respect to it. We give a few applications for 1 ( N ): an extension of the Eichler–Shimura isomorphism to the entire space of modular forms; the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms, which are independent of the period relations; and an explicit formula for Fourier coefficients of Hecke eigenforms in terms of their period polynomials, generalizing the Coefficient theorem of Manin.

Description: We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2 (5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.

Description: Let U R d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f : U -〉 R can be approximated by real analytic convex functions, uniformly on all of U . We also show that C 0 -fine approximation of convex functions by smooth (or real analytic) convex functions on R d is possible in general if and only if d = 1. Nevertheless, for d ≥ 2, we give a characterization of the class of convex functions on R d which can be approximated by real analytic (or just smoother) convex functions in the C 0 -fine topology. It turns out that the possibility of performing this kind of approximation is not determined by the degree of local convexity or smoothness of the given function, but by its global geometrical behaviour. We also show that every C 1 convex and proper function on U can be approximated by C convex functions in the C 1 -fine topology, and we provide some applications of these results, concerning prescription of (sub-)differential boundary data to convex real analytic functions, and smooth surgery of convex bodies.

Description: We show that for the undisturbed interstellar velocity vector $\boldsymbol {V}_{\rm IS}$ and magnetic field direction $\boldsymbol {B}_{\rm IS}$ defined by IBEX ( Interstellar Boundary Explorer ) Ribbon centre, the radial direction of Voyager 2 over the last decade, and the (thermal proton) plasma velocity measured by the spacecraft since 2010.5, are almost parallel to the ( $\boldsymbol {B}_{\rm IS}$ , $\boldsymbol {V}_{\rm IS}$ )-plane, which coincides in practice with the hydrogen deflection plane. In consequence the plasma flow velocity measured by Voyager 2 in the inner heliosheath rotates more in the transverse than in the polar direction (explanation alternative to McComas & Schwadron). Note that the ( $\boldsymbol {B}_{\rm IS}$ , $\boldsymbol {V}_{\rm IS}$ ) plane is a symmetry plane of the interstellar plasma flow at large heliocentric distances.

Description: Let $G$ be a compact connected Lie group, or more generally a path connected topological group of the homotopy type of a finite CW-complex, and let $X$ be a rational nilpotent $G$ -space. In this paper, we analyze the homotopy type of the homotopy fixed point set $X^{hG}$ , and the natural injection $k\colon X^G\hookrightarrow X^{hG}$ . We show that if $X$ is elliptic, that is, it has finite-dimensional rational homotopy and cohomology, then each path component of $X^{hG}$ is also elliptic. We also give an explicit algebraic model of the inclusion $k$ based on which we can prove, for instance, that for $G$ a torus, $\pi _* (k)$ is injective in rational homotopy but, often, far from being a rational homotopy equivalence.

Description: Coronal-Line Forest Active Galactic Nuclei (CLiF AGN) are remarkable in the sense that they have a rich spectrum of dozens of coronal emission lines (e.g. [Fe vii ], [Fe x ] and [Ne v ]) in their spectra. Rose, Elvis & Tadhunter suggest that the inner obscuring torus wall is the most likely location of the coronal line region in CLiF AGN, and the unusual strength of the forbidden high-ionization lines is due to a specific AGN-torus inclination angle. Here, we test this suggestion using mid-IR colours (4.6–22 μm) from the Wide-Field Infrared Survey Explorer for the CLiF AGN. We use the Fischer et al. result that showed that as the AGN-torus inclination becomes more face on, the Spitzer 5.5–30 μm colours become bluer. We show that the [ W 2– W 4] colours for the CLiF AGN (〈[ W 2– W 4]〉 = 5.92 ± 0.12) are intermediate between Sloan Digital Sky Survey (SDSS) type 1 (〈[ W 2– W 4]〉 = 5.22 ± 0.01) and type 2 AGN (〈[ W 2– W 4]〉 = 6.35 ± 0.03). This implies that the AGN-torus inclinations for the CLiF AGN are indeed intermediate, supporting the work of Rose, Elvis & Tadhunter. The confirmed relation between CLiF AGN and their viewing angle shows that CLiF AGN may be useful for our understanding of AGN unification.

Description: We present the discovery of two z  〉 6 quasars, selected as i -band dropouts in the Very Large Telescope Survey Telescope ATLAS survey. Our first quasar has redshift, z  = 6.31 ± 0.03, z -band magnitude, z AB  = 19.63 ± 0.08 and rest frame 1450 Å absolute magnitude, M 1450  = –27.8 ± 0.2, making it the joint second most luminous quasar known at z  〉 6. The second quasar has z  = 6.02 ± 0.03, z AB  = 19.54 ± 0.08 and M 1450  = –27.0 ± 0.1. We also recover a z  = 5.86 quasar discovered by Venemans et al., in preparation. To select our quasars, we use a new 3D colour space, combining the atlas optical colours with mid-infrared data from the Wide-field Infrared Survey Explorer . We use i AB – z AB colour to exclude main-sequence stars, galaxies and lower redshift quasars, W 1 – W 2 to exclude L dwarfs and z AB – W 2 to exclude T dwarfs. A restrictive set of colour cuts returns only our three high redshift quasars and no contaminants, albeit with a sample completeness of ~50 per cent. We discuss how our 3D colour space can be used to reject the majority of contaminants from samples of bright 5.7 〈 z  〈 6.3 quasars, replacing follow-up near-infrared photometry, whilst retaining high completeness.

Description: I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is comparable to w -term imaging algorithms, but by using a spherical rather than a Cartesian formulation this term has no special significance. The solution presented also allows direct identification of the scalar (spin 0 weighted) spherical harmonics on the sky. The method should be of interest for future multispacecraft interferometers, wide-field imaging with non-coplanar arrays, and cosmic microwave background spherical harmonic measurements using interferometers.

Description: We present Atacama Large Millimeter/submillimeter Array observations of 99.02 GHz free–free and H40α emission from the centre of the nearby starburst galaxy NGC 253. We calculate electron temperatures of 3700–4500 K for the photoionized gas, which agrees with previous measurements. We measure a photoionizing photon production rate of (3.2 ± 0.2) 10 53  s –1 and a star formation rate of 1.73 ± 0.12 M  yr –1 within the central 20 10 arcsec, which fall within the broad range of measurements from previous millimetre and radio observations but which are better constrained. We also demonstrate that the dust opacities are ~3 dex higher than inferred from previous near-infrared data, which illustrates the benefits of using millimetre star formation tracers in very dusty sources.

Description: We analyse the distinguishability of populations of coalescing binary neutron stars, neutron-star black hole binaries, and binary black holes, whose gravitational-wave signatures are expected to be observed by the advanced network of ground-based interferometers LIGO and Virgo. We consider population-synthesis predictions for plausible merging binary distributions in mass space, along with measurement accuracy estimates from the main gravitational-wave parameter-estimation pipeline. We find that for our model compact-object binary mass distribution, we can always distinguish binary neutron stars and black hole–neutron-star binaries, but not necessarily black hole–neutron-star binaries and binary black holes; however, with a few tens of detections, we can accurately identify the three subpopulations and measure their respective rates.

Description: We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.

Description: A notion of tangential thickness of a manifold is introduced. An extensive calculation within the class of lens and fake lens spaces leads to a classification of such manifolds with thickness 1, 3 or 2 $k$ , for $k\geq 1$ . On the other hand, calculations of tangential thickness in terms of the dimension of the manifold and the rank of the fundamental group show very interesting and quite surprising correlations between these invariants.

Description: Extending a classical result of Widom from 1969, polynomials with small supremum norms are constructed for a large family of compact sets $\Gamma$ : their norm is at most a constant times the theoretical lower limit ${{\rm cap}}(\Gamma )^n$ , where ${{\rm cap}}(\Gamma )$ denotes logarithmic capacity. The construction is based on a discretization of the equilibrium measure, and the polynomials have the additional property that outside the given set $\Gamma$ they increase as fast as possible, namely as ${{\rm cap}}(\Gamma )^n\exp (ng_{ \overline {{{}C}}\setminus \Gamma }(z))$ , with the Green's function with pole at infinity in the exponent. This latter fact allows us to use these polynomials as building blocks in constructing Dirac delta-type polynomials around corners: if a compact set $K$ has a corner at some point $z_0$ , then Dirac delta-type polynomials (fast decreasing polynomials) peaking at $z_0$ are polynomials $P_n(z)$ with $P_n(z_0)=1$ that decrease as $|P_n(z)|\prec \exp (-n^ \beta |z-z_0|^ \gamma )$ on the set $K$ as $z$ moves away from $z_0$ . The possible $(\beta , \gamma )$ pairs are completely described in turn of the angle $\alpha \pi$ at $z_0$ ( $\beta \lt 1$ and $\gamma \ge \beta /(2- \alpha )$ or $\beta =1$ and $\gamma 〉 \beta /(2- \alpha )$ ). As application of these fast decreasing polynomials sharp Nikolskii- and Markov-type inequalities are proved for Jordan domains with corners. The paper uses distortion properties of conformal maps, potential theoretic techniques as well as the theory of weighted logarithmic potentials.

Description: We consider for every $n\in \mathbb {N}$ an algebra $\mathcal {A}_{n}$ of germs at $0\in \mathbb {R}^{n}$ of continuous real-valued functions, such that we can associate to every germ $f\in \mathcal {A}_{n}$ a (divergent) series $\mathcal {T}(f)$ with non-negative real exponents, which can be thought of as an asymptotic expansion of $f$ . We require that the $\mathbb {R}$ -algebra homomorphism $f\mapsto \mathcal {T}(f)$ be injective (quasianalyticity property). In this setting, we prove analogue results to Denef and van den Dries’ quantifier elimination theorem and Hironaka's rectilinearization theorem for subanalytic sets.

Description: Suppose that $F(x)\in \mathbb {Z}[\![x]\!]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$ for an integer $b\geq 2$ . In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers. In particular, we prove that $F(1/b)$ cannot be a Liouville number. If, in addition, $F(x)$ is regular, we show that $F(1/b)$ is either rational or transcendental, and in the latter case that $F(1/b)$ is an $S$ -number or a $T$ -number in Mahler's classification of real numbers.

Description: We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class of $p$ -adic integrals under non-degeneracy conditions with respect to associated Newton polytopes. Our techniques prove to be especially useful for the computation of topological zeta functions associated with algebras, resulting in the first systematic investigation of their properties.

Description: During the late stages of their evolution, Sun-like stars bring the products of nuclear burning to the surface. Most of the carbon in the Universe is believed to originate from stars with masses up to a few solar masses. Although there is a chemical dichotomy between oxygen-rich and carbon-rich evolved stars, the dredge-up itself has never been directly observed. In the last three decades, however, a few stars have been shown to display both carbon- and oxygen-rich material in their circumstellar envelopes. Two models have been proposed to explain this dual chemistry: one postulates that a recent dredge-up of carbon produced by nucleosynthesis inside the star during the Asymptotic Giant Branch changed the surface chemistry of the star. The other model postulates that oxygen-rich material exists in stable keplerian rotation around the central star. The two models make contradictory, testable, predictions on the location of the oxygen-rich material, either located further from the star than the carbon-rich gas, or very close to the star in a stable disc. Using the Faint Object InfraRed CAmera (FORCAST) instrument on board the Stratospheric Observatory for Infrared Astronomy (SOFIA) Telescope, we obtained images of the carbon-rich planetary nebula BD +30° 3639 which trace both carbon-rich polycyclic aromatic hydrocarbons and oxygen-rich silicate dust. With the superior spectral coverage of SOFIA, and using a 3D photoionization and dust radiative transfer model we prove that the O-rich material is distributed in a shell in the outer parts of the nebula, while the C-rich material is located in the inner parts of the nebula. These observations combined with the model, suggest a recent change in stellar surface composition for the double chemistry in this object. This is evidence for dredge-up occurring ~10 3  yr ago.

Description: In this letter, we present results from intranight monitoring in three colours ( BRI ) of the blazar S4 0954+65 during its recent (2015 February) unprecedented high state. We find violent variations on very short time-scales, reaching magnitude change levels of 0.1–0.2 mag  h –1 . On some occasions, changes of ~0.1 mag are observed even within ~10 min. During the night of 2015 February 14, an exponential drop of ~0.7 mag is detected for about 5 h. Cross-correlation between the light curves does not reveal any detectable wavelength-dependent time delays, larger than ~5 min. Colour changes ‘bluer-when-brighter’ are observed on longer time-scales. Possible variability mechanisms to explain the observations are discussed and a preference to the geometrical one is given.