arXiv subjects

Andrew Swan

Publications and source records attributed to Andrew Swan.

At least 37 records · Page 2Linked to original sources

arXiv2023

An emerging and enigmatic spectral class of isolated DAe white dwarfs

Two recently discovered white dwarfs, WDJ041246.84$+$754942.26 and WDJ165335.21$-$100116.33, exhibit H$α$ and H$β$ Balmer line emission similar to stars in the emerging DAHe class, yet intriguingly have not been found to have detectable magnetic fields. These white dwarfs are assigned the spectral type DAe. We present detailed follow-up of the two known DAe stars using new time-domain spectroscopic observations and analysis of the latest photometric time-series data from TESS and ZTF. We measure the upper magnetic field strength limit of both stars as $B < 0.05$ MG. The DAe white dwarfs exhibit photometric and spectroscopic variability, where in the case of WDJ041246.84$+$754942.26 the strength of the H$α$ and H$β$ emission cores varies in anti-phase with its photometric variability over the spin period, which is the same phase relationship seen in DAHe stars. The DAe white dwarfs closely cluster in one region of the Gaia Hertzsprung-Russell diagram together with the DAHe stars. We discuss current theories on non-magnetic and magnetic mechanisms which could explain the characteristics observed in DAe white dwarfs, but additional data are required to unambiguously determine the origin of these stars.

astro-ph.SR↗

arXiv2022

The SNIa Runaway LP 398-9: Detection of Circumstellar Material and Surface Rotation

A promising progenitor scenario for Type Ia supernovae (SNeIa) is the thermonuclear detonation of a white dwarf in a close binary system with another white dwarf. After the primary star explodes, the surviving donor can be spontaneously released as a hypervelocity runaway. One such runaway donor candidate is LP 398-9, whose orbital trajectory traces back $\approx 10^5$ years to a known supernova remnant. Here we report the discovery of carbon-rich circumstellar material around LP 398-9, revealed by a strong infrared excess and analyzed with follow-up spectroscopy. The circumstellar material is most plausibly composed of inflated layers from the star itself, mechanically and radioactively heated by the past companion's supernova. We also detect a 15.4 hr periodic signal in the UV and optical light curves of LP 398-9, which we interpret as surface rotation. The rotation rate is consistent with theoretical predictions from this supernova mechanism, and the brightness variations could originate from surface inhomogeneity deposited by the supernova itself. Our observations strengthen the case for this double-degenerate SNIa progenitor channel, and motivate the search for more runaway SNIa donors.

astro-ph.SR↗

arXiv2021

A class of higher inductive types in Zermelo-Fraenkel set theory

We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo-Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class includes the example of unordered trees of any arity.

math.LO↗

arXiv2021

Collisions in a gas-rich white dwarf planetary debris disc

WD 0145+234 is a white dwarf that is accreting metals from a circumstellar disc of planetary material. It has exhibited a substantial and sustained increase in 3-5 micron flux since 2018. Follow-up Spitzer photometry reveals that emission from the disc had begun to decrease by late 2019. Stochastic brightening events superimposed on the decline in brightness suggest the liberation of dust during collisional evolution of the circumstellar solids. A simple model is used to show that the observations are indeed consistent with ongoing collisions. Rare emission lines from circumstellar gas have been detected at this system, supporting the emerging picture of white dwarf debris discs as sites of collisional gas and dust production.

astro-ph.EP↗

arXiv2021

A CHEOPS White Dwarf Transit Search

White dwarf spectroscopy shows that nearly half of white dwarf atmospheres contain metals that must have been accreted from planetary material that survived the red giant phases of stellar evolution. We can use metal pollution in white dwarf atmospheres as flags, signalling recent accretion, in order to prioritize an efficient sample of white dwarfs to search for transiting material. We present a search for planetesimals orbiting six nearby white dwarfs with the CHEOPS spacecraft. The targets are relatively faint for CHEOPS, $11$ mag $< G < 12.8$ mag. We use aperture photometry data products from the CHEOPS mission as well as custom PSF photometry to search for periodic variations in flux due to transiting planetesimals. We detect no significant variations in flux that cannot be attributed to spacecraft systematics, despite reaching a photometric precision of $<2$ ppt in 60 s exposures on each target. We simulate observations to show that the small survey is sensitive primarily to Moon-sized transiting objects with periods $3$ hr $< P < 10$ hr, with radii $R \gtrsim 1000$ km.

astro-ph.EP↗

arXiv2021

8.9-hr Rotation in the Partly Burnt Runaway Stellar Remnant LP 40-365 (GD 492)

We report the detection of 8.914-hr variability in both optical and ultraviolet light curves of LP 40-365 (also known as GD 492), the prototype for a class of partly burnt runaway stars that have been ejected from a binary due to a thermonuclear supernova event. We first detected this 1.0% amplitude variation in optical photometry collected by the Transiting Exoplanet Survey Satellite. Re-analysis of observations from the Hubble Space Telescope at the TESS period and ephemeris reveal a 5.8% variation in the ultraviolet of this 9800 K stellar remnant. We propose that this 8.914-hr photometric variation reveals the current surface rotation rate of LP 40-365, and is caused by some kind of surface inhomogeneity rotating in and out of view, though a lack of observed Zeeman splitting puts an upper limit on the magnetic field of <20 kG. We explore ways in which the present rotation period can constrain progenitor scenarios if angular momentum was mostly conserved, which suggests that the survivor LP 40-365 was not the donor star but was most likely the bound remnant of a mostly disrupted white dwarf that underwent advanced burning from an underluminous (Type Iax) supernova.

astro-ph.SR↗

arXiv2020

Random spanning forests and hyperbolic symmetry

We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter $β>0$ per edge. This is called the arboreal gas model, and the special case when $β=1$ is the uniform forest model. The arboreal gas can equivalently be defined to be Bernoulli bond percolation with parameter $p=β/(1+β)$ conditioned to be acyclic, or as the limit $q\to 0$ with $p=βq$ of the random cluster model. It is known that on the complete graph $K_{N}$ with $β=α/N$ there is a phase transition similar to that of the Erdős--Rényi random graph: a giant tree percolates for $α> 1$ and all trees have bounded size for $α<1$. In contrast to this, by exploiting an exact relationship between the arboreal gas and a supersymmetric sigma model with hyperbolic target space, we show that the forest constraint is significant in two dimensions: trees do not percolate on $\mathbb{Z}^2$ for any finite $β>0$. This result is a consequence of a Mermin--Wagner theorem associated to the hyperbolic symmetry of the sigma model. Our proof makes use of two main ingredients: techniques previously developed for hyperbolic sigma models related to linearly reinforced random walks and a version of the principle of dimensional reduction.

math.PR↗

arXiv2020

White dwarf pollution by hydrated planetary remnants: Hydrogen and Metals in WD J204713.76-125908.9

WD J204713.76-125908.9 is a new addition to the small class of white dwarfs with helium-dominated photospheres that exhibit strong Balmer absorption lines and atmospheric metal pollution. The exceptional abundances of hydrogen observed in these stars may be the result of accretion of water-rich rocky bodies. We obtained far-ultraviolet and optical spectroscopy of WD J204713.76-125908.9 using the Cosmic Origin Spectrograph on-board the Hubble Space Telescope and X-shooter on the Very Large Telescope, and identify photospheric absorption lines of nine metals: C, O, Mg, Si, P, S, Ca, Fe and Ni. The abundance ratios are consistent with the steady state accretion of exo-planetesimal debris rich in the volatile elements carbon and oxygen, and the transitional element sulphur, by factors of seventeen, two, and four respectively compared to bulk Earth. The parent body has a composition akin to Solar System carbonaceous chondrites, and the inferred minimum mass, $1.6 \times 10^{20}$ g, is comparable to an asteroid 23 km in radius. We model the composition of the disrupted parent body, finding from our simulations a median water mass fraction of eight per cent.

astro-ph.EP↗

arXiv2020

The geometry of random walk isomorphism theorems

The classical random walk isomorphism theorems relate the local times of a continuous-time random walk to the square of a Gaussian free field. A Gaussian free field is a spin system that takes values in Euclidean space, and this article generalises the classical isomorphism theorems to spin systems taking values in hyperbolic and spherical geometries. The corresponding random walks are no longer Markovian: they are the vertex-reinforced and vertex-diminished jump processes. We also investigate supersymmetric versions of these formulas. Our proofs are based on exploiting the continuous symmetries of the corresponding spin systems. The classical isomorphism theorems use the translation symmetry of Euclidean space, while in hyperbolic and spherical geometries the relevant symmetries are Lorentz boosts and rotations, respectively. These very short proofs are new even in the Euclidean case. Isomorphism theorems are useful tools, and to illustrate this we present several applications. These include simple proofs of exponential decay for spin system correlations, exact formulas for the resolvents of the joint processes of random walks together with their local times, and a new derivation of the Sabot--Tarrès formula for the limiting local time of the vertex-reinforced jump process.

math.PR↗

arXiv2020

The dust never settles: collisional production of gas and dust in evolved planetary systems

Multi-epoch infrared photometry from Spitzer is used to monitor circumstellar discs at white dwarfs, which are consistent with disrupted minor planets whose debris is accreted and chemically reflected by their host stars. Widespread infrared variability is found across the population of 37 stars with two or more epochs. Larger flux changes occur on longer time-scales, reaching several tens of per cent over baselines of a few years. The canonical model of a geometrically thin, optically thick disc is thus insufficient, as it cannot give rise to the observed behaviour. Optically thin dust best accounts for the variability, where collisions drive dust production and destruction. Notably, the highest infrared variations are seen in systems that show Ca II emission, supporting planetesimal collisions for all known debris discs, with the most energetic occurring in those with detected gaseous debris. The sample includes the only polluted white dwarf with a circumbinary disc, where the signal of the day-night cycle of its irradiated substellar companion appears diluted by dust emission.

astro-ph.SR↗

arXiv2019

The Magnetorotational Instability Prefers Three Dimensions

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilises a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disk theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, $S$, is near the two-dimensional onset value, $S_c$. For a Keplerian shear, three-dimensional modes are unstable above $S\approx0.10S_c$, and dominate the two-dimensional modes until $S\approx2.05S_{c}$. These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remain well past $2.05S_{c}$. These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, like stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

physics.plasm-ph↗

arXiv2019

Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process

We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The first is a direct connection between the VRJP and sigma models whose target space is a hyperbolic space $\mathbb{H}^n$ or its supersymmetric counterpart $\mathbb{H}^{2|2}$. These results are analogues of well-known relations between the Gaussian free field and the local times of simple random walk. The second ingredient is a Mermin--Wagner theorem for these sigma models. This result is of intrinsic interest for the sigma models and also implies our main theorem on the VRJP. Surprisingly, our Mermin--Wagner theorem applies even though the symmetry groups of $\mathbb{H}^n$ and $\mathbb{H}^{2|2}$ are non-amenable.

math-ph↗

arXiv2019

Analyticity for rapidly determined properties of Poisson Galton--Watson trees

Let $T_λ$ be a Galton--Watson tree with Poisson($λ$) offspring, and let $A$ be a tree property. In this paper, are concerned with the regularity of the function $\mathbb{P}_λ(A):= \mathbb{P}(T_λ\vdash A)$. We show that if a property $A$ can be uniformly approximated by a sequence of properties $A_k$, depending only on the first $k$ vertices in the breadth first exploration of the tree, with a bound in probability of $\mathbb{P}_λ(A\triangle A_k) \le Ce^{-ck}$ over an interval $I = (λ_0, λ_1)$, then $\mathbb{P}_λ(A)$ is real analytic in $λ$ for $λ\in I$. We also present some applications of our results, particularly to properties that are not expressible in the first order language of trees.

math.PR↗

arXiv2019

Interpretation and diversity of exoplanetary material orbiting white dwarfs

Nine metal-polluted white dwarfs are observed with medium-resolution optical spectroscopy,where photospheric abundances are determined and interpreted through comparison against solar system objects. An improved method of making such comparisons is presented that overcomes potential weaknesses of prior analyses, with the numerous sources of error considered to highlight the limitations on interpretation. The stars are inferred to be accreting rocky, volatile-poor asteroidal materials with origins in differentiated bodies, in line with the consensus model. The most heavily polluted star in the sample has 14 metals detected, and appears to be accreting material from a rocky planetesimal, whose composition is mantle-like with a small Fe-Ni core component. Some unusual abundances are present: one star is strongly depleted in Ca, while two others show Na abundances elevated above bulk Earth, speculated either to reflect diversity in the formation conditions of the source material, or to be traces of past accretion events. Another star shows clear signs that accretion ceased around 5 Myr ago,causing Mg to dominate the photospheric abundances, as it has the longest diffusion time of the observed elements. Observing such post-accretion systems allows constraints to be placed on models of the accretion process.

astro-ph.EP↗

arXiv2019

Every metric space is separable in function realizability

We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with synthetic topology, every $T_0$-space is separable and every discrete space is countable. It follows that intuitionistic logic does not show the existence of a non-separable metric space, or an uncountable set with decidable equality, even if we assume principles that are validated by function realizability, such as Dependent and Function choice, Markov's principle, and Brouwer's continuity and fan principles.

math.LO↗

arXiv2019

On Church's Thesis in Cubical Assemblies

We show that Church's thesis, the axiom stating that all functions on the naturals are computable, does not hold in the cubical assemblies model of cubical type theory. We show that nevertheless Church's thesis is consistent with univalent type theory by constructing a reflective subuniverse of cubical assemblies where it holds.

math.LO↗

arXiv2019

Astro 2020 Science White Paper: Evolved Planetary Systems around White Dwarfs

Practically all known planet hosts will evolve into white dwarfs, and large parts of their planetary systems will survive this transition - the same is true for the solar system beyond the orbit of Mars. Spectroscopy of white dwarfs accreting planetary debris provides the most accurate insight into the bulk composition of exo-planets. Ground-based spectroscopic surveys of ~260, 000 white dwarfs detected with Gaia will identify >1000 evolved planetary systems, and high-throughput high-resolution space-based ultraviolet spectroscopy is essential to measure in detail their abundances. So far, evidence for two planetesimals orbiting closely around white dwarfs has been obtained, and their study provides important constraints on the composition and internal structure of these bodies. Major photometric and spectroscopic efforts will be necessary to assemble a sample of such close-in planetesimals that is sufficiently large to establish their properties as a population, and to deduce the architectures of the outer planetary systems from where they originated. Mid-infrared spectroscopy of the dusty disks will provide detailed mineralogical information of the debris, which, in combination with the elemental abundances measured from the white dwarf spectroscopy, will enable detailed physical modelling of the chemical, thermodynamic, and physical history of the accreted material. Flexible multi-epoch infrared observations are essential to determine the physical nature, and origin of the variability observed in many of the dusty disks. Finally, the direct detection of the outer reservoirs feeding material to the white dwarfs will require sensitive mid- and far-infrared capabilities.

astro-ph.EP↗

arXiv2019

The unbiased frequency of planetary signatures around single and binary white dwarfs using ${\it Spitzer}$ and ${\it Hubble}$

This paper presents combined ${\it Spitzer}$ IRAC and ${\it Hubble}$ COS results for a double-blind survey of 195 single and 22 wide binary white dwarfs for infrared excesses and atmospheric metals. The selection criteria include cooling ages in the range 9 to 300 Myr, and hydrogen-rich atmospheres so that the presence of atmospheric metals can be confidently linked to ongoing accretion from a circumstellar disc. The entire sample has infrared photometry, whereas 168 targets have corresponding ultraviolet spectra. Three stars with infrared excesses due to debris discs are recovered, yielding a nominal frequency of $1.5_{-0.5}^{+1.5}$ per cent, while in stark contrast, the fraction of stars with atmospheric metals is $45\pm4$ per cent. Thus, only one out of 30 polluted white dwarfs exhibits an infrared excess at 3-4 $μ$m in IRAC photometry, which reinforces the fact that atmospheric metal pollution is the most sensitive tracer of white dwarf planetary systems. The corresponding fraction of infrared excesses around white dwarfs with wide binary companions is consistent with zero, using both the infrared survey data and an independent assessment of potential binarity for well-established dusty and polluted stars. In contrast, the frequency of atmospheric pollution among the targets in wide binaries is indistinct from apparently single stars, and moreover the multiplicity of polluted white dwarfs in a complete and volume-limited sample is the same as for field stars. Therefore, it appears that the delivery of planetesimal material onto white dwarfs is ultimately not driven by stellar companions, but by the dynamics of planetary bodies.

astro-ph.EP↗