arXiv subjects

Thomas Prince

Publications and source records attributed to Thomas Prince.

At least 19 recordsLinked to original sources

arXiv2026

The Physics of Mass Transfer in Substellar and Low-Mass Binaries

Several dozen binary ultracool and brown dwarf systems have been identified to date. These systems represent valuable probes of star and planet formation at the lowest mass scales. To date, the study of these ultracool binaries has been constrained to the non-interacting case. In this paper, we investigate the dynamics, stability, and evolution of mass transferring ultracool binaries using numerical simulations with accepted equations of state for brown dwarfs. We find that there exists a donor mass inversion, above which the donor dwarf is more massive than the accretor, but below which the accretor is more massive than the donor. Below the hydrogen burning limit, objects with mass ratios $q \sim 1$ are unstable, but slight deviations from this mass ratio are stable at the onset of mass transfer and remain stable throughout extended periods. We compute theoretical mass transfer rates using several angular momentum loss prescriptions and predict lifespans of $\sim 100$ Myrs. We predict that all mass transferring ultracool binaries are tidally locked and possess orbital periods ranging from just under $1$ hour to $3.5$ hours. We find that mass transfer proceeds via direct impact onto the accretor forming a UV or optically bright hotspot on the surface of the accretor.

astro-ph.SR↗

arXiv2026

A Mass Transferring Brown Dwarf Binary on a 57 Minute Orbit

Mass transfer in stellar binaries has been well studied in most stellar mass ranges, with the notable exception of ultracool stars and substellar brown dwarfs. We report the discovery of ZTF J1239+8347 with the Zwicky Transient Facility (ZTF), a brown dwarf binary currently undergoing stable mass transfer with an orbital period of 57.41 minutes. Optical time-series photometry reveals an extremely high amplitude ($> 2$ magnitude peak-to-trough) variability at short wavelengths indicative of an orbiting hot spot slightly buried inside the atmosphere of the accretor. We use parallax measurements from \textit{Gaia} along with optical and near infrared spectra to infer an accretion temperature of $T_\mathrm{eff} = 8904 \pm 54$ K, an atmospheric temperature of the accretor of $T_\mathrm{atmo} \approx 1500$ K, and a slightly inflated accretor radius of $R_{\rm acc} = 1.20^{+0.15}_{-0.11} \, \RJup$. ZTF J1239+8347 is a direct impact accretor, typically only seen in double degenerate white dwarf binaries, which are approximately a million times denser than the components in ZTF J1239+8347. The existence of an accreting brown dwarf binary suggests that angular momentum loss can be strong enough to make ultracool binaries interact in a Hubble time. The observed faintness ($\sim 20$ mag) and relative proximity ($\approx 300$ pc) of ZTF J1239+8347 suggests that many similar systems are likely to be found by the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST).

astro-ph.SR↗

arXiv2025

Circumstellar interaction in the extreme white dwarf merger remnant ZTF\,J1901+1458: A new class of white dwarf merger remnants with X-ray emission

Double degenerate white dwarf (WD) mergers can exhibit extreme magnetic fields exceeding $10^{8}$ G and rapid rotation, but their spectral-energy distributions and high-energy emission mechanisms remain poorly characterised. ZTF J1901+1458 stands out as the most compact and strongly magnetised object discovered in this class to date. Recent Chandra observations have revealed that the white dwarf is also a source of soft X-ray emission, inconsistent with a photospheric origin. We analyse new phase resolved UV spectroscopy from the HST combined with optical and near-infrared photometry and spectroscopy, with newly developed magnetic atmosphere models to determine its effective temperature, radius, mass, average surface magnetic field strength, and cooling age. Our results demonstrate that the spectral break at $\approx$3000 {\AA}, observed in several highly magnetised WDs, is well-reproduced by our new models, which take into account the effect of magnetic opacities on the structure of the atmosphere. Our best-fit parameters for the WD yield an effective temperature ($T_{\rm{eff}}=28,015\pm 20$ K) and larger radius ($2630\pm10$ km) than previously reported. Furthermore, the near-infrared data exclude the presence of a stellar or brown dwarf companion hotter than $\approx$700 K. We also jointly analyse the previously published Chandra data and new XMM-Newton X-ray spectra. The faint X-ray emission, $L_X =(1.3\pm0.2)\times10^{27}$ erg/s is very soft and highly pulsed on the rotation period of the WD. We suggest that the X-rays are powered by accretion or via the interaction of the WD magnetosphere with CSM. If the rapidly rotating magnetic field could power a weak wind along open field lines, material could be extracted directly from the surface of the WD. Alternatively, accretion of fallback material from the merger or the tidal disruption of a planetary body are possible sources of CSM.

astro-ph.SR↗

arXiv2025

A half-ring of ionized circumstellar material trapped in the magnetosphere of a white dwarf merger remnant

Many white dwarfs are observed in compact double white dwarf binaries and, through the emission of gravitational waves, a large fraction are destined to merge. The merger remnants that do not explode in a Type Ia supernova are expected to initially be rapidly rotating and highly magnetized. We here present our discovery of the variable white dwarf ZTF J200832.79+444939.67, hereafter ZTF J2008+4449, as a likely merger remnant showing signs of circumstellar material without a stellar or substellar companion. The nature of ZTF J2008+4449 as a merger remnant is supported by its physical properties: hot ($35,500\pm300$ K) and massive ($1.12\pm0.03$ M$_\odot$), the white dwarf is rapidly rotating with a period of $\approx$ 6.6 minutes and likely possesses exceptionally strong magnetic fields ($\sim$ 400-600 MG) at its surface. Remarkably, we detect a significant period derivative of $(1.80\pm0.09)\times10^{-12}$ s/s, indicating that the white dwarf is spinning down, and a soft X-ray emission that is inconsistent with photospheric emission. As the presence of a mass-transferring stellar or brown dwarf companion is excluded by infrared photometry, the detected spin down and X-ray emission could be tell-tale signs of a magnetically driven wind or of interaction with circumstellar material, possibly originating from the fallback of gravitationally bound merger ejecta or from the tidal disruption of a planetary object. We also detect Balmer emission, which requires the presence of ionized hydrogen in the vicinity of the white dwarf, showing Doppler shifts as high as $\approx$ 2000 km s$^{-1}$. The unusual variability of the Balmer emission on the spin period of the white dwarf is consistent with the trapping of a half ring of ionised gas in the magnetosphere of the white dwarf.

astro-ph.SR↗

arXiv2025

Deep learning to improve the discovery of near-Earth asteroids in the Zwicky Transient Facility

We present a novel pipeline that uses a convolutional neural network (CNN) to improve the detection capability of near-Earth asteroids (NEAs) in the context of planetary defense. Our work aims to minimize the dependency on human intervention of the current approach adopted by the Zwicky Transient Facility (ZTF). The target NEAs have a high proper motion of up to tens of degrees per day and thus appear as streaks of light in the images. We trained our CNNs to detect these streaks using three datasets: a set with real asteroid streaks, a set with synthetic (i.e., simulated) streaks and a mixed set, and tested the resultant models on real survey images. The results achieved were almost identical across the three models: $0.843\pm0.005$ in completeness and $0.820\pm0.025$ in precision. The bias on streak measurements reported by the CNNs was $1.84\pm0.03$ pixels in streak position, $0.817\pm0.026$ degrees in streak angle and $-0.048\pm0.003$ in fractional bias in streak length (computed as the absolute length bias over the streak length, with the negative sign indicating an underestimation). We compared the performance of our CNN trained with a mix of synthetic and real streaks to that of the ZTF human scanners by analyzing a set of 317 streaks flagged as valid by the scanners. Our pipeline detected $80~\%$ of the streaks found by the scanners and 697 additional streaks that were subsequently verified by the scanners to be valid streaks. These results suggest that our automated pipeline can complement the work of the human scanners at no cost for the precision and find more objects than the current approach. They also prove that the synthetic streaks were realistic enough to be used for augmenting training sets when insufficient real streaks are available or exploring the simulation of streaks with unusual characteristics that have not yet been detected.

astro-ph.IM↗

arXiv2024

The Birational Geometry of Ceva's Theorem

In this article we study Ceva's theorem and its higher-dimensional extensions from the perspective of algebraic and projective geometry. First, we situate the theorem within the study of algebraic surfaces by relating it to the defining equation of a del Pezzo surface of degree six inside the product of three projective lines. Second, by interpreting (higher-dimensional analogues of) Ceva's theorem in terms of projections from projective spaces, we recast these results as matrix completion problems. We use these ideas to offer proofs of some higher-dimensional analogues of Ceva's theorem. This article is written with a nonspecialist audience in mind and we hope that some useful context is provided in the form of remarks in the sections on surfaces for students of algebraic geometry.

math.AG↗

arXiv2020

Mutation equivalence of toric Landau-Ginzburg models

Given a Fano complete intersection defined by sections of a collection nef line bundles $L_1,\ldots, L_c$ on a Fano toric manifold $Y$, a construction of Givental/Hori-Vafa provides a mirror-dual Landau-Ginzburg model. This construction depends on a choice of suitable nef partition; that is, a partition of the rays of the fan determined by $Y$. We show that toric Landau-Ginzburg models constructed from different nef partitions representing the same complete intersection are related by a volume preserving birational map. In particular, various Laurent polynomial mirrors which may be obtained from these Landau-Ginzburg models are mutation equivalent.

math.AG↗

arXiv2020

On the cohomology groups of real Lagrangians in Calabi-Yau threefolds

The quintic threefold $X$ is the most studied Calabi-Yau $3$-fold in the mathematics literature. In this paper, using \v{C}ech-to-derived spectral sequences, we investigate the mod $2$ and integral cohomology groups of a real Lagrangian $\breve{L}_{\mathbb{R}}$, obtained as the fixed locus of an anti-symplectic involution in the mirror to $X$. We show that $\breve{L}_{\mathbb{R}}$ is the disjoint union of a $3$-sphere and a rational homology sphere. Analysing the mod $2$ cohomology further, we deduce a correspondence between the mod $2$ Betti numbers of $\breve{L}_{\mathbb{R}}$ and certain counts of integral points on the base of a singular torus fibration on $X$. By work of Batyrev, this identifies the mod $2$ Betti numbers of $\breve{L}_{\mathbb{R}}$ with certain Hodge numbers of $X$. Furthermore, we show that the integral cohomology groups $H^j(\breve{L}_{\mathbb{R}},\mathbb{Z})$ of $\breve{L}_{\mathbb{R}}$ are $2$-primary for $j \neq 0,3$; we conjecture that this holds in much greater generality.

math.AG↗

arXiv2019

Smoothing Calabi-Yau toric hypersurfaces using the Gross-Siebert algorithm

We explain how to form a novel dataset of simply connected Calabi-Yau threefolds via the Gross-Siebert algorithm. We expect these to degenerate to Calabi-Yau toric hypersurfaces with certain Gorenstein (not necessarily isolated) singularities. In particular, we explain how to `smooth the boundary' of a class of $4$-dimensional reflexive polytopes to obtain a polarised tropical manifolds. We compute topological invariants of a compactified torus fibration over each such tropical manifold, expected to be homotopy equivalent to the general fibre of the Gross-Siebert smoothing. We consider a family of examples related to the joins of elliptic curves. Among these we find $14$ topological types with $b_2=1$ which do not appear in existing lists of known rank one Calabi-Yau threefolds.

math.AG↗

arXiv2019

Real Lagrangians in Calabi-Yau Threefolds

We compute the mod $2$ cohomology groups of real Lagrangians in Calabi-Yau threefolds using well-behaved torus fibrations constructed by Gross. To do this we study a long exact sequence introduced by Casta\~{n}o-Bernard and Matessi, which relates the cohomology of the Lagrangians to the cohomology of the Calabi-Yau. We show that the connecting homomorphism in this sequence is given by the map squaring divisor classes in the mirror Calabi-Yau.

math.AG↗

arXiv2019

From Cracked Polytopes to Fano Threefolds

We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms a set of unimodular polytopes - using Laurent inversion; a method developed jointly with Coates-Kasprzyk. We also give constructions of rank one Fano threefolds from cracked polytopes, following work of Christophersen-Ilten and Galkin. We explore the problem of classifying polytopes cracked along a given fan in three dimensions, and classify the unimodular polytopes which can occur as 'pieces' of a cracked polytope.

math.AG↗

arXiv2018

Polygons of Finite Mutation Type

We classify Fano polygons with finite mutation class. This classification exploits a correspondence between Fano polygons and cluster algebras, refining the notion of singularity content due to Akhtar and Kasprzyk. We also introduce examples of cluster algebras associated to Fano polytopes in dimensions greater than two.

math.AG↗

arXiv2018

Cracked Polytopes and Fano Toric Complete Intersections

We introduce the notion of cracked polytope, and - making use of joint work with Coates and Kasprzyk - construct the associated toric variety $X$ as a subvariety of a non-singular toric variety $Y$ under certain conditions. Restricting to the case in which this subvariety is a complete intersection, we present a sufficient condition for a smoothing of $X$ to exist inside $Y$. We exhibit a relative anti-canonical divisor for this smoothing of $X$, and show that the general member is simple normal crossings.

math.AG↗

arXiv2018

A Note on Schoen's Calabi--Yau Threefolds

We study the topology of a real Lagrangian in Schoen's Calabi--Yau threefold $X$ and compute its mod $2$ cohomology using two methods; first via a concrete Mayer--Vietoris calculation, then by an exact sequence relating the mod $2$ cohomology of the real Lagrangian to the cohomology of $X$. We conclude that these two methods agree. This in particular corrects a previous computation made by Casta\~{n}o-Bernard--Matessi.

math.GT↗

arXiv2018

Lagrangian torus fibration models of Fano threefolds

Inspired by the work of Gross on topological Mirror Symmetry we construct candidate Lagrangian torus fibration models for the 105 families of smooth Fano threefolds. We prove, in the case the second Betti number is one, that the total space of each fibration is homeomorphic to the expected Fano threefold, and show that the numerical invariants coincide for all 105. Our construction relies on a notion of toric degeneration for affine manifolds with singularities, and the correspondence we obtain between polytopes and Fano manifolds is compatible with that appearing in the work of Coates-Corti-Kasprzyk et al. on Mirror Symmetry for Fano manifolds.

math.GT↗

arXiv2017

Del Pezzo surfaces with a single 1/k(1,1) singularity

Inspired by the recent progress by Coates-Corti-Kasprzyk et al. on Mirror Symmetry for del Pezzo surfaces, we show that for any positive integer k the deformation families of del Pezzo surfaces with a single 1/k(1,1) singularity (and no other singular points) fit into a single cascade. Additionally we construct models and toric degenerations of these surfaces embedded in toric varieties in codimension less than or equal two. Several of these directly generalise constructions of Reid-Suzuki (in the case k=3). We identify a root system in the Picard lattice, and in light of the work of Gross-Hacking-Keel, comment on Mirror Symmetry for each of these surfaces. Finally we classify all del Pezzo surfaces with certain combinations of 1/k(1,1) singularities for k=3,5,6 which admit a toric degeneration.

math.AG↗

arXiv2017

Laurent Inversion

We describe a practical and effective method for reconstructing the deformation class of a Fano manifold X from a Laurent polynomial f that corresponds to X under Mirror Symmetry. We explore connections to nef partitions, the smoothing of singular toric varieties, and the construction of embeddings of one (possibly-singular) toric variety in another. In particular, we construct degenerations from Fano manifolds to singular toric varieties; in the toric complete intersection case, these degenerations were constructed previously by Doran--Harder. We use our method to find models of orbifold del Pezzo surfaces as complete intersections and degeneracy loci, and to construct a new four-dimensional Fano manifold.

math.AG↗

arXiv2017

The Tropical Superpotential For $\mathbb{P}^2$

We present an extended worked example of the computation of the tropical superpotential considered by Carl--Pumperla--Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve, and calculate the wall and chamber decomposition determined by the Gross--Siebert algorithm. Using the results of Carl--Pumperla--Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, which we demonstrate to be identical to the Laurent polynomials predicted by Coates--Corti--Galkin--Golyshev--Kaspzryk to be mirror to $\mathbb{P}^2$.

math.AG↗