arXiv subjects

Guy Flint

Publications and source records attributed to Guy Flint.

5 recordsLinked to original sources

arXiv2026

An automated method for planetary nebula detection with SIGNALS: first applications to NGC 4214 and NGC 4449

Utilising the optical imaging Fourier transform spectrograph SITELLE, the Star-formation, Ionized Gas and Nebular Abundances Legacy Survey (SIGNALS) is designed to study the connection between star-forming regions and their environments. Targeting $31$ local star-forming galaxies, its data products also lend themselves to planetary nebula (PN) surveys. We present here a new pipeline to find PNe using automated emission-line diagnostics and morphology tests, that is able to distinguish PNe from contaminants with an accuracy similar to that of past visual methods. We also perform thorough completeness tests using mock PNe inserted into the data cubes with full spectra. We apply these tools to a pilot sample of two dwarf irregular galaxies from the SIGNALS survey, NGC 4214 and NGC 4449, with other galaxies to follow. For these two galaxies, we identify $25$ PNe (including $6$ new discoveries) and $23$ PNe (including $13$ new discoveries), respectively, and calculate PN luminosity function distances of $3.09^{+0.25}_{-0.46}$ and $3.91^{+0.33}_{-0.52}$ Mpc, respectively, the latter consistent with previous estimates. We also calculate the bolometric PN specific frequency of our galaxies ($\alpha_\mathrm{bol}$), as well as a newly defined $V$-band PN specific frequency ($\alpha_\mathrm{V}$) based solely on the galaxies' total luminosities in that band.

astro-ph.GA↗

arXiv2026

Extragalactic planetary nebulae -- tracers of kinematics and stellar populations out to 100 Mpc

Extragalactic planetary nebulae (xPNe) in galaxies beyond the Local Universe serve as discrete tracers for studying the element abundances and kinematics of galaxies covering a wide range of morphologies and masses at a variety of angular distances, from the centre well out into their haloes. They are direct stellar probes to identify the galaxy progenitors of haloes and the intracluster light. Even with new facilities, reaching higher angular resolution and sensitivity, xPNe are the only stellar tracers that can be directly and singularly detected and characterised out to 100 Mpc distance, making them crucial for tracing halo and intracluster light assembly. New wide-field spectroscopic instruments at 10+meter-class telescopes will allow the unprecedented characterisation of xPN populations from galaxy centres to their diffuse outskirts. Panoramic integral-field spectroscopy will enable the simultaneous study of xPN and stellar population properties, establishing their use as age- and metallicity-tracers while also improving post-AGB stellar evolution models.

astro-ph.GA↗

arXiv2016

Discretely sampled signals and the rough Hoff process

We introduce a canonical method for transforming a discrete sequential data set into an associated rough path made up of lead-lag increments. In particular, by sampling a $d$-dimensional continuous semimartingale $X:[0,1] \rightarrow \mathbb{R}^d$ at a set of times $D=(t_i)$, we construct a piecewise linear, axis-directed process $X^D: [0,1] \rightarrow\mathbb{R}^{2d}$ comprised of a past and future component. We call such an object the Hoff process associated with the discrete data $\{X_{t}\}_{t_i\in D}$. The Hoff process can be lifted to its natural rough path enhancement and we consider the question of convergence as the sampling frequency increases. We prove that the Itô integral can be recovered from a sequence of random ODEs driven by the components of $X^D$. This is in contrast to the usual Stratonovich integral limit suggested by the classical Wong-Zakai Theorem. Such random ODEs have a natural interpretation in the context of mathematical finance.

math.PR↗

arXiv2016

Wasserstein approximations of the Lévy area random walk via polynomial perturbations of Gaussian distributions

We construct a coupling between the random walk composed of Lévy area increments from a $d$-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used to produce a new pathwise approximation scheme for stochastic differential equations in the preprint [Flint-Lyons-2015]. The coupling arguments of the present paper are based extensively on the recent coupling results of Davie concerning a multidimensional variant of the Komlós-Major-Tusnády theorem and Wasserstein estimates for polynomial perturbations of Gaussian measures.

math.PR↗

arXiv2015

Pathwise approximation of SDEs by coupling piecewise abelian rough paths

We present a new pathwise approximation scheme for stochastic differential equations driven by multidimensional Brownian motion which does not require the simulation of Lévy area and has a Wasserstein convergence rate better than the Euler scheme's strong error rate of $O(\sqrt{h})$, where $h$ is the step-size. By using rough path theory we avoid imposing any non-degenerate Hörmander or ellipticity assumptions on the vector fields of the SDE, in contrast to the similar papers of Alfonsi, Davie, and Malliavin et al. The scheme is based on the log-ODE method with the Lévy area increments replaced by Gaussian approximations with the same covariance structure. The Wasserstein coupling is achieved by making small changes to the argument of Davie, the latter being an extension of the Komlós-Major-Tusnády Theorem. We prove that the convergence of the scheme in the Wasserstein metric is of the order $O(h^{1-2/γ-\varepsilon})$ when the vector fields are $γ$-Lipschitz in the sense of Stein.

math.PR↗