First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise

The aim of this paper is twofold. Firstly, we derive an explicit expression of the (theoretical) solutions of stochastic differential equa- tions with affine coefficients driven by α-stable white noise. This is done by means of Itˆo formula. Secondly, we develop a detection al- gorithm for the first jump time in simulation of sampling trajectories which are described by the solutions. The algorithm is carried out through a multivariate Lagrange interpolation approach. To this end, we utilise a computer simulation algorithm in MATLAB to visualise the sampling trajectories of the jump-diffusions for two combinations of parameters arising in the modelling structure of stochastic differ- ential equations with affine coefficients

The Global Star-Formation Law by Supernova Feedback

We address a simple model where the Kennicutt-Schmidt (KS) relation between the macroscopic densities of star-formation rate (SFR, $\rho_{\rm sfr}$) and gas ($n$) in galactic discs emerges from self-regulation of the SFR via supernova feedback. It arises from the physics of supernova bubbles, insensitive to the microscopic SFR recipe and not explicitly dependent on gravity. The key is that the filling factor of SFR-suppressed supernova bubbles self-regulates to a constant, $f\sim 0.5$. Expressing the bubble fading radius and time in terms of $n$, the filling factor is $f \propto S\,n^{-s}$ with $s\sim 1.5$, where $S$ is the supernova rate density. A constant $f$ thus refers to $\rho_{\rm sfr} \propto n^{1.5}$, with a density-independent SFR efficiency per free-fall time $\sim 0.01$. The self-regulation to $f \sim 0.5$ and the convergence to a KS relation independent of the local SFR recipe are demonstrated in cosmological and isolated-galaxy simulations using different codes and recipes. In parallel, the spherical analysis of bubble evolution is generalized to clustered supernovae, analytically and via simulations, yielding $s \simeq 1.5 \pm 0.5$. An analysis of photo-ionized bubbles about pre-supernova stars yields a range of KS slopes but the KS relation is dominated by the supernova bubbles. Superbubble blowouts may lead to an alternative self-regulation by outflows and recycling. While the model is over-simplified, its simplicity and validity in the simulations may argue that it captures the origin of the KS relation

Constrain the Dark Matter Distribution of Ultra-diffuse Galaxies with Globular-Cluster Mass Segregation: A Case Study with NGC5846-UDG1

The properties of globular clusters (GCs) contain valuable information of their host galaxies and dark-matter halos. In the remarkable example of ultra-diffuse galaxy, NGC5846-UDG1, the GC population exhibits strong radial mass segregation, indicative of dynamical-friction-driven orbital decay, which opens the possibility of using imaging data alone to constrain the dark-matter content of the galaxy. To explore this possibility, we develop a semi-analytical model of GC evolution, which starts from the initial mass function, the initial structure-mass relation, and the initial spatial distribution of the GC progenitors, and follows the effects of dynamical friction, tidal evolution, and two-body relaxation. Using Markov Chain Monte Carlo, we forward-model the GCs in a NGC5846-UDG1-like potential to match the observed GC mass, size, and spatial distributions, and to constrain the profile of the host halo and the origin of the GCs. We find that, with the assumptions of zero mass segregation when the star clusters were born, NGC5846-UDG1 is relatively dark-matter poor compared to what is expected from stellar-to-halo-mass relations, and its halo concentration is lower than the cosmological average, irrespective of having a cuspy or a cored profile. Its GC population has an initial spatial distribution more extended than the smooth stellar distribution. We discuss the results in the context of scaling laws of galaxy-halo connections, and warn against naively using the GC-abundance-halo-mass relation to infer the halo mass of UDGs. Our model is generally applicable to GC-rich dwarf galaxies, and is publicly available at https://github.com/JiangFangzhou/GCevo.Comment: 27 pages, 15 figures, ApJ accepte