# Identifying and Analysing Protostellar Disc Fragments in Smoothed Particle Hydrodynamics Simulations

## TL;DR

This paper introduces a new density derivative method for identifying protostellar disc fragments in SPH simulations, compares it with an existing method, and analyzes fragment survival and dynamics.

## Contribution

The study develops a novel density derivative technique for detecting disc fragments and demonstrates its effectiveness alongside the CLUMPFIND method in SPH simulations.

## Key findings

- All fragments are detected using the density derivative method.
- Fragments that survive are only detected by the gravitational potential method.
- A tentative relationship between azimuthal wavenumber and maximum semi-major axis is proposed.

## Abstract

We present a new method of identifying protostellar disc fragments in a simulation based on density derivatives, and analyse our data using this and the existing CLUMPFIND method, which is based on an ordered search over all particles in gravitational potential energy. Using smoothed particle hydrodynamics, we carry out 9 simulations of a $0.25$ M$_{\odot}$ disc around a 1 M$_{\odot}$ star, all of which fragment to form at least 2 bound objects. We find that when using all particles ordered in gravitational potential space, only fragments that survive the duration of the simulation are detected. When we use the density derivative method, all fragments are detected, so the two methods are complementary, as using the two methods together allows us to identify all fragments, and to then determine those that are likely to be destroyed. We find a tentative empirical relationship between the dominant azimuthal wavenumber in the disc $m$ and the maximum semi-major axis a fragment may achieve in a simulation, such that $a_{\mathrm{max}}\propto\frac{1}{m}$. We find the fragment destruction rate to be around half that predicted from population synthesis models. This is due to fragment-fragment interactions in the early gas phase of the disc, which can cause scattering and eccentricity pumping on short timescales, and affects the fragment's internal structure. We therefore caution that measurements of eccentricity as a function of semi-major axis may not necessarily constrain the formation mechanism of giant planets and brown dwarfs.