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Observatoire Astronomique de Strasbourg - UMR 7550
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67000 Strasbourg



simon.rozier@-Code to remove to avoid
03 68 85 24 99, bureau E29

Post-doctoral researcher among the GALHECOS team, my work focuses on theoretical aspects related to the way stellar systems react to external perturbations.


Stability of rotating spherical models

Growth rate of linear instabilities in spherical stellar clusters as a function of anisotropy (q) and rotation (α). The blue plane represents a region where no instabilities were detected. The elongated dark surface on the bottom right is the region of rotationally enhanced radial orbit instability. There, the cluster is radially biased (q>0), and the instability is enhanced by rotation (increasing α). The large orange surface on the top corresponds to the region of violent instability in tangentially anisotropic (q<0), fast rotators (α>0.5). This surface is a discovery of our work. Extracted from Rozier et al., 2019.

I did my PhD in Institut d’astrophysique de Paris between September 2017 and September 2020, under the joint supervision of Prof. Christophe Pichon and Dr. Jean-Baptiste Fouvry. There, I developed and implemented an analytical method to detect linear instabilities in spherical stellar systems. More specifically, I adapted Kalnajs’ matrix method (Kalnajs 1976) to the case of anisotropic, rotating globular clusters. Thanks to this new algorithm, I was able to determine the stability or instability of more than 1000 models of globular clusters, with varying degree of velocity anisotropy (radial and tangential), as well as different amounts of global angular momentum (net rotation). These results were confirmed by a positive comparison with dedicated N-body simulations, in collaboration with Dr. P. G. Breen, Dr A. L. Varri and Prof. D. C. Heggie from the University of Edinburgh and the Royal Observatory of Edinburgh (Rozier et al., 2019, see the figure on the right). While this study highlighted a regime of radial orbit instability, enhanced by the system’s rotation, we discovered another regime of dramatic instabilities in tangentially anisotropic, rotating systems. My subsequent work was largely focused on answering the tricky question of identifying specific processes responsible for these instabilities.

So, we followed up this collaborative work, using both the matrix method and N-body simulations to identify specific processes responsible for the instabilities of tangentially anisotropic, rotating spheres (Breen et al., 2021). The complementarity of the analytical and numerical methods allowed us to track down these processes on two separate lines: on the one hand, we used different series of N-body simulations to identify spatial regions in the cluster (in terms of inclination of the orbit and proximity to the centre) which were determinant in the destabilisation process. On the other hand, the matrix method informed us on the relevant resonances which interact in setting these instabilities. In the end, we were able to state that (i) the destabilisation process in these systems is much more intricate than for the radial orbit instability, (ii) it involves interactions between particles at different locations in the cluster – mainly high-inclination orbits close to the centre with low-inclination ones further away -, and (iii) it involves several resonant processes – mainly the inner Lindblad resonance leading to the circular orbit instability, and the tumbling resonance leading to the tumbling instability.


Secular relaxation of spherical clusters

By the end of my PhD, I got involved in an analytical and numerical study of the secular, collisional relaxation of globular clusters (Fouvry et al., 2021). The aim of this work was to compare the ability of two different theoretical frameworks to describe the long-term evolution of spherical stellar systems: the Chandrasekhar formalism (Chandrasekhar, 1943), and the Balescu-Lenard equation (Heyvaerts, 2010; Chavanis, 2012). The former theory is non-resonant, as it assumes that the cluster secularly evolves from the accumulation of single velocity kicks exerted on each star by all the other stars in the cluster, without considering neither the large scale correlations nor the very regular motion of the stars. Yet, it is rather easy to deal with numerically, and widely used in the astrophysical community. The latter theory incorporates more of the specific characteristics of a stellar system: (i) it takes into account the system’s inhomogeneity; (ii) it considers the stars as orbits, which can have correlated motion and can resonate; (iii) it includes the possibility of large scale effects, which can strongly impact the cluster’s evolution. In both theories, we extracted the predicted evolution of the action space distribution function of the cluster, and compared these predictions to measurements we performed in direct N-body simulations. The main result is shown in the figure below: while the resonant theory is more accurate at reproducing simulations results, both theories are globally consistent with each other. This implies that the new ingredients taken into account in the resonant theory (large scale, correlated and resonant effects) have a small contribution to the relaxation in the cluster we studied.

Variation of the action space distribution function predicted by the non-resonant (left) and resonant (right) theories, and measured in collisional N-body simulations (centre). Although both theories are qualitatively consistent with the simulations, the resonant one seems to reproduce them more closely.


Response of the Milky Way halo to the sinking Large Magellanic Cloud

Density response of the Milky Way dark matter halo to the LMC, obtained by a 2Gyr-long perturbation of the Milky Way by the LMC on its orbit with the matrix method. The Milky Way is represented by the full black circle, while the LMC in its current position is in dotted black style. The over/underdensities peak at the +60%/-40% level. The matrix method quantitatively reproduces the results from N-body simulations.

In October 2020, I moved to Strasbourg, where I started implementing a new matrix method to compute the time evolution a stellar system when perturbed by an external gravitational potential. I applied this new method to the case of the Milky Way dark matter and stellar halo perturbed by the infall of the Large Magellanic Cloud. I am currently collaborating with researchers in Strasbourg (B. Famaey, A. Siebert, G. Monari) to try and constrain the characteristics of the merger (mass of the LMC, anisotropy of the stellar halo) based on the recent observations by Conroy et al., 2021. For now, the method successfully reproduced the results from state-of-the-art N-body simulations by Garavito-Camargo et al., 2019 (see image on the right). The critical interest of the matrix method is its extreme numerical efficiency as compared to that of numerical simulations. For comparison, the image on the right was obtained by a 1 hour-long computation on a single CPU machine, while N-body simulations designed for this purpose can often take days on multiple GPU machines to perform. An article is in preparation on that topic, and will soon be ready for submission to journals.