Anna Rosen, Ph.D.Computational Astrophysicist

Jaxstro · Collisional dynamics

gravax

Differentiable collisional dynamics.

A JAX-native, hierarchical collisional N-body engine: high-order exact direct gravity with explicit ownership of binaries and compact subsystems, and gradients that survive the adaptive timestep — so a cluster model can be fitted to data, not only run forward.

Readiness

In developmentIn active development

Publications

Methods paperplanned

Close encounters are where a cluster’s history is decided, so gravax resolves them exactly rather than softening them away, and gives binaries and compact subsystems an owner of their own instead of letting them dissolve into the average. What sets it apart from the mature collisional codes is not speed: it is that the trajectory stays differentiable throughout, so I can ask how a cluster’s present-day state depends on the conditions it was born with and answer with a derivative rather than a parameter sweep. The integrators are checked against analytic solutions and independent reference methods rather than against sky data.

Exact direct summation is what makes that trustworthy, and it is also what sets the ceiling on (N). A differentiable treatment of the far field is in development to lift it. The goal is cluster models at the million-star scale that stay differentiable end to end, and followed far enough to cover a cluster’s whole life rather than its first few crossing times — from birth structure, through the epochs that rework it, to the point where it has been erased. That work is not validated yet, and nothing above depends on it.

What's working

Three panels. (a) A 512-star cluster in the x-y plane, points sized and coloured by stellar mass, with projected half-mass radii circled at t=0 and after three crossing times, and a central massive binary. (b) Binary and cluster scales against time in units of the half-mass crossing time: the half-mass and 90-percent radii expand while the binary semimajor axis drops in three discrete steps at marked encounters. (c) A four-by-four matrix of logarithmic sensitivities of endpoint observables to birth parameters, showing strong diagonal structure: cluster radii respond to the initial half-mass radius, while binary semimajor axis and eccentricity respond to their own initial values.
PreliminaryWhat the Endpoint Remembers. Birth conditions leave a readable fingerprint. A 512-star EFF cluster carrying a primordial 30.8+28.3 M⊙30.8 + 28.3\,M_\odot binary, evolved to 3tcr,h=2.447 Myr3t_\mathrm{cr,h} = 2.447\,\mathrm{Myr} under exact, unsoftened Newtonian forces. (a) Open symbols are the initial distribution and filled symbols the endpoint; the projected half-mass radius grows from 0.71 to 0.88 pc. (b) Three binary-single encounters harden the binary by 10.4%, from a0=1000a_0 = 1000 to 896 AU896\,\mathrm{AU}, while the cluster expands and the binary ends at e=0.538e = 0.538. (c) The point: each cell is the median logarithmic response ∂ln⁡y(T)/∂ln⁡θ0\partial\ln y(T)/\partial\ln\theta_0 of an endpoint observable to a birth parameter, across five clusters. The structure is physically legible — cluster size remembers rh,0r_{h,0}, while binary hardening and eccentricity remember a0a_0 and e0e_0. Derivatives taken straight through the reversible adaptive timestep agree with complete finite-difference reruns to 3.24×10−53.24\times10^{-5}, so the differentiability claim is measured rather than asserted.

What's coming

In active development. Near-term work turns the validated adaptive high-order scheme into the standard cluster entry point and extends it to realistic mass spectra and primordial binaries. The methods paper will cover where exact resolution is required rather than merely faster.