FASTAR

I. Continuous and differentiable evolutionary stellar population models

¹ Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n, E38205 La Laguna, Tenerife, Spain
² Departamento de Astrofísica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain
³ Departamento de Inteligencia Artificial, Universidad Nacional de Educación a Distancia (UNED), Calle Juan del Rosal 16, E-28040 Madrid, Spain
⁴ INAF-Osservatorio Astronomico di Capodimonte, sal. Moiariello 16 Napoli 80131, Italy
⁵ Department of Astrophysics, University of Vienna, Türkenschanzstraße 17, 1180 Wien, Austria
⁶ Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2 Brno 611 37, Czech Republic
⁷ Centre for Astrophysics and Supercomputing, Swinburne University, John Street, Hawthorn, VIC 3122, Australia
⁸ Observatoire de Paris, LERMA, PSL University, 61 avenue de l’Observatoire, F-75014 Paris, France
⁹ Université Paris-Cité, 5 Rue Thomas Mann, 75014 Paris, France
¹⁰ Instituto de Astronomía, Universidad Nacional Autónoma de México, A.P. 106 Ensenada 22800, BC, México

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 28 January 2026
Accepted: 13 April 2026

Abstract

The development of evolutionary stellar population models is central to interpreting observations of galaxies in terms of astrophysical quantities. Stellar population models must therefore be both accurate and compatible with inversion algorithms in order to extract meaningful information from the observed data. Here we present FASTAR, a fully differentiable stellar population synthesis code. Contrary to traditional, grid-based single stellar population models, FASTAR can be continuously evaluated at any age (between 20 Myr and 14 Gyr), metallicity (−2.5≤ [M/H] ≤ + 0.3), and initial mass function (IMF). Changes in the IMF parameterization are straightforward, allowing for consistent conversions of colors, magnitudes, and mass-to-light ratios, as well as the synthesis of models under the assumption of arbitrary IMF functional forms. FASTAR provides detailed spectroscopic predictions over the MILES wavelength range (3540–7400 Å) as well as more coarsely sampled spectral energy distributions across a wider 2000-to-12 000 Å, which can be directly convolved with any arbitrary set of photometric filters. FASTAR performs at the same level of state-of-the-art simple stellar population models benchmarked against observations of globular clusters and high signal-to-noise spectra of early-type galaxies, but it is faster, lighter, and more flexible. Moreover, its differentiable nature allows for a quantitative understanding of model behavior and uncertainties, as well as a natural framework for gradient descent inference algorithms.