Non-parametric SFHs

The star formation histories (SFHs) of galaxies hold a ton of information about the physical processes that influenced how they grew and quenched over time. However, all that information is summed up in the spectrum of a galaxy (with recent populations much more heavily featured than older ones), so it is a difficult problem to disentangle them. Traditionally, SFHs were dealt with as a nuisance parameter, something for people estimating stellar masses and star formation rates from galaxy spectra to marginalize over, but in recent times there has been a renewed focus on actually getting information about the SFH - partly because of better techniques and partly due to better data. In particular, a class of non-parametric approaches has been used to describe the shape of the SFHs that we are estimating from the data - non-parametric because it doesn't require a specific functional form, and is largely data-driven. The nice thing about this is that if your data is informative, you can get a lot of information about a galaxy's SFH without imposing prior beliefs on its shape, but if your data is poor you end up with larger uncertainties on all SFH-related parameters (like mass and SFR) due to the more unconstrained parameter space.

I've developed the Dense Basis method for non-parametric SFH reconstruction12, which works on the premise that one of the most efficient ways of describing the shape of a general function is through its percentiles/quantiles. In practice, this is implemented as a set of lookback times when a galaxy formed certain quantiles of its total stars. It can either be linearly spaced (the default option), or logarithmic (for slightly better reconstruction of the recent SFR, especially at high-z), or a set of custom quantiles. Now these quantiles by themselves do not uniquely describe an SFH, since they are just individual points (X% mass formed, t\(_X\)) between when the galaxy started forming stars (0% mass formed, t\(_{form}\)) and the time of observation (100% mass formed, t\(_{lookback}\)=0), and any interpolation function can be used to create a curve of (mass formed vs time), and taking its derivative gives us the SFH. With a linear interpolation, it is equivalent to SFR in bins that's used in methods like VESPA3. But we can do better!

By modeling the SFHs as a stochastic process (specifically a Gaussian process), we can incorporate physical information about how the SFH varies between two constraining times (tX). We do this using something called a kernel (or autocovariance function, or 2-point function, depending on what space you work in) that encodes the correlation between stat formation rates at two times \(K(t,t')\). Physically, this is interesting because it explicitly allows you to specify (and thus constrain) the extent to which galaxy star formation rates are correlated across time (by a common physical process acting to regulate the SFR, whether that's angular momentum support from the disk, elevated SFRs due to a gas-rich merger, or quenching due to AGN activity). While the default Dense Basis implementation corresponds to a scenario with a single correlation timescale, the GP-SFH project extended this using an extended regulator model4 which has a kernel with effective timescales corresponding to gas inflows, baryon cycling, and dynamical effects. Modeling SFHs as stochastic processes is well motivated by observations and theory (e.g.5), and has subsequently been used in a range of studies67.

In addition to the wealth of historical star formation activity unlocked by these methods, they also provide more robust estimates of galaxy properties including stellar masses and star formation rates by avoiding the biases of fixed functional forms1. These tools have been instrumental in analyzing data from large Hubble surveys like CANDELS and JWST surveys including CEERS & CANUCS, enabling systematic studies of galaxy evolution across cosmic time. These studies have revealed several interesting phenomena, including the prevalence of rejuvenated galaxies2, the increased burstiness in interacting galaxies at high-z8, or the earlier quenching in galaxies hosting active galactic nuclei (AGN) at low-z9. Dense Basis has also been incorporated into other modern SED fitting tools like Bagpipes, piXedfit and sleuth to further enhance its applications to analyzing spectrophotometry or spatially-resolved observations.

References:

  1. Kartheik Iyer and Eric Gawiser. Reconstruction of Galaxy Star Formation Histories through SED Fitting:The Dense Basis Approach. \apj , 838(2):127, April 2017. arXiv:1702.04371, doi:10.3847/1538-4357/aa63f0. ↩↩

  2. Kartheik G. Iyer, Eric Gawiser, Sandra M. Faber, Henry C. Ferguson, Jeyhan Kartaltepe, Anton M. Koekemoer, Camilla Pacifici, and Rachel S. Somerville. Nonparametric Star Formation History Reconstruction with Gaussian Processes. I. Counting Major Episodes of Star Formation. \apj , 879(2):116, July 2019. arXiv:1901.02877, doi:10.3847/1538-4357/ab2052. ↩↩

  3. R. Tojeiro, A. F. Heavens, R. Jimenez, and B. Panter. Recovering galaxy star formation and metallicity histories from spectra using VESPA. \mnras , 381(3):1252–1266, November 2007. arXiv:0704.0941, doi:10.1111/j.1365-2966.2007.12323.x. ↩

  4. Sandro Tacchella, John C. Forbes, and Neven Caplar. Stochastic modelling of star-formation histories II: star-formation variability from molecular clouds and gas inflow. \mnras , 497(1):698–725, September 2020. arXiv:2006.09382, doi:10.1093/mnras/staa1838. ↩

  5. Daniel D. Kelson. Decoding the Star-Forming Main Sequence or: How I Learned to Stop Worrying and Love the Central Limit Theorem. arXiv e-prints, pages arXiv:1406.5191, June 2014. arXiv:1406.5191, doi:10.48550/arXiv.1406.5191. ↩

  6. Neven Caplar and Sandro Tacchella. Stochastic modelling of star-formation histories I: the scatter of the star-forming main sequence. \mnras , 487(3):3845–3869, August 2019. arXiv:1901.07556, doi:10.1093/mnras/stz1449. ↩

  7. Enci Wang and Simon J. Lilly. The Variability of Star Formation Rate in Galaxies. II. Power Spectrum Distribution on the Main Sequence. \apj , 895(1):25, May 2020. arXiv:2003.02146, doi:10.3847/1538-4357/ab8b5e. ↩

  8. Yoshihisa Asada, Marcin Sawicki, Roberto Abraham, Maruša Bradač, Gabriel Brammer, Guillaume Desprez, Vince Estrada-Carpenter, Kartheik Iyer, Nicholas Martis, Jasleen Matharu, Lamiya Mowla, Adam Muzzin, Gaël Noirot, Ghassan T. E. Sarrouh, Victoria Strait, Chris J. Willott, and Anishya Harshan. Bursty star formation and galaxy-galaxy interactions in low-mass galaxies 1 Gyr after the Big Bang. \mnras , 527(4):11372–11392, February 2024. arXiv:2310.02314, doi:10.1093/mnras/stad3902. ↩

  9. Caleb Lammers, Kartheik G. Iyer, Hector Ibarra-Medel, Camilla Pacifici, Sebastián F. Sánchez, Sandro Tacchella, and Joanna Woo. Active Galactic Nuclei Feedback in SDSS-IV MaNGA: AGNs Have Suppressed Central Star Formation Rates. \apj , 953(1):26, August 2023. arXiv:2212.00762, doi:10.3847/1538-4357/acdd57. ↩