Reconstructing the star formation rate for compact binary populations with the Einstein telescope

• Main Authors: Singh, Neha, Bulik, Tomasz, Belczynski, Krzysztof, Cieslar, Marek, Calore, Francesca
• Format: Journal Article
• Language: English
• Published: 03-04-2023
• Subjects: Physics - Astrophysics of Galaxies; Physics - High Energy Astrophysical Phenomena
• DOI: 10.48550/arxiv.2304.01341

A&A 681, A56 (2024) The Einstein Telescope (ET) is a proposed third-generation, wide-band
gravitational wave (GW) detector. Given its improved detection sensitivity in
comparison to the second-generation detectors, it will be capable of exploring
the Universe with GWs up to very high redshifts. In this paper, we present a
population-independent method to infer the functional form of star formation
rate density (SFR) for different populations of compact binaries originating in
stars from Population (Pop) I+II and Pop III using ET as a single instrument.
We use an algorithm to answer three major questions regarding the SFR of
different populations of compact binaries. Specifically, these questions refer
to the termination redshift of the formation of Pop III stars, the redshift at
peak SFR, and the functional form of SFR at high redshift, all of which remain
to be elucidated. We show that the reconstruction of SFR as a function of
redshift for the different populations of compact binaries is independent of
the time-delay distributions up to $z \sim 14,$ and that the accuracy of the
reconstruction only strongly depends on this distribution at higher redshifts
of $z\gtrsim 14$. We define the termination redshift for Pop III stars as the
redshift where the SFR drops to 1\% of its peak value. In this analysis, we
constrain the peak of the SFR as a function of redshift and show that ET as a
single instrument can distinguish the termination redshifts of different SFRs
for Pop III stars, which have a true separation of at least $\Delta z \sim 2$.
The accurate estimation of the termination redshift depends on correctly
modelling the tail of the time-delay distribution, which constitutes delay
times of $\gtrsim 8$ Gyr.