No evidence that the binary black hole mass distribution evolves with redshift

Home

All issues

Volume 698 (May 2025)

A&A, 698 (2025) A85

Full HTML

Open Access

Table A.1.

Priors adopted on the hyperparameters used in our analyses.

Hyperparameter	Prior
log(ℛ_ref·Gpc³ yr)	$U$ ${\cal {{U}}}$ (-2, 1)
α	$N (- 2, 3)$ ${\cal {{N}}}(-2, 3)$
log(f_p)	$U$ ${\cal {{U}}}$ (-6, 0)
β_q	$N$ ${\cal {{N}}}$ (0, 3)
α_z	$N$ ${\cal {{N}}}$ (0, 4)
β	$U$ ${\cal {{U}}}$ (0, 10)
z_p	$U$ ${\cal {{U}}}$ (0.2, 4)
M_min	$U (5 M_{⊙}, 15 M_{⊙})$ ${\cal {{U}}}(5\,M_\odot , 15\,M_\odot )$
M_max	$U (50 M_{⊙}, 100 M_{⊙})$ ${\cal {{U}}}(50\,M_\odot , 100\,M_\odot )$
μ_m	$U (15 M_{⊙}, 60 M_{⊙})$ ${\cal {{U}}}(15\,M_\odot , 60\,M_\odot )$
σ_m	$U (1.5 M_{⊙}, 15 M_{⊙})$ ${\cal {{U}}}(1.5\,M_\odot , 15\,M_\odot )$
log(δm_min/ M_⊙)	$U (- 1, 0.5)$ ${\cal {{U}}}(-1, 0.5)$
log(δm_max/ M_⊙)	$U (0.5, 1.5)$ ${\cal {{U}}}(0.5, 1.5)$

Λ_high & Λ_low	Identical prior to p(Λ) above
log(Δz_Λ)	$U$ ${\cal {{U}}}$ (-1, 1)
${\bar{z}}_{Λ}$ $\bar z_{\Lambda }$	$U (0, 0.8)$ ${\cal {{U}}}(0, 0.8)$
log(Δm_Λ/M_⊙)	$U$ ${\cal {{U}}}$ (-1, 3)
${\bar{m}}_{Λ}$ $\bar m_{\Lambda }$	$U (20 M_{⊙}, 75 M_{⊙})$ ${\cal {{U}}}(20\,M_\odot , 75\,M_\odot )$

Notes: $U (a, b)$ ${\cal {{U}}}(a,b)$ indicates a uniform prior normalized between a and b, and $N (a, b)$ ${\cal {{N}}}(a,b)$ a Gaussian prior with mean a and standard deviation b. When varying a given hyperparameter as a function of mass or redshift, priors on the asymptotic values are identical to the priors listed in the upper portion of the table. When varying the mean of the Gaussian peak in the black hole mass spectrum, for example, we adopt $p (μ_{m, low}) = p (μ_{m, high}) = p (μ_{m}) = U (15 M_{⊙}, 60 M_{⊙})$ $p(\mu _{m,{\textrm {low}}}) = p(\mu _{m,{\textrm {high}}}) = p(\mu _m) = {\cal {{U}}}(15\,M_\odot ,60\,M_\odot )$ .

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.