Inefficient star formation in high Mach number environments - I. The turbulent support analytical model

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Volume 690 (October 2024)

A&A, 690 (2024) A43

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Table 1

.Main notations and abbreviations used in the article.

Notation	Description
G	Gravitational constant
m_p	Mass of a proton
µ = 1.4	Mean molecular weight, in unit of m_p

M₀	Total mass in the system
L₀	Scale of the system
R₀ = L₀/2	Typical radius of the system
n₀	Mean number density
ρ₀ = n₀µ m_p	Mean density
σ₀	Velocity dispersion at the system scale L₀
c_S	Sound speed
L_i	Injection length of turbulence
y_cut	Largest radius of structures considered is y_cutL_i

σ	3D mass-weighted velocity dispersion
ℳ	3D Mach number
ℳ_thres	Mach number at which the transition between the efficient and inefficient star formation regimes occurs
ℳ_eq	Expected Mach number in galaxies from dynamical equilibrium
τ_ff	Free-fall time
τ_rep	Replenishment time
τ_cont	Control time for star formation
SFR_ff	Dimensionless SFR per free-fall time

δ = ln(ρ/ρ₀)	Logarithmic density contrast
S_δ	Volume weighted variance of δ
T_CH	Temperature of turbulence (Castaing 1996)

M_J	Jeans mass
λ_J	Jeans length
λ_turb = ℳλ_J	Turbulent Jeans length
$\tilde{R} = R / λ_{J}$ $\tilde R = R/{\lambda _J}$	For any spatial quantity R, $\tilde{R}$ $\tilde R$ is the same quantity divided by the Jeans length.
$\tilde{M} = M / M_{J}$ $\tilde M = M/{M_J}$	For any mass M, $\tilde{M}$ $\tilde M$ is the same quantity divided by the Jeans mass.

n_v	Exponent of velocity powerspectrum
η_v	η_v = (n_v – 3)/2
n_d	Exponent of the natural logarithm of density powerspectrum
η_d	η_d = (n_d – 3)/2

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