Top: relationship between the density distribution width, σ_s, and sonic Mach number, ℳ_s. The red dashed curves show the case β = ∞, the blue curves β = 0.3, and green dash-dotted curves β = 0.05. The thicker (and higher) curves correspond to b = 1 and the thinner (and lower) curves to b = 1/3. The dotted line shows the best-fitting model with b²β/ (1 + β) = 0.30 ± 0.06. Bottom: the relationship between the magnetic field strength, β, and the compression parameter, b, for the model that best fits all data points. The thin solid, dashed, and dotted lines show the 1, 2, and 3σ confidence levels.