The interdependence between density PDF, CMF, and IMF and their relation with Mach number in simulations

Open Access

Table 1.

Different functions to describe the IMF–CMF and the scaling of the tail.

	f(m)	Tail	Index

Linear	ξ(m) = dn/dm	∝m^−α	−α



Logaritmic	ξ(log m) = dn/dlog m	∝m × m^−α	−α + 1



CCDF	$P (m) = \int_{m}^{\infty} ξ (m') d m'$ $P(m) = \int^{\infty}_{m} \xi(m\prime)\mathrm{d}m\prime$	∝m^{−α + 1}	−α + 1

Notes. The logaritmic version of the mass spectrums and the CCDF have the same scaling for the tail, but this is purely coincidental.

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