Parravano, McKee & Hollenbach (2011)

Abstract (paraphrased)¶

Assuming the disk IMF is universal and simple, the authors adopt a single smooth analytic form and constrain its parameters with integral observables (star counts, luminosities). The form approaches a power law at both ends — low-mass ($\psi \propto m^{\gamma}$) and high-mass ($\psi \propto m^{-\Gamma}$) — joined smoothly, which they term the Smoothed Two-Power Law (STPL).

What progenax uses (PDF-verified 2026-07-11)¶

• Eq. 1 (p. 2) — the STPL form.

  $$\psi(m) \;\propto\; m^{-\Gamma}\,\bigl\{1 - \exp\!\bigl[-(m/m_{\rm ch})^{\gamma+\Gamma}\bigr]\bigr\},$$

  (1)

  which is exactly progenax’s TaperedPowerLaw PDF $f(m) \propto m^{-\alpha}\,(1 - e^{-(m/m_{\rm peak})^{\beta}})$ up to the slope convention: PMH11 write $\psi$ per unit $\log m$ (their Salpeter is $\Gamma = 1.35$), progenax’s alpha is the linear-mass slope ($\alpha = \Gamma + 1$), and PMH11’s taper exponent $\gamma + \Gamma$ is the code’s beta. This convention mapping is a formal deviations entry on the tapered_powerlaw model card.

• Historical attribution (p. 2). The functional form was first proposed by Paresce & De Marchi (2000) for globular-cluster present-day mass functions; PMH11 adopted and calibrated it as a disk IMF (with Hollenbach et al. 2005 an earlier STPL step). Maschberger (2013) lists it as his comparison Eq. 12 — the route by which progenax originally cited it.

Connections in progenax¶

• progenax.imf.smooth.TaperedPowerLaw — implements Eq. 1 in the linear-mass convention.

• Maschberger (2013) — the house-default smooth IMF; the STPL is the closest sibling without a closed-form quantile (Newton ppf), which is why Maschberger remains the production default.