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Supersonic turbulence in the interstellar medium (ISM) is closely linked tothe formation of stars, and hence many theories connect the stellar initialmass function (IMF) with the turbulent properties of molecular clouds. Here wetest three turbulence-based IMF models (by Padoan & Nordlund 2002, Hennebelle &Chabrier 2008, and Hopkins 2012), which predict the relation between thehigh-mass slope ($\Gamma$) of the IMF, $\mathrm{d} N/\mathrm{d} \log M \proptoM^{\Gamma}$ and the exponent n of the velocity power spectrum of turbulence,$E_v(k)\propto k^{-n} $, where $n\approx 2$ corresponds to typical ISMturbulence. Using hydrodynamic simulations, we drive turbulence with an unusualindex of $n\approx 1$, measure $\Gamma$, and compare the results with $n\approx2$. We find that reducing $n$ from 2 to 1 primarily changes the high-massregion of the IMF (beyond the median mass), where we measure high-mass slopeswithin the 95 per cent confidence interval of $-1.5<\Gamma<-1$ for $n \approx1$ and $-3.7<\Gamma<-2.4$ for $n\approx 2$, respectively. Thus, we find that$n=1$ results in a significantly flatter high-mass slope of the IMF, with moremassive stars formed than for $n \approx 2$. We compare these simulations withthe predictions of the three IMF theories. We find that while the Padoan &Nordlund theory matches our simulations with fair accuracy, the other theorieseither fail to reproduce the main qualitative outcome of the simulations orrequire some modifications. We conclude that turbulence plays a key role inshaping the IMF, with a shallower turbulence power spectrum producing ashallower high-mass IMF, and hence more massive stars.

Testing the Turbulent Origin of the Stellar Initial Mass Function