A Core Mass Function Indistinguishable from the Salpeter Stellar Initial
  Mass Function Using 1000 au Resolution ALMA Observations
  We present the core mass function (CMF) of the massive star-forming clump
G33.92+0.11 using 1.3 mm observations obtained with the Atacama Large
Millimeter/submillimeter Array (ALMA). With a resolution of 1000 au, this is
one of the highest resolution CMF measurements to date. The CMF is corrected by
flux and number incompleteness to obtain a sample that is complete for gas
masses $M\gtrsim2.0\ M_\odot$. The resulting CMF is well represented by a
power-law function ($dN/d\log M\propto M^\Gamma$), whose slope is determined
using two different approaches: $i)$ by least-squares fitting of power-law
functions to the flux- and number-corrected CMF, and $ii)$ by comparing the
observed CMF to simulated samples with similar incompleteness. We provide a
prescription to quantify and correct a flattening bias affecting the slope fits
in the first approach, which is caused by small-sample or edge effects when the
data is represented by either classical histograms or a kernel density
estimate, respectively. The resulting slopes from both approaches are in good
agreement each other, with $\Gamma=-1.11_{-0.11}^{+0.12}$ being our adopted
value. Although this slope appears to be slightly flatter than the Salpeter
slope $\Gamma=-1.35$ for the stellar initial mass function (IMF), we find from
Monte Carlo simulations that the CMF in G33.92+0.11 is statistically
indistinguishable from the Salpeter representation of the stellar IMF. Our
results are consistent with the idea that the form of the IMF is inherited from
the CMF, at least at high masses and when the latter is observed at high-enough
resolution.
