An Improved HR Diagram for the Orion Trapezium Cluster
  In this paper, we present a study of the Trapezium cluster in Orion. We
analyze flux-calibrated VLT/MUSE spectra of 361 stars to simultaneously measure
the spectral types, reddening, and the optical veiling due to accretion. We
find that the extinction law from Cardelli et al. (1989) with a
total-to-selective extinction value of $R_{\rm V}=$5.5 is more suitable for
this cluster. For 68% of the sample the new spectral types are consistent with
literature spectral types within 2 subclasses, but as expected, we derive
systematically later types than the literature by one to two subclasses for the
sources with significant accretion levels. Here we present an improved
Hertzsprung-Russell (H-R) diagram of the Trapezium cluster, in which the
contamination by optical veiling on spectral types and stellar luminosities has
been properly removed. A comparison of the locations of the stars in the H-R
diagram with the non-magnetic and magnetic pre-main sequence evolutionary
tracks indicates an age of 1--2~Myr. The magnetic pre-main sequence
evolutionary tracks can better explain the luminosities of the low-mass stars.
In the H-R diagram, the cluster exhibits a large luminosity spread
($\sigma$(Log~$L_{\star}/L_{\odot})\sim$0.3). By collecting a sample of 14
clusters/groups with different ages, we find that the luminosity spread tends
to be constant ($\sigma$(Log~$L_{\star}/L_{\odot})\sim$0.2--0.25) after 2~Myr,
which suggests that age spread is not the main cause of the spread. There are
$\sim$0.1~dex larger luminosity spreads for the younger clusters, e.g., the
Trapezium cluster, than the older clusters, which can be explained by the
starspots, accretion history and circumstellar disk orientations.
