Systematic studies of the centrality and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="italic">NN</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math>dependence of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mi>E</mml:mi><mml:msub><mml:mi/><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>d</mml:mi><mml:mi>η</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mi>N</mml:mi><mml:msub><mml:mi/><mml:mrow><mml:mi fontstyle="normal">ch</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>d</mml:mi><mml:mi>η</mml:mi></mml:mrow></mml:math>in heavy ion collisions at midrapidity

The PHENIX experiment at the relativistic heavy ion collider (RHIC) has measured transverse energy and charged particle multiplicity at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at center-of-mass energies $\sqrt{{s}_{\mathrm{NN}}}=19.6,130$, and $200\phantom{\rule{0.3em}{0ex}}\text{GeV}$ as a function of centrality. The presented results are compared to measurements from other RHIC experiments and experiments at lower energies. The $\sqrt{{s}_{\mathrm{NN}}}$ dependence of $dE{}_{T}/d\ensuremath{\eta}$ and $dN{}_{\mathrm{ch}}/d\ensuremath{\eta}$ per pair of participants is consistent with logarithmic scaling for the most central events. The centrality dependence of $dE{}_{T}/d\ensuremath{\eta}$ and $dN{}_{\mathrm{ch}}/d\ensuremath{\eta}$ is similar at all measured incident energies. At RHIC energies, the ratio of transverse energy per charged particle was found to be independent of centrality and growing slowly with $\sqrt{{s}_{\mathrm{NN}}}$. A survey of comparisons between the data and available theoretical models is also presented.