The size and mass distribution of cold classical TNOs for $5<H<13$

Abstract: The cold classical trans-Neptunian objects (CCs) are the only observable \textit{in situ} population of planetesimal remnants believed to have escaped collisional grinding. Recent JWST observations make it possible to fit the differential absolute magnitude distribution $dN/dH$ of the CCs from $5&lt;H_r\&lt;13,$ and infer the differential mass distribution $dN/dM$ across $\ge5$ orders of magnitude in mass. We find $dN/dM$ well fit by a lognormal distribution, and equally well by a generalized $Γ$ distribution or a double power law. The maximum fraction of the total CC mass per log interval in $M$ is in bodies near 75~km diameter, or $\approx10^{-7.5}M_\oplus.$ Extrapolation of the fitted $dN/dH$ functions to $$H_r\&gt;13$$ is unwise, as the different analytic forms diverge. It remains unclear if $dN/dH$ turns over at faint $H.$ The uncertainty in the total mass of the CC belt is dominated by uncertainty in the relation between $M$ and $H$. A calibration using CC binaries suggests a total CC mass of 1.7--2.7$\times10<sup>{-3}\,M_\oplus.$ A trend toward lower density and/or higher albedo for smaller bodies may be present in the data, and would lower the estimated total CC mass. Qualitative comparison of the derived mass distribution to the results of numerical simulations of the streaming instability (SI) suggest the simulations produce $dN/dM$ distributions that are more sharply peaked, and steeper at the bright end, than the CCs. Such differences could be ascribed to inhomogeneous formation conditions in the classical belt that are not yet included in modeling. The variety and uncertainty of $dN/dM$ derived from state-of-the-art SI simulations currently preclude any definitive test of the SI hypothesis.