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I've been trying to find research articles where the mass density distribution $\mathrm{\Sigma = \Sigma(r)}$ is determined for protoplanetary disks, when $r<1$ au. For instance:

  • Here A. Miotello, S. Facchini, E. F. van Dishoeck, and S. Bruderer use radiative transfer and submm data to probe the surface density distribution with $^{13}\mathrm{CO}$ emission.

  • Here Jonathan P. Williams and Conor McPartland measured density profiles with ALMA.

Seems like the method is similar. Despite that, I know that the available resolution in this band does not allow us to conclude much about the mass when $r < 1$ au. ALMA's resolution reaches $\sim 0.02''$ "in the most extended 12-m array configuration ($\sim \,16 \;\mathrm{km}$), when observing at $230 \;\mathrm{GHz}$.

TW Hydrae is the nearest known protoplanetary disk. A(n "exquisite") resolution of $\theta \sim 3.5 \times 10^{-5}\;''$ would be needed to spatially resolve a diameter of $\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$.

TW Hydrae

Questions: Is it possible to measure $\Sigma$ at this distances ($d<0.1 \; \mathrm{AU}$)? Is there any work exploring on this? Are we limited mainly to models? (e.g., Philip J. Armitage's Astrophysics of Planet Formation textbook or Jonathan P. Williams and Lucas A. Cieza's review).

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    $\begingroup$ Those reviews should contain the info you want.... short answer is now, we can't measure the mass directly, because the bulk mass carrier ($H_2$) doesn't radiate actively at the low PP-disc temperatures. Instead one needs to link polar molecules, such as HD, CO, etc. via chemical modeling to the $H_2$ mass. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Jul 16, 2022 at 19:42
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    $\begingroup$ Has anybody ever done X? Here are two papers that do X. I don't understand what you are asking $\endgroup$
    – ProfRob
    Commented Jul 17, 2022 at 9:35
  • $\begingroup$ Hi @ProfRob My question is about the possibility to measure Σ at distances $d< 0.1$ au. I know that these two papers exist, but I don't know if that's the only known method... And I'm also not sure if reading J. Armitage, or Williams & Cieza's work will help me specificly with it. $\endgroup$
    – nuwe
    Commented Jul 17, 2022 at 20:33
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    $\begingroup$ I doubt we can do experiments on this... the scaling is aweful or the labs too small ;). We can observe, we can simulate it on the computer using numerics or we can model it ;) $\endgroup$
    – planetmaker
    Commented Jul 18, 2022 at 20:27

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