I've been trying to find experiments where the mass density distribution $\mathrm{\Sigma = \Sigma(r)}$ is determined for protoplanetary disks. 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 $\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$.

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).

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 $\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$.

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).

I've been trying to find experiments where the mass density distribution $\mathrm{\Sigma = \Sigma(r)}$ is determined for protoplanetary disks. 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 $\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$.

Questions: Is it possible to measure $\Sigma$ at this distances? 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).

I've been trying to find experiments where the mass density distribution $\mathrm{\Sigma = \Sigma(r)}$ is determined for protoplanetary disks. 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 $\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$.

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).