<p>I've been trying to find research articles where the mass density distribution <span class="math-container">$\mathrm{\Sigma = \Sigma(r)}$</span> is determined for protoplanetary disks, when <span class="math-container">$r&lt;1$</span> au. For instance:</p>
<ul>
<li><p><a href="https://www.aanda.org/articles/aa/pdf/2018/11/aa33595-18.pdf" rel="nofollow noreferrer">Here</a> A. Miotello, S. Facchini, E. F. van Dishoeck, and S. Bruderer use radiative transfer and submm data to probe the surface density distribution with <span class="math-container">$^{13}\mathrm{CO}$</span> emission.</p>
</li>
<li><p><a href="https://iopscience.iop.org/article/10.3847/0004-637X/830/1/32/pdf" rel="nofollow noreferrer">Here</a> Jonathan P. Williams and Conor McPartland measured density profiles with ALMA.</p>
</li>
</ul>
<p>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 <span class="math-container">$r &lt; 1$</span> au. <a href="https://almascience.nrao.edu/about-alma/alma-basics" rel="nofollow noreferrer">ALMA's resolution</a> reaches <span class="math-container">$\sim 0.02''$</span> &quot;in the most extended 12-m array configuration (<span class="math-container">$\sim \,16 \;\mathrm{km}$</span>), when observing at <span class="math-container">$230 \;\mathrm{GHz}$</span>.</p>
<p><strong><a href="https://aasnova.org/2016/04/11/featured-image-a-gap-in-tw-hydrae/" rel="nofollow noreferrer">TW Hydrae</a></strong> is the nearest known protoplanetary disk. A(n &quot;exquisite&quot;) resolution of <span class="math-container">$\theta \sim 3.5 \times 10^{-5}\;''$</span> would be needed to spatially resolve a diameter of <span class="math-container">$\mathrm{d_{TWH}} = 0.1 \;\mathrm{au}$</span>.</p>
<p><a href="https://i.sstatic.net/bREQW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bREQW.png" alt="TW Hydrae" /></a></p>
<p><strong>Questions</strong>: Is it possible to measure <span class="math-container">$\Sigma$</span> at <em>this distances</em> (<span class="math-container">$d&lt;0.1 \; \mathrm{AU}$</span>)? Is there any work exploring on this? Are we limited mainly to models? (e.g., <a href="https://rads.stackoverflow.com/amzn/click/com/1107653088" rel="nofollow noreferrer" rel="nofollow noreferrer">Philip J. Armitage's Astrophysics of Planet Formation</a> textbook or <a href="https://arxiv.org/pdf/1103.0556.pdf" rel="nofollow noreferrer">Jonathan P. Williams and Lucas A. Cieza</a>'s review).</p>

CC BY-SA 4.0
2022-07-16T19:42:21.757Z
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.
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-07-17T09:35:04.047Z
Has anybody ever done X? Here are two papers that do X.   I don't understand what you are asking
ProfRob
CC BY-SA 4.0
2022-07-17T20:33:13.343Z
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.
nuwe
CC BY-SA 4.0
2022-07-18T20:27:17.830Z
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 ;)
planetmaker
<radio-astronomy><star-formation><planetary-formation><proto-planetary-disk><radiative-transfer>
Has anybody measured the mass density profile $\Sigma = \Sigma (r)$ of a protoplanetary disk? (when $r<1$ AU)
nuwe
# Has anybody measured the mass density profile $\Sigma = \Sigma (r)$ of a protoplanetary disk? (when $r<1$ AU)

(Asked by: username_0 on 2022-07-15)

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](https://www.aanda.org/articles/aa/pdf/2018/11/aa33595-18.pdf) 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](https://iopscience.iop.org/article/10.3847/0004-637X/830/1/32/pdf) 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](https://almascience.nrao.edu/about-alma/alma-basics) reaches $\sim 0.02''$ "in the most extended 12-m array configuration ($\sim \,16 \;\mathrm{km}$), when observing at $230 \;\mathrm{GHz}$.

**[TW Hydrae](https://aasnova.org/2016/04/11/featured-image-a-gap-in-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](https://i.sstatic.net/bREQW.png)](https://i.sstatic.net/bREQW.png)

**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](https://rads.stackoverflow.com/amzn/click/com/1107653088) textbook or [Jonathan P. Williams and Lucas A. Cieza](https://arxiv.org/pdf/1103.0556.pdf)'s review).

**Tags:** radio-astronomy, star-formation, planetary-formation, proto-planetary-disk, radiative-transfer
> **Comments:**
> **username_1**: 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.  
> **username_2**: Has anybody ever done X? Here are two papers that do X.   I don't understand what you are asking  
> **username_0**: 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.  
> **username_3**: 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 ;)  

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## 0 answers

