Ambiguous sentence about hot/cold accretion

[keflavich]

I've had a hard time parsing this paragraph: https://github.com/Open-Astrophysics-Bookshelf/star_formation_notes/blob/525ff15a3634b664418f866598888caa1696d7aa/chapters/chapter17.tex#L149

in particular, the sentence: "There has yet to be a fully detailed calculation of this case, and instead the usual practice in the protostellar evolution community is to parameterize the uncertainty by adopting a value of Lin that lies somewhere between the minimum possible value, corresponding to the spherical case, and the maximum possible value, in which Lin is chosen so as to set the specific entropy of the material being added to the star equal to either the specific entropy of material at the stellar surface, or the mean specific entropy of all material in the star."

Is the maximum value of $L{in}$ when $s=<s>$ or `$s=s{surface}$`? For the convective case they're the same, but for non-convective, the surface term is greater, right?

Also, this sentence earlier: "The second implication of non-spherical accretion is that Lin might be much larger than in the spherical case." I was a bit thrown by the phrase "much larger". The limiting range is L_acc > L_in > 3/4 L_acc, right? So is "much larger" just $L_in \rightarrow L_acc$?

These are minor items, but I think could be improved. Or I simply misunderstood!

[keflavich]

One literature example is Vorobyov+ 2017, which defines $$\alpha = \frac{L_{in}}{L_{acc}}$$. They call $\alpha=10^{-3}$ "cold" and $\alpha=0.1$ "hot". That makes sense to me and I think contradicts the language in the quoted sentence. It also has $L_{in} < 3/4 L_{acc}$, but that's perhaps a different issue.

[markkrumholz]

This is a case where there is confusion due to differing conventions used to define L_in. As originally defined in the Stahler+ papers, where the fundamental equation is L(M) = L_acc + L_bb - L_in, it is clear that L_in = L_acc corresponds to L(M) = L_bb, i.e., all the energy delivered by accretion is radiated away, none is added to the star. More generally, larger L_in corresponds to more of the energy being radiated and less being added to the star, because of the minus sign. However, this is a somewhat strange convention, and later authors have defined L_in differently, in a more intuitive way, whereby larger L_in corresponds to more energy being added to the star. The problem here is that my convention is the old one from 1980, which is confusing when you read the newer papers. In any event, I will rewrite this text to make the variation in convention clear.

[markkrumholz]

Also, on the specific question of whether the maximum entropy is s_mean or s_surface: excellent question! There isn't a physically known answer, unfortunately, and this is, again, a case where different authors have adopted different conventions. Some consider "cold" accretion to mean s = s_surface, some consider it to be s = s_mean, and some consider it to be s = 0. Again, I will add caveats that this is an area where the definitions used in the literature are not at all unified.

[keflavich]

Thanks, much appreciated!

I see that the math works out as long as I don't try to read it in English. $L_{in}$ is the luminosity that does not go in.

[markkrumholz]

Yes! I was super-confused by that at first too. I never asked Steve Stahler why on Earth he chose that backwards convention, but maybe I should next time I see him. Anyway, I’m rewriting that text now to try to make the situation a bit clearer.

On 28 Jan 2022, at 9:33 am, Adam Ginsburg @.***> wrote:

Thanks, much appreciated!

I see that the math works out as long as I don't try to read it in English. $L_{in}$ is the luminosity that does not go in.

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[markkrumholz]

Just pushed a change to the repo. See if you think the new text is clearer.

[keflavich]

For future reference, the edits are here: https://github.com/Open-Astrophysics-Bookshelf/star_formation_notes/commit/56576edd67fcf14f2ea18968d9cf8509b0986022 and this version is much clearer to me.