[mesa-users] Solid-body rotation in convective zones?

Ben Brown bpbrown at astro.wisc.edu
Mon Dec 9 13:59:33 EST 2013

      I wanted to follow up on your quesiton and second Matteo's response. 
In stars like the sun, we expect the convection to create a differential 
rotation in the convection zone.  That's about all we can say; we see 
this consistently in 3-D simulations of rotating stellar convection 
but don't have a good handle on how the differential rotation scales 
(robustly) with mass, luminosity or rotation rate for lower main-sequence 
stars.  Here's a small bibliography of recent ASH global sim papers that 
try to answer parts of these questions (Augustson et al 2012 takes a crack 
at scalings across the lower MS in section 8, but beware that we've 
focused here on latitudinal rather than radial differential rotation).

Augustson et al 2012
Convection and Differential Rotation in F-type Stars

Matt et al 2011
Convection and differential rotation properties of G and K stars computed 
with the ASH code

Brown et al 2008
Rapidly Rotating Suns and Active Nests of Convection

I want to emphasize that the picture of these dynamics remains very 
unclear.  For instance, there's a persistent phenomena of anti-solar 
differential rotation that emerges in these models (seen in many ASH 
models, but reported most clearly in two different sets of convection 
models by Petri Kapyla & Thomas Gastine)

Gastine et al 2013
>From solar-like to anti-solar differential rotation in cool stars

Kaplya, Mantere & Brandenburg
Effects of stratification in spherical shell convection

These convection zones certainly also support magnetic dynamos, and there 
is certainly angular momentum transport and feedback on the differential 

We have no (robust) sense of the scaling, as we see different 
regimes of behaviour even under nominally similar stellar conditions 
(fixed rotation rate, mass, luminosity), where the differences between 
simulations come down to choices of grid-scale diffusion coefficients. 
Analgous to the high diffusivities in MESA, we have high diffusivities in 
3-D sims.  Ours are ~10^12 cm^2/s, which is smaller than MESA (~10^15)
but bigger than plasma values in stellar interiors (~10-10^3 cm^2/s).

Those caveats in mind, here is a small sampling of the burgeoning field of 
global stellar dynamo papers and the interlinking with differential 
rotation in convection zones.

Nelson et al 2013
Magnetic Wreaths and Cycles in Convective Dynamos

Brown 2011
Dynamos in Stellar Convection Zones: of Wreaths and Cycles
(fig 1 shows the disparity in diffusivities between 3-D models and solar 
plasma values)

And if you want a thesis on this,

Brown 2009 
Convection and dynamo action in rapidly rotating Suns

This reference list is biased; I'm hoping some other members of the 
stellar convection community will jump in to offer some of their own 
convection, rotation and dynamo thoughts.

btw: the story in massive core-convecting stars is possibly different, but 
I feel we know very little at this point.  See papers by Matt Browning on 
A-stars and M-dwarf stars, and Nick Featherstone too, for an idea of how 
differential rotation in core convection dynamos might differ.


> Message: 3
> Date: Tue, 3 Dec 2013 22:42:35 -0800
> From: Matteo Cantiello <cantiel at kitp.ucsb.edu>
> Subject: Re: [mesa-users] Solid-body rotation in convective zones?
> To: David Deschatelets <david.deschatelets.1 at ulaval.ca>
> Cc: "mesa-users at lists.sourceforge.net group"
> 	<mesa-users at lists.sourceforge.net>
> Message-ID: <1618600A-D743-448F-88C2-2F5219AC57D4 at kitp.ucsb.edu>
> Content-Type: text/plain; charset=us-ascii
> Hi David,
> On Dec 3, 2013, at 10:17 PM, David Deschatelets <david.deschatelets.1 at ulaval.ca> wrote:
>> Hello MESA users,
>> I've been analyzing for a while the effects of a Tayler-Spruit dynamo taking place within the radiative zone of a star.
>> The difference between a non-magnetic and magnetic simulation is easily observable and a near solid-body rotation can be seen in the radiative region due to angular momentum transport.
>> What took my attention on the evolution results is the angular velocity distribution in convective zones of the star (mostly when the star evolves away from the MS phase). I thought differential rotation was present in these regions (according to many papers I read) but what I'm observing is a constant angular velocity through the whole region.
>> This is well illustrated in Heger 2005 fig 1:  hhttp://m.iopscience.iop.org/0004-637X/626/1/350/fulltext/?providedHtml=61318.text.html
>> An explanation on this figure is: "In those regions large diffusion coefficients for angular momentum lead to nearly rigid rotation in all but the latest stages of the evolution", but I thought diffusion coefficients due to magnetic instability weren't present in such regions. Maybe are we talking here of another diffusion coefficient?
> The assumption in MESA (as well as in other stellar evolution codes, see e.g. the Heger et al. 2005 paper you refer to) is that in convection zones angular momentum is transported by turbulent viscosity.
> The value of the resulting diffusivity is usually quite high (~10^15 cm^2/s) and therefore leads to rigid rotation in the calculations.
>> Is there a dynamo in the convection layer that is responsible for this?
> No dynamo action is present in convective regions in MESA.
>> Same phenomenon can be seen in the second MESA instrument paper fig 30: http://arxiv.org/pdf/1301.0319v2.pdf
>> This constant velocity in convective regions is present whether magnetic field is on or off.
>> Also, what is the reason for such rotation braking when going from radiative region to convective region
> The reason is that, as explained above, in the calculations angular momentum is generally transported much more rapidly in convection zones than in radiative zones.
>> (and then of course, why is the angular velocity being constant once the convective region is reached).
> Again, because turbulent diffusivity enforces rigid rotation, i.e. constant angular velocity, in convective regions.
> Note that this is an assumption and other approaches are possible.
> For example some hydro calculations (I think mostly by David Arnett and Casey Meakin) might suggest that convection
> leads to a status of constant specific angular momentum (as opposite to the constant angular velocity mentioned above).
> Hope this helps,
> -M
> Matteo Cantiello  |  http://matteocantiello.com/
> Postdoctoral Fellow,  Kavli Institute for Theoretical Physics
> Scientific Advisor, Authorea  |  http://authorea.com/
>> Thank you all for your answers.
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