[FLASH-USERS] Equilibrium configuration

[Jesús Zavala Franco]

Hi John,

Thank you for your reply, I have tried different configurations and I always
get the same situation: the gas spreading outwards with velocities of ~20
km/s after 300 Myrs of evolution. This happens whether I spread the dark
matter particles or not. By the way, I tried using the point mass potential
that is implemented as an option in FLASH as you suggested. So I removed the
particles completely. I get exactly the same situation, so it is not related
to the particles.

I'm thinking that the problem is related to what Colin mentioned in his
answer (check following e-mail)

Cheers,
Jesus

2011/3/17 John ZuHone <jzuhone at cfa.harvard.edu>

> Jesus,
>
> I would actually not expect this setup to work all that well. Most
> certainly the central cell with the particles and the gas is not going to be
> in hydrostatic equilibrium. This would be true of the central cell even if
> you had the dark matter spread throughout, but in that case it would not be
> much of an issue since what you would get is some minor flattening of the
> gas density profile near the center.
>
> But if I read you correctly you have the particles all dropped into this
> central zone, and the mass of this central zone alone is much larger than
> the mass of gas in the entire system, which means each of your particles is
> very massive. What velocities do you have them set to? Even if you set them
> initially to zero and they are all at the center you're going to get some
> spurious velocities. Since the particles are so massive the potential is
> probably changing a lot and this is throwing things out of equilibrium in
> the center.
>
> Since the HSE is definitely broken in this cell and probably in a few cells
> surrounding it, I don't think it's surprising that you're seeing what you
> are. You are trying to simulate a point mass but severely underresolving it
> both in terms of spatial and mass resolution.
>
> Is there a particular reason you're trying to represent a point mass in
> this way? There is a point mass gravitational acceleration option in FLASH
> that would probably be better suited for this purpose.
>
> Best,
>
> John ZuHone
>
> On Mar 17, 2011, at 12:55 PM, Jesús Zavala Franco wrote:
>
> Dear all,
>
> I'm having problems setting up a sphere of gas in hydrostatic equilibrium
> under its own gravity + the gravity of a particle distribution.
>
> In the general case, I would like to have this particle distribution with
> the same density profile as the gas distribution (so I'm aiming at setting
> up a dark matter halo with a particle distribution, with gas inside), but to
> describe the problem I'm having, I will avoid distributing particles in the
> sphere and simply:
>
> 1) put 1000 particles in the centre of the sphere
> 2) put gas distributed spherical around this centre with a radial density
> profile (a NFW profile), and pressure given by the condition of hydrostatic
> equilibrium:
>
> dP(r)/dr = -(GM(<r)/r^2) * rho_gas(r)
>
> where M(<r) is the total enclosed mass, and rho_gas(r) is the gas density.
> M(<r)= M_DM+Mgas(<r), with M_DM the total mass of the 1000 particles, which
> by the way exceeds the total mass of the gas by almost an order of
> magnitude. To solve the equation I impose a boundary condition outside the
> sphere setting a pressure and a density which are reasonable according to
> the problem and the density profile I'm putting.
>
> So in short, what I have is a sphere of gas within a gravitational
> potential dominated by essentially a point source in the centre and with a
> pressure that should give support agains the gravitational collapse.
>
> I'm using a gird of 8^3 with 4 levels of refinement, an ideal gas equation
> of state, a Pfft Multigrid gravity solver, I'm using the default operator
> splitting technique to advance the solution.
>
> What I notice is that since the first time step, regardless of my choice of
> dtinit, the cells just next to the central cell (the one containing the 1000
> particles), acquire a radial outwards velocity, whit a size depending of the
> time step, and that once the time evolution reaches the typical times of the
> problem (~100 Myrs), this results in the gas in the inner parts propagating
> outwards, reducing the density in the core, after 1Gyr or so, this
> propagating gas reaches the boundaries of the sphere. In other words, the
> equilibrium set at first is broken.
>
> I have tried using the option ppm_modifystates=.true. since as described in
> the user guide:
>
> "The version of PPM in the FLASH code has an option to more closely couple
> the hydrodynamic solver
> with a gravitational source term. This can noticeably reduce spurious
> velocities caused by the operator
> splitting of the gravitational acceleration from the hydrodynamics"
>
> I thought this could help, but it didn't. I'm aware that if I wouldn't put
> the particles in the centre, this behaviour is just a resolution problem
> since the core is not being properly resolved and the density and enclosed
> mass is underestimated there, the pressure is therefore too high (since is
> initially set by solving the hydrostatic equilibrium equation with the
> assumed analytical profile) and it pushed the gas outwards. However, since
> I'm setting a significant gravity source in the center I wouldn't expect
> this to be the case. I have tried actually increasing the mass of the
> particles by a factor of 10, and not considering this mass increase in the
> solution to the pressure equation, this sets the overall pressure too low
> and you would expect a collapse. Even though when at first the velocities of
> the contiguous cells to the centre, point inwards, after a while, they are
> overwhelmed by an outward flow that develops in the cells next to these, and
> to my surprise, the sphere expands as well.
>
> I'm running out of ideas on the initial conditions setup, so I'm thinking
> this could either be a resolution issue, or a bad choice of hydro, gravity
> solver.
>
> Any hel will be much appreciated.
>
> Cheers,
> Jesus Zavala
> Department of Physics and Astronomy
> University of Waterloo
>
>
>
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