Evan's research blogBlogging about stuff
http://evaneschneider.github.io/site/
Outflow Parameters<p>As I’ve written previously, the Chevalier & Clegg outflow model is characterized by just three parameters: the starburst radius, <script type="math/tex">R_*</script>, the mass injection rate, <script type="math/tex">\dot{M}</script>, and the energy injection rate, <script type="math/tex">\dot{E}</script>. These parameters can be set for a given star formation rate by specifying how the total mass and energy injection compare to the rates that would naiively be expected from the products of stellar evolution. in previous posts, I’ve used the term <script type="math/tex">\beta</script> to indicate the multiplicative factor that accounts for mass in the hot outflow that is not a product of supernovae and stellar winds, i.e. <script type="math/tex">\dot{M}_\mathrm{hot} = \beta_\mathrm{hot} \dot{M}_\mathrm{SN+SW}</script> - this is the usage that appears in Strickland and Heckman (2009). However, by selecting an IMF and making some (reasonable) assumptions about stellar evolution, this <script type="math/tex">\beta_\mathrm{hot}</script> can be converted into a slightly different definition of mass loading, i.e. <script type="math/tex">\dot{M}_\mathrm{hot} = \beta_\mathrm{SFR} \dot{M}_\mathrm{SFR}</script>. In this version, <script type="math/tex">\beta_\mathrm{SFR}</script> tells us how the total mass in the hot outflow compares to the star formation rate in the galaxy. A wind that has zero mass-loading (and therefore only contains mass from the byproducts of stellar evolution) would have <script type="math/tex">\beta_\mathrm{hot} = 1</script> and <script type="math/tex">\beta_\mathrm{SFR} \sim0.25</script> (see discussion in Section 2.1.1 of Veilleux et al. 2005). The same calculation yields an estimate of the energy injected by supernovae and stellar winds as a function of star formation rate, with a typical number of <script type="math/tex">\dot{E}_\mathrm{SN} = 3.0\times10^{41}</script> erg <script type="math/tex">\mathrm{s}^{-1}</script> <script type="math/tex">\alpha \dot{M}_\mathrm{SFR}</script>, where the factor <script type="math/tex">\alpha</script> accounts for the fraction of the energy that is thermalized in the hot plasma (see Section 2.1 of Thompson et al. 2016).</p>
Thu, 22 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Outflow-Parameters/
http://evaneschneider.github.io/site//2017/Outflow-Parameters/Flux Corection<p>This post is dedicated to describing the simple but effective first-order flux correction I mentioned in my last post. When using one of Cholla’s unsplit integrators (CTU or Van Leer), simulations that involve extreme temperature/density contrasts and/or high mach numbers have a tendency to cause the code to crash. Typically, these sorts of crashes start when the high-order flux update of the conserved variables yields a negative pressure. These pressure errors then propagate, eventully leading to negative densities or total energies (or NANs) that cause the code to crash. In a previous effort to solve this problem, I introduced a dual-energy update in Cholla, described in a series of posts starting <a href="http://evaneschneider.github.io/site/2015/dual-energy-1/">here</a>, that allows the code to separately track and update the internal energy of the cells, and uses this non-conservative energy estimate if the total energy yields a negative pressure. While the dual-energy update did help, it was not able to completely solve the problem.</p>
Tue, 20 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Flux-Correction/
http://evaneschneider.github.io/site//2017/Flux-Correction/CC85 outflow (for real)<p>A lot has happened in the last 4 days. To quickly summarize:</p>
<ul>
<li>Once I started injecting the correct amount of mass and energy, the code started breaking.</li>
<li>I implemented a first-order flux correction to deal with the negative pressures.</li>
<li>Combined with the dual-energy scheme, the first order flux correction works!</li>
<li>I’ve successfully run several models of M82 with a Chevalier & Clegg style outflow.</li>
<li>The simulations are awesome.<br />
<br />
I’m dedicating a quick separate post to the first-order flux correction, so I’ll skip those bullet points for now. The important part is that the fix seems pretty robust, and so far, has been able to completely eliminate negative temperatures and densities in the simulation. I haven’t yet tested it with cooling…
<br />
<br />
<strong>The Simulation</strong></li>
</ul>
Mon, 19 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/CC85-outflow-2/
http://evaneschneider.github.io/site//2017/CC85-outflow-2/More outflow models<p>Recall that in the last post, I tested two outflow models. For a <script type="math/tex">256^3</script> simulation, when I used <script type="math/tex">R_{*} = 200</script>pc, <script type="math/tex">\dot{M}_{\odot} = 1 M_{\odot}</script>/yr, and <script type="math/tex">\dot{E} = 10^{43}</script>erg/s (aka CC85 parameters), I was able to generate an outflow, though the simulation crashed after 327 Myr. When I used <script type="math/tex">R_{*} = 300</script>pc, <script type="math/tex">\dot{M}_{\odot} = 2 M_{\odot}</script>/yr, and <script type="math/tex">\dot{E} = 10^{42}</script>erg/s (aka SR17 parameters), no outflow was generated, just a bubble of warm gas near the center.</p>
Thu, 15 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/More-Outflow-Models/
http://evaneschneider.github.io/site//2017/More-Outflow-Models/CC85 outflow<p>At the end of the last post, I showed an M82 simulation with mass and energy input that failed to drive an outflow. The model parameters were set to match the CC85 model we used in our 2017 paper: <script type="math/tex">R_{*} = 300</script>pc, <script type="math/tex">\dot{M}_{\odot} = 2 M_{\odot}</script>/yr, and <script type="math/tex">\dot{E} = 10^{42}</script>erg/s. At all times during the simulation, a small bubble of heated disk gas can be seen near the starburst region, but the bubble never propagates into the halo.</p>
Mon, 12 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/CC85-outflow/
http://evaneschneider.github.io/site//2017/CC85-outflow/M82 models<p>At some point, I’ll fill in some of the backstory from the past three months. In the meantime,
here’s where things stand currently:</p>
<ul>
<li>We have a working equilibrium model for the Milky Way with a hot, hydrostatic halo and a rotating disk in vertical hydrostatic equilibrium that is stable for a Gyr.</li>
<li>We have a working equilibrium model for M82 with the same structure.</li>
</ul>
Mon, 05 Jun 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/M82-models/
http://evaneschneider.github.io/site//2017/M82-models/Hydrostatic Blues<p>In the last post, I described the analytic calculation I’m doing in order to set up a 3D
disk in vertical hydrostatic equilibrium with my NFW + Miyamoto-Nagai profile. Here’s a density
projection of what the resulting disk looks like:</p>
Wed, 08 Mar 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Hydrostatic-Blues/
http://evaneschneider.github.io/site//2017/Hydrostatic-Blues/Milky Way 3D<p>Once we add a third dimension, the initial conditions for an isothermal disk get a bit more complex.
In addition to balancing the radial components of the gravitational potential with circular velocity,
I now need to balance the vertical acceleration via a pressure gradient, i.e. I need to make sure the
disk is in hydrostatic balance. Given that the pressure and density can be related for an isothermal
gas via the expression <script type="math/tex">P = \rho c_{s}^{2}</script>, this translates to calculating the vertical density profile
at each radial location in the disk.</p>
Wed, 22 Feb 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Milky-Way-3D/
http://evaneschneider.github.io/site//2017/Milky-Way-3D/Milky Way 2D<p>In order to simulate galaxy outflows, we need to start with reasonable approximation of a
gas disk that is stable over many rotation periods. This post begins what will be a series of
tests describing the setup of such a disk. For simplicity, I’ll start with a two-dimensional simulation.</p>
Wed, 15 Feb 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Milky-Way-2D/
http://evaneschneider.github.io/site//2017/Milky-Way-2D/Keplerian Disk<p>So we’ve seen how Cholla does with rotating flows in general, but how about the classic problem
of a disk in Keplerian rotation? Generally, there are two challenges in simulating such disks
with a static grid code: first, the orbital speeds near the center of the disk can get extremely large
as the resolution of the simulation is increased, and second, advection errors (like those seen in the
Gresho test) lead to artificial accretion through the disk.</p>
Mon, 06 Feb 2017 00:00:00 +0000
http://evaneschneider.github.io/site//2017/Keplerian-Disk/
http://evaneschneider.github.io/site//2017/Keplerian-Disk/