# Re: Comoving Density Conversion Question

From: Jared Coughlin <Jared.W.Coughlin.29_at_nd.edu>
Date: Thu, 6 Oct 2016 10:41:27 -0400

Thanks! I'll give it a go!
-Jared

On Oct 6, 2016 10:22 AM, "Cassandra Hall" <cxh_at_roe.ac.uk> wrote:

>
> Hi Jared - unfortunately I can't answer your question, but I *think*
> (although I may be wrong) that yt can do this for you?
>
> http://yt-project.org/
>
> ^ It generally makes life easier for simulation data
>
> Cass
> ________________________________________
> From: Jared Coughlin [Jared.W.Coughlin.29_at_nd.edu]
> Sent: 06 October 2016 04:42
> Subject: [gadget-list] Comoving Density Conversion Question
>
> Hello! I know this is a pretty stupid question, but I'm drawing a blank on
> it so I figured I'd ask. I want to know how to convert density from
> comoving gadget units to proper cgs units. I've run a cosmological
> simulation (so comoving integration is on), which means that Gadget is
> writing the densities in comoving internal code units. For ease of talking
> about them, I've been calling a gadget unit of mass a GUM and a gadget unit
> of length a GUL.
>
> (NOTE: I'm using the tex for gmail plugin on chrome, if that helps make
>
> That is,
>
> 1GUL = 3.085678e21 cm/h = X cm/h
> 1GUM = 1.989e43 g/h = Y g/h (the use of X and Y is just for ease of
> writing)
>
> in the default system, which is what I'm using. For one of my analysis
> codes I need to convert the densities from comoving gadget units to proper
> cgs units. Let a subscript c is for comoving, and a subscript p is for
> proper, and the cg subscript is for comoving gadget units.
>
> [\rho_{cg} = \left(\frac{|\rho_{cg}|\text{GUM}}{\text{GUL}_c^3}\right)\
> left(\frac{Y\text{g}}{h\text{GUM}}\right)\left(\frac{h\
> text{GUL}_c}{X\text{cm}_c}\right)^3\left(\frac{1\text{cm}
> _c}{\frac{1\text{cm}_p}{a}}\right)^3]
>
>
> Where the || just means the magnitude of the density (no units attached).
> This is the number contained in the snapshot. The above simplifies to:
> [\rho_{cg} = |\rho_{cg}|\left(\frac{Y}{X^3}\right)a^3h^2\text{gcm}^{-3}_p]
>
>
>
> Therefore, it seems to me, from the above, that the magnitude of the
> density in proper cgs units is the value given in the snapshot
> ([|\rho_{cg}|]) multiplied by the scale factor cubed and then the other
> constants. That is:
>
> [|\rho_{p\text{cgs}}|=|\rho_{cg}|\left(\frac{Y}{X^3}\right)a^3h^2]
>
>
> However, this seems wrong to me, as I know that:
>
> [\rho_c=a^3\rho_p]
>
>
> So it seems like I could do:
>
> [\rho_{pg}=\frac{\rho_{cg}}{a^3}]
>
>
> That is, the density in proper gadget units is just the value given in the
> snapshot divided by the scale factor cubed. This quantity could then
> undergo the conversion to cgs units as above, with the only difference
> being that this method has me dividing by the scale factor cubed, which is,
> of course, different than what happened the first time.
>
> I've thought myself into a corner on this, if that makes any sense, and so
> my question is this: Can anyone tell me the right way to convert the
> densities from comoving gadget units to proper cgs units? I would greatly
> appreciate it, and I apologize for such a stupid question. Thank you very
> much!
>
> Sincerely,
> -Jared
>
>
>
>
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