Re: Comoving Density Conversion Question

From: Jared Coughlin <Jared.W.Coughlin.29_at_nd.edu>
Date: Fri, 7 Oct 2016 00:05:29 -0400

It does, yes. Thank you for the help!
-Jared

On Thu, Oct 6, 2016 at 10:12 PM, Antonio Bibiano <antbbn_at_gmail.com> wrote:

> Hi Jared,
> You are right, my answer didn't actually respond.
>
> I went back and reread your mail and I think you have it right in the last
> part,
> rho_phys = rho_comoving / a^3
> Don't know excatly what's the error in the first formula, I suspect the
> last term should be elevated to the -3 .
>
> But this does not change the dimension conversion,when changing form Mpc/h
> to cm and
> M_sun/h to grams no factor of "a" should appear. They only appear when you
> convert from comoving to physical.
>
> So to recap:
> Gadget Sanpshot Units -> cgs:
> rho_cgs_comoving = rho * UnitMass_in_g / UnitLength_in_cm^3 *
> HubbleParam^2
> Comoving cgs -> physical cgs:
> rho_cgs_physical = rho_cgs_comoving / a^3
>
> Does this make more sense?
>
> Antonio
>
> 2016-10-07 12:42 GMT+11:00 Jared Coughlin <Jared.W.Coughlin.29_at_nd.edu>:
>
>> Hi Antonio,
>> Thanks for the response! I agree that what you wrote will convert the
>> density to cgs, but won't it still be comoving?
>> -Jared
>>
>> On Oct 6, 2016 9:19 PM, "Antonio Bibiano" <antbbn_at_gmail.com> wrote:
>>
>>> In the user guide it says:
>>>
>>>> Units are again in internal code units, i.e. for the above system of
>>>> units,
>>>
>>> rho is given in 10^10 h^-1 M_sun / ( h^-1 kpc)^3.
>>>>
>>> It's kind of confusing, but I think it might the same thing as every
>>> other quantity in the gadget snapshots.
>>>
>>> To convert to cgs you should just grab the number from the snapshot,
>>> let's call it rho, and do
>>> rho * UnitMass_in_g / UnitLength_in_cm^3 * HubbleParam^2
>>>
>>> With the last multiplication only if you want to get rid of little h.
>>>
>>> Let me know if the result makes sense.
>>>
>>> Antonio
>>>
>>> 2016-10-06 14:42 GMT+11:00 Jared Coughlin <Jared.W.Coughlin.29_at_nd.edu>:
>>>
>>>> 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
>>>> this more readable)
>>>>
>>>> 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.
>>>>
>>>> [image: \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:
>>>> [image: \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 ([image:
>>>> |\rho_{cg}|]) multiplied by the scale factor cubed and then the other
>>>> constants. That is:
>>>>
>>>> [image:
>>>> |\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:
>>>>
>>>> [image: \rho_c=a^3\rho_p]
>>>>
>>>>
>>>> So it seems like I could do:
>>>>
>>>> [image: \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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>>>
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Received on 2016-10-07 06:05:33

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