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From: Melanie Jo Clarke <mjdosaj_at_MIT.EDU>

Date: Mon, 30 Oct 2006 12:05:39 -0500

Hello,

My confusion stemmed from several things:

1) Given that the canonical momentum is p = a^2 * dx/dt, I couldn't see

where a

factor of sqrt(a) came in. I didn't know it was there for historical reasons,

so I tried to derive it. Although the equations given in your paper involved

p, it was stated in the manual that the time variable was ln(a), so I

went from

there. In reference to the conversion, the manual only stated that the

velocity

was in internal units.

2) sqrt(a) didn't work for me, so I tried to find something that did.

I should

have asked sooner where the factor came from.

I'm sorry, I misspoke when I mentioned the physical velocity. I meant the

peculiar velocity, of course. Also, the factor I gave was not d(ln a)/dt,

which is H(t), but d(ln a)/d(tau), where d(tau)=Ho*dt/a^2. I should have

composed my thoughts better before sending the email.

Thank you for your careful and patient reply. I am in conversation

with Michele

Trenti, who has generously offered to help me solve my conversion problems.

- Melanie

*> Hi Melanie,
*

*>
*

*> The manual is correct on this...
*

*>
*

*> I can only speculate where you got confused, but I'm guessing you have
*

*> mixed up the definitions of comoving, physical, and peculiar velocity.
*

*> Note that they are all different. Also note that the manual says that
*

*> the IC file should contain the *peculiar* velocity divided by sqrt(a),
*

*> not the *physical* velocity as you state above. Let "x" denote comoving
*

*> coordinates and "r=a*x" physical coordinates. Then I call
*

*>
*

*> comoving velocity: dx/dt
*

*> physical velocity: dr/dt = H(a)*r + a*dx/dt
*

*> peculiar velocity: v = a * dx/dt
*

*>
*

*> The physical velocity is hence the peculiar velocity plus the Hubble flow.
*

*>
*

*> I think your attempts to guess the correct conversion factor have caused
*

*> some additional confusion. Let me try to clarify: The internal velocity
*

*> variable of gadget2 is not given by dx/d(ln a). Rather, it is given by
*

*> the canonical momentum p = a^2 * dx/dt, which is different from the
*

*> definition you assumed. The IC-file and snapshot files of gadget don't
*

*> contain the variable "p" directly because of historical reasons of
*

*> compatibility with gagdet-1. Instead, they contain the velocity variable
*

*> u = v/sqrt(a) = sqrt(a) * dx/dt = p / a^(3/2), which is just what the
*

*> manual says. (The conversion between u and p is done on the fly when
*

*> reading or writing snapshot files.)
*

*>
*

*> Also note that d(ln a)/dt is not a*sqrt(omega_m/a + omega_v*a^2 + 1 -
*

*> omega_m - omega_v), as you say above... This factor is equal to the
*

*> Hubble rate, i.e.: d(ln a)/dt = H(a) = H_0 * sqrt(omega_m/a^3 + omega_v
*

*> + (1 - omega_m - omega_v)/a^2).
*

*>
*

*> If you can't solve your unit conversion problem, I'd suggest to talk to
*

*> Michele Trenti, who figured out the grafic->gadget2 conversion.
*

*>
*

*> Best wishes,
*

*> Volker
*

Received on 2006-10-30 18:05:57

Date: Mon, 30 Oct 2006 12:05:39 -0500

Hello,

My confusion stemmed from several things:

1) Given that the canonical momentum is p = a^2 * dx/dt, I couldn't see

where a

factor of sqrt(a) came in. I didn't know it was there for historical reasons,

so I tried to derive it. Although the equations given in your paper involved

p, it was stated in the manual that the time variable was ln(a), so I

went from

there. In reference to the conversion, the manual only stated that the

velocity

was in internal units.

2) sqrt(a) didn't work for me, so I tried to find something that did.

I should

have asked sooner where the factor came from.

I'm sorry, I misspoke when I mentioned the physical velocity. I meant the

peculiar velocity, of course. Also, the factor I gave was not d(ln a)/dt,

which is H(t), but d(ln a)/d(tau), where d(tau)=Ho*dt/a^2. I should have

composed my thoughts better before sending the email.

Thank you for your careful and patient reply. I am in conversation

with Michele

Trenti, who has generously offered to help me solve my conversion problems.

- Melanie

Received on 2006-10-30 18:05:57

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