From: Gabriele Garavini (garavini@in2p3.fr)
Date: Mon Jan 10 2005 - 02:35:51 PST
Hi Saul,
I think the exact formula is the following:
tau=tau_vmin*exp((v_min-v)/v_e)
tau is then set to zero for v > v_max
tau_vmin, v_min, v_e, v_max are input parameters.
I would state this in the following manner:
The parameters $v_{phot}$ and $T_{bb}$ set the velocity and blackbody
continuum temperature of the photosphere, respectively. For each ion,
optical depth $\tau$ at the minimum ejection velocity $v_{min}$ is
specified. Optical depth scales exponentially with velocity according
to the $e$-folding velocity parameter $v_{e}$, and is considered to be
zero for velocity greater than $v_{max}$. If $v_{min} > v_{phot}$ for
an ion, we refer to the ion as ``detached.''
I will send the new draft to Tony later today.
Cheers
Gabriele
On Wed, 5 Jan 2005, Saul Perlmutter wrote:
> Hi Gabriele,
> Let's see-- I'm still trying to make sense of this sentence about
> optical depth (the problem is that "according to e-folding velocity"
> doesn't really mean what I think you might mean). Is the following
> version correct? And if so, what goes in the space where I wrote [????]?
>
> "Optical depth scales exponentially with velocity, $tau \propto e^{-v_e}$, where $v_{e}$
> is defined as [????] and cannot exceed a maximum velocity given by
> $v_{max}$."
>
>
>
> After we finish up with this sentence, and if everything else looks
> right to you, then send the paper to Tony to post it on the collab web
> page, and he'll send out the request to the collaboration for them to
> read it (I'll talk to the scpexec tomorrow).
> Good work! --Saul
>
>
>
>
>
> Gabriele Garavini wrote:
>
> >Dear Saul,
> >
> >I have read your corrections and they all make sense to me.
> >For the answers to your questions please keep reading:
> >
> >______________________________________________________________________
> >
> >
> >>Optical depth scales exponentially with velocity
> >>***What does this phrase mean?: [[[according
> >>to an $e$-folding velocity]]]*** up to a maximum velocity given by
> >>
> >>
> >$v_{max}$.
> >
> >now reads:
> >"Optical depth scales exponentially with velocity according
> >to $e$-folding velocity, $v_{e}$, up to a maximum velocity given by
> >$v_{max}$."
> >
> >This means just that tau is proportional to exp(-v_e).
> >
> >_______________________________________________________
> >
> >
> >
> >>improve the agreement. [[[***This is puzzling: Why does extinction
> >>strongly affect either of these measurements???***]]]
> >>
> >>
> >
> >The whole sentence has been removed now. It was a residual of a previous
> >version of the plot that was showing Mag vs R(SiII). In that case,
> >of course, the magnitude was affected by extinction. In the
> >current version with delta_m_15 the effect of extinction is negligible
> >even if not zero (extinction depends on time).
> >
> >________________________________________________________________
> >
> >
> >My plan for the next few days is to read trough the paper carefully once
> >more and to make it available for the next step of the internal review,
> >that I believe should be to open it to the collaboration.
> >
> >
> > Thank very much you.
> > Cheers
> >Gabriele
> >
> >
>
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