(Steve Willner) wrote in message ...

Before we get to that, let's take a step back and see where we are.
What I've done is tell you how to interpret the data well enough for
a "sanity check" to see that time dilation is obvious.
I`ve done that and the results show,.. no time dilation is obvious.
And to back up that argument I`ve supplied the relevent data
again below.
The templates obviously include time dilation; otherwise they wouldn't
fit the data! This does not make them biased. I suggested using the
templates because the work is done for you, and it is easy to see what
is going on.
True the data can be made to fit the template if one uses the lower
end of the error margins, but they dont make as good a fit to the
`time dilation` template as they do to a `no time dilation`
interpretation. Look at 1998ek . The averaged measurements are
1.2 linear with an error margin that includes 1.0 at its lower end,
which is admittedly what a time dilation argument needs. Nonetheless
the middle of the error margin is 1.2 And 1.2 gives the 22/18.5 =1.18
ratio that supports a no time dilation argument. And so, undeniably,
within error margins a `no time dilation` is *also* supported and
because it uses the middle of the error margin range , supported
more strongly. On the whole the templates consistently under
estimate the peak observations where they are available. If one were
to remove the time dilation from the templates the peaks in the new
undilated templates would always be higher and that in turn would
give shorter time decays for a one mag decay from peak etc which in
turn would bring down the already favorable results closer to
`No time dilation`
However, if you don't like that, what you need to do is
find the slope of the light curve on the part well after maximum,
where the brightness (in magnitude units) is declining by a constant
amount per day. Compare the slopes for near and distant SNe at the
same magnitudes relative to maximum light. For example, you might
compare the time to go from (max plus 0.75 mag) to (max plus 1.5 mag).
The problem with this is that the distant SNe cannot always be
followed to 1.5 mag fainter than maximum, so I suggested the templates
as a shortcut. They do, after all, incorporate everything we know
about light curves based on nearby SNe.

There is nothing magic about the specific numbers 0.75, 1.5 mag, but
it looks to me as though they ought to work OK. The actual fitting
procedure is left to you, but be sure you take the error bars into
account.
OK. I`ll use peak + 1mag to peak +2mag seeing as you say its not
that important to use 0.75 and 1.5 mag. And what are the results?...
just as I expected.
1997ek (440nm restframe) I band takes 14 days to decay from
peak+1 mag to peak +2mag
1995S 440nm Restframe takes 12 days to decay from peak+1 mag
to peak +2 mag
Thats 14/12= 1.16 Now considering it should be 1.85 for a time
dilation argument I would say that 1.16 definitely supports a
`no time dilation` conclusion. What can I say Steve, no matter
what test you set, it always ends up supporting a
`no time dilation` outcome.

This is not a very good way to solicit my help, and in view of the
past history of this thread, you would be wise to adopt a more
skeptical attitude towards your own conclusions. I am beginning to
suspect that you are advocating a preconceived notion rather than
trying to understand the data.
But you have made mistakes so its not unfair of me to point them
out.
How else am I to argue the case for no time dilation?
Here for instance, You just made another in your latest post. You
claim below that 5.89 at day 50817.6, is 29 days before the HST
1.54 value.
The suggestion you are trying to make is that there is a 1
mag difference between 5.89 and 1.54! But thats a mistake because
it`s more than a 1 mag difference. It even contradicts a statement
you make in an earlier post where you claim that it takes 29 days
to decay 1 mag from 3.89 to 1.54 for the same SN! Surely you cant
accuse me of being rude or unhelpful when I point out obvious
errors like this?
And you too,are also advocating a `preconceived notion` except
yours is: time dilation. Are you not?
Anyways I`m sorry. I very much appreciate your input , dont get
me wrong. After all ,in a previous post it was *your* suggestion
that the best way to test for time dilation was to compare time
decays from peak mag between low and high redshift SN`s. And
thats exactly what I have done. And it helps my argument for
`no time dilation`. So I am in debted to you for giving me
an extra method to support a `no time dilation` interpretation
of data. Unfortunately you now say its *no*t an acceptable method.
In case you have some time ,these are the results of comparing
high redshift Sn`s I band lightcurves with lower redshift
comparable lightcurves. Notice how most support `no time dilation`

I band 1998ba where a 1 mag decay from
1.0 to 0.4 gives about 32 days which compares at z=0.43 to
a 569nm lightcurve which is about 27 days so thats 32/27=1.18
Thats much closer to 1 (no time dilation)than the expected
1.43 expected from time dilation .
And thats using the template!

Or take 1998as I band. Using the template its 34/27.5= 1.24
about 1/2 way but admittedly slightly favoring time dilation

1998aw I band template is 33/27= 1.2. Thats still closer
to 1.0 than a expected 1.44 for time dilation

1997ez I band is 30/20=1.5 against the expected 1.78 for
time dilation

1997eq is 30 days for a 1 mag decay from the template, or
using the actual peak observation of 1.15 flux density its
about 25-27 days. Thats 26/22=1.18 or using the template
one gets 30/22=1.36. Time dilation needs 1.54. Both
arguments can get support from this one,

1998ax I band template gives 1.48 against the time dilations
expected 1.5. A notable exception supporting time dilation.

2000fr I band using the template is about 30/22=1.36 and it
should be 1.54

1998bl I band using the template is 25/22=1.13 against time
dilations expected 1.74. Much closer to 1

1998be I band using template is 25/20=1.25 against time dilations
1.64 Closer to 1 than 1.64.

1998ay I band using the template is 31/21=1.47 against time
dilations 1.64

If you want to look at just
the HST measurements you`ll notice that the first HST reading
is 3.8. The second HST reading is the highest at 3.89 (1.0)
Thats the peak observation.

Please look again at what I wrote about error bars and (in the bit you
snipped) about the light curve being flat near maximum. You cannot
simply take the largest single measurement and call it the "time of
maximum." For 1997ek, all the measurements near "day 0" are
consistent with constant brightness lasting 8 days. The "time of
maximum" is in there somewhere. You can either determine it from the
template or else bypass determining the time of maximum altogether by
dealing only with the slope.
If we use your definition of peak, it is the "5.89" at day 50817.6, 29
days before the HST "1.54" value. (As noted above, this is not a
useful way to determine the time of maximum.)
As I mentioned before,...
The 5.89 reading at day 50817.6 is much more than 1 mag above 1.54.
So its irrelevent whether it takes 29 days to decay from 5.89 to
1.54 as a 1 mag decay from 5.89 would be to something much higher
than 1.54 and therefore less than 29 days.
I make it about 22 days. Certainly not as short as 17, which is what
1995E shows at B. In fact, 17*(1.35/1.01) = 22.7, which looks like
pretty good agreement to me. I don't see how you can possibly make
the decay as short as 20 days, let alone 17.
OK maybe 21 at a pinch and for you I`ll allow 22. But dont forget
that its being compared against a 444nm lightcurve , and not a B
band... (B band is 430/1.01=424nm restframe and V band
is 530/1.01=524nm). And according to Reiss` low redshift survey
424nm (B) takes 17 days to decay 1 mag and 524nm(I) takes approx
22 days to decay 1 mag from peak For 1995E and thus a 444nm
lightcurve is about 18 . So if the the 1998as R band restframe
of 444nm (600/1.85=444nm) decay is about 22.0 days decay for a
1 mag decay from peak then the ratio is at the outside...
22/18 = 1.2! Now thats a lot closer to 1.0 (no time dilation)
than 1.85(time dilation) no matter what spin one puts on it.
I also noticed that you managed to find one of the shortest
low redshift V band decays available at 21 days. Notice below
the other SN`s around the same 1995E redshift are all more
than 21 days. If I took lets say 1995S as an example then it
would be the following ratio 22/18.4=1.19. Thats even closer
to 1.0 than 1.85 and still a valid ratio as its using 1995S
data for B and V band.(the second column is heliocentric redshift)
1995al=3.18 = 23 days for B band
1995ac=3.1 = 22 days " "
1995E =3.5 = 21 days " " or 18 days for 440nm
1995S =3.6 = 23 days " " or 18.4 days for 440nm
1995bd=3.6 = 22 days " "
The I light curve isn't well sampled; there are no measurements at all
near peak. For R, the decay time from template-fitting is 20 days; we
expect 24 days from 1995E. However, there's a big error bar on the
first measurement, meaning the time of maximum is poorly determined.
The R band (restframe 419nm) yes, I agree, is 20 days using the
template and that compares approximately with the B band from SN1995E
(rest frame 424nm) which is about 18.5 days so one gets the ratio
20/18.4 or 1.08! Almost 1.0 or no time dilation . Thats supposed to
be 1.43 if there were time dilation. And the error bars are smaller
than those on SN1997ek I band measurements which you seemed quite
happy to use.
This is one where you have to look at the slope of the decay. And of
course for a sanity check, one is best advised to look at the SNe with
the highest redshifts.OK I`ll try the peak+x to peak+y method you now prefer on SN1998ba
R band (restframe 419nm ). It takes 12 days to decay from peak+1 mag
to peak+2 mag. (thats 0.4 to 0.16 on the graph)
And if the B band from 1994S is restframe 425nm and takes 10 days for
peak+1 to peak+2 then thats roughly comparable. So the ratio
is 12/10=1.2. Well thats about half way between both arguments
as it should be 1.43 for time dilation.
Then again dont forget the template `peak` is at the lower end of
the peak observations `error margin` so a time dilation argument
could use a peak ,within error margins, of about 1.1. That brings
forward the peak+1 mag to peak+2 mag timeframe on the lightcurve
which becomes steeper closer to peak. That in turn will reduce the
time decay and bring the ratio down closer to 1. By how much I dont
know, But as the 1.2 ratio is closer to 1.0 already I think this
favors no time dilation anyways , although by a smaller margin
than most of the others.
Using the I band (569 restframe) template one gets about a 22 day
decay for peak+1 to peak+2 decay. The comparable decay from 1994S
is 20 days for 525nm so we are looking at about at least an even
ratio of 22/22=1 if not less than 1.0. Thats very much no time
dilation. Mixed results there but still *definitely* favoring NO time
dilation, especially in I band.So what do you say? Am I wrong above?
If you think I am, dont just say "your wrong". Prove it by trying the
calculations yourself using peak +1 to peak+2 on the same SN and
then post your calculations. I`m proving a `no time dilation`
argument using only *your methods* and accepted data from NASA etc.
You can say that undergraduates study this or that for so many
years but it doesnt alter the fact that an undergraduate, or Steven
Hawking would both come to the same conclusions I have. That is IF
they use the data and do the simple calculations, which you
yourself have suggested,or at least agreed upon, correctly.One
doesnt have to be a graduate in astrophysics to see there is
a stronger argument for No time dilation then there is for
time dilation
Sean