Expansion-what formula for redshift?

On Tue, 15 May 2007 10:46:08 -0400, John C. Polasek
wrote:

On 14 May 2007 06:45:50 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On 10 May 2007 06:57:17 -0400, Joseph Lazio
JCP wrote:

Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M
= 25 + 5 log D_L, where D_L is the luminosity distance. In
equation (3) of this paper, he then gives the expression for the
luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for
more details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
z(2+z)\Omega_\Lambda]}

I had suspected a faulty calculation of redshift to account for
expansion, and my trepidations are not at all relieved by the above
expression. At the least I would question what model could produce
(1+z)^2*(1+z)Omega_k? Or even z(2+z)*Omega_lambda?
Just to evaluate the limit case of zero dark matter and no dark
energy, omega_k then would become unity and the expression seems to
reduce to
DL = c(1+z)/H_0*sin(integral (1+z)dz) =
c(1+z)/H_0*sin(z + z^2/2) =
cT(1+z)* sin(z + z^2/2)
But then it doesn't support the case for z = 0. Up to the sine term we
have cT stretched by 1+z, OK so far, but then the sine term imposes an
irreparable penalty it seems to me. I've probably made a simple
mistake.
Oops, my mistake; of course it's the expected result: no z, no D_L.
But sine of a squared z sounds like a fudge. It must be a fudge. Its
augmentation helps to make greater distance so as to agree more
closely with greater magnitude but it must not be enough of a boost if
there's still trouble left over (!).
I am still of the opinion that redshift is being misapplied
somehow, leading to suspicion of sudden expansion.

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each
SN Ia, I have two observables: its redshift z and its apparent
magnitude m. It appears that the absolute magnitude M of SN Ia is
essentially constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts,
then we can try to solve for the unknown quantities \Omega_m, H_0,
and \Omega_\Lambda.

JCP An interim note: The magnitude algebra (2.512*log) must be OK,
JCP but the redshift usage is new to me. With 2-plus omegas, I'd say
JCP there's quite a bit of room for algebraic error (my original
JCP balk) in finding that the SN's are dimmer than their z.

Not sure what you mean by "2-plus omegas."
I meant that you have 3 omegas, with the omeag_k being the one's-
complement of the sum of the other two.
The fitting assumes that
there is one value for \Omega_m, one value for \Omega_\Lambda, and one
value for H_0. That's the point of doing the fitting: To take the
measured values of m and z for the SN Ia and find the appropriate
values for the two different \Omega.

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups have
performed these kinds of measurements and conducted the fits. They
reach similar conclusions, giving confidence that there has not been
an error in the computer programs used to do the fitting.
John Polasek

On 14 May 2007 06:45:50 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On 10 May 2007 06:57:17 -0400, Joseph Lazio
JCP wrote:

Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M
= 25 + 5 log D_L, where D_L is the luminosity distance. In
equation (3) of this paper, he then gives the expression for the
luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for
more details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
z(2+z)\Omega_\Lambda]}

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each
SN Ia, I have two observables: its redshift z and its apparent
magnitude m. It appears that the absolute magnitude M of SN Ia is
essentially constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts,
then we can try to solve for the unknown quantities \Omega_m, H_0,
and \Omega_\Lambda.

JCP An interim note: The magnitude algebra (2.512*log) must be OK,
JCP but the redshift usage is new to me. With 2-plus omegas, I'd say
JCP there's quite a bit of room for algebraic error (my original
JCP balk) in finding that the SN's are dimmer than their z.

Not sure what you mean by "2-plus omegas." The fitting assumes that
there is one value for \Omega_m, one value for \Omega_\Lambda, and one
value for H_0. That's the point of doing the fitting: To take the
measured values of m and z for the SN Ia and find the appropriate
values for the two different \Omega.

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups have
performed these kinds of measurements and conducted the fits. They
reach similar conclusions, giving confidence that there has not been
an error in the computer programs used to do the fitting.
Joseph: Is it possible to quote some z and magnitude pairs that
represent the case for expansion? I have tried to study the
information on line and realize there's nothing too black and white
about it. I would like to do some work on it.
John Polasek

"John C. Polasek" wrote in message
...
: On 14 May 2007 06:45:50 -0400, Joseph Lazio
: wrote:
:
: "JCP" == John C Polasek writes:
:
: JCP On 10 May 2007 06:57:17 -0400, Joseph Lazio
: JCP wrote:
:
: Briefly, one determines the magnitude of the SN Ia. After
: appropriate correction, the distance modulus of a SN Ia is m - M
: = 25 + 5 log D_L, where D_L is the luminosity distance. In
: equation (3) of this paper, he then gives the expression for the
: luminosity distance in terms of cosmological parameters. I'll
: reproduce it the best that I can here, but consult the paper for
: more details:
:
: D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
: integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
: z(2+z)\Omega_\Lambda]}
:
: JCP Since H0, Wm and WL are undetermined, the problem seems
: JCP underspecified, together with the manifold appearances of 1+z,
: JCP 2+z, z(2+z), it looks more like my original question was
: JCP underspecified.
:
: Well, that's the point of conducting the observations. For each
: SN Ia, I have two observables: its redshift z and its apparent
: magnitude m. It appears that the absolute magnitude M of SN Ia is
: essentially constant.
:
: For any given SN Ia, you're right, the problem is underspecified.
: Once we have many observations of SN Ia, at different redshifts,
: then we can try to solve for the unknown quantities \Omega_m, H_0,
: and \Omega_\Lambda.
:
: JCP An interim note: The magnitude algebra (2.512*log) must be OK,
: JCP but the redshift usage is new to me. With 2-plus omegas, I'd say
: JCP there's quite a bit of room for algebraic error (my original
: JCP balk) in finding that the SN's are dimmer than their z.
:
: Not sure what you mean by "2-plus omegas." The fitting assumes that
: there is one value for \Omega_m, one value for \Omega_\Lambda, and one
: value for H_0. That's the point of doing the fitting: To take the
: measured values of m and z for the SN Ia and find the appropriate
: values for the two different \Omega.
:
: The "algebraic error" statement simply doesn't make sense. All of
: these calculations are done on computers. Two different groups have
: performed these kinds of measurements and conducted the fits. They
: reach similar conclusions, giving confidence that there has not been
: an error in the computer programs used to do the fitting.
: Joseph: Is it possible to quote some z and magnitude pairs that
: represent the case for expansion? I have tried to study the
: information on line and realize there's nothing too black and white
: about it. I would like to do some work on it.
: John Polasek

You want empirical data?
Good grief... be careful, that's thinking. I'd like some empirical
data for Algol, especially red shift. Empirical data is gold dust
in a theory-crazed world, it might disprove something.

"JCP" == John C Polasek writes:

JCP On 14 May 2007 06:45:50 -0400, Joseph Lazio
JCP wrote:

Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M
= 25 + 5 log D_L, where D_L is the luminosity distance. In
equation (3) of this paper, he then gives the expression for the
luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for
more details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
z(2+z)\Omega_\Lambda]}

JCP I had suspected a faulty calculation of redshift to account for
JCP expansion, and my trepidations are not at all relieved by the
JCP above expression. At the least I would question what model could
JCP produce (1+z)^2*(1+z)Omega_k? Or even z(2+z)*Omega_lambda?

General relativity.

Not quite sure where to recommend you start, though. Peebles,
_Principles of Physical Cosmology_, doesn't really discuss the
luminosity distance (at least not as far as I can see); it is
certainly derivable from the material in MTW, _Gravitation_, though it
might take a fair amount of work.

You might again check Ned Wright's cosmology site to see if there are
some pointers there.

JCP Just to evaluate the limit case of zero dark matter and no dark
JCP energy, omega_k then would become unity and the expression seems
JCP to reduce to DL = c(1+z)/H_0*sin(integral (1+z)dz) =
JCP c(1+z)/H_0*sin(z + z^2/2) = cT(1+z)* sin(z + z^2/2)

No. If there is no dark energy, then \Omega_\Lambda = 0. However,
\Omega_m is the density of matter, *all* matter, both dark and
luminous. The equation would reduce to

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m)]}

with \Omega_k = 1 - \Omega_m (assuming I haven't made any
transcription errors).

One would still have to do the fitting, though, clearly the equation
involved in more simple.

--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

"JCP" == John C Polasek writes:

JCP On 14 May 2007 06:45:50 -0400, Joseph Lazio
JCP wrote:

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups
have performed these kinds of measurements and conducted the fits.
They reach similar conclusions, giving confidence that there has
not been an error in the computer programs used to do the fitting.

JCP Is it possible to quote some z and magnitude pairs that
JCP represent the case for expansion? I have tried to study the
JCP information on line and realize there's nothing too black and
JCP white about it. I would like to do some work on it.

Start with the "gold sample" presented in Riess et al., URL:
http://arxiv.org/abs/astro-ph/0402512 .


--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

On 19 May 2007 19:35:01 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On 14 May 2007 06:45:50 -0400, Joseph Lazio
JCP wrote:

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups
have performed these kinds of measurements and conducted the fits.
They reach similar conclusions, giving confidence that there has
not been an error in the computer programs used to do the fitting.

JCP Is it possible to quote some z and magnitude pairs that
JCP represent the case for expansion? I have tried to study the
JCP information on line and realize there's nothing too black and
JCP white about it. I would like to do some work on it.

Start with the "gold sample" presented in Riess et al., URL:
http://arxiv.org/abs/astro-ph/0402512 .
Thank you. It is quite a lucid paper that I've partly studied. I
appreciate your cooperation.
John Polasek