аDate: Sun, 22 Sep 2002 23:08:18 GMT
From: email@example.com (Alex Chepick)
Newsgroups: sci.physics, sci.astro, alt.sci.physics.new-theories
Subject: Explanation of width-and stretch-factors
Key words: width-factor - stretch-factor
Explanation of width- and stretch-factors
for Type Ia Supernovae
Chepick A.M., Nizhni Novgorod
ааааааа Explanations of dependence on distance are given both for the w-factor of a light curve of an absolute magnitude Type Ia Supernovae and for s-factor not explained till now.
а 1. Introduction
Recently found out an expansion phenomenon (w-factor) of a light curve for absolute magnitude of Type Ia Supernovae would be considered as the brightest proof of the universe expansion if it was not accompanied by the not explained stretch-factor (s-factor) [Peter Nugent, Alex Kim and Saul Perlmutter, arXiv: astro-ph/0205351 v1 21 May 2002 K-corrections and Extinction Corrections for Type Ia Supernovae; further NKP2002]
аа 2. Light in the intergalactic environment
Speed of light practically always is less than constant in Lorentz's transformations because of the speed depends on environment in which light is traveling, and the "pure" vacuum is not exist in the nature. Certainly, change of speed of light cannot be large because of extreme low optical density of the intergalactic environment. We shall designate cU as average speed of a photon from the distant source. An influence of the rarefied intergalactic environment on each photon during their movement was various, as environment is very dynamical, first of all, because of a fast varied electromagnetic field of other photons, including background one. We shall count therefore that distribution of photons on speed have been defined by some average function F(v, cU), for example, Gauss law:
dn=(2πσ2)-1/2 аN exp[-(v- cU)2/(2σ2)] dv
where dn is number of the photons accepted in unit of time, which speed is in limits from v up to v+dv, N - the general number of photons radiated in unit of time and that then will get in the receiver; σ2 - a dispersion. N depends on time of radiation t (t=0 corresponds to the peakа radiation moment). We shall notice, that for a source there is no distribution in the speeds - all photons have speed "c". We shall assume, that values cU and σ2 do not depend on time and from length of a wave; and distanceа R from a source up to the receiver during supervision is changing insignificantly (much less of R).
Let n - the general number of the photons accepted in unit of time (depends on time of reception tТ). Let time t and t' are defined in a system of reference of the receiver, and t' =t + R/cU
n(tТ)=а ∫ N(t+ R/v - R/cU) F(v, cU) dv
The value of shift R/v - R/cU = (R/cU)(cU/v -1) is measured in days and means an epoch concerning time t from which photons come to the receiver at the moment of time tТ. And, the further Supernovae is situated, the more an epoch exist photons will come from.
On the contrary, for very close Supernova the value of shift will be practically equal 0 for any speed v, that is, simple conformity between epoch of radiation and reception is established. Accordingly, the further Supernovae is situated, the more an epoch exist photons will come to from one epoch of radiation.
ааа 4. Conclusions
All this results to that:
1.аа The width of a light curve increases proportionally to distance both for all spectrum, and for a separate range (w-factor);
2.ааа The peak of accepted radiation (absolute luminosity) decreases proportionally to distance both for all spectrum, and for a separate range (s-factor), and the factor of proportionality depends on absolute luminosity in this range (the formula (2) in NKP2002);
3.ааа Color B-V at peak B-band is proportional to distance and it is a consequence of the formula (2) as a subtractа of luminosities (the formula (3) in NKP2002).
4.аа As result of these reasons it is possible to estimate value cU, assuming, that the maximal speed v is equal "c" and that the width of a light curve makes up 60 day for a Supernovae, that situated on distance R=3*109 l.y.:
2(R /cU) (1ЦcU/ё) = 60 days
Whenceа cU = ё(1-3*10-11).
5. Accordingly, the optical density of the intergalactic environment should be equal 1+3*10-11.
6.аа We shall take into account, that the measurement accuracy of the speed of light (in experiments with long-basic interferometers and Cherenkov radiation) makes up some decimeters per second, that is 10-9c. Hence, it is not possible to confirm this hypothesis in direct laboratory experiment yet.
7.аа If it is possible to receive reliable estimations of optical density of the intergalactic environment, and these estimations is not coincide with that submitted calculations there will be one more opportunity of an explanation w- and s-factors, that is a hypothesis about not coincidence of the light speed in vacuum and the maximal speed of a matter interaction.
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Last correction 22.09.2002 22:22