Evolution of the electron and antielectron neutrino spectra as a
function of radius, for the inverted
mass hierarchy. Computed with two
flavors.
Download the movie file here.
Three flavor evolution
Same as above, but computed with all
three flavors.
Download the movie file here.
Three flavor
evolution to 10,000 km
This calculation extends the three-flavor calculation of the neutrino
spectrum to 10,000 km. For definiteness, we assume the matter density
profile falls off as r-3 for the entire region. The goal is
to illustrate the possible effects of the solar mass splitting on the
evolution. In a realistic model, the neutrino may encounter turbulent
density fluctuations and density discontinuity(ies) associated with
shocks.
Evolution of the electron and antielectron neutrino spectra as a
function of radius, for the normal
mass hierarchy. Computed with two
flavors.
Download the movie file here.
Three flavor evolution
Same as above, but computed with all
three flavors.
Download the movie file here.
Neutrino transition
probability in the mass basis
A more complete information about the final result of collective
oscillations can be given in the mass basis. The following two figures
show the three-flavor conversion probabilities for neutrinos and
antineutrinos, for the inverted mass hierarchy case.
Three-flavor conversion probabilities for neutrinos (PDF, JPG)
Three-flavor conversion probabilities for antineutrinos (PDF, JPG)
For example, P(nu_1 -> nu_2) indicates the probability, as a
function of energy, that the neutrino originally in eigenstate
|nu_1> transitions into eigenstate |nu_2> by the end of the
collective transformations (at 1000 km).
The top panels specify the labeling convention for the states.
Technical note on
displaying the animations
These movies should play in a variety of players. If you encounter
difficulties, a good, free, cross platform player is VLC, get it here.
I like these results.
May I use them in my talk?
You may use these movies in your research or presentations. Whenever
you do so, please cite
You say these animations are an integral part of the paper.
Shouldn't the arxiv.org
preprint server host this material?
Yes, but at the moment it doesn't.
It would be a very natural solution, by the way. This could be set up
as follows:
when uploading a paper to arxiv.org, authors
would be given an opportunity to upload not only a LaTeX file and
figures,
but also animations, data files, perhaps even codes -- anything they
deem necessary to present their research in the most comprehesive way,
within reasonable space limits (see below). The LaTeX file would
contain hyperlinks to the movies, etc. This would fully exploit the
electronic nature of the arxiv service, as compared with printed
journals. Importantly, the entire package would receive a time stamp of
the submission date, just like the LaTeX file and figures in the
current system.
But shouldn't the preprint server host "preprints" of papers?
A
traditional notion of a scientific paper is something that is made of
some text and possibly static figures,
formatted according to certain conventions. The folks running arxiv.org
seem to want to uphold this notion (consciously or not). Yet, if you
think about it, this form goes back to the days when a printed
copy of a journal was the main means of distributing scientific
results. The "paper" format is thus dictated by the technology of a
printing press. In today's world, the restriction of an electronic submission to text
+
figures is simply an atavism. (Now, I'm not advocating that the
paper format be abandoned. A paper could certainly be a
subset of the submission.)
But what about storage space considerations?
Back in the early 1990's, a
gigabyte of hard disk storage apparently
cost "under
$700". At that time, it made sense to impose a strongent limit on
the submission size, which is what was indeed done. Fast forward to
2010, when
the
same $700 buys you five
2-terrabyte hard drives (according to amazon.com). Yes, that is a
factor of ten
thousand more storage. As another example, Google now
offers over 7 gigabyte of space for free with your email
account. So, again, the storage constraint is a holdover from the years
past. A modest limit of, say, 100 MB, or even 10 MB per paper would fit
all these animations, and then some.
Anyhow, I predict that we will see arxiv.org
hosting animations, data files, etc, sooner or later. (I vote for
"sooner"!) In the mean time, webpages such as this one are the answer.
Incidentally, it should be noted that Physical Review Letters does in
fact have a
relatively unknown option to upload Supplementary Materials with a
paper. The animations and PDF files you see here were an integral part
of the PRL submission and review process. They are now hosted
online at aps.org at this link.
The history of this webpage.
This page was creates in early January 2010, when the preprint of the
paper was posted on arxiv.org.
It was updated in May 2010, after the paper was accepted to Phys. Rev.
Lett.
Alex Friedland, Jan 7, 2010; updated May 5 to match the
version accepted journal version; May 11 with the publication
information
