On 02/20/2012 10:29 PM, Jones Beene wrote:
Impressive! You take this quite seriously Mauro.
Not so seriously, really. I took it as an opportunity to learn new
things. And your hypothesis looked both interesting and appropriate.
This is actually a lot more complicated than it seems at first glance.
Probably because the 11 year cycle is not really exact, but the
statistical arguments are hard for me to follow.
Basically, there are mathematical methods to obtain the foundational
frequencies for a given signal. Any given signal can be decomposed in a
sum of components in frequency. That's called the spectrum of the
signal. You can Google Fourier transform, and Spectrum analysis, if you
like, as a good start.
I don't know much about the extensive and venerable mathematical
treatment, but the pragmatic and intuitive approach is immediate: obtain
the components in frequency of a given signal, no matter how complex,
and sort them according to relevance, that is, according to how well
defined and strong they appear in the original signal.
Another interesting thing is that you can later use those components to
reconstruct the signal, and that can be (and is) used as a compression
method. But that's another story, related to digital audio and video,
and to their ubiquity on the internet.
You have to wonder how accurate older data is as well.
Yes. Systematic data for the solar cycle starts in 1874, which is good.
Systematic data for Eta Carinae and Eta Carinae's cycle is only from
around 1948. I'm assuming Eta Carinae's cycle spans all the way to 1874
with the same frequency, which is a strong assumption. But if Eta
Carinaea is part of a binary system, as presumed, it's also a good one.
An interesting thing to try, by the way, is to perform spectral analysis
of the solar cycle, but only with data after 1948.
Is this your hobby only?
It's probably related to my work, but in unexpected ways. Basically, the
more you know, the better. That applies to all fields of life, by the way.
And I always wanted to learn to perform spectrum analysis. I think that
to be able to look for cycles and correlations is something very useful,
and that its use is in its infancy, at least in the Astrophysical sciences.
As I recall, your profession (like so many who turn up on vortex for
some reason) is software development, no?
Yes. Software development is an area where it's good to be constantly
learning, because the field is relatively recent, and is also developing
very fast. Things change, usually for the better, all the time, and it's
valuable and rewarding to be informed and know about new methods, new
languages, techniques, etc. That can be one of the reason many software
developers are lurking around here; always trying to learn new aspects
about things :-)
It's also a field where there are a lot of free and very powerful tools.
All that makes for a very good, and fruitful, combination.
Best regards. Thanks for the opportunity to chitchat a little bit,
Mauro
*From:* Mauro Lacy
I'll perform a power spectral density analysis of sunspot number/solar
activity data. If there's a 5.52 year cycle in solar activity,
it'll show up, along with the main 11 year cycle. I don't think
something that big can be easily overlooked,
but nevertheless... it bodes well with my modest attempts at statistical
signal processing :-)
More about this later, probably.
Well, here are the graphs:
http://maurol.com.ar/solar_cycle
The data was obtained from http://solarscience.msfc.nasa.gov/greenwch.
I used the daily sunspot area as an indicator of solar activity.
The method used is an estimate of power spectral density by the Welch
(1967) periodogram/FFT method, which is readily available, by example
in octave or Matlab. I had to do some manual preprocessing of the
data, and after fiddling for a relatively long time with the scales, I
finally began to obtain some meaningful values.
As can be seen in
http://maurol.com.ar/solar_cycle/daily_area-PSD3.png, there are two
peaks near Eta Carinae's period (5.539 years) of dimming X-ray
activity , at 5.51 and 5.3 years. They are both much less significant
than the main period of the solar cycle (which by the way, seems to be
actually near 10.6 years, not 11.04 years as usually stated), and
there's is not a period of exactly 5.539 years, but they are close
nevertheless. That is, there are (secondary) periods of the solar
system not in, but closer, to 5.539.
I obtained 5.539 years from the literature. This site in particular
was very helpful: http://etacar.umn.edu/
Regarding these results, I suppose you take it or leave it. I mean,
they really aren't *that* significant. But if you take it, there are
some interesting things to try:
1) smooth/consolidate the periodograms, to try to obtain less noise,
and higher peaks.
2) look for north hemisphere vs. south hemisphere cycles. As Eta Car
is south, maybe the periods in the south hemisphere are closer to Eta
Car's period. I'll do this next.
3) look for phase, not only frequency, correlations. I have yet to
learn how to do statistical phase analysis.
I hope you enjoy the pictures! If there are some people interested, I
can publish the scripts and techniques I used to obtain the graphs. It
really wasn't that difficult.
Best regards,
Mauro
