WZ Sge, and its period(s?) (fwd)

From: Joe Patterson <*jop_at_astro.columbia.edu*> Date: Mon, 30 Jul 2001 09:30:38 -0400 (EDT) · jop_at_astro.columbia.edu

Dear CBAers,

I just sent this note to Gianluca Masi, and it seemed like it might be of
interest to others.  So far it appears to me that WZ Sge is bumping
merrily along at its orbital period, as in 1978.  The flickering amplitude
is *remarkably* high for a dwarf nova in outburst - higher than any other
I know (most outbursting DN just sit there like light bulbs).  From the
1978 analogy, a transition to a longer period might perhaps begin
somewhere around August 3+-4.

I'm going to Germany for a CV meeting on Saturday, and I guess I'll be out
of the email loop for about a week - probably able to read email, maybe
able to answer, but probably not able to do any analysis of data till I
get back.  If you'd like to receive swaths of WZ Sge data, please let me
know.  I'll write again  before I leave for sure.

         joe

Dear Gianluca,

Thanks for all that data - what a great week you are having!  Let's see,
I'm pretty sure I have all the data through JD 119.9 now, a total of 5.5
days.  From my inspection I don't see any definite evidence for period
changes.  Naturally there could be some, but it's not big enough for me to
measure credibly.  One thing you might want to consider...

Period-measuring procedures are notoriously inaccurate in the presence of
an additional noise source of comparable amplitude.  The way to get around
this is to accumulate many cycles, i.e. densely packed data over a long
baseline.  One night is definitely too little for any secure conclusion,
and two is borderline - three is a lot better.  Some people use a "Rule of
Ten" - i.e. you need 10 cycles sampled for the properties of the periodic
process to be decently measurable.  Of course it depends on the size of
the noise ... you wouldn't have to be as conservative if the flickering is
small, and you might need as many as 20 cycles if the flickering were,
say, bigger than the periodic process.

I've noticed another Rule of Ten in my experience with CVs.  Maybe I
should call it the Rule of Point Ten.  It's this: the error of a frequency
measurement is about 0.10/N cycles per day, where N is the the duration of
the time-series in days.  I've been impressed with how universally this
applies to real data.  For WZ Sge, it implies an error of ~2 min in a
single-night measurement, or ~25 s if a two-night (consecutive) time
series is available.  This error is larger by a factor of 10-20 than
some of the errors being quoted now in internet postings.  On the
other hand, some people derive errors from common statistical notions,
like "half-width at half-maximum".  This latter prescription always
gives errors that are too big, by about a factor of 2.

At the risk of sounding silly, I'll reduce the latter point to another
Rule of Ten: that the actual 1-sigma error in frequency is the half-width
of the power-spectrum peak 10% of the way down from maximum.  (Or:
half-width at 90% of max).  Works pretty damn well.  (The reason we have
to invoke "rules of thumb" etc., rather than just learn from statistics
books, is that we always make these measurements in the presence of noise
sources - usually flickering - of unknown properties.)

Good luck pursuing WZ Sge - so far you've been the world leader in
getting these great light curves, I'm sure you can take a little rest ...
but not too much!

Oh, one last Rule of Ten.  For this advice I hereby rule that you now owe
me ten million dollars.  At an offshore bank, please, so I don't have to
pay those bothersome taxes.

              joe