Re: GSC 00445-01993

[jg <jg@jgws.freeisp.co.uk>]

aah@nofs.navy.mil wrote:
...
>   Note that if you do 'slide' the graph a bit, then you need to
> revise the error value since that is what AVE analytically determined
> and now you are using a different selection method.  I usually use
> the AVE error and the error from the difference between AVE's period
> and your eyeball period, and add the errors in quadrature.
> Arne

Unfortunately, Michael, periodogram analysis in astronomy is a black
art, so you've just got to pick it up as you go along.

For instance, where does AVE get its errors from?  As error is supposed
to be related to the nature/state/distribution of the data, how come
Arne mentions the difference in analytical techniques causing a
different selection method?  Are these error errors, standard errors,
standard deviations or what?  Read most of the papers on such things and
you still won't find the answers half the time.  Most just requote the
Stellingwerf (PDM) and Lomb-Scargle (DFT) original papers as reference,
which is naughty, because nobody uses those methods unmodified.

AVE doesn't even seem to give the "power" on it's periodogram plots that
I can tell.

Basically, if you pick a new frequency, the only change is the
semi-amplitude at that frequency, as opposed to the previous "test
frequency", and the standard deviation of the data after a sine wave of
that frequency and amplitude is removed (again, as opposed to what
happened with the previous test frequency).  The number of observations
used and the total duration of the observations are the same in all
cases unless you are actually analysing different subsets of the data
each time.


But that's talking DFT and sine waves, I suppose it may all be different
for eyeball adjustment of EW lightcurves' periods.


ANYWAY, the Percy (Ed) book you bought contains some discussion on
aliasing and (as one author therein entitles it) "pseudo-aliasing".

I did a spectral window function of your data last week and as expected
there were strong signals at 1 day, half a day, third or a day, quarter
of a day.  I stopped (more properly started) about there, my spectral
window functioning comes from a home grown bit of qbasic and is
therefore very slow to process, especially if a reasonable "resolution"
of frequency step size is used.

That means that your data has within itself strong periodicities that
are simple fractions of a day just due to the structure of your
observational regime.  The one day one is obvious, the simple fractions
are harmonics of that.  The period is also near a simple fraction of a
day (and it'll have harmonics), this leads to interference (ie frequency
can be slightly shifted, and "power" spread out across the peak at the
main frequency thus reducing amplitude... ...that is, the peak changes
shape and/or splits in to many clusters of close peaks dependent on
frequency step size used to investigate). This is called aliasing for
some reason I don't know, and when of this kind further called by a few
pseudo-aliasing.  "pseudo" because the intefering temporal signal(s) in
this case is/are not from any other periods within the data/object, but
from the data's temporal sampling structure itself.

(Heck, it's even difficult to talk in English about this stuff:  you try
writing a paper about a variable (star) whose period (cycle length) was
variable (changed) over a period (duration) of time, all the while
calculationg in frequency in cycles per day whilst using the
astronomical convention of quoting in periods in days etc ;^) Plenty of
room for little errors to creep in that you get "word blind" on)

Dirk mentioned much earlier, about a month or so ago, about these simple
fraction of a day objects being a quite tricky problem, and it is
especially so when attacking EW lightcurves, which aren't really
sinusoids, with DFT.  He mentioned an IBVS showing an example of one
where he and others resolved this (to my shame I forget the details).

As Arne has said in the past, Tom's observing regime actually has a
selection effect _towards_ detecting objects with these sorts of
periods.  You'll have to get used to it and learn how it works ;)

I'd assume the usual trick is to derive lots and lots of minima from
lots and lots of data via Kwee-Woerden or whatever they're called and
use O-C.

Such a route involves patience and a long period (duration) of
observation, maybe weeks to months.  Which I know is not ideal ;)

(If any new deltaScutids are eventually found we're all going to have to
figure out how Period98 works and leave AVE alone).

As to where KW techniques get their error, and/or the amazing quotations
of error from O-C that you'll often see (scariest "error case" going
that, but frequently important for both long and short period variables
in terms of statistical significance testing as any barely detectable
change in period due to evolutionary mechanisms within the star is
always going to be at or far less than the noise level), I dunno.

Dirk mentioned investigating an alternate route via templates, which
sounds promising.  After all, there are only so many kinds of
lightcurve, why assume infinite variations, a few a priori assumptions
can be reasonable.

All in all period analysis probably carries a helluva lot more
subjective decision that write ups own up to.


And Tom thought simple lightcurve pigeonholing was scary ;)

Cheers

John G.


PS

Looking things up in a statistics book won't be easy either: I found out
that what astronomers call a "periodogram" in DFT is a spectral window,
and what they call a "spectral window" is the "spectral window
function". Though I was looking at a UK English stats book and most of
this astronomical period analysis stuff comes from USA English authors,
and that could be the source of that discrepancy.