[vsnet-alert 11008] re QZ Vir: superhump period update. Period down, amplitude up.

[varposts at Safe-mail.net]

You do realise that as you have not quoted any errors on the periods you give it is difficult to assess this information?  First we have to assume that the significance precision of the fourth period differing from all the rest, and it looking very similar otherwise to the fifth period, is not a typographic or cut and paste error, then when the standard deviation of the five periods is 0.000442 days, 38 seconds, which gives nearly two minutes at three sigma, whilst difference of longest to shortest period quoted is around one and a half minutes.  This is assuming the periods are in days, which is not stated, but looks likely.

If you look for it the software you are using should provide error estimates for the derived periods, either via estimate from the residuals of the linear regression or whatever fit of the test period against the observed points or from assessment of the data itself.  I believe there is a mathematical principle wherein how precise a period _can be_ is estimate-able from factors including test period and data run duration too.  For instance, the January 26th entry amounts to three and three quarter cycles from which a period with six significant figures is quoted.

The data at face value suggests an (inverse) correlation between period and amplitude, which is fair enough, if the periods are meaningful, however it also shows the period lengthening then shortening.

Taking Kato Taichi's estimate of period decay here

<http://ooruri.kusastro.kyoto-u.ac.jp/pipermail/vsnet-alert/2009-January/002611.html>

leads to roughly a period decay of just over half a second per cycle if dotP over P is rounded to 0.0001  and the period crudely taken as 0.06 days from below.  (I quote values as then my abysmal arithmetic skills, as well as the assumptions I'm using, can be checked for accuracyand validity).  Taking the last and first JD quoted here, giving just over 70 cycles at 0.06 days, and the about half a second, that'd give just over half a minute decay in that time, similar to the standard deviation on the below periods, except the below periods increase over three days before dropping, which looks more like a statement on the spread rather an actual trend.

Whatever, I'd suggest you seek guidance on your error generation from the variable star organisations you are a member of.  A high significant figure period, no matter how much data it is based on, is meaningless without attendant quoted error.  In fact, formally, mathematically, not quoting an error for a value implicitly infers that the error is +/- 1 of the last digit, ie +/- 1 x 10^-6 in these instances.

It is certainly possible for period analysis to return results with precisions far beyond those meaningfully achievable.  Most analysis software doesn't address this, but it does usually allow some form of period error estimation in tandem with the period estimation.

John Greaves

Original Message was :-

"Measurements from the AAVSO observers George Sjoberg (SGOR) and William Stein (SWIL) indicate the following:

Jan 26 2009
2454857.77929 to 2454858.00544
Period 0.060258 with amplitude 0.15

Jan 28 2009
2454859.75902 to 2454860.00073
Period 0.060645 with amplitude 0.1

Jan 29 2009
2454860.74175 to 2454861.00102
Period 0.060981 with amplitude 0.1

Jan 30 2009
2454861.74389 to 2454862.00312
Period 0.0599947 with amplitude 0.22

Jan 30 2009 (SGOR)
2454861.79558 to 2454862.04933
Period 0.059947 with amplitude 0.23

The decrease in period combined with the increase in amplitude is noteworthy.

Martin Nicholson, Daventry, UK"