From: Jason Rowe <jasonfrowe@gmail.com>
Subject: Re: Some follow-up questions re: MOST observations of sigma Ori E
Date: January 23, 2012 5:47:31 PM GMT-02:00
To: Richard Townsend <townsend@astro.wisc.edu>

Hi Rich,

It's my understanding that column 2 (the instrumental magnitude) and column 13 (the star flux) represent essentially the same data, but with a couple of differences, viz:

(i) column 2 is in magnitudes, with a mean of zero; while column 13 is in flux units.
(ii) column 2 has had a variable stray light correction applied, while column 13 is 'raw'

Further, column 13 is in ADU, not e-.  The adopted gain was 6.1 e-/s.
.
Was 1.1908 the exact value used? The period of the star is slightly longer than this, and moreover the harmonics go out to more than 10th-order. So I'm wondering whether the sinusoidal series subtraction may have left some 'real' signal behind in the residuals.

The fit did leave behind some residuals, but it doesn't have to be
perfect, in fact, overfitting can also cause problems.  The satellite
has an orbital period of ~101 min (~14.1 c/d).  During each orbit the
background is strongly modulated.  Background levels go from ~3000 ADU
to 16000 ADU per exposure.  For whatever reason (gain variations?) the
instrumental magnitude is strongly correlated to the background level.
To correct this one usually just fits a polynomial to magnitude vs
background level.  The assumption is that any stellar-variations will
be averaged out and not affect the fit to the correlation.  For sig
Ori E, this assumption is not true because the astrophysical
variations are much larger than the stray-light amplitude.  Since the
sig Ori E variations are coherent I can pre-whiten the signal, then
fit for the stray-light.

The free parameters here are: what order to fit the stray light with
and how may harmonics to remove from the light-curve.  This was
answered by looking at improvements (or lack of) from a chi-squared
perspective.  I used 6,8,10 and 15 harmonics to fit for the
astrophysics and 2,3 and 4th order polynomials to fit for the stray
light and looked at the chi-squared statistic of the stray-light fit.
There was minimal improvement (less than 1 sigma) between 8th, 10th
and 15th order fits and likewise the 3rd and 4th order polynomials
showed little difference.  I adopted the least complex functions to
correct the data.

-A polynomial was fit and subtracted from the residuals the
relationship between the sky-background and instrumental magnitude.
If the above step is not taken than the stray light correction can
produce aliases related to 14.1 c/d


I'm not quite sure I follow this step -- can you clarify? Surely, the residuals will be dominated by the *periodic* stray light variation, and therefore using a polynomial to fit the residuals won't work so well?

I think my wording was confusing (that'll teach me to work till 3am!).
I fit a polynomial to the the sky-background vs instrumental
magnitude relation.  In this relation, all the points at low levels of
stray light will occur at the same phase, likewise for points at high
levels of stray light.

-outliers where clipped at the 5-sigma level.

-The sinusoidal fit was added back to the data.

(c) As a parallel question, am I correct in interpreting column 13 as the result of applying the steps described in sections 2.2.4 and 2.2.5 of Rowe et al. (2006) -- that is, background gradient fitting, cosmic ray removal, sky subtraction, and PSF-fitting/aperture photometry? So, column 13 is the flux prior to the variable stray light correction? And then column 2 results from the variable stray light correction, converted to magnitudes with the zero subtracted?

column 13 will only include sky-subtraction.  I use it as a diagnostic
to search for saturation and non-linearities and sometimes for flux
calibration.


Can I confirm that dividing column 13 by the exposure times in column 15 would give the star flux before the stray light corrections are applied?

No, this will not work.  You also have to fold in the stray-light
correlation which not linearly scale with exposure time.

As a final question -- given that you've already invested time in these observations, and moreover given that I'm taking up more of your valuable time right now, I'd like to include you on the author list for the paper I'm writing. Are you OK with that? Of course, I'll be circulating a draft once I get it done.

If you want me to write up a section of data-reduction then let me know.


That would be very helpful -- I'll let you know when I need the text!


If you think a phone conversation would help to clear up any
confusion, feel free to call me: 650-605-3468

Good luck,
Jason


-- 
Jason Rowe - Kepler Mission Transit Scientist
NASA-Ames Research Park
MS-244-30
Building 244, Rm 108
Moffett Field, CA 94035-1000
ph# 650-605-3468 / fax# 650-604-2338
