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Re: Everett and Howell Paper
Subscribers to PASP (Publications of the Astronomical Society
of the Pacific) can read an electronic version of the paper
by going to (I've broken the URL over two lines -- put them together)
http://www.journals.uchicago.edu/PASP/journal/issues/v113n789/
201154/201154.html
One can download a Postscript version of the paper from the
website of the Planetary Science Institute: go the Publications
page
http://www.psi.edu/esp/pubs.html
and click on "A Technique for Ultra High Precision Photometry":
http://www.psi.edu/esp/pasppaper.ps
Andrew Bennett asks:
> Can one translate this to what we could expect
> [fraction of stars showing variability]
> ... at the
> precision we are already getting with the Mk IV?
> (not much better than 0.01 mag)
The paper doesn't provide enough information to answer Andrew's
question, unfortunately. Their statement that a few percent of
the stars show low-amplitude with a timescale of more than a
few hours is all they say on the topic.
> ... does this mean that those high Welsh-Stetson
> statistics I got are real?
The only way to find out for sure is to continue to monitor
the stars and verify that the variations continue and (in some
cases at least) are periodic.
As Andrew notes, their uncertainty in the measurement of a single
bright star (where "bright" means V=14) is about 0.002 mag.
The best I've seen from a Mark IV system is about 0.005 mag
(for "bright" stars of V=8). Why the differences?
- is it the method of analyzing the extracted magnitudes?
No, I don't think so; they use an ensemble photometry
technique which is essentially the same as that used
near the end of Tech Note 76, and, as TN 76 shows,
the technique didn't reduce the scatter
- is it hardware, specifically full-well capacity or
effective PSF size? Again, I think "no".
Both groups use CCD chips with relatively shallow
full well capacities. The Everett and Howell paper
implies that they ignored pixels with more than 70,000
electrons (though they don't state it directly).
The Mark IV has a similar gain (3 electrons/DN),
and its full-well capacity is about 80,000 electrons.
We put all the light from a star into a relatively
sharp PSF, with a Full-Width-at-Half-Max of about 3 pixels;
one of the reasons is that our pixels are so big, about 7.5
arcsec on a side. E&H use a much smaller pixel scale
(0.43 arcsec/pixel), but focus the light into a FWHM
of 1.4 arcsec, which works out to about 3 pixels.
I think it's the extraction of magnitudes from the data.
The key differences is observing technique, and, specifically, flatfields.
Here's an extract from the E&H paper:
"Flat fields were obtained for each filter.
For the V-band filter a large number of flats
(120) was obtained over the 5 days of the
observing run and was later reduced to produce
a single flat-field calibration image. The same
reduced V-band flat was used to reduce each night's data."
Aha! Although this doesn't explain how they acquired the flats
(dome flat? twilight sky flat? night-sky flat?), it does imply
that the signal level in the combined flatfield image must have
been VERY large. Here's another extract:
"A master V flat was produced for the entire
run by taking a mean of the nightly flat fields.
The master V flat combines 120 individual
exposures of 40,000 e- pixel-1 apiece to obtain
a fractional uncertainty of 5 × 10-4 (per pixel)
in our flat, so flat-fielding is not a limiting
factor in our final photometric precision
(see, e.g., Newberry 1991). The UBRI flats are
filtered averages of typically 20 dome-flat exposures. "
Okay, it looks like they use dome flats. Note that EACH dome flat
has about 40,000 electrons per pixel, and they combined 120
of those to make a master flat. That's 4.8 million electrons
per pixel. Yow.
On the other hand, in my analysis of Tom's Data Disk 16, I combined
only 19 frames (not 120) to make the master flat. Each was a
night-sky image (not a dome flat), so it had a relatively small
number of electrons (because the night sky isn't very bright).
Let's see -- each V-band flat had roughly 1300 counts -> 3900 electrons.
Combining 19 such images yields 74,000 electrons.
electrons per pixel fractional statistical uncertainty
----------------------------------------------------------------
E&H 4,800,000 4.6 x 10^(-4) = 0.00046 mag
TN 76 74,000 3.7 x 10^(-3) = 0.0037 mag
Hmmm. Is it a coincidence that the noise floor in the magnitudes
measured in TN 76, about 0.005 mag, is just a big larger than this
value implied by the light level in the flats? I think not.
After I first published TN 76, Arne Henden and I corresponded on
exactly this issue. He attributed most of the noise floor to
the flatfielding technique, and eventually convinced me that he
was right. Arne sent me a list of the factors which help one to
reach millimag (0.001 mag) photometry, and I will hope he won't
be too angry with me if I share it with the whole list now:
Arne Henden's hints for high-precision photometry
>
> (1) photometric skies. Cirrus will cause millimag
> differences across a 10arcmin field. (This may
> be another reason why the TASS results have a floor.)
> (2) oversampling. A minimum of 6 pixels per fwhm.
> This helps in several ways: it averages out
> flatfield and subpixel errors, and keeps the
> peak signal down so that the dynamic range goes up.
> (3) dome flats with a minimum of 1M e-/pixel, usually
> more.
> (4) twilight sky flats with a minimum of 100K e-/pixel,
> used to correct for gradients in the dome flats.
> (5) carefully cleaned filters and dewar window, removing
> as many of the dust donuts as possible. Careful
> centering to keep program objects away from
> dust donuts.
> (6) long exposures, at least 60seconds, to remove
> scintillation and shutter vignetting.
> (7) observations near meridinal transit so that the
> objects are as high in the sky as possible,
> improving scintillation, refraction, and
> second-order extinction.
> (8) lots of biases/darks to remove all noise in these
> frames.
> (9) dithering the frames so that sequential frames do
> not use the same pixels. This removes some systematic
> effects at the millimag level.
> (10) instrumental magnitudes only, no transformations (again,
> adding error since you have two filters involved).
So, one of the bottom lines is -- use twilight sky flats or
dome flats, not night-sky flats, in order to reach the highest
precision.
Michael Richmond