Tom Droege took an image of M31 as part of the initial night-time tests of the Mark IV camera. I have done a little work on the image, and show herein some of its features.
Gross characteristics of the image
This image (called "D151847.FTS") was taken Dec 15, 1998, from the roof of Tom's house in Batavia. It was a 50-second exposure through the V-band filter. The coolant pump was turned off, so the chip wasn't quite as cool as usual.
I did some image processing, using a dark frame (D151643.FTS) and flatfield frame (D151707.FTS) taken on the same night. There were problems: the dark frame had a mean level somewhat higher than the data frame; Tom had mentioned a possible light leak in his notes. The flatfield frame was a 100-second exposure taken during twilight, and it showed a number of stars. I used a 25-pixel by 25-pixel "ring" filter to reduce the effects of the stars in the flatfield frame; basically, I applied a 25-by-25 pixel grid at each point of the image, picking 8 pixel values from the grid, finding the median of those 8, and setting the central pixel value equal that that median.
Here's what the flatfield frame looked like: the image is binned 4x4, as are all pictures in this note unless mentioned otherwise. It is also a negative image: areas which look dark below actually captured more light than average; areas which look white below actually captured less light than average.
The processing was less than perfect, but it makes the image look a little better. Here's the raw data frame of M31 ...
and here's the processed version:
In this image, North is (nearly) to the left, and East is (nearly) down. The plate scale, based on a set of 6 stars with positions from the HST Guide Star Catalog near nu Andromeda, is about 7.33 arcsec per pixel. The field is about 4.17 degrees across. Prominent features are
The raw image has pixel values at the bottom of about -24,700 DN. Pixel values near the center of the frame are about -23,961 DN. So I'd guess that the sky is roughly 750 counts above the bias. The standard deviation from the mean sky value is about 20 DN. Pixels saturate at about +2000 DN, so the overall range of pixel values is from -24,700 to +2000 DN, or about 26,700 DN. If we use the standard deviation in the sky as a measure of noise, the dynamic range is about (2000 DN - [-23,961 DN]) / (20 DN) = 1300 or so.
Now, a closeup of M31 and its satellites (blown up so that each CCD pixel appears as a 2x2 pixel square). You can see that the stellar images become comatic near the edges of the image. From a dark site, and with better flatfielding, the arms of M31 should extend beyond the borders of this closeup. It's possible to see faintly a dust lane in M31 to the northwest (upper right) of the nucleus.
The strange-looking artifacts below M31's nucleus are due to ice crystals on the chip, I think.
Now, a closeup of the area around nu Andromeda (again, zoomed in 2x2).
The ice-crystal defects are again apparent. In this portion of the image, near the chip's center, the stellar images are nearly round. The FWHM of the images is about 2.4 pixels, which works out to about 18 arcsec. I have identified and labelled 6 stars:
Label GSC_ID GSC_mag TASS_mag(*) ------------------------------------------------------------ 1 2801-1433 7.09 6.80 2 2801-1748 9.61 9.61 (matched) 3 2801-0006 11.10 10.91 4 2805-0249 13.05 13.29 5 2802-0778 12.69 12.82 6 2801-1692 12.88 12.86
Here, I calculated an instrumental magnitude by integrating light within a circular aperture of radius 5 pixels, using an annulus from 10 to 20 pixels radius to measure a local sky background. I then matched the instrumental magnitude of star "2" to its GSC value, and shifted all the other instrumental magnitudes to match. The agreement is pretty good.
It appears that this image, of 50 seconds exposure in a suburban location through a V-band filter, with moderately good focus, reaches down to about mag V = 13. But this is only a first guess.
I looked in the catalog of low-precision BVRI standard stars which Brian Skiff has been compiling for the LONEOS project. There was one set of stars which might appear in the Mark IV image:
# Loneos name RA Dec GSC B V R I M31_III-133 10.1829 40.2889 G 2801-0554 14.81 14.12 13.77 99.00 M31_III-40 10.1850 40.3261 G 2801-1101 11.84 11.37 11.08 99.00 M31_III-15 10.2008 40.3556 A 2801-0234 13.72 13.20 12.87 99.00 M31_III-13 10.2025 40.3794 A 2801-0821 15.72 14.77 14.20 99.00 M31_III-43 10.2567 40.3569 G 2801-1634 12.46 10.84 9.86 99.00 M31_III-42 10.2725 40.3636 A 2801-0108 11.85 11.32 11.03 99.00 M31_III-106 10.3396 40.3586 A 16.83 15.93 15.40 99.00 M31_III-107 10.3421 40.3544 A 16.24 15.72 15.41 99.00
I looked in the image, and was able to find the right area: stars 42 and 43 in the above list are at (237, 1060) and (231, 1064) of the image, respectively. I was able to see only the brightest three stars clearly; star 15 in the above list, with mag V = 13.20, was a very faint smudge, close to what I think is a cosmic ray hit. All the other stars are completely invisible. For those three stars, I used simply aperture photometry with a radius of 5 pixels to measure instrumental magnitudes from the image; stars 42 and 43 are so close together that they contaminate each other's measurement slightly. Here are the results:
star B V instr. instr-V (B-V)
--------------------------------------------------------------
42 11.85 11.32 16.28 4.96 0.53
43 12.46 10.84 16.15 5.31 1.62
40 11.84 11.37 16.64 5.27 0.47
The instrumental and V magnitudes of the three stars don't agree very well. If this were a result of color terms, then we would expect stars of similar color -- such as 42 and 40 -- to have roughly the same offset; but they do not. The PSF in this area of the image is somewhat comatic. Perhaps that, and the contamination of stars 42 and 43, explains the poor agreement.
Thanks to Brian Skiff, I found more stars with decent photometry to check against the Mark IV data. Brian's newest LONEOS catalog contains a set of 6 stars near M31, identified in the picture below:
star RA (J2000) Dec GSC V (B-V) ------------------------------------------------------------------- NGC 224 deV-14 0 43 14.1 +41 00 34 G 2801-2078 9.20 0.99 NGC 224 deV-19 0 43 38.2 +40 54 15 G 2801-1024 10.25 1.02 NGC 224 deV-25 0 44 30.6 +41 15 37 G 2805-0390 11.17 0.45 NGC 224 deV-26 0 44 33.5 +41 17 47 G 2805-0168 12.25 0.48 NGC 224 deV-28 0 44 41.3 +41 19 07 G 2805-0108 11.23 0.58 NGC 224 deV-29 0 44 47.5 +41 18 49 G 2805-0117 9.13 1.00
I used simple aperture photomety to measure the instrumental magnitudes of these stars in the Mark IV image; the aperture was 5 pixels in radius, and I subtracted a local sky from an annulus with radii 10 and 15 pixels. Here are my results:
instr.
star V mag (instr-V)
---------------------------------------------------
NGC 224 deV-14 9.20 14.50 5.30
NGC 224 deV-19 10.25 15.56 5.31
NGC 224 deV-25 11.17 16.37 5.20
NGC 224 deV-26 12.25 17.51 5.26
NGC 224 deV-28 11.23 16.59 5.36
NGC 224 deV-29 9.13 14.42 5.29
========
mean 5.29 stdev = 0.05 mag
The agreement is quite good! A shift of 5.29 magnitudes shifts the instrumental magnitudes onto the standard V-band scale, with a residual scatter of only about 5 percent. That's good news.
Tom Droege asked about the degree of coma in this image. One way to measure that is to look at the fraction of light of a star which falls inside circles of increasing radius. Coma increases towards the edge of the image, so we expect that stars near the edge will have more of their light thrown far from the centroid of their PSF. I made a very quick check for this effect on the upper-left quadrant of the image (the quadrant containing M31). I picked six stars, all reasonably bright, and measured the amount of light within circular apertures of a radius 1, 3, 5, and 10 pixels. I then divided each value by the amount of light within the 10-pixel aperture. In all cases, a local sky value was estimated from pixels in annuli with radii 20 and 30 pixels.
The results show that stars near the center of the frame have more light concentrated near their centers than stars near the edges. Keep in mind that this image probably isn't focused optimally.
I suspected that measuring stellar positions from the Mark IV image would be a challenge: the field is over 4 degrees on a side, which means that some of the convenient approximations we use in matching the image from a flat detector to the curved sky don't work very well. It turns out that I was correct.
The picture below shows the Mark IV image with several overlays: two boxes, and a bunch of stars with ID marks.
The marked stars are:
label Star RA (J2000) Dec -------------------------------------------------------- Mu mu Andromedae 00 56 45.20 +38 29 58.0 Nu nu Andromedae 00 49 48.80 +41 04 44.0 A 32 Andromedae 00 41 07.20 +39 27 31.0 B gsc 2802_1830 00 58 02.17 +40 31 17.8 C gsc 2798_1141 00 59 01.87 +38 56 02.3 D gsc 2806_1403 00 57 45.44 +42 28 03.3 E gsc 2801_2025 00 42 01.45 +40 41 17.8 F gsc 2797_0403 00 47 20.20 +39 01 47.0 G gsc 2792_1904 00 39 47.52 +42 23 01.0 H gsc 2802_0679 00 51 30.14 +41 13 54.8
The two boxes mark areas in which I extracted a small set of stars (6 in each box) and matched their positions against (RA, Dec) in the HST Guide Star Catalog. Each set of stars covers a small section of the image -- at most about 300 pixels (about 0.6 degrees) on a side. Over these small areas, one can do quite well by projecting the GSC coordinates onto a plane, then applying a linear transformation (rotation + shift + scale) to match the coordinates to the image plane. When I performed this linear transformation separately in each area, I found
scale rotation mean residual
(arcsec/pix) (degrees) (arcsec)
----------------------------------------------------------------------------
upper area, near M31 7.31 -178.5 1.1
lower box, around nu And 7.33 -179.5 0.7
The residuals are about as small as we should expect -- that's good! Keep these facts in mind:
When I use all 12 stars in two boxes together, over an area about 1.5 x 0.5 degrees, I find the following astrometric solution:
scale rotation mean residual
(arcsec/pix) (degrees) (arcsec)
----------------------------------------------------------------------------
both boxes together 7.33 -179.1 1.1
Again, pretty good!
However, if I use the stars marked A to H in the image above, which are almost all near the edges of the entire frame, the match between the projected catalog positions and the measured image positions isn't so good:
scale rotation mean residual
(arcsec/pix) (degrees) (arcsec)
----------------------------------------------------------------------------
near image edges 7.32 -179.4 5.5
Why do the residuals increase? Two reasons:
If we plan to measure positions from Mark IV images, we should use one of these approaches:
row = A + B*x + C*y
col = D + E*x + F*y
we might use
row = A + B*x + C*y + P*x*x + Q*x*y + R*y*y
col = D + E*x + F*y + S*x*x + T*x*y + U*y*y