Good equipment, good seeing and good technique - these all contribute to good photometry!

Supernovas are being discovered at about 1 or 2 per day, which is an amazing increase over past years.  This is due to robotic systems and better CCD technology.  Nevertheless, bright supernovas (SNe) are probably not being discovered at a faster rate because they have always been discovered at close to 100% of events that occur.

This supernova (SN) is of intermediate brightness.  It reached a maximum brightness of magnitude 14.3 with a red filter.  It is difficult for amateurs to establish an accurate "light curve" for such SNe, and professionals don't want to spend costly telescope time on these objects unless there is evidence of something very unusual about them.  I've chosen SN2003cg to determine how feasible it is for an amateur to establish a light curve for a 14th magnitude SN with a small telescope (10-inch aperture is considered small by serious amateurs).  Last year I did a pretty good job with SN2002ap, which reached a magnitude of 12.2 with a red filter. This SN, being ~2 magnitudes fainter, is only 15% as bright as SN2002ap.  The measurements shown here establish that it is feasible for amateurs with small telescopes to work with 14th magnitude SNe.

Figure 1. Color CCD image of SN2003cg in NGC 3169 (center), also showing NGC 3166 in the lower-right (southwest) corner.  The insert image is a less saturated version showing the SN's redness.  The field of view of the larger image is 16 x 12 'arc. The faintest stars in this image have an approximate magnitude of 19.6. The larger image has been processed by the MaxIm DL "digital development" procedure to show the SN with a less unsaturated galactic nucleus.  Total exposure times are 40, 39 and 399 minutes for the red, green and blue filtered images (taken during the 8-day interval March 23 - 30).  Data from the individual images have been used to construct a 3-color light curve (below). [10-inch Meade LX200 f/6.3 telescope and SBIG ST-8XE CCD camera, Hereford, AZ].

Figure 2. Three-color "light curve" of SN2003cg comprised of my observations during the first 4 weeks since its discovery.  Note the slight loss of "redness" based on R/V differences (starting at 1.0 magnitude and currently 0.6 magnitude).  The V/B difference shows a slight change from ~1.0 to 0.8 magnitude difference.

This figure could have included other people's observations but since every observer has an unknown offset unique to his hardware and analysis procedure such a graph would be noisy-looking.  My measurement set is the most comprehensive, so it is a natural choice for plotting a light curve.

Photometry Measurement Pitfalls

By mid-April it became obvious to me that the nearby bright galactic nucleus was interfering with supernova magnitude measurements.  This is illustrated in the next figure.

Figure 3.  Annulus pattern is centered on the SN.  The inner circle is where "signal" is measured and the annulus is where a "reference level" is measured.  The size of the circle and annulus can be specified by the user.  [April 16 R-filter image, average of 31 15-sec exposures, using median combine of groups of ~6 and an average of the median combine results].

Notice that the reference level annulus contains some galaxy brightness.  Usually this will reduce the apparent brightness of the SN.  The following profile of brightness versus x-location illustrates the "curved" nature of the galaxy background.

Figure 4.  Brightness versus pixel x-value, showing SN (vertical line and arrow) in relation to the host galaxy.

The galaxy brightness distribution versus x-location is non-linear in the vicinity of the SN.  In mathematical terms, the galaxy background has a positive second derivative away from the nucelus; or, the background profile is "concave" at the SN location. It is easy to imagine the growing importance of this non-linear background as the SN intensity decreases.  Since the average of the annulus will always be higher than the true background value at the center of the signal circle by a specific amount, the measured brightness of the SN will have a constant negative brgihtness offset, and as the SN fades it will take on a "negative" brightness after some stage of its fading.

It is also possible that the SN is located "on top" of a galactic knot of brightness, which could increase the apparent SN brightness. The opposite might occur, where the SN is located in a region of unusually low galactic brightness.  Indeed, this is probably the case for this SN, as can be seen by referring to the longer exposure of Figure 1; the SN appears to be located in a galactic arm "dust lane."

The only solution for these several confounding effects is to wait for the SN to fade completely and then make measurements exactly with the same annulus settings (offset location and sizes) as were used when the SN was measured.

Another source of error is possible when the user of MaxIm DL's photometry program allows the program to locate the SN annulus pattern automatically for a maximum SN intensity (excess of counts within inner circle compared with predicted number of counts based on average counts within the reference annulus).  The user allows the program to automatically select this annulus pixel location by checking the "Snap" box for the "Object."  When the "object" (the SN in this case) is located on a background that has a brightness gradient, the "snap" process pushes the annulus pattern away from the bright background (the galaxy in this case).  Even though the snapping movement is just one pixel, typically, the loss of signal is apparently small compared to the lowering of reference level, leading to a net "improvement" in "signal minus reference."  This may seem like a good thing to do, but when you consider that this snapping does not occur when the SN is bright, it becomes clear that unwanted trends can be unwittingly introduced to a SN light curve. Namely, when the SN is bright the snapping error may be non-existent, but as the SN fades the snapping effect will increase and produce "brighter" SN results than if the snapping were not allowed to occur. It is therefore a better practice to not allow snapping when the object (or refernce star) is faint.

There's another consideration when measuring faint objects.  It has to do with the reference level varying across a noisy field. Even when there is no object in a region it is possible for statistical fluctuations to occasionally produce an apparent object with a measureable magnitude.  This is because occasionally a noisy bright pixel will appear within the signal circle when a noisy dark pixel (or configuration of pixels) appear within the reference annulus.  The eye is a good pattern recognition system (sometimes "too good" - seeing things that aren't statistically significant).  In my experience, the eye recognizes a real star when the MaxIm DL moving annulus pattern states a SNR (signal-to-noise ratio) of about 8.  This works out to about 1.0 magnitude brighter than the SNR = 3 "limiting magnitude" level.  Whenever you're working with an object close to this limit it is important to manually place the annulus pattern over the visually discerned center, and not at a location having the maximum SNR value.  The SNR may be slightly better at a location 1 or 2 pixels away from the visual center, but this will be due to the random noise of pixels that enter and leave the reference annulus as it is moved, and to random noise of pixels entering and leaving the signal circle.  This effect can be reduced by increasing the size of the reference annulus, but only if this is allowed by the absence of a nearby object, such as a galactic nucleus.  There's also an optimum size for the signal circle, which will depend sligtly upon the object's brightness; usually the signal circle should be about equal to the FWHM (as measured by a bright star that isn't saturated).

These considerations can be partially overcome by using a larger aperture and observing during good seeing conditions.  The larger aperture just changes the magnitude region where the same considerations apply.  But the better seeing allows smaller sized annulus patterns, which can have dramatic effects upon whether a SN can even be measured!  The smaller the signal circle, the less noise it will contain.  A smaller signal circle also allows the reference annulus to be larger (it can expand inward), which reduces the amount of noise for the reference level.  Better seeing also allows the outer size of the reference annulus to be smaller, which reduces the effect of galaxy gradients.

Good equipment, good seeing and good technique - these all contribute to good photometry!

This may seem like a lot of work, but if you think of it as a lot of fun, then you'll do better quality photometry.


This site opened:  April 2, 2003 Last Update:  April 20, 2003