For historical reasons, astronomers measure the brightness of celestial objects in rank order. The smaller the rank number, aka magnitude, the brighter the object. Thus, a star of the first magnitude is much brighter than a star of the sixth magnitude, and it would take exceptionally good eyes and a very dark sky to see a star of the seventh magnitude. Now, it turns out that the human eye perceives brightness on a log scale, so magnitudes are numerically similar to log(brightness). And because they are a ranking list, it is always with reference to a standard. After some rough calibration to match human perception to true brightness of stars in the night sky, we have a formal definition for magnitude,
$$m = – \frac{5}{2}\log_{10}\left(\frac{f_{object}}{f_{standard}}\right) \,,$$
where f_object is the flux from the object and f_standard is the flux from a fiducial standard. In the optical bands, the bright star Vega (α Lyrae) has been adopted as the standard, and has magnitudes of 0 in all optical filters. (Well, not exactly because Vega is not constant enough, and as a practical matter there is nowadays a hierarchy of photometric standard stars that are accessible at different parts of the sky.) Note that we can also write this in terms of the intrinsic luminosity L_object of the object and the distance d to it,
$$m = – \frac{5}{2}\log_{10}\left(\frac{L_{object}}{4 \pi d^2}\frac{1}{f_{standard}}\right) \,.$$

Because astronomical objects are located at a vast variety of distances, it is useful to define an intrinsic magnitude of the object, independent of the distance. Thus, in contrast to the apparent magnitude m, which is the brightness at Earth, an absolute magnitude is defined as the brightness that would be perceived if the object were 10 parsecs away,
$$M \equiv m|_{d={\rm 10~pc}} = m – \frac{5}{2}\log_{10}\left(\frac{d^2}{{\rm (10~pc)}^2}\right) \equiv m – 5\log_{10}d + 5$$
where d is the distance to the object in [parsec], and the squared term is of course because of the inverse square law.

There are other issues such as interstellar absorption, cosmological corrections, extent of the source, etc., but let’s not complicate it too much right away.

Colors are differences in the magnitudes in different passbands. For instance, if the apparent magnitude in the blue filter is m_B and in the green filter is m_V (V for “visual”), the color is m_B-m_V and is usually referred to as “B-V” color. It is the difference in magnitudes, and is related to the log ratio of the intensities.

For an excellent description of what is involved in the measurement of magnitudes and colors, see this article on analyzing photometric data by Star Stryder.

And it is a statistical hitch, and involves two otherwise highly reliable and oft used methods giving contradictory answers at nearly the same significance level! Does this mean that the chances are actually 50-50? Really, we need a bona fide statistician to take a look and point out the errors of our ways..

The first time around, Voss & Nelemans (arXiv:0802.2082) looked at how many X-ray sources there were around the candidate progenitor of SN2007on (they also looked at 4 more galaxies that hosted Type Ia SNe and that had X-ray data taken prior to the event, but didn’t find any other candidates), and estimated the probability of chance coincidence with the optical position. When you expect 2.2 X-ray sources/arcmin² near the optical source, the probability of finding one within 1.3 arcsec is tiny, and in fact is around 0.3%. This result has since been reported in Nature.

However, Roelofs et al. (arXiv:0802.2097) went about getting better optical positions and doing better bore-sighting, and as a result, they measured the the X-ray position accurately and also carried out Monte Carlo simulations to estimate the error on the measured location. And they concluded that the actual separation, given the measurement error in the location, is too large to be a chance coincidence, 1.18±0.27 arcsec. The probability that the two locations are the same of finding offsets in the observed range is ~1% [see Tom's clarifying comment below].

Well now, ain’t that a nice pickle?

To recap: there are so few X-ray sources in the vicinity of the supernova that anything close to its optical position cannot be a coincidence, BUT, the measured error in the position of the X-ray source is not copacetic with the optical position. So the question for statisticians now: which argument do you believe? Or is there a way to reconcile these two calculations?

Oh, and just to complicate matters, the X-ray source that was present 4 years ago had disappeared when looked for in December, as one would expect if it was indeed the progenitor. But on the other hand, a lot of things can happen in 4 years, even with astronomical sources, so that doesn’t really confirm a physical link.