The estimation of a limiting stellar magnitude of an astronomical photograph in principal is an easy task. The method to derive a limiting magnitude by the identification of the faintest objects detected within a photography is a common method to describe the quality of an observation, a collection of photographic plates or a sky atlas. However, a few issues arise with the method, which lead to the conclusion that the method is not a very powerful indicator of quality. One of these issues surprisingly is the quality of the astronomical literature itself. These issues shall be discussed in this article.

Below picture of Messier 81 was taken by myself on 08 March 2010. It presents some objects identified and also stellar magnitudes of two point sources found with similar visual appearance and brightness. The distant dwarf galaxy UGC 5336 is a nice object and possibly resolved with amateur equipment. However, this dwarf galaxy clearly needs larger exposure times with excellent seeing to be resolved into its single components with brightnesses found above noise level. So we are looking towards the limiting magnitude for the image to perform a new calculation of exposure time.

The same recherche tool (Aladin) and related literature study yielded a large deviation in the estimated flux between both light sources A and B, which are marked in the picture. The irregular dwarf galaxy UGC 5336 is also shown in the picture. According to Georgiev & Bomans, the brightest objects of this galaxy present stellar magnitudes in the order of V=20...22. Astronomers measure this magnitude with the V filter of the Johnson filter system or a calibrated detector and filter close to this system. Georgiev & Bomans also present large discrepancies between the offsets of photometric data obtained from previous work. Indeed the differences between publications of several authors are presented in the order of 1 magnitude scale, which is a variation in brightness by of a factor of 2.5. 

Figure 1: Image of Messier 81. Click to enlarge. 

The true nature of the two marked objects A (V=19.5) and B (V=18.55) is not quite clear. With the angular resolution of the observation it could be foreground stars, stars clusters of the galaxy or an anonymous galaxy. The magnitudes are obtained from the Aladin database both taken from the same survey. The objects are shown for the demonstration of a magnitude difference of two objects, which nearly look the same. Different sources tell different magnitudes. The object given with V=19.5 in the above image, was found elsewhere having a magnitude of 20.9 V. This, however, seems far away from expectations, might be affected by a wrong identification. Finally, isn't it surprising, that UGC 5336 has a total magnitude of V=14? It is expected to appear brighter, than it is. In the above image I corrected the brightness of object A to 19.5 V instead of taking a value of 20.9 as I noted earlier on this webpage here. However, this does not explain the remaining discrepancy of brightness of about 1 magnitude in V found with the object within the same survey in the literature. A closer look will then show different colors for both objects, which might explain such a difference. With the magnitudes presented by Georgiev & Bomans the correct value of a limiting magnitude of about V=20 is close to the bright stars found in UGC 5336. This seems a reasonable estimation of the detection limit in this photography, as UGC 5336 is slightly at the limit. Considering a previous work of Perelmuter & Racine (1995) about globular clusters in Messier 81, it seems also more likely, that Georgiev & Bomans resolved faint star clusters instead of single stars.

A further source of wrong and/or systematic deviations of stellar magitudes and flux is based on the difference of spectral responses of the detectors used by Georgiev & Bomans and the observation described below. Thus, the magnitudes will only define an instrumental magnitude. Therefore the camera shall be carefully calibrated to obtain spectral response, adaptation to photometric standards  in astronomy, linearity and photo conversion rates. An estimated error of 1 magnitude in the visual is not very surprising. The deviations of magnitudes obviously increase when taking magnitudes derived from electronic imaging and compared to older photographic surveys in B (blue plates). There is no reasonable relationship between observations in the visual (green) and blue light (photographic). Thus, compared magnitudes may differ within 2 stellar magnitudes, depending on the color of the object. This is especially the case, when looking close to M 81. There are many globular clusters,  star clusters, H-II formations and young populations, which are mixed of both an emission line nebula and a young cluster. The colors may range from blue star formations over yellow, old clusters to the red of the hydrogen emission nebulae. The problem will increase, when observations are taken with a CCD and using no filter at all. A definition of limiting magnitude is not given for the special case of a wide spectral range. Therefore the limiting magnitude of a color photography have to be seperated and provided for B, G and R, which are the blue, green and red color bands of the camera.

Conclusion

The method of determination of the limiting magnitude by looking for the faintest objects in a photography is more a subtle than a quantitative method. In case of a colored picture, the errors are found in the order of one magnitude. Compared to the existing literature, the additional error of the zeropoint (offset) might cause one more magnitude error. With the error propagation this may mean a total error of 2 magnitudes in a worst case. Imagine, you now want to compute now the distance modulus of the galaxy based on the calculated brightnesses. An error of 2 magnitudes means, you wouldn't be able to tell the true distance, because the distance could also be 6 times larger (or smaller). I will present a different method in a later issue of the Monthly Notices.

References

Georgiev T. B., Bomans D. J., 2004, BVR photometry of the resolved dwarf galaxy Ho IX. A&A 423, p.87–95

Perelmuter J.-M.; Racine R., 1995, The globular cluster system of M81. Astron. J., vol. 109, no. 3, p.1055-1070 

Photometric values obtained from Simbad Query of M 81 and Aladin software respectively. 

Table of observation

Table of objects