Details relating to the galaxy photometry pages

Introduction

Galaxy magnitudes can trip up even the most experienced amateur astronomer. Catalogues that have been compiled for use by professionals usually do not give visual magnitudes. Rather, due in part to the first sensitive photographic emulsions having strong blue sensitivities, when a professional astronomer refers to the integrated magnitude of a galaxy, it is usually a blue magnitude. There are, in fact, many good reasons for observing galaxies in the blue portion of the spectrum even with modern CCDs, but that doesn't help visual observers.

Furthermore, the total integrated magnitude of a galaxy does not always match the ease with which a person can see a galaxy. Galaxies are extended objects, and the surface brightness of a of a galaxy falls off as you move away from the core in a manner that varies from one galaxy to another. Plus, some galaxies are large enough to show bright and dark areas in even modest telescopes, although such details do not show in the case where a galaxy is barely detected. Spiral galaxies that are seen more or less face-on can be a particular problem. A prime example of this issue is M33, which is visible to the unaided eye from a dark, rural site, yet because even the light in the core of the galaxy is quite spread out, it can be a very difficult telescopic object for a more typical observer in light-polluted skies.

It turns out that professional astronomers are also concerned with this issue of how the light from a galaxy decreases with increasing distance from the core. In fact, total integrated magnitudes for galaxies are usually determined based on that light distribution. Using either a photoelectric photometer with a variable aperture, or aperture photometry on a CCD image, one can measure the total magnitude of a galaxy within apertures of increasing size. One then fits some sort of decay function to this data. At some point near the visible edge of the galaxy, the function has leveled off to the point at which it essentially a flat line, i.e. the asymptote. That corresponds to the total integrated magnitude of the galaxy. The rapidity of the dropoff in light depends on the type of galaxy, its orientation as seen from Earth, and its apparent size.

Unfortunately, the blue bias rears its ugly head here, because professional astronomers generally do this analysis for blue magnitudes. On the plus side, they also often do a similar analysis on the color distribution, which is simply the relative amount of light at two different wavelengths. Most galaxies are fairly red objects, astronomically speaking, and are typically 0.5 to 1.0 magnitudes brighter at visual wavelengths than blue wavelengths. That why published galaxy magnitudes can be so misleading. For instance, in some lists of the Herschel 400 objects, some galaxies are listed as 13th magnitude, when in reality the faintest galaxies have visual magnitudes around 12. But, at least when the color analysis has been done, one can convert the blue magnitude to visual. If the integrated blue and visual magnitudes are B_T and V_T, respectively, and the integrated color is (B-V)_T, then:

V_T = B_T - (B-V)_T

where B_T and (B-V)_T are quantities often tabulated in catalogs, such as the 3rd Reference Catalog of Bright Galaxies (RC3).

Unfortunately, this is not perfect. (B-V)_T is not necessarily exactly equal to B_T - V_T, because the details of the light distribution in B and V may not be exactly the same. Also, some of the data in RC3 is becoming out of date as more and more galaxy photometry is published. Even where the RC3 is good, it would also be nice to know the actual V magnitude distribution. This allows one to not only derive an accurate total V magnitude, but one can also get a sense of how bright the core of a galaxy will be relative to the total brightness.

Technique

That's where I come in. I have taken an on-line version of the General Photometry of Galaxies catalog, and performed an analysis of the distribution of V magnitudes directly, using similar techniques to those used by researchers who study these sorts of things. I happen to be a research astronomer, but this is not my field. Still, this is mostly just fitting appropriate functions to data points, which is one of the most fundamental skills a scientist can have. This sort of project is not out of reach for an educated amateur astronomer, and my interest in this subject is completely geared toward my own interests as an amateur astronomy.

I'll spare you the full details of the fitting unless there ends up being particular interest. Suffice it to say that there is more than one way to do this, but I have chosen a reasonable method. I use a 4-parameter fit, which can then be used on all galaxies with at least 5 data points. Unlike RC3 and other researchers, I do not assume that all galaxies of a particular type have the same sort of profile, and that is why I need 4 parameters to fit a galaxy. This also allows for variation between galaxies that would otherwise be considered the same. This can be an advantage, because many large bright galaxies are peculiar in some way. It can be a disadvantage if the data for a single galaxy is not very complete; the average profiles can help constrain an otherwise poor fit. In rather clumsy ascii, my fitting function is:

V(x) = V_T + a1 * exp(-a2*x^(1/a3))

In this formulation, x is the size of the aperture. V_T is the total or "asymptotic" V magnitude. This is an exponential function which goes to zero, and so the constant you add to lift the function up to match the data is the total magnitude. The a1 parameter regulates the steepness of the curve near zero aperture and is related to the y-intercept. The a2 parameter is somewhat of a size indicator; i.e. how quick to flatten the curve at higher aperture. Finally, a3 is the power law index. If you look at the function carefully, you will see the the function behaves like a normal exponential if a3 = 1. This choice of function was inspired by work by J.L. Sersic in the 1960s. The main point is that it is a function that provides a good match to most galaxies without making any assumptions about the galaxy itself.

You can check out a page of sample fits to get a better feel for just how well this method works.

Detecting a galaxy

The fit immediately produces a very important parameter, V_T, the total visual magnitude. But, perhaps even more important is the brightness of the core of the galaxy. After all, if the issue is detection, you will only see the very core of a galaxy if you can just barely see it at all. In my experience, a "just detected" galaxy on the Herschel 400 list is almost always near 1 arcminute in length at around 100x with my 6" f/8 scope under dark skies. At lower power, the visible size of the galaxy might need to be larger to be detected, and vice versa. But, values of 0.5-2.0 arcminutes span the usual range for a mere "detection" of a galaxy. Thus, once I have determined the 4 fit coefficients, I also calculate the total magnitude for various sizes. The idea is that you might have two galaxies with the same total magnitude, the same size, but with a very different brightness dropoff with increasing distance from the center. By the standard techniques of assessing the likelihood of visually detecting a galaxy, you might expect the two galaxies to be the same. But, with a very steep profile, the inner 1 arcmin of one galaxy may be much brighter than the core of the other galaxy with a more gradual dropoff. Thus, the peak surface brightness will be higher and the galaxy will be more easily visible.

It turns out that in most cases V_T and the average surface brightness do give a reasonable accounting of how bright a galaxy might appear under marginal condition, but that is not always the case. As an example, consider the two galaxies, M95 and NGC 4535. Based on both the RC3 catalog and my fits, the former is about a quarter-magnitude brighter. They are essentially identical in size (7.4 x 5.0 vs. 7.1 x 5.0), and the average surface brightness based on the RC3 data for M95 is 22.3 mag/arcsec^2 vs. 22.5 for NGC 4535. That's a pretty closely matched pair, and one would expect M95 to only appear slightly brighter. However, M95 has a much brighter core region:

M95    V_T(RC3)=9.73, V(0.5)=12.0, V(1.0)=11.1, V(2.0)=10.5
N4535  V_T(RC3)=9.96, V(0.5)=13.3, V(1.0)=12.3, V(2.0)=11.2

Under typical "detection" conditions for your telescope/sky combination, M95 is about a magnitude brighter! That's a large difference, and probably one of the reasons that the former galaxy made it into Messier's catalog. Clearly, if you are just barely seeing M95, you need a significant increase in aperture and/or sky quality to see NGC 4535.

There are even better examples, but the Messier and H400 lists are strongly biased toward easy-to-see galaxies. More interesting contrasts can be seen when comparing a galaxy on the H400 list and one that's not. But, that's for another time.

Problems

Unfortunately, it is not all bread and circuses. Because I am not using profile templates for specific types of galaxies, my fits sometimes are not as well constrained as those in RC3 or other references that derive B_T and (B-V)_T. For that reason, my V_T values should be considered experimental. But, this is rarely a problem near the core of the galaxy, so my derived V magnitudes for 0.5, 1.0, and 2.0 arcminutes are almost always good to within 0.1 magnitudes or so. Problems tend to occur at larger apertures. My fits tend to make V_T too bright, especially for large galaxies where there isn't a lot of large aperture data. Although putting up more than 200 plots on this web page will not happen, rest assured that I have visually inspected each fit to see if there were any problems. The fitting code includes techniques for removing points that strongly differ from the rest of the data.

Even my derived small-aperture magnitudes can be problematic because not all galaxies have sufficient data coverage. In other words, instead of an interpolation within a rich field of data points, I have to use an extrapolation to smaller or larger apertures. These cases make V_T especially inaccurate as well. NGC 253 is a prime example; the galaxy is nearly half a degree long, but the V magnitude photometry covers less than the inner 3 arcminutes. Thus, my fit does not provide a reasonable value of V_T. The accuracy of the tabulated values is indicated by a color code which is explained on the table page.

One way to tell if my fit is wrong, or if there really is a big problem with V_T from RC3 (often because of new data within the last 10 years) is to look at the V magnitude at the largest available aperture. This aperture usually takes in very nearly the entire galaxy and thus gives a good estimate of V_T. But, not always. In any case, this value is given in the table and you may find it more useful than V_T from RC3 or from my fits. If not, the V_T values derived from RC3 are available for all but a handful of the most easily seen galaxies.

There is a more subtle problem with the aperture magnitudes I give for some galaxies, which has to do with the fact that circular apertures are used. Many galaxies are less than 2 arcminutes wide along the minor axis. In those cases, the actual surface brightness of the part of the galaxy within the 2 arcminute circular aperture will be brighter than another galaxy with the same magnitude that fills the aperture. Even the 1 arcminute aperture can be affected by this for a few galaxies. I may try to correct for that issue at some point, but until then you just need to be careful in those cases.


Contact information

Back to the galaxy photometry page

File last modified: 17 December 2004

Valid HTML 4.01! Valid CSS!