Abstract: Visual observations of a large number of galaxies were made with a 5" refractor. The data shows that neither magnitude nor surface brightness predicts the visibility of the galaxies observed. A simple (though possibly not original) formula is proposed which does appear predictive of visibility to resonable reliability.
Early Work: For most of my observing career I've attempted to correlate visibility of deep sky objects with easily-acquired quantities, such as magnitude and surface brightness. Over years I have intuitively felt that such numbers ought to be predictive of visibility, but experience has suggested that either of these figures alone is inadequate to the task.
It remained only to use the two quantities in conjunction, and in a variable and unspecified manner, to gauge the visibility of deep sky objects. For many years I have looked at both values in order to form a rough, "seat of the pants" judgement of how hard an observation might be. Although subjective, this has seemed much more reliable than using either quantity alone.
My first acquaintance with this principle from others was from Luginbuhl and Skiff [1989]: "...we have found that [surface brightness], combined with the integrated magnitude, gives a more consistent indication of the difficulty of an object in a particular aperture than the integrated magnitude alone." Despite some additional information on the rough limits these observers experienced, there was no discussion of any relationship between the two quantities that might be exploited to devise a more reliable predictor. In retrospect, I should have taken this language much more literally than I did.
A project was developed to evaluate my old observations in order to investigate the relationship between magnitude and surface brightness, and the visibility of celestial objects. The pipe-dream goal was to find a convenient mathematical way of using both quantities in a calculation which would result in a single number which would be highly predictive of visibility. Several problems were quickly encountered, with two of them being fatal to the exercise:
For an additional year or more I continued to use magnitude and surface brightness together in an intuitive way to predict visibilty, with mixed success. Soon, I experimented with various ways of combining the two quantities in order to derive a single unitless number that could be used as such a predictor. Some methods worked pretty well, especially where a group of objects split into seen and unseen groups all had fairly reliable or at least homogeneous data. By the spring of 2002, I decided that some sort of formal trial was justified.
Coma-Virgo Galaxy Observations: In April of 2002 I prepared charts of several fields in the Coma-Virgo area. The charts each plotted stars down to 15th magnitude in a three square degree region of sky. The declination of each region was between +10 and +20 degrees, so that at the meridian the fields were 60 to 70 degrees in altitude from the observing site.
Within these fields, galaxies were plotted according to complex input criteria. Galaxies as faint as magnitude 16.5 and as bright as 12.5 were listed for the fields covered by the charts. The magnitudes were taken from the RC3, and then from the PGC, as needed. Once a list of such galaxies was prepared for each field, the list was trimmed to exclude galaxies with surface brightnesses brighter than 12 magnitudes per square arcminute, and fainter than 17.5 magnitudes per square arcminute. This resulted in a field in which galaxies of faint magnitudes were much more frequent than brighter magnitudes (although perhaps not to the same extent as a non-cluster area of the sky). A script was written using VBScript that removed galaxies from the list in such a way as to leave roughly the same number of galaxies in each magnitude bin. The resulting list was imported back into the charting software and used to plot galaxies in each field. The charts were printed out and taken to the observing site.
The observations were made from Doug Snyder's observatory, at a true-dark site in Palominas, Arizona, at approximately 31 degrees north latitude. Because the area of sky of each chart was small, and because faint stars were plotted, once the field of the chart was located the telescope could be navigated using slow motion controls by looking through the main telescopic eyepiece. By using this technique, a large number of galaxies could be looked for in a short period of time. Galaxies which were seen were marked on the chart with a circle or by filling in their symbol. Galaxies that were not seen had an X put over their symbol.
I carried out the observations quickly, without regard to optimizing the observing in such a way as to maximize my limiting magnitude. Instead, consistency was striven for. A dim red LED flashlight was used to illuminate charts; this was kept on during the bulk of the observing. No hoods or shrouds were used, though the observatory walls blocked stray light from view. Only a few seconds were spent trying to see each galaxy. Where a galaxy was obviously seen, it was noted and I moved on without lingering. Where a galaxy was not immediately seen, I gave it a short amount of time before declaring the galaxy invisible. The average amount of time spent looking for each galaxy turned out to be thirty-eight seconds, though the average time for each galaxy subsequently declared 'unseen' was obviously much longer than the overall average.
The observations were made over two nights, totaling almost five hours of observation. Both nights had an identical naked-eye magnitude limit, of 6.8. The telescopic limiting magnitude was V=15.1 on the first night and V=15.0 on the second night [Skiff 2002]. Just under 500 galaxies were observed.
The above scatter diagram shows all the visible galaxies. A cone-shaped population is not unexpected, as the left side shows brighter galaxies are preferentially visible to faint ones.
Reduction: The following steps were taken to evaluate the data.
First, a list of galaxies that were looked for was prepared. For charting, the RC3 and PGC values were considered adequate, but for data reduction it was felt that more reliable magnitudes and sizes might be available from NED. A batch was prepared and processed; this formed the data source for all subsequent work.
A computer program was written (available as part of the Widgets component which can be downloaded from the author's website) which calculated surface brightnesses for each object based on the NED-supplied sizes and B magnitudes. Each galaxy was then plotted on a scatter diagram, one axis indicating magnitude, and the other surface brightness.
To increase the clarity of the chart and to speed up subsequent processing, the population was truncated. All galaxies brighter than B=13 (all of which were seen) and fainter than B=16.3 (all of which were not seen) were thrown out. All galaxies with a surface brightness brighter than 12.3 magnitudes per square arcminute (all of which were seen), and all with a surface brightness dimmer than 16.5 magnitudes per square arcminute (all of which were not seen) were also thrown out. This resulted in better clustering of data points on charts and a smaller set to work with when processing, but at the expense of artifically sharp boundaries along the top and left sides of the scatter diagrams. After analysis was completed and the conclusions presented here were reached, these truncated data points were checked to see if they contradicted any findings, with negative results.
This process resulted in 424 galaxies being treated in the reduction and in the following charts and evaluations. Of these, 150 galaxies were seen and 270 galaxies were not seen.
There are several interesting things about these 424 observations of galaxies.
First, magnitude is almost useless as an indicator of visibility near the threshold in this population. The brightest galaxy seen was magnitude 13.0, while the brightest unseen galaxy was magnitude 13.1. The dimmest galaxy seen was 15.2, the dimmest unseen was 16.3.
The data expresses a swath of galaxies only 3.3 magnitudes wide. Yet the zone in which it is possible to see galaxies is 2.1 magnitudes wide. A dramatic way of putting this is that there is a zone of uncertainty in which magnitude might, or might not, indicate that a galaxy can be seen. That zone of uncertainty is 63% of the whole! This can clearly be seen in the chart where any line drawn from top to bottom to the left of about 14.3 magnitudes will intersect many galaxies, both seen and unseen.
In real life, magnitude alone might be used to predict visibility of galaxies of from around 16th magnitude to 4th magnitude, that range being roughly from the brightest available in the sky to the faintest which is not wholly beyond all reason for the instrument (perhaps being a little generous on this last). The figure of 63% therefore overstates the size of the real zone of uncertainty. Under this more realistic scheme, and making generous assumptions, the zone drops to 18% of available magnitudes. Since the uncertainty creeps in just where things get interesting - at the faint end, near the threshold - this level of uncertainty is enough for me to conclude that for a given galaxy magnitude alone as a visibility predictor is useless in practice.
The second interesting thing is the fact that surface brightness is also a nearly useless indicator. Amongst these galaxies the zone of uncertainty is only about 1.5 magnitudes per square arcminute wide. In this selection of data, the zone of uncertainty is 31% of the total range of surface brightnesses represented.
The range of seen and unseen magnitudes and surface brightnesses expands as the range of observed objects magnitudes expands. The chart suggests that if the data sample included brighter but much larger objects, the zone of uncertainty would grow as data points were added to the upper left corner of the chart. A dwarf galaxy such as Leo II would lie almost in the upper left corner of the chart, and has gone unseen in the past; in such a situation the zone of uncertainty swells to three magnitudes. Indeed, the zone of uncertainty for surface brightness has to be related to the available range of surface brightnesses of objects in the sky. Instead of searching all available catalogs for the widest possible range of surface brightnesses, we have taken our values from the RC3 instead.
RC3 indicates that the highest surface brightness galaxy is 11.35 magnitudes per square arcminute, while the lowest is 18.22 magnitudes per square arcminute. If we take this as representative of the entire range of observable surface brightnesses, then the total range of available galaxy surface brightnesses in the sky is 6.87 magnitudes per square arcminute wide. The zone of uncertainty is therefore 19% of the total range, if we assume that this data represents the widest possible zone of uncertainty. (This is a very poor assumption, for the reasons given above, but worth making in order to pin a number on the size of that zone that can be used in a relative way.) As with magnitude, the reliability of surface brightness near the threshold is close to zero.
The third interesting thing, and by far the most significant thing about the chart, is the fairly sharp division between the two populations. A line can be drawn at a 90 degree angle to the axis of equal values, which very nearly serves as a boundary between the two populations. Data points to the upper right are almost all unseen. Data points to the lower left almost always represent galaxies that were seen. There are a few exceptions on one side of the line or other, no matter where the line is placed.
This supports the intuitive understanding I developed independently as well as the statement of Luginbuhl and Skiff [1989]. It is now clear from a set of observations tailored to the question that the use of the two numbers together - magnitude and surface brightness - does indeed serve as a predictor of visibility or a predictor of difficulty. Exactly how this is the case is also shown from the chart.
The 45 degree line which we can imagine placing as a boundary between the two populations can be described in several ways. The most straightforward is as a multiplication function 1 . If we select a point on the chart where the magnitude times the surface brightness equals, let us say, 200, and draw a dot there; and then find all such points where the product of the two values equals that and draw a dot at those points, we will end up drawing a straight line on the chart from the upper left to lower right. This is strongly suggestive that multiplying magnitude by surface brightness will result in a unitless number that is predictive of visibilty for this population. We will call that number "VF" and plotting the results in a one-dimensional series looks like this:
Here, all observed galaxies are shown, but it is clear there is at least a small zone within which some galaxies are seen and others unseen. Zooming in on this region will provide the most interesting data:
The range of included VF in this data is from 165 to 268. We can again conceive of a zone of uncertainty, within which galaxies might be seen or unseen, and that uncertainty drops significantly using this derived value. The total range of VF in the data set is 103 counts wide. The zone of uncertainty is only 6.6 counts wide. This is only 6.4 percent, which is much more reliable for objects near the threshold than either magnitude or surface brightness.
Again using the RC3 we can gain a sense of the range of possible VF values for galaxies in the entire sky. By using the brightest magnitude and surface brightness in the catalog, and the faintest magnitude and surface brightness in the catalog, we can see that the maximum possible range of VF is from 47 to 335. (Note that the brightest surface brightness and the brightest magnitude come from different galaxies, etc.) This is 288 counts wide. Based on this all-sky value, the uncertainty zone is only 2%.
Input Errors: Because the galaxies observed are bright and well-studied, most of them are assigned an error range for magnitude and surface brightness in the various sources that list it. This makes those quantities uncertain to within a specified range, and VF, as the product of the two, is also uncertain.
The "real" errors tend to be around 0.3 in magnitude and 0.5 in surface brightness [Skiff 2002]. However, for the selection of observed galaxies used here, the formal or "book" errors tended to be much smaller. Amongst galaxies near the boundary between the seen and not seen populations, the maximum error in magnitude was 0.15. In surface brightness the maximum error was 0.31. Neither value is as high as the expected errors, but most of the errors are taken from the RC3, which conservatively states uncertainties.
In some cases, the RC3 surface brightness values do not correspond well to the NED data. The surface brightness for the galaxies in the sample was calculated based on NED size data. RC3 provides an error for surface brightness based in some cases on observations other than the ones that NED is repeating for size.
The following table summarizes the results of a "worst-case" analysis of the errors. Values in parenthesis reflect the input values, while values outside parenthesis adopt the maximum error indicated in the source data, applied systematically in the most pessimistic manner (i.e., seen galaxies get fainter, not seen galaxies get brighter).
A scatter diagram utilizing the errors as summarized above, applied in the "worst-case" systematic manner described, follows.
Obviously, the application of errors makes the boundary between the seen and not seen populations significantly more fuzzy. Fitting that boundary still indicates it is perpendicular to the axis of equal values, but the confidence level of the fit deteriorates.
The formal errors included in the RC3 are probably underestimated. Harold Corwin often uses the RC3 error multiplied by 3 to derive a more realistic error [Skiff 2002]. By doing this we again increase the size of the pool of galaxies which might cross the VF transition, and also increase the fuzziness of that transition. Here is a summary of results using "Corwin-Style" errors:
Throughout this paper, I have described the reliability of magnitude, surface brightness, and VF as a predictor of visibility in terms of the zone of uncertainty. The zone of uncertainty is defined by the two values between which both seen and unseen galaxies are found. The following two charts illustrate the effects of applying worst-case scenario errors. The error types are defined as follows:
The first chart illustrates the uncertainty zone as a percentage of the total range of values in the observed population.
The next chart illustrates the uncertainty zone as a percentage of the total range of values available in the entire sky (taking the entire RC3 as representative of the possible range of values).
To interpret these charts, it should be kept in mind that the Y axis represents the percentage of the total range of available values that the uncertainty zone occupies when errors in the data are at their maximum and accumulate systematically in the worst possible ways. This is roughly indicative of the frequency at which the different values will fail in their mission of predicting the visibility of a given galaxy in the observed population. In light of this, the very shallow trend for magnitude in both charts might explain why magnitude has historically been most frequently and heavily used as such a predictor. It has been three or more generations of amateur astronomers who have preferred to use magnitude to indicate the difficulty of observations. This period extends well into times when photometry of deep sky objects was nearly non-existent and very unreliable where available. Under such circumstances, it appears observers did an excellent job of collectively selecting the predictor that was least sensitive to the gross input errors that were common at the time.
Similarly, the sharp upward trend for surface brightness in the second graph may explain why many observers don't trouble themselves with evaluating surface brightness even in modern times where that data is served up by star charting software as a matter of routine. Considering the input sources for such software, which are the primary sources of delivered surface brightnesses for most observers, the surface brightness values that a typical observer will normally encounter are subject to large errors. Observers have probably collectively or independently noticed that surface brightness is an unpredictable indicator, and the chart shows why this may be. (The steep upward trend is in part due to the bright extreme of the range of all possible surface brightnesses from RC3 having small errors.)
As is no surprise, VF, being the product of magnitude and surface brightness, does not fare well as errors are increased in the other two values. Under a Corwin-style error protocol, VF is only a third better than magnitude alone as a predictor in any given near-threshold case, and is six times worse than if the input values are considered valid. This should serve to emphasize the extreme importance of good input data into any function which predicts visibility. Still, VF's uncertainty zone is significantly smaller than that for either magnitude or surface brightness.
Theoretical Considerations: There are several theoretical considerations affecting such a study.
For example, it is obvious to any experienced observer that there must be an absolute limit to the faintness of objects seen. If a 16th magnitude star cannot be seen, a 16th magnitude galaxy should be just as invisible. During long sessions observing faint photometric fields, I have learned that even a slight focusing error can cause a star normally visible near the threshold to vanish. If this is the case, a galaxy, which would be approximated to some degree by an out of focus star, should be invisible at the same magnitude.
Based on prior experience, therefore, it seems likely that an upper magnitude limit for my observations with the 5" should be approximately 15.2 magnitude. In the scatter diagrams above, this should be represented by a vertical line in the right-hand side of the plot area. Nothing to the right of that line should be seen. Of course, some things to the left of it will also be invisible.
Similarly, it seems unlikely that there is no upper limit to visible surface brightness. The fundamental limit here is probably set by sky brightness, with objects only slightly fainter in surface brightness than the sky being visible near the threshold. Objects significantly lower than the surface brightness of the sky are probably overwhelmed. Even with CCD's, which sport a linear response and therefore have a tremendous advantage over the eye in capturing fainter-than-sky objects, the task of discerning such objects a magnitude or more below the sky brightness can be very difficult or impossible. Unlike with magnitudes, there is no clear indicator of where the absolute surface brightness boundary should be put, but if plotted, it would appear as a horizontal line somewhere in the upper end of the scatter diagram.
In theory, then, the true fit for VF should be a curved line which tracks these extremes but slices through the population presented here in such a way as to appear to be a straight line. Originally, I had intended to explore visibility predictors using observations culled from my notes over a number of years. While that is problematic, adding some observations from my notes with the 5" telescope on other nights illustrates that the VF boundary does not break down badly, even in very bright objects with extraordinarily low surface brightness, or vice versa. It seems probable that the simple factor will hold up across objects actually found in the sky, but that the fit will be concave to brighter objects in laboratory experiments.
It has also been proposed that VF fails to account for changing magnification. In a typical threshold observation, an observer will progressively increase magnification until some optimum is reached, which is frequently defined by apparent sky brightness or by the apparent size of the object. Clearly, if an optimum magnification had been used for a galaxy in the sample, say one on the unseen side of the boundary, it might have been seen - therefore causing an anomaly in the data.
This would be a procedural mistake, however. The process would have value only if all galaxies in the sample were observed at the optimum magnification for that galaxy. If this had been done, it could well be that additional fainter galaxies would have been visible. But the effect would have been an overall shift of the VF boundary toward fainter limits - not the creation of one or a handful of seen objects with anomalously high VFs. A similar procedural error is present in proposals that if more time had been spent looking for a given unseen galaxy, it might have turned out to be visible. While true, a careful, time consuming attempt to see every galaxy in the population would have tended to shift the VF boundary toward fainter limits overall, rather than the creation of a few anomalies. What is not known, of course, is how this might affect the function describing VF.
Finally, it has been suggested that the morphological type of the galaxy might affect its visibility. Typically it is suggested that highly concentrated S types would be more visible than comparable E type galaxies. In theory, this sounds good at first, but there are some attributes of human vision which make these conclusions uncertain. A highly concentrated galaxy will highly excite some retinal rods, which will of course contribute to ease of visibility. But because it is concentrated, the rods undergoing high excitation will be serviced by relatively few ganglion cells, which the visual machinery depreciates. In addition, the high excitation of a cluster of rods will tend to blunt the visibility of nearby fainter regions, rendering the spiral arms less conspicuous than if the bright core were not present (this effect is routinely noted by neophyte observers when first trying to discern spiral structure in galaxies). Therefore it would seem that the concentration could have both advantages and disadvantages.
Similarly, E type galaxies tend to have very even brightness profiles. While this situation does not excite any rods as highly as our S type galaxy, hence reducing visibility, the number of involved ganglions goes up by a significant amount. This favors visibility. So to a certain extent the morphological extremes theoretically tend to offset one another's visibility advantages and disadvantages. Based solely on experience, this conclusion might be surprising, since in a group of galaxies the E types tend to look like faded curtains compared to their S type companions. It seems likely, however, that this is merely a subjective psychological effect rather than a real indicator of the relative difficulty of seeing the different types.
While the population included here is not homogeneous - comprising significantly more S type galaxies than E types near the boundary - and is probably not large enough to settle the question for good, there is no discernable bias caused by morphological type near the threshold. In the uncertainty zone, there are a few galaxies of each type in an apparently random distribution of VF and visibility. No weighting of S types upward or downward will create a better fit. There are even fewer E types near the transition and it is probably best to withhold even a tentative verdict in this case.
VF is intended to be a unitless, and therefore relative, quantity. Fundamentally what it suggests is that an object with a higher VF will be more difficult to see than an object with lower VF, other conditions being equal. Users of it should therefore guard against unaccounted for changes in condition. Changes in transparancy, seeing, telescope size, hydration, and other effects will all make the VF boundary, over time, a fuzzy entity when evaluated in absolute terms. All of these terms might be appropriately included in a model to describe visibility on a given night, or visibility in absolute terms; but historically these models have tended to be either ineffectual or very complicated. The simplicity of VF makes it an easy quantity to compute but renders it inappropriate for absolute applications.
Conclusions: The primary conclusions reached are:
A number of things may affect our conclusions. Foremost, this selection of galaxies was picked specifically to cluster around the edge of visibility with a fairly narrow range of sizes and shapes. The true relationship between magnitude and surface brightness might be better represented with a more complex function. Perhaps the true boundary between the two populations is really a concave curve, which intersects the observations here in such a way as to emulate a multiplication function. It is possible that very bright but extremely large objects, such as Barnard's Loop, might lie significantly on the wrong side of the boundary if observed and properly plotted. If this were indicative of a significantly different boundary shape, this would go unnoticed until several hundred additional homogeneous observations of pathological objects were added to this data. Doing this is quite impractical.
It is also possible that simple multiplication is not indicated - perhaps one value must be weighted. Or perhaps special circumstances of brightness gradient affect the result, requiring the addition of new terms. The available data is inadequate to rule any of these possibilities out, though it does not suggest they are true.
In addition, while no provision is apparently needed for the brightness gradient of the galaxies, it is not known how VF will stand up to objects of complex or unbounded shape - such as the Canadian part of the North America Nebula.
On the other hand, magnitudes of objects of complex morphology are still generally unreliable, as observers of diffuse nebulosity well know. As with any function, this one will return garbage when fed it; so the attempt to model such shapes will probably be futile even if the principle behind VF remained valid. Therefore, the data seems to represent a fair sampling of the most common practical cases in which visibility might be evaluated, and this suggests that in most real-life applications, even if the function is seriously flawed, this would go unnoticed by most observers using it.
Two other limitations to our conclusions apply and bear repeating. The first is that the observations which informed this investigation were not designed to determine the absolute limits of visibility. Instead they were meant to evaluate the more or less immediate relative visibility of large numbers of objects. Based on experience and intuition, it seems to me that spending time on any of these objects will push the boundary to the upper right, but would not change the function. In other words, while the limits of visibility in this test are around VF=208, I believe that having spent more time on each object while optimizing observing techniques would have resulted in the limit of visibility being expressed by a significantly higher VF, without significantly increasing the size of the fuzzy zone. But this is a hypothesis that requires testing.
Finally, the true size of the fuzzy zone and indeed the value of VF in any given case is still hostage to the validity of the input data. NED was used to gather magnitudes and sizes for each galaxy because it was thought the NED values would be consistent one to the next. The area of sky was chosen as much for the density of available galaxies as for the expectation that professional interest in the region would be high, leading to highly reliable and consistent magnitudes and sizes. Anomalies of various kinds in this data set might be explained by poor inputs (possibly also causing the casual visibility of a 15.3 magnitude galaxy with a 5" telescope 2 ). The goal here, obviously, was not to rely too much on any single data point, but rather to overwhelm such problems with large numbers of troops.
Practial Applications and Necessary Further Work: In practical terms, the quantity VF should probably be considered no better than a rule of thumb when it comes to predicting the visibility of deep sky objects. Sky conditions and observer physiology vary, which demands that the limit of visibility be different from night to night or even hour to hour. It is probably impossible to say something analogous to "VF 250 is the absolute limit for a 5" telescope;" to then use this assertion as the basis for not observing things - because they shouldn't be visible - would be foolish.
VF, if used at all, should be used as an indicator of difficulty, rather than possibility. Based on the experiences I've gained developing this paper, I would expect VF 250 to be a difficult observation in my 5" telescope. This might induce me to wait until I have a favorable night to make the observation. It would not induce me to write off the possibility altogether. Even where VF was astronomically high, an exception to the rule might apply, or bad input data might be responsible. VF can never be used to rule an observation out.
Being an optimist, and on the basis of further experimentation not related here, I believe that VF is a more appropriate quantity to use to define the limits of charting deep sky objects than magnitude. Most of the charting software I use plots deep sky objects on the basis of their magnitudes alone. Often the deep sky magnitude limit (which is almost always separate from the stellar limits) can be manipulated by the user to bring into visibility fainter objects or to suppress them. But if VF is more indicative of the difficulty of observation, shouldn't VF be selectable as a limit for charting in lieu of, or in addition to, magnitude? This will not solve the problems of bad data in such software, but will go some distance towards resolving the meaningless use of it.
I also believe that the results are of sufficient interest as to justify additional work by other observers. I would be interested to see a plot of visibility vs. VF for other kinds of objects. Planetary nebulae are one class of object where some reliable magnitudes and sizes are available. Doing the experiment with a few dozen planetaries would help to show whether VF has any applicability to emission-line objects.
I would additionally be encouraged to see similar studies done with other telescopes, perhaps on galaxy fields in other parts of the sky and on objects with different selection biases. The sampling here is a tiny and insignificant fraction of the available celestial objects to which the concept behind VF might, or might not, be applicable.
Footnotes:
1: A line at 90 degrees to the line of equal values also indicates a condition in which addition (and other simple functions) will also accomplish the same feat, and this is the reason for my oblique statement that I should have taken Luginbuhl and Skiff literally in the first section. I have adopted multiplication as the function of choice here for two reasons. First, it is a preferred modeling function which lends itself more easily to weighting or curving, if that is proven necessary in the future. Secondly, an offhand remark about using multiplication, while this paper was being prepared, resulted in the method actually getting published in a book. I don't at this point want to change gears on the observers following the development of this method. However, Bill Gray [2002] has pointed out that "(mag + surface brightness) is the logarithm of (watts/meter)^2, a reasonable physical quantity," and using this approach might have more merit for someone trying to link visibility with some sort of unit. Return to Text
2: The observer is certainly not immune to error. Perhaps a circle was drawn on the chart when an X was meant. Return to Text
References:
Bill Gray, personal communication to author, Sep. 19 2002
Chris Luginbuhl and Brian Skiff, Observing Handbook and Catalogue of Deep Sky Objects, Cambridge 1989
Brian Skiff, Johnson-Cousins BVRI photometry for faint field stars, version: 11 Jul 2002, Lowell Observatory 2002
Brian Skiff, personal communication to author, Sep. 15 2002
THIS RESEARCH HAS MADE USE OF THE NASA/IPAC EXTRAGALACTIC DATABASE (NED), WHICH IS OPERATED BY THE JET PROPULSION LABORATORY, CALTECH, UNDER CONTRACT WITH THE NATIONAL AERONAUTICS AND SPACE ADMINISTRATION.
Acknowledgements:
The author wishes to thank Brian Skiff, Tom Polakis, and Bill Gray for early review of the paper and the making of numerous suggestions that have significantly improved it. Errors, however, remain my own.
magnitude
surface brightness
VF
Brightest Seen
12.96 (13.0)
12.2 (12.3)
158 (165)
Brightest Not Seen
12.99 (13.1)
14.15 (14.4)
201 (205)
Faintest Seen
15.27 (15.2)
15.98 (15.7)
218 (212)
Faintest Not Seen
16.41 (16.3)
16.61 (16.5)
273 (268)
Uncertainty Zone This Set
66% (63%)
41% (31%)
15% (6.4%)
Uncertainty Zone All-Sky
19% (18%)
26% (19%)
6% (2%)
magnitude
surface brightness
VF
Brightest Seen
12.7 (13.0)
11.9 (12.3)
144 (165)
Brightest Not Seen
12.7 (13.1)
13.8 (14.4)
193 (205)
Faintest Seen
15.4 (15.2)
16.4 (15.7)
230 (212)
Faintest Not Seen
16.6 (16.3)
16.8 (16.5)
283 (268)
Uncertainty Zone This Set
69% (63%)
53% (31%)
36% (6.4%)
Uncertainty Zone All-Sky
22% (18%)
38% (19%)
13% (2%)
Object VF Observation
Leo II 212 Not Seen
Sculptor Dwarf 191 Seen
NGC 3840 201 Seen
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