Surface Brightness

Some questions:

1) Is surface brightness like apparent magnitude in that the lower the number, the brighter the object?

2) Naked eye observability equals what in terms of surface brightness?

3) Do all objects have surface brightness?

Thanks.

Hi
1) yes

2-3 dont know :o

Some questions:

1) Is surface brightness like apparent magnitude in that the lower the number, the brighter the object?

2) Naked eye observability equals what in terms of surface brightness?

3) Do all objects have surface brightness?

Thanks.

Hi there. Well, to answer your questions:

1. Yes, that is correct. Surface brightness is usually measured in magnitudes per unit area of sky (usually in magnitudes per square arc minute for example). This means that the larger the number, the fainter the surface brightness is.

2. If something is visible to the unaided eye, this doesn't necessarily mean that it has a certain surface brightness. It just means that it is bright enough or large and bright enough to be seen. One example is the galaxy M33, which has a somewhat low surface brightness (13.9 mag./square arc min) but which from a dark sky site (and with eyes sensitive enough) can be glimpsed with averted vision with the naked eye. Its "total integrated magnitude" (and equivalent to if the object was a point source like a star) is about 5.7, and many people can see stars down to magnitude 6.5, so it is just within range of the unaided eye.

3. Stars do not have surface brightness as they are point objects. Other "extended" objects (planets, galaxies, nebulae, etc.) do have surface brightness. Star clusters generally are often given a total integrated magnitude which is a rough summation of the brightness of most of the stars in the cluster. Clear skies to you.

David did a great job of replying to your questions. It bears repeating that naked eye visibility doesn't necessarily translate to an object having a high (bright) surface brightness. His example of M33 illustrates this very nicely. Its total brightness is very high (bright) for a galaxy but its surface brightness is fairly low (faint) as galaxies go. So, while its surface brightness is a large number--thus indicating a faint surface brightness--this galaxy is considered bright because it has a small integrated (total) magnitude. I know, clear as mud

Bill in Flag

Thanks for the responses. One more question. I understand how the apparent magnitude and airmass metrics relate to observability. How do I use the surface brightness metric with respect to observability? Is it fair to say that observability increases as surface brightness increases?

Surface brightness is how bright each sqaure arc-second or arc-minute of an object is. You can have a planetary nebula with a magnitude of 6 such as the Helix and yet it is invisible from your home, while a 10th magnitude planetary such as NGC-7027 can be seen anytime from the same spot. The magnitude of an objects treats the light coming from it as though it comes from a point. Therefore that 6th magnitude nebula whose light is spread out across an area half the size of the full moon is going to be very dim whereas the 11th magnitude planetary nebula that is 15 arc-seconds across will be visible from a city. All objects that have a perceptible apparent size has surface brightness. So if you see an object that looks bright but has an apparent size of 20 arc-minutes, it's going to require dark and transparent skies to see. The apparent size and total magnitude taken together will determine if you can see any given object from any given site with your telescope(s). Surprisingly, there are a few DSO's with a low surface brightness that can be seen with the unaided eye, or the eye alone with a nebula filter.

Taras

One thing must be gotten straight, in order to avoid confusion. Surface brightness (SB) is more commonly--and certainly in the professional community--expressed as magnitudes per square arcsecond (MPSAS). as fas as I can discern, only some fraction of the amateur community uses magnitudes per square arcminute (MPSAM). It would simplify matters if those holdouts would adopt the standard. The Sky Quality Meter (SQM) uses MPSAS, a further incentive for standardization.

But it's easy to convert between the two. One square arcminute has an area 3,600 times larger than one square arcminute. This is a brightness ratio of 8.89 magnitudes. For a SB given in MPSAM, add 8.89 to get MPSAS.

And if you want to get an idea of SB in square degrees (MPSD), note? One square degree has a surface brightness 3,600 times larger than one square arcminute, with the same magnitude ratio of 8.89. And so MPSD = MPSAM + 8.89.

But what if you have MPSAS and want to find MPSD? You could do the two conversions, adding 8.89 to get MPSAM, and 8.89 again to get MPSD. Or you do it in one step, going directly from MPSAS to MPSD by adding 17.78.

Regarding visibility of an object. The first thing to consider is its SB and the SB of the sky it is seen through. This determines the contrast; the lower the object SB the lower the contrast. Some examples:

Let's say both values of SB are equal, at 20 MPSAS (this would be a suburban sky.) The light of the object and sky always add together, which in this case makes the object appear twice as bright as the surrounding sky, or 0.75 magnitude brighter. And so with the sky at 20 MPSAS, the object would have 19.25 MPSAS (even though intrinsically it is 20.) An object appearing twice as bright as the sky has pretty good contrast and is reasonably easy to see.

Now suppose the same 20 MPSAS object is seen through a very light polluted city sky of 18 MPSAS. Again, the light of both add together. The object is 2 magnitudes fainter than than the sky, which means it is 1/6.3 as bright. Sky and object together are thus 1.158 times, or 0.16 magnitude brighter than the sky. With the object now appearing 15.8% brighter than the sky, its contrast is low and is thus not easy to see.

Now we travel to the country, where the darkest possible sky is 22 MPSAS. Our 20 MPSAS object is now 2 magnitudes, or 6.3 times brighter than the sky. Sky and object, as always, add together, now making the object appear to be 7.3 times, or 2.16 magnitudes brighter than the sky. This is very high contrast, and the object would stick out like the proverbial sore thumb!

After determining contrast, one has to consider size. Depending on both brightness and contrast, an object must subtend some minimum size on the retina in order to be detected. At given contrast, smaller objects require higher magnification, which if view surface brightness is to be preserved, means larger apertures. At given size, lower contrast requires higher magnification and potentially larger aperture.

Just to provide a sense of what's involved, a very bright DSO (like a planetary nebula) might be well seen when it subtends a mere 10 arcminutes (1/6 degree) on your retina. But a very dim nebula of excessively low contrast must subtend several degrees (!) on your retina in order to be sensed at all.

In *general*, the smaller the object, and the lower the contrast, the larger the aperture required.

This gets to be a complex subject when all variables are considered. If you want to provide some strain to the brain, you can check out the chart and explanatory text about magnification and contrast in deep-sky observing in my Gallery, linked below...

Thanks for the responses. One more question. I understand how the apparent magnitude and airmass metrics relate to observability. How do I use the surface brightness metric with respect to observability? Is it fair to say that observability increases as surface brightness increases?

Surface Brightness is an important concept..

Mathematically, surface brightness is the visual magnitude divided by area, the unit being "magnitudes per square arc-second. Since a magnitude is logarithmic unit, the math is a bit more complicated than simple division. Usually the surface brightness is given for the entire object but for most objects, the surface brightness is not constant over the entire surface.

For a given size, objects with higher surface brightnesses are easier to see. When size is included, it gets trickier. In general though, lower surface brightness objects are harder to see. M101 is a good example. At magnitude 7.9 it seems like a reasonable target for the urban backyard astronomer. But that light, equal to the light from a magnitude 7.9 star, is spread out over an area nearly the size of the moon, so it's surface brightness is 23.3 magnitudes/square arc-second.. One must be viewing from a dark location to see M101.

Andromeda, is very large, about 3 degrees by 1 degree but has a surface brightness of about 22.1 magnitudes per arc-second, comparable to a very dark sky. Yet is is relatively easily seen from an urban setting because the core is much brighter.

Looking through a telescope, the surface brightness of an object is proportional to the area of the exit pupil, regardless of the aperture of the telescope. A larger scope does not make the object more intense, it makes it larger. This can seem to be quite counter intuitive, particularly when looking at small objects in a big telescope. It is useful to know, large objects like M101 can be seen in binoculars and small telescopes from a dark site because even at low magnifications, they cover enough of the retina that they can be detected.

The subject of surface brightness, contrast, exit pupils, aperture, magnification and how they all relate to the response of the human eye at low light levels is interesting, complicated and important in understanding why you see what you see and how to see more...

'nuff said.

Jon Isaacs

So in other words, surface brightness by itself does not correlate with observability. It's just data.

Surface brightness most definitely correlates with observability. Even if we could remove sky glow and make the sky as black as possible, thus improving contrast very much, the eye itself has a limit to detection of about 27 MPSAS. There are many nebulae and dwarf elliptical galaxies, for instance, which are in whole or in part fainter than this, and so quite invisible to the eye in any instance.

So in other words, surface brightness by itself does not correlate with observability. It's just data.

It's more than just data; it is a way to quantify an object's brightness. Integrated magnitude quantifies an object's total or overall brightness. Surface brightness quantifies its brightness per unit area. The dark-adapted eye being primarily a detector of contrasts--variations in brightness--integrated magnitude and surface brightness are two variables that go a long way in determining whether or not you will be able to see a celestial object.

To understand how this works, let's try a thought experiment. Imagine you're outside under a pristine dark sky with your telescope and have just centered two galaxies in the eyepiece. They are exactly the same size and shape but one is has an integrated magnitude of 12.0 and the other has an integrated magnitude of 13.0. One galaxy is brighter than the other, not only in total brightness, but in surface brightness, as well. Since the two galaxies are exactly the same size, the fainter of the two must have a fainter surface brightness. In fact, its surface brightness will be exactly 1.0 magnitude fainter. As such, it is both fainter and lower in contrast than the 12.0 magnitude galaxy of the same size. The bottom line is this, the fainter, lower contrast galaxy will be harder to see.

Now, suppose you swing over to a field occupied by two different galaxies. Both have integrated magnitudes of 12.0 and are identical in all aspects except that one is half the size of the other. In order for the smaller galaxy to have an equivalent integrated magnitude, its surface brightness must be brighter than its larger companion. In fact, the smaller galaxy's surface brightness will be 1.5 magnitudes brighter. This corresponds to a 4x difference in brightness, which exactly counters the larger galaxy being 4x larger in surface area.

But which of the two will be easier to detect? It's impossible to say with certainty because the outcome depends on the visual acuity and the perspective of the people doing the observing. And it's complicated by the fact that the dark-adapted eye isn't very good at seeing small objects. If both galaxies are tiny, the smaller of the two may be seen as stellar. In which case, you might not even recognize it as a galaxy. If both are large, the larger of the two may have such a low surface brightness that its contrast is below the threshold of visibility. There is no easy or obvious answer.

Finally, you turn your attention to two new galaxies. They are exactly the same in shape and surface brightness, but one is twice as large as the other. The larger galaxy will have a brighter integrated magnitude. In fact, it will be 1.5 magnitudes brighter. If a school bus full of children pulled up just now, most--if not all--the kids would notice the larger, brighter galaxy, first.

The visibility of deep-sky objects is pretty complicated stuff. What makes it complicated, is that it's almost impossible to isolate just one variable in an equation modelling an object's visibility. As we've seen in the above hypotheticals, size, integrated magnitude and surface brightness are all interrelated. If you change one variable, one of the other two must also change. This is why you can't generalize to say all objects of a certain integrated magnitude, size or surface brightness will be visible. One variable doesn't tell the whole story

Bill in Flag

Surface brightness most definitely correlates with observability. Even if we could remove sky glow and make the sky as black as possible, thus improving contrast very much, the eye itself has a limit to detection of about 27 MPSAS. There are many nebulae and dwarf elliptical galaxies, for instance, which are in whole or in part fainter than this, and so quite invisible to the eye in any instance.

I generally agree, but have to take it with a grain of salt as you might very well be able to still observe the core if significantly brighter than the rest of the galaxy.

good post.

2. If something is visible to the unaided eye, this doesn't necessarily mean that it has a certain surface brightness. It just means that it is bright enough or large and bright enough to be seen.

Well surface brightness can be a measurement for naked eye visibility, but as you said it has to be

A.) big enough and
B.) the signal/noise ratio has to be ok(if the background is to bright, the object will fade into the background noise)

B.) also directly limits the visibility in a telescope. It doesnt matter how big your scope is, you wont be able to see the object properly. The signal is still there tho, this means if you can filter the noise away you can see the object (pollution filters, narrowband filters etc. can do that)

3) Do all objects have surface brightness?

as long as they have a perceptible surface, yes. The average surface brightness should be nothing but Magnitude/surface.

Heres a short paper which contains M31 surface brightness profils/ data.

http://iopscience.io..._628_2_L105.pdf

Well surface brightness can be a measurement for naked eye visibility, but as you said it has to be

A.) big enough and
B.) the signal/noise ratio has to be ok(if the background is to bright, the object will fade into the background noise)

B.) also directly limits the visibility in a telescope. It doesnt matter how big your scope is, you wont be able to see the object properly. ...

Actually, the size (aperture) of your scope is central to how discernible an object will be and how detailed it will appear. As aperture increases, the threshold contrast at which objects of a given size can be seen is reduced. Also, objects that were at the threshold of visibility in a smaller scope will appear both more obvious to the eye and more detailed when more aperture is applied. Of course, there are practical limits to how large an aperture one can build for visual observing and this does place a limit on how faint one can reasonably expect to go. But there are many thousands of deep-sky objects which appear more obvious and detailed as you step up from modest, to large and, ultimately, very large aperture.

Bill in Flag

. Also, objects that were at the threshold of visibility in a smaller scope will appear both more obvious to the eye and more detailed when more aperture is applied.

Once the exit pupile reaches 7mm the image wont get any brighter. The bigger scope can ofc. display a bigger image with the same expit pupile, but the surfacebrightness will stay the same.

this, ofc. ignores resolution. But we are talking about borderline visibility here. I dont think being able to detect tiny details really makes a huge difference in that case.

A telescope isnt about making an object brighter/area, its about making it bigger while keeping the brightness as high as possible

A telescope isnt about making an object brighter/area, its about making it bigger while keeping the brightness as high as possible

A large telescope allows higher magnifications at the same exit pupil. Or, it allows brighter images, up to the diameter of the observers dark adapted pupil, at the same magnification.

The upper limit of the brightness of an extended objects is always what you see with your naked eye. Compared to the naked eye view, a telescope can make the object larger, it can make it dimmer to the eye but it cannot make it brighter, more intense.

Jon

Leo I has a magnitude of 11.5 but try observing it! The surface brightness is extremely low despite what the "apparent" magnitude says it is. There is a thread about it on the Deep Sky Forum right now. It's one of those objects that is extremely hard to see despite its size and apparent magnitude becasue of LSB.

. Also, objects that were at the threshold of visibility in a smaller scope will appear both more obvious to the eye and more detailed when more aperture is applied.

Once the exit pupile reaches 7mm the image wont get any brighter. The bigger scope can ofc. display a bigger image with the same expit pupile, but the surfacebrightness will stay the same.

None of which changes the fact that increasing aperture reduces threshold contrast. As a result, the object that was at the threshold of visibility in a smaller aperture is well above the threshold of visibility in the larger aperture. It becomes more obvious to the eye. Also, the fact that you are now able to see lower contrast details and resolve finer details makes objects appear more detailed. And, of course, lower contrast objects can also now be seen.

The beauty of the concept of threshold contrast, is that it explains the advantages of increased aperture without violating the physical limitation that an apparent object's surface brightness is at its maximum to the naked eye. More important, it explains those advantages without violating the fact that an object's contrast versus the surrounding sky is fixed in all apertures and at all magnifications.

This is crucial because the fully dark-adapted eye is primarily a detector of contrasts. It is terrible at resolving fine detail and is incapable of discerning color. The one advantage of a fully dark-adapted eye is that it is exceptionally sensitive to faint light sources. This allows observers to discern the contrast between two faint objects--such as the night sky and a distant galaxy. If you don't understand visual observing within the context of contrast detection and the role aperture plays in that process, then you don't understand visual observing.

this, ofc. ignores resolution. But we are talking about borderline visibility here. I dont think being able to detect tiny details really makes a huge difference in that case.

You're missing the advantage of being able to detect lower contrast details and the advantage of details which were at the threshold in a smaller aperture being more obvious to the eye in a larger aperture.

A telescope isnt about making an object brighter/area, its about making it bigger while keeping the brightness as high as possible

A telescope collects light and brings light to focus. That's what a telescope is about. Observers are about seeing more objects and more details in objects. What visual observers have recognized for centuries is that increasing aperture allows those goals to be achieved.

To gain an appreciation of the role aperture plays in allowing observers to see both more objects and more detail in faint objects, I recommend reading Lowering the Threshold.

Bill in Flag

The beauty of the concept of threshold contrast, is that it explains the advantages of increased aperture without violating the physical limitation that an apparent object's surface brightness is at its maximum to the naked eye.

I think is just easier to say that as the surface brightness of an object decreases, it must cover a larger region of the retina for the eye to detect it. This is all about the eye and it's capabilities.

Sometimes an object is too big to be seen, it covers the entire retina, so it is necessary to use a smaller scope...

Jon

The beauty of the concept of threshold contrast, is that it explains the advantages of increased aperture without violating the physical limitation that an apparent object's surface brightness is at its maximum to the naked eye.

I think is just easier to say that as the surface brightness of an object decreases, it must cover a larger region of the retina for the eye to detect it. This is all about the eye and it's capabilities.

Sometimes an object is too big to be seen, it covers the entire retina, so it is necessary to use a smaller scope...

Jon

Easier but incomplete. Many objects that are beyond the reach of a 4 inch scope at some magnification are visible in a 10 inch scope without increasing magnification. They're not covering a larger area of the retina but they are being observed in a scope with a lower threshold contrast for that size object.

Bill in Flag

The beauty of the concept of threshold contrast, is that it explains the advantages of increased aperture without violating the physical limitation that an apparent object's surface brightness is at its maximum to the naked eye.

I think is just easier to say that as the surface brightness of an object decreases, it must cover a larger region of the retina for the eye to detect it. This is all about the eye and it's capabilities.

Sometimes an object is too big to be seen, it covers the entire retina, so it is necessary to use a smaller scope...

Jon

Easier but incomplete. Many objects that are beyond the reach of a 4 iat the same magnification in a 10 inch scope without increasing magnification. They're not covering a larger area of the retina but they are being observed in a scope with a lower threshold contrast for that size object.

Bill in Flag

Bill:

The reason the object might be seen in a larger telescope at the same magnification is simply that the image is brighter, the contrast has not changed at all, at these resolution scales, telescopes do not change the contrast, contrast is a ratio of brightnesses.

A larger telescope can provide a brighter image at the same magnification, a larger image at the same brightness or some optimized combination of the two. However, unless one is viewing very bright objects like the planets, a telescope does not increase the contrast and only marginally decreases it.

For given a low surface brightness object, the variables here are image size, image brightness, contrast is essentially fixed. The observer plays with the image size and brightness with different eyepieces, different telescopes, hoping to optimize the presentation to the retina.

So again, for viewing small faint objects, it comes down to a brighter image is easier for the eye to detect, a larger image is easier for the eye to detect, both these can be used advantageously to detect lower contrast objects.

Last night I was looking for Hickson 68 in my 4 inch. I couldn't see it at 45x, I knew was close but I couldn't see it. I went back to the16 inch verified my position, decided to increase the magnification, jumped it up to 78x and I was already on it, it was right there, I just couldn't see it. Increasing the magnification was all it took.. matching the image to my eye, the galaxies were more than bright enough, just not big enough.

Jon

Bill,
You are perennially ascribing to your 'threshold contrast' a kind of mythical third parameter which goes beyond the two which matter; surface brightness and subtended angle on the retina. In reading your explanations it always comes across that a larger aperture increases contrast.

From the reading of your descriptions, it seems as though small scale contrast as applies to the photopic regime of subject brightness is in some way applicable, but where it cannot because of the eye's poor resolving power at such low light levels. But it's more than that, and I just can't put my finger on it. For the past couple of years we have danced around this issue but have never not fully resolved it. In some undefinable way we seem to have our wires crossed on the subject.

Here are discussions of two studies of threshold visibility. Rather technical to the beginner - sorry, but it can't be helped:

Here is one about limiting magnitude of stars.

It is based on a paper by Bradley Schaefer. I have taken Schaefer's quite abstruse units (like starlight in footcandles!) and converted to magnitude units to make it easier (it is still by no means easy - I have also brought up a few critical points for discussion).

This allows calculation of visibility, depending on object magnitude, angular size, background, atmospheric transmission, telescope parameters, eye pupil, experience etc. Routinely calculating would be rather boring, I think, but it should give you an idea how those parameters affect visibility.
This is built on the scientific paper, I believe the version in S&T long ago is a bit simplified.

Also there is a discussion of visual sensitiviy based not on astronomy but on laboratory testing (during WW2) of visual thresholds. While most astronomical objects do not have the same simple light distribution, the data still allow a few important conclusions about magnification: increasing magnification will give darker background and thus allow better dark adaptation and lower threshold magnitude. At least as long as the object is not magnified beyond about one degree apparent angle, and the background is very dark, the eye can integrate the responses of many separate rods.

If you still are with me, here is a somewhat simpler discussion of limiting magnitude in binoculars.

Nils Olof

Glenn, I don't ascribe any mythical quality to threshold contrast. Nor have I written or implied that increasing aperture increases object contrast versus the surrounding sky. That is how you have characterized what I've written. But that characterization is not accurate. Anyone who reads my online article, Lowering the Threshold will find that threshold contrast and the role it plays in visual observing is based in research and math. The original research was done by others. The concept of threshold contrast did not originate with me. The conclusions I have reached and the arguments I make are, however, informed by my own work exploring several key factors impacting the visual detection of faint extended objects. For that, I gladly take credit for anything of value and willingly accept responsibility for any errors.

Clearly, you (as well as others) don't share my position. This is one of those situations where reasonable people disagree...hopefully, without being disagreeable. What led me to acknowledge the critical role of threshold contrast was research and math. More of the same would be needed to move me from this position. Until then, I will continue to educate the amateur community on the central role threshold contrast plays in our ability to observe galaxies, nebulae and other faint, extended objects. Along the way, I look forward to engaging in robust discussion with you and others on the subject.

Bill in Flag

The simple fact is that increasing aperture does not allow to see subtler contrasts. It allows to see finer detail.

I understand the concept of 'threshold contrast'. When used in the context of the visibility of a specific object and the visibility of structural detail, it's quite useful.

But in a generalized discussion on surface brightness *not* focused on one specific object, 'threshold contrast' need not be invoked. For then the problem is essentially one of a most simple reciprocity; if you want to see objects or details half as large, double the aperture.

It's critical to avoid giving any impression that a larger aperture allows to see lower contrast. Assuming equal quality, the contrast detection threshold of a 2" scope is identical to that of a 20" scope; the latter simply allows to see details 10 times smaller.