Integrated Magnitude and Comet Holmes
Published on Nov 4, 2007 at 12:26 pm.
3 Comments.
Filed under astronomy, comets.
Raw observational data for magnitude estimates for Comet Holmes suggest that the comet is holding at a magnitude of about 2.5 or so. Some estimates are a bit brighter, and some are a bit dimmer. But, people are asking me why it is getting harder to see the comet if it is staying the same brightness, particularly for people living in urban areas.
When Comet Holmes suddenly brightened over a week ago, it quickly became visible to the naked eye. Within a matter of less than a day, it brightened by an amazing amount. But, then the rate of brightening slowed, and finally the comet stabilized in brightness. But, if you look at the link above, most of the reported magnitude estimates are visual, and they tend to be all over the place. And, even though the magnitudes estimates have not changed much in a week, many people that I talk to say that it looks like the comet is getting dimmer to them.
To explain what is going on, we need to talk about how astronomers measure brightness. The standard way of expressing how bright a celestial object appears is to give its magnitude. The magnitude is a measure of brightness that dates back to ancient times. Originally, stars were grouped according to “importance,” with first magnitude being brighter, and thus more important, than second magnitude. Second magnitude was brighter, and thus deemed more important, than third magnitude, etc. So, the larger the magnitude number, the dimmer the star. That is exactly opposite from the way that most people would think to categorize things today, but it is how we still do things in astronomy. You can read an entry that I wrote about magnitudes this past summer for a more compete explanation.
As a rule of thumb, you need to have something brighter than about 6th magnitude to be visible to the naked eye. However, it has to be sometimes much brighter than that to see from light polluted urban skies. Comet Holmes quickly got up magnitude 2.5, easily seen from even heavily light polluted skies unless you happened to be standing directly underneath a bright light. The comet has remained nearly that bright, but it has been fading in the sky. Huh? How is that possible?
I can make the previous statement because of the way that magnitudes are applied to celestial objects. When you are dealing with stars, the magnitude system is just fine. You can compare how bright stars appear pretty well just by comparing magnitudes. There are some irregularities, of course, in that many people find reddish stars a bit harder to see that bluish stars of the same magnitude. Different people, due to genetics and age, see different colors differently. If your eyes don’t pick up exactly the same colors equally well as someone else, then someone may see two stars of different colors as slightly different brightness than someone else sees them. That makes comparing magnitudes between stars of different spectral types a bit tricky when done using the eye.
However, there is a different effect going on with Comet Holmes, and with many other objects such as galaxies, nebulae, and globular clusters. The magnitude number assigned to such extended bodies is determined by measuring how much light they send our way. So, saying that a galaxy shines with magnitude 8.3 means that when you measure how bright the galaxy appears, you get as much light as if you were measuring a star of magnitude 8.3. However, that may not mean that the galaxy is as easy to see in the telescope as a star of magnitude 8.3. The reason is that stars appear as point sources in the sky. Extended bodies, by definition, are extended — they cover some area of the sky. That means that the same amount of light that would be given off by a point source, such as a star, is spread out. We call this equivalent light the integrated magnitude of the object. The integrated magnitude can be thought of as the equivalent magnitude computed by adding up all of the light across the surface of the extended object.
In this diagram, you can see two objects. The object on the left is a fuzz ball. The one on the right is a dot. The dot appears brighter because all of the light is concentrated. Now, both may be the same brightness, but the concentrated one is easier to see. That is because all of the light falls on only a few detectors (whether they be rods and cones in your eye, grains on film, or pixels on a CCD). That means that there is more light on the detectors to measure. But, the object on the left has its light spread out. So, while the light falls on more detectors, each detector gets less light to work with. That makes the object harder to see in several ways. First of all, less light per detector means less response. If the response is too low, then it does not register. Secondly, the sky itself is not perfectly black. There is always some background light. In urban skies, there is a lot of background light. So, the light from the object is mixing with the ambient light. That means that the more spread out the light from the object is, then the smaller percentage difference the detectors have to work with between the ambient light and the ambient light plus the light of the object. That reduces the contrast between the object and the sky. And, that reduced contrast makes it harder to see.
When Comet Holmes first erupted, whatever violent even happened to spew dust and debris out into space caused all this debris to suddenly be flung outwards where it could catch the sunlight and shine. But, the comet’s nucleus is very tiny — just a few miles across. This cloud of debris expanded to hundreds of miles across, then thousands of miles across. As it expanded, it thinned and allowed more sunlight to reach throughout the cloud to reflect off of the material thrown outward. The comet brightened. Eventually, the cloud thinned to the point that it was not effectively shielding itself from the sunlight. The Sun could shine through the cloud to its far side to reflect. The comet quit getting brighter. Now, the nucleus has continued to shed material, for sure, but not at the fantastic rate as its first violently explosive outburst. But, even with the cloud of debris thousands of miles across, at the distance of this comet, that was still very small in the sky. To the naked eye, it was basically a point. Even in binoculars, it was scarcely more than a point, and in a telescope it was just a small disk. But, the cloud expanded to tens of thousands of miles across. Now, the cloud was a very tiny disk seen to the naked eye, and a small fuzz ball seen in binoculars. Still, the light was pretty well concentrated, so the comet appeared as bright. But, now the cloud of debris is several hundred thousand of miles across. To the naked eye, it would appear as a blob nearly half the diameter of the full moon, except that the total light is still the same. From the bright city lights, that puts the surface brightness down close to that of the background sky, and that makes the comet hard to see. So, someone who does not understand integrated magnitudes would think that the comet is getting dimmer.
Now, soon, I do expect the comet to be getting dimmer as the material thrown outward dissipates. Already, it is now quite as easy to see with the naked eye as it was a week ago. However, it is still extraordinarily bright, and it is still visible from most light polluted urban skies. It simply is not quite so visible from the very brightest skies due to its lower contrast. If you haven’t seen it yet, then make sure that you go look for it. The comet from here on out is only going to be getting tougher to see unless some other outburst happens.
-Astroprof
Astroprof’s Page » Comet Holmes is suddenly news (after 2 weeks) on November 6, 2007 at 12:28 am: 1
[…] Wow. Back on October 24, almost two weeks ago, I heard about the sudden outburst of Comet 17P/Holmes. I wrote about it hours after observing it. There was quite a bit of news about the comet around the internet. Just over a week ago, I posted a photograph of the constellation Perseus, with the comet marked. This has turned out to be one of the brightest comets in a long time, second only to Comet McNaught early in the year. Comet Holmes was clearly visible to the naked eye. Now, as it expands, it is getting harder to see, as I explained recently. And, in all those nearly two weeks, the comet has been virtually ignored by the news media. I saw a brief mention in USA Today, but that was all until Sunday when an amateur astronomer associated with a planetarium in the area wrote about it in the monthly column for the local paper. Then, I see this today. Yeah, they are sure on top of things. […]
Tavi on November 8, 2007 at 2:01 pm: 2
In observing Comet Holmes over the past two nights, it appears to have suddenly dimmed significantly, both directly and as compared to field stars. I understand that the expanding debris field is now nearly twice the diameter of the sun, thus it would make sense that the comet’s surface brightness might “appear” to be dimming. However, I am curious, are there any new - past two days - estimates of its current magnitude? All things considered, I am still convinced that the comet has dimmed quite a bit from its 2.5 magnitude.
This comet has been a great learning experience for me, and I want to continue to learn from it.
Thanks
Reviewing Comet Holmes | Orbiting Frog on April 18, 2008 at 4:56 am: 3
[…] Comet Holmes was a very dim, and expected comet. Until October last year. During the period October 23rd to 24th 2007, it suddenly brightened. If you want to know more about why it suddenly became visible, I’d recommend reading Astroprof’s post on Integrated Magnitudes. […]