Presidential

One of the things I like most about Obama is that he has really played to his strengths in the campaign. He's a great speaker, and so most of the news clips are of him giving a speech rather than him doing a photo op in a tank or visiting a historic landmark or whatever. The focus is all about his speeches, and if you listen to any of them, I think you have to be impressed even if you disagree with what he's saying.

He's always calm, cool and collected, and that's the perfect antidote for the Moron American who fears the Angry Liberal. Obama agrees with most everything that Angry Liberals want, which to end the war in Iraq responsibly, reduce the deficit by making taxes fair again and provide health care coverage for everyone, among other smaller issues. But he manages to be for these things without sounding angry or accusatory, just very matter-of-fact.

I'm afraid if he allows himself to get swept up in the emotion of the campaign even once, if he has a "Dean scream" moment, it could really end up going badly for him. He (and his advisors) seem smart enough to avoid that. I hope so. Here is a recent speech he gave in response to a predictable Republican attack that his foreign policy amounts to appeasing terrorists. Very nice way to deal with that kind of attack.

He doesn't ignore it or respond with some vague message that goes over everyone's head. He responds directly, and he sounds very presidential doing so.

The F Word

I got a call at home yesterday afternoon from the 13-year-old's school. It seems that C*dy was messing around with some friends in the hall, and he said something like, "Fuck no!" right as the assistant principal was walking by. So they call me and put him in all-day detention today. When the lady called me and explained what happened, I just said "okay" thinking it is a pretty stupid thing to put him in detention for all day but I know how these things are.

Then the lady says, "Do you want to talk to him?" Here I missed a chance. I told her I would just talk to him when he got home, but I should've asked for him. I would've told him to hold the phone away from his ear, then I could yell into the phone, "WHAT THE FUCK DO YOU THINK YOU'RE DOING, YOU STUPID FUCK?!? CUSSING IN SCHOOL? GODDAMN FUCKING IDIOT! FUCK!!!"

Then he could put the assistant principal back on, and I could very politely explain that I have no idea where he gets this from but I'm sure it will never happen again.

Probably better that I didn't. C*dy is getting to be subversive enough as it is without my encouraging it.

I almost forgot the best part, which was the note they sent home. In big all capital letters on the first line of the "your kid is in deep shit" form, it says, "C*dy said FUCK to another student." I guess they don't sugarcoat it on the forms, do they?

Glasses

Little Obi-Wan turned 2 today, but we are waiting to celebrate his birthday until this weekend. He doesn't know any better, so why not? Unfortunately, we've noticed for the past few weeks that his right eye has been turning in a bit, almost so that he looks cross-eyed sometimes. So we took him yesterday to a doctor to get him checked out.

The gave him some drops to dilate his eyes, and then after a 30 minute wait, it took the doc about 10 seconds to diagnose him with farsightedness. I'm not sure quite how he did this, but he shined a light at Ben's eye and held up various lenses in front (perhaps until he could see the back of the retina in focus?) until he found one he liked and then wrote the little guy an eyeglasses prescription.

He says once Ben isn't straining to focus, his eye won't turn in anymore, and he said it is normal for kids to grow out of this condition by the time they are teenagers when it does happen. We looked around a bit tonight for glasses, but the place we really wanted to go was closed early today, so we'll try to go tomorrow at lunchtime and get something. How will we get Ben to wear them is another story.

It could've been a lot worse. If they had had to do surgery to correct his eye muscles or, worse, if it were some kind of tumor ... well, let's just say I'm glad it is only glasses. As far as I'm concerned that's the best possible outcome given his symptoms.

Coma Berenices

Just north of Virgo and east of Leo is a small, faint constellation containing lots of deep sky fireworks, the constellation Coma Berenices. This was once considered an asterism as a part of Leo's tail, but Tycho Brahe first set it apart in his star atlas in 1602 as a separate constellation, and the designation stuck. The name comes from the Egyptian queen Berenice II. When Berenice's husband went on an expedition to Syria in the 3rd century BC, she was so grateful upon his safe return that she promised to sacrifice her famously long, beautiful hair to the goddess Aphrodite. She placed it in the temple, and it was gone the next day, and the court astronomer declared that it was now in the heavens. Coma Berenices translates as the Hair of Berenice.

Alpha Coma Berenices is also known as Diadem, a close binary star with two sun-like main sequence stars, much like the star Porrima in the constellation Virgo. These orbit each other nearly edge-on every 26 years, and their maximum separation on the sky is only about 1 arcsecond from a distance of about 60 light years. Beta is nearly identical to the Sun and only about 30 light years distant, and it has been a target in the search for extrasolar planets and dusty disks, but so far, we've found nothing here.

Also located in this region of the sky is the North Galactic Pole, so we are looking directly up out of the plane of the Milky Way's disk along a line of sight with very little dust and gas. That's one reason so many galaxies are easy to find in this part of the sky. Most of the remaining moderately bright stars in this constellation are in the open cluster about 270 light years away known as Melotte 111 or the Coma Berenices Cluster. The cluster is about twice as far away as the Hyades and so takes up a smaller area on the sky (only about 5 degrees in diameter), and its age is about a half billion years old. Here is a nice photo of this cluster on the sky.

There are seven (!) Messier objects in this small region of the sky, and I'll start with the nearest one to us, the globular cluster M 53. This cluster is orbiting currently up over the top of the galactic nucleus and about 60,000 light years away from us. Typical of halo clusters, this is very metal-poor, meaning it formed early in the history of the galaxy before the interstellar medium was enriched with heavy elements from the first generations of stars. Just one degree southeast is another globular, NGC 5053. These two clusters are fairly close together in space, though far enough apart so as not to gravitationally influence one another. NGC 5053 is moving in the opposite direction compared to M 53, but both are bound to our galaxy.

Among the extragalactic Messier objects, six of them are galaxies located in the Northern half of the Virgo Cluster, about 5 degrees due East from the tail of Leo the Lion, the bright star Denebola. Starting from the Eastern end of the group is Messier 91 (or NGC 4548), a classic barred spiral galaxy about 60 million light years away. This is one of the faintest and most difficult Messier objects, looked like an elongated blob in most telescopes since all you can see is the brightness of the bar.

A little less than a degree to the West is Messier 88, a somewhat brighter and more concentrated spiral. Though M 91 and M 88 are very close together on the sky and both members of Virgo, they are moving through the cluster in opposite directions at very high speed, with M 88 moving away from us and M 91 moving so quickly relative to the cluster center that it almost overcomes the overall expansion speed of the cluster (the Hubble flow) and so is almost stationary for the moment with respect to our own galaxy.

M 88's claim to fame is that it is one of the nearest and brightest Seyfert galaxies. Seyfert galaxies have very active nuclei and strong emission lines from highly ionized gas. The mechanism heating up the gas is likely a supermassive black hole accretion disk in the center of the galaxy. The Doppler broadening of the emission lines is indicating of the very fast rotation that should accompany an accretion disk around a gigantic (20+ million solar mass) black hole with an event horizon roughly the size of our solar system. There are narrow emission lines, too, but their brightness doesn't vary as quickly and so they come from a much larger region. Because the broad-lined emission can vary on short timescales, it must come from a very small region of space (due to light travel time considerations).

Moving about 2.5 degrees North and slightly East from M88 brings us to the next Messier object, Messier 85, a lenticular galaxy (disk-like spiral without the normally associated gas, dust and star formation) on the Northern edge of the Virgo cluster. Two degrees back to the South and a little further East, we find the lovely grand design spiral, Messier 100, seen nearly face-on. You can see only a circular blob of light through a small telescopes, but with photographic techniques and larger telescopes, the spiral arms really come out beautifully. The structure of this galaxy is so intricate that it was used to test the optics of the Hubble Space Telescope after the initial optics fix. This photo shows a type Ia supernova that erupted in this galaxy in 2006, very useful as the HST had already determined the distance to this galaxy via Cepheids.

Now moving a degree or so Southwest, we come to Messier 99, also known as the Coma Pinwheel galaxy, a faint face-on spiral galaxy. Among the Virgo Cluster galaxy, this one has one of the highest peculiar velocities, meaning that perhaps it has recently been accelerated by a close encounter with another galaxy. As you can see in this photo, this galaxy is somewhat asymmetric, which also may indicate a recent interaction with another galaxy, possibly a recently discovered "dark matter galaxy", a large mass of dark matter and Hydrogen gas with very little associated luminosity (detected via 21 cm Hydrogen emission).

About a half degree west from M 99, we find Messier 98, an even fainter mostly edge-on spiral galaxy with a peculiar velocity so large relative to the center of the cluster that its net motion is towards us. Of course, this won't continue, but right now, M 98 is likely passing near the center of gravity of the cluster and so like a pendulum nearing the bottom of its swing is near its maximum speed. As it continues to approach us, it will slow down over the course of millions of years and ultimately remain bound to the cluster.

The final Messier object in Coma Berenices is Messier 64, also known as the Black Eye Galaxy. This galaxy is about 5 degrees Northeast of the group of galaxies associated with the Virgo Cluster, but it is not a member of that cluster at a distance of only about 17 million light years away. The odd structure of this galaxy leads us to believe it is the result of a recent merger as there are two distinct stellar populations in the galaxy rotating in opposite directions! The dark dust band that gives the galaxy its name is easily visible with dark skies and a 6 or 8 inch telescope. In this nice Hubble poster, the inner part of the galaxy is orbiting clockwise while the outer part is moving counterclockwise.

Moving away from the galaxies near the center of the Virgo Cluster toward the Northern half of this constellation, near the Coma Berenices star cluster, we find another, smaller grouping of galaxies, some of which may be associated with the Virgo Cluster. The first of these galaxies we'll study is NGC 4565, about 1-2 degrees East of the center of the star cluster. This is a very pretty edge-on spiral, resembling a needle in a telescope (hence it is sometimes referred to as the Needle Galaxy). It is at the right distance to be a part of Virgo (30 million light years or so), but its overall space motion (in the plane of the sky) can't be determined well enough to be sure that it is bound to that cluster.

Another 2-3 degrees to the East is NGC 4725, seen in the linked image through the new Spitzer Space Telescope with an emphasis on its infrared colors (which brings out the dust in the arms). Here is a nice visible light photograph. This one is about 40 million light years away and may be associated with Virgo. Its claim to fame is that it seems to have only one spiral arm instead of the usual two. Perhaps it is more appropriately a ring galaxy thanks to a recent merger. Another nice nearly edge-on spiral at about the same distance is a degree North of NGC 4565, and that is NGC 4559.

A couple of degrees north of the star cluster is another nice pair of galaxies, the two spirals NGC 4274 and NGC 4314, seen together in this wider view. NGC 4314 is clearly a ringed starbust galaxy, having just undergone a violent interaction in which another galaxy likely passed right through its center. The subsequent shock wave has propagated radially outward through the galaxy, lighting up a ring of luminous starlight.

Finally, we turn to a little patch of sky within about a degree of the North Galactic Pole, about a degree West of Beta Coma Berenices, the Coma Cluster of Galaxies. This cluster is about 10 times further away than the Virgo Cluster, making it about 300 million light years away or more. The only two galaxies in this cluster which may be visible through a large amateur telescope are the two giant ellipticals at the heart of the cluster, NGC 4889 and NGC 4874.

Though the cluster is several million light years in diameter, it takes up an angular space in the sky of a box about one degree on a side, maybe four times larger than the full moon. Perhaps the best visual highlight of the coma cluster is the pair of interacting galaxies known as "the mice" (or NGC 4676). These are two spiral galaxies locked in a gravitational embrace that has lasted hundreds of millions of years and created enormously long tidal tails and massive waves of star formation.

Though only about twice the size of our local group, the Coma Cluster is an unusually rich grouping of galaxies, containing as much as 50 times the mass of our little group of galaxies. The extended halo of this cluster is a circle of about six degrees in radius centered on the two giant ellipticals, and in this great circle, one can find nearly 30,000 galaxies brighter than 19th magnitude, almost all of which are associated with this cluster. If you consider a bubble of the visible Universe centered on us and extending out far enough to encompass the Coma Cluster, that bubble contains hundreds of thousands of galaxies, and this bubble represents about 1/100,000th of the volume of the visible Universe.

Truly staggering when you stop and think about it.

Faire

Very nice faire weather today, and we took advantage. Some of my fondest memories as a kid growing up were going to the big ren fest with my parents and later my friends in high school, and I definitely want the kids to experience that. It's really just an excuse to spend the day outside and pig out, which we all did. I've got to remember to get more than 6.5 hours of sleep the night before, though. If there had been a hammock shop there, I would've bought one just to get a chance to have a 20 minute nap during the afternoon. Hard to believe how quickly the time went. We got there at 1030, blinked, and it was 5pm.

We've got a birthday coming up next weekend, the beginning of a 9-week whirlwind with 6 birthdays, starting with Ben, who is turning two and ending with Daniel, who is turning five. So begins the summer season.

Different Standards

The last time we had a guy running for president who basically got his fortune by marrying a super rich heiress (Teresa Heinz Kerry), the traditional media thought it was Vitally Important to Democracy and Transparent Politics that she release her tax returns.

Apparently, the same standard doesn't apply to Cindy McCain. I'm sure the situation is COMPLETELY and totally different; otherwise, our "ultra-liberal socialist America-hating terrorist-loving media" would be screaming bloody murder.

Surely they would.

Duck!

Ducking office hours worked well today. Rather than go into detail, I'll just say it had the desired effect on me and defused a couple of potential confrontations. As a great fictional man once said, I love it when a plan comes together. Now if only my students would finish their finals early so I could have time to go to lunch before picking up the little ones.

And I have all of my grading done except for this last test, which I'll tear through tonight. The weather forecast looks good, too, so we may have another end-of-semester celebration this weekend by going to the local ren fest thing.

Almost Done

Maybe it was the double overload in the Fall or just the weird schedule this Spring, but either way, I'm very ready for the semester to end, which happens tomorrow. I've been pretty sloppy this semester in responding to student emails (in some cases confirming wrong answers as correct, which then came back to bite people on exams so I had to fix that a few times), and I've had a few really high-maintenance students this semester that have at times sucked the life force out of me. Mostly grade grubbing.

Summer will be busy, but I'm ready for a change. My last office hour of the semester is tomorrow, and I will probably just skip it and go to the bookstore. Better for all concerned. There's nothing that can't be solved by email or corrected after the semester is over, if needed, and I'm crabby enough at some people that I would otherwise possibly say something I would later regret.

I already was sarcastic to one person this morning, expressing how NOT shocked I was that they came to my office an hour before the final with detailed questions even though I told them I never do that sort of thing on test day (for a variety of very good reasons). Oops. Not so bad, but then later another guy showed up with a ton of questions even though my office hours had ended a while back. I dealt with him, but I'm sure my lack of enthusiasm was infectious.

Spam Killer

It is very gratifying that I finally found an easy solution to spam, which was turning off comments on archived entries. People can still comment off of main page links just not on links from individual entries, and that has killed 99.99% of spam that used to hit the site, a much better batting average than blacklist had (though blacklist still blocks 99% of what remains, which is still way too much).

I forgot to mention earlier that at the festival this weekend we saw a really interesting little band called Ume. Punk rock, and a little blond girl on lead guitar was also the lead singer, and she spasmed all over the stage, then after offered a petite little "thank you, we're Ume" like a cartoon character. This video is fairly representative. I couldn't listen to it for any extended length of time, but it was a neat little show.

Virgo

Just North of the Corvus/Crater/Hydra combination is the second largest constellation in the sky, Virgo. Many cultures share a similar story of this constellation as a maiden or virgin carrying a stalk of wheat (indicating by Alpha Virginis, or Spica, which translates to ear of wheat). Even in Greek mythology, this constellation sometimes represents Persephone, who was lured into the underworld by her uncle, the God Hades, where she ate the seeds of a pomegranite and was eventually forced to spend half of her life there as a princess after some negotiation by her father Zeus (this is related to the seasonal cycle).

Other stories identify her as Callisto, who also figures prominently in the legends of Ursa Major and Ursa Minor. Or perhaps she is Astraea the goddess of justice (which is fitting given the nearby Libra the Scales in the sky), who ruled a benevolent age of the Earth until the ways of mankind became so violent and upsetting that she retreated back to the heavens. The story that seems to have passed the test of time is that of the winged harvest goddess holding the ear of wheat.

The bright star Spica is surely the easiest to spot in Virgo, found most easily by following the arc of the handle of the Big Dipper through Arcturus and on to Spica. Spica is very close to the ecliptic plane, so the moon and the planets frequently pass very close to it, and the moon even occults Spica occasionally. Spica is a closely-paired system of two hot blue stars, the combined light of which is over 2000 times the luminosity of the Sun, making it a bright 1st magnitude star even at 260 light years away (30 times further than Sirius).

While these two stars do not eclipse each other from our perspective, the light curve does vary a bit as the stars orbit. That's because the two stars are so close together that their shapes are tidally distorted, so sometimes we see them elongated and sometimes end-on, making the total light from the system vary. Kaler reports that lunar occultation studies confirm the presence of more than two stars in this system, perhaps as many as three more dim companions, but they are very hard to study individually due to the intense amount of light given off by the central binary.

Spica was important to the Egyptians, and it was identified with their goddess of love Hathor. A temple was built at Thebes in such a way as to align with the rising of Spica on the autumnal equinox, when it was time for the harvest, but over time, the precession of the Earth has caused that alignment to shift noticeably. This is an example from the field of archeoastronomy, and it provided some of the first evidence that precession means the celestial sphere is not fixed.

About 20 degrees Northwest of Spica, a bit less than halfway along a line drawn from Spica to the tail of Leo the Lion, Denebola, is the 2nd brightest star in this constellation (though it is designated Gamma Virginis), named Porrima after the goddess of prophecy. Porrima makes up the vertex of a right-angled cup that extends about 20 degrees North and 20 degrees West, opening up toward Leo (see the star chart here for visual help).

Between this "cup" and Leo, you will find all of the Messier objects in Virgo except for M 104 (the famous Sombrero Galaxy). This is no coincidence as the nearby Virgo cluster of galaxies is located in this direction, so this an extremely rich field for extragalactic astronomy. The stars in the cup are all five in the neighborhood of 3rd or 4th magnitude. Porrima is actually a double star, with the two virtually identical stars separated by a very small angle, currently about 3 arcseconds apart (an arcsecond is the diameter of a stellar image in a telescope if the viewing conditions are excellent). The two stars are both on the main sequence and only a little more massive and hotter than the Sun, about 40 light years away.

Kaler points out that stars like Porrima mark an interesting transition point for stellar behavior. First of all, at about this mass, the nuclear fusion process in the core becomes more efficient (using Carbon, Nitrogen and Oxygen as a facilitator instead of purely the proton-proton chain), so the luminosity increases a bit faster as mass increases. Also, at this mass and higher, stars begin to transition away from having large convection zones in their outer layers like the Sun. Instead, their interiors are dominated largely by their radiative zones (at the extreme, very hot stars have no convection and are ionized all the way through, meaning spectral absorption lines are very weak or non-existant).

Convection helps a star generate a strong magnetic field, which in turn helps slow down the star's rotation. When the field interacts with the gas and dust that usually exists in a surrounding disk after the star forms, this acts as a brake on the star's rotation. For more purely radiative stars, this braking action doesn't exist and so they can become very fast rotators. Remember Regulus in Leo? Or Gamma Cassiopeia? There are plenty of hot blue stars in the sky that are very fast rotators thanks to this.

Porrima probably should've been named Zavijava, which is the name given to Beta Virginis, at the Western tip of the cup, 15 degrees due South from Denebola in Leo. Zavijava translates to "the angle of the dog kennel" and was originally the name given to what is now Porrima, but confusion over the years has changed our conventions on this and so we're stuck with Zavijava at the end of the line rather than at the true vertex of the angle.

Zavijava is very similar to either of the two stars in the double-star system Porrima that we discussed previously, and it is at about the same distance, 36 light years away. About halfway between Porrima and Zavijava on the Western arm of the cup is Eta Virginis, or Zaniah. Zaniah is almost exactly on the Celestial Equator, which splits the constellation Virgo into a Northern and Southern half, and one of the two intersections of the Celestial Equator and the Ecliptic is located halfway between Zaniah and Zavijava: the autumnal equinox. This is the location in the sky of the Sun on the first day of Autumn. Recall that Virgo is usually associated with harvest time because the Sun has historically been near this constellation at this time of year. This is likely also why Persephone (who spent Fall and Winter in the Underworld, then Spring and Summer in freedom) is associated with this constellation.

Zaniah is a very close triple of hot blue stars. They are so close (and the system so distant at 250 light years) that it is very difficult to separate the light from each component to study them all individually, though this was recently accomplished using optical interferometry. The name originates from another name for this angle of stars, the mouth of the barking dog or perhaps the kennel of the barking dogs (al zawiah translates to kennel). Moving North from the vertex at Porrima, about six degrees NNE, we run into Delta Virginis, which some have named Awwa or Auva for "angle" or "turn", so now you can see where Zavijava got its name, from a mish-mash of al Zawiah and Awwa. Awwa is a cool M-class red giant star about 200 light years away.

Finally, at the Northern tip of the cup, about 12 degrees North (and 1 degree West) from Porrima, we find the third brightest star in Virgo, for some reason designated Epsilon Virginis: Vindemiatrix. This name translates to the grape gatherer, as this star rises just before dawn during the grape harvest. The star is a yellow giant, about 100 light years distant, very similar to one of the components of the bright double star Capella in Auriga. Wikipedia notes that this star shares some characteristics (distance, motion or composition, not sure which) with the stars of the Hyades cluster in Taurus, but I have not been able to find a source to back up this claim.

It seems unlikely to me as the Hyades is on nearly the opposite side of the sky, and I'm certain we are not completely enveloped by the Hyades cluster so that we would have members all over the sky. The cluster is about 150 light years away and estimated to be less than 100 light years in diameter with most stars being in an inner 10 light year diameter sphere. Just goes to show that while Wikipedia can be very useful, it is important to read what's there with a skeptical eye and always look for credible backup sources if it is an important topic.

Moving on, I will now talk about some of the eleven Messier objects in the constellation Virgo. I suppose one way to do it systematically is to move from the Southernmost and work North toward the center of the Virgo cluster, so I'll start with Messier 104, also known as the Sombrero Galaxy. This is an outlier but generally accepted as a member of the cluster. The Virgo Cluster of galaxies is found mostly in a square whose opposite corners are Spica and Denebola (the tail of Leo). The central concentration is about halfway between Denebola and Vindemiatrix, a star I talked about previously.

The Virgo Cluster is a large group of galaxies (between 1000-2000) centered on a point about 60 million light years from us, and our own Local Group is a little bubble of 30-40 galaxies about 10-20 million light years in diameter that forms another part of the supercluster we share with Virgo. Most of the cluster galaxies are in the direction of Virgo, but some lie just across the border into Coma Berenices, a constellation I will talk about next time. Getting back to M104, this is a very nice nearly edge-on spiral (tilted about six degrees toward us) on the front side of the Virgo Cluster, about 30 million light years away from us. At 8th magnitude, it shows up nicely in a 8" or 10" telescope, which is ideal for most of the bright Messier objects I will talk about in this constellation.

In this deep image, you can see that it is a large, extended, low surface brightness halo with a couple of tidal tails extended from within the bright center. Like our own galaxy, the Sombrero has some satellite galaxies that it is slowly devouring, though this galaxy is only about half the visible diameter of our own Milky Way. The dust lane in the disk of this galaxy can be very clearly seen in this Infrared image taken by the Spitzer Space Telescope, and it doesn't look very disturbed.

Though we are pretty good at determining distances to galaxies these days, the distance to the Sombrero is still somewhat uncertain. I see quotes of distances anywhere from 28-50 million light years, though I tend to trust the lower end projections since they fit so many other aspects of the galaxy. The problem is that galaxies in the Virgo Cluster are a little bit too far away from our normal distance determination methods (using Cepheids or Planetary Nebulae or star clusters or bright stars) to work well. Normally, with an accurate value for Hubble's constant (which we have now thanks to observations by WMAP), we can use Hubble's Law to find the distance.

That's just d = v/H where v is the radial velocity of the galaxy and H is Hubble's Constant. The problem is that galaxies in Virgo have large peculiar velocities since they are in a cluster. They are swarming about the center of mass like a bunch of angry hornets, and this velocity adds a random component to their Hubble flow speeds. Ideally, a galaxy 60 million light years away should be receding from us at a speed of 1400 km/sec, but the peculiar velocities in Virgo can be as high as 2000 km/sec, overwhelming the "signal" we get from cosmological expansion. Since the cluster is close to us, this random component is very large compared to the cosmological expansion velocity, so that makes using Hubble's Law very tough. As our technology improves, so does our ability to pick out standard candles in these distant galaxies and improve our distance accuracy.

Now, a quick aside about dark matter. I mentioned that the peculiar velocities in this cluster are very high, on the order of 2000 km/sec. This fact and our knowledge that the cluster is bound together is another piece of evidence that tells us of the existence of dark matter. Here's how: when we look at galaxy clusters, we assume they are bound. That means all (or almost all) of the galaxies are gravitationally bound to their clusters. This is a good assumption because most galaxies exist in clusters, and we don't see clusters in varying degrees of dissipation in our Universe.

Compare the state of affairs for galaxy clusters with that of open clusters in our galaxy. Open clusters in our galaxy are NOT bound (due to the strength of tidal forces in the disk of the galaxy), and so we see them in varying degrees of concentration. Some very young ones are very tightly grouped together while most older clusters are very loosely bound, sometimes almost to the point where they are unrecognizable as clusters. With galaxy clusters, they are all pretty similar in terms of their concentration and velocity distribution, much like the globular clusters in our galactic halo, so we assume they are bound together.

The escape velocity of a cluster is like a speed limit. If a galaxy is moving faster than the escape velocity, then it will escape, and it is considered to be not bound to the cluster. The escape velocity depends on the mass and size of the cluster. The more massive the cluster, the harder it is to escape the cluster's gravity. So, if we count up the mass of all of the visible matter in Virgo, which means all of the stars, gas and dust, we can estimate the escape velocity of the Virgo Cluster. We get a number of about 1000 km/sec.

This is a problem, because if the escape velocity of Virgo were really that low while galaxy velocities are often as high as 2000 km/sec, then the cluster should be flying apart! The solution comes with dark matter: When we make the assumption that dark matter is 10 times more common than visible matter, like it is in our own galaxy, the escape velocity from Virgo grows to about 4000 km/sec, easily high enough to contain all of the "angry hornets" buzzing around the cluster's center of mass at 2000 km/sec or so.

There is also very hot gas bound to galaxy clusters, seen in X-ray images due to its high energy radiation. If we measure the velocity of such gas (which is related to the temperature), we also get a very high number. If we assume the hot gas is bound to the cluster, then you need a lot more mass than what you can see to contain that gas, and so the need for dark matter appears. Fritz Zwicky was the first to advance this argument for dark matter way back in the 1930's, but his ideas weren't generally accepted until more evidence came to light decades later. The problem is not so much that Zwicky was unfairly ignored, it's just that he had a lot of crazy ideas, many of which turned out to be wrong, and so when he claimed to discover dark matter, he wasn't taken as seriously as, say, Einstein or Hubble would have been.

Moving North about 15 degrees toward the center of the cluster, we move into the Messier Objects contained in Virgo's cup, starting with M61, a 10th magnitude galaxy very similar in properties to the Milky Way and located about 60 million light years away. This makes it one of the largest spirals in the Virgo Cluster. Moving North about four degrees brings us to the next Messier object, M49, one of the giant elliptical galaxies in the cluster with a major axis of 160,000 light years in length or possibly longer depending upon the angle of orientation with respect to us. It is at least five times more massive than our own galaxy, which is itself one of the largest galaxies in our own little cluster.

Going north another four degrees or so, we stumble across a string of galaxies known as Markarian's Chain, at the heart of the Virgo Cluster. In the linked image, that's roughly the same angular size as a standard photograph of the Pleiades. Most prominent on the Western end are two giant elliptical galaxies, M84 and M86. Proceeding East from there, we see a pair of connected galaxies that looks at first glance like a pair of eyes, known as Markarian's Eyes. They are also known as NGC 4438 and NGC 4435, and you can see in the linked image the dramatic effects of tidal forces on these two closely passing galaxies. A full moon would just barely cover the two ellipticals and the two eyes, to give you some idea of how separated these objects are in a line on the sky.

A degree or so Southeast of the Eyes, we find Virgo A, also known as M87, probably the largest galaxy in the Virgo Cluster, probably at least 20 times more massive than the Milky Way galaxy. In deep exposures, the surface brightness of the extended halo of this galaxy fills a region in the sky roughly equivalent to the Full Moon, and this is a galaxy that is 60 million light years away! At the heart of Virgo A is likely a supermassive black hole, from which is emanating an enormously powerful jet, a stream of plasma extended around 5000 light years from the core of the galaxy.

Another couple of degrees East from M87 is a cluster of five messier objects loosely arranged in a 180 degree arc of a circle that it about 3 degrees in diameter. The Southeastern part of the arc is anchored by the giant elliptical galaxy M60 and a close companion spiral galaxy known as NGC 4649 (seen better in this image). A little less than a degree West of M60 is M59, another large elliptical galaxy. To give you some idea of how big these big ellipticals are in Virgo, M59 has about 2000 globular clusters in orbit around it, over ten times more than our own Milky Way galaxy has. Each of these clusters contains anywhere from 50,000 to 10 million stars.

The last three Messier objects in the "cup" of Virgo formed by Vindemiatrix, Porrima and Zavijava about 25 degrees Northwest of Spica are M58, M89 and M90, three galaxies within about a degree of one another and about 1-2 degrees West of Virgo A. M58 is one of the few barred spiral galaxies in Messier's list, and it is also a rare spiral to be found so close to the directional center of Virgo. It is hard to say how far this is from the true center of Virgo. With a velocity about half that of the highest peculiar velocities, it is likely safely outside of the true core and so not subjected currently to the kind of tidal forces that can strip its gas and disrupt its structure.

M89 is another giant elliptical, almost perfectly round in shape. It isn't clear whether it is a true sphere or just an ellipsoid being viewed end-on from our perspective. Deep images of M89 show a little bit more asymmetry, including a jet-like feature similar to that seen in M87 (Virgo A). Most of the scruff surrounding the main body of this galaxy is probably tidally disrupted remnants of galaxies that have been devoured in the recent past.

M90 is another bright spiral with a two-phase structure. The inner disk is lumpy and clearly split into regions thick with dust and clumps of vigorous star formation. Then about a third of the way out from the center to the visible edge of the disk, it transforms into a very smooth appearance similar to that of a lenticular galaxy, which it may be evolving into. M90 also has a high enough peculiar velocity that it should be able to escape the Virgo Cluster. The peculiar velocity is so high that it is currently larger than the expansion velocity of the cluster as a whole and so the net radial motion is toward us, one of a very small fraction of galaxies in the sky that seems to "violate" Hubble's Law. It is only a technical violation, really, as I talked about previously.

Some other galaxies in this same little area that are not to be missed: NGC 4216 is a pretty nearly-edge-on spiral about 4 degrees West of Markarian's Chain. The pair NGC 4762 and NGC 4754 is also a very nice target a few degrees east of M60, at the eastern edge of the group of Messier objects I've been describing. Four degrees South from M58 is a large, bright face-on spiral NGC 4535. This spiral has been a good target for finding Cepheids and has helped the Hubble Space Telescope establish a proper distance to the Virgo Cluster.
Just half a degree South from NGC 4535 is another beautiful spiral, NGC 4526, reminiscent of the Sombrero Galaxy with its prominent dust lane and bright central region. This one is famous for hosting an elusive Type Ia supernova in 1994, a type of explosion that is an extremely important brightness standard used in distance determination.

Before I move out of the Virgo Cluster region of the constellation Virgo, I should point out a very nice sky chart of the "cup" of Virgo and the cluster galaxies within it. Now for a few more highlight galaxies in the Virgo Cluster. Next up is NGC 4527, a nearly edge-on spiral reminiscent of Andromeda but about 20 times further away on the near side of the cluster. Right next to it on the sky is NGC 4536, but distance estimates seem to put this one on the far side of the cluster, about 70 million light years away (a distance obtained thanks to a bright type Ia supernova, 1981b, which also made this a target for the Hubble Space Telescope years later). These two galaxies are so close together in the sky that they would fit within a full moon angular diameter, and they are found about 4 degrees Northwest of Porrima (the vertex of the cup), just across on the north side of the Celestial Equator.

Nearby, just a couple of degrees East of this pair, we find the giant elliptical galaxy NGC 4636, recently a target of the Chandra X-Ray observatory. The goal was to measure the concentration of dark matter in the galaxy by measuring the detailed properties of the hot gas in the galactic halo. Turns out the dark matter is very concentrated, not a diffuse extended halo as some theories might predict, and this rules out a few models (such as that dark matter can diffuse outward or puff up like a halo of stars in a globular cluster or a galaxy). NGC 4636 isn't much to see visually, just an ordinary elliptical, almost perfectly spherically symmetric (but the X-rays tell a different story).

To finish off the bright galaxies in the Virgo cluster (in this constellation, anyway), we need to look several degrees to the East of the main body, about 22 degrees due Northeast from Spica, and there we find the bright spiral galaxy NGC 5566, a barred spiral with a ring of stars around the center. It is imaged here with a couple of fainter companion galaxies. There are still a few galaxies left to cover, though, and they are in a little group just South of Spica and north of Gamma Hydrae. Their membership in the Virgo cluster is on the iffy side, but some are at the right distance.

NGC 5247 is the most prominent of this group, a face-on grand design spiral about 50 million light years away, and just a couple of degrees to the West is a tilted 11th magnitude spiral about 90 million light years away (probably not a member of the cluster) known as NGC 5054. South of these two is a nearby spiral NGC 5068 only about 20 million light years away but rather faint for this distance, indicating it is a small galaxy. Finally, a little further south is another small member of the group, NGC 5084, seen in this gallery of Virgo galaxies.

Over near the Eastern end of Virgo, following the Celestial Equator east from Porrima about 45 degrees and just a few degrees north is the faint star 109 Virginis, marking one of Virgo's feet. Right next to this star is the edge-on spiral galaxy NGC 5746. This is another galaxy that recently drew the attention of the Chandra X-Ray observatory. Chandra discovered a hot halo of gas surrounding this galaxy, which is a little unusual because most galaxies with hot halos have that gas due to vigorous star formation (and stellar explosions), but NGC 5746 shows a rather quiet history. Instead, the hot gas is actually gas from the intergalactic medium falling into this galaxy and heating up as it does so.

The final object I want to mention in Virgo is a frequently overlooked globular cluster, NGC 5634, just under 5 degrees due East from the bright star Syrma in the Southeast corner of Virgo near its border with Libra. Astronomers speculate that this globular cluster once belonged to the Sagittarius dwarf galaxy, a small irregular galaxy currently being tidally ripped apart thanks to repeated passages through the disk of the Milky Way galaxy. This cluster is located in the extended tidal stream of the dwarf galaxy and also has a similar population of stars (and similar composition) to the clusters associated with this dwarf.

Weekend Trip

M*chelle and I went out of town for the weekend, thanks very much to a grandma who was willing to babysit the clan for 48 hours. We stayed at a nice hotel. We even got the first night comped thanks to a room mixup where they checked our room out to someone else at 9pm. At least we had the latch on the door so they didn't just barge in. We were just sitting on the bed watching "Juno" after a nice relaxing hour or so in a hot tub.

We had lots of good food, and we got to see lots of live music, which made M*chelle happy. Unfortunately, the place we went Saturday night to watch music started off ok. We got there 30 minutes before the show in a little open courtyard between two big buildings. There were about two dozen tables, and we sat in the front.

As time went on, more and more people showed up, and it was becoming abundantly clear there weren't going to be enough chairs and tables for everyone, so people just started standing in front of us. Oh well, I guess we have to stand for the show. Then it got so packed that we were like sardines. Our chairs were useful to have behind us so we could have a little bit of a buffer between the rest of the crowd on one side and also so we could sit between sets.

Fun, very loud show, and the crowd was fairly drunk and unruly. Me, I'd rather be on the couch watching a baseball game, but it was an interesting experience, definitely my first one in what effectively turned into a mosh pit.

This morning, it is back to reality with an 8am final. I didn't like taking them as a student, and I don't like giving them as a faculty member.

Talking Down to the Rubes

Several blogs have pointed to this story in the NY Times in which they send several food reviewers out into the hinterlands to pass judgement on the horrible chain restaurants that populate the areas where the rubes reside in the flyover states.

It is almost impossible not to hate such a snooty attitude. It's a shame, really, because the reporters who work for that paper still do very important work occasionally when their corporate editors allow them to do something besides research Obama's bowling technique.