Stellar Evolution: The Effects of Convection

In my first post in this series on stellar evolution, I set up the basic model of how stars live, and die. The next two posts looked at theoretical models and showed that they can reproduce where stars should and should not be on the H-R diagram reasonably well.

One thing that, until now, I haven’t mentioned is another important process that occurs in stars and allows for another important set of tests for stellar evolution. That process is convection. For various masses of stars, convection occurs at different places in the star. In our own sun, we know this occurs on the surface. We can see this in the form of granules (from SVST).

But convection doesn’t always have to occur at the surface. In other stars, convection may occur in the cores, or somewhere in between. In some cases, the whole star may be convective! Convection tends to occur when radiative processes (photons traveling through space) are insufficient to carry the energy of the star towards the surface. This would be due to things such as the density getting sufficiently high that the photons just can’t get anywhere before being reabsorbed or scattered off in a random direction (possibly back towards the center of the star). Another thing models tell us is that the properties which determine how effective radiative transport is, will change over time. This, in turn, means that convection will start and stop at various points throughout the stars lifetime.

When observing stars, it should go without saying that the only thing that we directly observe is whatever is on the surface. Convection is important because it can dig down into the star and bring up material from deeper down, or carry fresh material down closer to the core where temperatures are hotter. In the case of some special elements, this can destroy them.

By comparing these predictions of abundances of elements in various phases of a stars life to observations, we can get another test of on stellar evolution.

The first case, in which different material is brought to the surface, occurs when convection digs deep enough into a star that it encounters a layer in the star’s interior that had previously been subject to fusion. Since fusion creates heavier elements than what would be present on the surface, the convection would make this visible as it brings it up. This process is known as “dredging”.

Dredging may occur at several points after a star leaves the main sequence. The first occurs shortly before the onset of helium fusion in the core of stars while the star is in the red giant phase.

So what we can do is look at stars on the evolutionary tracks I mentioned in the previous post, and compare the ratios of abundances before and after this dredge up phase. What we should see, if the theory is correct, is an increase in certain heavier elements. And not only that, models should also be able to predict, fairly well, how much those ratios should change.

In this first dredge up, one of the most notable changes will be the ratio of C₁₃ to C₁₂. In the second dredge up phase, models predict that there will be increases in He and N content. Sufficiently massive stars should also undergo a third dredge up, in which carbon and oxygen will be brought up.

All of these changes have been confirmed observationally, and within reasonably amounts, they conform to the predicted ratios. As should be expected, some variation is inevitable due to difference in initial abundances.

But, as I mentioned earlier, increasing surface abundances isn’t the only effect that periods of convection should have. Certain elements, if subjected to convection should be destroyed. Lithium is the most prominent in this case.

Since lithium isn’t something that’s readily created, the amount stars start off with is pretty much all they’re ever going to get. Lithium is also fairly easily destroyed at higher temperatures. The surfaces of most stars aren’t quite hot enough to do so, but if lithium is pulled down to depths where temperatures are hotter through convection, then the surface abundance of lithium will be depleted. Again, models predict at what phases in evolution we should begin seeing lithium depletion, and again, they’re reasonably accurate.

So let’s quickly what we’ve discovered in this series thus far: First off, evolutionary models predict where we should and should not see stars on the H-R diagram. They match where they will speed along, and when they’ll clump. In this post, we’ve explored how models also predict and match chemical abundances throughout the evolutionary process.

In future posts, we’ll explore even more tests of these models to ensure that they do indeed conform to reality.

Didn't see it coming

Many places have strange laws on the books that have never been repealed. Philly is no exception. One law bans psychics or fortune tellers that operate for profit.

But unlike many places, the Department of Licenses and Inspections in Philly has decided to actually enforece this law closing down 16 shops.

87th Anniversary of the “Great Debate”

Although not as notable as some recent events in astronomical history, today is the 87th anniversary of what set the stage to be a major revolution in the astronomical field.

Prior to the early 1900’s, the scale of the universe was thought to be quite small. Astronomical distances at that time were ones that could be dealt with without having to resort to scientific notation. We had our nice little home in our galaxy. There were stars, dust, and some nebulae. But of particular interest were a set of what were then dubbed “spiral nebulae”.

On April 26, 1920 two prominent astronomers, Herber Curtis and Harlow Shapley got together for a debate on this issue. The question was whether or not these odd structures were relatively nearby objects, within our own galaxy, or far more distant than astronomers until that point had dared imagined, lying far beyond our own galaxy as their own, unique “island universes.”

Shapley held the former position, suggesting the extent of our galaxy was effectively the entire universe. He required that it be fairly large to do this (about twice the size we estimate today). Another prominent astronomer of the time, Adriaan vanMaanen, supported him.

On the other side, Curtis claimed that our own galaxy was much smaller, being at most about 30,000 light years in diameter. This left room elsewhere for more distant objects.

Shapley began the talk, first presenting his side. One of the first points he made is that, our own galaxy is so large, if we assume that these spiral nebulae were similar sizes, that would put them at inconceivably large distances. He also pointed out differences in the surface brightness between our galaxy and what was observed for these spiral nebulae. Our own was much fainter, which would suggest that they are different beasts. His main piece of evidence, however, was based on observations from vanMaanen in which he claimed to have shown that the spiral nebula M31 rotated once every 10⁵ years. If these objects were really that far away, there would be no way we could observe them rotating. Additionally, if they really were that large, their outer edges would have to be moving much faster than the speed of light to complete a full rotation that frequently.

Curtis followed, making several points to suggest that these objects were much further. His first point was that there was a large range in the observed sizes of the spiral nebulae. Some were big (like M31 and M100). Others were much smaller. It did not seem plausible that the same processes could make objects with such disparate sizes. As such, they were probably all similar sizes, but at varying distances, which would require that they be much further than Shapley claimed. Curtis also observed novae in the Andromeda nebula (M31) and noticed that they were extremely faint compared to ones in our own galaxy. He assumed that, if they were indeed the same process, then the faintness must be due to extreme distances. Lastly, he noted that the Doppler shifted spectra of these objects did not match with other objects we knew to be in our own galaxies. They traveled at much higher relative velocities, and as such, must be independent systems. He also wondered about the distribution of these nebulae. Most non-spiral nebulae seemed to be confined to near the plane of the Milky Way whereas these objects had no apparent preference.

While this debate didn’t definitively decide the matter, it did set the stage for more research, leading up to Edwin Hubble’s discovery of Cepheid variables in M31 in 1923. What was interesting was the evidence provided by both sides.

Shapley’s first argument against a large universe was simply an argument from incredulity, very similar to the ones we see today from the ID proponents. His second, that the surface brightnesses were dissimilar between our galaxy and those spiral nebulae was a major blow at the time, but ended up being solved upon the discovery of absorption caused by dust in our own galaxy which made ours seem much dimmer. The observations he relied upon from vanMaanen ended up wrong just due to sloppiness on vanMannen’s part.

But Shapley wasn’t the only one that got things wrong.

The novae Curtis cited as subluminous weren’t actually just regular novae. They were supernovae, which put M31 even further away than was realized. Even Hubble didn’t get things quite right. At that time, the distance calibration for Cepheid stars wasn’t terribly accurate because we didn’t have well-established distances for the calibration stars (now we have trigonometric parallaxes which are the most accurate distance measurement). It was also later realized that there’s two distinct populations of Cepheids with slightly different calibrations. His original distance estimate was about half the current.

Since then, we have discovered ever more about our galaxy, and our universe and most certainly, the future will bring even more understanding.

No Special Privileges?

It's no secret that Christians in this country receive all sorts of little bonuses from the government. They get to have their religion endorsed on currency and in the pledge, they get special access to public land, are infinitely more likely to be elected to public office, get special consideration with their half baked "theories", get free, unmonitored handouts to do unspecified good work,...

And now, it seems, knowing your bible can also get you out of jail time. That's right.

An Ohio Judge decided that a man caught using a stolen credit card was trustworthy enough to be released on an appearance bond because he could recite Psalm 23. Not much of a challenge given that it's one of the more popular passages out there.

Perhaps the judge should have picked something more obscure. Perhaps something on, oh, I don't know, stealing?

Liberal Plot to Destroy the Climate

It looks like Connie M. Meskimen, a divorce lawyer from Little Rock, AR has figured out the evil liberal plot to heat the world.

According to her letter to the editor, she posits that March was so warm because of the daylight savings time change. It adds an extra hour of daylight which of course is going to make things warmer.

And who's to blame? That damned liberal congress. Except, the time change was part of the Energy Policy Act of 2005. In other words, a time when congress was still under republican control. Sad thing is that it didn't have jack shit of an effect of energy usage.

Similarly, it doesn't have jack shit of an effect on the climate. Why? Because the length of the day didn't really change. It's fixed. Let's explain.

Hokay. So here's the Earth.That is a sweet Earth. The blue line sticking out, is the line that's perpendicular to the plane of the solar system. The red line is the actual axis of rotation. They're off by 23.5º. As we're looking at it in this picture, we're essentially looking at the Earth from the point of view of the Sun given that we can see the whole Earth lit. You can tell this is also atumnal equniox as I've drawn it since, if the Earth would contintue on in it's counter clockwise orbit, the southern hemisphere would soon be pointing towards the Sun.

But instead of looking at this from the equinox, let's take a look from a different location and switch to the summer solstice (left). I've also drawn in some lines of constant latitude in green to help in explaining things.

First, let's look at the lower line. As the earth spins, a point along that line will come around the left edge of the Earth, as we're seeing it, at noon their time, swing around, cross into darkness, and at midnight, disappear over the right edge.

Yeah, that's nice. But what does it have to do with the length of the day? Well, since the Earth spins at a constant rate (once every 24 hours), the amount of time it's in the daylight is proportional to the length of that line. In the summer, days are longer because that line is longer. Don't believe me? Look what happens if I chop those lines off and compare their lengths:
Here we can clearly see why the day is going to be considerably longer during the summer. In fact, the higher you go in latitude, the longer your day will be. If you go all the way up to the upper circle I have drawn, it never goes into the shadow. So spin all it wants, it's never going to be dark. At least until the Earth orbits to a position that has the other half lit.

Alternatively, at the winter solstice, the other half of the Earth will be lit, reversing the lengh of those two lines. Half way in between (the equinoxes), the lines will be the same length. All of this is due to the angle of Earth's axis with the perpendicular to the plane of orbit.

In other words, it doesn't change based on what time system we use! So what's the big fuss with changing our clocks twice a year?

The idea behind this is that we can arbitarily pick what we define to be "noon". In the most general sense, it's when the sun crosses the meridian (an imaginary line runing along the sky between north and south). But who says it has to be that way? What would happen if we decided to define noon as, say an hour before then?

Well, that would mean that morning would last less time, but then there'd be more afternoon. That's great for businesses and sports that rely on there still being light after people get off of work. Sucks for farmers.

The idea behind the switch this year was that, if we adjusted our system so we'd be up more during the light hours, we'd conserve more energy since we wouldn't have to be using artificial lighting. Sadly, this failed.

But going back to the original letter, arbitrary definitions of our time keeping system have absolutely no effect on the realistic matter of the length of a day.

If God doesn't even get to mess with Earth's rotation Congress sure as hell can't.

Hubble Turns 17

It seems like only yesterday the HST turned 16.

However, it's been a full year and to celebrate the anniversary, they've released a new set of pictures to commemorte the occasion. Last year was starburst galaxy M82.

This year, it's a gigantic picture of the Carina Nebula: a star forming region visible from the southern hemisphere. Phil Plait's already done a detailed write-up looking at many objects in the nebula, so instead of rewriting it here, I'll just point to him.

Stellar Evolution: Isochrones

In this post on stellar evolution, I’ll be discussing what are known as “isochrones”. In my last post we looked at evolutionary tracks on the H-R diagram for constant masses across time.

Isochrones are the opposite. They are plots of on the H-R diagram at constant time across all masses. Another way to think of this is to take thousands of stars, of varying masses, get them started at the same time, wait some millions of billions of years, come back, and see where they lie on the H-R diagram.

As I pointed out earlier (and common sense should tell you even if I didn’t), we can’t create stars in labs and we most certainly can’t just sit around for billions of years to see what happens. Instead, our chief tool is modeling. Astronomers will make a model, applying all applicable physical laws, such as the ideal gas laws, gravity, and the like. Models can then be fast-forwarded to any point in time, and then checked against observations and refined.

So let’s start by taking a look at a basic isochrone. The image to the right shows a typical H-R diagram with hot, blue stars to the left, and cool red stars to the right. Going diagonally from the upper left to the lower right, we can see a large section of the main sequence. Branching off from that are three trails which represent the distribution of stars after 10⁸, 10⁹, and 10¹⁰ years. What we learn from this is that, as this conglomeration of stars ages, stars will “peel off” the main sequence, starting with the massive stars in the upper left. The turn off will then work its way down the main sequence with the path it takes from there changing as it does.

That’s all well and good of course, but now how to test this aspect of the models? To apply some data to these, we need a large number of stars that all formed at very nearly the same time, but at a variety of different masses. Fortunately, nature provides a wonderful opportunity to find just such things: clusters.

Clusters form from a single cloud so the chemical composition is the same for all stars involved. The formation occurs relatively quickly in astronomical time scales, so now we have everything we need to be able to see if models can accurately reproduce the observed shape that nature creates.

So let’s take a look at a few and see how they do:

Here’s a set of isochrones for the globular cluster m92. The scale is different than the isochrone I presented and it actually covers a lot more area of the H-R diagram than mine. You’ll notice that the isochrones are only plotted for the part near the main sequence and one part later while there are data points that continue past the end of the theoretical tracks. The reason for this is that the tracks tend to merge as they approach that upper line which is known as the red giant branch (RGB). Thus, there’s no real point in plotting it over there.

What we can see is that this cluster fits the shape of these particular isochrones very nicely. It’s not perfect though. Many effects, such as unresolved binaries, slight differences in chemical composition, unusually fast rotations, and other things, contribute to the scatter. But overall, the data fits the isochrones pretty well.

47 Tucanae is another globular cluster (visible only from the southern hemisphere) which has a very nice fit with the theoretical models.

This sort of fitting is one of the goals of the research I participated in this summer. Our data wasn’t nearly as pretty though. Part of the reason is that we were studying an open cluster, which by definition has far fewer stars, but also because there was interference from an interstellar cloud which caused reddening and extinction.

But general shape matching isn’t the only thing that we should be able to predict based on isochrones. As with the evolutionary tracks, we should also see gaps where stars don’t spend much time. Again, we should, and do, observe the Hertzsprung Gap.

Another feature that we should observe and is one I’ve used, is known as the Red Giant Clump. This is a particular point near the RGB where stars slow down in their evolution for a time and tend to bottleneck. This happens at a fairly consistent color and luminosity, which gives it a feature astronomers can exploit to make corrections.

Are models perfect? Absolutely not. Models are still limited by what we’re able to realistically calculate. As computing power improves, we are able to take more and more into consideration, which should bring our models into better agreement with the data.

One example of this is that models are now beginning to consider a feature known as convective core overshoot. In this, convection that occurs in the interior of some stars, is able to provide the core with additional hydrogen, thus slightly changing the evolutionary features of the star.

So as with the evolutionary tracks I mentioned in my previous point, our main test of these theoretical models are to check where stars should and shouldn’t be, where they clump, and where they go, to observations of reality. If they match, we gain confidence in our models.

As you might expect, the general shape isn’t the only feature of models that we can test. In my future posts on stellar evolution, I’ll briefly discuss other properties of stars for which we can hold models accountable.

Jesus makes you bullet proof

Tragedies seem to be a wonderful time for the religious right to spout their propaganda.

While Phelps may be the one making headlines for his vitrolic comments, he's far from the only one. Others like Brother Jed, Pat Robertson, and the rest of their ilk aren't far behind the Phelps family.

The Virginia Tech shootings have brought out another round of idiocy from them.

PZ Myers has already seen pundit Debbie Schlussel blaming Muslims. As soon as it was revealed that the shooter was Asian, she attempted to use that to reenforce her xenophobia.

Over at Answers in Genesis Ken Ham blames atheists and evolution.

Brother Jed was on campus again yesterday with a flock of his followers. One of them claimed that the students that died, did so because they didn't believe in Jesus. As if belief could stop the bullets.

EDIT: Looks like Phelps will be protesting at the funerals of those that died at Virginia Tech.

Hey, when did that happen?

I didn't realize it until just now, but the beginning of April brought my 1 year anniversary of joining the blogsphere. My first post was on April 3, 2006.

Oops. I let that date slip by.

Regardless, it's been a fun experience, and 330 posts later I still have no intention of quitting. So here's no another year!

So... which is it again?

Over at Pharyngula, PZ points us to a creationist clown car.



The funniest thing I see about this is that, yet again, even the creationists recognize that Intelligent Design is no different than their biblical literalism. Also included is a picture of an eye, calling it irreducibly complex.

Again, I get a chuckle, because as I've pointed out eleswhere, ID proponents have dropped the eye as an example of design.

This date in history: First human in space

Today, in 1961, Yuri Gagarin became the first human in space aboard the the Vostok spacecraft.

Since then, we've put men on the moon, built space stations, sent probes to every (current) planet, and more.

Humanity has come a long way, but the universe is a big place, and there's always more to explore.

We're on to you Ms. Coulter

For the most part, I believe taht humans are generally good people who strive towards rational answers to life's questions. So occasionally, when someone says something that's astoundingly stupid, I'm quite willing to believe they're putting us all on.

Combine this with April Fool's day and I'm quite able to be fooled when someone does in fact believe something utterly stupid.

But sometimes, I still have to wonder. Why would an otherwise intelligent person go on to make horribly stupid arguments, relying on age old mischaracterizations and fallacies? I can't fathom a reason, beyond satire.

Writer Peter Olofsson at Live Science, wonders the same thing about Ann Coulter. In her book, Godless, she attacks evolution, spewing out tired creationist arguments, mostly stolen from Jonathan Wells' book Icons of Evolution.

But when is the critical mass of stupidity reached, that one can conclude no one could actually be that stupid and still have a functioning brain? That's a hard question to answer, but Olofsson ventures that Coulter has crosed that line and is indeed engaging in subtle satire of the entire creationist movement.

I'm not sure that I feel she's crossed that line, but taken with some other comments she's made encouraging discrimination based on race, gender and religion, "raping" the environment, demolishing the first ammendment, and more, I'm tempted to say she's getting pretty close.

Either that or perhaps she really is crazy.

Water, water, everywhere

Within our own solar system, water is surprisingly common. The majority of the surface of our planet is covered in it. Mars has it frozen into the surface. It's found in the atmospheres of all the gas planets. Comets have it in large amounts...

So it's not too much of a stretch to think that it should be abundant elsewhere in the universe (unless our solar system is special for some reason). Water has been detected in interstellar clouds, and now, for the first time on a planet outside our solar system.

Pretty nifty stuff.

Ultimate in Easter Research

Happy Easter everyone!

I feel that today I should share with you some of the most important research being done in science today, in conjunction with this holiday.

Enjoy.

The worst part about living in a dorm...

There's many worst parts really. I've got some really horrible roomates this year. One is completely tone deaf and insists in singing loudly in Spanish (his native language). He also doesn't ever sleep for extended periods, just takes "siestas" throughout the day, so often there's bad singing along with bad laptop speakers at 3 in the morning.

But right now, I think the worst part is that they've already turned the heat off for the rest of the semester (since we had all that nice 80º weather last week) and now it's been in the 30º's for the past 4 days. So our room has slowly cooled down to be in the mid 50's.

Nothing like having to wear a coat to sit at the computer. I'm sure Mollishka would sympathize.

Jesus thinks you're an idiot too...

For those that aren't familiar with my school, KU has a large open area where many groups will advertise their events. The space is open to anyone that wants to use it and is typically called "Wescoe Beach". It can be used for anything from promoting races for student senate, to Brother Jed preaching his own version of eternal damnation.

He was out on Wednesday, although I didn't have the time to listen to him. Friday, however, saw a live action reenactment of the crucifixion, complete with a large cross, and an actor in a loincloth holding onto some nails in 30º weather while people chanted at him.

Not exactly what I'd be doing for fun, but it sure sounds better than what religious groups in the Philippines do. Apparently when they reenact the crucifixion, they do it for real. Real people. Real nails.

But if having nails driven through your hands isn't enough, you can try beating yourself with chains or having someone beat you with glass embedded wood.

I'm not particularly religious, but as I understand it, the whole purpose of Jesus' sacrifice was to save us from this very sort of punishment. So perhaps this is just my silly overly critical atheism speaking, but wouldn't rejecting his sacrifice to do it yourself be something of an insult?

$15!?

There's many rather silly stereotypes about atheists. Some are more annoying than others. Some are just bizarre.

In the annoying category is the myth that there are "no atheists in foxholes." I shouldn't need to point out that this isn't the least bit true.

On the bizarre side, many people think we're secretly worshipping Satan, or eating fetuses and kicking puppies. I'm afraid we don't worship something we don't believe in, no amount of ketchup could make the second the least bit appetizing, and although I don't particularly like dogs, I have no ill will in that regard.

But another very common myth is that atheists never do anything for charity. As the Society of Open-Minded Atheists and Agnostics (SOMA) does every year, we went and dispelled that myth as well.

One of SOMA's annual events is a "soul auction". These work very much the same way as date auctions in which the seller promises offers various services and auctions off their time to perform them. Tasks range from dates, to cooking, to swordfighting lessons.

This event took place Thursday night and went very well. I was given the role of playing the Devil and was given the task of setting the starting bid and making sarcastic comments. I was a bit leery of this because I haven't done much theater since high school but I've had a number of people tell me that they enjoyed it.

Over $800 was collected from 23 sellers with most going for $20-30. The high was $100 and the low $12. The proceeds from this event are split with the Douglas County AIDS Project. SOMA members also frequently volunteer by participating in the AIDS walk.

Traditionally, SOMA has been one of the largest contributors to this charity, beating out a large number of religious groups. One year, before I began attending KU, SOMA was poised to donate the largest sum, but rather than be beat out by a bunch of atheists, a religious group collected money from the members for a last minute donation. But that's fine with us. If we can guilt someone into donating more for a good cause, we're fine with that.

If anyone's curious as to what services I was offering to perform, I offered my culinary skills (I specialize in cream sauces and have recently been perfecting flambè'd desserts which fit the theme), as well as tutoring in Astronomy or Dance Dance Revolution.

So what is my soul worth? Apparently only $15.

Stellar Evolution: Model Evolutionary Tracks

In my last stellar evolution post, I went through a quick version of the life and death of stars. Here, we’ll explore a bit more of the current understanding of all this. Namely, how do astrophysicists support the stellar evolution theory, when we can’t actually create stars in labs and fast forward time to watch the process unfold before our eyes, or even resolve the surface of more than a handful of stars aside from our sun?

Let’s start off with what we can observe pretty directly. As I’ve mentioned before, looking at the spectra of stars, we can learn what they’re made of, at least at the surface. As you’re probably aware, stars are gigantic balls of primarily hydrogen. There’s about 20% helium, and 1% other stuff.

Another property we can obtain pretty directly is the mass of a number of stars. To do this, we look for stars in binary systems. From there, we observe the period of the stars around the center of mass. Using Kepler’s laws, we can derive the ratio of masses. But while the ratio is all well and good, we’d like to know the masses of each one independently.

Fortunately, nature occasionally provides us with the ability to make another set of observations, which fully solves the system of equations. About 50% of stars in our galaxy seem to appear in binary systems. Statistically, some of them will have planes of orbit that align with the Earth. That is to say that, from Earth, we the stars eclipsing one another. Such systems are known as eclipsing binaries.

The reason they’re useful is that as the stars orbit around one another they will be moving towards Earth for part of their orbit, and then heading away for another part. By measuring the doppler shift we can measure the precise speed with which the stars are orbiting.

Lastly, we can determine the ratio of sizes from the period of the eclipse. If, for the sake of example, we assume that one star is smaller, as it passes in front of the larger star, it will block the light from the larger causing a dip in the overall brightness as long as it’s in front of the other. As it passes behind the larger star, there will be another dip in brightness as the larger star blocks the light from the smaller. If you want to play with some computer simulations of these objects, try checking out StarLight Pro. It can be use for real life astronomy, but it’s fun to play with even if you don’t know what you’re doing.

Put all these observations together, do some math, and you can pop out information such as radii, and relative brightnesses. But these aren’t the only features we know. As I described in this post we can also determine surface temperature and distance.

So there’s three intrinsic quantities we have right there: Radius, chemical composition, and temperature (at least for the surface for the latter to).

This gives astrophysicists a starting point. From there we can start building models and make up our temporal limitations through mathematics.

We start off with a mathematical model of a big giant ball of hydrogen not doing much of anything. From there, we plug in known physical laws; things like gravity, the ideal gas law, laws governing radiative transport, etc…

I don’t intend to go into the math here, as there’s not nearly enough room. After all, my entire astronomy course for last fall was just doing the basics of all this math for the atmospheres of stars.

So cutting all of that out, let’s talk about some of the things these models predict that we can confirm observationally.

One of the things that the models make perfectly clear is that stars do indeed evolve over time. It also makes it clear that the more massive the star, the faster it will evolve and die. Observationally, this should mean we see less high mass stars than we do low mass ones. They’re simply not around long enough for us to see many. This is something we observe very distinctly.

Another extremely important prediction of these models is to let us know how these stars will evolve across the H-R diagram. The models tell us that stars will spend most of their life (~90%) of their lifetimes all along a single line we call the main sequence. Thus, when we look around, we should see that same amount of stars on this line. If you look at this H-R diagram that line jumps out as the diagonal conglomeration running from the upper left to the upper right.

From there, we can ask what happens when stars run out of the hydrogen in their cores and begin their deaths. If we take sample stars of various masses and chug through the math, we can generate tracks on the H-R diagram for these various stars. Let’s take a look at one of those:

The main sequence isn’t drawn in on this graph, but you can get a feeling for where it is. Again, it’s running from the upper left to the lower right, going through those filled circles labeled 1 on each track. The masses are listed next to those points in units of solar masses (the circle with the dot in it is the symbol for Sun).

Let’s look at some of those other points for a minute. The points labeled one are when hydrogen fusion first starts in the core. This marks the beginning of the star’s life and is known as the “Zero Age Main Sequence” or ZAMS.

From there, the stars are slowly evolving to point two, which is where the core runs out of hydrogen. As we can see, this evolutionary process requires that the main sequence have some width to it. If you look back at that H-R diagram I linked to earlier, you’ll see this is precisely the case.

From points two to three, this is the phase of contraction until the point where the area outside the core gets hot enough to initiate shell fusion of hydrogen. This kicks the star over to point five pretty quickly in astronomical time scales (something like 1% of the time the star spent on the main sequence). So here we have another prediction: We shouldn’t see many stars in this region of the H-R diagram. Again, observations confirm this. This sparsely populated region is known as the Hertzsprung Gap.

The rest of the points start getting horribly complicated so I’ll skip out on those, although that's not to say that complicated means impossible. However, it should be noted that we can’t watch a single star go along these tracks. Fortunately, there’s another way to plot the data that gives us a whole different way to analyze the data. In this plot, we looked at position on the H-R diagram for different stars across time at constant masses.

Alternatively, we can look at position on the H-R diagram for different stars across mass at constant time. Such diagrams are known isochrones (meaning same time) and I’ll explore them in my next post.

Recapping what we learned from this post, a good number of predictions can, and are, made based on these mathematical models based on an extremely solid understanding of physical laws. The observations, thus far fit very well, so stay tuned to see how well they stack up for other tests.

MARAC

It looks like I'm going to be heading to the Annual Mid-American Regional Astrophysics Conference next weekend. I'm not going to be giving any talks or anything, but I'll be around. So if anyone that reads this blog is going to be there, make sure to say hi!

More on Stellar Evolution

A few months ago, I had a rather lengthy post concerning stellar evolution. However, that post was mainly presented as a response to a rather absurd set of creationist arguments.

But instead of always doing things in response, I think it’s good to occasionally be more pro-active and cover topics in a more educational manner. So in this series of post I intend to first lay out the basic picture of stellar evolution, from the main sequence to death, and later, get into how this theory is derived and supported.

The first thing that I think is important to point out, is that, despite the equivocation of creationists, stellar evolution has absolutely nothing to do with biological evolution. It’s an entirely different theory based upon an entirely different body of evidence. Stars don’t have inheritable characteristics, and even if they did, they don’t reproduce, so the basics of biological evolution just don’t make any sense here.

Instead, “evolution” in the stellar sense refers to the colloquial definition in which it just means a change over time. But what sorts of changes? Well, changes could include such things as temperature, pressure, chemical composition, and a whole array of other features, such as mass, size, luminosity, most of which are determined by the first three.

Astronomers know these features change, albeit very slowly (usually).

I’ll discuss the rather sudden changes later on, but more important, is to begin to explain how we know stars are evolving even when we claim the timescales are hundreds of millions, to billions of years (far too long to witness in the entire course of human history), and the changes nearly imperceptible.

Perhaps the largest reason we know stars evolve, is because stars shine.

This seems like a very confusing statement at first, but if you think about it a bit more, it makes sense. A star shining means that it’s giving off energy. For stars like our sun, they’re giving off a lot of energy. The sun gives off just under 4 x 10²⁶ Joules of energy per second.

In 2000, the US consumed 1 x 10²⁰ Joules of energy. This means that, in 1 second, the sun generates enough energy to last the US 4 million years. That’s a lot of energy.

And it’s got to come from somewhere.

To figure out where, we start off by looking at what’s available. By looking at the spectra of the sun, we know it’s about 75% hydrogen, 24% helium, and 1% everything else (if you need a refresher on what spectra are, go here). This rules out a lot of possibilities of where the energy comes from right off the bat.

Early ideas suggested that the sun was a ball of fire. However, fire requires the presence of oxygen. Thus, that’s right out. Additionally, there’s just not enough chemical energy available to sustain the sun for the amount of time we’ve known the solar system to exist.

The sun shrinking under its own gravity and exchanging gravitational potential energy for other forms was another possibility. But the sun’s not shrinking fast enough to account for the energy generation of the sun and again, the timetable doesn’t fit.

So astronomy required something that generated a lot of energy using hydrogen and could be sustained for billions of years. Fusion fits the bill perfectly. It also fits well because, when physicists realized that fusion will emit neutrinos and we went looking for them and found them (although only 1/3 the predicted number originally. For more on the missing neutrino problem, go here).

Now that we know that fusion is the source of energy generation for the sun and other stars, we can start to ask what the consequences are.

One consequence that fusion has is that it converts hydrogen into helium. This means that there’s going to have to be a change in chemical composition. Why? Because it shines. If it didn’t, there would be no need for fusion to change the chemical composition and there wouldn’t be any evolution.

Another side effect of this, is that, give it long enough, and you’ll use up all your hydrogen. When that happens, it means you’re not going to have much energy generation anymore. This doesn’t mean the star stops shining all the sudden. It takes light a long time to work its way to the surface and escape due to the fact that it’s going to be scattered off lots of particles along the way. But this does mean that the brightness is going to change. Again, the star evolves.

Aside from sustaining the luminosity of the star, the out flowing radiation has another important effect: It provides pressure to keep the star from collapsing in on itself. With this pressure gone, the star will inevitably contract. This happens relatively slowly, but due to the large mass of stars, and the large radius, this can generate a lot of energy.

And it does. This energy primarily goes into the interior of the star (since that’s what’s being squished). The extra energy heats the interior until some of the hydrogen outside of the core can begin fusion (known as H-shell burning). This supports the star somewhat, but doesn’t quite halt the slow contraction.

Rather, the core continues getting squeezed, and heated, until the point at which it gets hot enough that the Helium atoms can begin fusing. Again, the star has a strong energy source supporting it. This extra energy pushes back against the matter on top of it, causing the star to poof up into a red giant. It eventually stabilizes, and becomes something like a normal star again.

Eventually, the helium too runs out. If the star is massive enough, more cycles of contraction, shells of fusion, and new forms of fusion in the core will occur. If not, the star will go through one last bit of the cycle, where the outer layers are pushed out and released as a planetary nebula.

For those more massive stars, the cycles can continue until iron is built up in the core. This is one of the points where things happen fast.

Out of all the forms of fusion, Hydrogen is the most efficient. Each successive cycle is less so. By the time you hit iron, you’re barely getting energy out of it. With iron, you get none at all.

Once iron builds up to a critical mass in the core, it very suddenly collapses in on itself. Several suns worth of mass crashes down, releasing more energy in that act, than the rest of the entire galaxy it lives in. This is known as a supernova.

So that’s the basic story of stellar evolution. But at this point that’s all it is. In my next post, I’ll get more into how this theory of stellar evolution is all determined, both by mathematical modeling and comparisons of those models to direct observations.

Who's more foolish: The fool, or the fool who follws him?

For those of you that have been living in a cave the past month and decided to come out just now, or read only this blog and somehow missed every other blog talking about it, last month, the Discovery Institute hired a fellow by the name of Dr. Egnor.

Engor is a neurosurgeon that claimed evolution isn't used at all in his field and made all sorts of other stupid claims spattered with creationist idiocy. But apparently, it was just an April Fool's joke started a month early.

I had a good chuckle, but for a very different reason than the DI intended. This does not, as the DI claims, highlight "blind bigotry", but rather, reveals that the bad thinking of creationism and Intelligent Design are so similar, it's impossible to tell them apart.

Indeed the similarities are so similar, that the "Darwinian horde" wasn't the only one taken for a ride. Over at Reasonable Kansans, FTK called Egnor's falsehoods "quite insightful".

I'm curious as to just how many other people that are supposedly informed enough to understand Intelligent Design theory that they accept it, were still suckered because, when it came right down to it, they just couldn't tell the difference between ID and creationism. Since I don't follow any other pro-ID blogs, I can't say for certain, but I'm willing to bet it's quite a lot.

So to all the ID folk out there, have your laugh at us. But remember to save some of it for yourselves.

EDIT: As was pointed out on Good Math, Bad Math's post, this site is apparently a fake, being evolutionnews.net as opposed to the actual evolutionnews.org. The header image is also off on a few points. It looks like Panda's Thumb is having us all on. Or are they?

I suppose I should add the humor tag to this one.

Pareidolia: part n + 5

Of all places you'd expect to see a holy visage St. Peter's Basilica is a pretty good one. After all, millions of people flock here, so if you want a grand entrance, that'd be a very nice place to do it.

This image was taken during a trip by retired police man, Andy Key. It appears to show a strange angel like figure floating over the heads of the people present.

The article claims that photo experts can offer no explanations for the spectre. By looking carefully you can see that the "head" is just another part of what was an elongated shape, offset due to being projected onto a foreground pillar.

Since the pillar is curved, we know that the light source cannot be to the left of the pillar (since the light is on the right), and there's a wall to the right, so the most likely place for the light to be coming from is from roughly in front of the camera. If that's the case, then there should be quite a bit of light on the heads of the people near the bottom of the image. Is there? Let's take a look!

Looks like the mystery is solved! There's something in that general area that's reflecting light onto the wall. What it is, we can't say because the photographer only got the very tips of people's heads and there's big fat one right in the middle of what we need to see.

So while I'll agree that we can't say precisely what object caused this, it's nothing amazing. But it seems that some people, when presented with a lack of evidence, will automatically conclude it's supernatural.

However, what I really want to know, is that if there were hundreds of people there, why did not a single person notice this supposedly divine presence until afterwards, when the image was downloaded to computer?

It would seem that angels need to work on their PR department.