Friday, July 31, 2009

Answers to the informal quiz, Part 3: The Sun

I know it's been a while since my last post, but research and conferences have been taking up all of my time lately...at least I've got a new first-author paper submitted to the journals! Nonetheless, I extend my deepest apologies to my loyal readers.

So with my mea culpa out of of the way, let's get to the next set of answers!
  • Compare the Sun to the stars.
So, this is a bit of a trick question. The standard answer is that the our Sun is an "average-to-small" star. In some sense, this is true - stars can range from 100 times more massive to 10 times less massive than our Sun. They can also be 8 times hotter, or 2 times cooler. Finally, they can be 1,000,000 times brighter or 10,000 times dimmer than our Sun. So, in this sense, our Sun is in the middle of these ranges (though a little on the smaller side).

However, there are far, far more small, cool, dim stars than big, hot, bright stars...the vast majority of stars in our universe are small little red dwarf stars. In fact, the distribution is so lopsided that the mass of all the small stars put together is many times larger than the mass of all the big stars put together (though exactly how many times is still debated). So, in that sense, our Sun is actually bigger, hotter, and brighter than most other stars.
  • Why does the Sun shine?
Deep in the core of the Sun, hydrogen atoms are packed under such great pressure and temperature - being gravitationally compressed by the outer layers of the Sun - that nuclear fusion ensues. This is similar to how a hydrogen bomb works. In our Sun, four hydrogen atoms will collide together to eventually make one helium atom.

However, the resulting helium atom weighs just slightly less than the four hydrogen atoms that went into it. This tiny bit of missing mass is actually converted into pure energy via Einstein's famous equation E=mc^2. This energy, which leaves the nucleus of the atom as an extremely energetic gamma ray photon (a particle of light), bounces around the interior of the Sun countless times, getting absorbed and re-emitted by surrounding atoms and losing just a little energy to them each time. By the time it reaches the surface of the Sun - a process which takes, on average, about 1 million years - the photon has lost enough energy to emerge, on average, as yellow light...and that's why the Sun looks yellow.

This is also what makes movies like "The Core" utter nonsense. If the core of the Sun suddenly stopped undergoing fusion, we wouldn't really notice the effects until a million years later, once all the photons had managed to escape.
  • What happens to the Sun at night?
Okay, this was a softball question: the Sun is still there, it's just shining on the other half of the Earth. At any given time, it's always day for one half of the Earth, and night for the other half.

Still, I've heard some pretty wacky wrong answers for this, like the idea that space itself is lit up during the day, and dark at night. Meanwhile, Socrates thought that every night the Sun passed through a giant hole in the middle of the Earth. Those wacky ancient Greeks...
  • What is the sun made of?
Mostly hydrogen (about 75% by mass), some helium (about 24%), and about 1% everything else (carbon, oxygen, iron, etc.). The Sun's hydrogen is primordial - it comes from the big bang. The helium is partially from the big bang, and partially manufactured from the Sun turning hydrogen into helium. That 1% of everything else comes from exploded stars which seeded the interstellar gas cloud from which the Sun formed.

Note that this also goes for the planets and everything on them...So, all that hydrogen locked up in the water in your body came from the big bang, while all the carbon, oxygen, iron, etc., in your body originally came from ancient exploded stars.

If you're a romantic, you can say, "we are all stardust." Meanwhile, if you're a pessimist, you can say, "we are all nuclear waste products."
  • What causes a solar eclipse?
This occurs whenever our Moon passes between the Earth and the Sun and blocks out the sunlight. When the Moon only blocks out part of the Sun, it's a partial solar eclipse. If the Moon manages to block out the entire disc of the Sun - though this is only visible in a narrow range of locations - it's a total solar eclipse (which just happened in Shanghai a couple weeks ago).

Now, it doesn't happen every New Moon because the Moon's orbit around the Earth is tilted 5 degrees to the orbit of the Earth around the Sun. Only when the orbits line up during New Moon (about once every 6 months), does the Moon block out the Sun's light...otherwise it passes a couple degrees below or above the Sun from our perspective.

Just by chance, both the Moon and the Sun span about half a degree on the sky, so they have to be lined up just right for a total solar eclipse to occur, and it's only visible at just the right location on Earth. This wasn't always the case - in Earth's past, the Moon used to be quite a bit closer to us, meaning it appeared quite a bit larger in our sky.

Currently, the Moon is moving away from Earth at a rate of about 1.5 inches per year. This is all because of the tides...the difference in the Moon's gravity felt on the Earth raises two bulges on the Earth which rotate roughly once per day (anyone who's lived near the ocean knows the cycle of low-tide and high-tide). These act as a very subtle brake on Earth's rotation, just like slightly depressing the brakes in your car.

This causes the Earth's rotation to slow down ever so slightly - this is why every now and then you'll hear about the powers-that-be inserting a leap second to keep the clocks accurate. So, the days on Earth are getting slightly longer...but all this rotational energy the Earth is losing has to go somewhere. The moon ends up absorbing it, causing it's orbit to slightly spin-up, which makes it's orbit slightly wider every year.

So, in the distant past, total eclipses were much more common. Likewise, in the distant future total eclipses will no longer occur - the Moon's apparent size will just be too small to block out the entire Sun. It's a rather happy circumstance we were all born at a time in Earth's history when the two brightest celestial objects are the same size on the sky.

Tuesday, June 9, 2009

Answers to the informal quiz, Part 2: The Moon

Back with more answers to the informal quiz...this time: mysteries of our Moon.
  • Why does the Moon go through different phases?
The most common mistake here is that the phases are caused by Earth's shadow falling on the surface of the Moon, thus producing the "dark" part. It turns out moon phases have nothing to do with Earth's shadow at all. If it did, then the moon would always have to be "behind" Earth (on the other side of the Earth from the Sun) in order for Earth to cast its shadow there. The only time you see Earth's shadow on the Moon is during a lunar eclipse.

So, the real answer: At any given time, exactly half of the moon is lit up - the half of it that faces the Sun. The other half of it is dark. The same goes for Earth (and all the planets), actually...that's why at any given time half of the Earth is experiencing daytime, while the other half is experiencing night.

Now, as the moon orbits the Earth, we see different amounts of the lit half depending on the geometry. During a full moon, we only see the lit half. During a new moon, we don't see any of the lit half. During, say, a crescent, we only see a small fraction of the lit half. Hopefully this diagram will help, since describing the geometry in words is a bit tough:


In the above diagram, we're looking top-down on the Moon-Earth system - that's meant to be the North Pole in the middle of the Earth figure (thought to be more accurate I should've put less ice). From this perspective, everything moves counter-clockwise: the Earth's rotation, and the Moon's motion in its orbit around the Earth. Sunlight is streaming in from the right, illuminating the right side of the Earth. Note that as the Moon moves round the Earth, its right side always stays illuminated. The pictures in each of the boxes are the phases we would see on Earth for each of the positions of the Moon in its orbit, based only on what percentage and which side of the Moon's lit surface we can see.
  • Why is the Moon bright?
I asked this one just to highlight that the moon does not produce its own light. Rather, we only see it because it reflects sunlight.

That said, I've received some answers that the "Moon is made of very reflective stuff". Turns out that isn't actually true, it's quite dark. Its "albedo" - in other words, what percentage of incoming light it reflects - is only round 11%. That's roughly the same reflectivity as a blackboard.

Its surface is made of relatively unweathered basaltic lava. If you've every seen a relatively fresh lava field, you know it's pretty dark stuff. I've promised Stephanie I'll do a follow-up on this one once all the answers are up...
  • Can you see the Moon during the day?
Absolutely! Some people are still amazed by this when they see the moon in the clear blue daytime sky.

As shown in the diagram for the moon phases, a good chunk of the Moon's orbit takes it quite close to the Sun from Earth's perspective, which would mean seeing it in the daytime sky near the Sun. The caveat here is that the phases seen around that part of the orbit only show a very small percentage of the Moon's illuminated half. You can't actually "see" a New Moon, since none of the illuminated half is visible from Earth...but once it gets into a part of its orbit to produce a decent-sized crescent, seeing it in the daytime sky is no problem.
  • Does the Moon rotate?
Okay, so I put this one here because I actually got into a heated argument with my 5th grade science teacher, who absolutely insisted the Moon does not rotate. Just for the record, I was right.

If you watch carefully over time, you'll notice the Moon always keeps the same face pointed towards us. I'm not talking about the illuminated half here, but the actual surface topography - we always see the side with the "man-in-the-moon" image (just illuminated from different angles). Many people use this as justification for why the Moon does not rotate. However, the Moon is also orbiting us. If you picture the geometry in your head, in order for it
to always keep the same face pointed towards us, it must rotate at the exact same rate as it orbits. In other words, it orbits once every 27.3 days, and it rotates once every 27.3 days.

Now, is this just a coincidence? No, not at all. I promised Chris I'll do a follow-up on this question, too.
  • Why does the moon appear larger on the horizon?
The common wrong answer here is that the atmosphere magnifies the image of the Moon, a theory also espoused by my 5th grade science teacher (how they let this person teach science, I'll never know). This is not correct...in fact, it slightly shortens the image in the vertical direction.

The reason is solely a matter of perspective. The diameter of the Moon spans roughly 1/2 of a degree of angular size in the sky, no matter whether it's on the horizon or over your head. We don't realize how large 1/2 degree is when the Moon is overhead because there are no terrestrial objects in our immediate vision for comparison. Only when it's on the horizon do we have a basis for comparison to everyday objects like trees and buildings.

If you don't believe this explanation, measure it! Hold your pinky finger at arm's length when the moon is on the horizon and note its comparative size. Then, later, try this again when it's overhead...you'll find it's the same.
  • Is there gravity on the moon?
Yes, there is! As seen in this video which I posted before, things fall on the surface of the moon, albeit with only 1/6 the gravitational force found at the surface of the Earth. I've had many students who somehow acquire the incorrect notion that no atmosphere means no gravity. For an amusing anecdote related to this misconception, read this.

Thursday, May 28, 2009

Answers to the informal quiz, Part 1: Earth

Okay, one week has passed, and I've been getting lots of feedback from the informal quiz. Since there's quite a few questions, I'll post the answers in parts, starting with the question about Earth. In addition to the correct solutions, I'll also post the most common mistakes. Without further ado, then, here are the answers many have been eagerly awaiting...

  • Why does the Earth experience seasons?
By far the most common mistake here involves distance. Many people believe Earth is closer to the Sun in summer than in winter, thus making it hotter or colder, respectively.

This seems like a reasonable explanation, but breaks down when you consider that the Northern Hemisphere and Southern Hemisphere experience opposite seasons. When it's summer in the USA and Europe, it's winter in Australia, and vice versa. It runs into more trouble when you consider the Earth is actually closest to the Sun in January, and farthest in July...exactly the opposite of what you'd expect for the Northern Hemisphere if this explanation were true.

The real answer here involves the Earth's "axial tilt". The axis about which the Earth rotates is at a constant tilt of 23.5 degrees. This means at certain times of the year, the Northern Hemisphere is more directly facing the Sun, while 6 months later when the Earth is on the other side of the Sun, the Southern Hemisphere is more directly facing the Sun. Note the diagram:


I've marked the equator and the axis of rotation in red. The hemisphere which more directly faces the Sun is the one which experiences summer. The hemisphere angled away from the Sun is the one experiencing winter.

Another common "almost right, but not quite" answer I've heard several times involves the tilt, but in the wrong way. Those folks maintain that because the Earth is tilted, one hemisphere is closer to the Sun than the other. However, this effect is minuscule, since the tilt only accounts for a difference in distance to the Sun of a couple thousand kilometers, while the average distance to the Sun is 150 million kilometers. Again, seasons have nothing to do with distance, it's all about angles.

  • Why is there a 24 hour day-night cycle?
This one is relatively easy. The Earth rotates about its axis every 24 hours, bringing the Sun into view for half of that time period.

(Now, technically, the Earth makes a full 360 degree rotation in only 23 hours, 56 minutes...but because the Earth has also traveled about 1 degree in its orbit around the Sun during that time, the Earth must rotate an extra 1 degree to bring the Sun back to the same relative position. Thus, the 4 extra minutes.)

Most folks get this one, but there are still some who maintain that the Earth doesn't rotate at all, and just orbits once around the Sun per day. Woe is them.

  • Why is the sky blue?
In spite of being a question asked by every 5-year-old in existence, this is without doubt the most frequently incorrect answer.

I've gotten simply wrong responses such as "the sky is simply reflecting the ocean". In the middle of a continent far from any ocean, though, the sky is still blue. I've also gotten the "almost correct" response that the atmosphere is refracting the sunlight. It does involve the atmosphere interacting with sunlight, which is good...but still not quite right.

The correct answer here has to do with scattering, specifically - "Rayleigh scattering". When light has a wavelength close to the size of a gas molecule it's passing near, there's a good chance the light will essentially "bounce" off the molecule and start heading in a different direction.

Moreover, the chance of scattering is also very dependent on wavelength - it scales as 1 over the wavelength to the fourth power. In other words, short wavelengths are much more likely to scatter than long wavelengths. Our eyes interpret the different wavelengths of light as different colors. Red light's wavelength is roughly twice as long as blue light, so blue light is 2 to the 4th power = 16 times more likely to scatter than red light.

So, imagine incoming sunlight coming from the Sun and passing through our atmosphere. Remember, the sun emits every colors of the rainbow, it's just that when the colors are all combined, they appear to us as white light. Now, the red light is more likely to make it through unhindered, while the blue light gets scattered everywhere and appears to an observer on the ground to be originating from a direction other than the Sun. Hopefully this diagram will help explain the concept:



As you can see, most colors on the red side of the spectrum appear to be coming from the direction of the Sun. The blue light (and a bit of the green), however, appear to be coming from elsewhere in the sky. This process happens all over the sky, so it appears that blue light is coming from everywhere.

This also explains why our sun appears slightly more yellow than it would from space. Some of the blue gets scattered out of our line of sight towards the Sun.

  • Why are sunsets red?
The "blue sky" answer above also explains this question. At sunset (and sunrise), sunlight has to pass through far more atmosphere to make it to an observer on the ground, vastly increasing the chances of scattering even the not-so-blue light. Only the very reddest light makes it to the observer without getting scattered...thus, a red sunset.

  • How does the Earth compare to other planets?
So, this is meant as just an open-ended question...I only ask as there seem to be quite a few folks who think that Earth is the largest planet.

Within our own Solar System, planets can be divided into two groups - the inner, terrestrial rocky planets (Mercury, Venus, Earth, and Mars) and the outer gas giant planets (Jupiter, Saturn, Uranus, and Neptune). Earth is the largest of the inner rocky planets, but many times smaller than the outer gas giants. So, it could be said to fit somewhere in the middle, albeit slightly on the smaller side.

On the other hand, if you take the ~300 planets known around other stars, Earth is quite dwarfed. Just about all of these "extrasolar" planets are massive gas giants - many larger than Jupiter - and most of which are found orbiting incredibly close to their parent star. Within that population, Earth is no more than a puny wet rock.

Of course it's quite likely that this known collection of extrasolar planets are not representative of the population of planets as whole. The problem is that our observing techniques for detecting these distant worlds are severely biased towards only detecting very large planets which orbit very close to their parent star. The hope is that with improving technology, we'll start detecting Earth-like planets in a matter of a few years, particularly with space-based missions such as Kepler.

  • Why does a feather fall slower than a bowling ball?
The common mistaken belief here is to think that because the bowling ball is heavier, it falls faster.

It turns out that the only thing which slows down the feather is increased air resistance. In essence, it has a much lower terminal velocity than the bowling ball. (Terminal velocity is the fastest a given object of a given shape can fall - it's the speed at which the Earth's gravitational acceleration is perfectly balanced by the force exerted by air friction.)

Take away the air, and everything - no matter its weight - falls at the same rate. Check out this video from one of the Apollo moon landings - you'll see that in the absence of any air, a hammer and a feather fall at exactly the same rate.

Now, technically the bowling ball, with a larger mass, feels a stronger gravitational force. However, because it has a larger mass, it's inertia is also greater...in other words, you need more force to get it going. It turns out that its increased gravitational force perfectly balances its increased inertia, resulting in all things falling at the same rate (in a vacuum).

Thursday, May 21, 2009

An informal quiz...

Based solely on my experiences teaching undergrad students, I've found there's quite a few commonly held misconceptions about astronomy. See if you can answer these seemingly intuitive astronomy questions. (No looking 'em up on the interwebs! That's cheating!)

Answers will be posted in one week...if you really don't want to wait until then, email me and I'll send you the answer key.

Earth:
  • Why does the Earth experience seasons?
  • Why is there a 24 hour day-night cycle?
  • Why is the sky blue?
  • Why are sunsets red?
  • How does the Earth compare to other planets?
  • Why does a feather fall slower than a bowling ball?
Moon:
  • Why does the moon go through different phases?
  • Why is the moon bright?
  • Can you see the moon during the day?
  • Does the moon rotate?
  • Why does the moon appear larger on the horizon?
  • Is there gravity on the moon?
Sun:
  • Compare the Sun to the stars.
  • Why does the Sun shine?
  • What happens to the Sun at night?
  • What is the sun made of?
  • What causes a solar eclipse?
Universe, etc:
  • What's the difference between the Solar System, the Galaxy, and the Universe?
  • What is a star?
  • How are planets different than stars?
  • Where do the stars go during the day?
  • What's the farthest human beings have ever traveled in space?

Saturday, May 16, 2009

Does the universe actually look like that?

Okay, I'll admit it, the last post had a lot of math. For those who are less inclined to slog through equations, let's talk about all those astronomical pretty pictures we see.

Karl asks:
I always hear that photos of cosmological objects (like that photo of the Ring Nebula in your previous post) have been enhanced in some way. What would those things look like if we just saw them exactly as the telescope or camera picked them up? And when the photos are enhanced, are they always enhanced the same way, or does the formula vary?

Finally, does the enhancing serve some scientific purpose, or is it done basically to make the pictures prettier? (I suppose that's a scientific purpose too, in the long view, since pretty pictures make it easier to get funding. Don't worry, I won't tell!)
So, it's totally true, the final images given out for press releases have usually been heavily processed from the original raw images. Just like the pictures you took at a party where you throw them into photoshop and remove your friends' red-eye, there are a set of "standard" processing steps for astronomical images.

That said, there's usually not outright deception the way advertisers airbrush images - no astronomer is going to try and make their planet look skinnier or add lolcat tags. To understand this a little better, let's talk about how modern astronomical images are actually taken.

First off, almost all optical images are taken with a Charged Coupled Device (CCD) mounted to the back of a telescope. This is the same kind of chip that's in the back of your ordinary digital camera, albeit more sensitive and more expensive. Essentially, it's just a thin piece of silicon divided into a narrowly-spaced grid of cells. Each cell in the grid can hold electrons which might get excited when a photon hits them. At the end of an exposure, each cell reports how many energetic electrons it contains. Our image just translates each cell into a pixel, and the brightness of that pixel is just how many electrons it contains.

Now, notice there's absolutely no color information here. The CCD just reports the number of excited electrons, and doesn't know anything about whether it was a red photon or a blue photon which excited it...so this just produces a black & white photo. This means we have to use filters if we want to get any color information. If we put, say, a red filter on our CCD before taking the image, then we know only red photons can get through.

So, first we take an exposure with a red filter, then another with a green filter, and then another with a blue filter. We combine them all at the end to produce our fancy color image.

Okay, you're probably already asking, "then how does my digital camera takes color photos all at once without any color filters?" The answer is that it uses filters all the time - here's a schematic of the filter mosaic used in most digital camera CCDs. By filtering alternating pixels with different colors, in only one exposure the camera can get an image in each filter...albeit at lower resolution than the entire grid. The fancy camera software then interpolates these separate staggered color images to produce a single color image.

So with all this said, let's take a look at an actual single raw image of a galaxy:


You'll want to click on the image above to look at the original with all its glorious artifacts. Let's also take a look at close-up with some artifacts highlighted:


So, there's several issues we have to contend with to make this into a "pretty picture".

In red, I've highlighted a particularly annoying cosmic ray trail (though they're all over the image). Unlike digital camera photos which only open the shutter for a fraction of a second, astronomical images - particularly of faint objects - can be upwards of an hour long. During this time, high-energy particles known as cosmic rays - which are always whizzing around - have a much greater chance of interacting with your CCD and exciting electrons completely independent of any photons coming through the telescope. The annoying ones come in at an oblique angle to the CCD, leaving a trail of excited electrons across the chip. The even more annoying ones do this directly over the CCD cells you're using to capture an image of your object. Thankfully, there are some pretty good cosmic ray removal packages out there which use sophisticated image detection algorithms to remove this...so that's a processing step right there.

In blue, I've highlighted pixel bleed. We're going for a long exposure of a pretty faint galaxy here, so any bright stars in the field will become oversaturated. In essence, the CCD cell containing the image of the bright star begins to overflow with energetic electrons, pouring them out into adjacent cells.

In green, I've highlighted a row of bad pixels. With millions of cells across the entire chip, statistically many are eventually going to fail. For earth-based observatories, it's untenable to keep throwing out CCDs which cost many thousands of dollars whenever some pixels go out...so you work around it. For spacecraft, meanwhile, there's really nothing you can do about bad pixels even if you had the money to replace it.

There's a couple other artifacts noticeable in the original image, as well. Notice the steady gradient of dark-to-light in the background. Unfortunately, not all the pixels have the same sensitivity. Send 100 photons to one cell, and you might get 50 excited electrons...send them to another cell, and you might only get 40.

You have to account for this by taking "flat fields". Essentially, you take images (ideally just before or just after taking your astronomical images) of a uniformly lit surface with each color filter. The idea is that the surface should be sending out a constant number of photons to each cell, so the only signal you'll see will be the change in sensitivity across the CCD. You then divide the astronomical image by the flat field on a pixel-by-pixel basis to remove this sensitivity effect. Finding a truly flat field, though, can be a chore in itself...often times the best flat field you'll get is an image of the twilight sky before the stars come out.

Another artifact you may notice in the original is the weird wavy pattern, particularly noticeable on the left. Ideally you want your CCD chip to be as thin a piece of silicon as possible - this makes it more sensitive. However, particularly for longer wavelengths of light, photons reflecting off the back surface of the CCD can interfere with photons hitting the front surface and produce thin film interference - very similar to the wavy colored patterns you'll see in soap bubbles or with oil on water. Hopefully this too will be removed by flat-fielding.

Finally, as for the purpose of enhancing images, all of the above steps are necessary to get good science. Otherwise, you're just measuring your signal buried in a whole lot of noise. If you're going to take an image this far, though, you might as well go one step further to make a press release photo.

This serves several purposes, but not least of which is to share your own fascination of an astronomical object with the general public. Imagine if the Hubble Space Telescope *never* made press release photos available and only was used for hard science in the journals...public support wouldn't be nearly what it is today. Besides, it's the taxpayer's dollar which goes to fund it - the least we can do is give them some pretty pictures in return.

So, if you want to make a pretty picture, there's one more step you'll have to take - and this is a big one - because the above image was taken through an infrared filter. By definition, the human eye can't see this wavelength of light, so if we were to represent it in "true-color", the entire image should be black.

Creatively mapping various single filtered images to RGB space as well as some tweaking of colors needs to happen to for this to be visible - and aesthetically pleasing - for human vision. This color manipulation doesn't have the same tried-and-true formula as the above sequence of processing steps, and is often just manipulated until one gets something that just "looks good".

Piloting a spaceship through a galaxy cluster.

Blair writes:

In your post, you state

http://dearplanetaryastronomermike.blogspot.com/2009/03/dark-matter-stars-and-gas-wheres.html

"Now, this gas is actually the material from which stars are created. Its most ubiquitous form throughout a galaxy is as a hot diffuse medium (somewhere around 10,000K)"

and

"Eventually, a whole cluster of galaxies is created, surrounded by a massive cloud of unused, superheated hydrogen gas (in the incredibly hot 100 million K range) known as the intracluster medium (ICM)."

Could human spaceships fly through these? I guess they may be hot, but the density is very low, so how much heat would the spaceship absorb and could it radiate the heat away?
This is actually a really cool question. My guess is that the intracluster medium is probably sparse enough that one wouldn't need to worry. A little back of the envelope math here:

- Let's say there's 500 galaxies in a cluster, each at around 10^12 solar masses (or about 2 x 10^45 g) so that gives us a total mass of around 10^48 g for the cluster's galaxies. The Intracluster Medium (ICM) should be about 10 times that, or about 10^49 g.

- However, the cluster is huge...if the milky way is roughly 25 kiloparsecs in diameter, a fair estimate for the cluster size is on the order of a megaparsec in radius. That translates to a volume of roughly [(10^6)(3 x10^18 cm)]^3 = 3 x 10^73 cm^3. That leaves us with a pretty low density of about 4 x 10^-25 g/cm^3. We throw in Avogadro's number for good measure, and assume pure hydrogen, and we end up getting about 1 hydrogen atom for every 5 cm^3...it's actually kinda weird how those huge numbers end up canceling so well.

So, yeah, a given atom will be crazy energetic - temperature scales linearly with kinetic energy - but there's so few of them I don't think it would be a huge issue heat-wise. The radiative constant of the ship should easily compensate for the occasional high-energy atom.

I think the concern would be more of a sputtering problem - at these energies, I'd worry about slow ionization of the ship's outer hull. Each hyper-energetic hydrogen atom the spaceship ran into might strip molecules from the crystal lattice of whatever alloy the spaceship was composed of. Sometimes it'll strip multiple molecules per collision, sometimes none, so let's just do an order of magnitude estimate and say 1 molecule stripped per collision. At 1 hydrogen atom per 5 cm^3, it doesn't seem like a big deal, but I think as it starts to cover spaceship-sized distances it might be an issue. Let's consider this in terms of cross-section:

For each square centimeter of spaceship hull surface hurtling through the cluster, a molecule of the hull will be stripped every 5 cm. If we want to travel from the edge to the center, we're talking about 3 x 10^24 cm, or roughly 6 x 10^23 molecules stripped. Again, weird that we just happen to hit on Avogadro's number again - roughly 1 mole of material per square centimeter will be stripped.

Assuming we're talking about, say, iron here, that's a molecular weight of 56, so 56 g/mole. So, behind each square centimeter of hull, 56 grams will be stripped traveling to the center of the cluster. With iron at a density of 8 g/cm^3, that would mean a 7 cm thickness would be stripped traveling to the center.

So, I guess the answer here is that if you add 7 cm of hull thickness (at least to the front of your spaceship) as an ablative shield, you should be okay. You actually probably want to double that, since presumably you'd like to leave the cluster at some point, too.

Tuesday, May 12, 2009

It's Twitter time.

You can now follow me on Twitter and ask various astronomy question there, too. Yay, technology!

Username: "astronomer_mike"

The Main Asteroid Belt and Future Impacts

Okay, folks, sorry for the languishing blog, but it's been a heck of a semester. Meanwhile, on with the show!

Ben writes:
What's the history of our solar system's asteroid belt? There seems to be a consensus that it's inevitable that another Cretaceous-ending-like asteroid will hit the Earth again someday; do such asteroids typically come from the asteroid belt?
First, a little background: The main asteroid belt is a collection of random rocky debris found in the large gap between Mars and Jupiter. Here's a nice plot from the Minor Planet Center, the organization responsible for tracking and naming the objects. The four inner turquoise circles are the orbits of the four inner planets (Mercury, Venus, Earth, and Mars), and the outer turquoise circle is the orbit of Jupiter. Within the sizable gap between these, each green point is an asteroid in the main belt.

While there's a lot of individual objects known - literally millions - their total mass isn't much. In fact, Earth's moon is roughly 25 times the mass of the entire asteroid belt combined.

There's been a lot of speculation that the asteroid belt comprises the remains of a "failed planet" which couldn't form in our early solar system due to Jupiter's strong gravitational pull constantly rending apart any protoplanets. This may be true, but the jury is still out - it is compelling that there's such a large gap between inner and outer planets, and that there's such a large gravitational force nearby. On the other hand, there obviously wasn't a whole lot of mass to work with in this region (though Jupiter likely stole a good deal of it during its own formation). Moreover, current models suggest that Jupiter may not have even formed in its current location, but actually migrated.

Either way, Jupiter continues to exert a strong gravitational effect on the main asteroid belt today...enter the concept of "Kirkwood Gaps". Now, in the above plot from the Minor Planet Center you'll notice little order in the position of the asteroids locations at a given time.

However, if we plot their *average* distance from the Sun (their so-called "semi-major axis") versus how many are at that distance, something very different happens:



They seem to be grouped into families at specific distances, with no-mans-land in between - our Kirkwood gaps.

More interestingly, an object's average distance from the sun is directly proportional to the time it takes to complete one orbit. Those little numbers at the bottom of each Kirkwood gap (3:1, 5:2, 7:3, and 2:1) correspond with the number of orbits the asteroid makes in a given time versus the number of orbits Jupiter makes. This is what's known as an "orbital resonance". A similar phenomenon occurs with particles in the rings of Saturn in resonance with Saturn's moons, as well as Kuiper Belt objects in resonance with Neptune.

So, what's really going on here? Let's say we place an asteroid in the 3:1 Kirkwood gap. For every 3 times it goes around the Sun, Jupiter goes around once. This will mean the asteroid keeps meeting up with the asteroid in the same part of its orbit over and over...the gravitational force exerted by Jupiter will always be in the same direction each time.

It's a bit like being a little kid on a swing while a big kid keeps pushing you over and over in the same place...eventually, you'll fall out and go flying off. Similarly, asteroids that wander into a Kirkwood Gap due to random interactions won't stay in that gap for long, and Jupiter will send them off on some fairly random orbit. There's good evidence to suggest that many of the asteroids which cross Earth's orbit (i.e. the ones we really need to watch out for), experienced this fate.

So, the answer is a pretty strong yes to this question - a good deal of potentially hazardous impactors probably started out in the main asteroid belt, accidentally wandered into a Kirkwood gap due to mutual asteroid interactions, and were sent hurtling into the inner solar system by Jupiter. Since the nature of this process is inherently chaotic, it's extraordinarily difficult to predict which main belt asteroids this will happen to and which subsequent orbit they'll end up on...but statistically we can say that another major impact is really more a matter of "when" than "if".

Saturday, March 14, 2009

Neutron Stars

Jared asks:
My 10-year old daughter asked me what a neutron star was a couple of days ago. From what I understand, a neutron star is one possible outcome of the death of a star. At least, that is what I always thought. When I tried to explain to her what a neutron star was and how it came to be, I mangled in explanation and probably left her more confused and than anything. I'm sure I also shook her faith in the idea that "daddy knows everything." :). Anyway, how can I explain a neutron star to a curious and intelligent 10 year old girl?
Well, you're right - neutron stars are one possible outcome of a star in its death throes. Among the fascinating menagerie of astronomical objects, they're a curious case.

There are generally three possible results produced when a star runs out of fuel for fusion at its core: usually a white dwarf, rarely a neutron star, and in exceptional cases...a black hole. It's all entirely dependent on how massive the star was to begin with.

It's a bit difficult to consider neutron stars outside of the whole context of a star's life, so let's think about the internal processes of a star. First, it's important to realize that a star is in constant balance - gravitational pressure squeezing it smaller, and internal energy generation pushing it outwards. Only a small deviation from this balance would cause a star to very quickly undergo catastrophic collapse or explosion in a matter of minutes.

Now, normal "main sequence" stars happily shine away, undergoing fusion at their core. The mechanism is different depending on their mass (and thus their internal pressure), but the general result is the same: they convert 4 hydrogen atoms into a single helium atom.

Eventually, however, a star will run out of hydrogen at its core to fuse, with only a lump of inert helium "ash" left over from all that fusion. As the reaction can no longer proceed at the center of the core, fusion of hydrogen will then begin in a shell surrounding this helium by-product. As the fusion now proceeds in a layer a bit closer to the star's surface, the outer layers of the star will balloon outwards, and the whole star becomes what we term a "red giant" - a star much, much larger than our own Sun, but very cool at the surface due to that expansion (well, cool for a star, anyway).

This "shell-burning", too, will begin to consume all the hydrogen fuel available to it. With only gravitational pressure, the star is out of balance and will begin to collapse...but before it does so, all that increased pressure will suddenly cause the inert helium at its core to ignite. Fusion will begin again, but in a different manner, with 3 helium atoms fusing into carbon (or possibly 4 helium atoms fusing into oxygen, depending on internal conditions).

The process continues in this way for some time, with the material at the core and then the shell fusing its way up the periodic table. Inert carbon/oxygen ash will build up at the core and helium shell-burning will start. At some point the carbon/oxygen ash will ignite to start fusing into silicon or sulfur. This process continues until carbon/oxygen ash shell-burning begins, and eventually even the silicon/sulfur ash will ignite to star fusing into iron. The result is an onion-skin layering of the star's interior, with iron at the center, a surrounding shell of silicon/sulfur, a shell around that of carbon/oxygen, a shell around that of helium, and a surrounding envelope of hydrogen.


The above image shows a simplified model of the interior of star with the onion-layer structure (with some elements removed for clarity). Just how far it can get up the periodic table depends strongly on a star's mass - only the most massive stars will have the full onion-layer structure I outlined above. Smaller stars such as our Sun might only get to the helium fusion stage...there's simply not enough mass to gravitationally squeeze the core enough to undergo carbon/oxygen fusion. Very small stars may not even be able to start fusing helium.

Additionally, the speed at which all these processes occur depends sensitively on their mass, with huge stars using up their fuel quite quickly (a few million years), while very small stars can burn for 100 billion years. It's a bit similar to celebrities - superstars like Britney Spears shine brightly but quickly burn out, while minor stars such as Foghat are still touring to this day.

Now, this process cannot continue ad infinitum...iron is the limit. This is simply because any fusion reaction of atoms iron-sized or larger is actually *endothermic*. It doesn't give off energy as all the previous reactions do, but actually requires energy to continue. As a result, there's no longer any internal energy to push outwards against gravity's compression inwards, and the star begins to collapse.

What happens at this stage is also highly mass dependent. For stars about 5 times the mass of our Sun or smaller, it's more "out with a whimper" than "out with a bang". The core of the star is first to collapse and as it shrinks it begins to heat up. This causes a gentle radiation "wind" which pushes the outer layers gracefully away from the star. The outer layers form what is known as a "planetary nebula". (It has no actual relation to planets, it was simply named that because early observers though it bore a resemblance to a planet's image in a telescope.)

The core itself will squeeze down as small as it possibly can. The laws of quantum physics state that there's only so tight that you can pack mass before all the electron orbitals are essentially touching one another with no room to pack any more in. This state - known as "electron degenerate matter" - is precisely what happens. The result is an incredibly dense, former stellar core roughly the size of the Earth made of this exotic degenerate matter, known as a "white dwarf". It no longer generates its own energy, but it is quite hot - one can think of it a bit like a dying ember from a former campfire. The electron degeneracy pressure keeps it from collapsing further.


The above image is a photo of the Ring Nebula, a planetary nebula which demonstrates what will happen to our own Sun in roughly 7 billion years. The tiny dot at the very center is the white dwarf.

If, on the other hand, the star is larger than roughly 5 times the mass of our Sun, something quite different happens. The exact process is still debated, but the general thought is that as the core collapses, somehow shock waves are set up throughout the outer layers and a violent explosion ensues - a supernova. It is also in this process that all elements heavier than iron are fused. Only a supernova has enough energy to contribute to these heavier-than-iron endothermic fusion processes.

Meanwhile, something very odd happens in the core itself. If the core is more massive than roughly 1.4 times the Sun's mass - a critical threshold known as the Chandrasekhar limit - then there's enough gravitational compression that even electron degeneracy pressure cannot prevent it from collapsing further. There's enough pressure that every proton in the core begins pairing off with an electron in the core, and the two combine to form a single neutron while emitting a few neutrinos. With a mass of at least 1.4 solar masses, there are countless protons and electrons, resulting in a wave of even more neutrinos...one theory is that this wave of innumerable neutrinos actually causes the violent explosion of a supernova.

The result is a compact stellar remnant made almost entirely of neutrons - a "neutron star". As with the electrons in a white dwarf, they too are packed as close as quantum physics will allow, forming "neutron degenerate matter". Instead of forming an object approximately 10,000 kilometers across in the case of a white dwarf, a neutron star is a mere 10 kilometers across. Packing a sun's mass into an object the size of a city makes neutron star unimaginably dense. I believe the oft-repeated figure is that a teaspoon of neutron star material would weigh roughly as much as an aircraft carrier. Whoa.


In the above image, we see two photos of the Crab nebula, a supernova which occurred in 1054 A.D. The image on the left we see the outer layers blown off from the explosion in visible light. The image on the right shows the area around the central neutron star as seen in X-rays. The neutron star is strongly affecting the hot gases surrounding it. This is because in the process of collapsing down from a Sun-sized object to a city-sized object, two interesting things happen:

- Magnetic field lines which were once sparse are also compressed together. The result is an object with a magnetic field billions of times greater than Earth's.

- Angular momentum must be conserved. Just as a spinning ice skater who pulls her arms in begins spinning faster, a Sun-sized object spinning once a month which collapses down to a city-sized object will speed up to spin on the order of many times a second.

These strong magnetic field lines will spin with the neutron star, sweeping out a circle a bit like a lighthouse. If they're oriented properly towards our line of sight, we'll see a radio pulse many times a second...such a properly-oriented neutron star is known as a pulsar. The Crab Nebula above is host to the Crab Pulsar. Spinning 30 times a second, we receive radio waves from it at the same frequency.

Now, if the conditions during a neutron star's formation are just right, a dynamo effect can be set up which will not simply squeeze the magnetic field lines together, but actually greatly amplify them. This results in an object with a magnetic field thousands of times greater than an average neutron star - such an object is known as a "magnetar". Again, I believe the oft-quoted figure is that a magnetar at the distance of the moon could pull the car keys out of your pocket.

Finally, just as electron degeneracy pressure can only support the gravitational compression of an object 1.4 times the Sun's mass, so neutron degeneracy pressure can only support the gravitational compression of an object roughly 3 times the Sun's mass...though that exact figure is still debated depending on whose equation of state you believe.

What the stellar remnant then becomes is also debated. It was the general idea that simply nothing could fight against such a strong gravitational force, and the object would collapse to a singularity - a black hole. Recently, some astronomers have theorized the existence of one more intermediate state: quark stars. Quarks are the elementary particles from which protons and neutrons are made. Just as electron degeneracy and neutron degeneracy can prevent further collapse, it's possible that quark degeneracy could act similarly. So far, though, no one has ever seen such a quark star - they're simply on the theoretical drawing board at this point.

Tuesday, March 10, 2009

Planetary Astronomy, Clouds, and the Space Station

Jen writes:
I have a couple of questions, driven by my 5 year old's insatiable curiosity. First, what exactly is a planetary astronomer? We are not sure which questions fall within one's domain and which do not?
Well, planetary astronomy is usually described as just the study of solar system bodies. The specific fields of study fall under a few categories:

  • Planetary atmospheres - winds, storms, clouds, and the like (this is what I personally research)
  • Planetary geology - surface features, volcanism, earthquakes, tectonics, tidal processes, etc.
  • Planetary interiors - core processes, mantle processes, convection - anything under the crust.
  • Planetary magnetism - interaction of a planet's magnetic field with the space environment
  • Small bodies - Comets, meteors, and such
  • Rings - gravitational interactions of planetary rings with moons, gravitational wakes, etc.
I'm probably forgetting a few aspects here, so forgive me if my list isn't entirely exhaustive...but hopefully you get the idea.

That said, I'm happy to answer any astronomy questions I can get my hands on. The previous post was all about the much, much larger scale of galaxies and galaxy clusters. Thankfully, I did some galactic cluster research earlier in my grad school career, and have taken classes in most aspects of astronomy.

Jen continues:
Second, my son has not been happy with any of my explanations of how clouds are formed (this is one reason for the first question, since I was pretty sure it doesn't qualify as planetary astronomy). I have told him, so far, that they are made when water evaporates, that the water freezes, etc. but I think the concept of freezing bits of water floating around in the sky just sounds like mom most have something wrong :).
Ah, this question is right up my alley. You're actually mostly correct here.

I think the difficult part to conceptualize is the idea of "water vapor" always in the air. We're not talking about rain or mist particles here, but water as an actual gas. Simply by virtue of having liquid water on our surface, there is vapor pressure - some of that liquid will evaporate and become a gas floating in the air.

Depending on which climate you live in, it's usually ubiquitous (though here in the desert we have fairly little). It's mostly invisible, though noticeable as a white haze when you look at really distant objects like mountains or skyscrapers on the horizon. It's definitely noticeable on a muggy day when you step outside and can just "feel" the humidity, though...you'll notice on those days that distant objects appear even hazier.

It's also painfully apparent when collecting spectra from a telescope. A major difficulty is removing the signal of Earth's water vapor...particularly if you're looking for water vapor on other planets. In fact, whole sections of infrared wavelengths are simply unusable because they're so saturated with the signature of water vapor.

I think the best way to conceive of water vapor is if you have an ice-cold beverage on a hot, humid day. Within seconds, the outside of the cold glass or can becomes wet. The water wasn't just spontaneously created, and didn't leak from inside the glass...though technically it did "materialize from thin air".

The issue it this: just like hot tea is better at dissolving sugar than iced tea, so a warm atmosphere can hold more water vapor than a cold atmosphere. This is also why your weather forecast will talk about "relative humidity" - 50% humidity at 90° F has quite a bit more water vapor dissolved in it than 50% humidity at 40° F. The percentage symbol in there is just the percent of how much total water vapor the atmosphere at that temperature *could* hold. We refer to a humidity of 100% as being saturated. Anything above this, and the atmosphere won't be able to easily hold on to all that water vapor.

Now, imagine a parcel of warm atmosphere at the surface, holding quite a bit of this invisible water vapor. If that atmosphere begins to rise - usually due to convection - it will encounter a colder environment as it increases in altitude. As it's also at a lower pressure higher up, the parcel will begin to expand and cool down in the process - so what happens to the water vapor?

Well, let's say the parcel started out at 90% relative humidity. As it cools, that colder air reaches a point of going beyond its 100% saturation value. Even though the total amount of water vapor doesn't change, the amount of water vapor the parcel could potentially hold is decreased as it cools, until it's holding more than its limit.

That "super-saturated" water vapor has to go somewhere. Usually water will start condensing out onto the surface of tiny particles suspended in the air, known as nucleation sites. There's lots of natural sources of nucleation sites - suspended dust, for example - though smog particles work equally well, if not better.

So, as this water condenses out, it goes from a gas phase to either liquid water or ice...it all depends on what the ambient temperature is. The low fluffy cumulus clouds we see are usually liquid water, since temperatures aren't *that* cold as they form fairly low. The high, wispy cirrus clouds are formed in a much higher, colder environment, so they're usually made of ice.

The same thing happens to your ice-cold beverage on a hot muggy day. The air right around the glass is a bit colder than the surrounding air, so water vapor begins condensing out onto the outside surface of the glass.

It's also extremely similar to the process for making rock candy. Loads of sugar are dissolved into hot water, until it reaches its saturation point. As one then begins to cools the water, it becomes super-saturated and the sugar tries to condense out into crystals onto whatever nucleation site it can find...usually a stick is placed in the solution to provide a nucleation point, resulting in a tasty, diabetic-coma-inducing snack.

Now, there's one other interesting bit here...I mentioned in a previous post about water on the moon that 32° F ice has much less energy than 32° F liquid water. Similarly, liquid water at a certain temperature has much less energy than water vapor at the same temperature. As the water vapor condenses out into liquid water, then, that extra energy has to go somewhere - usually into heating up the surrounding parcel of air. As a result, the parcel is even more buoyant and will continue rising, possibly condensing out even more water vapor depending on ambient conditions aloft. So, there's a weird feedback cycle which causes a parcel to lose most of its water vapor as it continues to ascend.

Jen also asks:
His last question is: What is the space station for? Is it like a train station in that rockets stop there and then travel onwards? When do space ships visit it, or not visit it?
Well, that's actually a question a lot of us have been wondering.

The original concept was to provide exactly this sort of train station, but so far that hasn't really panned out. At this point, the only space ships visiting it (the Space Shuttle and Russian Soyuz capsules) have been to resupply, swap crew, and boost its slowly degrading orbit.

I think part of it was established with the idea that manned space exploration never made such leaps and bounds as when we were in a space race with the Russians. Now that the cold war has ended, manned space exploration has been proceeding at a lethargic pace. Some of the reasoning may have been that we could jump start the program again by introducing a spirit of cooperation this time instead of competition. The whole point was to have multiple nations contributing to its construction to foster a renewed level of innovation.

Unfortunately, this hasn't panned out terribly well. Several of the International Space Station (ISS) mission modules have not been up to spec - I believe the Russian-built Zvezda module had terrible noise problems. (Remember, in space there's nowhere for sound to go, so once you start ringing a bell, it keeps ringing.) To some extent there's a feeling the ISS has become a white elephant, funneling manned exploration resources that could be used for something more constructive.

That said, it's still a bit of a thrill to watch it pass overhead. If you want to see it for yourself, check out the Heavens-Above website. In the configuration section, enter your location using the map or database feature, and submit. You'll be given fly-over times for the ISS as well as star map so you know where to look for it at which times. In fact, it will do this for all visible satellites for any given night - the ISS just happens to be the brightest. Cool stuff.

Friday, March 6, 2009

Dark Matter, Stars, and Gas: Where's the Missing Mass?

David writes:
I recently read this article in Discover magazine and it got me thinking. The article is titled "Violent Birth of the Stars" by Adam Frank and it's in the February 2009 issue. It was all about star formation.

Anyway, here's the part that caught my eye: "A typical cluster will extend across a few light-years. Its parent cloud can stretch across 300 light years and contain enough matter to make a million stars. But a million stars do not form. Instead, star formation across a giant molecular cloud is a rather anemic process, and relatively few stellar nurseries arise. Only 10 percent of the mass of the cloud, on average, is converted through gravitational collapse into stars. The rest of it never collapses and eventually disperses into the tenuous interstellar medium throughout the galaxy."

What struck me about that is that in discussions of dark matter the usual argument is that there is not enough mass in a typical galaxy to explain its rotation. We're missing 90 percent of the mass. But the calculation of mass is based on luminous material. It would seem to me, based on the quote above, that no bizarre form of matter is necessary and it may simply be that the missing mass is gas and dust in the interstellar medium.

Am I reading this right, or is there more to the story than that?
Excellent question. To answer this, let's take a step back and talk about the background of galaxies and dark matter.

For those who don't know, galaxies are structures in our universe which can be thought of as giant "star cities", comprising billions of stars all gravitationally bound to one another. Our own galaxy, the Milky Way, contains around 300 billion stars. It's visible at night from dark locations, extending as a luminous band around the sky. That band is actually the combined starlight of billions of distant stars both like and unlike our own Sun.

Galaxies comes in a few different flavors, the most common being spirals, ellipticals, and irregulars:


Spirals tend to be disc-shaped with a distinct central bulge and noticeable spiral arms. Ellipticals tend to be very homogeneous and redder than spirals (indicating an older population of stars). Irregulars tend to be just that: irregularly-shaped.

In addition to all these billions of stars, spirals and irregular galaxies have an appreciable amount of hydrogen gas and dust. In the case of many irregulars, more mass will be found in their gas than in their stars. For a spiral galaxy like our Milky Way, gas may comprise a good 25% of the mass found in stars. Many ellipticals, on the other hand, appear to have no gas at all.

Now, this gas is actually the material from which stars are created. Its most ubiquitous form throughout a galaxy is as a hot diffuse medium (somewhere around 10,000K). Occasionally, however a large swath of hydrogen gas begins to cools down enough such that its thermal molecular motions can no longer fight against its own gravity, and it begins to collapse. So the "giant molecular cloud" is born.


Note that in the above picture, it's not that there's a mysterious lack of stars at some point in the sky. Rather, there's a very cold (roughly 50K), very dark cloud of hydrogen gas blocking the background stars. This cloud will play host to a stellar nursery.

Inside the cloud, individual local over-densities of gas will continue to gravitationally collapse until enough has accrued for a star to form - essentially that occurs at the point when densities and pressures increase to the point that fusion can occur. Once this fusion ignition happens, a star is born and begins to shine brightly.

Now, this new star will have considerable effect on the surrounding nursery. The stellar wind will push outwards on the giant molecular cloud, and its luminosity will heat it up. This will cause the cloud to shine in its own light...we're left with what's known as an HII (pronounced "H 2") region.


The above image is a photo of the Orion Nebula, an HII region in our own spiral arm of the Milky Way, and visible with even a small pair of binoculars on a winter night. Additional HII regions can be seen throughout the image of the spiral galaxy further up as little red "nuggets".

This process of heating up the gas prevents the cloud from gravitationally collapsing further to create more stars. The stars which were lucky enough to be formed early will rend apart the stellar nursery from which they were born, returning the gas to the diffuse hot state found throughout the galaxy.

So, in this sense, star-formation can be described as an anemic process...there's a negative feedback cycle of newly-formed stars preventing further star formation. Over time, though, the gas will cool down again to form future stars, but it's a slow process happening in measured amounts. At least, this is the case for a galaxy in isolation.

This brings us to elliptical galaxies. Their red color indicates an old population of stars (many have become red giants). This jives nicely with the fact that there's very little if any gas at all in these galaxies...new, blue stars simply aren't being formed because there's no gas to form them from, leaving an aging population of stars. It's also extremely significant that elliptical galaxies are rarely found in isolation - they usually occur in galaxy clusters. Spirals, on the other hand, *are* usually found in relative isolation.

The missing piece of the puzzle seems to be that when galaxies collide or pass near one another (tidally disturbing each other), there is a massive outburst of star formation, resulting in so-called "starburst" galaxies. A curious thing happens when galaxies collide... stars themselves are spaced far enough within a galaxy that they rarely collide, and simply pass through the other galaxy unhindered. Diffuse gas being ubiquitous, however, will interact to form massive shocked sheets resulting in many overdensities and vastly increased star formation. Gas which isn't formed into stars will be widely dispersed around the interacting galaxies. Here's a rather nice spiral galaxy pair in just starting to collide, as captured by the Hubble Space Telescope:


You can actually see the massive starburst there as luminous young blue stars. Lots of gas there, too, visible as the dark region obscuring stars.

So, this is still highly speculative, but the emerging picture astronomers have put together of galaxies seems to be this: A lone spiral is slowly producing stars at its anemic rate, until it stumbles upon another spiral in space. Their mutually gravitational pull causes them to collide. Their gas either interacts and undergoes massive star formation or is superheated and dispersed far around the region, while the elegant spiral patterns of stars are entirely destroyed, producing a homogeneous elliptical group of stars...and so an elliptical galaxy is formed.

Now, let's talk about galaxy clusters for a moment. As these galactic interactions occur, the total gravitational pull of the system is increased, making future interactions even more likely. Eventually, a whole cluster of galaxies is created, surrounded by a massive cloud of unused, superheated hydrogen gas (in the incredibly hot 100 million K range) known as the intracluster medium (ICM). As more spiral galaxies are pulled in, simply the act of crossing the threshold of this ICM produces enough ram shock pressure to strip out the spiral's gas, which combines with the rest of the ICM.

The above scenario is supported by the observation of "lenticular galaxies", which have the nice spiral structure of stars, but seem to be missing all their gas. These strange galaxies only seem be found in clusters, particularly in the outskirts. It seems likely that they've had their gas stripped, but haven't yet interacted with other galaxies in the cluster to disrupt the spiral pattern of their stars.

Now here's the shocking bit: Of all the "regular" matter in the universe - by which I mean made of protons, neutrons, and electrons that we can see - most of it is not found in stars, nor in the gas in lone spirals. Rather, observations indicate that 90% of it is found in the ICM. Whoa.

This sounds a little odd, since the ICM should come from galaxies which should have on average around 20% gas by mass. The two solutions seem to be either: most clusters were formed before individual galaxies could form an appreciable number of stars, or there's an even greater reservoir of intergalactic gas that the cluster is slowly vacuuming up.

Finally, let's get to the 800-pound gorilla in the room: dark matter. There are two major reasons we have believe dark matter exists, and both are gravitational observations.

The first has to do with galactic rotation. Each star orbits around the center of a galaxy, usually on a roughly circular path. With the use of doppler-shifted light, we can actually detect the speed of the stars moving about their orbits. The problem is this: the stars are moving too quickly. Orbits should be a balance between a gravitational attraction towards the center, and tangential velocity sideways. If we estimate the mass of the galaxy based on all the mass we can see, there's simply not enough matter (and therefore not enough gravitational pull) to keep the galaxy together. It should fly apart, but it doesn't. This isn't just the case with one or two galaxies, but *every* galaxy we observe. There needs to be about 10 times more mass than what's observed in order to properly stabilize all the orbits.

The second has to with gravitational lensing. As mentioned in the previous post, starlight bends around the gravity well of massive objects. The problem here is, again, if we estimate the mass based on everything we see, there's simply not enough mass to explain the amount of bending we see. Here, too, there needs to be about ten times more mass to explain the amount of lensing we observe.

Now, finally getting to your question: Could the dark matter just be gas? Well, it's very unlikely. The problem is that we can see hydrogen gas in galaxies emitting in a variety of ways from x-rays down to radio waves. These observations of gas are incorporated into the final estimate of galaxy mass, and there's simply not enough of it. Even in clusters, where 90% of the mass is in the ICM, one still needs another 10-fold mass to explain the lensing effect. There must be some kind of matter which simply can't be seen causing all these gravitational effects...thus, dark matter is inferred.

Now, you could be saying, "Well, maybe astronomers are just really underestimating the mass of gas inferred from observations."

I would answer this with a very specific galaxy cluster known as the Bullet Cluster. It is, in fact, two galaxy clusters which have just collided, passing through each other for the first time. Here's a useful picture of it...I recommend clicking on it and looking at the full-size version:


Now, when galaxy clusters collide, it's a bit like galaxies colliding. In this case, the galaxies themselves are sparse enough that they'll usually pass right through the other cluster unhindered. The ICM, on the other hand will form a massive shock wave right in the center.

So, in the above picture there are a couple of combined observations. The red central area in the picture is an observation taken in X-rays, showing the massive quantities of hot, shocked ICM interacting. We also see on the left and right of this the two constituent groups of galaxies from either cluster which have passed through each other. The real clincher are the blue regions: according to the gravitational lensing of background galaxies produced by the interacting clusters, the blue regions are where most of the mass lies.

Thus, in spite of 90% of the visible matter being in the hot central red region, there's 10 times as much dark matter in the region of the galaxies themselves. Apparently, whatever this mysterious dark matter is, like the galaxies it too has the ability to pass straight through the other cluster unhindered.

Tuesday, March 3, 2009

Follow-up: When stars are not where they appear

There have been some good comments and email from the last post, so I wanted to cover one other case of when star are not when they appear, as well as an interesting consequence.

In the comments of the last post, Naurgul asks:
Wait, I thought another factor was that gravitational forces distort the course of the light. Doesn't that play a role in this?
Similarly, Terry previously asked:
I understand that light bends as it passes a strong gravitational field.
With this in mind, is anything where it seems to be in the Universe?
Both good points. Let's delve into the phenomenon of "gravitational lensing".

Einstein's theory of relativity says that mass doesn't just create a force of gravity, but actually bends the fabric of space and time. A good way to think about this is a bowling ball sitting in the middle of a mattress...the weight of the ball will put a dimple in the surface of the mattress.

Now, if I'm an ant trying to travel the shortest path from one side of the mattress to the other, it may actually be faster for me to take a curved path around the bowling ball than to travel a straight one.

Similarly, a large mass will put a dimple in the surface of space-time. Even though light has no mass (and thus won't be affected by the force of gravity), it will be affected by this dimple. Light always travels on the shortest possible path - known as a "geodesic" - so in a curved space-time this will often be a curved path.

Consider the following diagram:


We have a distant quasar which lies directly behind a galaxy cluster as seen from Earth. Light traveling from the quasar which is initially *not* on a path towards Earth can actually get bent by the curved space-time surrounding the cluster and start heading towards Earth. As a result, the image of the quasar will be shifted - it won't appear directly behind the cluster, but above it.

In some cases, multiple paths might be the shortest, in which case we'll actually see multiple images of the quasar. Here's an example, known as Einstein's Cross, where we see four images of a quasar bent around a galaxy at the center. If the lensing object is perfectly aligned with the background object, we'll actually see the background object's light as a perfect ring around the lensing object.

Note this probably doesn't apply to the prior post's example of Arcturus, since the light needs to pass fairly close to a pretty large mass to be considerably lensed; the smaller the mass, the closer it needs to pass. In general, this won't happen for nearby stars.

That's not to say that gravitational lensing isn't used in our own galaxy, though. Astronomers have actually searched for rogue planets wandering through our galaxy with this technique. Normally such a galactic wanderer would be far too dim to see in any telescope. However, if the rogue planet just happens to perfectly pass in front of a background star, we'll see the star undergo a characteristic brightening due to being lensed into that perfect ring. So far we've caught quite a few of these events.

Okay, so there's one more interesting interaction I want to mention between gravity, light, and position: the Poynting-Robertson effect.

Remember from the last post, even our Sun doesn't appear exactly where it is due to the aberration of light. Since we're moving around it, incoming light seems to come from a point slightly ahead of us.

We'd expect the same effect for the Sun's gravity particles/waves (or whatever it is that mediates the gravitational force)...but it turns out this isn't the case. If we carefully work out the relativity equations, we find that the amount of aberration of gravity is perfectly canceled by the amount space-time is bent by our Sun. It turns out this is quite a good thing, since if there were an aberration of gravity, no orbits would be stable.

Still, we're left with an interesting situation. The gravity from the Sun comes from a source located exactly where the Sun really is...but the light from the Sun comes from a source slightly ahead of that. So what? Well, consider the following diagram:


In the top half of the diagram, we have Earth merrily moving around its orbit...its direction of motion is indicated by the blue arrow. The gravitational force from the actual location of the Sun (indicated by the dotted circle) exerts a force inwards on the Earth, keeping our planet on its happy orbital path. The image of the Sun (indicated by an actual Sun image), slightly shifted from its true position, is also exerting a force outwards: radiation pressure.

I've greatly exaggerated the magnitude of the radiation pressure force for clarity - it's nowhere near as strong as the gravitational force - but it's there, nonetheless. Now, if radiation pressure outwards were coming from the exact same location as the gravitational force inwards, they would balance and the only effect would be that the Sun's gravity would be slightly lessened and Earth would travel slightly slower in its orbit.

However, this is not the case. From the bottom half of the diagram, we see that when we combine the two forces, there's a leftover component (the red arrow) which is in the opposite direction of the Earth's motion. This ends up acting like a drag force on orbiting objects, slowing them down.

Now, don't panic just yet. For planet-sized objects like our Earth, radiation pressure is truly negligible compared to gravity. Gravity is a function of the mass of the planet, while radiation pressure is a function of the surface area of the planet - how much surface can absorb incoming light. For objects with a large surface area-to-mass ratio, though, this becomes important.

Okay, so what do I mean by surface-to-mass ratio?

- If I make an object 10 times bigger than the Earth, its surface area will be 10^2 = 100 times greater, but its mass will be 10^3 = 1000 times greater. So it has a surface area-to-mass ratio 100/1000 = 0.1 that of the Earth.

- If I make an object 100 times bigger, its surface area will be 100^2 = 10,000 greater, but its mass will be 100^3 = 1,000,000 times greater...it's surface area-to-mass ratio will be 10,000/1,000,000 = 0.01 that of the Earth.

As we make objects bigger and bigger, their surface area-to-mass ratio decreases. Similarly, as we make smaller and smaller objects, this surface area-to-mass ratio keeps increasing.

If we keep making objects smaller, by the time we get to grains of dust the surface area-to-mass ratio is big enough that radiation pressure is significant compared to the gravitational force. Grains of dust which are in orbit will keep feeling this drag force, continuously slowing them down and making their orbits tighter and tighter. Eventually, they'll spiral all the way in to the surface of the star and be consumed.

For this reason, whenever we observe a dust ring around a star, we know that the star must be very young. Anything more than, say, a million years (a tiny amount of time for a star), and the dust ring would've already spiraled in.

Monday, March 2, 2009

When stars are not where they appear...

Cynthia asks:
When we look at the night sky and see a star or planet are we seeing it in it's exact location - or - are we seeing the light from the star or reflected light from the planet at some closer point to which the light has traveled and become visible to us?
Excellent question. So, there are two reasons why we don't see a star or astronomical object where it *actually* is:

1) It's moving.
2) We're moving.

First, we'll tackle the first reason, since it's a little easier. Let's say you go outside tonight and observe Arcturus, a nice, very bright orange giant star. Now, Arcturus happens to be 36 light-years away (roughly 200 trillion miles). That means the light that you see tonight has been traveling for the past 36 years towards Earth. It left the surface of the star back in 1973, when Nixon was president, and disco was still awesome.

Now, since that time, Arcturus itself has actually been moving around the center of our galaxy - what astronomers call "proper motion". In thirty-six years, it would've moved about 1/40th of a degree on the sky (an angular distance just barely discernible to the naked-eye). However, you wouldn't see at its current location, you'd see it where it was back in 1973. Depending on whether you learn better from images than text, a diagram might be helpful here:


In the above figure, the vertical axis is time, and the horizontal axis is the distance between Earth and Arcturus. The orange squiggly arrow is the light emitted by Arcturus back in 1973, which, traveling at the speed of light, hits Earth in 2009. Notice that Arcturus moved between 1973 and 2009...but here on Earth we don't know anything about it since we're only currently receiving light from 1973. (For simplicity, I assumed that Earth isn't moving.)

Basically, we have no information about the state of Arcturus since 1973. For all we know, Arcturus could've gone supernova in 1980 (unlikely, but hypothetically speaking....) and we wouldn't know until 2016.

(Historical side note: I specifically chose Arcturus for this example because it was the first star discovered to have proper motion. In the 1600's, Edmund Halley - of Halley's comet fame - was perusing the 1500-year-old star charts of Ptolemy, and noticed Arcturus was not in the same position. The only logical conclusion was that Arcturus had moved over the eons.)

So, that's the first reason why stars are not where they appear. Now for the second, slightly more complex reason: Earth *is* moving.

Let's imagine for a moment that we're sitting in a car in a rainstorm. There's no wind, so the rain is falling straight down, presumably from a storm cloud directly above us. For some reason, we've decided to strap a bucket to the top of our car to collect rainwater...maybe we just really love the flavor of it. Whatever the reason, though, if we point the bucket straight up, we'll collect the most water.

Now, let's say we start driving really fast. It turns out that pointing the bucket straight up is not the best way to collect water - we're better off tipping it slightly in the direction of our motion. This is because if the bucket is angled it's easier for the rain to clear the the bucket's front lip and make it down to the bottom. So long as it gets inside the bucket before the back lip passes over it, it'll be collected...the following diagram of two moving buckets might help:


Notice the straight bucket produces a "rain shadow" at its front lip. Also notice the tilted bucket managed to catch some rain a moment earlier that's now covered by the back lip, but will still fall all the way to the bottom.

Now, from our perspective moving in the car, things are different. There's more rain hitting our front windshield than our back window, so we figure that rain isn't coming straight down, but at an angle. To us, our tilted bucket strategy works better because it appears the rain is coming in at an angle from a storm cloud that's both above us as well as a little ahead of us...this is the vital piece of the analogy. Again, another diagram might help:


So, instead of thinking about storm clouds, rain, buckets, and cars, let's rephrase this in terms of stars, light, telescopes, and the Earth.

If the Earth were holding still, the light from a star would come from the star's true direction (at least at the time the star emitted it). Because we're moving, though, it appears that the light comes in at slight angle from a source slightly ahead of us - just like with the rain - so we see the star as slightly ahead of us. This phenomenon is known as the "aberration of light".

Since Earth is moving around the Sun, even the Sun itself is shifted from where it "actually" is located by about 1/200th of a degree. It's not enough to notice with the naked-eye, but telescopes can easily pick up that shift.

Saturday, February 28, 2009

What's up in the sky: Comet Lulin and Venus

The currently visible planets from Earth are always changing. In fact, the term "planet" comes from the Greek term, "wandering star", since they don't move like the rest of the sky.

That being said, I thought it would be informative to have a "What's up in the sky" section every couple of months to let people know what's visible if they just step outside and look up in the evening. Even from the middle of the most light-polluted cities, bright planets are still visible. I've already received a few questions pertinent to this.

Fitz asks:
I'm in Chicago, and I keep seeing what looks like a really bright star in the west. Is that Venus? What's the best way for a non-astronomer to find out these sorts of things (other than asking you!).
That's definitely Venus you're seeing. Other than the occasional airplane or bright satellite pass, Venus is the third brightest object in our sky after the Sun and the Moon. In fact, it's the object most frequently reported as a UFO.

Venus will be visible in the early evening sky in the West for the next month or so. As a planet on an orbit interior to Earth's orbit, it's currently "rounding the track" to pass in between us and the Sun, a phenomenon known as inferior conjunction. Because of this geometry, it's currently exhibiting a nice crescent phase and getting larger each night as it approaches us. At this point, with a good pair of binoculars and some keen vision, you should be able to make out that it's not merely a point of light, but a tiny crescent.

To answer the last part of your question, Sky & Telescope's This Week's Sky at a Glance provides a good overview of what's visible at any given time. Additionally, picking up some Planetarium software is also a good idea since it can be customized to your location and any date you want...there are some really good options out there. If you're a fan of open source software, I'd highly recommend Stellarium which can be downloaded from their subversion repository (side note: props to my subversion peeps).

Ben asks:
Comet Lulin is coming closest to earth tonight. Do I have a snowball's chance ... in space ... of seeing it?
Similarly, Tami asks:
I overheard a conversation yesterday that sounded like there was a comet in view the last few days, however it has been hazy here so there wasn't much view. Was there a comet visible recently? Which one? When? Where? Do you have any pics? How close is it to the earth? Is Armageddon inevitable?
Every couple of years we get a comet which is able to break the visible brightness barrier and can be seen with just the naked-eye. Comet Lulin is an example of this. Current estimates of its magnitude (brightness) place it at just above the naked-eye limit for a dark-sky site.

This comet is a bit of an interesting one. Its closest approach to the Sun was over a month ago, at a distance a good 20% greater than the Earth-Sun distance, but the geometry works out so that its closest approach to Earth was just four days ago at a distance just 40% of the Earth-Sun distance. (No worries, though, this is not even close to hitting us.)

Its orbit carries it *very* far from the Sun - over 3 light-years, in fact. At this distance, the Sun is not the only gravitational force acting on its orbit, but the gravity of other stars may start to be significant, so it's a little unclear if this comet will actually return to our solar system. Even if it does return, it won't be for another 50 million years. Whoa.

Now, that all said, it's not terribly spectacular with just the naked-eye...don't expect something similar to Comet Hale-Bopp back in 1997. You'll need a very dark sky to see it unaided, and it won't look like much more than a smudge. On good nights I can see the Milky Way from my yard, but I was unable to spot this comet with just the naked eye. With a decent pair of binoculars, though, it should stand out.

However, you'll have to hurry if you want to see this one. It's now moving away from Earth on its way out of the solar system, and won't be visible for long. It's currently rising over the Eastern horizon around sunset in the constellation Leo, though a finder chart is almost certainly necessary. You can find one here.

As for images, I'd recommend Spaceweather's Comet Lulin gallery...over 16 pages of images submitted by amateur astronomers.