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 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,'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 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, 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'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.