# Why do gas giants have clearly delineated surfaces, whereas the Earth's atmosphere fades into space?

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I've just seen this Forbes article.

Why do gas giants appear to have clearly delineated surfaces, whereas the Earth's atmosphere fades into space?

Is it just a matter of scale? Or is there some form of "surface-tension" for the hydrogen gas?

In an isothermal atmosphere, the exponential scale height of the atmosphere is $$h sim frac{k_mathrm B T}{mu g},$$ where $$g$$ is the gravitational field, $$mu$$ is the mean mass of a particle and $$T$$ is the temperature (in kelvin).

i.e. The pressure/density of the atmosphere falls exponentially, with an e-folding height given by the above expression.

I suppose what matters when you look at a photo, is how this height compares with the radius of the planet. $$frac{h}{R} sim frac{k_mathrm B T}{mu g R}$$

Jupiter is half the temperature, 11 times the radius and with 3 times the gravity of Earth. However $$mu$$ is about ten times smaller (hydrogen vs nitrogen/oxygen). Overall that means $$h/R$$ for Jupiter is of order 5-10 times smaller than for Earth and so it will appear "sharper".

EDIT: If you put some reasonable numbers in for Jupiter ($$T sim 130$$ K, $$mu=2$$, $$R=7 imes 10^7$$ m), then $$h/R sim 3 imes 10^{-4}$$. This means even if Jupiter fills a photo that is 3000 pixels across, the atmosphere will be about 1 pixel high.

## Why does VS Code fail type acquisition for Vue?

When I open the test-proj directory and open hello.js , VS Code's type checker reports three errors:

Now, I modified jsconfig.json so that VS Code will automatically acquire types for all three:

. which makes VS Code recognize that jQuery and React can be used in my script. However, as you see here, it still does not recognize Vue:

TLDR: Why does VS Code fail to acquire type definitions for Vue, when it can do so for React and jQuery?

(Note: This is not a Node.js project. I do not have package.json or node_modules/ under my project directory. I also checked my globally installed npm packages, just to be sure, but I do not have react or jquery installed.)

## Graph for lower and upperside bound absolute value function

Normally we plot the area where the relation holds good is where the graphs overlap , But here they don't seem to overlap. So I don't know how to plot the graph ?

I tried it in wolfram alpha to see how the graphs |x| > k-1 and |x| < k look separately and from which the overlapping area is where the entire relation holds good (I assumed k=2 for plotting) for |x|<2

for |x| >1

One graphs area is outside the |x| boundary and other area is within it . How can the area overlap , how can I plot the relation in graph for the combined relation which I gave in line 2 of this question .

But the answer for this relation was given in a book as following

May I know how they arrived at this solution . Please correct me where I am going wrong in my understanding .

## ELI5: Are gas giant planets gassy? As in could I land on a gas giant and like poke my finger through?

25 16 19 & 11 More

If you tried to land on a gas giant, you'll first encounter an atmosphere, similar to what you would expect on earth.

It would start very very thin and becomes more substantial as you go down.

As you get deeper the pressure would increase to very high levels, the temperature would rise, then the gas would turn into liquid.

Unlike earth, where the transition between the atmosphere and the ground happens at a very defined point, gas giants transition smoothly. So the atmosphere would become thicker, then soupy-er, until it's basically a liquid.

You would be very dead long before this point, but if you somehow continue to dive deeper, you would encounter another smooth transition, from the liquid mantle made of mostly hydrogen to the solid and rocky core.

and like poke my finger through?

Not really. The atmosphere doesn't start at a set altitude. Vacuum just become less and less void as you get closer to the planet, and there is no point where the change is abrupt enough that it would feel like poking something.

 Many people are asking why we can see gas giants so sharply if their atmospheres doesn't have a clearly defined boundary. This happens because the transition zone from hard vacuum to dense atmosphere, while being several hundred kilometers in height, is very small compared to the overall planet (like a fraction of a % of the radius). The decrease in pressure is also exponential, so only the very lower layers are dense enough to see. You can actually see the fuzzyness in some close up photos. The same is true for earth's atmophere.

## Earth

Of the four terrestrial planets, Earth is the largest, and the only one with extensive regions of liquid water. Water is necessary for life as we know it, and life is abundant on Earth — from the deepest oceans to the highest mountains. Like the other terrestrial planets, Earth has a rocky surface with mountains and canyons, and a heavy-metal core. Earth's atmosphere contains water vapor, which helps to moderate daily temperatures. The planet has regular seasons for much of its surface regions closer to the equator tend to stay warm, while spots closer to the poles are cooler and in the winter, icy. The Earth's climate, however, is warming up due to climate change associated with human-generated greenhouse gases, which act as a trap for escaping heat. Earth has a northern magnetic pole that is wandering considerably, by dozens of miles a year some scientists suggest it might be an early sign of the north and south magnetic poles flipping. The last major flip was 780,000 years ago. Earth has one large moon that astronauts visited in the 1960s and 1970s.

Mars has the largest mountain in the solar system, rising 78,000 feet (nearly 24 km) above the surface. Much of the surface is very old and filled with craters, but there are geologically newer areas of the planet as well. At the Martian poles are polar ice caps that shrink in size during the Martian spring and summer. Mars is less dense than Earth and has a smaller magnetic field, which is indicative of a solid core, rather than a liquid one. While scientists have found no evidence of life yet, Mars is known to have water ice and organics — some of the ingredients for living things. Evidence of methane has also been found in some parts of the surface. Methane is produced from both living and non-living processes. Mars has two small moons, Phobos and Deimos. The Red Planet is also a popular destination for spacecraft, given that the planet may have been habitable in the ancient past.

## Earth Loses 50,000 Metric Tons of Mass Every Year

According to some calculations, the Earth is losing 50,000 metric tons of mass every single year, even though an extra 40,000 metric tons of space dust converge onto the Earth’s gravity well, it’s still losing weight.

Chris Smith, a microbiologist, and Dave Ansel, a Cambridge University physicist provided the answer in BBC Radio 4’s More or Less program. The 40,000 metric ton of mass that accumulates comes from space dust, remnants of the formation of the solar system.

When people build structures on Earth, it doesn’t add any mass since they are using baryonic matter that’s already present on the planet. It just changes shape. Launched satellites and rockets that end up in orbit will eventually fall towards Earth’s gravity well.

The Earth’s core loses energy, since much of it is consumed in a planet’s lifespan, but that only accounts for a loss for about 16 metric tons per year. The biggest mass loss comes from escaped hydrogen and helium, which escape with 95,000 metric tons of mass and 1,600 metric tons respectively. These elements are too light to stay permanently in the gravity well, so they tend to escape into space.

The net loss is about 0.000000000000001% every year, so it doesn’t account for much when compared to the total mass of the Earth, which is 5,972,000,000,000,000,000,000 metric tons. It will take trillions of years for all of the hydrogen to be depleted. Helium represents 0.00052% of the atmosphere and it’s a scarcer element.

### Helium-Shrouded Planets May Be Common around Other Stars in Our Galaxy

#### 61 Comments on "Earth Loses 50,000 Metric Tons of Mass Every Year"

I never realised how much the Earth weighed! I didn’t even know Quintillions existed lol

The loss of Hydrogen from atmosphere is only 10^-15% every year, whereas for complete depletion of Hydrogen , it will take 10^15 years further. We should not talk in terms of actual magnitude of loss of the Earth’s mass, which is very negligible when compared to the actual mass of the Earth which is gigantic in proportions. Same will be the case with every other planet in the Universe. This Hydrogen which was responsible for the formation of stars is going back to the cosmos as interstellar nebula. Being very light, they form solid earths from their nucleosynthesis, and the remaining is sent back to cosmos. Thank You.

Of course it’s losing weight! All systems tend toward disintegration and entropy. It’s an empirically observable fact. Not us, our world, or anything else is built to last forever. It’s just the way it is. Neurosis comes from taking it personally.

How could the Earth possibly be losing mass, according to those calculations? I can understand that the Sun could lose mass, but the Earth?

When stars are having Hydrogen as the primitive substance for nucleosynthesis for the formation of Helium and other elements, why do you exclude earth alone to be devoid of primitive Hydrogen in its atmosphere? Hydrogen is everywhere in the nebulae, galaxies and inter-galactic space. Hydrogen had undergone chemical combination to become CH4, NH3, H2O etc in the planets atmosphere. Not all can combine and the rest major portion of Hydrogen in the primitive atmosphere has got to escape to the surroundings only resulting in depletion of Earth’s mass. Thank You.

If earth losses mass every year will it come to an end one day.i”uka

Same thing I thought. I think it will but it will take 10 quadrillion years. Or even more.

There is a counter to this though. The lost mass is likely ozone which tje planet can still pick back up as it goes back around the sun. It won’t recover all of it, but some. There are also sources of mass other than cosmic dust – such as meteorites and the occasional asteroid. How much net mass from meteorites enter each year? Can an asteroid impact – as rare as it is – offset the remainong loss?

Estimates range from 37-78 thousand for the added mass meteorites give to Earth. This author just picked a number that suited his argument. He wants there to be a net loss so…

How do they calculate the mass loss ?
And if we are talking about Hydrogen and Helium, then we are talking about the atmosphere, not the solid or liquid mass. So, how much mass do we have in the earth’s atmosphere ? Then we can calculate when are we going to stop breathing.
In the space, the only friction that would take any mass from the earth is the solar wind. Is the solar wind strong enough to rip 50,000 tons of mass from the earth every year?

The earth’s mass is 5.972 × 10^24 kg

According to me mass of earth is increase because sunlight is convert into carbohydrate and carbohydrate is convert into soil so mass is increase

This is interesting. I am also wondering whether sunlight increases the mass of earth through photosynthesis process, I’m not sure about that what about you??

Can’t they discovered about that we are decreasing to the earth. Surely that is an art that had been created by Allah…

I agree with this article, earth is losing mass also by nuclear decay of potassium, uranium and thorium. Earth losing mass is another way of saying ground potential is falling. In my theory (ground potential) I have calculated that ground potential is falling by around 0.005 Volts per year. I hope this can one day be proved by measuring an increasing mass in the electron.

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I’m curious about the weight of the people, flora and fauna, being born and die. 7 billion people on the planet that will die has to add some weight, no? Does this affect the weight of the planet?

No, the lifeforms on this planet are composed of mass acquired from the planet, so we’re just moving mass from one form to another.

Surely that number is a little more serious if you take into account the fact that the atmosphere and sea (and thus the inhabitable area of earth) are just a wafer thin blanket over a large ball of uninhabitable rock.
what percentage of our atmosphere and water goes? the rock underneath isn’t breathable or drinkable.

This article doesn’t make logical sense. The debris we’re accumulating is mostly rock, and I think it’s safe to say the overwhelming majority of that material never leaves. Also, we can clearly see that the continents have spread apart. The supercontinent theory with all the continents grouped in one corner of the planet and then spreading across it is like a child’s attempt to rationalize evidence that contradicts the prevailing theory. Any idiot can see that the planet was once much smaller and has expanded, causing the continents to separate.

I agree with your statement. I would definitely think once the rock gets here it stays here & adds its mass to the planet. Extrude that over millennia & sure we’ve added mass. A tremendous amount I would think. k water that

Also the theory that icey comets have brought loads of water too. That’s not lost.

Just wondering if the billions of barrels of fossil fuels taken out of the ground and burned will help reduce the weight of earth?

I just have to say that the change in the planets mass is also due to the removal of oil that is dearly needed in the planet or else it would not be there. It was fine when we were only removing a smaller amount but 35 billion barrels a year really do the math people just sayin just sayin

Sir ! Sunlight cannot increase the mass of the earth since it only splits the water into hydrogen and oxygen already existing on earth already besides using carbon di oxide that was available in atmosphere. No material contribution from the sun on earth by its radiation. Thank You.

But if we change the state of the renewable resources in earth, wouldn´t more grow back and that would create more mass

Interesting subject and comments. The law of physics that states we can neither create or destroy mass stops the idea we can have loss of mass via burning fossil fuels. We have simply changed the form, in this case to gas. We do acquire electrons and protons from the solar winds. Do we also gain helium and hydrogen from the sun? We do acquire space dust, meteors, and other space debris at the rate of 40,000 tons per year according to the article. If the article is correct we have a net lose or approx. 50,000 tons per year. If we are losing and the sun is losing shouldn’t the net effect be negligible. Or maybe chicken little was right, “The sky is falling!!”

Is oil and coal in your calculus of the earth losing weight.

People burn oil and coal to get electricity

Earth Loses 50,000 Tonnes of Mass Every Year

Sincerely. Hendrik Johannesen

NATURAL RESURSIS (OIL,GAS,COAL) – IS A BALANS OF PLANET – FOR THIS ORBIT CHANGE !

How could Earth lose mass since gravity holds everything in place? The way I see it, Earth would only lose mass if another heavenly body with with a stronger gravitational pull pulled mass away from it. Take Saturn’s satellite Titan for example, It’s atmosphere is much denser than Earth’s but it’s gravity is only 10% as strong.

So explain it for us simple minded people. Our planet was created from our Sun, at first it was a ball of fire, like the Sun is. Over billions of years it has cooled down so we can live here. BUT it will keep cooling down and the fire inside our planet will go out. When that happens most of the water left will gravitate to the Earths core and freeze. The part of the planet we live in will dry up, and what water didn’t freeze will escape in outer space, because the gaseous bubble that we lived in will have burst. It will take some time and some people may profit from it, and live quality lives,while others may not.

I have wondered about the increased volume of the land as a result of carbon fixation. Certainly we must accrue some carbon from meteorites. Accretion from plant growth and decomposition is apparent everywhere, as plants absorb gaseous carbon from the atmosphere and convert it to solid plant material. Top soil builds up and buries previous “surface” layers in our lawns and forests and everyplace covered in plants. Yes, much of that carbon should come from within the system, but if any is from external sources, there would be some offset to the loss of gaseous hydrogen and helium.

So… Maybe I’m missing something, but does the Earth not increase in mass due to all of the plant growth. A seed falls to the ground and grows into a tree, that seed that weighed only a fraction of an ounce can weigh many tons by the end of its life cycle. Therefore over many years the Earth has to gain weight and mass. Right?

What does that seed build the tree out of? Elements that are here. So no net gain.

If what I’ve read is correct, if we’ve removed 39 trillion gallons of oil from the earth, doesn’t that equate to a much higher mass of loss to the earth?

The system of mass the is being measured is all mass within the earth gravity well that results in a terminal trajectory (Will eventually fall to earth). What that means is no matter what we do on our planet doesn’t really effect its mass unless we launch mass far away from it. We could burn every single drop of oil within the planet and it would not effect the amount of mass present. Plant growth also is using mass already within the system, its just changing how the mass is arranged. The loss and gains this article is talking about are what is coming into said system and what is leaving it.

It’s a complex system but there’s something you are missing. When we burn anything from wood to fuel to kerosene that heat rises up and eventually is cooled by space. It’s not the gases that we lose it’s the fuel turned into heat. We are losing heat to space from every engine every air conditioner every house that is poorly insulated. The solution? We need ice and mass from other planets, we can’t get it from the moon, because that’s part of our total mass make up. Like a bola spinning in space if we take from the moon it is a zero mass gain. The energy expended to pull a chunk of asteroid into near earths orbital path would be minimal and depending on size it would have to be broken up before we let it add to the mass of the earth. Hopefully something made mostly of water. If we did this and it was large enough and done gradually we could effect the whole planet. The swings up and down in temperature are from a net change in where out water is. It’s in more people more pipes more water towers. Water vapor and water stabilizes weather makes more plants grow. If we add mass to the whole thing we can again increase population and desalinate the oceans and continue to grow for perhaps the next thousand years.

earthscience304524629.wordpress.com visit the above link, it has further info regarding earth’s weight loss.

If the earth is losing mass would that change the distance between the earth and the moon’s orbit? If so perhaps that would account for weather pattern changes? Also the distance from the earth and sun is increasing by 1.6 cm per year – would this cause any temperature changes on earth?

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Hope these comments will continue to be posted for another million years.

Not satisfied. How can helium escape earths gravity. ( solar wind) hmm what is that? Helium still has mass and weight. What I read implies that solar wind is stronger than gravity. Not convinced

I call BS!. Every plant and animal spawned on this planet leaves some material behind. We have cosmic dust meters small ones hitting this planet or entering our atmosphere all the time constantly, the earth is getting larger, not smaller. common sense people. the reasons we have higher CO2 in the atmosphere is we are covering more land with stuff not plant life. Yes, we are adding it to…but let’s say we went to flying cars instead of ground-based transportation?. How much land would be freed up for farming and forests?… No roads highways off ramps how much could we save?.

I’m so glad that none of you are astrophysicists. I’m not either. Our climate is changing in my lifetime of almost 64 years. The Earth is a complex ecosystem and is out of balance with the progression of human interaction with it. The earth is alive and human interference of the natural course of how the earth would have evolved has been changed. There is no way of knowing whether the earth would be different today without humans. So far the longest living creatures ever recorded were not humans but dinosaur fossils, and they were around during different stages of the evolution of earth and they were around for a millennium. So hopefully governments and large corporations can change their money hungry ideas and try making positive decisions on environmental choices to eliminate the decline of the human impact of waste. Humans are a higher form of intelligent life not like dinosaurs so we are capable of figuring things out, unfortunately we are better at designing items for bad(war,eg) and not so much good(pyramids,eg). I use pyramids only because they show longevity of how long ago something can still be around thousands of years later. All the great minds need to come together, but unfortunately no one of any importance will probably listen to their plea for change. Two decades ago scientists said global warming will cause changes to our environment no one listened, now I’m seeing it in my part of the world. Everyone will be affected in one way or another. There’s my two cents of knowledge. Thanks for reading.

it gains 40,000 tonnes per year in dust and looses 90,000 in gases which gives a loss of 50,000 tonnes per year. which makes no sense because it would be gone in under 12 million years..

Authorities claim we waste too much water. Impossible, the water is absorbed, turned into vapor and redistribution as rain. We drink the same water as the dinosaurs. Water is a recurring theme, it’s never wasted because it’s brought back…glacier melt, rain, fog, etc….am I right??

One day, one day in heaven.

I am curious as to whether any of the materials being lost to space from the earth are alive. Bacteria can form spores when environmental conditions are not conducive to growth. These spores can withstand some very bad environmental conditions. If they get into space there may be a chance they could travel to a more hospitable location such the interior of an asteroid or a moon where liquid water is present and the can grow. I believe in the Asimov view of extraterrestrial life. It will all come from the source planet – Earth.

What about human bones? With the world’s population on the increase, that means we are adding more weight with people. Even when we die we leave behind either ashes or a skeleton which in the end would be a net gain.

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i am shocked, this is mention in the Holy Quran.in a book written 1450 years ago… seriously i am shocked…

What about matterials that are going in space e.g sattelites ? What about fuel that is consumed outside the gravity field. Imagine 1000 reusable rockets sending people in space an coming back , that would make a net loss even though not significant.

Whatever is written in this article is tru. Fourteen years ago today, Allah had told in the Qur’an that the earth is shrinking. To date, no one can has been able to disprove a single word Qur’an. That verse is written below.

Surat No 13 : سورة الرعد – Ayat No 41

اَوَ لَمۡ یَرَوۡا اَنَّا نَاۡتِی الۡاَرۡضَ نَنۡقُصُہَا مِنۡ اَطۡرَافِہَا ؕ وَ اللّٰہُ یَحۡکُمُ لَا مُعَقِّبَ لِحُکۡمِہٖ ؕ وَ ہُوَ سَرِیۡعُ الۡحِسَابِ ﴿۴۱﴾

Have they not seen that We set upon the land, reducing it from its borders? And Allah decides there is no adjuster of His decision. And He is swift in account.

If you are not sure, ask Allah for guidance. Open your heart eye and see world. Do not call others terrorists without any reason or logic.if you call then you are brainless.

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Jupiter being a gas giant is not about its appearance, as another answer stated. It's only about the mass distribution of a planet.

Jupiter's mass is 320 Earth masses, while we know from the Juno mission that the rock/ice in the core account for 5–25 of these Earth masses. So the rest of about 300 Earth masses is gas.

Thus Jupiter is a gas giant. It is really that simple. The more exotic states of matter that the solids in its interior probably exist in, don't affect the definition of a gas giant.

To put that into perspective:

• The same thing goes for Saturn, 95 Earth masses total, with estimated 20 Earth masses in the core. So 75 Earth masses of gas. Gas giant. and Neptune are different. Their masses are 14 and 17 Earth masses, respectively, with at least half of that in rock/ice. Thus they're not gas giants, but loosely named 'ice giants'.

Another way of inferring what Jupiter is made of, is taking a look at its average density. This is how it was done historically, before we had sophisticated computer models and high-pressure lab experiments.

Knowing Newton's laws, one can measure Jupiter's mass $M$ from its orbiting moons. Its size $r$ is known from the distance. Thus one can calculate its average density $ar < ho>= frac<4/3 pi r^3>$ and finds a value of $ar< ho>_♃ = 1.326 mathrm$. This is significantly lower than what Earth has ($ar< ho>_ = 5.55 mathrm$) and the other rocky planets.

Through simple weighted averaging with some rock mass of a few percent, it was then realized early on that one needs a lot of gas to reach such a low average density for such a planet as Jupiter.

An interesting detail here is, that one cannot build Jupiter of gas only, the resulting average density would be lower than the real one. This is how it was realized that some very dense material needs to exist somewhere in Jupiter, possibly a core of solid material.

One reason they are called gas giants is because they are mostly composed of elements that are gaseous at Earth like temperatures and pressures.

Jupiter is primarily composed of hydrogen with a quarter of its mass being helium, though helium comprises only about a tenth of the number of molecules.

Jupiter's upper atmosphere is about 88–92% hydrogen and 8–12% helium by percent volume of gas molecules. A helium atom has about four times as much mass as a hydrogen atom, so the composition changes when described as the proportion of mass contributed by different atoms. Thus, Jupiter's atmosphere is approximately 75% hydrogen and 24% helium by mass, with the remaining one percent of the mass consisting of other elements. The atmosphere contains trace amounts of methane, water vapor, ammonia, and silicon-based compounds. There are also traces of carbon, ethane, hydrogen sulfide, neon, oxygen, phosphine, and sulfur. The outermost layer of the atmosphere contains crystals of frozen ammonia. The interior contains denser materials - by mass it is roughly 71% hydrogen, 24% helium, and 5% other elements.[21][22] Through infrared and ultraviolet measurements, trace amounts of benzene and other hydrocarbons have also been found.

So Jupiter and Saturn are almost totally composed of hydrogen and helium, elements that are gaseous at Earth like temperatures and pressures. Of course the temperatures and pressures deeper inside Jupiter and Saturn are not exactly Earth like!

But the elements that they are composed of are commonly called gases even though they might be in exotic conditions such as liquid metallic hydrogen under the immense pressure and temperatures inside the planets. Most of us think of hydrogen and helium as gaseous elements, not liquids, or solids, or highly exotic forms of matter.

Thus Jupiter and Saturn are "gas giants".

A second reason they are called "gas giants" is historical. Famed science fiction writer James Blish wrote a science fiction story called "Solar Plexus", published in Astonishing stories, September, 1941. "Solar Plexus" was rewritten and republished in an anthology Beyond Human Ken, edited by Judith Merrill, 1954. The 1954 rewritten version contained the line:

A quick glance over the boards revealed that there was a magnetic field of some strength near by, one that didn't belong to the invisible gas giant revolving half a million miles away.

Science fiction readers who knew anything about the structure of giant planets thought that "gas giant" was a very fitting phrase to describe them. And some of them were professional astronomers. Thus the phrase began to be used by astronomers to describe the giant planets in the solar system.

## Jovian Planets Vs. Terrestrial Planets

Size: The basic difference between these two types of planets is their size. While Jovian planets are gigantic, their terrestrial counterparts are considerably small in size. In fact, the smallest Jovian planet is 10 times larger than the Earth―the largest terrestrial planet.

Mass: Even in terms of mass, Jovian planets score over terrestrial planets, with the smallest planet in this category having 15 times the mass of the Earth.

Density: The density of terrestrial planets is five times that of water, while that of Jovian planets is as much as that of water.

Surface: The surface of Jovian planets is made up of gases, while that of the terrestrial planets is made up of solid rock.

Atmosphere: The atmosphere of terrestrial planets is predominantly made up of nitrogen and carbon dioxide, while that of the Jovian planets is made up of hydrogen and helium.

Inner and Outer Planets: As far as the distance from the Sun is concerned, terrestrial planets are closer to the Sun, and hence, are referred to as the ‘inner planets’, while Jovian planets are farther, and hence, are referred to as the ‘outer planets’.

Rotation Speed: Surprisingly, the speed at which the outer planets rotate is much faster than that of the inner planets.

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Number of Natural Satellites: While terrestrial planets either have none or a very few natural satellites (Mercury – 0, Venus – 0, Earth – 1, and Mars – 2), Jovian planets have a large number of them (Jupiter – 67, Saturn – 62, Uranus – 27, and Neptune – 14).

These were some of the most prominent points of distinction between Jovian and terrestrial planets. Among the various Earth-like planets, planet Mars has been a subject of fascination for mankind for quite some time now. Scientists believe that this planet resembles the Earth the most in terms of various aspects, and hence, the probability of life existing on it―in some or the other form―cannot be dismissed entirely.

## The gas giant planets

Why do we call them "gas giants?" Because they are really big planets, much larger than the Earth. Look!

Source for the images can be found at http://spiff.rit.edu/classes/resceu/ss_planets/earth_moon_lineup.html

Image courtesy of NASA/JPL-Caltech/SwRI/MSSS/Christopher Go

We can make the comparison quantitative, too. If we do, we can learn another difference between the terrestrial and gas giant planets.

The densities of the giant planets are much lower than the densities of the terrestrial planets. Note that Saturn's density is less than that of water. It is often stated that

 Saturn would float in water! Image courtesy of NASA

Rhett Allen provides some pretty good arguments against this scenario , but if it helps you to remember this feature of the giant planets, then, go right ahead and think it.

So, why are the densities of the gas giants so low? Well, you could just read the next section heading .

#### Gas giants are gas

Planets in the inner solar system are composed primarily of solid matter. The Earth, for example, has an iron core, a semi-solid mantle of dense minerals, with a solid crust floating on top. The atmosphere is just a tiny extra layer -- the skin of an apple has roughly the same relative thickness as the atmosphere of the Earth.

Image courtesy of NASA (and Wikimedia)

But the atmospheres of the giant planets are more than a thin skin -- they occupy a large portion of the entire volume. In Jupiter and Saturn, the gaseous atmosphere accounts for roughly half the planet's radius in Uranus and Neptune, perhaps a quarter.

#### Lots of moons

All four of the giant planets have moons -- and lots of them. Some of them are the largest moons in the Solar System, and quite a few are larger than our own Moon.

Montage by Emily Lakdawalla. Data from NASA / JPL, JHUAPL/SwRI, SSI, and UCLA / MPS / DLR / IDA, processed by Gordan Ugarkovic, Ted Stryk, Bjorn Jonsson, Roman Tkachenko, and Emily Lakdawalla.

But there are also a plethora of much smaller objects in orbit around these giant planets. Since the smaller objects lack the gravitational force to overwhelm the structural forces within icy or rocky materials, they tend to be irregular in shape: potatoes, rather than spheres.

Here are the "big" Saturnian moons, from Titan at 5150 km (upper right) and Rhea at 1500 km (center) to little Hyperion, only about 250 km in diameter (lower right corner).

Image of some Saturnian moons courtesy of NASA / JPL / SSI and Emily Lakdawalla

And these START with Hyperion at around 250 km, and go down to objects with diameters of just a few km. (Click on the image for a much larger and more detailed version).

Some of these objects were formed together with their host planet, in the same swirling region of the proto-solar nebula, some 4.5 billion years ago. That's probably true for all the big satellites, with one exception which we'll discuss when we get to Neptune. But some of the smaller moons are very likely captured asteorids, objects that took a right turn at Albequerque, passed too close to a giant planet, and were unable to escape its gravitational attraction.

Compare the locations of the four big moons of Jupiter, with their nice, circular orbits .

. to the locations of the smaller moons:

Most of the small, outermost moons have orbits that are retrograde -- in the direction opposite to Jupiter's own rotation, and the revolution of the inner moons. This is another clue that these objects didn't form together with Jupiter, but were captured long afterward. (Click on the image below to watch a short movie)

Astronomers are very glad that the gas giants have moons -- especially the big, bright ones -- because by measuring the orbital properties of these moons, we can deduce the mass of the planets. How? By a slight alteration of Kepler's Third Law. You remember it, right?

But if we study objects orbiting around another body, like Jupiter, and continue to use the same units for period and semi-major axis, we need to make a small addition to the formula:

• pick one satellite -- I recommend Europa or Ganymede
• figure out the period of the satellite, in days
• measure the radius of the satellite's orbit, in tick marks

Then, convert your measurements to the proper units:

Finally, you can use Kepler's Third Law to compute the mass of Jupiter. The result will be in solar units: the ratio of Jupiter's mass to the mass of the Sun.

#### A ring for every giant

Everyone knows that Saturn is surrounded by beautiful rings even a small telescope in the backyard will show them clearly.

Image taken by Cassini, courtesy of NASA/JPL-Caltech/Space Science Institute/G. Ugarkovic

But did you know that Jupiter has rings, too? They just aren't as big or as bright. The picture below, for example, was taken by the Galileo spacecraft as it flew through the shadow of Jupiter. A look back towards the Sun shows the faint, thin rings scattering light into the shadow.

Image courtesy of NASA, JPL, Galileo Project, (NOAO), J. Burns (Cornell) et al.

Jupiter's rings are due to tiny dust particles which are blasted off the surface of its inner moons by meteor impacts.

Uranus' rings were first noticed in 1977, when astronomers aboard NASA's Kuiper Airborn Observatory. The astronomers measured the brightness of a star as Uranus slowly moved past it. They noticed several short dips in brightness -- occultations -- before and then after the planet blocked the star.

Image taken from Physics Today, June 1977 based on data in Millis, Wasserman and Birch, Nature 267, 330 (1977)

These rings are very faint and very thin, as a closeup taken by Voyager 2 in 1986 attests.

Image courtesy of NASA/JPL

Neptune hid its rings very well. In the early 1980s, astronomers looked very hard for occultations which might reveal such rings, and found some evidence but the definitive proof was not obtained until Voyager 2 swept past Neptune in 1989. These rings are also very thin, and very faint .

Image courtesy of NASA/JPL

. but they present a new twist: the particles in the rings aren't distributed uniformly, but in CLUMPS in some places.

Now, did you notice that word I used just a moment ago? I wrote the particles in the rings. How do we know that the rings are made of particles? Couldn't they be solid sheets of icy material?

Well, one way we know the answer is that, in the past few decades, we have spacecraft flying past the rings. Some of the pictures they have taken provide clear evidence that the rings are made of millions and billions of tiny little particles, not solid sheets.

Images of Saturn's F ring from Voyager 1 (left) and Cassini (right) courtesy of NASA/JPL

Image courtesy of NASA/JPL/Space Science Institute

But a fellow named James Clerk Maxwell (does that name ring a bell?), way back in 1859, published a paper stating that the rings could NOT be solid sheets. He showed that only if the rings were made of tiny little particles, orbiting the planet individually, would the rings be stable over long periods.

Long before any spacecraft visited Saturn, there was an observational confirmation of Maxwell's claim. Taking a spectrum of Saturn and its rings showed a pattern of features like this:

Spectrum of Saturn and rings taken from Gingerich, Sky and Telescope, Nov 1964, p. 278

Notice how the lines are slanted in wavelength: each line is due to atoms which are absorbing light of one particular wavelength, but that wavelength can be modified by a Doppler shift if the atoms are moving.

Look at the lines in the upper half of the disk's spectrum: they shift to LONGER wavelengths as one moves from the center of the disk to the top edge, because that side of the disk is rotating AWAY from us. Now look at the absorption features of the rings on the same side of the planet.

If the rings are made of a solid sheet of material, the outer edges would be moving faster (away from us) than the inner edges, and so should be shifted to longer wavelengths.

No! They do not show fast motion away from us at larger radial distances. If anything, they show a slant the other way: towards slower motions at larger radial distances.

A solid sheet would rotate more quickly at the outer edges . but tiny particles orbiting independently would move more slowly at the outer edges.

Well, Mr. Kepler would explain it in terms of "sweeping out equal areas in equal times," and Mr. Newton would use terms like "gravitational force" and "inverse square law," but both would agree: objects orbiting Saturn will move more slowly if they are farther from the planet.

Remember what Zombie Feynman says:

The wonderful XKCD comic is drawn by Randall Munroe

#### Summary

• The gas giant planets are much larger than the Earth
• Their density is much lower than that of terrestrial planets -- roughly 1000 kg per cubic meter, compared to roughly 5000 kg per cubic meter.
• The gas giant planets are mostly gas -- hydrogen and helium
• Gas giant planets have many moons
• large moons close to the planet have orbits in the plane of the planet's equator, and rotate in the same direction (prograde). This suggests that they were formed at the same time as the planet, from the same gas cloud
• small moons far from the planet have orbits which are tilted relative to the planet's equator. Some rotate in the same direction, others in the opposite direction (retrograde). This is evidence that they may be captured asteroids

Celestia is a free software program that allows you to fly through the Solar System and view planets and moons from any vantage point.

## Introduction to neutron stars

Welcome to my neutron star page! I need to emphasize that the stuff I have here represents my opinions, and errors aren't the fault of those patient pedagogues who tried to cram this information into my head. I'll try to indicate when there is a dispute in the community, but I won't always be successful, so don't use only this page to study for your candidacy exams! For those with serious interest in neutron stars and other compact objects, an excellent reference is "Black Holes, White Dwarfs, and Neutron Stars", by Stuart Shapiro and Saul Teukolsky (1983, John Wiley and Sons).

For those who want a quick intro to selected cool things about neutron stars and black holes, check out a poster I made for a science fair at the University of Chicago. If you'd like more detail about quasi-periodic oscillations in particular, I wrote a pedagogical review based on my summer school lectures in Dubna, Russia, in August 2004. Here are the Postscript and PDF documents.

• The basics
• Neutron star formation
• Neutron star internal structure
• Neutron star thermal and spin evolution
• Isolated neutron stars (including pulsars)
• Accreting neutron stars (e.g., X-ray bursters)
• Classical gamma-ray bursts
• Soft gamma-ray repeaters

## Getting started on neutron stars

At these incredibly high densities, you could cram all of humanity into a volume the size of a sugar cube. Naturally, the people thus crammed wouldn't survive in their current form, and neither does the matter that forms the neutron star. This matter, which starts out in the original star as a normal, well-adjusted combination of electrons, protons, and neutrons, finds its peace (aka a lower energy state) as almost all neutrons in the neutron star. These stars also have the strongest magnetic fields in the known universe. The strongest inferred neutron star fields are nearly a hundred trillion times stronger than Earth's fields, and even the feeblest neutron star magnetic fields are a hundred million times Earth's, which is a hundred times stronger that any steady field we can generate in a laboratory. Neutron stars are extreme in many other ways, too. For example, maybe you get a warm feeling when you contemplate high-temperature superconductors, with critical temperatures around 100 K? Hah! The protons in the center of neutron stars are believed to become superconducting at 100 million K, so these are the real high-T_c champs of the universe.

All in all, these extremes mean that the study of neutron stars affords us some unique glimpses into areas of physics that we couldn't study otherwise.

## So, like, how do we get neutron stars?

At the very high pressures involved in this collapse, it is energetically favorable to combine protons and electrons to form neutrons plus neutrinos. The neutrinos escape after scattering a bit and helping the supernova happen, and the neutrons settle down to become a neutron star, with neutron degeneracy managing to oppose gravity. Since the supernova rate is around 1 per 30 years, and because most supernovae probably make neutron stars instead of black holes, in the 10 billion year lifetime of the galaxy there have probably been 10^8 to 10^9 neutron stars formed. One other way, maybe, of forming neutron stars is to have a white dwarf accrete enough mass to push over the Chandrasekhar mass, causing a collapse. This is speculative, though, so I won't talk about it further.

## The guts of a neutron star

Anyway, imagine starting at the surface of a neutron star and burrowing your way down. The surface gravity is about 10^11 times Earth's, and the magnetic field is about 10^12 Gauss, which is enough to completely mess up atomic structure: for example, the ground state binding energy of hydrogen rises to 160 eV in a 10^12 Gauss field, versus 13.6 eV in no field. In the atmosphere and upper crust, you have lots of nuclei, so it isn't primarily neutrons yet. At the top of the crust, the nuclei are mostly iron 56 and lighter elements, but deeper down the pressure is high enough that the equilibrium atomic weights rise, so you might find Z=40, A=120 elements eventually. At densities of 10^6 g/cm^3 the electrons become degenerate, meaning that electrical and thermal conductivities are huge because the electrons can travel great distances before interacting.

Deeper yet, at a density around 4x10^11 g/cm^3, you reach the "neutron drip" layer. At this layer, it becomes energetically favorable for neutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons. As the density increases, you find what has been dubbed the "pasta-antipasta" sequence. At relatively low (about 10^12 g/cm^3) densities, the nucleons are spread out like meatballs that are relatively far from each other. At higher densities, the nucleons merge to form spaghetti-like strands, and at even higher densities the nucleons look like sheets (such as lasagna). Increasing the density further brings a reversal of the above sequence, where you mainly have nucleons but the holes form (in order of increasing density) anti-lasagna, anti-spaghetti, and anti-meatballs (also called Swiss cheese).

When the density exceeds the nuclear density 2.8x10^14 g/cm^3 by a factor of 2 or 3, really exotic stuff might be able to form, like pion condensates, lambda hyperons, delta isobars, and quark-gluon plasmas. Here's a gorgeous figure (from http://www.astroscu.unam.mx/neutrones/NS-picture/NStar/NStar-I.gif) that shows the structure of a neutron star:

Yes, you may say, that's all very well for keeping nuclear theorists employed, but how can we possibly tell if it works out in reality? Well, believe it or not, these things may actually have an effect on the cooling history of the star and their spin behavior! That's part of the next section.

## The decline and fall of a neutron star

At the moment of a neutron star's birth, the nucleons that compose it have energies characteristic of free fall, which is to say about 100 MeV per nucleon. That translates to 10^12 K or so. The star cools off very quickly, though, by neutrino emission, so that within a couple of seconds the temperature is below 10^11 K and falling fast. In this early stage of a neutron star's life neutrinos are produced copiously, and since if the neutrinos have energies less than about 10 MeV they sail right through the neutron star without interacting, they act as a wonderful heat sink. Early on, the easiest way to produce neutrinos is via the so-called "URCA" processes: n->p+e+(nu) [where (nu) means an antineutrino] and p+e->n+nu. If the core is composed of only "ordinary" matter (neutrons, protons, and electrons), then when the temperature drops below about 10^9 K all particles are degenerate and there are so many more neutrons than protons or electrons that the URCA processes don't conserve momentum, so a bystander particle is required, leading to the "modified URCA" processes n+n->n+p+e+(nu) and n+p+e->n+n+nu. The power lost from the neutron stars to neutrinos due to the modified URCA processes goes like T^8, so as the star cools down the emission in neutrinos drops sharply.

When the temperature has dropped far enough (probably between 10 and 10,000 years after the birth of the neutron star), processes less sensitive to the temperature take over. One example is standard thermal photon cooling, which has a power proportional to T^4. Another example is thermal pair bremsstrahlung in the crust, where an electron passes by a nucleus and, instead of emitting a single photon as in standard bremsstrahlung, emits a neutrino-antineutrino pair. This has a power that goes like T^6, but its importance is uncertain. In any case, the qualitative picture of "standard cooling" that has emerged is that the star first cools by URCA processes, then by modified URCA, then by neutrino pair bremsstrahlung, then by thermal photon emission. In such a picture, a 1,000 year old neutron star (like the Crab pulsar) would have a surface temperature of a few million degrees Kelvin.

But it may not be that simple.

Near the center of a neutron star, depending on the equation of state the density can get up to several times nuclear density. This is a regime that we can't explore on Earth, because the core temperatures of 10^9 K that are probably typical of young neutron stars are actually cold by nuclear standards, since in accelerators when high densities are produced it's always by smashing together particles with high Lorentz factors. Here, the thermal energies of the particles are much less than their rest masses. Anyway, that leaves us with only theoretical predictions, which (as you might expect given the lack of data to guide us) vary a lot. Some people think that strange matter, pion condensates, lambda hyperons, delta isobars, or free quark matter might form under those conditions, and it seems to be a general rule that no matter what the weird stuff is, if you have exotic matter then neutrino cooling processes proportional to T^6 can exist, which would mean that the star would cool off much faster than you thought. It even appears possible in some equations of state that the proton and electron fraction in the core may be high enough that the URCA process can operate, which would really cool things down in a hurry. Adding to the complication is that the neutrons probably form a superfluid (along with the protons forming a superconductor!), and depending on the critical temperature some of the cooling processes may get cut off.

So how do we test all this? We expect that after a hundred years or so the core will become isothermal (because it is then superfluid), and we can estimate thermal conductivities in the crust, so if we could measure the surface temperatures of many neutron stars, then we could estimate their core temperatures, which combined with age estimates and an assumption that all neutron stars are basically the same would tell us about their thermal evolution, which in turn would give us a hint about whether we needed exotic matter. Unfortunately, neutron stars are so small that even at the 10^6 K or higher temperatures expected for young neutron stars we can just barely detect them. Adding to the difficulty is that at those temperatures the peak emission is easily absorbed by the interstellar medium, so we can only see the high-energy tail clearly. Nonetheless, ROSAT has detected persistent X-ray emission from several young, nearby neutron stars, so now we have to interpret this emission and decide what it tells us about the star's temperature.

This ain't easy. The first complication is that the X-ray emission might not be thermal. Instead, it could be nonthermal emission from the magnetosphere. That could carry information of its own, but it makes temperature determinations difficult basically, we have to say that, strictly, we only have upper limits on the thermal emission. Even if it were all thermal, we need to remember that we only see a section of the spectrum that is observable by an X-ray satellite, so we could be fooling ourselves about the bolometric luminosity. In fact, some early simulations of radiation transfer through a neutron star atmosphere indicated that a neutron star of effective temperature T_eff would yield far more observed counts than a blackbody at T_eff. Thus, a blackbody fit would overestimate the true temperature. These simulations used opacities computed for zero magnetic field. Thus, especially for low atomic number elements such as helium, there weren't any opacity sources at 500 eV (where the detectors operate), so in effect we would be seeing deeper into the atmosphere where it was hotter. Such simulations may be relevant for millisecond pulsars, which have magnetic fields in the 10^8 G to 10^10 G range.

Most pulsars, though, have much stronger fields, on the order of 10^12 G. In fields this strong, the binding energies of atoms go up (as mentioned before, the ground state binding energy of hydrogen in 10^12 G is 160 eV), meaning that the opacity at those higher energies rises as well. Thus, the X-ray detectors don't see as far down into the atmosphere, and the inferred temperature is less than in the nonmagnetic case. The details of the magnetic calculations are very difficult to do accurately, as they require precise computations of ionization equilibrium and polarized radiative transfer, and these are nasty in strong fields and dense, hot, matter. It seems, though, that when magnetic effects are included a blackbody isn't too bad an approximation. Stay tuned.

So what does all this mean with respect to neutron star composition? Yep, you guessed it, we don't have enough data. If you squint and look sideways at a graph of estimated temperature versus age, you might convince yourself that there is some evidence of rapid cooling, which wouldn't fit with the standard cooling scenario. But, unfortunately, the error bars are too large to be definite. We really need a large area detector that can pick up more stars. Features in the spectra would be nice, too, but at the moment that's just a dream. In the meantime, here's some recent data, plotted against several representative cooling curves that make various assumptions about the internal composition (this graph is from www.physik.uni-muenchen.de/sektion/suessmann/astro/cool/:

Neutron stars rotate very rapidly, up to 600 times per second. But how are they spinning when they are born? They may be born rotating very fast, with periods comparable to a millisecond (although evidence is ambiguous). After that, they spin down ever after because of magnetic torques. This seems to be supported by the fact that some of the youngest pulsars, such as the Crab pulsar (33 ms) and the Vela pulsar (80 ms) have unusually short periods. After a pulsar is born, its magnetic field will exert a torque and slow it down, with typical spindown rates of 10^-13 s/s for a young pulsar like the Crab.

Although overall the tendency is for isolated pulsars to slow down, they can undergo very brief periods of spinup. These events are called "glitches", and they can momentarily change the period of a pulsar by up to a few parts in a million. The effects of glitches decay away in a few days, and then the pulsar resumes its normal spindown. In current models of glitches, the superfluid core and normal crust are presumed to couple impulsively, and since the crust had been spun down by the magnetic field while the superfluid kept rotating at its original rate, this coupling would speed up the crust, leading to the observed spinup. It is very difficult to treat this process from first (nuclear) principles, because the critical angular velocity difference at which the crust and superfluid finally couple depends sensitively on various ill-determined properties of neutron superfluids, and since these properties aren't directly accessible by experiments we may have to be satisfied by our current phenomenological description. Incidentally, the glitch should also heat up the crust, and late in the lifetime of the neutron star heating by rotational dissipation can actually become a significant source of heat and affect the temperature evolution.

Fine, so that's an isolated neutron star. If the star has a companion, it can accrete from the companion and have its rotational frequency altered that way. If the companion is a low-mass star, say half the mass of our Sun or lower, accretion tends to proceed by Roche lobe overflow (more on that later). This type of flow has a lot of angular momentum, so the matter forms a disk around the star. The radius of the inner edge of the disk is determined by the strength of the magnetic field the stronger the field, the farther out it can control the accretion flow (for a given accretion rate). The star then (more or less) tries to come to equilibrium with the Keplerian angular velocity of the matter at the inner edge of the accretion disk. This means that neutron stars with relatively small (10^8 to 10^9 Gauss) magnetic fields can be spun up to high frequencies, and this is the accepted picture of how we get millisecond pulsars.

If the companion of the neutron star is a high-mass star (over 10 solar masses) instead, then the matter that makes it onto the neutron star goes in the form of a low angular momentum wind. Therefore, the neutron star isn't spun up to such high frequencies in fact, some pulsars that are in high-mass systems have periods longer than 1000 seconds. The process of wind accretion is a very complicated one, and numerical simulations of the process push the limits of computers. It appears that, in some circumstances, a disk may form briefly around the neutron star, only to be dissipated and replaced by a disk going the other way. One barrier to understanding this kind of accretion is that, even with today's computers, high-resolution 3D simulations just aren't feasible now, so we have to derive what insight we can from good two-dimensional calculations.

## Misanthropic (aka isolated) neutron stars

This changed dramatically in 1967, due to serendipity and the diligence of an Irish graduate student by the name of Jocelyn Bell. Bell and her advisor, Anthony Hewish, were working on radio observations of quasars, which had been discovered in 1963. Bell and some other graduate students constructed a scintillation array for the observations, then she got down to examining the charts of data produced (she had to analyze the miles of charts by hand, since this was in the days before powerful computers!). One day she noticed a bit of "scruff" that appeared on the charts every second and a third. The scruff was so regular that she first thought it must be artificial. However, careful checking showed that indeed the signal was extraterrestrial, and in fact that it must be from outside the solar system. This source, CP 1919, was the first radio pulsar to be discovered.

The discovery initiated a storm of activity that has still not abated. A number of other pulsars were discovered, including one in the Crab Nebula, site of a famous supernova in the year 1054 that was observed by Chinese, Arabic, and North American astronomers (but not recorded, as far as we know, by Europeans). Within a year or so of the initial discovery, it became clear that (1) pulsars are fast, with periods known in 1968 from 0.033 seconds (the Crab pulsar) to about 2 seconds, (2) the pulsations are very regular, with a typical rate of change of only a second per ten million years, and (3) over time, the period of a pulsar always increased slightly.

With this data, it was realized quickly that pulsars had to be rotating neutron stars. With certain exceptions that don't apply in this case, if a source varies over some time t , then its size must be less than the distance light can travel in that time, or ct (otherwise the variation would be happening faster than the speed of light). Thus, these objects had to be less than 300,000 km/s times 0.033 seconds, or 10,000 km, in size. This restricts us to white dwarfs, neutron stars, or black holes. You can get a periodic signal from such objects via pulsation, rotation, or a binary orbit. White dwarfs are large enough that their maximum pulsational, rotational, or orbital frequencies are more than a second, so this is ruled out. Black holes don't have solid surfaces to which to attach a beacon, so rotation or vibration of black holes is eliminated. Black holes or neutron stars in a binary could produce the required range of periods, but the binary would emit gravitational radiation, the stars would get closer together, and the period would decrease , not increase (and would do so very quickly, too!). Pulsations of neutron stars typically have periods of milliseconds, not seconds. The only thing left is rotating neutron stars, and this fits all of the observations admirably. Here's an animated gif of a pulsar.

There have now been more than 1000 radio pulsars discovered, with periods from about 1.4 milliseconds to more than 5 seconds. Their discovery is considered one of the three most important astronomical discoveries in the latter half of the twentieth century (along with quasars and the microwave background), and in part for his role in the discovery of pulsars Anthony Hewish shared the 1974 Nobel Prize in physics.

## Social (aka accreting) neutron stars

If the companion star has less than the mass of our Sun, the mass transfer occurs via Roche lobe overflow. If part of the companion star's envelope is close enough to the neutron star, the neutron star's gravitational attraction on that part of the envelope is greater than the companion star's attraction, with the result that the gas in the envelope falls onto the neutron star. However, since the neutron star is tiny, astronomically speaking, the gas has too much angular momentum to fall on the star directly and therefore orbits around the star in an accretion disk. Within the disk, magnetic or viscous forces operate to allow the gas in the disk to drift in slowly as it orbits, and to eventually reach the stellar surface. If the magnetic field at the neutron star's surface exceeds about 10^8 G, then before the gas gets to the stellar surface the field can couple strongly to the matter and force it to flow along field lines to the magnetic poles. The friction of the gas with itself as it spirals in towards the neutron star heats the gas to millions of degrees, and causes it to emit X-rays. Some characteristic dimensions of this sort of system are displayed in the figure.

Here, from wwwastro.msfc.nasa.gov/xray/openhouse/ns/, is a cartoon of the inner region where the neutron star's magnetic field controls matter:

Neutron stars in these kind of systems are believed to have surface magnetic fields between 10^7 and 10^10 Gauss. This means that the accreting gas can spiral very close to the neutron star before it is grabbed by the magnetic field. At such a close distance, the orbital frequency is very high (hundreds of Hertz), so the neutron star is spun up rapidly. As mentioned earlier, this is how we think we get millisecond pulsars. Those millisecond pulsars, by the way, are extremely stable rotators the best are at least as stable as atomic clocks! There have been suggestions that using millisecond pulsars as cosmic clocks could tell us about all sorts of exotic things, such as the presence of a background of gravitational radiation left over from the Big Bang.

Another fun phenomenon associated with neutron stars that have low-mass companions is X-ray bursts. These typically last a few seconds to a few minutes, and have a peak luminosity nearly a hundred thousand times our Sun's luminosity. The model for these bursts is that as hydrogen and helium is tranferred to the neutron star from the companion, it builds up in a dense layer. Eventually, the hydrogen and helium have been packed in a layer so dense and hot that thermonuclear fusion starts, which then converts most or all of the gas into iron, releasing a tremendous amount of energy. This is the equivalent of detonating the entire world's nuclear arsenal on every square centimeter of the neutron star's surface within a minute! Some of these binaries can be amazingly close to one another. Here's an artist's conception (from heasarc.gsfc.nasa.gov/Images/exosat/slide_gifs/exosat18.gif) of one particularly extreme case, that of 4U

1820-30, which has a binary period of just over eleven minutes! Too bad the distances are in miles.

If the companion to the neutron star has a mass between one and ten times our Sun's mass, the mass transfer is unstable and doesn't last very long, so there are few objects in this category.

If the companion to the neutron star has a mass more than about ten times our Sun's mass, the companion naturally produces a stellar wind, and some of that wind falls on the neutron star. The neutron stars in these systems have strong magnetic fields, around 10^12 Gauss (similar to typical isolated pulsars). At field strengths this high, almost all the accreting gas is forced to flow along field lines to the magnetic poles. This means that the X-rays primarily come from the resulting hot spots on the poles. It also means that if the magnetic axis and rotation axis of the star aren't co-aligned, the radiation sweeps past us once per rotation and we see X-ray pulsations. These systems are therefore called "accretion-powered pulsars", to distinguish them from the "rotation-powered pulsars" that Jocelyn Bell discovered.

For some recent results on accreting neutron stars, check out a poster from a science fair for grownups held at the University of Chicago.

## What the @#\$% makes gamma-ray bursts?

Loosely speaking, gamma-ray bursts are, well, bursts of energy that appear mostly in gamma rays and come from outside the Earth. The flux at earth is between 10^-8 erg/cm^2/s and 10^-3 erg/cm^2/s, the duration of the bursts is between 10 ms and 1000 s, and the photons typically have energies between 100 keV and 2 MeV, although energies down to 5 keV and up to 18 GeV have been seen from some bursts. The flux as a function of time varies from burst to burst, but often a spike within a burst follows the "fred" profile (fast rise, exponential decay). Here's an animated gif showing a simulation of a burst as we'd see it on a map of the Galaxy (left) and its brightness as a function of time (right). All in all, gamma-ray bursts are extremely heterogeneous, so it is tough to extract characteristic behaviors that would lead to easy classification (see a typical time profile for a GRB).

Can we at least tell how far away gamma-ray bursts are? Until recently, the answer was "no", not with any certainty. From the early 1970s it has been apparent that gamma-ray bursts come from all parts of the sky with approximately equal probability. Since other aspects of gamma-ray bursts (such as the fast rise time [ research page