Science Clock Series: Part I

For Christmas my parents got me a novelty clock with scientific references for the numbers which I put up in my office. It's a nice clock, although this was the best picture I could get of it:

Now, since there are a lot of different scientific references on this clock I decided to write a mini-series on them, each post focusing on one of the numbers. Although I'm familiar with nearly all of them there are a few that I myself need to look up, so it'll be a learning experience for me as well. I'll be explaining as many of the scientific concepts that come up as I can for those who aren't familiar with them.

Today I'm going to start with number one:

\[\rho\ \text{of}\ \text{H}_2\text{O}\ (\text{g/cm}^3\ \text{at}\ 4^\circ\text{C})\] The Greek lower-case letter \(\rho\) (rho) is traditionally used to represent density in chemistry; H\(_2\)O is water, made up of two hydrogen atoms and one oxygen atom. The g/cm\(^3\) notation means grams per cubic centimeter, so the whole expression means “the density of water in grams per cubic centimeter at four degrees Celsius,” which refers to one.

Why it equals one is rather interesting. Fundamentally it equals one by definition; water is such an important and ubiquitous substance (it makes up 65-70% of the human body, covers 70% of the Earth's surface, etc.) that it was chosen such that the mass of one cubic centimeter of water was equal to one gram (or equivalently one gram of water occupies one cubic centimeter), so that the density of water is exactly one by definition. Thus, you can immediately tell if a substance is more or less dense than water at a glance by seeing whether its density is greater or less than one. If a substance's density is less than water it will float in water; if greater, it will sink. Sodium, for example, has a density of 0.968 g/cm\(^3\), or 96.8% that of water, meaning that sodium will just float on water. (Or at least, it would if it wasn't reacting so incredibly fast with water to produce hydrogen and igniting it in powerful explosions.) Magnesium, with an atomic number merely one higher than sodium, has a density of 1.738 g/cm\(^3\), 70.38% more dense than water, so magnesium would sink in water.

However, there's a wrinkle with this whole scenario that the critically-minded among you may have been wondering about: it turns out that the density of a substance varies with temperature. For most substances, the density decreases as the substance gets hotter, and increases as it gets colder. The reason for this is that greater temperature means greater average energy on the molecular level, which translates into higher average molecular speed, which tends to lead to increased molecular spacing and thus the same amount of mass taking a slightly larger area. Typically the changes in density are fairly small for liquids and solids, larger for gases.

As I mentioned, most substances increase in density as the temperature decreases, and this is mostly true for water; however, it has a slight hiccup as it approaches its freezing point. Rather than decreasing monotonically as the temperature decreases to 0\(^\circ\)C, the density of water reaches a minimum at 4\(^\circ\)C, then begins to increase slightly as it approaches its freezing point.

This behavior is unusual, thought not entirely unique; there are a few other substances that display similar quirks. However, in water's case, this little quirk is quite important for life on Earth. Because of this quirk, ice floats on liquid water, which is highly unusual (most solid substances sink in their liquid forms). Ice is a pretty good insulator, so ice forming on the surface of lakes helps keep the water beneath it from freezing more, leaving liquid regions underneath throughout the winter where fish and other creatures can survive. And when spring comes, the ice floats on the surface of the water where it can be melted by the Sun, rather than sitting out of reach on the bottom of lakes and rivers.

This quirk of density is but one of the many ways water is a very unique substance (one reason it was chosen to define density), but that isn't the focus of this post which is already getting a bit long. Next time we'll take a look at something from nuclear physics! Click here to jump directly to it.

Supernova Remnants, and the Pulsars that Light Them

Last week I showed you a picture of what happens to small stars (those less than ten times more massive than our Sun) when they run out of fusible hydrogen in their core. Today, let's take a look at what happens to a big star.

Upon running out of hydrogen to fuse, large stars initially proceed very similarly to their less weighty brethren. They begin to fuse the helium produced by hydrogen fusion into heavier elements such as carbon, oxygen, and neon, but unlike smaller stars they have enough mass and gravitational force in their cores to continue. Neon gets fused into heavier elements such as silicon, magnesium, and calcium, slowly working up the periodic table until the star starts making iron in its core. Iron is an interesting element because its nucleus has the highest binding energy per nucleon of any element. (Though certain isotopes of nickel have virtually the same binding-energy that iron does.) What this means, practically, is that you cannot get any energy from iron by either fusion or fission, either by fusing it into more massive elements or by splitting it apart.

Once a star arrives at iron in its core, it's done. It can't squeeze any more energy out of its core, so all that is left supporting the star against its own great weight is electron degeneracy pressure in a slowly-growing iron-nickel core. Electron degeneracy pressure is a quantum mechanical effect with no real analog in classical mechanics. Simply put, electrons exert pressure because two fermions (a class of particle of which electrons, protons, and neutrons are a member) cannot be in the same place and the same quantum mechanical state at the same time. Squeezing them together causes all the low-energy states to be taken, so the electrons vigorously resist any further compression, which would require large amounts of energy to raise electrons into high-energy states. However, there is a limit to how much pressure electrons can exert; if the mass of the core exceeds the Chandrasekhar limit of about 1.38 solar masses, electron degeneracy pressure catastrophically fails and the core collapses in on itself.

At this point, if the star is less than about 20 solar masses there is only one mechanism that can save the star from collapsing into a black hole: neutron degeneracy pressure. Similar to electron degeneracy pressure but involving neutrons, the star's core collapses into a neutron star, a sphere of neutrons packed as tightly as an atomic nucleus and about the size of a city.

As the core collapses into a neutron star, the star's outer layers fall inward tremendously fast, at speeds up to 23% of the speed of light. The neutron star at the center, however, is already packed as tightly as it possibly can be, so the infalling material rebounds off the core in a colossal shockwave to produce what we see as a supernova.

(There is a lot more going on at the same time, of course – supernovae are incredibly fascinating events where relativity and quantum mechanics are both in play, and I'm giving you merely the barest overview of all the processes happening.)

If the star in question started off heavier than about 20 solar masses, even neutron degeneracy pressure will be unable to support the core and nothing in the universe can prevent it from continuing to collapse into a black hole. However, I'm going to focus on neutron stars in this post because the picture I have for you today contains one. The story behind this particular supernova is ancient and varied, so settle in...

The story starts about a thousand years ago, in Anno Domini 1054, when a new star appeared in the constellation Taurus. As was customary, Chinese and Japanese astronomers noted the appearance of a "guest star" and recorded its location. It was also apparently observed by as least one person in the Arabic world. This star was apparently bright enough to be seen in the daytime for a period of several weeks, after which it slowly faded over a period of about two years and finally disappeared, whereupon it dropped out of history.

In 1731 a mysterious nebula (one of the first discovered telescopically) was discovered just off the tip of one of the horns of Taurus by one John Bevis. In 1758, while searching for the return of Halley's comet, Charles Messier stumbled upon this nebula and initially mistook it for his quarry. After watching it for a few weeks he realized that it wasn't moving, and came up with the brilliant idea to publish a catalog of objects that looked like comets but weren't, so that other amateur comet hunters wouldn't be fooled as he had. Thus, this nebula became the first object on what would become his now-famous list of not-comets: Messier 1.

In 1844, almost a hundred years later, the nebula was sketched for the first time by William Parsons, 3rd Earl of Rosse, whose love of astronomy and independently wealthy nature led him to build the largest telescope in the world at that time ("the Leviathan of Parsontown", 6 feet in diameter). His sketch reminded him of a crab, and so he gave our nebula the whimsical name the Crab Nebula. It remained a popular object of observation with astronomers, both amateur and professional.

In 1921 the American astronomer Carl Lampland noted changes in the Crab Nebula which implied a small size for it. In the same year, another astronomer demonstrated that the nebula was expanding. Several astronomers noticed its proximity to the "guest star" of 1054, but nothing was made of it until 1928 when the venerable Edwin Hubble definitively proposed that the nebula be associated with the star. However, it wasn't until later, when the theory behind supernovae had been worked out, that Nicholas Mayall showed that the Crab Nebula was nothing less than the remains of the supernova that exploded into the sky nearly 900 years earlier.

Although the association of the nebula with a supernova was now clear, it wasn't until the 1960's that neutron stars were first predicted by Franco Pacini. A few short years later, in 1968, a neutron star was detected in the center of the Crab Nebula, which made it both the first neutron star ever known and a shining confirmation of Pacini's hypothesis. It also explained why the nebula was so much brighter than a 900-year-old supernova remnant was expected to be.

The neutron star that lurks at the center of the Crab Nebula – known as the Crab Pulsar – is a fascinating beast by terrestrial standards. It is about 25 kilometers (about 15.5 miles) across, and makes a complete rotation every 33.08471603 milliseconds – 30 times a second! As the neutron star spins, it sends out a constant stream of electromagnetic radiation all across the electromagnetic spectrum (including visible light) from both poles of its extremely powerful magnetic field. The axis of its magnetic field is not the same as its rotational axis (much like the Earth, though a bigger offset), and as it spins around it sends off a powerful beam that appears to "blink" on and off as seen from Earth, much like the beam from a lighthouse. The neutron star is thus known as a pulsar, a portmanteau of pulsating star.

This electromagnetic energy being given off comes from the rotational energy of the Crab Pulsar, which is slowly slowing down by 38 nanoseconds per day. The energy being given off along with the star's powerful magnetic field (thousands of times more powerful than the Earth's) being spun through the Crab Nebula 30 times a second causes it to light up. Electrons are accelerated to nearly half the speed of light and spiral along the magnetic field lines of the pulsar, giving off synchrotron radiation as they do, which create a blueish glow visible in the center of the Crab Nebula in long exposures.

Now, after all this background, I suppose I should show you the picture you no doubt read this post for. I hope you can now better appreciate just how amazing this object is, even if my picture cannot do it justice. Here it is, the Crab Nebula:

The Crab Nebula, Messier 1, in Taurus.

While the Crab Pulsar itself is quite invisible in a small telescope such as the imaging telescope, you can easily see the remnant of that titanic explosion 958 years ago. Within that shell of gas exist fantastic filaments and mysterious structures, brought about by electrons powerfully accelerated to relativistic speeds by the pulsar's magnetic field. Despite being around 6,000 light-years away it is persistently the strongest source of X-rays and gamma rays from outside the solar system. The central neutron star itself is a sphere of ultra-dense matter more massive than the Sun compressed into an area smaller than New York city and spinning over 30 times a second. This matter (commonly called "neutronium") is so dense that a single thimble-full would weigh over 100 million tons. I could go on and on at length about how fascinating this single member of the group of objects know as pulsars are, but you get the idea.

I hope this post has given you a sense of the wonder and excitement I get when I study astronomy and physics. Learning more about the incredibly varied denizens of our universe never fails to amaze and astound me, and I enjoy nothing more than bringing that feeling to others. If this post made you stop and think at all, then I will feel I have succeeded. A hui hou!