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Supernova

In Supernovae by Brian Koberlein0 Comments

Last time I wrote about how a special type of variable star known as a Cepheid variable could be used to determine galactic distances out to about a hundred million light years. To determine greater distances we need another useful tool. This turns out to be a special type of supernova known as Type Ia.

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Supernova light curve. Source: Berkeley Lab

A Type Ia supernova has a unique light curve. In other words if you measure its luminosity as a function of time, its brightness decays in a very particular way. This is because the energy it gives off is dominated by the radioactive decay of Nikel-56 to Cobalt-56 to Iron-56. As a result all Type Ia supernova have the same decay of brightness over time. This light curve is in fact how we identify them as Type Ia rather than some other type of supernova.

The other interesting aspect of these supernova is that they all have an absolute magnitude of about -19.3. This means we can measure their apparent magnitude and use their absolute magnitude to determine their distance. Observations from the Hubble telescope have measured Type Ia supernova more than 10 billion light years away. As a result we can measure the expansion very precisely. So precisely that we now know the universe is accelerating.

The light curves of these supernova also allow us to prove that the red shift we observe in distant galaxies is really due to their motion away from us, and not due to some unknown physics. When we observe the curves distant supernova, we find that they have the same shape, but decay more slowly. The supernova appears slowed down because of its rapid motion away from us. This time dilation effect is exactly what we would expect for a supernova that’s racing away from us.

Now we just have to figure out why it’s accelerating.

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Cepheid Variables

In Stars by Brian Koberlein1 Comment

A while ago I wrote about how you can use depth perception (in astronomy we call it parallax) to measure the distance of nearby stars. While this works well, it only works if the stars are closer than about 1500 light years. So how do we measure more distant objects, such as nearby galaxies which are millions of light years away? For that we use an interesting type of star known as a Cepheid variable.

Cepheid variables are stars that vary in brightness over a period of days. The first such star to be observed was Delta Cephei in 1784, hence the name. For nearby Cepheids, we can determine their distance via parallax. We can also determine their apparent magnitude, and given their distance we can determine their absolute magnitude. I’ve written about the relation between apparent brightness and distance earlier.

It turns out there is a linear relationship between the average brightness of a Cepheid variable star (its luminosity) and the period at which its brightness varies. In the figure below I’ve plotted the luminosity of some Cepheid stars vs their period. You can see there is a nice linear relation between them.

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Brightness vs period for Cepheid stars.

What this means is that if you determine the period of a Cepheid variable you can calculate its absolute magnitude. By measuring its apparent magnitude you can calculate its distance. From the Hubble telescope we have observations of Cepheid variables in nearby galaxies. From this we can measure galactic distances up to about 100 million light years.

So by using parallax we can determine the distance of nearby stars. We can also prove the Cepheid variable relationship. From the Cepheid relationship we can determine distance to nearby galaxies. For more distant galaxies we have to use a different trick involving supernovas, but that is a story for another time.

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Echo of the Big Bang

In Cosmology by Brian Koberlein0 Comments

Last time I wrote about the Hubble constant, and how observations show the universe is expanding. Of course if the universe is expanding it must have been smaller in the past. We can use this idea to trace the history of the universe back to a point when the universe was a hot, dense fireball known as the big bang. Our simple calculations put that point about 14 billion years in the past. More accurate calculations put the age of the universe at 13.75 billion years.Read More

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Hubble’s Constant

In Cosmology by Brian Koberlein16 Comments

One of the more interesting astrophysical discoveries of the 20th century is the fact that the universe is expanding. The result was so unexpected that even Einstein discarded its prediction within general relativity. Einstein went so far as to introduce an extra constant in his equations specifically to prevent an expanding universe model. He would later call it his greatest blunder.

But how do we know the universe is actually expanding? For this we need to use the handy-dandy Doppler effect. You might remember that the observed color of light can be effected by the relative motion of its source. If a light source is moving toward us, the light we see is more bluish than we would expect (blue shifted). If a light source is moving away from us, the light is more reddish (red shifted). The faster the source is moving, the greater the shift.

We have measured this color shift for lots of stars, galaxies and clusters. We’ve also determined their distances (exactly how will be a post for another day). If we plot a graph of the distance of galaxies and clusters versus their redshift we find something very interesting. I’ve plotted such a graph below, and you can see there is almost a linear relationship between distance and redshift.

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Distance vs speed for galaxies.

This means galaxies are not simply moving at random, as you would expect in a stable, uniform universe. Instead, the more distant the galaxy the faster it is moving away from us. This relation between distance and speed is the same in all directions, which means the universe seems to be expanding in all directions.

Since this relationship is linear, you can fit this data to a line. The slope of the line is known as the Hubble constant, named after Edwin Hubble, who was one of the first to observe this relationship. When I did a simple linear fit to the data (the dashed line), I got a Hubble constant of 68.79 km/s per megaparsec. This is in the range of the accepted value.

Of course if the universe is expanding, then it must have been smaller in the past. If we assume the universe expands at a constant rate, then we can trace its size back in time to a point where the universe would have zero volume. In other words, the universe has a finite age, and it began very small, very dense (and therefore very hot). We call that starting point the big bang. If you do the math, the age of the universe is simply the inverse of the Hubble constant. Given our value, this puts the age of the universe at about 14.5 billion years. More accurate calculations put the age at 13.75 billion years.

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Rotating Stars

In Stars by Brian Koberlein0 Comments

I’ve been posting about stars lately. Yesterday I talked about how to build a better model star. So far, however, I’ve assumed the star wasn’t rotating. Usually this isn’t a problem since many stars rotate fairly slowly. Our sun, for example, has a rotational period of about 25 days (though it varies a bit by latitude). At that speed you can usually ignore its rotation. But some stars such as Regulus rotate very quickly. These stars rotate so fast that they bulge out along their equator. Of course this raises an interesting question: what is the fastest rate a star could rotate?Read More

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Connected

In Chemistry by Brian Koberlein2 Comments

The most common elements in our solar system are hydrogen, helium, oxygen, carbon, and nitrogen. Hydrogen makes up roughly 91% of our solar system and helium makes up a bit less than 9%. All the other kinds of elements add up to less than 2 out of every 1000 atoms in our solar system. Hence the joke that the astronomer’s periodic table has three elements: hydrogen, helium, metal.

The “metal” elements of the top five (oxygen, carbon and nitrogen) aren’t numerous overall, but if you pick any 10 “metal” elements in the solar system, about 6 will be oxygen, 3 carbon, and 1 nitrogen.

But here’s where it get’s interesting. About 63% of your atoms in your body are hydrogen. The rest of your body consists of “metals”. If you pick any 10 “metal” elements from your body, about 6 will be oxygen, 3 carbon, and 1 nitrogen. Since helium is a noble gas it doesn’t react much with other atoms chemically.

In other words, the ratio of elements in your body roughly corresponds to the ratio of useful chemical elements in the solar system.

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Star Light, Star Bright

In Astronomy by Brian Koberlein0 Comments

When we look at stars in the night sky, it is clear that some stars are brighter than others. When early astronomers started measuring the brightness of stars, they used a designation known as apparent magnitude. Early on, apparent magnitude was as basic as “These stars look the brightest, so we will say they are magnitude 1. Those are the next brightest, so they are magnitude 2.” and so forth. As we got better at measuring stellar brightness, the process was formalized, but the basic idea is still the same. The brighter the object, the smaller its magnitude. We can even carry it into negative numbers for planets and the Sun. For example, the maximum magnitude of Jupiter is about -1.6, while the Sun has a magnitude of about -27.Read More

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Building a Better Star

In Computation by Brian Koberlein1 Comment

In an earlier post I talked about a very simple model of a star consisting simply of a mass of hydrogen and helium held together by gravity. The simple model ignored some important stellar properties such as the fact that stars radiate light and undergo nuclear fusion in their cores. So it wasn’t surprising that our model predicted a core temperature for the sun that was too cool by a factor of 100. But even this simple model demonstrated that the temperature and pressure of the sun is high enough to undergo nuclear fusion.Read More