Blackbody Radiation

The first question is, what exactly is a blackbody? Briefly, it’s a hypothetical object that absorbs all the radiation directed at it, without reflecting any (so it would appear black in the visible range, as well as every other part of the electromagnetic spectrum). A blackbody also radiates energy “perfectly”, which is to say that it emits the maximum amount of radiation possible for its temperature, and that it radiates energy equally in all directions — or as physics would say, it radiates isotropically.

Now that that’s cleared up, we move onto the second question: why do we even care about blackbodies in astronomy? The answer is that many cosmic objects can be modeled as blackbodies because they are close enough to being perfect blackbodies that we can approximate, even though perfect blackbodies are thought to only exist in the realm of theoretical physics. Planets, stars, the universe itself…

Wait, the universe?

Indeed.

In 1989, NASA launched the Cosmic Background Explorer satellite to, well, explore cosmic background radiation (they’re very creative with naming things, it seems). The Far Infrared Absolute Spectrophotometer was designed to measure the Cosmic Microwave Background, and it found that the CMB matches a blackbody curve for T=2.725 K almost perfectly! This might not seem like much of an accomplishment, but the FIRAS data is very strong evidence supporting the “hot Big Bang” theory — which basically states that the universe used to be really hot, until it expanded and cooled off.

COBE FIRAS data for CMB

Credit: NASA JPL at Caltech

Radiation curves show how much energy is given off by a blackbody at varying wavelengths. In the graphic below, you can see that the curves climb sharply, peak, and then decay away towards zero as the wavelength increases (however, they will never actually reach zero, since blackbodies radiate energy at all wavelengths).

So what can these radiation curves tell us?

Firstly, we can see that the peaks are at different wavelengths for blackbodies of different temperatures — the peak for a higher-temperature blackbody has a shorter wavelength than the peak for a cooler blackbody. This explains why we see cooler stars as reddish in color and hotter stars as bluish, but more on that later in a separate post. We can also see that as the temperature increases, so does the total energy emitted (the area under the curve), so a star at 6000 K will emit more energy than one at 4000 K.

Radiation Curves

Credit: University of Michigan

At this stage, you may be thinking, it’s all well and good that radiation curves can tell us things, but is there a way to be quantitative about how much the peak wavelength shifts, or how much energy is emitted? For the answers, we must once again venture into the dark depths of mathematics, which is unfortunately unavoidable in astrophysics. Remember that units must always match and that significant figures count.

You may remember from one of our history posts that Rayleigh and Jeans tried to describe the shape of a radiation curve, but they ran into the “ultraviolet catastrophe” when they got to short wavelengths. Wien tried to do the same thing, but his equation ran into problems with long wavelengths. Then Planck did some thinking and combined the Rayleigh-Jeans Law and Wien’s Approximation into Planck’s Radiation Law, which works at all wavelengths. This equation also allows us to calculate the amount of energy given off at a certain wavelength by a blackbody at a certain temperature.

Neither of us have ever needed Planck’s Radiation Law for a test (and one of us has a testwriter who would be the type to try and include it), so we won’t give you a practice problem for it, but the equation is included above just in case.

Wien’s Law, also known as the Wien Displacement Law, allows us to calculate the peak wavelength from the temperature or vice versa. From this equation, it’s easy to see that higher temperatures result in shorter peak wavelengths, and lower temperatures result in longer peak wavelengths.

Ex. Assume the temperature of the Sun is 5800 K. What is the Sun’s peak wavelength?

Answer: 5.0 * 10^-7 m

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The Stefan-Boltzmann Law, derived independently by Josef Stefan and Ludwig Boltzmann, allows us to calculate the area under the curve described by Planck’s Radiation Law. This is the flux of the blackbody — the power per area. You can see that a small change in temperature will cause a large change in flux, since temperature is raised to the fourth power.

The Stefan-Boltzmann Law can also be found in an alternate form that calculates the TOTAL energy emitted by the star or other blackbody.

(The geometrically astute will realize that 4πr^2 is the formula for surface area of a sphere, and that we are simply multiplying “power per area” by area to get total power.)

Ex. Assume the temperature of the Sun is 5800 K. What is the Sun’s flux?

Answer: 6.4 * 10^7 W/m^2

Ex. What is the luminosity of the Sun? Its radius is 6.9599 * 10^8 m.

Answer: 3.9 * 10^26 W

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TL;DR — Blackbodies are objects that absorb and radiate energy “perfectly”. Many astronomical objects (most importantly stars) can be modeled as blackbodies. Radiation curves can tell us a lot about the objects they come from — Planck’s Radiation Law lets us plot the shape of the radiation curve, Wien’s Law lets us calculate the peak wavelength, and the Stefan-Boltzmann Law allows us to calculate the flux and/or the luminosity.

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Sources and links for further reading:

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Spectra

Spectra (plural of spectrum) were mentioned throughout this blog, and they will be mentioned many more times.  It is the best kind of spectrum, the electromagnetic.  They can be used to study stars, DSOs, and even the planets and moons!  Since stars can emit all sorts of light they are also split into classes based on their spectra.  Let’s get right into this extremely useful tool, but be warned that there will be some math.

Atoms have quite the history and must be understood to understand those lovely spectra since all atoms produce different spectra.  The atom below is the Bohr model, named after Niels Bohr, of a Hydrogen atom.  Also, the electron paths are called orbitals or shells.

Simply this (astronomyonline.org physics concepts-the atom).

There are essentially seven energy levels, numbered one to seven, represented as n=# (n is known as a quantum number) and referring to the orbitals, such that one is the closest to the nucleus and seven is the furthest.  A relationship exists showing that as an electron gets further from the nucleus it gains energy, usually coming from a photon or from heat.  When an atom is in the ground state all of its electrons are in the lowest possible energy level, while when it is in an excited state at least one electron is in a higher energy level from the lowest possible.  This is known as jumping energy levels, but please don’t think that this involves a child that drinks caffeine and gets all energetic and jumpy.  (In fact, it is probably recommended to not give children caffeine but that’s another story.)  Moving on, ionization can be more specifically defined as when the amount of energy the electron absorbs is greater than the allowed energy of all orbits.  Atoms want to be fairly stable, unlike jumpy little kids, which is why all sorts of things form, from salt to water.  So, an atom that is excited ultimately will have the electrons jump back down to the ground state.  But to have gone to a higher energy level the electron had to gain energy, meaning that for it to drop to a lower energy level, it has to emit energy.  That is where spectra come from.

Basically this. Sadly if the atoms produce gamma rays it won’t turn people into the Hulk. In fact, if atoms produce gamma rays it is recommended to go far far away and to hide (astronomyonline.org physics concepts-the atom).

Spectral lines can be produced at specific wavelengths from atoms.  Electrons that absorb energy must either absorb all or none of it since this energy comes in packets called photons.  Therefore, it is true that each and every single atom that has a different structure MUST absorb and emit different amounts of energy.  In essence, this process starts with absorption of energy and ends with emission of energy.  Atoms have certain lines which show optimally in certain temperature ranges, so this is yet another hint they can show about stars.  Spectra can be split into three types: continuous spectrum, emission lines, and absorption lines.

A continuous spectrum is basically a rainbow, all colors of light.  This is the prime, beautiful example of a spectrum that anyone has seen in nature.  We noted in the history section that it took many people to explain the effects seen in the continuous spectrum as it is normally seen and the dark lines seen by Fraunhofer. Notably Kirchoff did this, and the rules are:

1. A luminous solid or liquid emits a continuous spectrum of all wavelengths.  It has no lines in it.

2. A rarefied luminous gas emits light whose spectrum shows bright lines.  These lines are called emission lines.

3. If the light from a luminous source passes through a gas, the gas may extract certain specific energies from the continuous spectrum.  We then see dark lines where the energy has been removed.  These dark lines are called absorption lines.

Three types of spectra

Very colorful (NASA spectra introduction from Imagine the universe)!

To explain its usefulness in stars, certain elements will show prominently in the spectral lines since stars are insanely hot.  In general, certain objects show more emission lines or absorption lines depending on their composition, and every single aspect to spectral lines can be studied to learn immense amounts of information about stars.  They are made of plasma, but since that is ionized gas the 2nd and 3rd rules apply.

Since Hydrogen is the most abundant element in the universe, a variety of people developed series to explain its various spectral lines.  It was understood that series existed to show different energy wavelengths produced as emission lines by Hydrogen.  The major series consist of the Paschen series in the infrared, the Balmer series in the visible, and the Lyman series in the ultraviolet.  For the Lyman series the shortest transition seen is called Lyman-alpha (n=2 to n=1) at the 122 nm line.  For the 103 nm line (n=3 to n=1) it is called Lyman-beta.  For the Balmer series the 656 nm line is Balmer-alpha or more commonly H-alpha (Hα).  After this the 486 nm line (n=4 to n=2) is H-beta.  Hopefully a trend is shown that the highest nm line transition is named alpha, and then after it goes beta, gamma, etc.

It is from Wikipedia, but do use other sources with Wikipedia when doing research.

Just to make this colorful, we will also show what the Balmer series would look like to us, but it wouldn’t be fun to just have Hydrogen.  Let’s show all the elements!

The wavelengths are measured in Angstrom which is 10^-10 meters, but besides that it’s colorful (ucolick.org under spectra lab)!

From here we must depart to the land of math as the mathematical definition can better show our knowledge of spectra.  If a letter is used once it will not be repeated unless to make a note about it or to change units, so if it isn’t mentioned look to one of the last equations mentioned.  Remember UNITS MUST ALWAYS MATCH.

Going from the Hydrogen series there is a formula known as the Rydberg formula.  It was discovered around the same time the Balmer series was first discovered.  It is highly important because it can be used to calculate the wavelength for energy transitions from emission spectra of Hydrogen, the most abundant element in the universe.  We will show how the formula works.

First, it is important to know the two major equations relating to light.  One is λν = c.  Where:

  • Lambda or λ is wavelength in meters
  • ν or nu (pronounced “new”) is frequency in wave crests or cycles per second
  • c is the speed of light in a vacuum or 2.998 x 10^8 m/s

The other equation is the de Broglie equation E=hν.  Where:

  • E is energy in joules
  • h is Planck’s constant as 6.626 x 10^-34 Joule*seconds.

Using the above equation and substituting for frequency it can be represented as E=c*h/λ.  Both the speed of light and Planck’s constant can be found to have more significant figures, but

For calculating the energy change of an electron:

\begin{displaymath}<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
{\mit\Delta} E = E_0\left(\frac{1}{n_f^{\,2}}-\frac{1}{n_i^{\,2}}\right).<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
\end{displaymath}

Where:

  • $n_i$ is the initial quantum number
  • $n_f$ is the final quantum number
  •  Eo is the initial energy or the energy of the groundstate

For the energy change of the electron if it is negative then the electron should emit a photon of frequency$\nu=- {\mit\Delta}E/h$.  If the energy is positive then the electron should absorb a photon of frequency $\nu={\mit\Delta}E/h$.  This is exactly what leads into the Rydberg formula.  Since $\lambda^{-1}=\nu/c$, the Rydberg formula when substituting is:

\begin{displaymath}<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
\frac{1}{\lambda} = R\left(\frac{1}{n_f^{\,2}}-\frac{1}{n_i^{\,2}}\right),<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
\end{displaymath}

Where:

    Lambda is in nanometers

   $n_i$ and $n_f$ are the same, but it is assumed in the Rydberg formula that $n_f<n_i$ since it is used for emission lines of Hydrogen.  This gives the definition that the Lyman series is a transition to the ground state ($n_f=1$) releasing UV light, the Balmer series is a transition to the first excited state ($n_f=2$) releasing visible light, and the Paschen series is a transition to the second excited state ($n_f=3$) releasing infrared light.

    And the Rydberg constant R:

With this now even you can relate energy, wavelength, and frequency all from spectra.  In fact, combined with the Doppler effect these equations can be used to analyze and see the composition, temperature, or presence of certain objects.

To finish, some jokes that hopefully will be amusing after we have shed light on yet another subject:

An electron sitting in a prison asked a second electron cellmate,”What are you in for?”

To which the latter replied, “For attempting a forbidden transition.”

Q: Why does hamburger have lower energy than steak?

A: Because it’s in the ground state.

Q: What happens when electrons lose their energy?

A: They get Bohr’d.

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TL;DR: Spectra are up there with one of the best tools to use to analyze objects in Astronomy.  Atoms can absorb specific wavelengths of light or emit specific wavelengths of light depending on their size and structure.  This produces spectral lines which appear on a spectrum of light, and this will be different for all atoms of different structure.  Since most of the objects being studied are made of atoms, we find that they produce spectral lines. Hydrogen has been studied extensively because it makes up so much of the universe, and the Rydberg formula helps us calculate hydrogen’s spectral lines.

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Sources and further reading:

 

Nuclear Reactions: Powering Stars

As we’ve said before (somewhere), stars produce energy through nuclear fusion, combining lighter elements to produce heavier elements. This is as opposed to nuclear fission, used in nuclear power plants here on Earth, which usually involves bombarding heavy elements with neutrons until they become unstable and decay into lighter nuclei, releasing energy in the process. The problem with using fission as an energy source is that it tends to produce some nasty radioactive byproducts along the way — not so with fusion, which is why achieving controlled fusion is one of the “holy grails” of science. But enough about the earth and our energy woes, we’re here to talk about stars.

First, we’re going to assume you’re familiar with the notation for nuclear isotopes, but if you’re not (or if you’ve forgotten), here’s a quick refresher. In normal nuclear notation, which is used in most of the diagrams below, the top number represents the number of nucleons (neutrons + protons), while the bottom number is the number of protons (aka the element’s atomic number). Isotope notation, which we are forced to use because of technical limitations, is simply the element’s name followed by the number of nucleons.

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Stars which are approximately the size of our Sun, or smaller, mostly use the proton-proton chain to produce their energy. This is the most basic of the nuclear fusion reactions that power stars.

Proton-Proton Chain

Credit: Windows to the Universe

First, two protons fuse into deuterium, a “heavy” isotope of hydrogen. One of the protons is converted to a neutron through beta-plus decay, causing a positron (a positively charged electron) to be released, as well as a neutrino. The deuterium then combines with another proton to form He-3 and release a gamma ray. Finally, two He-3 nuclei react to form a helium nucleus and two protons. And don’t forget about the positrons — they will collide with electrons and annihilate, releasing more energy.

Note that this is the so-called PPI chain, which takes place around 70% of the time. The PPII and PPIII chains contain further reactions, but in the end, all three branches of the proton-proton chain convert hydrogen into helium.

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Stars over ~1.3 M(sun) mostly rely on the CNO cycle for their energy because these more massive stars tend to have higher core temperatures, and the CNO cycle becomes much more effective at higher temperatures than the P-P chain. The name “CNO” refers to the three elements whose different isotopes drive the cycle.

CNO Cycle

Credit: Australia Telescope Outreach & Education

It starts with a C-12 nucleus, which combines with a proton to produce  N-13 and a gamma-ray photon. One of the protons in N-13 beta-decays into a neutron, spitting out a positron and a neutrino in the process. So now we have C-13, which fuses with a proton to form N-14 (and a gamma ray), and then another proton to form O-15 (and another gamma ray). A proton in O-15 beta-decays into a neutron, producing N-15 and ejecting another positron and another neutrino. N-15 combines with yet another proton…but this time, the nucleus splits apart into an alpha particle (He-4) and C-12.

And then the cycle starts all over again.

This is the simplest iteration of the cold CNO cycle, which is the type that generally powers stars (it’s termed “cold” because it takes place at relatively low temperatures). There are three other branches of the cold CNO cycle, all of which are relatively rare — a nucleus fails to emit an alpha particle and instead stays together as a heavier element, which is then used as a catalyst for further reactions. In the hot CNO cycles, taking place under conditions of higher temperature and pressure, certain nuclei capture protons before they can beta-decay, leading to a different series of reactions.

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The P-P chain and the CNO cycle both convert hydrogen into helium, which is all well and good for most of a star’s lifetime. But for most stars, the pressure and temperature at the core eventually rise high enough to ignite helium fusion.

Triple-Alpha Process

Credit: Australia Telescope Outreach and Education

Enter the triple-alpha process, which fuses together helium nuclei (aka alpha particles) into progressively heavier elements as shown in the diagram above. The triple-alpha process is extremely unlikely because Be-8 is extremely unstable, but under high enough temperature and pressure, Be-8 is created fast enough to continuously exist in a small amount. If Be-8 manages to fuse with another alpha particle before it disintegrates, stable C-12 is produced. The endpoint of the process is considered to be C-12 (which is three alpha particles fused together, hence the name), although stable O-16 and Ne-20 can be produced by smashing more alpha particles into the C-12 nuclei.

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Further nuclear reactions take place in stars above 8-11 M(sun). In the first stage, carbon burning, two C-12 nuclei react to form a variety of products, most often forming N-20 and spitting out an alpha particle. Neon burning involves Ne-20 either disintegrating into O-16 and an alpha particle, or capturing an alpha particle to become Mg-24. Then in oxygen burning, two O-16 nuclei fuse to form several products, most notably Si-28 and S-32. Finally, silicon burning repeatedly adds alpha particles to a silicon nucleus until it becomes Ni-56 (which will eventually decay into Fe-56). But when the star tries to fuse Ni-56 into Zn-60, energy is consumed instead of produced, and the core promptly collapses.

Elements heavier than iron are produced in supernova explosions through neutron capture processes, since neutrons are much easier to add to a nucleus than protons are. The S-process (slow) involves the capture of only one neutron at a time, which then beta-decays into a proton, producing a new element. On the other hand, in the R-process (rapid), many neutrons are captured at once, which then begin to beta-decay into protons.

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Even with all this talk of these different reactions, we still haven’t really explained how stars can even produce energy from nuclear fusion. The answer can be found in Einstein’s famous equation E=mc^2. In certain fusion reactions, the end product has slightly less mass than the sum of its components. This missing mass is termed the “mass defect” and it shows up because nuclei require slightly less energy per nucleon to bind themselves together as the number of nucleons increases. Well, at least up to iron — for elements heavier than iron, it actually takes more energy per nucleon to bind a nucleus together, which is why fusion reactions to form elements heavier than iron consume energy instead of producing it. The energy released through fusion reactions can be calculated through E=mc^2; while the yield from one reaction is small, the sheer number of atoms in a star makes the total quite significant.

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TL;DR — Sun-sized and smaller stars mostly produce energy through the P-P chain, which turns 6 protons into an alpha particle and 2 protons. More massive stars use the CNO cycle, which uses C-12 as a catalyst for a series of reactions that also turn hydrogen into helium. Stars that burn helium (which is most of them) do so through the triple-α process, which keeps smashing alpha particles together to form heavier elements. If the star is massive enough, elements up to iron can be produced; elements heavier than iron are produced in supernovae. The mass defect explains how stars produce energy through nuclear reactions.

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Sources and links for further reading:

What are stars?

A good question.  Are they like people?  They live.  They die.  They have populations and clusters.  Technically as Carl Sagan said “we are star-stuff.”  So people and stars are sort of similar.  But the main difference is that they are gigantic spheres of extremely hot plasma.  Okay, so not exactly the same thing, but they are still assuredly awesome.  One could even say stellar.

A star is a large amount of gas, mostly Hydrogen, and is held together by two forces that are essentially equal.  This is called hydrostatic equilibrium.  The name comes from fluid dynamics, where the only fluid, incorrectly, was thought to be water.  The first force is gravity.  On a large scale gravity has more importance and attracts this massive amount of gas together.  But with only gravity attracting the gas inwards there has to be an outwards force to create equilibrium.  This force comes from fusion.  We say fusion powers the Sun because it releases insane amounts of energy and can create a radiation pressure that works outward against the force of gravity.  It has so much energy, it ionizes the gas and is the reason why stars are made of plasma.  The Sun and in fact the whole night sky is all thanks to fusion.

Stars have many qualities which will be discussed later, but an important aspect is that just like anything else they have a structure.  Here is the Sun:

Parts of a Star

If it could talk, it would probably be bragging how hot it is (even though it’s not that hot for a star) and that it is like an onion; it has many layers.

Stars have many shells or layers.  Fusion begins with fusing Hydrogen into a shell of Helium.  In general, as fusion occurs, heavier nuclei sink towards the core or center and form these shells from convection.  The core therefore has the most energy since it takes more energy for higher level reactions to occur and it is the central area of energy production.  But going to the outside of the star it begins to cool down.  This occurs at first through radiation, the transfer of energy by light.  The light travels quickly through a Radiative zone where the light is emitted or scattered.  Then the star transfers energy with its chief method of energy transfer, convection, the transfer of energy through a fluid to balance temperature.  This occurs in the plasma of the star in the Convection zone.  On the Sun, hot fluid rises and moves out of the star, while cold fluid sinks, which is why it balances in temperature and cools down going towards the outside of the star.  Note that energy leaves a star by radiation, not convection, since energy from a star leaves with emitted light travelling through space, and space is not a fluid or solid.

The photosphere is similar to the radiative zone, but it more specifically refers to the presence of light and energy created. It represents the area where the light makes a star become opaque.  The chromosphere is similar to the convection zone and is where the colors of the Sun are mostly seen.  It technically can’t be seen except during a solar eclipse or with a light filter since the light of the photosphere over powers it.  The chromosphere also contains spicules, spikes of gas that eject out to the next part of the Sun, the corona.  This is similar to the Sun’s atmosphere and is made of plasma too.  A mystery still keeping scientists up at night is that the corona is hotter than the surface of the Sun.  But it isn’t just a little hotter.  To compare temperatures, the core is about 15-16 million K, the photosphere, closer to the surface, is about 5700 K, the chromosphere can be 5000-4400 K, and the corona is a million K.  Iron detected in the atmosphere could be the cause, but scientists are unsure.

The Sun also has a magnetic field just like the Earth.  We know it has one due to something known as the Zeeman Effect.  Atoms can produce light associated with magnetism when excited or ionized.  When this light is released lines of light at certain wavelengths can be seen, and these lines can be seen to split due to magnetism.  The magnetic field is most likely due to the movement of plasma which creates an effect similar to a dynamo, which uses motion to rotate a coiled magnet and through some awesome science this creates electricity.  On the Sun it’s a bit different, but theoretically the plasma convecting should be conductive and extremely magnetic, therefore the massive amount of rotation on the Sun  should create a magnetic field.

Many things that occur on the Sun involve this magnetic field, the following are examples.  Sunspots are relatively cool (emphasis on “relatively” since they can be 3000-4500 K) and appear dark.  The magnetic field shifts around a lot since there is so much plasma moving around.  This creates differential rotation (parts rotating differently) in the Sun.  It can get so twisted up it can become like a rubber band, curling up and piercing the outside of the Sun.  This creates a spot where the magnetic field leaves and reenters the Sun.  There is an 11 year sunspot cycle because the magnetic field of the Sun flips like the Earth’s (just a lot more often since it is humongous) and can be traced to have minima and maxima.  Solar winds are streams of charged particles shot out of the Sun which can use the energy of the corona to escape the Sun’s gravity.  These can be the cause of geomagnetic storms, which can affect satellites and technology on Earth or be a possible danger for astronauts.  Coronal Mass Ejections or CMEs are an explosion where all that coiled up magnetic force throws out material into the Corona.   Solar flares are sudden, intense variations in brightness in the Sun.  This results in massive CMEs.  Both CMEs and solar flares are caused by sunspots and are associated with solar winds, but whether CMEs and solar flares are associated is still being researched.  Some of these can be characterized as a solar prominence.  No, not how the Sun is so awesome it is important, famous, or noticeable (though, that should be an alternate definition as the Sun does do that), it is something which can cause a loop-like shape starting in the photosphere and entering out into the corona.

If the Sun could talk here it may say how loopy it is.

There are multiple measurements for stars using the Sun.  They are useful since the Sun is a fairly average star, and it acts as a good basis for comparison.  There is the Solar mass (about 2X10^30 kilograms, fitting the mass of the Earth about 30,000 times), Solar luminosity (about 4X10^26 W, an average lightbulb is 100 W…it’s fairly obvious that the Sun is brighter), Solar radius (sadly not an easy 1 million km, but it is about 700,000 km; able to fit the Earth about 110 times), and age of the Sun (currently about 4.5-5 billion years, which is really long…there is really no other way to put it)

Next is the naming of stars.  Sadly, if you are looking to “buy a star” and name it (perhaps for romantic reasons) you will be disappointed.  At least, if you expect it to mean anything.  Most stars have been cataloged and therefore buying a name for it is the same thing as pointing to a star and making up a name for it, except you’d have to pay for it.  Ancient Astronomers would generally name stars for a relationship to a constellation to make them easier to remember, but now there are catalogs and designations based on the imaging used, coordinates, and properties of the object being studied.  There is the Bayer designation, naming a star based on the constellation and brightness related to a Greek letter (so, the brightest star in the constellation Taurus would be called Alpha Tauri, but ancient Astronomers would call it Aldebaran which is sometimes used as a common name).  But now there are modern catalogs, the major ones being the Messier (as mentioned, M), New General Catalog (NGC), and Index Catalog (IC).  There are many more catalogs, but in general cataloging stars is extremely important.  They allow Astronomers to know where they are looking, what they are looking at, and how to revisit or calculate positions of an object that is being looked for.

One of the most interesting things to all this: these processes and more occur in stars in the whole universe.  As Carl Sagan said, “Billions upon billions”, referring to how the universe has billions and billions of galaxies, each having billions and billions of stars, all functioning more or less the same way.  In fact, the same processes that occur with light bulbs and power plants on Earth occur on the magnificent scale of the Universe, and that is nothing short of mind-blowing.

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TL;DR — Stars are amazing.  They act as prime examples of how mechanics demonstrated on Earth can be applied on extremely large scales.  Stars develop from large clouds of Hydrogen which condense from gravity, and radiation from fusion repels this to maintain a star.  This makes magnetic fields and pretty much a giant ball of plasma.  Stars have been studied for 1000’s of years, and still have many mysteries to be found, which reveal more about the Universe as we study them.

The Doppler Shift

WARNING: This post involves copious amounts of semi-difficult math. If you don’t like the realm of radicals and fractions below radicals, I suggest you stay away from the math portions of this.

Most of you know of the existence of a phenomenon called the Doppler Shift (or Doppler Effect, they’re the same thing). You know, when a train moves towards you, the sound it makes is higher, when it moves away, the sound is lower. How high or low the sound is to you is referred to as the “pitch”. There’s another version of the Doppler Shift in relation to light and astronomy. It’s called the relativistic Doppler Shift.

The relativistic Doppler Shift works the same way the regular Doppler Shift does, only it’s with colours instead of pitch. When the train moves away from you, the pitch drops because the frequency of the waves that carry sound are dropping, and therefore the pitch goes down. (For those of you who have never taken physics, a lower frequency means a lower pitch. A higher frequency means a higher pitch.) In the same way, if an object moves towards you, it appears blue because of a shorter wavelength, and if it is moving away from you, it appears red because of a longer wavelength.  In light, a smaller wavelength means you go towards the blue end of the spectrum, and a larger wavelength means you go towards the red.

Basically, everything here is relative. The relative motion of the source (i.e. some star a few dozen light years away) makes the wavelength in front of it to look relatively decreased, and the wavelength behind it to look relatively increased. And when wavelengths appear decreased or increased, the colour appears different. That’s called shifted wavelength. (Definition of shifted wavelength: How short or long the wavelength appears to be from the vantage point of the observer.)

However, the relativistic Doppler Shift can only be observed from objects moving at very great speeds a great distance away—you aren’t going to see a relativistic Doppler Shift from a car. From Earth, the only objects that have a relativistic Doppler Shift are celestial objects. Stars, deep sky objects (DSOs), distant galaxies—you can see Doppler Shifts from those. The Doppler Shift is important for figuring out just how fast a DSO is moving away or toward us. That’s why you should learn this for astronomy.

The math for the Doppler Shift is annoying and long and involves a bunch of fractions and radicals. There are five equations: the blue-shift wavelength equation, the blue-shift frequency equation, the red-shift wavelength equation, the red-shift frequency equation, and the velocity equation. Four of the five equations look incredibly similar to one another.

And there you have it. A crash course in the relativistic Doppler Shift. It’s a total of 666 words. Not too bad, eh?

And this, kids, is how the Doppler Shift works.

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TL;DR

It’s not complicated. Really.

Light and Matter

Light is both a particle and a wave. Why? Because physics says so.

Light is a Wave/Particle

Also, because the universe likes to screw with us. (Credit: Douglas Hofstadter)

Light acts both as an electromagnetic wave, and as particles called photons. For a long time, scientists thought light was just a wave, but experiments involving the photoelectric effect (this is what Einstein won his Nobel Prize for!) established that light acts like a particle too. In fact, wave-particle duality theorizes that waves sometimes act like particles and particles sometimes act like waves. We could call it an atomic example of a bipolar disorder, but that may take it too far.

After all, light is basically the only way we can truly explore the universe, since the distances are far too great for us to traverse. Assuming we could travel at the speed of light, it would take nearly a decade for a space probe to reach the nearest star and transmit information back to Earth, and it would take 50 000 years to travel to the nearest galaxy and transmit information back. Heck, human civilization hasn’t been around for 50 000 years, and it’s debatable whether we’ll survive the next one thousand without blowing ourselves up. But we can’t travel at anything close to the speed of light — the highest speed achieved by the Helios II solar probe, the fastest man-made object ever, is only a tiny fraction of the speed of light (about .00023 c) — so it would take many, many times longer.

Would it surprise you to know that astronomers use time travel on a regular basis? The distances involved in astronomy can be so astronomically huge that it takes light a very significant amount of time to reach us. So we see distant stars as they appeared thousands of years ago; they could have gone supernova in the meantime and we wouldn’t know until the light from the supernova reaches us. The most distant galaxies we can observe are seen as they would appear billions of years ago, nearly at the beginning of the universe. That’s right, light is a time machine.

It’s not just visible light, though. There’s radio waves, microwaves, infrared, ultraviolet, x-rays, and gamma rays, oh my!  But all these forms of radiation, along with our boring old visible light, are just part of the electromagnetic spectrum — all the fancy names are because scientists didn’t realize they were just naming different versions of the same thing.

Electromagnetic spectrum

The electromagnetic spectrum in all its glory.

And then there’s matter, which is stuff. You know, matter, made up of protons, neutrons, electrons, weird bosons (possibly of the Higgs variety)… It’s also mostly empty space, since atoms are basically a tiny speck of a nucleus and a whole lot of nothingness with a couple electrons zooming around in it. Yes, that means if you punch a brick wall, you are punching mostly empty space. We shouldn’t have to tell you this, but don’t try that at home. Please.

Matter can be converted into energy with perhaps the most famous physics equation of all time, E = mc^2, which is derived from Einstein’s Theory of General Relativity. Unfortunately, neither of the two astronomy geeks who write this blog understand relativity well enough to explain how exactly one would derive the equation. Suffice it to say that E = mc^2 works, and it is very relevant to stars, which release massive amounts of energy as they smash together nuclei and fuse elements into heavier elements.

Everyone knows that there are three states of matter — solid, liquid, and gas. Well, not exactly. Under the extreme conditions out there in the universe, matter can exist in all sorts of strange states, such as plasma or degenerate matter. Plasma is basically ionized gas, where electrons have been added or stripped away, turning regular atoms/molecules into ions. Degenerate matter is where plasma has been crammed into such a tiny space that it refuses to be compressed any further because all the “available” energy states fill up (Pauli Exclusion Principle). These two unusual states of matter are especially relevant to astronomy because stars are made of plasma, and white dwarfs and neutron stars are made of degenerate matter.

NGC 2440

The white dwarf at the center of this planetary nebula (the bright dot near the center) is made of electron-degenerate matter. Science Olympians who did Astronomy in 2012 should recognize this image.

But that’s just boring old regular matter. There’s also antimatter, and dark matter.

Antimatter is really just the opposite of matter. Regular matter is made of protons and electrons, while antimatter is made of antiprotons and antielectrons; regular subatomic particles are made of quarks, while antimatter subatomic particles are made of, you guessed it, antiquarks. A word of advice: if you ever meet your antimatter counterpart, do not high-five each other, as both you and anti-you will be annihilated in a blast of energy and leave behind nothing but a giant crater. (Being science geeks, the two of us have since been distracted by trying to figure out how big said crater would be…)

As for dark matter, we only know it exists because it has effects on regular matter, particularly on the galactic scale. We have absolutely no idea what the heck it is, but we wonder, is dark matter a very MACHO type of matter or is it just a WIMP? Yes, these are actual candidates for dark matter. MACHO stands for MAssive Compact Halo Object, and WIMP for Weakly Interacting Massive Particle — if you can’t tell, astronomers like to have fun with acronyms.

I do hope this post, shall we say, “shed a little light on the matter”.

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TL;DR — Astronomers use light, as well as other non-visible forms of electromagnetic radiation, to explore the universe. It even allows us to look back in time! Many interesting objects in astronomy are made of exotic states of matter, or perhaps not even made of ordinary matter.

Seven Minutes of Success

A lot of people who are involved with astronomy also work with robots, whether as part of Science Olympiad or on the side. So I want you to imagine the following scenario:

You are part of a team working on building a new robot. It needs to successfully complete a certain maneuver without any assistance from you or your partners at the time. But wait- the maneuver it has to make involves slowing to a stop from well over 10,000 mph. In just a few minutes.

And also landing on the ground.

After an eight month voyage.

Through space.

To MARS.

If you aren’t hiding behind the couch yet, you should be. But NASA stepped up to the challenge and said, “No big deal. We got this.”

It’s not THAT complicated…

NASA’s new Curiosity rover, which landed on Mars last night, has been in the works for over a year. For the past eight months, it’s been speeding through space towards the fourth planet, and last night it finally made its touchdown.

Don’t be fooled, though, NASA was scared out of its wits last night. Just to make everything even more challenging, the type of landing used by Curiosity had never been attempted in space before. Thus, NASA dubbed the landing “Seven Minutes of Terror.” We’re thinking NASA might have been thinking ahead to potential movie deals.

To give you an idea as to the extreme difficulty and the precision required with this project, just look at how happy NASA is when they hear (14 minutes after the landing) of its success:

While this landing will give us a great deal of new information about the red planet (Life on Mars-????????), it also represents the future of the United States space program. It might sound crazy calling an unmanned rover the flagship of the space program, but that’s exactly how it should be perceived. Let’s go back to last year.

The big news-making event involving NASA last year had nothing to do with discovery or exploration- it was the end of the space shuttle. The space shuttle was our ticket to send humans into space; without it, we have to rely on the Russians and commercial spacecraft for at least about five years. The loss of the space shuttle was taken as a big step back for the space program, but then, options were limited. NASA’s budget has taken a hit in recent years, and the government just doesn’t seem interested in space exploration.

The end of an era

We heard it everywhere: “The US will begin to fall behind in the space race.” China and Russia would take the lead and the US would become an inferior nation when it came to space exploration and development.

But let’s take a look at the Mars scoreboard: U.S.  7, The Rest of the World 0. The U.S. now has nine spacecraft on Mars, all but two operating for a substantial amount of time. (The other two failed during the landing. The Soviet Union sent three spacecraft to Mars; two failed during landing, one transmitted just 15 seconds before failing).

The U.S. is still leading the Space Race because the goal of the Space Race has changed. No longer is the objective to get people into space, into orbit, onto the moon. Now, the Race is less competitive- who can first develop the technology to explore the unknown, and to improve our way of life? The successful landing of Curiosity proves that the U.S. is still light years ahead (pun completely intended) of other countries in this area- great news for students thinking of going into aerospace and engineering or astronomy, but doubting NASA’s future.

So now we turn to NASA’s future- where to next? The popular idea is, of course, sending astronauts to walk on Mars. Yet I’m almost certain this isn’t the path NASA will choose to follow. Walking on Mars is still a reasonable minimum of twenty years away, and there are many logistical problems still to be solved. However, there are other options that could benefit human life even more.

Why not pay a visit to Saturn’s moon, Titan, or Jupiter’s moon, Europa? Both moons are some of the best chances to find life beyond Earth.  We’ve landed a probe on Titan, and it gave us an amazing photograph (seen at right)- the only picture of a planet or moon’s surface beyond Mars. There are already plans in the work to send orbiters to both moons, and sending a rover to either one would be an impressive feat- though it would be several years before that would be feasible, and several more years before any spacecraft would actually arrive at the moons.

Or, we could look at some options closer to home. While we don’t seem to be in any immediate danger from asteroids, asteroid detection and deflection technology might be worth looking into. We still haven’t found everything that’s out there, and there is a small possibility Earth could be hit by a sizable asteroid in the near future. The good news is, we’re working on this too. One of the brightest possibilities was called “Mirror Bees” and involved sending several dozen satellites to reflect sunlight at a spot on an asteroid to destroy it. (They actually worked better than nuclear warheads!) Lasers were later discovered to work better, so now they’re called “Laser Bees”.  And as great as that sounds, I just can’t shake the idea that these laser bees will turn against us and lead a terrifying robot rebellion.

This will be you

One final path NASA might choose to take could solve the energy crisis. Space based solar power isn’t a new idea, but we’re finally developing the technology to take advantage of a virtually unlimited source of energy: The sun. Collecting solar power in space is much more efficient than on Earth, but the current problem lies with transporting that energy back to earth. Once this problem is solved and the technology becomes cost-efficient, however, space based solar power could solve a lot of energy problems.

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NASA proved once again last night that America is at the forefront of developing new technology for space exploration. The potential for NASA moving forward into the future is sky-high (and beyond!). Perhaps President Obama put it best in his official statement: The successful landing of Curiosity – the most sophisticated roving laboratory ever to land on another planet – marks an unprecedented feat of technology that will stand as a point of national pride far into the future. It proves that even the longest of odds are no match for our unique blend of ingenuity and determination.”

Space enthusiasts like myself can rest easy knowing that the future of space exploration is in good hands. If NASA continues these feats, we very well may go Onward to the Edge within our lifetime. The landing of Curiosity last night through seven minutes of terror was one small touchdown for a rover, but one giant leap for space exploration.

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TL;DR: NASA scientists are awesome. You should send them a gift card.

Image credits: NASA (diagram), Wikipedia (shuttle, Titan, Curiosity), The Planetary Society (laser bees)

Video credit: Telegraph