Metallicity and Star Populations

No, star populations are not the number of stars in a specific galaxy or the universe or whatnot. No, it has nothing to do with numbers of stars. In fact, these “populations” are actually classes of stars.

To begin with, we need to discuss metallicity. As you (probably) know, stars are almost completely made up of hydrogen and helium. So any other element found in a star would be considered a “metal”. In astronomy, carbon, neon, and fluorine are all considered metals. (And also every other element not hydrogen or helium.) So when you study astronomy, you really must forget all those silly little things taught to you in chemistry class (assuming you have ever had a chemistry class before, of course). Metallicity is essentially the amount of a star that isn’t made up of hydrogen or helium, and the symbol for metallicity is generally Z.

Anyways, the amount of metal found in a star is its metallicity. And metallicity is also divided up into several classes (called populations), depending on the amount of metal in the star. And that, friends, is what a star population is.

There are three categories of metallicity: Population I, Population II, and Population III. Each population, respectively, has decreasing metallic content and increasing age (theoretically—I don’t think anyone has ever tried to go out and sample stuff from a star…). To make all this a lot clearer, I’m going to try to explain in the next few paragraphs.

First off, let’s talk about Population I stars. These are the young stars, having more metal than the other populations (because of the development of heavier elements over billions and billions of years). In a galaxy, they are usually located towards the centre of the galaxy, usually in the disk of the galaxy. For these stars, Z~0.02, and up to 0.03.

The next class is called Population II stars. They are the old stars, with very little metal (because they were formed in a time when heavier elements were nonexistent). They are found more at the outer edges of galaxies, significantly above or below the disk. The metallicity content of these stars is about Z~0.001. And since the kinematics, positions, and chemical compositions of Population I and II stars are different, they provide us with a wealth of information about the Milky Way.

Between Population I and Population II stars, we have the intermediate, or disk population. Those are the stars that just kind of loiter around somewhere in the galaxy, somewhat between the Population I and II stars. They have a medium amount of metal, and they just kind of float around the place. These are your average, every-day, middle-age stars. In fact, they are so average that they get a special name, just to make them feel better. Although sometimes, astronomers like to just put these stars in Population I or II categories, which personally I think is just idiotic. They don’t match the definition, in any case. Do note, though, that just like middle-aged people, they’re there…but the other people on either side of their age range are just as numerous. They don’t have a set metallicity or even a set range; they just are.

And then we have Population III stars. We don’t know if these exist. That’s right, folks, even the existence of this class of stars is purely theoretical. These are the stars that are thought to contain no metal at all. So their metallicity is essentially Z~0. Cool, huh? But the thing is…we’ve never found a Population III star. Those would have to have been formed right at the Big Bang, and with such high mass and energy, they would have burned out fairly (very) quickly. Theoretically, at the time of the big bang, there was only hydrogen and helium, with trace amounts of lithium and beryllium. There were no heavier elements, and apparently lithium and beryllium didn’t really make its way into the stars. So these stars contain just about no metal, are indefinably old, and are purely theoretical. My personal favourite, really. So if on a test they ask you “What population is <star>?”, don’t put Population III. They don’t exist (at least, not definitely).

Our galaxy is actually mostly Population I stars (assuming the classification of disk population into Populations I and II, of course), because Population II stars are very old and most of them have burned out. Really, the only Population II stars that are easily visible to the eye are the globular star clusters, and I’m sure that all of you have studied globular star clusters very extensively.

By percentage, our sun has a 1.8% of metals. But in metallicity, that’s apparently not relevant. The Sun is a standard of comparison for any other star’s metallicity (the sun’s metallicity being equal to 0). By using the metallicity calculations (which are underneath this paragraph), any star with a metallicity<0 is automatically Population II, and any star with a metallicity>0 is automatically Population I. (Again, this irritates me to no end because of the fact that there is a disk population.) Because we are egotistical gits, everything has to be based on our sun, so the range of metallicities in our galaxy ranges from -5.4 to 0.6. Bit skewed? Yes. Obviously, our sun is on the metal-rich side, and yet, we still call it “neutral”.

Then we have the calculations for metallicity. They are complicated, insane, and involve higher mathematics. If you have not taken Algebra 2 (or know what logs are), you might want to stay away from this section. It’s like the equilibrium constant stuff, just not quite as complex. But if you don’t know logs and enjoy torturing yourself greatly, go ahead and read this.

The measurement of metallicity actually comes from the amount of iron in the star. Not every bit of non-hydrogen/helium in the star, but simply iron. It serves as a basis for comparing the ratios of iron to hydrogen in relation to our sun, and it’s the general way to figure metallicity. Now, iron is not the most abundant metal in stars (or even close to it, really), but it’s among the easiest to measure with the technology that we have now. So since we decided to be lazy, this is what we get.

VERY IMPORTANT: The equation below is a RATIO of how much metal is in the star. It is the most commonly used form, but it is NOT a value. The value is what is in the paragraphs above. I hope that clears up any confusion.

Now, the general formula for deriving metallicity is this:

If all of you know the law of logs that states that  , then you can simplify that thing up there to:

which, by the way, is much, much more helpful to solve. The whole  thing is in fact not division, but actually a representation of the logarithmic ratio of the abundance of iron in a star in comparison to the Sun.  means the number of iron atoms in a given amount of volume, and  is the number of hydrogen atoms in a given amount of volume.

According to the age-metallicity relation, a higher amount of iron means it’s a younger star. However, the universe doesn’t like simple laws that are set in stone, and therefore has to make it more confusing. Because the age of a star is basically based on the amount of iron it has, the universe uses Einstein’s probability and statistics laws to make everything very misleading. For example, Type Ia supernovae (abbreviated as SN Ia) are responsible for the vast majority of iron production, and significant numbers of them don’t even appear until about 10,000,000,000 years after star formation begins. So there’s really not that much iron going around the interstellar medium. And even after the SN Ia events occur, it’s not going to mix evenly throughout everything. So essentially, one region may get lots of iron, and another region? Not so much. So even though the stars in both those regions are the same age, the stars in region 2 seem older. Bit problematic, right?

And that concludes metallicity and star populations. If you have any questions, you can (attempt) to email me.

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TL;DR – Metallicity is the metal content of a star (in astronomy, a metal is anything that’s not H or He). Stars are divided into populations based on their metallicity, with Pop I stars being metal-rich, Pop II stars being metal-poor, and theoretical Pop III stars having no metals at all. The equations for metallicity compare the amounts of iron and hydrogen in the star to the amounts in the sun (because we base everything off our own star). Metallicity doesn’t necessarily show the age of a star, since Type Ia supernovae scatter iron unequally throughout their surroundings.

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I like typing in British English. A lot. So if some things look misspelled…check to see if it’s the British spelling first before calling me out.

ALSO:

Q: How many astronomers does it take to change a light bulb?

A: What’s a light bulb?

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Spectral Classes and the H-R Diagram

We previously mentioned the development of spectral classification in our History posts, but now we can really understand the science behind it.

Edward Pickering and Williamina Fleming (you remember them, don’t you?) originally classified stars based on the strength of hydrogen spectral lines — stars with the strongest hydrogen lines were class A, the next strongest were class B, and so on through class N. Later, Antonia Maury started to rearrange Fleming’s spectral classes, and then Annie Jump Cannon further rearranged them into the modern order OBAFGKM, which orders stars by temperature. O-stars are the hottest, typically >30 000 K, while M-stars are the coolest at between 2000 K and 3500 K. These classes are each divided into ten subclasses 0-9; for example, the hottest F-stars are F0 and the coolest are F9.

Stellar Spectra

Credit: University of Arizona [click for full-size image]

Characteristic spectral lines:

  • O — relatively weak H; strong HeII, neutral He; Si IV; double-ionized N, O, and C.
  • B — stronger H; neutral He (max intensity around B2); ionized O, N , Ne, Mg, Si.
  • A — very strong H (strongest at A0); ionized metals (Fe II, Mg II, Si II, Ca II).
  • F — weak H; both ionized and neutral metals.
  • G — weaker H; neutral metals (Fe, Ca, Na, Mg, Ti), especially Ca II in hotter stars.
  • K — even weaker H; Ca II, neutral Ca; neutral metals; TiO in cooler stars.
  • M — very weak H, if visible at all; neutral Ca; molecules like TiO, VO, and CN.

As one can see in the image below, the relative strength of spectral lines depends heavily on a star’s temperature. Spectral line strength can be described by the combination of the Boltzmann and Saha equations (both rather complicated). Basically, as the temperature rises, more atoms will be able to elevate their electrons to higher energy levels and thus produce absorption lines. However, if temperatures are too high, the atoms will have absorbed enough energy to be ionized and will not have the necessary electrons to excite to produce absorption lines.

Temperature Dependence for Spectral Lines

Credit: KCVS at The King’s University College (Alberta, Canada)

It should be noted that there are more spectral classes than just OBAFGKM — here we present a brief survey of those you’re mostly likely to cross paths with in Astronomy. Classes L, T, and Y are reserved for stars/substellar objects with temperatures progressively cooler than 2000 K. Class W (or WR) indicates a Wolf-Rayet star, a supergiant whose powerful stellar winds have blown away most of the hydrogen in its atmosphere. Carbon stars, dying supergiants with a large amount of carbon in their atmospheres, are spectral class C. White dwarfs are classified as D, because they are made of degenerate matter. Objects like neutron stars and black holes aren’t given a spectral class, because they are stellar remnants rather than stars.

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However, our discussion of spectral classes merely serves as an introduction to the Hertzsprung-Russell diagram, which is perhaps the most single important graph-chart-diagram-thing that you’ll ever encounter in astronomy (a slightly idealized version is shown in the image below). The H-R diagram is named after Ejnar Hertzsprung and Henry Norris Russell; they discovered it independently after plotting the luminosity of stars against color or spectral type, both of which are proxies for the star’s temperature.

H-R Diagram

Credit: ESA

This H-R diagram has double axes, showing the link between temperature and spectral class, and between absolute magnitude and luminosity. The numbering on some of the axes does seem to be going the wrong direction, but by convention, high temperatures are on the LEFT and larger absolute magnitudes are towards the BOTTOM (this is partly due to the fact that the entire magnitude system is “backwards”). Alternately, the x-axis may be labeled in terms of the stars’ B-V index, but no matter, it’s still an H-R diagram.

The main sequence appears as a diagonal line across the H-R diagram, clearly showing the link between luminosity and temperature for these stars — actually, both are dependent on a third factor, but we’ll cover that later. Above the main sequence are giant stars, which are relatively cool but have swelled up enough to cause an increase in overall luminosity. Even further above that lie the supergiants, very large stars that are also extremely luminous. Below the main sequence lies white dwarf stars, which are dim but rather hot. They will eventually migrate to the lower right as they cool off.

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When Hertzsprung and Russell plotted their data, they found for classes G, K, and M, there were a wide range of stellar luminosities. Independently, they both decided to call the brighter stars “giants”, since for two stars of the same temperature, the more luminous one must also be larger.

This led to the development of the Morgan-Keenan spectral classification, which sorts stars by not only spectral class but also by luminosity class. Stars in luminosity classes I-V are progressively less luminous and smaller in size for their spectral class. The luminosity classes correspond to supergiants, bright giants, giants, subgiants, and dwarfs (NOT white dwarfs, just main sequence stars). Class 0 has been tacked on for incredibly luminous “hypergiants”, while on the other end of the luminosity spectrum, classes VI and VII used to designate subdwarfs and white dwarfs but have since fallen out of common usage.

To give a familiar example, the Sun is a G2V star — its spectral class is G2, so it is slightly cooler than the 6000 K of a G0 star, and it is a main sequence “dwarf” as indicated by luminosity class V.

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Perhaps most practically, H-R clusters can be used to determine the age of star clusters. Imagine that a cluster has just been formed, with stars of all masses. This forms a “perfect” main sequence (ZAMS, the Zero-Age Main Sequence) when the H-R diagram of that cluster is plotted. As the highest-mass stars end hydrogen core fusion, they migrate away from the ZAMS towards the red giant branch, and the H-R diagram for the cluster starts to form a hook shape. The point where the hook starts to diverge from the ZAMS is called the main-sequence turnoff point.

H-R Diagram Clusters

Credit: Mike Guidry, University of Tennessee (through Penn State University)

After pinpointing the main-sequence turnoff, we can now find the age of the cluster. The stars located right at the turnoff point have just reached the end of their main-sequence lifetime; therefore, by determining their ages, we can determine the age of the cluster as a whole. The main-sequence life expectancy of a star is approximately: T = 1/(M^2.5), where M is in solar masses and T is in solar lifetimes (1 solar lifetime ≈ 10 billion years).

As shown in the image above, young clusters like h + χ Persei have turnoff points towards the left of the main sequence, since only the most massive stars in the cluster have had time to evolve off the main sequence. Old clusters like M67 have turnoff points closer to the middle or right side of the ZAMS because less massive stars have also had time to evolve off the main sequence.

And thus concludes our explanation of spectral classes and the H-R diagram. We do hope it was…stellar.

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TL;DR — Stars are divided into spectral classes O, B, A, F, G, K,  and M (and several others that are less common), each of which is characterized by certain absorption lines. The absorption lines depend on temperature, so spectral class is also an indicator of temperature. The H-R diagram typically plots temperature against luminosity; the main sequence stretching across the diagram shows the correlation between greater luminosity and greater temperature. The Morgan-Keenan luminosity classes show how luminous a star is for its temperature. The age of a cluster can be determined through its H-R diagram, by seeing where the cluster stars are beginning to leave the main sequence.

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Sources and links for further reading:

Apparent/Absolute magnitude, Color Index

Before we begin, for those who didn’t see the About page, we’re sorry but we have to limit posts to one per week.  This is because we both have piles of schoolwork to do, but we will try to keep up with one post a week.

This post will involve more about light, as we said it’s quite important.  In fact, this post will discuss how we can use light to predict distances from Earth.  At this point, math should be expected, along with checking units and significant figures.  In fact, we will be introducing one of the most important equations for distance calculations in an Astronomer’s arsenal.

Now we go on the next part of our journey, to Greece of course, where we are joined by the man Hipparchus. He developed a system of apparent magnitudes (denoted as m), which determines how bright stars were by looking at them here on Earth.  For some reason he decided that it would be more logical to say that as the numbers decreased the stars became brighter, resulting in the scale ranging from m=1, the brightest stars, to m=6, the dimmest.  This was mainly because no highly accurate equipment was available, but this is still extremely important as it describes how objects would appear from an observer on Earth.  Originally the system was just based on naked-eye observations, but modern astronomers decided to fix it up.

Now the scale is logarithmic and compares ratios of apparent magnitudes for stars.  Apparent magnitude is now considered to be brightness or flux measured in Watts per square meter.  It was decided on this scale that 100 would correlate to a magnitude difference of m=5.  This should be emphasized as a difference since for the brightness ratio of  B1/B2 should be equal to the magnitude difference of m2-mwith the formula:

B2/B1=100(m1-m2)/5

Taking the log of both sides we get:

m1-m2 = -2.50 log(B1/B2)

With that we can show that when the brightness ratio equals 100 then we take log(100) which equals 2, multiplying by -2.50 to get -5.  But this still works since the scale shows that the object is brighter as the magnitude value decreases.  In addition, that means that if you were to measure between one magnitude it would be a factor of 100.4 which is equal to approximately 2.512 since it comes from 1001/5.  So, a 1st magnitude star would be 2.512 times as bright as a 2nd magnitude star, and 2.512or about 6.310 times as bright as a 3rd magnitude star.  Also, Hipparchus’s scale has had an increased range of magnitudes.  The Sun for example is now m=-26.83.

Next we need to establish how we can show radiant flux, denoted F, or those brightnesses.  Earlier we mentioned it as watts per square meter, which is exactly shown by a familiar manipulation using light and surface area of a sphere.  This is the inverse square law (we can call this brightness or flux, we will now be using F for flux):

F=L/(4πr2)

Now that we have explained how we can view objects with the unaided eye and defined brightness we have to show how to find the actual magnitudes of all objects.  How would this be done, though?  Astronomers decided to create a system of absolute magnitudes, denoted as M or Mv, which shows what the magnitude of stars and objects would be at a set distance of 10 parsecs.  This works since instead of having all sorts of objects with different actual magnitudes and different distances from the Earth an established sphere of points can be used to better show the magnitudes.  With that and the inverse square law in mind we can create a flux ratio to show how much the magnitudes would be from this set distance.  Again, 5 magnitudes separate the apparent magnitudes of two stars which would show a flux ratio of 100.  This is the very same brightness comparison formula we had earlier.  We can actually manipulate that into something called the distance modulus.  We can say that:

100(m-M)/5=F10/F=(d/10 pc)2

This shows that for the flux ratio of a star’s apparent magnitude to its absolute magnitude and for F10, which would show how the star would appear from 10 parsecs, would equal the distance to the star if it were at 10 pc away.  This can therefore have multiple manipulations to show a star’s distance away:

d=10(m-M+5)/5 pc

Or a star’s apparent and absolute magnitudes:

m-M=5log(d/10)=5log(d)-5

If you were wondering how this could be useful if we don’t necessarily know the distance or absolute magnitudes of every star (you could certainly find the apparent magnitude as it is defined by how an observer would see it from Earth), that is a very good question.  Later we will discuss that for certain stars the absolute magnitude is extremely consistent and can be used to find distances very well.

There is still more to this story.  The apparent and absolute magnitudes mentioned are measured as bolometric magnitudes, which detect flux from a star across all wavelengths of light.  It would be nice to do this, but it is generally easier to target specific wavelengths especially since certain objects can be analyzed better in them.  For this we have to look at what we use.  UBV wavelength filters are used to find a star’s apparent magnitude and color.  U is the ultraviolet magnitude with a filter at 365 nm and bandwith of 68 nm, B is blue magnitude with a filter at 440 nm and a bandwith of 98 nm, and V is for the visual magnitude (sometimes considered green) with a filter at 550 nm and a bandwith of 89 nm.  This creates multiple color indices which compare the different wavelength filters to show a star’s apparent or absolute magnitude.  The actual device, the bolometer, uses an association between temperature and color as mentioned in the last post to show them.  The indices are differences between magnitudes of the U, B, and V to equal absolute magnitudes shown as:

U-B = Mu – Mb

and

B-V = Mb – Mv

Since we already noted as the magnitudes increase the brightness decreases we can say that a star with a smaller B-V index would be bluer (as the blue was filtered out more) and would show both that the star is brighter and hotter.  The same would apply for the U-B in that lower values would be more ultraviolet and therefore be brighter and hotter as well.  So, overall the purpose of U-B and B-V is to quantitatively show what the color and temperature of a star is.

With this we can next say that there is the bolometric correlation, or BC, which shows the comparison between bolometric and visual magnitudes (mboland Mbol are really just m and M):

BC = mbol– V = Mbol – Mv

There is another factor influencing these formulas.  It is called interstellar extinction which creates the effect known as interstellar reddening, denoted A as another magnitude.  When it isn’t noted in the question you should ignore this, but it is good to know all the factors influencing this important distance equation.  Interstellar extinction refers to the presence of interstellar dust that absorbs or scatters light from an object.  The effect is stronger at shorter wavelengths, which interact more strongly with dust. Therefore, red light can be seen more,  and if something appears more red than it “should”, then dust is present.  This was proven after comparison between expected and observed emissions showed that there was an inaccuracy.  If a question mentions some amount of reddening the following corrections are made:

The distance modulus becomes d = 10 0.2 (m – M + 5 – AV)

B-V values since the color is changed it becomes

True color = (Bo-Vo), Observed color is (B-V)

(B-V)=(B+Ab) – (V+Av)

(B-V)=(Bo-Vo) + (Ab – Av) = Intrinsic color + color excess

Since extinction will occur more in the lower wavelengths, this increases the V values relative to the B or U values.  A test can also ask about how this can show in ratios, where it would show Ab/Av or Au/Av.  In this case you would have to be given the value of the Av, and then multiplying the two ratios by the Av would get Ab and Au, such that you can correct either your B-V or U-B values.

The last thing to note is the color-color diagram.  This relates U-B and B-V indices for stars, and it can show temperature and color as well.  Stars actually aren’t perfect blackbodies, so even if they get close the diagram won’t form a straight line.  Here is an example, but know that a color-color diagram can be applied to objects with many stars, which will look different:

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TL;DR: Developing methods of organizing stars and understanding distances is important in Astronomy since this allows Astronomers to better understand our place in the universe and to construct formulas which explain it well quantitatively.  Apparent magnitude is how bright something appears to be, while absolute magnitude shows how bright something actually is from a set distance of 10 pc.  With this the distance modulus can be derived to find the distance to most objects.  Color indices also are studied to show the temperature, color, and characterize stars better.  Lastly, a correction must be made for interstellar dust.

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Sources and further reading:

Saying Goodbye to Neil Armstrong

Neil Armstrong passed away a week ago today at the age of 82. The first man to walk on the moon (as everyone ought to know- take to Twitter and you’ll find out differently), he will be remembered as one of the pioneers of aviation and the space program. His name will forever be linked with such legends as the Wright Brothers, Earhart, Gagarin, and Shepard.

With the loss of Armstrong, we’ve lost our last great frontiersman. We’ve explored the entire surface of our world. We’ve climbed to its tallest point, and have arrived at both ends of the Earth. Armstrong was the first man to walk on the surface of another world- and now there are only eight people still alive who can claim they’ve done the same. It is entirely possible that in a few years, there will be no one left who has walked on another planet or moon. When this happens, it will be a sad day indeed.

However, now is not the time for politicking the space program. It is a time of sorrow and remembrance for our great lunar hero, Neil Armstrong. He will be missed, but never forgotten.

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NBC News’ Cosmic Log has a list of ways Neil Armstrong is being remembered- and how you can help honor him, too

Worried about the situation mentioned at the end of the last paragraph? Don’t be. I looked at this in another blog post, and xkcd’s Randall Munroe went even deeper than I did. If we use 2030 as a reasonable ballpark figure to get to Mars, things are looking up.