# Star Clusters

This is a lovely post for us to write because we get to all come together, but also slightly sad because this is the last of our posts on stellar evolution. Yes, we finally get to star clusters.  First question to ask any astronomer investigating clusters would be, “open or globular?”  Yes, just like any other astronomical object these have the same old tools we’ve used for many years, some types, and some very interesting problems.  Let’s see what clusters have to offer us astronomers.

Clusters in general are fantastic tools for any astronomer, with photometric, spectroscopic, and other studies done to find out what they are and why they’re important.  They are groups of stars that all formed from the same nebula.  This means they are all at the same distance, and there’s a higher than normal density of stars in that location that have the same age, the same chemical composition, and different masses.  The difference in mass is important, and it reflects how different stars can form in a region.  For all these reasons, clusters are perfect for studying stellar evolution, finding distances to phenomena, or better understanding properties of galaxies or certain stars.  Guess these clusters really show how “united we stand” can be quite the useful strategy (at least for us astronomy nerds anyway).

So let’s open up the first mystery present, open clusters.  These are famously filled with all sorts of massive, higher metallicity stars.  Yep, that means they can produce all sorts of fancy objects as per our understanding of stellar evolution.  Since they are massive, we also consider these clusters to be younger (millions of years old).  This logically follows into another observation.  Open clusters are defined by being in a galaxy’s disk.  This is the area of most star formation, and it makes sense younger star clusters would be forming there.  Last for these clusters is that they are usually sparser in member stars, having hundreds or thousands if a lot, because of the high mass stars.

The Pleiades, or M45 because it is easier to pronounce, spell, and it gives us an excuse to bring up the Messier catalog again.

If we still have your attention then great.  If not, then perhaps we can look into the celestial sphere for a far more well-rounded cluster.  Alright, bad introductions to the next type aside, we have globular clusters.  These are older clusters up to gigayears old, in a galaxy’s halo (outside the disk that is normally seen) and typically having millions of stars.  Since they are older, they also have lower metallicity, and cluster members are not as massive stars.  As shown, clusters link together mass, evolution, age, and density of stars in different locations.  But don’t let these general properties fool you, globular clusters can still have blue stragglers.  Blue stragglers are unusually massive stars in globular clusters, which may be caused by some sort of binary star.

This would be the brightest globular cluster we can see, Omega Centauri.  There are all sorts of fancy random-looking blue lights, and just look at that bright core…hopefully it doesn’t somehow cluster together against us.

So far we’ve defined what clusters are, and how they’re useful.  Let’s exemplify how useful they are.  The Color-Magnitude Diagram is essentially an H-R Diagram that plots up the color and magnitude of stars (determined using photometry, or amount of light, and spectroscopy, or the type of light we receive).  This may not sound useful, but by taking different clusters at different ages, astronomers can actually see how a whole entire cluster of stars evolves over time.  If you’re wondering how, we’ve mentioned it previously in this post because by seeing the different ages for clusters, then we can see the numbers of stars, the location of the stars, and qualities of those stars.  They in fact show exactly how population I (like stars in open clusters) and population II stars (like stars in globular clusters) are distinguished .

One last aspect of clusters to explore is how we classify them.  People have actually spent time trying to systematically distinguish certain clusters from one another.  One example is the Shapley-Sawyer morphology classification, which classifies different globular clusters by how dense they appear.  There is also a Trumpler classification of open clusters, which shows how nebulous and rich (concentrated with stars) the open cluster is.  Well, enough classes, that’s all for this lesson.

So yes, this is how they classify open clusters. As you can see, they all look fairly similar, so basically Trumpler developed really good skills at distinguishing clusters.

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Color-Mag Diagrams

Blue Stragglers, Stellar Evo with clusters

Open

Globular

Both types of clusters

Cluster classification

Images

Omega Centauri: NASA/APOD, http://apod.nasa.gov/apod/ap130501.html

Trumpler Classification: http://www.astrophoton.com/trumpler_class.htm

# Exotic/theoretical objects

As both of your authors are away doing research over the summer (yes, of course, we’re both doing astro research), we haven’t had the time to post new and exciting blog posts for a while (not to mention the constant pile of schoolwork). Once we return, we’ll explain the research that we each did (or maybe astronomical requests if we get some!), but in the meantime, here’s a new post to satisfy your needs for astronomy knowledge.

Well, I guess we can’t say that rarity rocks since this is not a geology blog (unless the readers out there like that).  But let’s get going about some rare stuff that’s out of this world!  Yes, in the universe there are exotic, weird, and sometimes mind blowing objects that we shall explain in this post.

Exotic stars are technically defined as compact objects that are not made of electrons, protons, and neutrons and are in a degenerate state (those degenerates!).  But to change things up we’ll also introduce some other weird objects.  After all this is astronomy, when can we ever leave it simple?  Mind you much of this is theoretical, so most people would be as confused as you or we are, but it’s interesting anyway.

To start, there are exotic stars.  Please don’t scratch your head too much yet.  But let’s make a list to explain:

• Quark and strange stars: If a neutron star manages to compress further, then just like with white dwarfs to neutron stars, they can compress into quark matter.  This increases density, and a specific type is known as a strange star (strange, we know).  They are made up of strange quarks (a specific type of quark…hopefully that wasn’t too quarky).

If you look closely enough there’s a difference. Theoretically. Maybe…just trust us here.

• Electroweak stars: Apparently in this case quarks can be turned into leptons by the electroweak force , which is what keeps electrons in orbit around a nucleus and allows for nuclear fission.  They again arise when a quark star becomes denser.
• Preon stars: The next step in our evolution of this post.  A bit more compact and a possible dark matter candidate.  But there is some argument against their existence, though that applies to all of these objects  in general, considering they are all theoretical.
• Boson stars: A boson is essentially a force.  So as to not force you to take forever to read this, this star is somehow made of pure force (yes, the force is indeed strong with this one).  They are also a possible dark matter candidate.  Let’s not forget that they are theoretically transparent and in general would be difficult to detect.

In general, the stuff here isn’t necessarily normal.  But what that’s not to say that black holes, pulsars, and anything we talk about in the future or past are not weird.  We just wanted a post for these objects.  Pretty much out of all of these so far the quark star is most likely (there are possible quark novae, most famously SN 2006gy).  Now to name a few more astronomically odd objects.

That is one big bang (oh wait, it’s not a big bang!). But it is SN 2006gy in all its luminous glory.

This may also be relatively confusing, but there is also the dark star (it is made of dark matter, there is annoyingly another dark star).  Dark matter interactions produces heat instead of normal fusion with matter.  This is thought to form in the earlier universe and normal fusion wouldn’t occur because the dark matter collisions holding the star would prevent the normal matter in it from fusing.

Next up to confuse us all is the quasi-star.  Another early universe star.  These are thought to be black hole stars that are held by matter falling into a black hole.  This could come from massive protostars to an extent collapsing into a black hole, but without outer layers being blown away. (The matter normally gets blown away and leaves a black hole with supernovae).  These are associated with the theoretical population III stars that were the earliest stars in the universe.

Hopefully this can explain somewhat how quasi-stars are made.

There are also theories about how stars or degenerate objects can tidally capture each other.  One possibility is the Thorne-Zytkow object (TZOs, we needed at least one new acronym, we know how you all missed them).  This oddball consists of a giant star that manages to capture a neutron star that sinks to its core.  So yes, a neutron star within a giant star (we’re hoping you have that nerdy astro moment where you go woah as well).  Apparently the outer layers of the giant star can be shed such that a white dwarf core is left over, forming a binary system with the neutron star.

So how does any of this have to do with stellar evolution?  To start, the exotic stars themselves serve as logical in-between phases from neutron stars to black holes.  After all, with some room between the Chandrasekhar limit and the TOV limit then perhaps there could be some more room between when a star is pure neutron matter and when a star condenses far enough to become a black hole.  Also, theoretical physics likes to make things more complex (because why not).  In addition, there are many objects which astronomers just plainly have trouble explaining, like binary compact objects or the earliest stars.

This friends is how black holes are made (next up, even more in between steps!).

So, as a final note from rvtau and astroisstellar, may your summer be quite…stellar.  Also, thank you to anyone who keeps reading, we really appreciate it!  Perhaps when we get back we’ll make some sort of anniversary type of thing.

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Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd edition, p. 691

Images

# Binary Stars (Part III)

To start, we apologize for the delay…some of the equations weren’t working, and we didn’t want everyone to be disappointed (and it could have been worse…if this was in binary it would’ve taken longer).  So now that we’ve discussed binary stars at length, we must also address some very necessary calculations for dealing with binary systems — but don’t worry, it’s nothing too complicated. We will not show derivations for the equations we use; they may be found in the sources/links below that cover orbital mechanics in greater depth.

If you’ll remember, Kepler’s Third Law showed that there was a direct relation between the square of a planet’s period and the cube of its orbit’s semi-major axis. We can use a slightly modified version of Kepler’s Third Law  to solve for the total mass of any binary system:

$\frac { { a }^{ 3 } }{ { p }^{ 2 } } ={ M }_{ 1 }+{ M }_{ 2 }$

• a = average separation of the two components
• p = orbital period (doesn’t matter which component — their periods are the same)
• Note that Kepler’s Third Law in this form requires specific units — AUs, Earth years, and solar masses.

If our problem is written with standard MKS metric units, we turn instead to Newton’s Form of Kepler’s Third Law. Yes, this form of it looks strange, but don’t worry, it IS equivalent to Kepler’s Third Law (multiplied by a constant):

${ p } ^ { 2 } = \frac { 4 { \pi } ^ { 2 } { a } ^ { 3 } } { G ( { M }_{ 1 } + { M }_{ 2 } ) }$

• G = universal gravitational constant, 6.67 * 10^-11 m^3/s^2/kg
• a = average separation between the components
• p = orbital period

And now for something completely different. In our last post about binaries, we mentioned that it was possible to use the shifts in spectra to determine the velocity of stars in a spectroscopic binary system. But how exactly would we do this?

For a spectroscopic binary system, we can use the non-relativistic Doppler shift formula:

${ \lambda }_{ obsv }={ \lambda }_{ emit } ( 1 \pm \frac { v }{ c } )$

• λ_obsv = observed wavelength of a given spectral line
• λ_emit = “normal” wavelength of the same spectral line (i.e. what it would be in a laboratory)
• v/c is positive when the source is moving away from us, and negative when it is moving towards us

When a star’s spectrum is at its most redshifted, the star is moving away from us at its fastest rate; similarly, maximum blueshift indicates the greatest velocity with which the star is approaching us. A greater difference between the observed and emitted wavelength translates to a more pronounced Doppler effect and a higher velocity for the star. We must apply this equation to both stars, since one is (almost always) more massive than the other and therefore they travel at different speeds.

Now that we have the components’ tangential velocities, we can calculate other vital information through Newtonian mechanics (all circular motion equations are valid, if you are willing to approximate the binary system orbits as circular). There are, however, a few equations you probably won’t see in a normal physics book, such as:

$\frac { { M }_{ 1 } }{ { M }_{ 2 } } = \frac { { d }_{ 2 } }{ { d }_{ 1 } } = \frac { { v }_{ 2 } }{ { v }_{ 1 } }$

Center of mass (barycenter) is where:

${ { M }_{ 1 } }{ { d }_{ 1 } } = { M }_{ 2 } { d }_{ 2 }$

• d_1 is the distance from component 1 to the center of mass
• d_2 is the distance from component 2 to the center of mass

Thus, if we can find both the sum of the masses and the ratio of the masses, we can determine the individual mass of both components of the binary system!

But as we said, we have yet to introduce some general circular motion (which is where we can get some of Kepler’s laws stated).   This includes mainly orbital velocity:

$v=\sqrt{GM/r}$

• v=orbital velocity

This in a sense comes from $v=C/T$, meaning circular velocity is just the distance around a circle (circumference) divided by the time taken (period).  But this applies with bodies orbiting another (like the Earth around the Sun, the Moon around the Earth).

Let’s review another common diagram, which we would like to call the binary star velocity graph:

Time to get you all moving again. From: http://www.astronomynotes.com/starprop/s10.htm

We may have shown this little bugger in the past, but we shall now apply some of the math we learned in this post.  We may not go too in depth, but here the motions of both stars can clearly be seen and plotted.  These curves can tell us whether the radial velocity (or as stated how fast a star is moving) of stars are moving away or towards us (positive means away, negative means towards).

This graph can be in part constructed by finding the doppler shift of a spectrum, finding the velocities of stars, and plotting this graph over time.  Afterwards, more data can be collected about temperature, stellar radii, period of orbit, and orbital separation to further calculations.  But knowing the recessional velocity and orbital velocities of binary stars can be useful to finding mass and other aspects of a binary system.

Up until now we assumed aspects of binaries where we calculated mass were viewed face-on (the plane of orbit is perpendicular to our line of sight), and that our spectroscopic binary systems have been viewed edge-on. But of course, this is almost never the case in reality, and things become more complicated when we take into account the possible inclination of the binary system, not to mention elliptical instead of circular formulas.  For now, let’s just talk about inclination.

Just as anything in physics (kind of) they can be summarized by some formulas!  Ah, life made easy (maybe).  Here is a visual demonstration (the first is no inclination, the second is with a binary inclined at an angle from our view of i):

and

Before this is further explained, an inclination of 90 degrees gets the lower limit of the sum of the masses (when the inclination angle is irrelevant essentially).  Now let’s explain why that’s important by showing what happens when we get an inclination=i.

${v}_{r} = v\sin(i)$

${v}_{r}$ = velocity measured by the doppler shift (it is measured along our line of site, and we know we can use the doppler effect to calculate velocities from spectra)

and this can be plugged into our formula relating period and velocity (and this is orbital velocity, which again brings up the importance of the binary star velocity graph):

$\frac{P { ( {v}_{1,r}+{v}_{2,r} ) }^{3} }{2 \pi G {sin}^{3} ( i ) } = {M}_{1}+{M}_{2}$

This takes into account the orbital velocities for each star to get the total mass of the system.  In addition, increasing the angle increases the speed seen.

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# Binary Stars (Part II)

Well, we rotate again within this topic.  Now in your view is on how we classify these binary stars, after those lovely properties described.  Also, remember, some past topics in the general/history sections still apply, like Kepler’s laws.  But now for types, we will even include binary stars that only appear to be binary stars.  Each type effectively uses a major astronomical technique to better understand the motion and properties of a binary system.  We will explain all the concepts that go behind it here, and then the math to apply it after this.

To start, let’s see what we have to work with.  What I mean by that is an optical double of course!  As stated, these are stars that just appear to move as binaries, but aren’t really.  They are produced when two stars fall into one’s line of sight, and they generally can pop up if you’re looking through a telescope at stars that aren’t even  within hundreds of parsecs of each other.  Some stars that appear close, like with a constellation, can do this at times.  Simply looking at a light curve (like we did with the variable star posts) reveals great distinction.

Seeing double again? From: UNL Astronomy.

Next we get physical with our binaries (no violence intended, disclaimer: this site is for all ages).  Physical binaries are bound by gravity; basically they are real binaries.  Therefore, we have various types based on the many ways we determine the properties of  systems.  This goes into finding the mass of the whole system or each object, rotational speed, recessional or radial velocity (speed towards or away from us), and various qualities of each star.

Yes, with this we can finally see the truth! From Discovery Space.

The first we shall talk about are the visual binaries and astrometric binaries.  We can spot the orbits of the binary stars in both these cases, and therefore the motions can tell us information about the period and separation of orbit for the two stars.  This is important since with that we can apply Kepler’s Laws (this is the perfect time to give a blast from the past with our Kepler post).  But the orbit can be at an angle, which is known as an inclination from our line of sight.  This has to be resolved when making calculations.  Afterwards, the total mass of a system and the center of the mass can be determined, which can lead to figuring out the mass of each star or object, and the types of stars or objects in the system.  Observing two stars can reveal a TON of data (which is a true theme of astronomy: making observations and calculations can lead to major discovery).  But you cannot do all this without knowing the system’s distance from us.  Without that, you cannot know the angular separation or inclination, linear distances, etc.

Also, you may be wondering whats the difference between visual and astrometric?  The visual part you can see, the astrometric part you measure.  Binary systems in a nutshell (yum, nuts…don’t call us astro people crazy now!).  The only real things to add on about that is much of this is because one part of a system can be brighter or too close to distinguish, and therefore basic laws of physics like Newton’s laws can be applied to find out much about the system.  This has extended to discovering exoplanets around stars, since these laws apply to any two orbiting bodies in the UNIVERSE.

Moving on, we have yet again those eclipsing binaries.  Okay, we’ve mentioned them a few times…they come up.  We already sort of discussed their set up, but let’s talk more explicitly about measuring them.  As stated, one object can block the other.  An interesting result is that we can find both the time of orbit or eclipsing and the brightness of an orbiting object.  Since we can find the brightness of each object, we can find distance, and all the other stuff mentioned with astrometric binaries.  So, a light curve plotting the brightness and eclipsing is extremely important here.  Looking at the shape and amount of dip after each eclipse can sometimes tell about relative size (whether one star much larger/more massive than another).  Very regular, very neat.  Eclipsing binaries can also be something called spectroscopic, another type of binary star.  But again, here eclipsing binaries and timed blocking can result in important exoplanet discovery.

Let’s talk quickly about spectrum binaries next.  This is the case where two stars cannot be resolved (sort of like the opposite of an optical double).  But the spectra produced by the stars immediately show the binary system.  Certain stars show more absorption lines of helium or calcium because stars have different masses, temperatures and different amounts of elements.  One star cannot be simultaneously hot and cold, so the presence of spectral lines associated with both hotter and colder stars would lead astronomers to consider a binary system.  The Doppler effect, where the lines of a star can be shifted, also takes place here so radial velocities of the stars can be measured by spectra.

If a binary pair orbits along our line of sight, a shift in spectra can be seen, known as a spectroscopic binary.  This is if the luminosities of the star can be compared, a double-line spectroscopic binary.  But there is also the case where one star can be brighter than the other, meaning only one set of spectra can be seen, a single-line spectroscopic binary.  In addition to looking at the spectra lines themselves, the velocity of a spectroscopic binary can be plotted to see their blueshift, redshift, or periods and radial velocities.  Therefore, an eclipsing binary’s analysis or photometry can show the brightness or period, and the spectroscopic aspect can show the Doppler effect, which can link to the speed of the system.  The double-line is better for analysis since you can actually see the whole system and analyze the speed and mass of the objects.

A double-line spectroscopic binary in all its beauty. First (double-line spectroscopy showing movement) and third (velocity curve) from Dept. of Phys and Astro at University of Tennessee. Second (showing Doppler effect in spectral lines and motion of a binary system) from Australia Telescope Outreach and Education

So you’re a normal piece of matter, say an electron, going along, and you suddenly get hit by a proton!  What happens when you get this high speed collision?  Well, you get X-ray radiation of course!  When you have two stars having a ton of this occur because of matter accretion (or accumulating matter from one star due to gravity pulling off a layer from another star) it’s called an X-ray binary.  This means that a compact object must have enough gravity to pull off material from its binary partner.  This can be created by a normal mass star turning into a white dwarf through stellar evolution while a star in the system is still a red giant, meaning the white dwarf will have enough gravity to pull off the loose Hydrogen layer from the red giant.  Alternatively, more massive stars can become neutron stars or black holes and still retain the system.  We mention them because they are quite important, and they too can be measured using a variety of physics between the rate of accretion and the angular motions and energy transfer that occurs with accretion.

This system sure is hot stuff! From Northern Arizona Meteorite Laboratory Glossary.

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TL;DR

The post summarized the different classifications of binary stars.  They are characterized by various methods of identification and analysis of data, all of which is very important.  In addition, many binary systems can have compact components and can exist in a variety of ways.  They can be a pair of any objects, be it brown dwarfs, white dwarfs, black holes, neutron stars, any type of star at any point of its stellar evolution except perhaps protostars, and planets and moons even.  Therefore, it is important to not only classify the systems by the type of objects, but by the way we see and understand our surroundings.

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Sources and links for further reading (links to images are below, some topics covered above that aren’t found are found in the General):

General

Eclipsing binary

Spectroscopic

Visual

Optical

Astrometric

Photometric

XRBs

Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd edition, p. 180-198

Images

Discovery Space: http://www.discoveryspace.net/index.asp?Cat_id=631

Dept. of Physics and Astronomy at University of Tennessee: http://csep10.phys.utk.edu/astr162/lect/binaries/spectroscopic.html

Australia Telescope Outreach and Education: http://outreach.atnf.csiro.au/education/senior/astrophysics/binary_types.html

Northern Arizona Meteorite Laboratory Glossary: http://www4.nau.edu/meteorite/Meteorite/Book-GlossaryX.html

# Binary Stars (Part I)

And now, we bring you a topic that hopefully will have you seeing double — in terms of stars, that is. Some astronomers say that a majority of stars are in binary or multiple star systems, but this is rather controversial, so suffice it to say that a significant number of stars are binaries or multiples. They are so important to astronomy that we can’t cover everything in one post, so we’ll split our discussion of binaries into a trilogy, with Part I (this post) covering general properties and evolution, Part II the types, and Part III the related math.

Before we really get into binaries, we should make it clear that a binary is not a “double star”, or optical double. An optical double is simply a pair of stars that, by chance, appear in nearly the same position in the sky but do not interact with each other in any way — perhaps the most famous example is Mizar and Alcor in Ursa Major. A true binary system has its stars gravitationally bound to each other, with both orbiting around the center of mass (also called the barycenter).

A schematic of a very basic binary star system (Credit: University of Oregon)

The formation of binary systems is still shrouded in mystery, with many competing theories all seeking to explain this stellar phenomenon. The old explanation for binary formation was that a rapidly rotating star could deform so much that it distorted into a “barbell” shape and eventually split into two stars that would then orbit around each other. However, this theory has been discredited in recent years due to simulations that show that stars tend to form accretion disks when spinning rapidly, rather than turning into barbells.

Binaries may also form from the fragmentation of molecular gas clouds as they collapse into protostars. However, the original cloud may not be able to immediately fragment into multiple clumps, so it may have to first collapse, then stop collapsing before it can divide into smaller chunks that then give birth to a gravitationally bound multiple star system. Alternatively, an accretion disk around a protostar may continue to…accrete…more mass from the molecular cloud around it. If this disk grows more massive than the star it orbits, it becomes unstable, and may clump together under its own gravity to form a second star and therefore produce a binary.

Stars that have formed separately may interact with each other to form a binary system, but this requires very high densities of stars, such as in globular clusters. Gravitational capture of an object requires a loss of energy from the system (referring to the two stars that will eventually become the binary), because of the principle of conservation of energy. In tidal capture, the excess energy goes into distorting the interior of the two stars as they pass each other at close quarters. However, this method of binary formation requires the two stars to interact at a very precise distance — too great a separation and the interaction won’t drain enough energy from the system to form a binary, but too small a separation and the two stars will just smash into each other to form a single, larger star. In three-body gravitational capture, excess kinetic energy is transferred to a hapless third star, which is then flung away at high speed while the other two stars become a binary system.

Castor sextuple star system, made up of three pairs of binary stars… because if you’re going to do it, you might as well overdo it. (Credit: Jodrell Bank Center for Astrophysics, University of Manchester)

The evolution of binary systems depends heavily on the degree to which the two stars in the system transfer mass. Each star has a Roche lobe, which is basically the space where a star has gravitational influence. If a star expands outside its Roche lobe, then material can flow to the companion star and lead to odd stellar evolution such as the Algol paradox, named for a binary system composed of a K0 subgiant and a B8 main sequence star. The theories of stellar evolution predict that the more massive B8 star should have evolved off the main sequence to the giant phase before the K0 star, but this is not the case — thus a paradox. However, astronomers have resolved the paradox by positing that the Algol system started out as a pair of main sequence stars, with one much more massive than the other. As the more massive star entered its red giant phase, it overfilled its Roche lobe and transferred away so much mass that it ended up as a subgiant while its companion became a massive blue main sequence star.

Gas flow simulations in the Algol system (Credit: M. Ratliff and M. Richards, PSU)

In a detached binary (wide binary), the two stars are both within their Roche lobes, so stellar evolution proceeds just as it would if the two stars evolved separately.

A semi-detached binary occurs when one star fills its Roche lobe and transfers mass to the other. Semi-detached binaries can produce interesting objects such as novae or x-ray binaries. Novae form from binary systems of a white dwarf and a main sequence or giant star, where mass streams onto the white dwarf and eventually ignites a nova outburst. An x-ray binary, on the other hand, forms from a system of two massive stars, where one has gone supernova — without disrupting the binary system — and left behind a neutron star or black hole. When the second star becomes a red giant, it streams mass onto an accretion disk surrounding the NS/BH, which emits strongly in x-rays. The x-ray radiation may even be powerful enough to vaporize the companion star that powered it in the first place.

Contact binaries are the strangest of the lot. The two stars share much of their mass (both are overfilling their Roche lobes) and orbit within a common envelope. The components may spiral in towards each other, due to loss of orbital energy to friction of orbiting within an atmosphere, and eventually merge into a single rapidly-rotating star. For more examples of what may happen to interacting (semi-detached and contact) binaries, check out the links below, especially this paper by P. Podsiadlowski of Oxford University.

Types of binary systems (Credit: David Darling)

Once both stars in a binary system have reached their end stages of evolution, end results vary wildly. One binary system made of two low-mass stars may end up as a pair of orbiting white  dwarfs (remember RX J0806.3, 2012 Astronomy folks?). Meanwhile, another binary system composed of a neutron star and a supergiant might turn into two runaway stellar remnants heading in opposite directions at high speeds, if the system is blown apart when the supergiant eventually goes supernova.

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TL; DR — Binary systems are pairs of stars that are gravitationally bound together. They may form due to fragmentation of molecular clouds or protostellar disks, or more rarely, from gravitational capture. Stars within binary system may transfer mass to each other if they expand outside their Roche lobes, and mass transfer leads to fascinating examples of stellar evolution in semi-detached and contact binary systems.  Even more than that the amount of mass in the system or for each component can also change the properties, leading to many variations of the system.

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# Extrinsic Variable Stars

We don’t have quite the humongous post for you, sorry, we were both busy and unsure how to present these types of stars (but no worries, we are back in your view for this new post!).  Interestingly, it’s not always what’s on the inside that counts.  So, this post considers extrinsic variables.  Following weeks will probably cover either math, more about certain variable stars, or other general information.  But now, shall we move onto all our lovely extrinsic variables?  These things don’t have the same large number of types as their intrinsic cousins in terms of causes, but they are quite important in our search for life outside the solar system, making them quite close to home…

The power of the sun (varies over time). Yep, one of the closest variable stars. From: NASA, Sun picture

The principal topic here will involve binary stars, but some can be non-binary stars.  They may not seem common because they require all sorts of optical conditions or non-uniformity in a star, but they are definitely out there.  Events on the outside of the star are the essential cause.  For this, the two chief classes include eclipsing binaries and rotating types.

Let’s start by exploring the Rotating variables.  Circle around these  folks, things are about to get pivotal!  Rotating variables pretty much are the extrinsic variables that aren’t always in a multiple star system.  Interestingly, differences in luminosity can be created by magnetic fields, stellar spots (like the sunspots we talked about in the what are stars post, it makes a lot of sense considering what they are!), and non-spherical shapes for stars.  These stars really aren’t spotty at all in fact!  After all, sunspots are characteristic of this class since they are cooler regions on the outside of a star, related to magnetic fields created from rotation.  This makes the pulsations and discovery fairly consistent.

Yep, a real deal picture of starspots. Hopefully the magnetism here attracts you (hopefully not fatal attraction?)! From: University of St. Andrews

Here are the major types (sadly, we have to introduce…long names):

Alpha2 Canum Venaticorum (ACV): Main sequence stars of type B8p-A8p (the p means having peculiar spectral lines) with strong magnetic fields.

Light curve. From: Planet Hunters, ACV light curve

Rapidly osccilating Alpha2 CVn (ACVO): These non-radially pulsate, and they are of type A spectral class (meaning they are massive) with relatively fast periods.

BY Draconis (BY): White dwarfs with occasional light changes and even flares.  This is from the rotation making the spots on the star, creating non-uniform surface brightness.  Our Sun could even be considered of this type, and sometimes they can be considered eruptive variables too.

Light Curve. From: BY Draconis light curve

Rotating ellipsoidal (ELL): Close binaries with ellipsoidal components (ones where the stars of a system can actually be stretched from gravity of each star in the system pulling eachother).  Spica is a famous example.

Light curves…again…it’s ellipsoidal? Sorry if this is getting repetitive. From: Ellipsoidal variable light curve

FK Comae Berenices (FKCOM): Rotating giants with non-uniform surface brightness (types G to K).  They can be spectroscopic binary systems, where the variability is caused by sunspots from rotation (in case you haven’t noticed, yes the pattern is as we said, you definitely want to read the stars post about sunspots for these rotating variables or perhaps we’ll make a post more on binary stars).

But yep, we’re back with another light curve. From: FK Comae Berenices light curve

Optically variable pulsars (CM Tau, PSR): These rotate very quickly and are known for strong magnetic fields (basically, pulsars are rotating, extrinsic variables, so yes even post-supernova objects can be classified as variable stars…classify all the things!).  Refer to the neutron star post for more on this (heh, not going to bother with another light curve).

SX Arietis-type (SXARI): Main sequence type B stars that are high temperature forms of ACV types.  Helium is prevalent in spectra, and they have those good ol’ sunspots and magnetic fields.

Now be ready, we don’t want to block your view from learning at all.  But we have eclipsing binary stars up next!  To start, the general definition is that the orbit has to be oriented so when we see it one object can pass in front of the other (this is termed lining up with the ecliptic, basically the stars line up with our line of sight).  They have VERY characteristic light curves and dips.  These stars are really nice in their periodic motions and observations, which makes O-C diagrams extremely useful here (in fact, their predicted variability can be theoretically easier than intrinsic variables).

I hope we are all inclined to see this. The system can be tilted to our view, sometimes one star can block another. From: University of Tennessee eclipsing binaries

Okay fine, that wasn’t the end of light curves. But hey…it’s what’s on the inside that counts, right? Oh wait…From: David Darling

Looking at the graph above we can derive two facts if values were given.  Pretty much, we could figure out the apparent magnitude of the stars depending on the dips (as seen, the larger dip is from the larger star, but you would have to assess that from data given) and the period of the system if not given (which as said can be useful for O-C diagrams).

We can name three major examples (this also could includes the not as stellar planetary transits used to detect exoplanets…those can be eclipsing, but we’ll leave those for another day):

Algol: Yes, a ghostly star, sometimes considered a demon.  A spectroscopic binary observed since Egpytian times.  They are ellipsoidal, with one B-type star and a K-type star (so it can be blue and red).  Aside from the usual, it presents what’s called the Algol paradox.  Normally a star with more mass evolves and reaches end stages more quickly.  Somehow, the lower mass star is a giant in this case, while the higher mass star is on the main sequence.  This is most likely due to accretion of matter.

The Algol system, notice the various dips. Hopefully this uneclipses all our views as to what this could look like. From: University of Tennessee the Algol system

Beta Lyrae: Yet another secretive star known since ancient times.  It follows traditional definition, but it has a particularly large rate of period change, making it most likely an active system (this could be similar to the Algol paradox).

Beta Lyrae…not much more to say on this…light curve again? From AAVSO Beta Lyrae light curve.

W Ursae Majoris: Out of the examples, a relatively more recent discovery.  The peaks for this system seem almost equal.  But it most likely is also an active system like with Beta Lyrae.  This has probably created some period variation that has been detected over time, and the system also seems to have some star spots.

Hah, yes, another light curve! You really aren’t escaping these, sorry. From: AAVSO W Ursae Majoris light curve

Epsilon Aurigae:  Just to throw it in here because it is probably one of the most mysterious eclipsing binaries ever.  It has a REALLY long period, even the eclipse itself is long.  In fact, there was a year of astronomy around 2009 where people in part made lots of observations because of its rare period.

It may actually be caused by a gap in a relatively large accretion disk that occasionally doesn’t block the light. Yes, this is probably the definition of weird. It’s like having pizza dough in space spin, get really large, and normally it doesn’t happen, but it gets so thin you can sort of see through it. From: AAVSO Epsilon Aurigae

Another model of the system. Again, extremely unlikely. Hopefully you didn’t think we wouldn’t end with one last light curve! From: Hopkins Phoenix Observatory Epsilon Aurigae

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TL;DR

Oh, the beauty of stars.  They prove that it’s BOTH what’s on the inside AND the outside that matters!  Extrinsics, though, show what’s on the outside.  Whether it be pushing and pulling, magnetism, and rotation for rotating variables, or just straight on eclipsing lined up with our sight sadly blocking out stars on occasion, these stars are yet again far out.  While they may not seem exciting, some can be…quite weird.

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General:

Rotating (ellipsoidal)

Eclipsing

Images:

# Intrinsic Variable Stars

Good day, folks. Fair word of warning: this is one of the longest posts we’ve done, at 2300 words (though there are lots of pictures). This is our second installment in our variable stars series, and today, we’ll be dealing with intrinsic variables. As we mentioned last week, intrinsic variables are the stars that change brightness because of processes that happen within them—internal factors.

So the first thing you need to know about intrinsic variable stars is that there are a lot of them. And I mean a lot. Within the group of intrinsic variable stars, there are three classes: pulsating, cataclysmic (or explosive), and eruptive. Within those three classes, there are further types for each one.

Pulsating types include Cepheids, RR Lyrae, RV Tauri, and long period variables, among others. Two of these types have further types—Cepheids split into Type I Classical and Type II W Virginis, and long-period variables split into Mira type and semiregular.

Cataclysmic types include supernovae, novae, dwarf novae, recurrent novae, symbiotic stars, and R Coronae Borealis.

Eruptive types include luminous blue variables, flare stars, supergiants, protostars, and Orion variables.

Very important features in identifying variable stars are their periods, population type, and of course, their light curves. The light curves for each kind of star are very distinctive, but there are a lot of them, so it may be a bit challenging at first to memorise all of them. To help you along, we’ve provided light curve examples for every kind of variable star we mention. The maximum luminosity is referred to as the maximum or maxima, and the minimum luminosity is referred to as the minimum or minima.

Now, we’ll walk through all of that information bit by bit, starting with pulsating types, by far the most common and most well known type. As we said last week, pulsating types are stars that actually change their size and brightness in a cycle. The length of one cycle is referred to as a period (and this is applicable to all variable stars). The periods of a pulsating star can range from a few seconds (ZZ Ceti stars) to years (long-period variables). The following table gives a good general view of the various pulsating variables and their period.

 Type Period Pop. Spectral Classes Long-Period Variables 100-700 days I, II Varying RV Tauri 20-100 days G, K Classical Cepheids 1-50 days I F to G/K W Virginis 12-45 days II F to G RR Lyrae 1.5-24 hours II A7 to F5 d Scuti 1-3 hours I b Cephei 3-7 hours I ZZ Ceti 100-1000 sec I

We’ll start with the most well-known kind of variable star: classical Cepheids. δ Cephei, the prototype of this class, was discovered by nineteen-year-old astronomer John Goodricke in 1784. Cepheids are very luminous and very large variables, at least 50 times the mass of the sun. The spectral classes of classical Cepheids generally change from F at a maximum value and a G or a K at a minimum value, typically fluctuating between a 0.5 and 2 magnitude. They have a very distinctive light curve as well—a very sharp rise in luminosity followed by a more gradual decline.

Light curves of Classical Cepheids. Credit: University of Arizona

As mentioned earlier, they are by far the most well known type of variable star—and on good grounds, too. They are extremely important to astronomy for several reasons. These stars can actually help measure distance in astronomy by a combination of the distance modulus and the period-luminosity relation. For now, we’ll only worry about the period-luminosity relation, because that’s what is really applicable to all these variable stars. Astronomers a long time ago discovered a whole bunch of Cepheids in the Small Magellanic Cloud, and realized that since all of the Cepheids were about the same distance away, then the difference between the absolute and the apparent magnitude had to be the same as well. This also led to a discovery that the length of the period was actually directly related to its luminosity, which—gasp—gave us the period-luminosity relation:

${ M }_{ (v) }=-2.81\log _{ 10 }{ { P }_{ d } } -1.43$

where M(v) is the absolute magnitude and Pd is the period in days. This equation actually proves that the longer the period of the star is, the brighter it is. Because of how bright Cepheids already are (being massive, pulsating, luminous stars), they allow astronomers to use them as standard candles of the universe, which can be used to determine distance. This method can measure much farther away than parallax can, as parallax can only measure distances up to 100 parsecs away.

There are a few other pulsating types, and we won’t go as much into detail about those. W Virginis stars (Type II Cepheids) are just like classical Cepheids, only slightly dimmer. Their period-luminosity relationship is exactly parallel to the classical Cepheid’s, and therefore, they also work as standard candles. However, because they are not as bright, we can’t use them to determine large distances. These stars are also much older than the classical Cepheid, being population II stars and therefore also rarer than classical Cepheids. Their spectral classes range from F to G.

Light curve of W Virginis. Credit: C. Hoffmeister / Strasbourg Astronomical Data Center

RR Lyrae stars are even older than the W Virginis stars. What is special about these stars is that they all have almost the exact same luminosities, so they too can be used for distance measurements in astronomy. They have a rather short period of up to a day, and range from 0.3 to 2 magnitudes. They are smaller than Cepheids, but they also have a well-defined period. RR Lyrae stars actually have several subtypes, based on the light curve of the star in question.

Light curve for an RR Lyrae star. Credit: Michael Richmond (RIT)

RV Tauri stars are yellow supergiants with an odd pulsation pattern. From the maximum, pulsates in an alternating pattern of shallow and then deep minimas. The period is measured from deep minima to deep minima. They vary from F to M and up to three magnitudes.

Light curve for an RV Tauri star. Credit: South Carolina State University/AAVSO LCG

δ Scuti stars are somewhat evolved F-class stars located closer to the centre of the H-R Diagram than most of the other variable stars. ZZ Ceti stars are actually pulsating white dwarfs—core remnants unstable enough to change and pulsate.

d Scuti-type light curve. Credit: Russian Astronomical Network

ZZ Ceti-type light curve. Credit: C. Hoffmeister / Strasbourg Astronomical Data Center

Long-period variables have, well, long periods, ranging from a few months to several years. They are AGB stars, which means that they are always quite large. The Mira-type long-period variable has a huge variation in brightness—up to ten magnitudes! The minimum variation in brightness is about 2.5 magnitudes. These pulsate regularly and have some outer layers in their atmospheres that get heated up and shocked when they pulsate.

Mira, in fact, was the first variable star discovered—in 1595, a young pastor who also happened to be an amateur astronomer began to observe ο Ceti, and found that over many months, it disappeared and then reappeared! He named this strange star Mira, “wonderful”.

The light curve of Mira, the prototype of Mira-type long-period variables. Credit: AAVSO LCG

Semi-regular variables are also long-period variables, but they have sporadically have periods of stability. The change in brightness is also much less—usually less than 2 magnitudes. Their light curves vary greatly because of the irregularity of their pulsations.

A semi-regular variable light curve. Credit: AFOEV / Kyoto University

On the H-R diagram, these pulsating stars are located on a special place called the instability strip, where—surprise—the stars are not stable and therefore pulsate. The exceptions to this are the long-period variables and the b Cephei stars. Long period variables are located to the right of the instability strip, while b Cephei stars are located to the left.

HR diagram showing location of pulsating variable stars. Credit: Case Western Reserve University

Of course, the next question we must go through is: why do stars pulsate? Most stars are stable in their respective phases of hydrostatic equilibrium, but sometimes, hydrostatic equilibrium isn’t reached. If the internal pressure of a star, which pushes outwards, is greater than the gravitational force, which pushes inwards, the outer layers of the star will expand. Once the star expands, the gravitational force is lessened somewhat, but the internal pressure drops very much, very fast. This means that when the star hits the point of hydrostatic equilibrium, it still has a lot of momentum—which means it carries the star past this point of hydrostatic equilibrium. When this happens, the force of gravity becomes greater than the internal pressure pushing outwards, so the star collapses inwards. When that happens, the internal pressure once again becomes greater than gravity, and everything happens all over again. It’s a vicious cycle, we know.

The physics of stellar pulsation are a bit painful to go through, so we’ll not deal with that too much. The most important thing you need to know about that is that pulsating stars, like sound, has fundamentals and overtones, and pulsates on these frequencies.

Next, we’ll go through cataclysmic variables. These are also called explosive variables, because they, well, explode. In fact, supernovae are a kind of cataclysmic variable. Yes, that’s right—a major stellar explosion that is a star’s death counts as a kind of variable star. No, I don’t know what’s wrong with astronomers’ brains either. As we have already discussed supernova (thank you, astroisstellar), I don’t feel the need to go any more in depth about these things. If you want to know more, please refer to our earlier post.

Generalized light curves for Type II SNe. Credit: Swinburne University of Technology

Another cataclysmic variable is the nova, which is actually a binary system comprised of a white dwarf and a companion star, usually a giant. The gravity of the white dwarf sucks—excuse me, accretes—matter from the companion star until it hits the Chandrasekhar Limit, at which point it triggers a thermonuclear reaction that blasts the shell off into space. This cycle repeats over and over again until there’s nothing left.

A light curve of a nova. Credit: NASA Goddard Space Flight Center / William T. Thompson

A recurring nova is exactly like a nova, only it has occurred at least two or more times and the period of its outburst is up to 200 days. There’s not much else special about it; it’s just a recurring nova.

Recurrent nova light curve. Credit: VSOLJ / Kyoto University

Dwarf novae are binary systems consisting of a white dwarf and a larger star. These stars are pretty dim, but have a sudden spurt of brightness over a few days with intervals of weeks or months. No one is exactly sure what causes these sudden increases in luminosity, but the most popular theory is the disk instability model, which states that the accretion disk of the white dwarf is thermodynamically unstable, which causes outbursts—but not explosions. Not much material is ejected when this happens, so it fits in with the rest of what happens.

Dwarf nova light curve (SS Cygni). Credit: AAVSO LCG

The next kind of cataclysmic star is the symbiotic nova. These are close binary systems comprising of a red giant and another hot star (be it a white dwarf, neutron star, or a main sequence star) in a cloud of dust and gas. A defining feature of these systems is that their periods are incredibly slow. It takes decades for them to go through one pulse. What happens with these stars is that the outer layers of the red giant is actually expelled due to stellar winds, and the hot companion star accretes this expelled matter. When there is enough matter, periodic explosions occur.

Light curve for symbiotic nova RR Telescopii (look at the dates along the bottom!). Credit: AAVSO LCG

Eruptive stars are much rarer—in fact, there is only one main type of these stars. These stars are called R Coronae Borealis stars, which are rare, luminous supergiants. Their “outburst” isn’t brightening, like every other intrinsic variable, but rather fading. For most of the time, they are at maximum brightness and even appear stable. Then suddenly, their brightness will decline by up to 9 magnitudes, and then slowly crawl back up to maximum luminosity over the course of a few months to a year.

R Coronae Borealis light curve. Credit: Wikipedia / AAVSO LCG

And whoo, we’re finally through! Of course, there are more types than the ones we’ve got listed here, but if you want to look at that, you might as well go to AAVSO’s 57-page document listing all the kinds of variable stars, listed here:

http://www.aavso.org/vsx/help/VariableStarTypeDesignationsInVSX.pdf

Nowadays, we’ve also got the GCVS, which is the General Catalogue of Variable Stars. It has about 46,000 catalogued variable stars from our own galaxy, 10,000 from outside our galaxy, and over 10,000 prospective ones. However, there are estimated to be millions simply in our own galaxy. We just haven’t gotten around to cataloguing all of them yet.

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TL;DR

There are a ton of variable intrinsic stars, and it is divided into three categories: pulsating, cataclysmic, and eruptive. There are many more subtypes within these stars. A common way to identify these stars is by using light curves. Pulsating stars are by far the most common and the most  studied, because of their uses as standard candles and pulsation periods, but cataclysmic and eruptive variable stars are quite…stellar…too.