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.

See Explanation.  Clicking on the picture will download the highest resolution version available.

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.

See Explanation.  Clicking on the picture will download the highest resolution version available.

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.


Sources and links for further reading (links to images are below):

Color-Mag Diagrams

Blue Stragglers, Stellar Evo with clusters



Both types of clusters

Cluster classification


Pleiades: NASA/APOD,

Omega Centauri: NASA/APOD,

Trumpler Classification:

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.


Sources and links for further reading (links to images are below):

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


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.



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.


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


Eclipsing binary







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


UNL Astronomy:

Discovery Space:

Dept. of Physics and Astronomy at University of Tennessee:

Australia Telescope Outreach and Education:

Northern Arizona Meteorite Laboratory Glossary:

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).

Visual Light Curve

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



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.


Sources and links for further reading (links to images are below):


Rotating (ellipsoidal)



Supernova Remnants

Well, this post will hopefully be smaller, but just as explosive (or implosive?) as the last one!  Today, we are dealing with the actually large topic of supernova remnants, or SNRs.  These things are technically nebula, but not the kind that we start a star off with. No, these are actually for the end of a star!  There are many types, stages, effects, and definitely much significance from yet another one of our magnificent acronyms.

As for types, there are effectively two ways to categorize them.  One is by the original SN that created them.  Let’s start off with that (but technically this isn’t an exact type like the actual SNR types).  Essentially, a SN happens and we are left with the star expanding and releasing heat at extremely high rates.  For all SNs, the SNR that is produced essentially follows the properties of that SN.  For example, Type Ia SNRs would all generally be around the same mass, and the most massive element in them would be iron.  SNRs are also used to find the progenitor event or SN.  Some Type Ia SNRs have been used to create models of white dwarf explosions, leading to the double degenerate progenitor model.  Type Ib, Ic, and II SNRs, on the other hand, give us even higher mass elements, such as gold and even up to uranium. They can also have interesting objects (neutron stars and black holes) left over, and produce neutrinos – which sadly cannot travel faster than light.  I guess you could say they just make quite the big bang.

You’d better thank SNRs for this! Credit: Thomas Jefferson National Accelerator Facility

Next we have the actual way they are classified.  For these remnants of the past, there are many types based on the shape of the SNR and the radiation detected.  Shell types are characterized by being…a shell.  That is, the outer edges are brighter compared to the inner edges.  Next, there are crab remnants, plerions, or pulsar wind nebulae (PWN).  They have less exact shapes than their shelled-up cousins.  They also notably have a pulsar in the center and emit X-rays.  But yes, it basically is based after the Crab Nebula in case you haven’t guessed it.  Then we also have composite remnants, mixtures of both depending on what wavelength is being viewed.  This creates two subtypes of composites.  Thermal composites stay cooped up in shells in the radio, but in X-rays they are crab-like (though, not exactly…), while plerionic composites somehow only show spectral lines in certain parts of the x-ray spectrum, and also have shells.

Cas A, a shell SNR. Credit: University of Minnesota and HST

The Crab Nebula, a crab-type SNR (we figured we might as well go with the obvious example). Credit: European Southern Observatory

W44, a composite SNR (radio = orange, infrared = red, x-ray = blue, gamma-ray = magenta). Credit: NASA/DOE/Fermi LAT Collaboration, ROSAT, JPL-Caltech, and NRAO/AUI

As for stages, there are a few different opinions.  Since NASA uses three, we will too (just for fun).  You may be asking, how are there stages for an SNR?  All the stages of stellar evolution are already over!  But wait, these stages generally just explain what happens after the SN goes bang.  So, we start off with free expansion, where the a shock wave is formed at constant temperature and expansion velocity.  That lasts a few hundred years.  Then we have the Sedov or adiabatic phase (adiabatic means no heat flow occurs).  During this phase the SNR starts to slow down and cool, and parts of the SNR start to mix.  This develops a magnetic field inside, and it lasts from 10,000 to 20,000 years.  The reason we say no heat transfer occurs is because energy is not actually released by radiation from the gas.  Pretty much, so far the SNR has gotten bigger, and it’s starting to have the original insane amounts of heat dissipate throughout it a little bit.  But then we come to our third phase, the snow-plow phase (sadly, no snow will be used in this explanation).  After the SNR has cooled down, electrons actually recombine with elements that were ionized, radiating energy to the point where the SNR actually starts to cool down Remember however, that this is astronomy, so our “cooling down” means it is still pretty hot.  But the snowball effect of recombining causes the expansion speed continues to slow down, and eventually, the material goes into the interstellar medium (ISM), forever…until it is used for another star! Got to love the circle of (stellar) life.

There are a few confusing things that maybe should be cleared up.  So let’s switch wavelengths (or topics)!  For an SNR, there is certainly a forward shock wave or bow shock.  What this means is that the magnetic fields that are being created meet space, and end up forming a curved shape, like a bow.  The word “shock” itself mainly refers to the transfer of energy carried by the expansion.  Sometimes a reverse shock also drives inward, slowing down the expansion.  The next topic of discussion are cosmic rays.  Pretty much, they are high energy radiation of charged particles, but they are puzzling because their energies are so high that we don’t know what they could have come from.  Theoretically, they may come from SNRs, which have a mechanism that accelerates charged particles like electrons to extremely high speeds.  Another aspect that we haven’t mentioned yet is Rayleigh-Taylor instabilities, which are basically differences in density that create mixing and loss of energy within an SNR.  For example, if you’ve ever seen two fluids with different densities (such as oil and water) in a cup, you’d know the more dense substance would sink.  But space isn’t precisely a cup…meaning we get a sort of twisted finger-like structure.

Rayleigh-Taylor instabilities in a glass of water. Credit: American Physical Society


TL;DR — After all this talking, if you haven’t noticed, SNRs are actually important to astronomy.  They are classified based on the type of SN that produced them, or by their shape and radiation.  We aren’t always able to see SNs, but we can find their SNRs to see their properties.  They show fantastic examples of how elements spread around the universe, which means you better thank astronomy for your gold watch or jewelry!  SNRs can show interesting properties such as bow shocks and Rayleigh-Taylor instabilities. To add more fuel to the fire (or star going supernova), they may even produce the mysterious cosmic rays.  Also, they just look pretty awesome.

Sources and links for further reading:

Carroll and Ostlie, An Introduction to Modern Astrophysics 2nd edition, p. 633 to 646


We apologize for the absence, as we have been extremely and unexpectedly busy.

It’s Christmas time folks!  And what do we have at the top of the tree (if you celebrate)?  A star, right?  The perfect reminder to bring us back to our lovely discussion on stars!  So, we have discussed the life of a star.  Now things get interesting.  We have reached the end of a star’s lonely existence.  Yet another difference between a star’s end and a human’s end is that in some cases a star can have one of the most awesome events in the universe: a supernova.  Summarized, it is an explosion of a star.  But in detail there are multiple types, all fascinating.

Take that and put it on your Christmas tree! Okay, maybe you don’t celebrate or it doesn’t seem that festive, but it’s still awesome. From:

Each type has a progenitor, which makes spectra important as they show the amount of elements present and rate of fusion.  For example, during an SN enough energy is released such that higher than average fusion can take place.  So, if you ever wondered where iron or even heavier than iron elements came from, thank SNe.  Other ways to determine the type follow similar reasoning, including light curves, energy, and progenitor events.  The main summary of the types of SNe is the popular Minkowski-Zwicky scheme or classification. We will now begin splitting up these wonderful things, despite the fact that SNe involve fusion.  There are two types: I and II.  A major way to characterize them is by spectra.  Type I SNe lack Balmer hydrogen emission lines, while type II SNe show Balmer hydrogen emission lines in their spectra.


The Type Ia (thermonuclear) SN is the most different.  It consists of a binary pair of two stars, one being a white dwarf.  As stated previously in the WD, PN, Type Ia post , they go through an uncontrolled thermonuclear explosion as the white dwarf becomes unstable upon reaching the Chandrasekhar limit.  The mechanism of explosion is important to note as the other three main types explode from gravitational collapse.

The other three main types are known as core-collapse SNe, which we explained at the end of our post on high-mass stellar evolution.  As the name indicates they collapse from the sheer amount of matter in one space, creating the appropriately named implosion-explosion event.  Type Ib and Ic are thought to mostly come from WR stars, so they appeared to be very similar.  But they were differentiated by spectra, where the Type Ib has shed its hydrogen shell before collapsing, while the Type Ic has shed its helium shell too. (Despite being caused by totally different mechanisms, both Type Ia and Type Ic lack hydrogen and helium lines; they are differentiated by the strong silicon lines in Type Ia.) As we said last time, the shedding of layers before explosion makes them sometimes named stripped-core collapse SNe.  Type II SNe are massive stars, of generally about 8 to 12 solar masses that have enough mass to collapse and then either continue collapsing or explode.

They also differ by location.  Type Ia are located in most areas as they only require a white dwarf and a binary system, and this is a more likely outcome for most stars.  Type Ib, Ic, and II all are generally in the galactic spiral arms in areas of relatively recent star formation since they require more massive, population I stars, which have to be massive enough to explode.

Another difference involves energy and light curves.  Type Ia SNe have the highest and most consistent peak; the rest depend on mass.  Also, out of the SNe, the only one with the possibility for a plateau or non-linear falling luminosity is the type II SN.  Visually the light curves are like so (click to enlarge):

From Wikipedia Supernova Light Curves

Next is the Type II SN and its core-collapse.  As the core collapses, protons and electrons are pushed together, forming neutrons and neutrinos.  This accounts for the high neutrino signatures that come from these types.  In fact, the relatively recent issue of faster than light neutrinos involved this very type of SN!  The neutrinos have such high densities that they develop radiation pressure, but the star essentially collapses in on itself, rebounds, and creates a shock wave.  These effects are named neutrino outburst and rebound shock.  Type II SNe can also be split up into types P, L, n, and b.  Type II-P and II-L stand for plateau and linear, which are the shapes of the light curve. The plateau type forms from hydrogen ionizing after the explosion, increasing luminosity, while the linear type fully expels its hydrogen layer.  Type IIn SNe are detected by narrow hydrogen emission lines in spectra, sometimes thought to be caused by LBVs.  Type IIb SNe show weak hydrogen lines initially, but the lines later become untraceable and it starts to resemble the spectra of a Type Ib SN.  The famous example of this is Cassiopeia A.  Another very high mass explosion is the hypernova, or a pair instability SN.  The pair instability occurs when atoms collide with gamma rays to form electrons and positrons, which creates a pressure to slightly reduce the core’s overall pressure.  This leads to a large-scale collapse.

For all the supernovae remnants (SNRs) can form.  For type Ia SNe they will always be large nebulae, but the other types can leave massive objects too.  These include a neutron star or a black hole.  The cause for the neutron star is that neutronization or neutrino outburst from neutron degeneracy pressure, analogous to the electron degeneracy pressure holding up a white dwarf, stops full collapse.  Black holes, on the other hand, collapse to a point.  Both objects have very odd and interesting properties.

To finish off we aren’t fooling that there are also supernova impostors, originally thought to be a type V SN.  These are also possibly LBV eruptions, but they don’t seem to be full supernovae.  As stated LBVs are unstable, so they can throw off large amounts of mass and heat that up.  They are recent but important events that are still being researched.



The easiest summary of supernovae is that they are characterized by many ways.  But they have great importance.  They explain how we could have any jewelry (in case you wanted to get some for a holiday present).  Even greater, they allow for a better understanding of the universe.  This is by giving ways to calibrate distance measures and  understand properties of stars.  Just to the point, they’re awesome.  It’s not Thanksgiving, but we should certainly thank SNe anyway.


References and further reading:

SNe in general:

Type Ib+Ic SNe:

Type II SNe:

SN imposter:

White Dwarfs, Planetary Nebulae and Type Ia Supernovae

In our last post about low-mass stellar evolution, we left off at the AGB.  So, what comes next?  We said of white dwarfs (WDs) and planetary nebulae (PNe), but these can get somewhat detailed, so they deserve a post of their own.  Especially since WDs have a very interesting relationship to a certain event we call a supernova (SN; we adore our acronyms).

After a star gets to the pulsating red giant phase, it eventually gets to the point where it doesn’t have the energy to continue fusion, usually by the C/N/O elements.  When this happens there is insufficient radiation pressure outwards to repel the gravity pushing the star inwards, making it condense (sadly we can’t condense all this astronomy information).  With that, the outer layers of the star shed off to form a PN.  Some may ask why they are called planetary nebulae, since they in fact do not have any planets at all.  It comes from the fact that early astronomers couldn’t see them clearly, and with PNe being generally green-blue, they looked similar to the planet Uranus.

Most PNe are indicators of the later stages of a low-mass star.  Therefore, they are generally found with Population I stars, younger stars closer to the galactic plane or center.  Like other nebulae, they also look awesome and are among the most popular targets for astrophotography.  An interesting fact is that they don’t only form as a spherical shell, but they can come in many shapes, such as a bipolar shape, and also rings and ellipses.  In general, PNe are distinguished by shape, so another major question is how these shapes form.  Many of the different shapes are theorized to be from high-speed stellar winds, but the rings most likely come from an ejection of material that occurred at a different time from the main ejection.

As for their colorful nature, PNe have red emission lines from hydrogen and have green lines from doubly ionized oxygen, or OIII.  They are created from the star’s light ionizing atoms, ripping electrons away and then recombining.  The lines from a PN are also known as forbidden lines, not because they shouldn’t happen, but because in a lab we could normally only produce these spectra under high density.  Space, on the other hand, is an odd, low-density environment.

The many shapes, colors, and sizes of these PNs. They may not be planetary, but they are certainly stellar! Credit: Bruce Balick and HST from

There are also Fast-Low Ionizing Emission Regions (FLIERs).  These are strange red-colored regions of a PN that are exactly what their name says.  But sadly their origin is not fully understood.  Some say they seem like they should be moving outward, but they could be stationary or even moving inward.  So yes, this lovely universe of ours likes to seem to make little sense.

Saturn Nebula (NGC 7009)

You can see the FLIERs at the sides. So…perhaps you can see what’s going on here. Credit: David Darling


They can have multiple features.  They may seem like degenerates for being aged as they are, but really they are fascinating.  They can be categorized as many types of stars. They can go ahead and nova or even go SN (for fun, let’s just say that they are little things with quite the Napoleon complex).  Yes, my fellow astronomy-lovers, we have gotten to the white dwarf (WD).

WDs are the result of  a star collapsing in on itself due to lack of radiation pressure, disrupting hydrostatic equilibrium, and allowing gravity to push inwards.  They come from stars that have run out of fuel, and they’re very small, being around the mass of the Sun shrunk down to the size of the Earth.  They are made mostly of the C, N, O elements because by that point a medium-mass star can’t fuse much more.  The color of the WD comes from the fact that it’s quite hot. It may not seem like it, but WDs can actually be detected in X-ray better than in visible light.

So then, the next question would be why doesn’t the star just continue to collapse?  It doesn’t even have fusion occurring to oppose the collapse.  Well, WDs actually have stability. They fulfill hydrostatic equilibrium, due to the Pauli exclusion principle, which works independent of temperature.  The compaction of the WD produces such a high density that all the atoms are smashed together to the point where electrons start to collide.  The Pauli exclusion principle says that two particles cannot occupy the same space with the same energy and spin, since they are effectively identical.  So, what happens when you have a lot of electrons in a little space?  Some that are in the same state collide.  Blasphemy!  In actuality a pressure keeps these two electrons apart, which creates pressure that stops total collapse.  This state of matter, as mentioned in the light and matter post, is known as “degenerate matter.”

Similar picture with electrons

And to summarize this. There’s not much space, so we are under high pressure here! This can oppose even the strong force of gravity. Credit: Chandra X-ray

Next, how do we detect them?  Well, Friedrich Bessel did manage to spot the white dwarf companion of Sirius in the visible range through careful observation (we’ll call this one Sirius business).  WDs can (and often do) form in binary star systems, which is an especially important way to detect any sort of object that’s normally tough to see, because if we cannot see the target object, the companion is still affected by that object.

And yet another interesting part to the WD is the famous discovery of one Subrahmanyan Chandrasekhar.  To get to the point, he found that WDs actually have a mass limit.  His work was highly debated at the time, but now it is heavily accepted.  So just how large can a star be before its mass overcomes even the pressure trying to oppose gravity?  The answer is about 1.4 solar masses.

What’s interesting about this is that there are actually multiple types of WDs, because the Chandrasekhar Limit is an upper mass limit.  This means smaller stars (even red dwarfs) can still form WDs, which have differing amounts of the elements C, N, O, and Ne.  For an analogy of how massive a WD is imagine one teaspoon of WD matter.  This is about 16 tons.  That is, if we had a beach ball of WD matter, that would still be heavier than an ocean liner.

white dwarf types

And now the summary of WD types. Credit: David Darling

Ultimately these stars would form into black dwarfs, fading away into another boring death.  But does this always happen?  Well, since it’s the universe, of course not!  In fact, WDs not only have multiple types, but they can even pulsate.  This will be discussed in more detail later (see, we like to mimic stars and evolve this blog as we go along).  Aside from spectral differences from different elements they also can differ by the presence of magnetic fields.


But the mass limit has even more interesting implications.  See, WDs can be in binary systems with a red giant star with unstably held outer layers.  Those layers can be ripped off the companion star and accumulate around the WD in a process known as accretion.  Aside from our fancy names, accretion allows for material to get close enough to the WD such that fusion can occur.  This flash of very high amounts of fusion all at once is what we call a nova.  The name comes from the fact that when astronomers first saw these bright flashes, they thought new stars were being made.  But the even greater thing is that when a WD gains more than 1.4 solar masses, it produces one of the many magnificent events in the universe, an supernova.

Now, to be specific SNe can be split into two types, and they are further split up from there.  The type of SN produced by a WD is known as a Type Ia SN.  There is hot debate over what causes it, perhaps at a thermonuclear level!  Okay, not that hot, but one theory is the above mentioned accretion.  There is also what’s known as the double degenerate progenitor (a progenitor is a fancy word meaning “the thing that created it”), which states that a binary system of two WDs with a total mass greater than 1.4 solar masses collided and, exceeding the limit, exploded. But what is the exact cause of an SN?  Well, so much mass is gained in such a little space that runaway thermonuclear fusion occurs when it burns up all at once, releasing a massive amount of energy.

A nice summary of the SN’s creation. Credit: hyperphysics

Type Ia SNe are well-known for multiple reasons.  They are located almost everywhere, since WDs are just older low-mass main sequence stars.  They are thought to be able to fuse carbon/oxygen all the way up to iron/nickel, creating the heavy elements of the universe. The spectra is noted for a lack of Balmer hydrogen lines, and further distinguished by the presence of silicon in their spectra.  Another major note is that since there is a mass limit on WDs, the light curves of a Type Ia SN should always be the same. This means they are what’s called a standard candle; that is, they can be used to consistently measure what distance the SN was from earth.  The absolute magnitude for a Type Ia is approximately -19.5.  This is essential for understanding distances across the cosmos and can be used to calibrate Hubble’s Law.

Lastly, we will show how this is really, really powerful.  An initial comparison is that some note that this is enough to equal the entire Sun’s energy emitted over its whole lifetime.  But let’s continue to show another way.  We said earlier in the apparent/absolute magnitude post that we can relate brightness or luminosity to magnitudes.  Let’s apply this now.  Given the absolute magnitude of the Sun is +4.83 and a solar luminosity is about 4×1026 W we can now find it:


L of the SN/1 solar luminosity =100(4.83+19.5)/5

=5395106225.15 solar luminosities = 2×1036 W.

Now to put this relative.  The global energy consumption per year is about 15 terrawatts.  That is, we could run the entire world’s energy supply and then some  for oh about 1023 years.  I believe it is undebatable to say this is insane.  Now, others say that the energy output is about 2×1044 J.  So, take this all as you will.



Now to condense (perhaps into a star, or even a WD!) all this information.  After we have a red giant star it sheds its loosely held layers to form a PN.  This PN can have many different colors and shapes.  At the center the remaining core of mass condenses into a white dwarf, composed of degenerate matter.  This means it is so condensed electrons repel eachother, creating an electron degeneracy pressure opposing gravity.  Beyond that, WDs have a mass limit known as the Chandrasekhar limit, being 1.4 solar masses. WDs can also form in binary systems.  If the partner accretes, or accumulates, matter to the WD then the WD can quickly fuse it and form an extremely bright nova.  If either this goes past the Chandrasekhar limit OR if a WD combines with another WD and exceeds the limit then the result is a beautiful Type Ia SN.  Type Ia SNe are valuable for creating heavier than normal elements, being common, and being standard in peak luminosity.  This is useful for calculation of large distances which leads to a better understanding of what we like to call the universe.


Sources and further reading:

Planetary Nebulae:


White Dwarfs:

Type Ia SNe:

Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd edition (pg 446-474,  524-529, 557-578)

Star Formation, Part I

Sorry we’re late, we just had to take the time to evolve this post.  That’s right, we are here to discuss the first step in a star’s evolution!  In one of my many twisted analogies I said that stars are like people.  So, we have the early stages of a star’s life!  Just like how people have baby and teenage years we have the topic of star formation and nebulae (again, twisted analogies…but I think we can all deal with the puns and any bad humor presented here).

Interstellar medium (ISM) is quite literally “the stuff between the stars”. And by stuff, we mean the gas and dust that stars form out of, and often, spew back into space during their lifetimes through stellar winds or supernovae. Unsurprisingly, hydrogen makes up most of the ISM as HI (neutral), HII (ionized), or H2 (molecular), and helium makes up most of the remainder. It’s hard to detect neutral hydrogen because its single electron is in the ground state, so it cannot jump down an energy level to release radiation, and only rarely does a photon of the right energy come along to boost the electron to a higher energy level. However, astronomers can still detect HI using the 21 cm line. This relies on the fact that electrons and protons both have a quantum “spin”. A hydrogen atom has slightly less energy when they are spinning in opposite directions as compared to when they are spinning in the same direction – the photon corresponding to this difference  in energy has a wavelength of, you guessed it, 21 cm.

While it doesn’t make up a large percentage of the ISM, dust blocks light and also reddens it, since longer wavelengths are less likely to interact with dust grains. It is sometimes found in the form of Polycyclic Aromatic Hydrocarbons (PAHs), which are relatively complicated hydrocarbons with ring structures. Why do we mention PAHs? Not for any important reason, they’re just thought to be necessary for life (even though we consider them scary carcinogens down here on Earth).

Thus, we start our evolution with stuff.  What is this stuff?  Oh, various things.  Hydrogen, helium, lithium… Yes, lithium in fact would exist, but we will ignore this until a bit later into the post.  But we just have stuff, what do we need to make a star?  Well, this stuff, at this point forming a nebula, literally meaning cloud, is not condensed.

The Eagle Nebula

Soar like an Eagle Nebula (yes, nebulae are pretty). Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA. From

Before we go further, we should note that there are several kinds of nebulae. Reflection, emission, absorption/dark, planetary, supernova remnants… heck, people used to call galaxies and star clusters “nebulae” as well. Note that this post will deal with star forming regions or cloud complexes, so there won’t be SNRs or planetary nebulae because they don’t really apply to the start of a star. Emission nebulae are formed when gas molecules are excited (yes, you be excited as well) by radiation from a nearby star and release radiation; they are typically red in color because of their hydrogen content. Reflection nebulae occur when starlight doesn’t have enough energy to excite the electrons and just reflects off dust particles instead (typically blue because shorter wavelength light is easier to scatter). Both these types of nebulae signal regions of star formation. Absorption nebulae, or dark nebulae, appear “dark” because they’re made of relatively dense clouds of dust that simply block light from behind them.  And why study these?  Well…they’re dark for one.  So yeah, they block out light, how annoying!  Luckily we have some ideas of how they block out light, but if we didn’t it would be quite the nuisance.  But then what else could they involve (you know, since astronomy just can’t leave something as is)?   Well, there are these things known as Bok globules.  They are smaller dark nebula that are also regions of star formation in HII regions, and they can also hint at some star formation in general since they can be in molecular clouds.

Horsehead Nebula (a dark nebula)

One of the most famous dark nebulae in the sky. Credit: NASA


Barnard 68-the other most famous blotch of black stuff in the sky that is actually stuff. Credit: NASA and

Thackeray’s globule-the other OTHER most famous blotch of black stuff in the sky indicating star formation. Yay for Bok globules! Credit: HST and

But back to stars. For a star to form, a chunk of the gas cloud has to increase in density to such a point that it collapses under its own gravity. Either random turbulence within the gas cloud itself may achieve this critical density, or an outside source, such as collision with another gas cloud or shock waves from a nearby supernova, may be involved. Astronomer James Jeans derived an equation to show the minimum mass necessary for a cloud of a certain radius to collapse; we of course know this as the Jeans mass. However, the Jeans mass neglects external gas pressure (which is factored in by the Bonner-Ebert mass) as well as several other factors that may influence collapse. The initial gas cloud fragments into several pieces, for reasons that we don’t quite understand yet, and these pieces may fragment further until their density is so great that they just keep collapsing.  And you guessed it, this is called fragmentation!  These are important because they can form binary stars and relate clusters of many stars, both of which are quite useful.  Fragmentation itself stops and changes due to differences in density and energy radiated as the collapse occurs.  Aside from this, factors influencing protostars are mainly motions (rotational or angular) and magnetic aside from atoms.

And to further the fascination let’s add some more factors.  As we said there is rotation and magnetic fields.  There are also differences in density.  Another factor?  Well, a commonly seen occurrence is to see stellar winds from massive stars blowing at or ionizing the protostar such that they are eroded away.  So, what do we get from these complications?  Birth lines!  Yes, they really are just like humans, well not at all actually, since these are actually lines for the beginning of protostars’ evolution.

Also, massive stars may not form from large amounts of mass collapsing, but from multiple smaller stars coming together because the high temperature, luminosity, and radiation associated with large stars are thought to be hard to achieve by collapse.  But this may not be needed because mass can fall into an accretion disk (an accumulated disk of material) around the star.  This could then make a massive star grow, and it wouldn’t be fully ionized, which could prevent collapse.

bate1.gif (33637 bytes)

“A typical interstellar cloud is supported against collapse by internal turbulent motions.”

bate3.gif (29165 bytes)

“Once such a cloud is “tipped over the edge” and starts to collapse, it reaches a state where gravity can pull the gas together to form dense “cores”. “

bate8.gif (27444 bytes)

“These cores continue to collapse, often fragmenting further, until they form star – sized clumps.” To show what we have been explaining thus far. Credit for the above three pictures: and Matthew Bate

So, are we at a star yet?  Nope, we still have a ways to go. You see, like we said stars evolve, like life theoretically, but we can track them much better (see, stars are so much more stellar than other things).  Tracks we say?  Yes, evolutionary tracks in fact!  These curves show major tracks for different mass stars.  The energy produced during this time is created from falling material going so fast that it goes supersonic and has what’s called a shock front, which basically just means that we get this whole mix of really fast moving stuff slowing it down to the point where energy is released.  Another note is that material is accumulating, or accreting (yes, it’s a word that will be used many many times) around the star as it collapses.  In fact, the collapse that occurs appears to be of infrared sources which appear in Bok globules.

Alright, but now what do we have?  Well, we’ll just say by this point we’ve gotten a protostar.  This collapses through the Kelvin-Helmholtz mechanism of gravitational contraction which can release potential energy as heat, explaining the light we see from a protostar.  Moving on we have the oh so important Hayashi Track!  In fact, Hayashi did many things with these early stars, but let’s just start with this.  The Hayashi track shows that for a collapsing protostar the opacity of a star increases from slight ionization of hydrogen.  This results in convection in the envelope, which he managed to show as a vertical line on the H-R diagram.  This line shows that the collapse eventually decreases luminosity and increases temperature.  The best part about this track?  It actually forbids certain types of stars from forming, greatly helping our search for star formation.

Hayashi Track

Credit: David Darling

After all this and some modelling we get what’s called pre-main sequence evolutionary tracks.  These are basically more tracks to see the evolution of stars.  Interestingly, a core and convective zone begins to form at this point, which can allow some slight fusion through the PP chain and the CNO cycle, but not enough to really stop collapse.  This can produce a slight expansion such that luminosity would actually slightly decrease.  In lower mass stars carbon generally can’t be burned, so later in life the CNO cycle wouldn’t really occur as much, but in massive protostars it’s slightly different since the CNO cycle would be more dominant.  So, what does this show?  Basically that mass matters.

We’ll cover types of Pre-Main Sequence objects and more star formation in Part II.


TL;DR – Stars form out of interstellar medium, massive clouds of gas and dust. A gas cloud becomes denser in one area, which collapses under its own gravity and also fragments to form several protostars. These not-quite-stars follow evolutionary tracks as they evolve towards the main sequence on the H-R diagram.  And what is basically the most important factor?  Mass.  This beginning stage is important to understand where to look for types of stars and events, to understand the processes in stars, and to help make better interpretations of how the universe works.




Star Formation (these sites cover most of the star formation post in general, which is why this isn’t split up so much)

Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd edition (pg 398-445)

Keeping Time in Astronomy

We are sorry this post was so untimely, but you see it was to show how important keeping time is (okay, just bear with us).  Yes, it’s about time for this post!  But why?  That’s because it’s about time of course!  Time is completely derived from watching the motions or being able to see the light of the Sun, Moon, and other objects.  Things can appear slow, fast, or like nothing in terms of time, it’s all relative of course.  In fact to an extent we can say that these clocks have driven us cuckoo!

The basis of time is the SI unit, the second, a special little s that is the only unit that can’t follow our normal SI system of 10.  Where could this even come from?  It used to be one second of minute of one hour of one solar day, therefore being 1/86,400 of a solar day.  Now we can use the wonders of the atomic clock!  The reason is because of all sorts of interference with complex “leap” times; there is even a leap second along with the leap year.  These leap times were done to correct the calendar due to all sorts of errors.  All these factors have led scientists and astronomers to develop many definitions of time.

To start, we have the year.  On average it is about 365.25 days.  So, where does the decimal come from?  To start we have a few different ways to keep time.  Sidereal time, or sidereal motion, looks to the revolution of the Earth with respect to DISTANT STARS.  This comes from observing the sky.  Solar time, also known as synodic motion, is with respect TO THE SUN, it is a daily observation to see when it rotates to get to the same place.  How much of a difference could this make?  Well, the solar day is about 24 hours.  The sidereal day is 23h 56m 4s.  In addition to the slight error, think about how the stars are moving in space.  We are slowing down/speeding up throughout the year, and on the scale of billions of years, or even a few years, these errors can make a fair amount of difference.  To be direct, the motions of the Earth are quite inaccurate.  That alone is reason to develop more accurate time-keeping.  Also, the sidereal year is an orbit around the sun relative to stars, while the tropical year measures between two successive spring equinoxes.  This alone creates a difference of 20 minutes in the year, so  this too builds up over time.

You can see not only is this revolutionary, but it is also timely (from Prof. Richard Pogge, Astronomy 161: An Introduction to Solar System Astronomy,, listed below ).

What would astronomy or science be without have more than a few ways to do something?  There is also standard time.  This was using railroads and telegraphs to standardize time.  It synchronizes clocks of different locations within a time zone not exactly using solar time.  This goes into time zones, dividing the Earth into zones of 15 degrees of longitude.  But this links into Universal Time (UT).  This was used to develop time offsetting from the Prime Meridian.  It was to replace the Greenwich Mean Time (GMT) which had multiple definitions.  UT is technically closer to a Mean Solar Time, with Greenwich as the reference.

But then there is more of course.  Eventually, with all these errors scientists decided that our definitions were a bit faulty.  So, the second was defined again.  The interesting thing about the second is it’s the only unit that isn’t regularly used with multiples of 10.  So, this develops into atomic time.  By using Cesium-133 (this is a specific isotope, but if you get your hands on cesium in general…well, please be responsible/have fun with the explosion) has a specific number of cycles with decay.  This has developed  into the notable atomic clock.

Another type of advanced time keeping is Ephemeris Time (ET), based on observing the motions of the planets and the sun.  ET was briefly used to define the SI second, but it has since been phased out as we have discovered better ways of timekeeping.  Now we’ll return to something nuclear.  Nuclear time involves an H-3 (tritium) isotope that beta decays to He-3.  When tritium reaches its half life a nuclear time elapses.  Next we have something very astronomical: pulsar time, the use of binary pulsars (yes, massive stars rotating around each other) to find periods varying by less than a second because of their relatively definite motion.

Lastly, we have one of the more important astronomy-related methods of keeping time.  These are Julian Dates (JD).  This is a continuous count of days since noon Universal Time on January 1, 4713 BCE (this would be on our everyday Julian calendar).  This may seem quite arbitrary, but the reasoning was that at the time of its development, there were no known historical events before this year, so as to avoid negative dates or BC/BCE/AD.  It also links to solar and lunar cycles.  About 2.5 million days have occurred since then, and it may not seem obvious, but this calculation has to take into account leap years, days, minutes, seconds, and other inaccuracies.  However, it is much more accurate and can better show second differences in data collection.  To make life easier, below we have these formulas:

a=\frac { 14-month }{ 12 } \\ y=year+4800-a\\ m=month+12a-3

For dates in the Gregorian calendar:

\\ JD=day+\frac { 153m+2 }{ 5 } +365y+\frac { y }{ 4 } -\frac { y }{ 100 } +\frac { y }{ 400 } -32045

For dates in the Julian calendar:

\\ JD=day+\frac { 153m+2 }{ 5 } +365y+\frac { y }{ 4 } -32083

Aside from this we should note what a common notation is-J2000.  This is related to epochs, saying that time is starting from the JD on the date January 1, 2000.



Time can be taken from keeping track of specific stars in the sky, relative to the sun, from atomic clocks and pulsars, or simply by measuring the amount of time from a specific date.  While time may not seem directly important, but a lot of work has been put into this concept.  It is the basis of a large portion of physics and technology.  Astronomy itself benefits immensely from being able to orderly be able to keep track of time for objects.  So next time your clock wakes you up in the morning, remember to not throw it across the room, because it’s just another way of reminding us how important time is.  Also, it means that you should get the heck out of bed or else you’ll be late.



Time in general

Julian Dates

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:


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):


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:


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


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:


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.


Sources and further reading: