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

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

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

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:

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.



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.

Further Reading


Variable Stars

We may think that stars generally only change and evolve on timescales too great to observe within human lifetimes, but astronomers have discovered that many stars exhibit some variability in luminosity, size, or another physical property within relatively short time frames. Unsurprisingly, they refer to stars that vary in brightness over time — since brightness is the main property of stars that we are able to observe — as variable stars (or varstars, sometimes variables, as we like to call them). Throughout this post, please be aware of the distinction between brightness, how much light we observe coming from a star, and luminosity, the amount of light the star produces.

V838 Monocerotis, one of this year’s DSOs and a very mysterious varstar. Credit: NASA, the Hubble Heritage Team (AURA/STSci), and ESA

Any star that shows any kind of variations in brightness can be a varstar; the changes don’t have to be periodic (though many types of varstars do show some kind of periodicity). With such a broad definition, there is obviously a plethora of varstar types, so astronomers must classify them — we’ll give a general overview now and explain some of the specific types of varstars in greater detail in the weeks to come.

First of all, there are two main kinds of varstars, which distinguish the general cause of the star’s variability.  Intrinsic variable stars vary in brightness because of changes within the star that cause it to vary in luminosity. Extrinsic variable stars, on the other hand, do not vary in luminosity but vary in brightness because something other than the star itself changes the amount of light that we receive from it.

A light curve for Delta Cephei, the namesake of Cepheid varstars. Credit: Michael Richmond (RIT)

Intrinsic varstars are generally split into three main classes — pulsating, eruptive, and cataclysmic — with some catalogs recognizing a fourth class of x-ray variables. Pulsating variable stars expand and contract, causing variations in brightness and size, among other properties. They are further subdivided into radial pulsating varstars, where the entire star undergoes these periodic pulsations at the same time, or non-radial pulsating varstars, where parts of the star expand and contract differently. Most pulsating varstars are post-Main Sequence stars located above the Main Sequence in an area known as the instability strip, which is named for the fact that stars located there are unstable and undergo pulsations. Eruptive variable stars vary in brightness because of violent flare-ups or other stellar processes, usually involving matter either being lost from the star or being gained by it. Cataclysmic variable stars (sometimes also known as explosive variables) are somewhat like eruptive variables, since they also undergo occasional outbursts, but in cataclysmic varstars the outbursts are caused by thermonuclear processes. Yes, supernovae — and regular novae — are considered to be cataclysmic variables! Finally, x-ray variables are defined as optical variables  closely associated (often in a binary system) with a strong, variable source of x-ray radiation.

Extrinsic varstars are classified as either eclipsing or rotating. Eclipsing variable stars are part of multiple-star systems that are aligned just right so that as we observe from Earth, one star passes in front of the other as the system orbits. When this happens, the total brightness of the system is reduced, causing a noticeable dip in the light curve; we also see a smaller dip in brightness at the secondary eclipse (when the stars’ positions are switched and the other one is eclipsed). Rotating variable stars either have uneven surface brightness due to sunspots or magnetic fields, or are non-spherical in shape. Therefore, as the star rotates, we receive different amounts of light from it depending on what areas are visible.

Artist’s conception of Epsilon Aurigae, an odd eclipsing binary. Credit: NASA/Caltech JPL

Of course, it is worth noting that there are varstars that cannot be definitely classified.  This is because either they haven’t been studied closely enough to determine their type, or because they are oddball varstars that don’t fit nicely into any classification that astronomers have discovered.

The fact that we’ve devoted a whole series of posts to varstars should tell you that they’re pretty important to astronomy, but how exactly are they important? Eclipsing varstars are by necessity part of a binary system, and studying these stars can tell us more about the system or about binaries in general. Some types of varstars, such as Cepheids, can be used as “standard candles” to determine distances to individual stars, clusters, or even galaxies. Pulsating varstars in the instability strip can tell us more about stages of post-Main Sequence stellar evolution. And of course those wonderful detonating varstars, novae and supernovae, can tell us about the end stages of stellar life.


TL;DR — Variable stars are, well, stars that vary in brightness. They can be divided into intrinsic or extrinsic varstars; intrinsic varstars are then classified as pulsating, eruptive, cataclysmic, or x-ray variables, while extrinsic varstars are subdivided into eclipsing and rotating variables. Varstars are very important to astronomy for a multitude of reasons, including learning about the stages of stellar evolution and determining distances.  Even the Sun is a varstar, making it a topic that is certainly close to home.


Sources and links for further reading:

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

Black Holes

Apologies for the lengthiness between posts all!  We had a combination of immense amounts of work and a slightly confusing topic (though, mainly the former).  But wait, that’s a perfect progenitor to create the title object!

Black holes—one of the great mysteries of the universe. They made Stephen Hawking’s head hurt, helped spawn relativistic theory…they are, indeed, wonderful objects that may or may not confuse the heck out of you.

In general terms, black holes are warped regions in spacetime where singularity points (singularities) with infinite density have enough gravity to pull in anything—including light, which means that we can’t see them. It is infinitely dense because density = mass/volume, and the volume of a singularity is a point or zero. There are a lot of technicalities in black holes—we’ll cover them one by one.

Firstly, let’s look at how black holes are formed. They are giant—maybe even supergiant—stars that explode into a supernova and then collapse in on themselves. Normally, they would turn into a neutron star and stay there, but if the neutron star exceeds the Tolman-Oppenheimer-Volkoff limit, then it collapses and turns into—drumroooooll…a black hole.

An illustration of Cygnus X-1, widely thought to be a black hole. Credit: CXO

Now we’ll go over general black hole anatomy. The fabric of spacetime is usually smooth and even, with paths going out equally in all directions that can be traveled on. A black hole warps that—it makes a hole, essentially, that pulls everything in. The paths don’t go equally in all directions anymore, but instead all lead towards the center of the black hole. The centre of a black is a singularity of no mass, which warps spacetime to an infinite degree. Around it, there is this thing called an event horizon, which is the “point of no return”. Once an object goes past the event horizon, it cannot escape the black hole’s gravitational pull. A black hole may grow in size by accreting other objects of mass (contrary to popular belief, black holes do not “suck”), slowly growing larger and larger.

A black hole has three independent physical properties (which means properties that can be observed from outside the black hole): mass, charge, and angular momentum. Any two black holes found to have the same values for all of these are said to be indistinguishable and therefore black hole “twins”, if you will. This is what we call the no-hair theorem. There are two main kinds of black holes—the kind that rotate, and the kind that don’t.

The ones that don’t rotate are called Schwarzschild black holes. These black holes have no electric charge or angular momentum, but only mass. They are as simple as you get—unmoving, gravitational vortexes in the spacetime continuum. These are also just about the only objects in the universe that are perfect—and I mean perfect—spheres. They’re also special in another way—once you get past the event horizon, there is absolutely no way you will be able to avoid getting sucked into the singularity. None. You don’t stand a chance against the forces of a black hole.

Kerr black holes, on the other hand, do rotate. There is a theory—just a theory, mind—that states that it is possible, under perfect conditions, for matter to travel through its rotating ring of a singularity. The theory says that when you exit the black hole, you will most likely end up in another universe, with the black hole acting as an Einstein-Rosen bridge, or wormhole.  This is because the spinning produces what’s called frame dragging, producing an ergosphere.  This actually spins the fabric of space time, making objects able to travel around the black hole, and sometimes around the singularity as we said.

Theoretically, charged black holes exist as well, but in reality, the charge tends to attract particles of the opposite charge, which quickly cancel it out. Charged black holes that don’t rotate are called Reissner-Nordström black holes, and the ones that do rotate are called Kerr-Newman black holes.

The event horizon (Schwarzschild Radius) of a black hole. Credit: University of Colorado, Center for Astrophysics and Space Astronomy

There is also something called the Schwarzschild radius (we know, we know, you’re tired of hearing about Schwarzschild, but bear with us) that tells you a lot about this kind of black hole. The Schwarzschild radius is the radius at which the Schwarzschild metric, or gravitational field of a black hole, becomes singular—it becomes one, massless point. Therefore, the Schwarzschild radius is often referred to as the radius of a black hole and gives its size. The event horizon is actually situated right at the edge of the Schwarzschild radius, so the radius can even be thought of as the distance from the singularity to the event horizon.  The weirdest part to this is that for the whole black hole itself this gives it an actual density.  Okay, maybe what would be weirder is that some black holes can have a low density.

The Schwarzschild radius (derived from escape velocity for those who are curious) is given by the equation { R }_{ s }=\frac { 2GM }{ { c }^{ 2 } } , where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

Another way to change up black holes is by mass, which is shown with that there Schwarzschild radius.  Black holes are normally created by stars with masses between lower and upper mass limits of about 3 to 100 solar masses.  In real life…weird results have come up with impossibly massive stars or stars very close to the lower limit).  But even then, there are all sorts, theoretical or not. The types include:

  • Micro black holes—Hawking theorized that low-mass black holes could be formed by high pressures in the early universe, if these exist, they might emit bursts of Hawking radiation in the (relatively) near future as they evaporate.  They also may, for an instant, be created here on Earth in the LHC!  Alternatively, we hear of work being done with lasers to make them (oh, how science is awesome).
  • Stellar-mass black holes—3 to 15 solar masses, the major example used is usually Cygnus X-1, and they can form high energy X-ray binaries.
  • Intermediate mass black holes—100 to 1000 solar masses, theoretically the center of globular clusters, may form from mergers of stellar-mass black holes, and may eventually merge into a supermassive black hole.
  • Supermassive black holes—10^5 to 10^9 solar masses, the theoretical centers of spiral galaxies, thought to explain AGNs and quasars.
  • Primordial black holes—very large and small ones that formed in the early universe, 10^-8 to 10^5 solar masses.  They aren’t fully understood.

Black holes also have another effect called gravitational lensing, which is when gravity causes light to bend so much that we can see multiple images of the same object. We follow the light rays in a straight path (which is normally what’s done with lenses), so we can see their apparent locations. Cool, huh? And if the black hole is perfectly symmetrical with respect to the line from Earth to whatever object we’re viewing, well, we can see an entire ring of the object. It looks something like this:

Credit: NASA Goddard Space Flight Center

Unfortunately, however, the black hole is rarely ever perfectly in line with Earth and the object we’re trying to view. So, instead, we see two images, like this:

Credit: NASA Goddard Space Flight Center

So what happens if you fall into a black hole, you ask? Well, it’s really not pretty. Once you get past the event horizon, you’re basically dead meat. There are ways to slow your descent into the singularity, but really…it’s hopeless. Once you get to a certain point, you just get sucked into the singularity, where your body is crushed into infinite density and added to the mass of the black hole. Right before that, however, you get torn apart by tidal forces of gravity and turn into a long, noodle-ish looking thing. That’s called spaghettification. It is really not pleasant. I would advise you to never try that.

But wait! There’s more! How do we know black holes exist if we can’t see them? The answer is this: Even though we can’t see them, they have effects on the surrounding regions that lets us know that they are indeed there. Their gravity is still great enough that they have effects on surrounding objects, though really, it’s not obvious enough that we’d be able to find it. But the most obvious thing they do? Because they accrete so much stuff, they radiate X-rays and energy like you wouldn’t believe. Just tons and tons of X-rays and energy—and best of all? Usually, they’re accompanied by these giant relativistic jets of gas, spouting from either end of the black hole. We don’t know why, or how, but there you go. Huge jets of glowing gas blowing out of black holes. And that is how we know they’re there.

Active galaxy Cen A, with jets powered by the supermassive black hole residing at its center. Credit: European Southern Observatory

There’s also something else called a naked singularity, which technically isn’t a black hole because it lacks an event horizon, but for all other purposes and intents, is the same thing. It is a massless singularity of infinite density that sucks in just about everything around it—it just doesn’t have an event horizon. However, no naked singularities have been discovered yet, so it seems that black holes like to stay clothed (as stated by the Cosmic Censorship Theory).

We mentioned Hawking radiation earlier in the post, but what exactly is it? Well, the real explanation is beyond the comprehension of any of your resident astro geeks, but we’ll just say that sometimes particle-antiparticle pairs are created at the event horizon, and one escapes and one does not. These particles result in evaporation, which takes away energy and therefore mass from the black hole.  Hawking radiation increases as the black hole loses mass, so at the very end of a black hole’s life, it releases a powerful burst of high-energy radiation.  In fact, some primordial black holes are thought to be going through this right about now.

Another point to make is what happens when “stuff” falls into a black hole. This “stuff” has various properties that are dubbed information. From there, there is a debate.  Perhaps not the Great Debate, but a fairly important one that has resulted in the black hole information loss paradox. This pretty much debates whether information is lost by a black hole. Some say it is, some say it isn’t (cue the Thorne-Hawking-Preskill debate). It is a paradox because two scientists, Hawking and Bekenstein, found that with Hawking radiation, a black hole evaporating information thrown into it would make that information permanently disappear. Forever. But then this violates some more quantum mechanics that are somewhat difficult to comprehend. Some say that the information should also exist just in a slightly…changed form. Again, we don’t even pretend to really understand these theories, but it just goes to show how complicated these strange astronomical objects are.


TL;DR: Black holes are the condensed remnants of extremely massive stars. Their density is so high that all sorts of pressures that would normally oppose gravity can’t fight anymore, and the battle for equilibrium is over.  So the mass basically condenses down to a point with many properties that aren’t fully understood. First of all, black holes technically can’t directly be seen, as light would warp around it.  But we can still manage to infer properties with this major disadvantage!  For example, properties of a black hole can be focused to mass, charge, and spin—these factors result in different types of black holes, but that’s beside the point (see what we did there?).  Black holes also have tons of anatomy to them, even if this isn’t biology.  Most importantly, their “size” is defined by a Schwarzschild radius, which defines the event horizon, the outer limit where the black hole’s effects exists. Hawking radiation is where black holes lose mass through some fancy quantum physics that we don’t pretend to begin to fully comprehend, but it does show that black holes don’t actually last forever.  Interestingly, they also end with a bang.

Sources and links for further reading:

Hawking Radiation:

Information paradox:

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

Neutron Stars

In our last post, we discussed supernovae in all their explosive stellarness, and this week, we’ll discuss some of the “leftovers”, so to speak. Yes, these are the first of our lovely stellar remnants — the neutron star and its relatives the pulsar and the magnetar.

A neutron star (NS) forms from the collapsed core of a star that explodes in a Type II supernova, and much like its name suggests, it is a highly compact ball of neutrons. A typical NS has a few solar masses of matter packed into a sphere 20 km or so in diameter (about the size of a large city), a density roughly equivalent to packing every human being on the planet into the volume of a sugar cube. When the core of the original star collapses, conditions are so extreme that protons and electrons are squished together to make neutrinos and neutrons. The surface of a neutron star is a thin solid crust made mostly of regular nuclei, but as you go towards the core, you find nuclei with more and more neutrons; eventually you would reach the “neutron drip” layer, where neutrons leave their nuclei and move around freely, and then… well, no one really knows what kind of exotic matter lies at the core.

Neutron star structure

Neutron star structure (Credit: Wikipedia)

Much like electron degeneracy pressure keeps a white dwarf from collapsing, neutron degeneracy pressure holds up a neutron star against its own gravity, but if it is above ~3 solar masses (the Tolman-Oppenheimer-Volkoff limit, or TOV limit), even neutron degeneracy pressure can’t hold out against gravity, and the stellar remnant collapses into a black hole instead. Some astrophysicists also theorize that when a stellar remnant has a mass between a neutron star and a black hole, exotic remnants like quark stars may exist. However, the neutron star itself started off as just a theory too — it was first proposed in 1933 by Fritz Zwicky and Walter Baade, only a year after the discovery of the neutron itself!

Now, we skip forward a third of a century to 1967, when Cambridge grad student Jocelyn Bell Burnell, working under adviser Antony Hewish,  discovered a curious radio source that emitted pulses so regularly that it was thought to be a signal from an extraterrestrial civilization, and even named LGM 1 for “little green men”. Astrophysicists discovered several more of these sources, eventually realized that they had to be rotating neutron stars (see here for a detailed explanation), and named them pulsars as a contraction of “pulsating stars”. Two of this year’s DSOs are particularly interesting pulsars — one because it’s among the oldest pulsars ever discovered, the other because it rotates so darn slowly for its relatively young age.

Crab Pulsar

One of the most famous pulsars in the sky – the Crab Pulsar in M1 (Credit: NRAO/AUI and Joeri van Leeuwen (UC Berkeley) / ESO / AURA)

Going back to characteristics of these massive, compact objects.  When the core of a massive star collapses to form a neutron star, it starts to spin very rapidly. The original star was rotating slowly, and now conservation of angular momentum dictates that its angular velocity will increase because its radius — and therefore its moment of inertia — decreases (that is to say, it spins faster because it is now smaller and has less resistance to change in its motion). The classic analogy is a figure skater who starts spinning with her arms extended, and spins faster as she pulls her arms in to her body. The magnetic field also becomes much stronger, because the field lines get closer to each other as the star collapses.

Just like not all rectangles are squares, not all neutron stars are pulsars. We only see a pulsar if the neutron star’s rotational and magnetic axes are misaligned in such a way that the radiation beam produced at the magnetic poles sweeps across earth as the NS rotates. This is called the lighthouse effect, because the pulses we see from a pulsar are analogous to the beam from a lighthouse appearing to blink on and off to an observer far out at sea. Rotation-powered pulsars, such as the Crab Pulsar represented in the image above, spew out synchrotron radiation from high-energy particles above their magnetic poles. Most rotation-powered pulsars are found in radio wavelengths, but a few can also be detected in x-rays or gamma-rays (the Crab can reportedly even be seen in the visible). Accretion-powered pulsars, on the other hand, are typically visible in x-ray wavelengths. These pulsars are part of a binary system, accreting matter from a companion. The pulsar’s magnetic field may direct the accreted matter towards the magnetic poles (in the process heating the matter until it’s hot enough to emit x-rays), where it creates a “hot spot” that emits x-ray pulses as the pulsar rotates.

pulsar diagram

Diagram of a pulsar (Credit: NRAO)

The period of a pulsar slowly increases with age, as it gradually radiates energy into space. However, there are two important ways in which a pulsar can speed up. Glitches are sudden, small decreases in a pulsar’s period that last for a short time before the pulsar resumes its normal slow increase in period. Astrophysicists don’t know for sure what causes glitches, but it is thought that the crust and “mantle” interact in such a way that the crust shifts and the NS shrinks by a tiny amount, increasing its spin speed (again thanks to conservation of angular momentum). The other way in which a pulsar can speed up is accretion from a companion star. Matter spirals in around the NS, contributing angular momentum and spinning it up to a period of a few milliseconds — hence the term “millisecond pulsar” (MSP). They are also called “recycled pulsars” because the infalling matter has restored the pulsar to a faster spin rate.

Vela Pulsar Glitches

Glitches in the Vela Pulsar – individual glitch events are labeled with arrows (Credit: GAE-UCM (High-Energy Physics Group at the Complutense University of Madrid))

Magnetars are pulsars with extremely high magnetic fields — hundreds or thousands of times stronger than the already powerful magnetic fields of a regular NS. It’s thought that they are created with spin speeds much faster than normal pulsars, and this increased spin strengthens the magnetic field, amplifying it to many times more powerful than normal. However, a magnetar also ceases to emit beams of radiation much sooner than a comparable regular pulsar, because its strong magnetic field quickly slow downs its rotation rate. These strange NSs were first theorized in 1992, when Robert C. Duncan and Christopher Thompson attempted to explain how magnetic fields were created around pulsars in the first place. They found that under ideal circumstances, neutron stars could create fields thousands of times stronger than observed in regular pulsars. Magnetars have been used to explain strange cosmic phenomena such as Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs).

Alas, as fascinating as these stellar remnants are, we humans may never be able to study them up close, as one would be quite dead — in multiple ways — before even getting to a neutron star.


TL;DR — Neutron stars are made of, well, neutrons; they are prevented from collapsing by neutron degeneracy pressure until their mass reaches the TOV limit. Most neutron stars spin very quickly, and if conditions are right, we see them on Earth as pulsars. There are two main kinds — rotation-powered pulsars (high-energy particles in magnetic field) and accretion-powered pulsars (radiation emitted from heated, infalling matter). Pulsar periods can be sped up through glitches or by accretion in “recycled” pulsars. Magnetars are neutron stars with abnormally powerful magnetic fields.


Sources and links for further reading:


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:

High-Mass Stellar Evolution

We’ve spent the past couple weeks discussing low-mass stellar evolution and its results, but now it’s time to move onto bigger and better things. That’s right, now we’re going to explore high-mass stellar evolution, otherwise known as “the stars that do go BANG”.

First, we should clarify that by “high-mass stars“, we mean those with masses from approximately 8 M_sun to 100+ M_sun. The upper mass limit for a star is not definitively known, but it is approximated by the Eddington Limit, where the radiation pressure outwards is so strong that it overcomes inward gravity and blows the star apart.


High-mass stars form just like low-mass stars — only with, well, more mass. Also like low mass stars, they start their lives on the Main Sequence, fusing hydrogen to helium. However, high-mass stars have much shorter Main Sequence lifetimes than low-mass stars.  This is because even though they have more mass, that additional mass results in an increased rate of fusion which burns through their fuel faster. Thus, high-mass stars quickly leave the Main Sequence and become RSGs/BSGs, LBVs, WR stars, and SNe (yes, we really do love our acronyms in astronomy).

High-mass RSG structure

The inner structure of a high-mass red supergiant (Credit: New Mexico State University)

RSG and BSG stand for “red supergiant” and “blue supergiant“, respectively. Just like low-mass stars, high-mass stars also migrate to the right side of the H-R diagram when a helium core builds up and hydrogen shell-burning starts. The increased radiation pressure from faster fusion causes the star’s outer layers to expand and cool. So, we have a RSG. When the helium core ignites (this time without an explosive flash, since the core is not degenerate), the star heads back towards the “blue” part of the H-R diagram. So, we have a BSG. Then, when the star can no longer fuse helium in its core, it will become a RSG again; when the carbon core ignites, it will revert to a BSG; and so on. A high-mass star will make many treks across the H-R diagram from “blue” to “red” and back as successively heavier elements fuse in its core, with each journey producing less energy and lasting for a shorter period of time, until it reaches an iron core…

LBV Eta Carinae

Luminous Blue Variable Eta Carinae (Credit: CXO/NASA)

LBVs are Luminous Blue Variables (also called Hubble-Sandage variables, or S Doradus variables), which are basically exactly what they sound like — they are massive, luminous stars that are blue in color and vary in luminosity over time.  They spend most of their time in a quiescent state, varying by a magnitude or two over a period of years.   But occasionally they undergo violent outbursts, which can be so bright that they have repeatedly been mistaken for supernovae. Quiescent LBVs generally appear as B-type supergiants that shed mass at high rates, but during an eruption, they become cooler, become  redder and eject huge amounts of mass. It is thought that really massive stars pass through a short LBV phase on their way to becoming WR stars, but no one knows for sure.

WR star in NGC 2359

WR star in NGC 2359 (Credit: P. Berlind and P. Challis of the Harvard-Smithsonian Center for Astrophysics)

WR stars are Wolf-Rayet stars, named for astronomers Charles Wolf and Georges Rayet, who discovered these fascinating stars. These massive and incredibly luminous stars are primarily noted for their powerful stellar winds, which cause extremely high rates of mass loss. Unlike normal stars, WR stars have prominent lines of helium in their spectra, along with nitrogen (WN), carbon (WC), or rarely oxygen (WO) (there is logic here since these elements are in the CNO cycle). WN stars can be further divided into “late” classes (L) and “early” (E) – WNL stars have hydrogen emission lines in their spectra, while WNE stars do not. Like the LBV stage, high-mass stars do not spend a long time in the WR stage, so these weird stars are quite rare.

SNe of course stands for those wondrous exploding stars, supernovae! Massive stars are thought to be the causes of every type of supernovae except Type Ia (if you will recall, those are caused by exploding white dwarfs).  These include Type Ib and Ic, and all the subtypes of Type II.

The precise stages that a high-mass star will pass through depend on its mass. There is significant variability in the exact masses and stages from source to source, so we have avoided trying to compile everything into one table because it would just end up as a mess. In general, stars on the low end of the “high-mass” spectrum tend to turn into RSGs or BSGs, then going supernova. More massive high-mass stars generally evolve into LBVs, then WN stars, then WC stars (or very occasionally, WO stars), before finally exploding as supernovae.


While all these changes are taking place in the exterior of the star, the stellar interior is constantly fusing heavier and heavier elements. As we mentioned in the post about nuclear reactions, massive stars above 8 M_sun can fuse elements all the way up to iron (technically up to cobalt and nickel, but these isotopes are radioactive and decay into iron). Any fusion past the so-called “iron peak” consumes energy instead of releasing it, which undermines exactly what the star has been trying to accomplish throughout its entire life.

When the core becomes hot and dense enough to fuse iron, photodisintegration (the splitting of elements by, you guessed it, photons or light) of heavy elements into light elements consumes energy and recently-formed neutrinos carry energy away, causing the core to collapse. The core will eventually reach such a high density that it refuses to be compressed any further and “bounces”, sending a shock wave outwards into the rest of the collapsing star. The shock wave stalls, but then accelerates again due to the neutrinos that are forcing their way outwards as well (neutrinos typically don’t like to interact with regular matter, but since there are so many of them here, they have quite an appreciable effect) — this is a core-collapse supernova. The exact mechanism of collapse and rebound for a supernova is not fully known, but overall this is what’s expected to occur…and hey, we are talking about giant massive stars, give some credit that our good astronomers could even find this much.  When stars have their outer envelopes shed, they are instead called stripped core-collapse supernovae (with this massive stars encompass all the non-Type Ia SNe).

M1 Crab Nebula

The famous M1 Crab Nebula, created by a core-collapse Type II supernova (Credit: HST)

After exploding, the core either forms a giant supernova remnant (SNR), becomes a neutron star or has so much mass that it collapses further into a black hole.  We shall save these interesting objects for another post, as this post would be intolerably long if we tried to discuss those here as well. (We will also cover all the different types of supernovae in a further post, since they are so important that they deserve a post of their own.)


TL;DR — High-mass stars start off their lives very much like low-mass stars.  While low-mass stars will become a red supergiant, eject PNe, and turn into WDs,  high-mass stars cycle between red and blue supergiants or turn into Luminous Blue Variables and Wolf-Rayet stars. In the end, high-mass stars will explode in (sometimes stripped) core-collapse supernovae and produce strange stellar remnants.


Links and sources for further reading

General High-Mass Evolution:

Luminous Blue Variables:

Wolf-Rayet stars:

Type II SNe:

Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd edition, p. 518 to 534