# The Big Bang and Cosmology

The night sky is, for the most part, dark.

This observation has undoubtedly been made many times over, but in the nineteenth century, Heinrich Olbers realized that this simple fact contradicted the existing steady-state model of the Universe. If the Universe is infinitely old and infinitely large (and also homogeneous on large scales), then no matter which way one looks in the night sky, one’s line of sight must eventually find a star and therefore the night sky should be a blazing sphere of light. This is Olbers’s Paradox — he was not the first to draw this conclusion, but he is the most well-known for it.

Even when we consider the fact that less light reaches us from more-distant stars, Olbers’s Paradox is still not resolved. If we picture a series of “shells” of stars, centered on the Earth, we can see that while the light reaching us from each individual star is proportional to $\frac{1}{{d}^{2}}$ as a consequence of the Inverse Square Law, the number of stars per shell is directly related to the surface area of the shell and scales with ${d}^{2}$. Therefore the light reaching us from each shell is the same and the paradox still stands.

Illustration of Olbers’s Paradox (Credit: Htkym / Wikipedia)

Of course, the solution to Olbers’s Paradox is that the Universe is not both infinitely old and infinitely large.

The theory of the Universe beginning with a Big Bang was first proposed by Georges Lemaître in 1927, as part of a solution to the Einstein field equations. (Einstein himself believed in a static universe and had to introduce a “cosmological constant”, Λ, into his equations to compensate.) Edwin Hubble demonstrated concrete proof of an expanding Universe when he noticed that galaxies further from the Earth were moving away at a faster rate; this is now called Hubble’s Law, with recessional velocity equaling Hubble’s constant (H0) times distance. Hubble’s constant is thought to currently be ~ 71 $\frac{km/s}{Mpc}$, but it is worth noting that Hubble’s constant is not truly a constant, as it may change with the expansion of the Universe.

Rough Timeline of the Big Bang / Early Universe

• t = 0 — BANG! (not really an explosion)
• t < ${10}^{-44}$ sec — Planck era, quite literally our idea of it is limited to “?????”
• t = ${10}^ {-36}$ to ${10}^{-34}$ sec — Universe inflates dramatically, increasing in size by 10^(50) times, strong force becomes distinct
• t = ${10}^{-12}$ to ${10}^{-10}$ sec — Electromagnetic and weak forces become distinct
• t = ${10}^{-6}$ to ${10}^{-5}$ sec — hadrons (protons, neutrons, etc.) and leptons (electrons, positrons etc.) form from quarks
• t = 1 sec — annihilation of matter and antimatter has slowed, matter dominates even though they should have been created in equal amounts
• t = ${10}^{2}$ sec — the nuclei of Hydrogen and Helium (and small amounts of Lithium and Beryllium) are formed in what’s called “Big Bang Nucleosynthesis”

A brief history of everything — click to expand to a readable size (Credit: CERN)

About 380,000 years after the Big Bang, the Universe had finally cooled off enough for atoms to form (on the order of 3000 K), thus allowing photons to travel through space without being constantly scattered by free electrons. Due to the ongoing expansion of the Universe, the radiation from this point in time has been cosmologically redshifted to the point where it now falls in the microwave part of the EM spectrum. Thus, we call it the Cosmic Microwave Background Radiation (CMBR). The CMBR was first detected by Arno Penzias and Robert Wilson in the 1960s, as a faint bit of microwave noise coming from, well, everywhere. Data most famously collected by the Cosmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP) shows that this “noise” matches almost exactly with what we would expect from a cosmologically redshifted version of the 3000 K blackbody radiation curve.

The CMBR as observed by Planck — yes, it’s not from WMAP, Planck is more recent and we like it more (Credit: ESA and the Planck Collaboration)

After around 1 billion years, stars and galaxies have finally formed and the universe as we know it has started to take shape. But as we observe the beginnings of the Universe, we also wonder, what will be its eventual fate? To determine this, we must turn to some rather complicated cosmology.

Cosmologists define a density parameter ${\Omega}_{total}$, which is the density of (for lack of a better term) stuff in the Universe — we can’t call it matter because only a fraction of it is matter — as compared to a critical density, ${\rho}_{crit}$. This critical density is just enough for the Universe’s expansion rate to slow down to zero as time approaches infinity. There are three main possibilities:

• ${\Omega}_{total}$ > 1 (ρ > ${\rho}_{crit}$) — a closed Universe, it will eventually reach a maximum size and then start collapsing (“Big Crunch”)
• ${\Omega}_{total}$ = 1 (ρ = ${\rho}_{crit}$) — a flat or critical Universe, the expansion rate of the Universe will approach zero as time goes on
• ${\Omega}_{total}$ < 1 (ρ < ${\rho}_{crit}$) — an open Universe, it will expand forever, but the rate of expansion may be constant or it may be increasing

Different fates of the Universe — orange = closed, green = flat/critical, blue = open, red = open and accelerating (Credit: NASA GSFC)

Data from distant Type Ia supernovae and the CMBR appear to support a model where ρ is very close to ${\rho}_{crit}$, but the Universe is still accelerating. However, this raises another problem — the amount of mass that we can see and measure out in the universe is about 4% of what is required to match ${\rho}_{crit}$. This is where the stuff we referred to earlier comes into play.

First of all, astronomers have noticed that galaxies and clusters appear to contain much more mass than we can actually see. Rather unimaginatively, they named this invisible source of mass dark matter. Even the combined amount of regular matter and dark matter is nowhere near enough to match ${\rho}_{crit}$, but the presence of dark matter still doesn’t explain why the expansion rate of the Universe is increasing. Cosmologists believe that another type of stuff, dark energy, actually creates a “negative pressure” (that is to say, it repels other stuff), thus causing the acceleration.

Distribution of matter and energy in the Universe (Credit: NASA / JPL-Caltech / T. Pyle)

Whew.

We thank you for sticking with us through that, as theoretical cosmology is not exactly our strong suit as astronomy geeks, but we hope you enjoyed our attempt to — quite literally — explain the Universe.

==========

# Binary Stars (Part III)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Center of mass (barycenter) is where:

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

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

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

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

$v=\sqrt{GM/r}$

• v=orbital velocity

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

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

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

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

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

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

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

and

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

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

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

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

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

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

==========

# Binary Stars (Part I)

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

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

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

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

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

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

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

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

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

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

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

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

Types of binary systems (Credit: David Darling)

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

———-

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

———-

# 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.

———-

# 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 (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.

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.

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.

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.

———-

# 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).

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…

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 (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).

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.

==========

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

# Star Formation, Part II

So last week we talked about how new stars are formed from collapsing clouds of gas and dust, and how these protostars make their way towards the Main Sequence. This week, we’ll go over some of the different kinds of Pre-Main Sequnce objects as well as other things related to early stellar evolution that we find interesting.

T Tauri stars and their higher-mass counterparts Herbig Ae/Be stars are temperamental things, perhaps somewhat like toddlers (or teenagers). These young stars are still accreting matter from a thick surrounding disk and spewing it out in high velocity jets. The rotating disk is formed through conservation of angular momentum, since the initial collapsing cloud had at least a little bit of rotation to it, and therefore the speed of rotation increases as the cloud collapses. The jets produce Herbig-Haro objects, which are luminous patches of stuff moving away from a protostar. Material ejected from the star collides with ISM and causes it to glow brightly.

Two Herbig-Haro objects in the Carina Nebula (yep, one of last year’s DSOs). One can easily see the outward jets and the bow shocks generated as things collide. (Credit: Hubble Heritage)

We know that T Tauri stars are young stars because of the amount of lithium they still contain in their atmospheres, since lithium is burned up quickly and cannot exist in such large quantities in old stars. They’re also irregular variables, with random changes in luminosity over a matter of days (mood swings, perhaps?). In fact, they’re so irregular that unlike basically every other kind of varstar, it’s impossible to classify stars as T Tauris based on their light curves and astronomers have to resort to looking at their spectra instead. From spectra, we can also distinguish two classes of these stars. Classic T Tauri stars (cTTs) have large accretion disks and show strong emission lines, while weak T Tauri stars (wTTs) hardly have any disk.

T Tauri spectra often show something called a P Cygni profile, a blueshifted absorption line right before an emission line (typically of hydrogen-alpha), first discovered in Luminous Blue Variable (LBV) P Cygni. This is a sign of mass loss, since the absorption line shows that light from the star is being absorbed by gas in front of it, and its blueshift means that the gas producing it is moving towards us, and therefore away from the star itself. The broad emission peak results from the fact that the star is expelling matter in all directions, and so some of it appears blueshifted to us and some of it appears redshifted.

Credit: Wikipedia

FU Orionis stars, or FUors (yes, they really are called that), are T Tauri-like stars that undergo sudden increases in mass accretion. Matter from the inner disk falls onto the star, both causing the disk to shine so brightly that it outshines the star itself and creating extremely high speed winds. It is thought that all T Tauri stars go through several FU Orionis “temper tantrums” before settling down on the main sequence.

To put it bluntly, brown dwarfs are slightly pathetic “failed stars” with masses less than 0.072 Msun but greater than that of a gas giant planet such as Jupiter. They simply don’t have enough mass to ignite the hydrogen fusion reactions necessary to form a main sequence star. Brown dwarfs generate energy mostly through the Kelvin-Helmholtz mechanism of gravitational contraction or through the burning of elements such as lithium or deuterium. We shouldn’t make fun of them too much, though, since there are a huge number of brown dwarfs in our galaxy and they’re extremely hard to detect (although Spitzer has discovered quite a few of them through observations in the infrared), so you never know where one may be lurking…

On the other end of the star-mass spectrum, there are things called OB associations and superbubbles (sadly you cannot have the fun of popping them).  OB associations are associations of O and B-type (i.e. high mass) stars that have similar radial or kinematic motions, forming what’s called a kinematic group.  They are an association also because they generally have similar ages, forming from the same collapsing gas cloud.  This goes into the study of stellar kinematics, which is relatively broad and won’t be fully mentioned, but it should be appropriately fascinating for all you evolving stars, I mean, readers out there.  Superbubbles come from high stellar winds associated with OB associations.  The reason they form is that multiple winds and shock waves from supernovae can form bubbles in a sort of spherical shape as they spread out from the star, and then combine with other bubbles to form superbubbles.

A superbubble. Isn’t astronomy pretty? (Credit: European Southern Observatory)

Some more fascinating features to our lovely early stars are circumstellar disks and protoplanetary disks (propylds).  Very simply, the circumstellar disk forms around a protostar as it spins and accretes a disk of material.  A propyld is when that disk is, as the name indicates, possibly able to form a planet.  So yes, we came from a bunch of spinning, hot stuff in space. To quote Carl Sagan and others, “we are star stuff.”  We are literally star stuff, yes, be happy for our stellar-ness and the fact that everyone’s relative is the Sun.  Moving on from our little side rant of how awesome space is, these disks are major hints as to protostars, their development, and how binary stars or planets are formed.

Well, we’ve gotten this far.  Yes, we’ve discussed quite a lot about the variety of ways that a protostar forms, and what it’s influenced by.  So, we have reached the Zero-Age Main Sequence (ZAMS)!  This may sound odd, but it makes quite a bit of sense.  It refers to the line across the H-R diagram for masses when a star is formed, or when it is at age zero on the main sequence (see what we did there).  There is in fact an inverse relation between star formation and time it takes to form.  This can reveal the Initial Mass Function (IMF), which basically defines again star formation.  It shows that most stars form with lower masses due to fragmentation and other reasons that make massive star formation more difficult.

———-

TL;DR — T Tauri stars are young stars still in the process of accreting matter, which they may spew out in jets to form Herbig-Haro objects. They often have P Cygni profiles in their spectra, which show that they are ejecting matter. FUors are thought to be T Tauri stars that suddenly have matter dumped onto them from the disk and increase greatly in brightness. Brown dwarfs are “failed stars” without enough mass for the fusion of hydrogen to helium to take place. A group of massive stars may be part of an OB association, which may in turn be home to a superbubble. Circumstellar disks and protoplanetary disks are… well, exactly what they sound like. Once a protostar has stabilized, it reaches the Zero-Age Main Sequence on the H-R diagram. The Initial Mass Function illustrates the formation of stars of different masses.

———-

T Tauri/Herbig-Haro:

P Cygni:

FU Orionis:

Brown dwarf:

Superbubbles/OB:

Propyld: