A new kind of supernova

We are sure that at least two kinds of astrophysical black holes exist, one kind correspond to black holes of stellar mass (around 8 times the mass of the sun or bigger) and the black holes at the centers of galaxies with millions of solar masses. For some time there was speculation about the existence of some intermediate mass black holes with masses around few thousands the mass of the Sun, evidence from the rotation of stars in globular clusters gave the first evidence for the existence of intermediate mass black holes.

Despite evidence from the rotation of stars around the centers of globular clusters, the case is far from closed, the centers of globular clusters are regions of high density, filled with degenerate stars (mostly white dwarves) and maybe the rotation speeds can be explained by an overabundance of stars. A new paper (available here) by Stephan Rosswog, Enrico Ramirez-Ruiz, and William R. Hix proposes a radically new method for searching this black holes.

In close binary systems composed by a red giant and a white dwarf, the white dwarf can steal some matter from the red giant star (which has a low surface gravity), matter falling into the white dwarf has angular momentum and as a result of that an accretion disk is formed, white dwarves are supported against gravitational collapse by electron degeneracy (essentially if you try to pack electrons too closely they will start to move faster as a consequence of the uncertainty principle), this degeneracy can only support a mass of about 1.4 solar masses (otherwise the electrons would move faster than light), this is known as the Chandrasekhar limit, so when the white dwarf has "stealed" enough mass from its companion it will eventually surpass this limit, in this case the star is reignited by a mechanism known as carbon deflagration, creating a supernova explosion of the IA type.

Now, enter intermediate mass black holes. Computer simulations including gravity, hydrodynamics and nuclear physics show the effects of a close interaction between a white dwarf and an intermediate mass black holes. The star is heavily disrupted by tidal effects and acquires a pancake-like form, as the star is squeezed there is a dramatic increase in pressure and the star is reignited and creates a new kind of supernova, around half of the mass is ejected and the other half falls into the black hole creating an accretion disk that should emit x-rays.

This image shows the interaction of a white dwarf and a black hole, the star is heavily deformed in the first two frame, in the intermediate frames the star reignites and explodes, the "bubble" is the ejected material and at the bottom left corner an accretion disk is formed, the last two frames follow the evolution of this disk.

While this supernovas should be much scarcer than usual IA supernovas, new surveys like the LSST should detect enough supernovae to have a good chance of detecting this events, and x-ray emission should be detectable by the Chandra Space Telescope. The light curve should be different, although I haven't seen any detailed model. Considering that globular clusters are composed mostly of old stars and large populations of white dwarves this events should be happening relatively frequently around the universe and might give us unequivocal evidence of intermediate mass black holes.

Star formation 101. Part 1

The time has come to pay one of the old debts of this blog: A mini-course on star formation. The night sky is full of little twinkling stars, but despite their obvious abundance its formation is still far from being a closed case.

Gravitational collapse (a cloud of interstellar gas collapses and produces stars) is the obvious way to produce stars , but it leaves us with a startling question, we can estimate the time of this collapse using the expression:

which is called the free fall time and as you can see it only depends on the density of the cloud and not of its size, for a typical cold cloud this time is around one million years, this is obviously problematic because we know galaxies are much older than that and we can observe star formation in practically every spiral or irregular galaxy.

This indicates us that other forces are acting on molecular clouds, slowing the process of gravitational collapse. There are four hurdles that star formation has to overcome, as we will see in this star formation series it is surprising that even a single star can overcome this hurdles! This hurdles are:

• The pressure hurdle: A homogeneous, spherical gas cloud is stabilized against collapse by its own pressure gradient. This means that the temperature of the cloud despite being small still implies enough energy for the particles in the cloud to overcome their own gravitational attraction. We can estimate the size at which the cloud is doomed to collapse, this is called the Jeans radius and is given by
  
  
  
  
  
  where k is Boltzmann's constant, T the temperature of the cloud, m the mass of the particles and n the numerical density of particles. The Jeans mass is simply , when we plug numbers into it we realize that stars similar to our Sun require cooler and/or denser regions than the average of the interstellar medium. This regions are the molecular clouds.
• The dynamical hurdle: As the cloud collapses it is heated, the energy required to heat the cloud comes from its own gravitational potential and it eventually reaches an equilibrium state when
  
  
  
  
  
  where K is the kinetic energy and V the potential energy, when this condition is satisfied we say that the cloud is virialized. So we can see that star formation requires cooling, otherwise the cloud will get virialized and reach a stable configuration halting the collapse. Thermal conduction and convection are remarkably ineffective in this regions and most of the cooling is radiative.
• The angular momentum hurdle: As gravitational collapse shrinks the cloud, angular momentum conservation amplifies any initial angular momentum (which is usually of the same magnitude of galactic rotation) by an enormous amount, the spin frequency is amplified by around 10¹⁶, this is such an spectacular increase in the spin that the cloud should be teared apart by the centrifugal effects. Dissipation is required to get rid of this excess of angular momentum, it is thought that this excess leads to proto-stellar disks.
• The magnetic flux hurdle: Lorentz force implies that charged particles are free to move in the direction of the magnetic field but have a hard time moving perpendicularly to it, so the magnetic field behaves as a spring refusing to compression. Collisions between the charged particles and the neutral ones eventually transfer this "springy behavior" to the rest of the cloud. A process known as ambipolar diffusion eventually allows the neutral component to fall through the ionized component.

The current state of star formation is centered around two paradigms: The "standard model" based on the collapse of isothermal clouds under ambipolar diffusion and the "turbulent model" based on the redistribution of energy at diverse scales of the cloud, making some "lumps" where star formation takes place.

In future post I expect to explain you how each of this hurdles can be overcome and give an overview of this two paradigms.

Milkomeda

The local group of galaxies consists of two big spiral galaxies: our own Milky Way and Andromeda, and a rather small spiral galaxy known as the Triangulum and about 40 small galaxies of varied morphology.

Unlike most galaxies which are redshifted due to the expansion of the universe, Andromeda is blueshifted meaning that it is moving towards us. Eventually the Milky Way and Andromeda will collide, this is a bit uncertain because the only way to know for sure if the local group is bound we need to measure the radial and transverse velocities of its members, we can measure the radial speed from the redshift but transverse speeds are quite complicated to measure. Despite that, the measurements of the radial velocity of Andromeda are of 120 km s-¹ towards us and a transversal velocity of around 100 km s-¹ and it is certainly smaller than 200 km s-¹ (Loeb A., Reid M. J., Brunthaler A., Falcke H., 2005, ApJ,633, 894). Using this values we can conclude that the system is indeed bounded and that the merger is quite likely to happen.

The galaxies of the local group. Andromeda is clearly the biggest member (this doesn't means it is the most massive, we have reasons to believe that the Milky Way has more dark matter and is more massive). The only other major galaxy is Triangulum which is significantly smaller. The rest of galaxies are small and many of them have irregular morphologies like the Small Magellanic Cloud.

Kahn and Woltjer pioneered the study of the dynamics of the local group (Kahn F. D., Woltjer L., 1959, ApJ, 130, 705), they argued that Andromeda and the Milky Way formed quite closely and then separated with the expansion of the universe, then started to approach each other due to their gravitational attraction. From this suppositions they were able to estimate the mass of the local group and the size of the orbit.

A detailed simulation of this merger has been produced by T.J. Cox and Abraham Loeb (arxiv:0705.1170v1). They used a model of the local group proposed by Kyplin et al (Klypin A., Zhao H., Somerville R. S., 2002, ApJ, 573, 597) which has as much as 20 times more dark matter than baryonic matter. The diffuse intragroup medium was supposed to have a mass comparable to the mass of the galaxies. The simulations were carried with the GADGET 2 code (if you are computer and astro savvy, you can download this code and run your own simulations of astrophysical phenomena in your computer).

In this simulation we have the first detailed scenario for the Sun as the merger happens. This merger will start in less than 2 Gyr, first with tidal interactions that will create a stream of matter between the MW and Andromeda. As we mentioned in a previous post, the Earth will be out of the habitable zone in about 1.1 Gyr, unless some advanced civilization enlarges the radius of Earths orbit (Korycansky D. G., Laughlin G., Adams F. C., 2001,Ap&SS, 275, 349). Despite that, let's continue to discuss the fate of the solar system.

During the first close encounter, there is a 12% chance that the Sun will be pulled out of it's current position in the outer arms of the MW and reside in the extended tidal material between the MW and Andromeda, during this phase we expect a burst of star formation. After the second encounter the chance of residing in the tidal material rises to 30% and a more interesting outcome arises, there is a 2.7 % chance that the Sun will be captured by Andromeda. In this scenario any astronomer in the Earth will be able to see the MW (or rather its remains) from Andromeda in the night sky.

This is the simulation by Loeb et al. You can see that the collision won't be a head-on merger, but rather the two galaxies will spiral into each other, the final result of the merger is an elliptical galaxy.

After the merger is completed, the simulation suggests that the Sun will habit in the outer halo of a massive elliptic galaxy, which Cox and Loeb call Milkomeda. This is only a possible scenario using realistic assumptions about the local group, in their paper Cox and Loeb report a dozen of additional runs with different values of the density of the intragroup medium and the transverse medium and find that the outcome is esentially the same. The resulting galaxy has the R^(1/4) brightness distribution that is typical of elliptical galaxies, so our own local group will act as a prototype of the late forming elliptical galaxies.

Tomorrow the AAS anual reunion starts, so we can expect some nice news in astronomy for the next week!

Life and death of interstellar dust

In this part of the "dusty posts program" we will talk about formation and destruction of dust in the interstellar medium. Before we embark on this questions we need to know at least two things about dust: its size and composition.

As we mentioned in the last post, the dust betrays its presence by absorbing light, the absorption efficiency at some wavelength depends on the size of dust grains. Absorption is a rather complicated phenomenon because there are many physical processes that can cause absorption in our sightline, light might be literally absorbed by the dust grain or it might be scattered out of our sightline. Scattering is also dependent on the ratio between the wavelength of the scattered light and the dust grain diameter. If this ratio is small we talk of Rayleight scattering, otherwise the process is known as Mie scattering.

Detailed analysis of absorption curves leads us to believe that scattering is caused by small solid solid particles which have a diameter comparable to the wavelengths of visible light (this explains the 1/lambda behavior in the visible part of the spectrum), nonetheless we still need other components to explain some features of the absorption curve.

An average absorption curve, the far infrared is on the left and the ultraviolet on the right. There are some variations in different zones of the galaxy, but the shape of the curve is usually quite similar. We can see the peak of absorption are at 200 nm (or 1/lambda = 4.6 ).

Now let's move to the composition of dust. The Sun being so close to Earth is readily observed and we (somehow naively) assume that it is a typical star and its composition is assumed to be fairly typical of the Galaxy. We can then use the Sun abundance of elements as a guide for relative abundances between it and the interstellar medium.

We know that the relative abundances of the Sun and the interstellar medium are different. The main difference is that some elements have an underabundance of elements compared to the Sun. This elements are usually refractory, meaning that this elements can survive high temperatures without being sublimated, this directly points us to dust, as this elements can condense in dust grains that can survive in the vicinity of stars. Depletion is defined as

and as we can see below, this elements are among others Cr, Fe, Ni, Co, Ti. Despite that, the bulk of a grain is quite similar in composition to the dust you can find in your backyard and is mostly divied in to graphites, silicates and olivines.

Interstellar elemental abundances compared relative to hydrogen compared with the Sun. We can see that refractory elements are heavily depleted. The depletion is a logarithmic quantity defined, meaning that some elements like Ti are depleted by three orders of magnitude.

So, how are dust grains formed? The first idea is to think that they grow slowly in the interstellar medium. The problem with this idea is that actual calculations show that this will take too much time, suppose that at time t=0 the grain has a radius r(0), if we suppose the grain grows by addition of species i with mass m_i moving at a mean thermal speed v_i then the radius at a later time t will be

where epsilon is a "sticky coefficient" that meassures the probability that the m_i will remain attached to the grain and s is the density of the solid grain. Using the typical values for interstellar medium we find that for a typical grain (about the size of visible wavelengths) the time required is

which is too much time if we consider that the value of epsilon is smaller than one, and that the age of the universe is around 13 Gyr.

The solution comes from considering denser regions, in particular the atmospheres of cool stars. The material in stars is originally so hot that it did not contain any solids, but as it outflows in later phases of the life of the star it starts to cool with much higher densities than the interstellar medium and the atoms can arrange themselves in to the most stable molecules at that temperature (usually around 10³ K). When this outer layers are ejected in stellar winds the dust goes in to the interstellar medium. There is some controversy about the formation of dust in the early life of the universe, the most accepted view is that this dust was formed around active galactic nuclei.

Now let's move to grains destruction. The simplest way to destroy a grain is to heat it enough so it sublimates. That indeed happens in the vicinities of young, hot stars. The sublimation temperatures depend on the composition and size of the grain, this results in a stratification of the dust with large graphites closer to the star, followed by smaller graphites and large silicates, at larger distances from the star we can find smaller silicates, olivines, fused quartz and silicates with ice mantles.

A more interesting mechanism comes from accumulation of electric charges in the surface of the dust, if the grain is spherical with a radius a and is carrying a charge of Z electrons then the electrons capture cross section if the speed of the electrons is u_e is given by

When enough electric charge accumulates on the surface the stress it causes on the grain as it tries to redistribute, causes the grain to literally explode! Quite an interesting consequence for the well known fact that charges redistributes on a surface!

It actually results that the capture of species by dust grains has a crucial importance in astrobiology, keep tuned!

Dust in the interstellar medium

Today I will give you a brief overview of a topic that's quite close to me: the effects of dust in interstellar medium. There are some regions in the sky that seem to be almost magically depleted of stars, even in very dense regions. The classical example of this "dark nebulae" is the coalsack in the Crux constellation.

The coalsack dark nebula is the best known region where interstellar dust is so dense that it blocks all the light (in the visible frequencies) in it's sightline.

This regions are not depleted of stars, but rather the light of the stars in the sightline is absorbed by dust. This is far from obvious, after all there is no a priori reason to discard the idea that this regions simply lack any stars.

The first conclusive evidence of light absorption in the interstellar medium came from the work of Robert Trumpler who measured the angular sizes of globular clusters trying to calculate its distance from Earth. The idea was simple, let's assume that globular clusters are roughly the same size, then the smaller a particular cluster seems to us, the farther it is. When Trumpler carried on this plan he realized that the there was a linear relation between the size and the distance, i.e. the clusters were bigger as the distance to them increased. This was quite unexpected and also seemed to point to the rather disturbing conclusion that Earth is located in a special place where globular clusters are smaller.

Rather than that, Trumpler realized that the distance was systematically overestimated (so the clusters weren't that big, after all). Then he assummed that the reason for this bias was extinction in the interstellar medium, meaning that something (presumably dust) was absorbing light on its way to Earth.

Further evidence for dust comes from light polarization. When light is reflected from a dust grain it is polarized depending on the alignement of the grain, if the grains are aligned with Milky Way's magnetic field, we can then use the dust polarization as a measure of the direction of the magnetic field.

Measurements of dust polarization, this measurements show that optical polarization is aligned with the magnetic field.

What is the composition of this dust? This depends on many factors. Nonetheless the most important one is the distance to a star, particullary to hot, young stars. This stars (known as early spectral type) are so hot that that dust sublimates in its vecinity. The grains composed of carbonites are more resistent (and bigger grains have a better chance of survival), then the silicates enter the stage. In colder enviroments larger molecules appear on the surface of the grains.

How are this grains formed? Why is dust relevant for astrobiology? Which are the effects of dust on ionized regions? Keep tuned for later posts!

Doomsday

What will happen to the Earth in the far future? Can humanity or it's successors live forever in it? By now most of you know the lore: the sun will eventually consume all of its "fuel" (hydrogen and later helium) in 5 billion years, expand in to a red giant that will devour Mercury, Venus and the Earth. After that the Sun will eject the outers layers of its atmosphere and leave a stellar corpse: a white dwarf which is small, extremely hot object supported by the pressure of electron degeneracy. The ejected outer layers will be ionized by the radiation of the white dwarf and form a nice planetary nebula, like the Helix.

The Helix nebula is one of the best known planetary nebulae, in the astro-lore it is usually asummed that the Sun will produce a similar nebula when it dies.

Well, I recently attended a talk by Klaus Peter-Schroeder, from University of Guanajuato, in his talk he disputed this scenario. Now, let's discuss the good, the bad and the evil ...

• The good: Previous models assumed a "naive" modeling of mass loss as the Sun ejects it's outer layers based on Reimer's Law, which is basically based on dimensional arguments. An improved version of this law applied to the Sun shows that it will loose enough mass to allow Earth's orbit to enlarge sufficiently to avoid the doomsday scenario.
• The bad: Well, that doesn't mean that Earth will be an habitable planet. It will be too uncomfortably close to the Sun, but you might still think that we have around 5 billon years to worry about that. Well, that's wrong. The Sun will increase it's energy output in around a billion years (still a lot of time) by a sufficient amount to increase Earth's temperature around 10 K. You might think that it will be an uncomfortable but still bearable change, nonetheless climate models predict that effects of such a change will be catastrophic.
  
  
  
  

  

  In "The End of the World", the Doctor travels to Earth's last moments before being engulfed by the Sun. In the show the writers imagined that some "gravity satellites" held back the expansion of the Sun, we now know that it will be tidal dragging to blame for Earth's destruction.
  
  
  
• The evil: Well, life on Earth will end one day, but at least will Earth survive to total destruction? Not really, despite that the Sun won't grow enough to engulf Earth, a process known as tidal dragging (you can think of it as a sort of "tidal friction" assisted by dynamical drag) will cause the Earth to spiral into the Sun! The model is extremely sensitive to little details, but we can estimate that the doomsday will happen just 500 000 years before the Sun reaches the tip of the AGB branch.

So the lore is actually quite wrong in practically every detail, but wait! There is still a final twist to this plot. The nice planetary nebula that will act as a sort of mausoleum to the star that made life on Earth possible actually requires stronger stellar winds than the Sun can provide. This is still a point of controversy, but at least among the attendants the consensus was the Sun might produce an irregular planetary nebula at best.

Addendum: It results I was being very naive with the raise of temperature. In Klaus own words:

"It is 1 Gyr for a rise of 10% in the solar irradiance, which makes the Earth leave the habitable zone. But in order to raise the temperature by just 10K, we need much less time! It is difficult to compute because a detailed knowledge of the various positive (and negative) feed-backs is required, but it should be of the order of 100 mio years. That is still very long compared to the timescale of the current climate change....! "