Friday, January 25, 2008

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.

Thursday, January 10, 2008

No asteroid impact on Mars

We ended last year commenting the possibility of an asteroid impact on Mars, this asteroid (2007 WD5) had rather small change of crashing on Mars.

The latest data has ruled out this possibility, the use of archival photos and observations from the German-Spanish Astronomical Center, Calar Alto, Spain; the Multi-Mirror Telescope, Mt. Hopkins, Arizona; and the University of Hawaii telescope, Mauna Kea, Hawaii yielded and impact probability of cero.

We will need to wait for this kind of serious fireworks in the future!

Sunday, January 06, 2008


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!