How far away is that star?

On a clear night, far away from the city lights, one can look up and enjoy the beauty of the starry sky. This display must have enticed people for as long as people existed and I’m sure the question has often come up: how far away are those stars?

Well, there is an interesting tale of discovery related to the progression of measuring sticks that give the ability to determine the distances to astronomical objects. Part of this tale is how Edwin Hubble discovered that the universe is expanding.

The realization that we live in an expanding universe complicates the answer to the question of how far away astronomical objects are. Apart from the fact that the distances change, there is also the issue of what distance we observe at a given point in time. If I use the apparent brightness of a star with a known absolute brightness, then one may think (at least I would have) that the implied distance is between us (the earth) and the location of the star at the time the light was emitted. This is not the case.

Diagram of light from a star or galaxy propagating to be observed on earth

The above diagram tries to explain what happens. The black dots represent a star or galaxy (the source of the light) at different locations in an expanding universe. The blue dot is the earth which is kept it at a fixed location in the expanding universe. The red circles represent the expanding sphere of light after being emitted by the source at some point in the past. Assuming that the universe expands uniformly, we see the source would always remain at the center of the expanding sphere. Moreover, since the observed apparent brightness is given by the total emitted power divided by the total surface area of the sphere, the associated distance is the distance from the earth to the current location of the source. This is called the proper distance to the source.

Amazing, we are able to know the distance to an object at its current location even if we cannot see that object now. Who knew?

Neutrino dust

It is the current understanding that the universe came into being in a hot big bang event. All matter initially existed as a very hot “soup” (or plasma) of charged particles – protons and electrons. The neutral atom (mostly hydrogen) only appeared after the soup cooled off a bit. At that point, the light that was produced by the thermal radiation of the hot matter had a chance to escape being directly re-absorbed.

Much of that light is still around today. We call it the microwave background radiation, because today that light has turned into microwave radiation as a result of being extremely Doppler-shifted toward low frequencies. The extreme Doppler-shift is caused by the expansion of the universe that happened since the origin of the microwave background radiation.

It is reasonable to assume that the very energetic conditions that existed during the big bang would have caused some of the hydrogen nuclei (protons) to combine in a fusion process to form helium nuclei. At the same time, some of the protons are converted to neutrons. The weak interaction mediates this process and it produces a neutrino, the lightest matter particle (fermion) that we know of.

So what happened to all these neutrinos? They were emitted at the same time or even before the light that caused the microwave background radiation. Since neutrinos are so light, their velocities are close to that of the speed of light. While expansion of the universe causes the light to be red-shifted, it also causes the neutrinos, which have a small mass to be slowed down. (Light never slows down, it always propagates at the speed of light.) Eventually these neutrinos are so slow that they are effectively stationary with respect to the local region in space. At this point they become dust, drifting along aimlessly in space.

While, since they do have mass, the neutrinos will be attracted by massive objects like the galaxies. So, the moment their velocities fall below the escape velocity of a nearby galaxy, they will become gravitationally bound to that galaxy. However, since they do not interact very strongly with matter, they will keep on orbiting these galaxies. So the neutrino dust will become clouds of dust in the vicinity of galaxies.

Hubble Space Telescope observes diffuse starlight in Galaxy Cluster Abell S1063NASAESA, and M. Montes (University of New South Wales)

Could the neutrino dust be the dark matter that we are looking for? Due to their small mass and the ratio of protons to neutrons in the universe, it is unlikely that there would be enough neutrinos to account for the missing mass attributed to dark matter. The ordinary neutrino dust would contribute to the effect of dark matter, but may not solve the whole problem.

There are some speculations that the three neutrinos may not be the only neutrinos that exist. Some theories also consider the possibility that an additional sterile neutrino exists. These sterile neutrinos could have large masses. For this reason, they have been considered as candidates for the dark matter. How these heavy neutrinos would have been produced is not clear, but, if they were produced during the big bang, they would also have undergone the same slow-down and eventually be converted into dust. So, it could be that there are a lot of them drifting around aimlessly through space.

Interesting, don’t you think?