A Universe of extremes

 

Caustics_Zoom10_Spera_50muasx625muas_ROT

Ever wondered how space looks like? This apparently silly question is actually one of the most fundamental questions in Science. Space (and time), the framework where everything we experience happens has some unknown structure on its most fundamental scale which we do not understand yet. On larger scales, the General Theory of Relativity tell us that space time and matter are closely interconnected.   One of the most revolutionary concepts of the 20th century was Esintein’s realization that the geometry of space is determined by the energy content of the Universe.

Thus, a very massive object can curve space around itself. If the object is massive enough, the curvature of space around it can be large enough so it can be measured. Nowadays, the curvature of space has been measured on scales ranging from planet solar system scales to the size of the observable Universe. On the largest scales, the Universe appears as having very small or no curvature. This is what one would expect if the size of the Universe were much larger than the size of the portion of the Universe we can actually observe. Think of yourself at a boat in the middle of the ocean and with a clear view of the horizon. If you measure the curvature of your portion of the Universe (that is, everything around you up to the horizon) you will conclude that the space is flat but if you were able to jump on a spaceship conveniently stored in your boat you will see that as you go higher and higher you can start to see the curvature of Earth. In a similar fashion, our limited view of a small portion of the Universe makes us erroneously believe that we live in a  flat Universe.

On the other hand, if you were to look from your boat not at the horizon but at the surface of the water, you would see waves in the water and conclude that on small scales, the water (the Universe) is not flat but it has regions with positive curvature and regions with negative curvature.  Similarly, the Universe on small scale has ripples in space, like the waves, that can be measured. But how?

Imagine now that you jump from the boat and go scuba diving. In your journey to the bottom of the  Ocean you look up and see a bright spot of light, the Sun. But the Sun looks different now. It does appear  to fade for an instant and then get brighter, and it repeats the same pattern of fading and brightening,  again, and again, and again.  This change in brightness of the Sun is a consequence of the curvature of the water (the waves) that, as they move on the surface, act as lenses focusing the light into your eyes during a small instant where you see a brighter Sun and one instant after the focus moves away from your eyes so you see the Sun fade. You have to wait for another wave to align with your eyes so they focus again the light into your eyes and so on. In theory, you could learn a lot from the waves by simply looking at the change in brightness of the Sun. By measuring how many times the Sun brightens every minute, you could estimate the number of waves (and their speed) that pass through a given point per minute. By measuring how much brighter the Sun is during a maximum than during a minimum,  you could say something about the shape of the waves. Are they tall waves that give you big differences between the maxima and minima or are they small waves where the change in flux is much smaller?

The curvature of space can be measured in a similar way. By looking at a bright distant object, if a massive object (a lens) moves between us and the bright object, it will curve the space around the massive object, the same way the wave curves the surface of the Ocean. The massive object will act as a lens (we call them gravitational lenses since the curvature of the space is proportional to the gravitational force of the object acting as a lens) and the bright object may brighten or fade as the massive object moves between us and the bright object. This technique is known as gravitational lensing. By measuring the change in brightness of the bright object we can learn things about the massive object acting as a lens. In particular, we can estimate the mass of that massive object.

Now, this is where things become more interesting. Having a reliable method to measure masses of distant objects is (one of ) the holy grail(s) in Astrophysics in general, and Cosmology in particular.  One of the biggest mysteries of Science (actually the biggest for some of my colleagues) is to understand the nature of dark matter. What is it made of? Is it even real or just a (huge) flaw in our models? One candidate for dark matter, which is  discussed in some of my earlier posts, is Primordial Black Holes (see this post for instance) or PBH for sort. If PBH account for a significant fraction of dark matter, they should be producing ripples in space that could be measured using the gravitational lensing technique mentioned above. In particular, as discussed in the post mentioned earlier, PBH with masses about 20 to 50 times the mass of the Sun are particularly interesting 1) because this is pretty much the only range of masses where PBH have not been excluded yet and 2) because LIGO is finding a surprisingly large  number of PBH in this mass range. Could it be that dark matter is made (at least part of it) of PBH? If enough PBH are moving around in the Universe, occasionally they may align with a bright object in the background so  the gravitational lensing effect would produce a change in the brightness of the object that could be used to measure the mass of the PBH. The chance of these alignments is however very small and it is very unlikely to witness one of these alignments (they can last a relatively sort period of time of a few days or weeks). However, we, astronomers, are great at gambling though, because we always cheat.

Instead of waiting for one of these rare alignments looking at a random bright object far away, we can search for these alignments in a place where we know the odds of observing one alignment are much bigger. These places are the caustics of large lenses, generally groups of galaxies or clusters of galaxies. In the Ocean analogy, imagine that while you are scuba diving and looking up at the Sun, a Tsunami moves on the surface of the Ocean. The Tsunami creates a giant wave extending over hundreds of meters. The giant wave acts as a giant lens collecting light from hundreds of meters and focusing all the light into a narrow line  that moves together with the Tsunami.This line is called a caustic (for its similarity with the caustics produced by regular lenses). When this line (or caustic) passes by you, you will see the Sun much brighter (in fact, it might blind you) than when the much smaller waves were focusing the lights. But if you look closer, you will see that the caustic is not a perfect line. Instead, the surface of the Tsunami is not perfectly smooth but it still contains small ripples (or microcaustics) caused by the smaller waves riding the Tsunami. If you count the number of microcaustics that travekl surrounding the big caustic of the Tsunami, you will find that the density of microcaustics is very high. The Tsunami is concentrating also the light from all the ripples (microcaustics) extending hundreds of meters into a small region near the caustic of the Tsunami. All the sudden, the odds of having one of those microcaustics aligning with your eyes is much higher when you look at the Sun through the Tsunami. In a real observation, the Tsunami would be a very massive object like a group or cluster of galaxies and the small waves, or ripples, would be the PBH (or other type of small objects like regular stars, stellar black holes or neutron stars). In 2016 we witnessed the first example of an alignment of a very bright star at a cosmic distance being magnified by a star or black hole in a galaxy cluster (see this previous post). Only a few days ago (June 5 2018) the same star went through another ripple and we expect more in the near future. By measuring the frequency of these alignments and studying in detail the way the brightness of the star changes as it moves through the ripple we expect to learn more about dark matter or at the very least, put a cross in another model as an invalid one.

The image accompanying this post shows a crowded field of microcaustics at the position were the caustic of cluster would be if there were no microlenses. If microlenses (PBH for instance) were not included in this simulation, there would be simple a horizontal bright line, the  caustic of the cluster of galaxies. In a recent paper we discuss this result in detail and estimate the probability of having this type of alignments using as bright background objects supernovae, very bright stars including Pop III stars and gravitational waves.

Follow this link to read the paper

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