The importance of Prior-itizing

The quest for lensed gravitational waves

We are all subject to personal biases, even when we try not to be biased. In Science, a popular tool to select among a variety of models is inspired on Bayesian theory. According to this theory, the most likely model is the one that offers the best description to the current data (i.e fits the data), and given by its likelihood, but also is consistent with previous knowledge on some of the parameters that are being fitted. Previous information is accounted for by a term known as the prior. Good priors result in fairs results. Biased priors often lead to the wrong conclusion.

In a recent paper, the LIGO-Virgo collaboration (LVC) studies the possibility that gravitational waves (GW) are being strongly lensed. If lensing is taking place, a fundamental prediction from gravitational lensing theory is that multiple occurrences of the same GW should take place, with a time separation between them of typically days to months. LVC presents a series of candidates which show high consistency with the lensing hypothesis, or in the Bayesian terminology, have a good likelihood of being pairs of images of the same GW. All these pairs are later discarded as possible lensed images based on the prior term, that heavily penalizes pairs of GWs separated by more than a few weeks. They finally concluded that lensing of GWs is unlikely, based on their final score.

Distribution of time delays of observed lensed quasars (orange) and gravitational waves (red)

This is however a conclusion that is obtained after adopting potentially bad priors. The LVC does not provide sufficient information regarding their prior, but in a recent study we show how the prior used by LVC is in tension with observations of time delays from real gravitationally lensed pairs of images. In fact, the distribution of time delays between the pairs of gravitational waves which LVC found to be good candidates to be strongly lensed, is consistent with the known distribution of time delays from quasars and from analytical models.

LVC finds that approximately half the events published in the O3 catalog can form pairs of lensed GW events (that is, there is another GW which shows high consistency in terms of GW parameters and sky localization, as predicted by lensing). As shown in the image accompanying this post, the separation in time between the two GWs forming the pair (solid red curve) is consistent with the known distribution of time delays (dashed orange curve). In the LVC analysis, pairs of GWs with time separations of approx 4 months are directly assigned a probability of zero, contradicting real observations where such time delays are possible. LVC concludes that none of their candidates to be pairs of gravitationally lensed GWs favours the lensing hypothesis, but this conclusion is biased by the adoption of a prior that intrinsically negates the possibility that realistic time delays are possible.

The use of a better (unbiased) prior does not necessarily mean that the opposite conclusion is true (ie. that lensing is favored), but it begs the question of whether the conclusions from LVC could have been reversed.

If you want to find more about this discussion you can check our latest work, or our earlier work where we present a model that predicts that gravitational lensing of GWs has already been observed.

The Kaleidoscopic Universe

In very few scientific fields, color matters more than in Astronomy. First photographic plates, and later CCDs, capture the light of distant objects by integrating during long exposures. When photons hit the CCD, small electric currents record the light intensity. Current CCDs working in the optical, UV and NIR range are basically insensitive to the “color” of the arriving light and filters need to be placed in front of the CCD to select the spectral range, or color, that wants to be studied. Often, these filters are “wide” in the sense that they allow a generous amount of light to go through (since distant objects tend to be faint), and the entire optical spectrum can be covered with 3 filters. However, their are situations where much narrower filters would be desirable. Astronomical objects tend to emit light in a combination of continuum (free-electrons being captured by the atoms) and spectral lines (electrons jumping between atomic levels). The spectral lines carry very valuable information about the conditions (like temperature and metallicity or abundance of elements heavier than Helium) that get diluted when observing the objects with wide bands. On the other hand, sufficiently narrow bands can resolve these spectral features.

Today (July 7th 2020) we published the first results of the J-PAS survey pathfinder (or miniJPAS). J-PAS is a narrow band survey of 15% of the sky, with an unprecedented number of narrow band filters (54). The image below shows the 54 narrow-band filters, plus 5 of the wide-band filters.

Using the narrow-band filters, J-PAS can identify features as the H-alpha line, or the 4000 Angstrom break, allowing for precise SED fittings and photometric redshifts of all galaxies in the catalog.

J-PAS will be particularly powerful at detecting rare objects with string emission lines. Chief among these, high redshift quasars, where the bright Lyman-alpha gets redshifted into the J-PAS spectral range, allowing for unambiguous estimation of the quasar redshifts. Earlier estimations suggest that J-PAS will be capable of detecting half a million quasars in the surveyed area.

The superior power of J-PAS to estimate photometric redshifts will open the door also to do tomographic studies and unveil the 3D structure of the galaxy distribution to unprecedented detail. Stay tunned for more. First light of the full scientific survey is expected to take place in late 2020 or early 2021. You can also find the first data release in J-PAS website and explore the images directly from your browser using the Sky Navigator

You can find the paper below and in this link

Is LIGO really seeing Mass Gap events?

The recent publication by LIGO of two events (GW190412 and GW190814) with high mass ratios, and with one of the masses close to the mass gap (that is, a mass between 3 and 5 solar masses which are difficult to explain with standard models) has created an intense debate on the nature of these objects. If confirmed, the implications of these observations are important since they can give us information about the equation of state of neutron stars (where one can study exotic forms of matter, such as axions or hyperons), or reveal a new type of black hole, including a leading dark matter candidate, primordial black holes.

However, a simpler alternative could be that these events are strongly lensed. Gravitational lensing can amplify the signal of observed gravitational waves, allowing their observation from much farther distances (and hence much larger volumes). In earlier work, we showed that if the rate of mergers (that produce gravitational waves) at redshift z>1 is sufficently high, observation of these distant events by LIGO is not only possible, but unavoidable. On fact, for rates larger than a few times 10^4 mergers per year and Gpc^3, lensed events will dominate over not-lensed events, in a similar fashion as lensed gravitational lensed IR galaxies dominated over not-lensed IR galaxies in the bright end of Herschel observations.

The left plot shows the prediction from our lensing model (colored circles) compared with the observations (squares and diamonds with error bars). All events concentrate around two locus regions. BBH and NSBH. Note how observations match perfectly the prediction.


Lensed gravitational waves get stretched due to cosmic expansion as they travel from their originating source to the detector. The farther the source is, the lager the stretch. The stretch is proportional to (1+z), where z is the redshift if the source. Higher z translates into gravitational waves that, when observed, appear as having a longer wavelength. If the gravitational wave is being magnified by strong lensing, and this magnification goes unnoticed (there is no way a priori to know if a gravitational wave is being magnified), the longer wavelength will be missinterpreted as being due to a larger mass of the two compact objects that ar causing the gravitational wave. For instance, if a neutron star with a mass of 1.3 solar masses is merging with a black hole of 12 solar masses (these are the typical masses found in our Galaxy for these objects) at redhift z=1, the observed gravitational wave will appear identical as the one from a much closer merger (z =0) with a neutron star of 2.6 solar masses and a blackhole with 24 solar masses. This example is not arbitrary since it was chosen to match the observed masses of the latest published gravitational wave event , GW190814, interpreted as being a local event (z=0), but which based on our interpretation could be also a lensed event at z=1 or z>1.

The lensing model interpretauon makes a series of interesting predictions, but among these, it is interesting to pay attention to the predicted mass ratio for binary black holes and neutron star black hole mergers. As shown in the figure illustrating this blog, lensing predicts these type of events will appear in the M1-M2 plane in two well defined regions. Interestingly, all observed data points so far agree remarkably well with this prediction. The two possible mass gap events are marked with a big yellow circle and follow well the predicted locus for lensed NSBH events. If confirmed, our lensing model would offer a simple solution to the mass gap problem, and would imply a much higher rate of events at z>1 that previously thought. 

You can see our full work below. A Fun Fact about this paper is that it was put “On Hold” by arxiv moderators after being submitted to arxiv on June 19 (Friday). After requesting an explanation from arxiv, none was given. At the time of our original submission, we where unaware of the upcoming publication, by the LIGO team, of the GW190814 “Mass Gap” event. The following week, in June 24 we saw in arxiv the LIGO paper with the values of M1 and M2 for GW190814. The same day, the “Hold” on our paper was lifted and we where able to just add the new data point to our figure (see point marked GW190814 in the figure above), before it appeared on arxiv the following day (June 25). I do understand (and support) the need for moderation in arxiv, but this process is far from transparent. The lack of communication and explanation of why papers are being put on hold, inhebitably leads to one suspect foul play, which is something that should be avoided at all cost, specially in portals such as arxiv, that makes research freely available. 


Link to paper

Click to access 2006.13219.pdf

Seeing through Dark Matter with gravitational waves

We covered the topic of dark matter before in this post (Dark Matter under the microscope). Dark matter remains one of the bigegst mysteries of Science. One of the candidates for dark matter are Primordial Black Holes or PBH. PBH are black holes that formed during the first instants of the universe. Like dark matter, PBH do not emit light and interact with the rest of the universe basically only through gravity. The LIGO experiment has been detecting a surprisingly high number of massive black holes. The origin of these black holes is uncertain but one of the possibilities is that they could be PBH. We also discussed LIGO detections in this earlier post (Did LIGO really see massive black holes?) . In order to explain the current observations by LIGO, only a fraction of the dark matter needs to be in the form of PBH. In particular, a fraction as small as 1% of the total dark matter would be sufficient to explain the unusually elevated rate of black hole mergers with masses above 20 solar masses.

In a new work we discuss a novel method to explore the possibility that PBH constitute part of the dark matter. Our latest paper (see link at the end of this post) studies for the first time the interference produced when gravitational waves cross a portion of the sky populated with a realistic distribution of stellar bodies (stars, neutron stars or black holes) or microlenses. Earlier work have considered only the simple, but unrealistic, case of isolated microlenses and at most assuming that they are located near a larger lens (galaxy or cluster) but always on the side with positive parity (a tecnicallity that describes one of the two possible configurations for a lensed image). Our work goes further than these simple exmaples by studying the combined effect produced by a realustic population of microlenses and also considers the unexplored regime of macroimages with negative parity (they constitute roughly half  the images produced in the string lensing regime). The figure accompanying this post shows an example of a single microlens embeded in a macrolens and on the side of the lens plane with negative parity. The numbers in orange represent relative time delays (in milliseconds) between the different microimages (the numbers in white indicate the magnification of each microimage and the grey scale shows the magnification in the lens plane with the critical curves shown as two white circular regions. The inset in the bottom-right shows the corresponding magnification in the source plane with the position of two sources, one white and one yellow). At LIGO frequencies (approx 100-500 Hz), a time delay between 1/500 seconds or 1/100 seconds (that is or 2 or 10 milliseconds  respectively)  can produce constructive or destructive interference in the incoming gravitational wave at the detector. For the example in the figure, the microlens has a mass of 100 solar masses. These type of masses where known before to be capable of producing such interference but what our work show is that the mass can still be significantly smaller (a few solar masses) provided several microlenses can work together to produce time delays of order several milliseconds. This cooperative behaviour takes place naturally when one is observing gravitational waves that are being lensed by large factors (of order 100 or more) since in this case, two microlenses which are relatively distant from each other in the lens plane, can overlap their regions of high magnification (known as caustics) in the source plane, if the magnification from the macromodel (galaxy or cluster) is sufficiently large (in a fashion similar to how a magnifying glass works that can bring photons that are separated by some relatively large distance to come together at the focal point of the magnifying glass). Our study shows that interference of a gravitational wave with itself due to microlenses is not only possible, but unavoidable if the magnification from the macromodel is sufficiently large.

This result opens the door to constrain the abundance of PBH. If PBH are as abundant as 1% of the total dark matter, the interference signal observed in detected gravitational waves here on Earth would be significantly different. Next in the list is to study by how much we can constrain this abundance as a function of the mass function of the PBH. Stay tunned …

Preprint to the science article

A Universe of extremes



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

Did LIGO really see massive black holes?

GW being emitted by a pair of black holes

The LIGO (and now Virgo) experiment has opened a new window to explore one of the most mysterious objects in nature, black holes (BH). When two black holes merge, they create a cataclysmic event that sends waves through the fabric of space itself and can travel cosmic distances. This is similar to an earthquake shaking Earth. These waves are known as gravitational waves (GW) and until 2015 they were just pure speculation as no experiment was ever able to detect them. Despite the tremendous amount of energy released when two BH merge (a binary BH merger), these waves, or ripples in space-time, are incredibly difficult to observe. The distortion  that a binary BH merger  in a nearby galaxy induces in space-time is minuscule when it reaches Earth. So minuscule that LIGO need to measure tiny shifts in the relative position between two mirrors which are several orders of magnituude smaller than the size of the smallest atom. This is an incredible achievement.  LIGO’s first detections of GW have brought a few surprises though. And they started with a bang!

The first event detected by LIGO in 2015 was interpreted as a heavier than expected binary BH merging in a  closer than expected galaxy. Similar events have been observed since raising several questions. Are these events more common than previously thought? Why have not we see them farther away if they are stringer than expected?  The mass of the individual black holes forming the binary BH were inferred to be approximately 30 solar masses each. Note that I say inferred because these masses could not be measured directly. What LIGO can measure with relative high precision is what is known as the observed chirp mass.  The intrinsic chirp mass is some combination of the two masses of the binary black hole. If both masses are similar, the chirp mass is similar to those masses as well. If the two masses of the binary BH are very different, the chirp mass will be a value in between these two masses (but closer to the mass of the lightest component). The observed chirp mass is related with the intrinsic chirp mass by the factor (1+z) where z is the redshift of the binary BH. The redshift is a measure of the distance so more distant objects have a larger redshift (our redshift is zero).  In other words, what LIGO can measure with good precision is Mo=Mc*(1+z) where Mc is the intrinsic chirp mass. Mo determines the frequency at which the GW is oscillating, a number that LIGO can estimate quite well. For that very first event, LIGO found that Mo had to be approximately 30 solar masses and that the distance was relatively small, that is z was close to zero. Hence, the intrinsic chirp mass (and mass of the individual BH before they merged)  had to be also close to 30 solar masses. This came as a surprise since many predictions made years earlier anticipated that such high values for Mo should be very rare. In fact, what was expected was to find values for Mo between 7 and 15 solar masses. This was in part motivated by observations of X-ray binary stars in our Galaxy, for which  it is possible to estimate the mass of the BH. An X-ray binary is a pair of closely orbiting  objects where one is a star and the other one is either a neutron star or BH. In this article we consider only the BH case. Roughly speaking, by measuring the amount of light emitting by the gas (from the star) spiraling towards the BH one can measure the mass of the BH.  In our Galaxy, the mass of about a dozen BH has been measured using this technique. The results show that the BH masses are between ~7 and ~14 solar masses. So far, no BH with a mass higher than 20 solar masses has been found in our Galaxy raising another, even more fundamental, question. Is our Galaxy special or is there something else we are missing regarding the BH masses and distances inferred by LIGO?

This is the question we address in our latest work. Owing to the degeneracy with the redshift described above, would it be possible that the intrinsic chirp mass was smaller if the redshift was higher? If the redshift is, let’s say z=1, instead of z~0 then, the intrinsic chirp mass could be a factor of two times smaller than the value inferred by LIGO (while keeping the observed chirp mass constant) bringing it into agreement with the BH masses observed in our Galaxy. There is one caveat though.  If the GW was originated in a galaxy far away at redshift z=1, instead of in a galaxy nearby (z~0), the intensity of the GW would have been much smaller than what LIGO observed. The intensity of the GW  is (to first order) the quantity that is used by LIGO to determine the distance. The observed intensity determined then that the inferred distance had to be relatively small. A mere few hundred Mpc instead of several thousand Mpc which would be the distance for a galaxy at redshftz~1 so one would conclude that the GW originated in a nearby galaxy and consequently, the intrinsic chirp mass had to be high. But this is the funny thing. Nature has interesting ways of playing with us. One of these ways is gravitational lensing thanks to which, an object that is far away may appear to us as if it were much closer (that is, it can amplify the intensity mentioned above). Note that I used the expression infer again when referring to the distance estimation by LIGO. This estimation is made under the assumption that gravitational lensing is not intervening. This is normally a good assumption since, after all, only a very small fraction of distant objects get (significantly) affected  by gravitational lensing. To be more precise, 1 in approximately 1000 or 10000 objects at redshifts larger than z=1 are substantially magnified by the gravitational lensing effect. Hence, is it still possible that a significant fraction of the LIGO events are distant lower mass events that are being magnified by gravitational lensing?  In our work we find that lensing can just make the trick. At large distances, the volume of the universe that is reaching us now (and by this I mean the volume where the light or GW we see now originated) is much  larger  than the corresponding volume at much smaller distances. To visualize this, imagine the volume of a shell of radius R. This volume goes like the square of the radius. So a large shell with a radius 10 times larger than a smaller shell will have 100 times the volume (if they both have the same thickness).  By precise calculations of the gravitational lensing effect over distant gravitational waves we prove that the massive and nearby events found by LIGO can in fact be interpreted as normal but more distant events with masses comparable to the ones found in our Galaxy. This solves the puzzle mentioned at the beginning of this article. Is our Galaxy special? And if it is not, where are the masses that LIGO claims is finding in nearby galaxies? The answer is that those masses would be the same in our Galaxy and in other galaxies. What is wrong is the interpretation of the observation since the amplification due to lensing has been ignored (this story is very similar to the puzzling first bright galaxies detected by Herschel that turned out to be all gravitationally lensed distant galaxies) .

So why has not anybody realized this earlier? That is a good question and the answer is not because people have not thought about this before. For our model to work, there is one little thing that sets our study apart from other similar attempts. As we mentioned earlier, at z~1, only one in a few thousand events could be magnified substantially by gravitational lensing. On the other hand, by observing more distant objects one is observing a larger volume, so one is observing more events. The gain in volume with respect to nearby distances is in the range of two orders of magnitude (more precisely about 1.5 orders of magnitude between z=0.1 and z=1 for a shell of thickness dz=0.1). This gain in volume is not enough to compensate the small probability of lensing at z~1 (1/1000 or less). A significant rate of lensed  events (enough to explain the rate of observed events)  can be obtained ONLY IF (and this is the little thing)  one increases the rate of intrinsic mergers at z=1 with respect to the rate at z=0. Such evolution in the intrinsic rate is expected and has been considered in the past. Our study shows that in order for the lensing mechanism to work and be able to explain the LIGO observations (with the troubling masses), the rate at z=1 needs to be more extreme than previously considered. This is not necessarily a problem since we simply don’t know what this rate is and also there are models that predict such rapid evolution in the intrinsic rate of events between z=1 and z=0 but, surprisingly, this type of strong evolution models were not considered in the past so the role played by lensing  was not recognized.

So then. Are we right? Are we wrong? Time will tell. After all, only one (if at all) of the many interpretations proposed to explain the LIGO massive events will be the correct one. An important aspect of any model is that it needs to be testable and this one is. If lensing is the culprit, at high magnifications one would expect a pair of images with similar magnifications and with a small time delay between them (hours to days depending on the lens mass, lens distance and relative source-lens-observer position).  LIGO detections don’t come in pairs (at least no such detections have been reported yet). If the time delay is several hours or days, it is possible that one of the two lensed events falls below the detection threshold of LIGO since the visibility (determined in part by the geometric factor in LIGO, a technicality whose explanation is beyond the scope of this article) may have changed substantially.  For simplicity, we can say that an event that is directly overhead the detector results in a significantly stronger signal-to-noise ratio than the same event near the horizon. Since Earth rotates once every 24 hours, a position in the sky (like the Sun for instance) can move from the zenith to the horizon in six hours. Hence, two identical GW originating in the same spot in the sky may have significantly different signal-to-noise if they are separated by approximately six hours. There is however a limit for how many times you may get the unlucky configuration that permits to hide one of the two images. Eventually two events should be observed that have virtually the same observed chirp mass and a distance estimate that is consistent with the uncertainties introduced by the geometric factor. The ratio of signal-to-noise between the two events should be compatible with the angle rotated by Earth during the time separation between the two events. Finally, the inferred location in the sky (derived from the time difference between detections in different observatories) should be also consistent with being the same for both events. Data mining of the LIGO data may unveil some of these missing events in the near future and confirm the lensing nature of the massive LIGO events.

Link to the publication

You can download the paper with our study in this link







Dark Matter under the microscope

Caustic_ColorDark matter remains one of the main unsolved problems in modern physics. Despite the growing evidence for its existence coming from astronomical observations, all efforts to detect it in a lab on Earth have failed. One possible candidate for dark matter that can not be detected on Earth (and let’s hope it stays like that) are primordial black holes (or PBH). This type of black hole was created during the first moments of the universe and may have survived till today. PBH are invisible (they don’t emit light, or extremely low amounts  if they are not very massive) and pretty much interact with the rest of the universe only through gravitational forces. This is basically the same behaviour as dark matter. Most types of PBH have been already ruled out but they can still exist in certain mass ranges (also, high spin PBH may not have been considered in detail in previous studies and may be harder to exclude). One of these possible  mass range is about 30 solar masses (think LIGO) and the second one is around the mass of a brown dwarf or a planet. A new type of observation may be able to prove these masses and rule out the possibility that PBH could be a sizeable fraction of the dark matter. This observation relies on caustic crossing events like the Icarus and Iapyx events observed in the galaxy cluster MACS1149. The interpretation of these events is that a very distant and luminous background star (z=1.55) is moving in a region that lies very close to  one of the caustics of the cluster (a caustic is a position which results in a large fraction of the light emitted from the star being focused to us at the focal point of the gravitational lens). As it moves, the light of the star gets amplified by the effect known as gravitational lensing. In its path to us, this light passes near stars (microlenses) in the galaxy cluster and the magnifcation changes depending on the distance to  the microlenses. Caustics are normally assumed to be smooth curves. In the presence of microlenses, caustics are disrupted like in the figure accompanying this post that shows a caustic being blown up by many PBH, each with 30 times the mas of the sun (without the PBH the caustic would resemble a single straight line instead of the web shown in the figure). We have studied this new type of observations and shown that through continuous monitoring of caustic crossing events it is possible to constrain the fraction of dark matter in the form of microlenses. So far, preliminary results do not favour an scenario where even a modest fraction of the dark matter ( a few percent) can be made of massive PBH (~ 30 solar masses).

You can read the scientific papers in the links below.

Observation paper

Theory paper


Seen stars in motion

A wise man said once that ; “A picture is worth a thousand words“. The wiser man replied, “A movie is worth a thousand pictures“. The movies below show a few examples on how the flux of the background star would change as the star moves across the field of microcaustics in the cases where only stars (and remnants) in the cluster act as microlenses and in the case where 1% of the dark matter is in the form of PBH with 30 solar masses each. For the first four movies the star is made unrealistically large in order to better see the effect (R=70000 solar radii). The magnification does not show large fluctuations as a consequence of this extreme radius.

Video 1) Icarus event with ICL stars

Video 2) Iapyx event with ICL stars

Video 3) Icarus event with ICL stars and 1% dark matter as PBH

Video 4) Iapyx event with ICL stars and 1% dark matter as PBH

An even higher resolution of the effect can be found in the two videos below where the resolution is increased by a factor ~30 and a more realistic star with 1000 Rsun is considered star (this is a typical radius for a giant star) . The first movie considers the more likely scenario where the direction of motion of the star with respect to the cluster caustic is at an angle. The movie considers an angle of 30 degrees but the result would be very similar at any angle larger than few degrees. The second case considers the special case (unlikely) where the motion of the star is aligned almost perfectly with the direction of the cluster caustic. In this case the star approaches the caustics through the cusps of the caustics producing a different pattern in the magnification. The caustic map is shown in the right panel of the movie with the position of the background star shown as a cross. For these movies we only consider microlenses from the intracluster medium (i.e, no PBH) and the central microlens has a mass of one solar mass.

Video 5) Star travelling at an angle with the caustic.

Video 6) Star travelling parallel to the caustic.

Similar movies but with just one microlens can be found in the two links below.In tehse movies, three nearby background stars cross the same caustic from a single microlens having M=1 Msun. The movies show how the same microlens can produce very different magnification patterns depending on the trajectory of the background star.

Video 7) Zoom in on Icarus side. Three stars travelling at an angle with a single microcautic from a microlens with M=1Msun

Video 8) Zoom in on Iapyx side. Three stars travelling at an angle with a single microcautic from a microlens with M=1Msun


You can read the scientific papers in the links below.

Observation paper

Theory paper







Where did the dark matter go?

Galaxias are supposed to be made mostly of stars, gas, dust and  … dark matter. Dark matter is the most mysterious substance in the Universe. We know HOW MUCH there is, we know WHERE it is, but we don’t know WHAT is it.  Dark matter has eluded detection by multiple experiments here on earth yet we continue gathering evidence of its existence on cosmological scales. Dark matter is responsible for the accelerated rotation of galaxies in the outer regions of these galaxies. It is also reponsible for the distribution of matter in the Universe on very large scales and also it is largely responsible for the so called gravitational lensing effect.  In galaxies, most of the mass is in the form of dark matter as evidenced by the rotational curves of galaxies that tell us ho much mass is inside a given distance from the centre of the galaxy. In some heavy galaxies, the amount of dark matter is so large that the space warps around these galaxies producing the optical illusion that another galaxy that is far behind these galaxies is seen in two, sometimes in three or more locations. This is the gravitational lensing effect predicted by the  general theory of relativity , thanks to which we can study the distribution of dark matter in these galaxies.


The most spectacular examples of the gravitational lensing effect can be found in galaxy clusters where the concentration of dark matter is greatest. Among the observations of the gravitational lensing effect, the recent Hubble Frontier Program is producing the best data around colliding galaxy clusters offering a unique opportunity to study dark matter (in a manner that tries to emulate particle accelerators that smash particles against each other).  In a recent work we use the gravitational lensing effect around a special type of galaxies, known as BCG (or Brightest Cluster Galaxy) and find something unexpected. Our results show that these particular galaxies have no dark matter at all (or a very small amount). Our study relies on two gravitationally lensed galaxies (marked with 7.2, 7.3, 19.1 and 19.2 in the figure above) that can be explained only if the two BCG galaxies in these cluster have most of their mass (if not all) in the form of stars and no dark matter (or very little). If these galaxies were normal galaxies, that is, having a significant amoount of dark matter , the two images shown above would be curved  towards the BCG galaxies, something that can be ruled by the observations. If confirmed, our findings would require new developments on galaxy formation  to explain this type of galaxies. We discuss several scenarios that could result on this type of galaxies. One of the most promising ones and that has not been explored sufficiently in the past is that these galaxies form as a consequence of cooling and not as the result of merging of several smaller galaxies. Future observations could confirm or reject this hypothesis but that will be a different story …

Link to paper:





Gravitational waves (II)

LIGO has announced the detection of gravitational waves.

This is a remarkable achievement made possible after steady technological progress on detector technology. The detection of gravitational waves is relevant for different reasons. First, it confirms one of the main predictions made by General Relativity, that space itself can be shaped and dragged by massive objetcs such as black holes and that ripples in the space-time can be produced by such moving objects and move at the speed of light. This idea, that gravity “moves” at the speed of light and is not instantaneous like in Newtonian physics,  is what got Einstein in the first place to develop an alternative theory to the classical (Newtonian) gravitational theory. If gravity travels at the speed of light, its natural to think of it as a wave, similar to photons.  Although the curvature of space was long confirmed by observations of gravitational lensing, and the influence of massive bodies over time has been also confirmed (and applied to current technology like the GPS) the gravitational wave prediction remained elusive form the experimental point of view. Indirect confirmations was provided nearly half a century ago by the slowing down of the periods of a pair of orbiting neutron stars.

Web_NASA_binary star merger__gravitational_waves
Two stellar objects sipinning around each other and “radiating” gravitational waves. The two-black hole picture would be similar except we could not see the black hoes.


The discovery of gravitational waves is important also because ot opens a new window for research, not only of cataclismic events like the collision of two massive black holes but also for studying the origin of the Universe. A different type of gravitational waves (the primordial type), created right after the formation of our Universe are expected to be detected in the near future. A year ago, a claim was made about their detection but it turned out to be a false alarm. The technology to detects this primordial gravitational waves is however advancing at great speed and is just a question of time (1-5 years) till we can see the primordial gravitational waves. Once detected, they will give us valuable information about new phenomena, such as inflation, responsible for the structure of the Universe that we see today.

Solving a long standing mystery

Planck helps solve a long standing mystery

Virgo cluster (marked with a big circle) is near the centre of the image. The signal detected by Planck extends well beyond the limits of the cluster probing part of the missing baryons.

One of the puzzles of modern astronomy is what is known as the missing baryon problem. Baryons are the ordinary matter we are familiar with. You are made of baryons as it is everything you touch, eat and see. The best known form of baryons are electrons and protons. Together with neutrons (another form of baryons) they form atoms and atoms form molecules and molecules form … well, everything else. Detailed observations of the distant Universe tell us how many baryons are out there and the amount we can see agrees very well with what is expected from the standard model that describes the Universe so there is nothing surprising there. The story changes when we look at the Universe but at distances much closer to us. In theory, we should see the same amount or proportion of baryons that we see in the distant Universe right here, in our neighborhood but they are no where to be found, so where are they?

Baryons follow a similar law than energy, they don’t get created nor destroyed (for the most part), they transform  (with the transformation between a neutron and an electron plus a proton or viceversa being a classical example). If there were baryons in the early universe, pretty much the same number of baryons should exist today. Instead, observations of the local Universe reveal a significant deficit of baryons when compared with the expectations and the observed number of varions in the most distant Universe.   It is commonly believed that most of these missing baryons are in the form of a plasma which emits very small amounts of light (mostly at high energies like UV or X-rays) which has not been detected so far. Howevere, the same plasma produces also a distortion in the light that originated soon after the Big Bang (more rpecisely, 300000 years after the Big Bang). This light, known as the Cosmic Microwave Background, or CMB,  has been travelling through the Universe since the time it was first produced and permeates the entire Universe. When the CMB light crosses a region filled with plasma, it gains a small amount of energy. This small gain of energy can be measured with current telescopes like the Planck satellite through an effcet known as the Sunyaev-Zel’dovich, or SZ ,effect. The SZ effect has been studied with Planck in dense and hot plasma regions, usually found at the centre of galaxy clusters. In a recent work, we have focused our attention to one particular cluster, the Virgo galaxy cluster. This cluster is special because it is the closest cluster to us. In fact, it is so close that  our galaxy is falling towards the centre of this cluster due to its ginat gravitational attraction. The distance from our galaxy to the centre of Virgo is only about six times  the distance from our galaxy to our closest sister galaxy, the Andromeda galaxy. The apparent size of Virgo in the sky is about 15 times larger than the apparent size of the full moon. This large size, allowed us to do a detailed statistical analysis that takes advantage of the large size of Virgo and maximizes the small distortion that the missing baryons around Virgo produce over the CMB light.  Our findings (summarized in the figure accompanying this post) reveal vast amounts of plasma beyond the previously established limits of the Virgo cluster. The signal around Virgo observed by Planck coincides with what was the expected signal emerging from the missing baryons around galaxy clusters confirming that the missing baryons are probably forming diffuse clouds of plasma around the biggest structures in the Universe, like galaxy clusters. Although the missing baryons found by Planck don’t account for all the missing baryons, it does reduce the amount of baryons that are still evading a firm detection. Future analyses based on Planck and ground-based experiments will continue  the hunt for the few remaining missing baryons …


The paper with all the details and results can be found in the following link :