A Closer Look at Black Holes: Part 1

thank you very much Estie indeed I'll describe observations but I'll also describe a theory astrophysics theory which mathematicians may regard is close to observations but we think of it as theory and I wanted to start with this slide since today is the evening of the Chinese New Year and so on the left you see a depiction of PHA a goat I mean it does look like a goat and that's the symbol for the new year on the right side you see actually what nature produces which looks pretty similar to that except that it's on the scale of a hundred thousand light years and what you see here is a jet ejected by a central black hole that we can't see a tiny region of space that produces this huge jet stretching across the entire galaxy and here in the middle you see the dust rain of that galaxy and so to celebrate the new year we might as well look on this side and that will be the side that I'll focus on in this talk so the topics that I'll this discuss today are several I'll start with imaging black holes silhouettes the black hole itself is a dark region it doesn't emit any light but material around it emits light and it that the black hole casts a shadow and I'll discuss it we have the technology actually to image that shadow and then talk about pairs of black holes black hole binaries just like with humans when you put two black holes together they form a binary system that is stable if you put a third one it's unstable just like with humans again and then I'll discuss the recoil of black holes as a result of either a merger of a binary or a triple systems black holes kicking one of them at large speeds then I'll discuss the fate of stars near black holes in particular we wrote a couple of papers over the past few months with a postdoc James will adjourn about the possibility of accelerating stars like the Sun close to the speed of light which is quite remarkable if you think about it and near black holes and the near a pair of black holes and the pair of black holes acts as a slingshot that ejects a star if a star gets too close to a black hole it can be disrupted by the tide that is raised on the star just like tides raised raised by the moon are observed in the oceans on earth when you get close to a black hole the tide is so strong that a star can be ripped apart and finally I'll discuss the possibility that very small black holes may have been produced in the Big Bang and in principle they can account for the dark matter in the universe whose nature we don't know so the story starts a hundred years ago actually exactly a hundred years ago this is a special year during which there are lots of conferences celebrating the general theory of relativity Einstein wrote the equations and published the first paper around the November to 1915 and a month later cars watered found an analytic solution to the equations that Einstein did not appreciate he was at that time he was at the German front after he joined the military in Germany and he sent a postcard to Einstein telling him that he found an analytic solution for a point mass Einstein was thrilled to get this postcard and communicated its content to the Berlin Academy and a year later koshwal chill died at the German front so the lesson from this story is that if you want to work out the full consequences of a theory for an extended period of time you better off being a pacifist because ice both of them were German Jews the difference was that instan was a pacifist and Karsh watch it was a patriot so he volunteered to the German army he was back then the director of the Potsdam Observatory nevertheless he gave up on his academic pursuit joined the army and fought and found his death within a year but he managed to solve to find this solution by the way when I mentioned this joke in a colloquium I gave in Germany that was not much laughter in the audience and Schwarz solution is actually the full solution for a point mass in spherical symmetry and it's characterized by a singularity physical singularity in the middle meaning that if you were to make a black hole by collapsing a star or a cloud of gas then the density of the matter will diverge at the given point in space and at that point Einstein's theory of general relativity breaks down that's why we call it a singularity that means that the theory is incomplete and we know why it's incomplete because on very small scales you have to incorporate quantum mechanics so we have the fear of quantum mechanics on the one hand the theory of gravity on the other hand and we would like to marry the two Einstein himself try to do that without success these days there are hundreds of or maybe thousands of string theory is attempting to do that it's one of the frontiers in in theoretical physics but we don't have that theory as of yet so at the moment we don't really know what happens near the singularity of a black hole it would be nice to know one way to find out is to jump into one of these Astrophysical black hole I'm talking about problem is that once you get there you won't be able to write a paper and publish it because the information cannot go out a black hole is the ultimate prison you can get in you can check in but you can never check out and there is this horizon the Schwartzel horizon at a distance of twice times Newton's constant times the mass of the black hole divided by the speed of light squared inside of which there could be no communication to the outside world what you see here as these lines are trajectories of photons particles of light that have zero mass if they are directed towards the black hole they get absorbed if they are directed from this point outwards they may escape and there is this photon orbit that for ash watch it black hole and on spinning black hole is one and a half times the Schwarzschild radius where a photon can execute a circular orbit so in fact at that radius if you were to look straight you might see your back because photons coming from your back will reach your head so a photon is gravitationally bound to a circular orbit at this radius and you can see that in principle what an observer at infinity sees if the observer is sitting on this side of the black hole the observer will see a shadow cast by the black hole so the question is what happens to an observer close to the black hole and and that question was addressed in the movie interstellar and to address this question Kip Thorne in collaboration with a very with a variety of people imagined a camera located near a black hole and ask what will the camera see taking into account the effects of the deflection of light gravitational lensing and translation and so forth and that's the image that they came up with for a black hole surrounded by a disc of gas that is emitting radiation that you can see in the movie frankly I I I didn't enjoy much this movie because the science was not accurate and the plot other than that was not particularly exciting but but this is the image produced and in fact it was just posted on on the archive on Astra pH last week so you can read more about it in this archive paper how they produced it in the past people scientists did not really worry about a camera next to a black hole because nobody wants to be close to a black hole so in fact we want to test the structure of space-time near a black hole to check whether choix chilled was right a hundred years ago and so one aspect of it is testing the general theory of relativity the other one is testing the physics of gas accretion the info of gas into the black hole usually because of the strong gravity the black hole sucks matter from the surrounding galaxies and that's the matter we see and so the over the past 30 years or so there were theories for how this matter behaves in particular if the matter is called it makes an accretion disk in which matter just like near a faucet matter is spiraling into the black hole by losing angular momentum through viscosity or viscous stress and we would like to test these theories by now there's numerical simulations of that process the second aspect as I mentioned is testing general relativity in the strong gravity limit so the one important aspect of switch watchit solution is the existence of an event horizon which is a one-way membrane matter can fall in but cannot get go out and if there was a hard surface of course matter in pinching on the black hole would radiate much more energy so we can easily test whether a black hole horizon exists if we could image the vicinity of the black hole there were some papers recently talking about quantum effects that may show up in the context of four example fire wars something like a surface although it may be hidden just behind the horizon so if there is anything pathological anything unusual that may exist around the black hole we would like to see it there are of course paradoxes about black holes for example the information paradox matter falls in carrying a lot of degrees of freedom a lot of information but the black hole itself can be characterized only by three numbers its mass its spin the level of rotation that it has and its charge and in astrophysics black holes do not have significant charges because if it had a charge opposite charges will be immediately accrete onto it and cancel each charge make make it neutral so we actually have only two numbers and the question is where does this information go and of course there is the process of Hawking evaporation where radiation is emitted from the black hole so perhaps that carries some of the information but recent studies of that process say that no it's actually not there so this is an unresolved the puzzle in fundamental physics the information paradox there is also the breakdown of general relativity at the singularity that I spoke about before so clearly black holes are good experimental laboratories for getting to study physics beyond the standard model that we have right now so let's say talk about the black the biggest black hole closest to us which is black hole at the center of the Milky Way galaxy Sagittarius a star we know that it's a black hole because we can monitor the orbits of stars close to it just like planets in the solar system tell us what the mass of the Sun is we can infer that the mass of the central object is about four million solar masses four million times the mass of the Sun and it's very compact the tightest orbit of star of a star around the black hole is as big as the solar system and so we within as scale of the solar system we need to pack four million times the mass of the Sun no way of pack there is no way of packing this with ordinary matter such that the matter would be stable and not collapse to a black hole and so we are pretty confident since we don't see that matter and it looks like a dark object that is weighing a lot and it's extremely dense that this is a black hole now not only over the past three years we haven't only seen stars orbiting the black hole in in one set of observations that was actually evidence for a cloud a gas cloud approaching the vicinity of the black hole this is an artist's depiction a simulation of the behavior of the gas cloud in fact this particular simulation with the in which the cloud is held by external pressure is ruled out because as you can see from the date when the cloud passes near the black hole it was supposed to be disrupted and it was not actually passed earlier this year or a few months ago the cloud was discovered back in 2012 and you can see how it moves on the sky it moves it as at the speed of a few thousand kilometers per second and it has roughly the mass of three Earth's and the size of the solar system roughly and you can see the trajectory of this cloud here in bracket gamma radiation this is a particular line of hydrogen that allows us to trace the cloud relative to the background one there are various ways of making such a cloud one is to have a star in the middle that we proposed with ruth-marie clay here at the Center for Astrophysics another one which appears more plausible at the moment is a model that we proposed with the postdoc James village shown were the this cloud is one out of several pees on on a bead so these are honest you can imagine a stream of gas on in that fragments into clumps and one of these clamps is passing near the black hole right now there are more clumps along the way and this stream of gas was produced by ripping out the outer envelope of a star so there is a star which is not in the middle of the gas cloud it's somewhere else but it basically shed off a fraction of its envelope and that's the stream of gas that is now clumping and we see one of these gas clouds and when I was asked by the New York Times about what the origin of this cloud might be I was able to say something that made it to the quotation of the day but a year ago I said that the experience is as exciting for astronomers as it is for parents taking the first photos of their infant eating and the experience here is watching the black hole being spoon-fed by a star passing near it so astronomers do like to watch this process going of spoon-feeding the black hole in real time during our lifetime we can see this cloud moving around the black hole and possibly feeding it now the special thing about Sagittarius a star that this black hole at the center of the Milky Way is that it's the largest on the sky if we wanted to image the silhouette you would like to look at the black hole that is the biggest on the sky and this is Sagittarius a star and one can imagine sending a technician for example this Verizon technician from a commercial a few years ago that goes around and asks can you hear me now you can send that person to the vicinity of Sagittarius a star and you can imagine what would happen as this person gets closer and closer firstly it encounters the he encounters the inner most stable circular orbit and that means that if once he gets inside of it he cannot move on a stable circular orbit around the black hole that's at three times the Schwarzschild radius then he gets to the photon orbit which is one and a half times the Swart radius eventually gets to the Schwartz Ragus now nothing would happen to his body at that point because the black hole is four million solar masses the tidal force across a couple of meters roughly the height of that person the difference in force between his legs and his head is not large the overall acceleration is almost a million times the acceleration on the surface of the earth but it acts almost uniformly on the body of this person so a person in freefall actually doesn't feel anything due to gravity this was Einstein's insight that if you are in a free-falling elevator you won't be able to tell that you are in a gravitational field and so the only way to tell is if there is a difference in forces between your head and your toes and that actually happens eventually within ten minutes this person once it crosses the photon orbit within ten minutes it will reach the singularity and then be ripped apart and of course we would see from outside this person getting redder and redder with his voice getting sort of dilated we when never seen him crossing the horizon but from in his frame of reference he would actually fall all the way to the singularity within ten minutes black holes were called originally frozen stars because people thought of it if you make a black hole from a star that is collapsing at infinity you see the matter only reaching the horizon so it's sort of like frozen image and by the way the same frozen image occurs in cosmology now it seems like the universe has a horizon the de sitter horizon and when we look at galaxies as they exit from the de sitter horizon in the future their image will be frozen just like in the context of a black hole in fact there are lots of similarities there so one way to probe the space-time that is very effective is to put a clock around the black hole that is moving in orbit and you might think oh how do I cut a clock in orbit I mean if you don't want to risk a technician going there you might do it remotely and we do have precise clocks in astronomy in fact the almost as precise as the best atomic clocks and these are called pal stars these are neutron stars that emit a beam of radiation and they the emission Direction is processing around the spin axis of the neutron star and you see it like a lighthouse you see a beacon of light passing the telescope every so often hurry Adak lee and by timing the arrival time of these pulses you can measure time and if there is a pulse or near Sagittarius a star that would be fantastic we could actually map space-time so that we proposed back in 2004 and over the past decade no pulsar was found in the vicinity of such a star only except for last year actually two years ago 2013 there was a pulsar discovered serendipitously by chance unfortunately this particular pulsar which is very highly magnetized it called the magnetar is located a fraction of a light year away so it's not really very close to the black hole and the search is on for finding paths close in so imagine a hot spot not a pulsar a hot spot in the accretion disk moving around you see it in the upper right panel and that's the way the observer would see it and here we are tilting the orbital plane as a function of time and you see that the image of this hot spot looks quite different depending on the inclination angle there is one side that appears brighter than the other side and this is simply due to the Doppler effect that the beaming as material is moving in the direction of the observer it shines more brightly due to special relativity there is also the effect of gravitational lensing photon trajectories are deflected by gravity so you can get more than one image and in fact there are several images that one gets you see it here in blue and green depending on the orientation of the orbital plane relative to the observer there is the primary image from the hot spot and then there is the secondary image where the photons are moving around the black hole and are seen from a different direction and finally there is a third image which is much fainter where the photons execute a full circle around the black hole and come back on the other side and altogether one gets an image that looks like a crescent of the moon for example and you can see this Crescent here it depends that the exact shape of this Crescent depends on the inclination of the orbital plane so what you've seen the top panel is a hot spot orbiting 30 degrees from the line of sight without any spin to the black hole so that's what you would get here again a non rotating black hole - watch it black hole with no spin but at 10 degrees inclination and at the bottom panel you see a rapidly spinning black hole and you can see that the Crescent looks a bit different of course in all of these crescents there is a dark region due to the fact that when radiation is emitted behind the black hole it gets absorbed the black hole catches these photons as I was mentioning before and you get a silhouette a dark shadow of the black hole and this shadow is the signature of the event horizon the scale of this shadow is of the order of 50 micro arc seconds so if you are an amateur astronomer and you use a back a small telescope in your backyard you can perhaps under the best visibility conditions reach resolution angular resolution of a few arc seconds here we are talking about a resolution which is a factor of a hundred thousand better and obviously even the biggest telescopes in the visible light in optical ban cannot resolve such scales right now however there is a there is a way of detecting it as I'll mention in a few minutes the spin of the black hole matters because the scale of the horizon depends on the spin so here I plot the size of the horizon in Swart chilled radius units as a function of this norm normalized the dimensionless spin parameter so a maximally spinning black hole has a spin parameter of one a counter rotating black hole spinning to the opposite direction has spin parameter of minus one this is a black hole spinning at the speed of light opposite to the direction of motion of a test particle and you can see that the size of the horizon becomes roughly half the Swart you'd rather use in fact exactly half the Swart radius for maximally spinning black holes then there is the inner most stable circular orbit which is abbreviated as east core and that's the the smallest radius for a circular orbit that is stable around the black hole and for a counter rotating orbit this is five times the Swart radius for co-rotating test particle it is the Swart chilled it is ash water arrives for a maximally rotating black hole and it is roughly three swatching radii for low spin then there is the concept of the relative efficiency in principle if matter can orbit on a circular orbit it can release its binding energy in radiation and the tighter the orbit is the more ashin can come out so the efficiency of converting rest mass into radiation depends on the radius of the ESCO the inner most stable circular orbit and for a spin parameter of unity it can reach 42% so in fact you can think of black holes is very efficient engines that can convert up to 42% of the rest mass of material into radiation that's the most efficient engines except for engines based on an inhalation of matter for a non spinning black hole the efficiency is 5.7 percent now here you can see simulations of an accretion disk that has to balance in a which showed the image that an observer at a large distance would see and there is still this shadow and crescent shape in red here but it's it also has some small scale structure due to the turbulence and there are lots of details in such simulations that we are not sure about for example how the radiation is produced but roughly speaking all of them show this crescent shape with a shadow in the middle now why do we hope that to actually detect this shadow to constrain it mother nature was very kind to us it's not always the case there are problems in physics where you can work for decades like the problem that string theories are trying to tackle and you are still not sure that you're on the right track but in this case mother nature was very kind to us and there because there are three fortunate coincidences one of them is that the matter falling into Sagittarius a star is transparent to radiation with a wavelength shorter than one millimeter and we are talking about radio waves emitted by the material so Sagittarius a star was originally detected in in the radio at wavelengths shorter than one millimeter the material falling into Sagittarius a star right now is transparent to the radiation to synchrotron self-absorption which is the dominant absorption process and this is just now if more material were to fall into Sagittarius a star in the future it would be opaque we won't be able to see all the way through another coincidence that has nothing to do with the first one is that when you look at Sagittarius a star at radio wavelengths there is intervening matter in the inner galaxy which is blurring the image scattering the radio waves and it turns out that this blurring becomes insignificant again for wavelengths shorter than one millimeter so we can actually see the image of this silhouette without being without the image being blurred by the interstellar medium of our galaxy and finally a third coincidence is that the scale of the horizon of Sagittarius a star and also the horizon of the black hole in a giant galaxy called the m87 that is much farther away from us can be resolved as long as you build a telescope with an aperture that has the diameter of the earth for a wavelength of one millimeter so in other words the resolution of a telescope is the wavelength of the radiation divided by the size of the aperture that you can read in any textbook on optics so if you take the wavelength of one millimeter and ask how big should my telescope be in order for me to resolve the shadow of Sagittarius a star you find that it has to be just the size of the earth okay that sounds ridiculous how can you build a telescope as big as the earth but it is possible in fact there was a senior thesis back in the 60s that a student wrote with John Wheeler on imaging black holes and the student concluded that it's not feasible and then moved to work in a different sub on a different field he is now a professor at UC Davis and I actually contacted him and I said said to him that it was the wrong move because we can actually do it now but it's too late I guess and so these are images of the shadow of Sagittarius a star at different frequencies of radiation the higher the frequency or the shorter the wavelength the less blaring you get by the interstellar medium and also the less absorption you get by the material next to the black holes you get sharper images and the way to construct a telescope as big as the earth is to have stations distributed around the earth and here you see the view of the earth from the direction of Sagittarius a star so if you were to sit on such a star and look at the earth this is what we would see and you see here a number of millimeter observatories that can detect radiation at a wavelength of one millimeter and if you were to measure not just the amplitude of the electromagnetic wave that arrives at these stations but also the phase you can correlate the arrival phase of the wave and in principle if you have a large enough number of stations you can produce an image with a resolution on the scale of the black hole horizon and in fact this observational project is led by chef Dolman that is sitting somewhere in this audience over there with his son is it yes and the idea is to connect these observatories and correlate the signal that is detected at the different stations so far we have looked analyzed data from three stations that were correlated and I'll talk about that in a minute in principle there is this concept of the event horizon telescope the full-fledged system of all these telescopes connected to each other not just three of them and to show you an example of what such an array of stations can do here you see a simulated image of Sagittarius a star with lines indicating the polarization of the radiation coming from the material near the black hole this study was led by Mike Michael Johnson a postdoc at the Center for Astrophysics and you can see the polarization directions and this is what the event horizon the full event horizon telescope would be able to produce to reconstruct from the observations and we will not only get a sense of how strong is the magnetic field near the black hole but also its orientation so that can be used to test theoretical models for what how the gas behaves in the vicinity of the black hole right now the event horizon telescope is composed of these three stations one is in Hawaii it's called the submillimetre array SMA related or led by the Smithsonian Astrophysical Observatory of the harvard-smithsonian Center for Astrophysics and the second is JC MT nearby two that in Hawaii and then another station is in California it's called Karma the abbreviation for that is this is number two and number three is the in Arizona and these three form a triangle that can be used to set constraints we can't get an image of the shadow but we can set constraints on it and in fact in a paper that we published almost five years ago we try to fit the emission spectrum from Sagittarius a star and get the best fit model to the set of observational constraints that were available at that time and we ended up with the conclusion that there is a probability distribution for spin per and it's most likely a very low spin for this black hole we got a probability distribution for the inclination angle and another orientation angle so this is good we get close to Sagittarius a star but but no cigar in the sense that we don't have an image yet there is another galaxy that I mentioned it's called m87 it's a giant elliptical galaxy sort of the type of galaxy that we will become that the Milky Way will become once it merges with Andromeda galaxy its sister galaxy and so the black hole inferred in the middle of m87 has a mass that is much larger than the mass of Sagittarius a star by some three orders of magnitude 'm almost a factor greater than than a thousand fourteen hundred times more massive than Sagittarius a star but it's at a distance that is 2,000 times greater than the distance of Sagittarius a star because this is the distant galaxy but if you take the ratio of these two numbers you get the number of all the unity meaning that we can in principle hope to image the shadow of this black hole there is a big difference between m87 and the Milky Way in the sense that there is a jet just like the jet I had in my first slide celebrating the Chinese New Year this is the jet that you have in a in m87 and it's a very tightly collimated jet going all the way out and usually theoretical models that produce a jet require the black hole to have a high spin and so this black hole we know has a high spin probably and these are theoretical similar models of what the shadow around such a black hole might look like and the different assumptions that's a paper that we wrote with every broderick when he was a postdoc in our theory group and you can see that the image near this black hole depends also on what you assume about the base of the jet and how the emission takes place in the vicinity of the black hole so you can get different images it's not just dependent on the spin but it does depend on the spin and this is from a nature paper led by Shep published a couple of years ago where the size of the meeting region was constrained to be smaller than the inner most stable circular orbit for a non spinning black hole so the conclusion from this paper was the black hole must have a spin because we can see a mission from a scale the base of the jet is coming from a scale that is smaller than the Isco for a non spinning black hole and in fact if you do a detailed analysis trying to fit the image you get that the spin has to be pretty close to unity the spin parameter has to be bigger than 0.9 or 0.96 depending on assumptions about the mass of the black hole now obviously if there is a black hole at the Centers of galaxies and almost every galaxy has a black hole at its center when two such galaxies merge you make a black hole pair the Milky Way itself will merge within a few billion years with Andromeda galaxies we see this galaxy coming at us the night sky will change it would be a spectacular event to watch actually as the Andromeda galaxy is colliding with the Milky Way but we see these events on the sky quite frequently and here is an example where you see two cores of galaxies coming together and are many more such examples where you see two cores of galaxies coming together at different separations so here the separation is close to 30 thousand light years at the top left and at the bottom right the separation is less than six thousand light-years and beyond that below that separation it's very difficult to separate with the resolution of these telescopes separate the two cores but we believe that such cores of galaxies spiral towards each other because of friction gravitational friction dynamical friction on the background matter background stars and gas and eventually the black hole themselves get very close to each other after the stars surrounding them gets stripped and then eventually they come together due to the emission of gravitational radiation so here you see two black holes close to each other in x-rays so this is a galaxy that has a lot of dust you can't see much through the dust but in x-rays just like in the airport you can actually image the center of this galaxy and tell that there are two centers of light and here you see a double black hole system in the radio and these black holes emit jets so you can see two jets coming off here is another example there are plenty of examples this is the tightest black hole observed in the radio the separation is around 20 light-years and the total mass is estimated of the two black holes is estimated to be about a billion times bigger than the mass of the Sun so one way to tell that the binary exists is to look for periodic variation of the light and I analyzed this signature about five years ago where I argued that in principle you can find these binaries by looking for periodic modulation of the light and if you ask what would be the characteristic period when for example gravitational radiation takes over and starts to be dominant at the dominant mechanism of bringing these two black holes together compared for example to the friction on the surrounding gas then you find that the period is convenient it's about seven years comparable to the duration of a PhD thesis in our department not sure how long is the PhD thesis in math but you can always imagine the two black holes coming even closer and earlier actually just a few weeks ago there was a paper published in nature arguing that perhaps there is evidence for such a system where the period is of order five years the evidence is not very strong because they have observed this system only for about eight years but it's indicative when more data is needed to figure out if indeed this is a system that gets to the point where the rotational radiation takes over and this binary black hole system will merge in less than the age of the universe due to the emission of gravitational waves now you don't have to stop at two black holes as I mentioned even among humans there are triple systems and that can happen for example if two black holes are in the process of coming together and then another galaxy comes in and joins the party and then you can get three black hole systems and we calculated in some papers with Jewish Kulkarni and Loren Hoffman the likelihood of getting such triple systems and we figured that in fact these are unstable and and one of the black holes gets gets ejected with speeds that can exceed a few thousand kilometers per second so in principle such a speed would imply that the black hole crosses the diameter of the earth in a few seconds okay so these are very high speeds and such black holes with escape from their host galaxies so you can find these ejected black holes in the intergalactic medium no in fact the most common cases are once in which you have the third body being less massive because or two of them being less massive because they're men more of those than massive black holes here we see a pair of black holes coming together by the emission of gravitational radiation and this problem was very challenging to solve numerically with computer codes until about five years ago where a breakthrough was made and and right now it's there are codes that solve Einstein's equations in vacuum except for two point masses orbiting each other in full and calculate the emission of gravitational waves and that's what you saw here now it turns out that when the two black holes come together eventually they get to the east core the inner most stable circular orbit and then the small black hole plunges into the big black hole so the gravitation waves are emitted in a preferred direction and by conservation of momentum there is a rocket effect the remnant black hole that results from the measure of the two black holes gets kicked in the opposite direction and what you saw on the right hand side is that the kicked black hole the recoiled black hole could in principle escape from the host galaxies and so these numerical simulations were able to calculate what is the recoil speed and we incorporated that into galaxy merger simulations with my former student Laura Blanca and found that you could find recoil black holes moving out of galaxies just due to the gravitational wave emission the rocket effect from that and then a question arise arose as to whether such systems are found on the sky and the best candidate for such a system is shown here these are two centers of light that represent two black holes and they are they have a relative speed of about a thousand kilometers per second and an offset of around seven thousand light-years just a month ago we posted on the archive and interesting suggestion for detecting gravitational waves so these gravitational waves that are emitted by black hole pairs have very low frequencies they have a characteristic I mean the two black holes even in the disco have an orbital time of order a thousand seconds if they have the mass of Sagittarius a star so we're talking about a wave period of order a thousand seconds or a wave frequency of amelie Hertz and NASA together with ISA the European Space Agency are promoting a concept to detect these waves in space you can't do it on the ground because there is seismic noise but you can in principle put laser beams separated apart that will measure the slight change in distances between the lasers as the gravitational wave is passing by and that's the concept for a mission that is planned for launch 20 years from now just measuring the change in distances using interferometry this is called the ELISA mission now we thought of something different just over the past year the precision of atomic clocks improved dramatically by orders of magnitude and so our suggestion was to use atomic clocks to detect gravitational waves and the idea is as follows there was a historic experiment that tested Einstein's theory of gravity done at Jefferson Lab the building next to this one where the physics department is it was done by pound and Rebka so here you see one of them at the basement of jeff Jefferson Lab talking on the phone with his colleague at the top of Jefferson Lab and measuring the frequency of gamma-ray photons emitted by nuclei at the top of the building to be different due to the gravitational redshift due to the fact that the gravitational field of the earth changes the frequency of the photons and using the most power effect they were able to reach a very high precision that allowed them to see this tiny shift due to the Earth's gravity so here is the earth causing the gravitational shift now imagine moving the earth under the experiment back and forth tying it with a rope and pulling the earth and then pushing in well one way to do that is to put another earth in a binary orbit then obviously what pound and Rebka would find is a time dependent time dilation effect or time dependent gravitational redshift effect that is changing periodically this is a gravitational wave so if you have a precise enough clock then you should be able to detect gravitational waves and the idea that we proposed was now with the precision of atomic clocks that in particular optical lattice clocks the technology of optical lattice clocks one can reach a precision of order 10 to the minus 18 one part in a million trillion in other words over the age of the universe such a clock would not be off the exact time by more than a second over 10 billion years and if you put such clocks in a triangular configuration for example around the orbit of the earth around the Sun and you shine laser beams that communicate the ticking rate of each clocks you would be able to tell that one for example if there is a passing gravitational wave and the two clocks are separated by 1/2 of wavelength then you would be able to tell that they are ticking at different rates now this is different from measuring changes in distances the current design of ELISA because you're basically measuring the change in the ticking rate or the frequency of the clocks relative to each other you're not you don't care about the fact that the distance changes you just care about the fact that the clocks are not ticking if they were synchronized to start with you can record that they are ticking at different rates at 1/2 a wave period at one time one clock is faster than the other and half a wave period later it's the other way around and this repeats periodically so this is a different concept than interferometry for measuring distances and well the issue of comparing it to interferometry is a subtle one and we are looking at it now but the point is that the precision of these clocks of 10 to the minus 18 in in fractional time precision is comparable to the amplitude of the gravitational waves that you would get from a binary black hole system that has a mass similar to Sagittarius a star at a jig a parsec okay in fact such a binary system at the Pathak will have 10 times the amplitude you can see it here the amplitude is almost 10 to the minus 17 at a distance of parsec or 3 billion light years for black holes with a million solar mass at a frequency of a milli hertz which actually corresponds to half a wavelength comparable to the orbital radius of the earth around the Sun okay so that's the convenient coincidence that the orbital rise of the earth around the Sun is just corresponding to the type of frequency you get from a binary black hole system and such a binary system in fact will coalesce within 10 wave period so if you catch it it's very close to coalescing in and the period the wave period will change with time there is this chirp that makes the period get shorter and shorter as the two black holes get closer and closer so you can actually not only infer the mass of the system but also the distance because you have two equations one telling you how to hear the wave period or the wave frequency changes with time and the other one telling you what the wave amplitude is and you can constrain the mass and the distance from this now when two black holes come together and one of them gets recoiled that means that black hole can get ejected from the host galaxy so there is actually an interesting prediction that one can make the Milky Way galaxy was made out of building blocks early on in the universe there were smaller galaxies dwarf galaxies that came together to make the Milky Way galaxy so the earlier generations of galaxies were smaller than the present-day galaxies that we have and so you can imagine that whenever two dwarf galaxies came together the two black holes at their centers joined and due to a gravitational wave emission the merger remnant got recoiled now the gravitational potential of the host dwarf galaxies is relatively shallow much shallower than that of the Milky Way it's usually it corresponds to speeds of all the 10 km/s whereas the Milky Way has a potential well of 200 kilometers per second so the black holes typically get ejected with the speed of order a few hundred kilometers per second or less and so such black holes would get expelled from the host warf galaxies but they would still remain bound to the region that eventually makes the Milky Way and so what you would end up with are floating black holes in the hellos of the Milky Way galaxy that's a prediction from this process and there should be of order a hundred such black holes we analyzed it in a paper with my former a graduate student Ryan O'Leary and they should carry very compact star clusters that were taken with them so you can look for these compact star clusters and we looked at the survey of the sky called the Sloan Digital Sky Survey and found some candidates for those that have to be looked at more carefully another interesting phenomenon can take place is you have two black holes with their star clusters due to the merger of two galaxies it turns out that the two black holes tend to get into eccentric orbits by scattering background stars they tend to plunge towards each other and when the secondary black hole for example gets very close to the primary black hole the stars around that are tightly bound to the secondary black hole can get expelled this is a slingshot effect imagine the two black hole acting as slingshots and they eject the star gravitationally then you can end up with stars that are moving almost up to the speed of light and together with James bulletins we calculated the statistics of such stars and we found that there could be stars reaching almost the speed of light so think about it if you are sitting if you are occupying a planet next to such a star this would be the journey of your life the star would be ejected from the host galaxies move through the universe traverse it close to the speed of light so you would be able to look at a vast volume of the universe almost you would almost make the journey of a photon through the universe and we are talking about real stars you know them stars like the Sun or more massive than that but of course the numbers of very fast stars is small that there are more stars moving less than the speed of light we call them semi relativistic hypervelocity stars and we define them as new cosmological messengers because if you if you look at the literature on studying the universe the study of cosmology people use primarily photons particles of light okay and here you have the opportunity to use material objects that move almost the same speed as photons and bridge across cosmological distances so these are new cosmological messengers and if you ask how many of them other within let's say a distance of 3 billion light years one Giga parsec depends on the on the speed but you know there could be 10 to the power 15 such stars moving at a speed that is about a tenth of the speed of light but fewer of them moving at the speed close to the speed of light of the order of a few thousand now when such stars move across the universe this is the metric describing our universe as it turns out our universe is very simple once again nature was kind we think we might know why but not sure yet basically geometry is flat okay so the sum of angles in a triangle that you draw through the universe and as you note Riemann originally wanted to figure out if the if space is flat or not by drawing triangles we now know that on the scale of the universe the universe is flat okay so you can describe it with them and it's also expanding so this is the metric of a flat spatial component of the metric expanding with a scale factor that is changing with time so the spatial scales are being stretched with time and then there is the time component that is ticking at the same rate everywhere in the universe and if you have material objects instead of photons that are emitted from a galaxy then their velocity would be degraded or would be reduced as time goes on due to the expansion of the universe the way to think of it is that in quantum mechanics every particle has a debroglie wavelength and the de Broglie wavelength of a particle is just like the wavelength of light it gets stretched by the expansion of the universe and so for a massive particle could be a star or anything that the broadly wavelength scales like one over the momentum or one over the velocity and it's being stretched like the scale factor so therefore the velocity is reduced inversely with scale factor and that's indifference from photons where the velocity speed of light is constant so you get a different relation between distance and travel time then you get four photons and and you get a change also in the brightness of the star due to relativistic beaming and a star could get deflected by an intervening galaxy due to the gravitational effect of that galaxy the effect is similar to gravitational lensing and so we calculated those effects and you can find them in our paper if the star gets too close to the black hole then it can get ripped apart by the tide as I mentioned and such events occur once per hundred thousand years for galaxies that have a single black hole but the rate can be enhanced by almost a factor of a thousand for black hole pairs and black holes that are too massive like more than a hundred million times the mass of the Sun they would swallow the star hole they would not repeat repeat apart because the gravitational tide would be too weak but but black holes that are less massive than a hundred million would rip apart a star like the Sun and the feeding rate of the black hole would be huge and it could lead to outflows so here you see a simulation that was made by my collaborator Kimi hayasaki with my former student Nick stone where you see a star being shredded into a spaghetti like stream of gas this is called spaghetti ization of the star and you can see this stream going around the black hole in this case the black hole has a spin and it's counter rotating it's with a spin of minus 0.9 when the chance of the of the stream intersecting itself is actually larger than if the string the stream was pro-grade moving in the same direction as the spin of the black hole and so you see the stream intersecting the stream of gas this is the XY projection this is the y'see projection of the same process and eventually the material intersects itself and makes an accretion disk around the black hole now this is the case where the gas is cooling very efficiently so the stream becomes very thin in the simulation this simulation was completed I mean the paper was posted just last month and it's it represents state-of-the-art calculations of this process if you allow the gas to cool very efficiently the situation is quite different you can see here that the stream becomes very thick because it heats up due to the stream stream collisions and then you make a torus of gas that is rather thick around the black hole much more quickly the tidal disruption rate could be enhanced if the black hole has a recoil for example when two black holes come together the would be gravitational wave emission and after that the black hole will be kicked and then it will see fresh material that it can eat along the line of sight so it can actually capture stars along the path of the recoil and produce many more tidal disruption events we found with Nick stone we found that roughly every hundred years in such a case you can get a disruption of a star so there is a chance that the PhD student would see to such events coming from the same galaxy and in fact a couple of years ago there was actually more than that three and a half years ago there was one tidal disruption event of a star observed at the cosmological distance that likely produced a jet pointed at the observer and we can see such a jet because it's so bright all the way to the edge of the universe and an interesting question about the jet is whether the jet will be aligned with the spin of the black hole or whether it will be aligned with the orbital plane I mean perpendicular to the orbital plane of the debris from the disruption of the star because the debris from the disruption of the star has no knowledge of the spin axis of the black hole so in Prince can be aligned at an arbitrary angle and then the question is where will the jet go will it be aligned with the angular momentum vector of the orbit of the original star or with a spin of the black hole turns out that since this system with a jet was seen steadily for two weeks without changing in brightness we can rule out the possibility that there is precession of a jet around the black hole spin axis and the most likely situation is that in fact the jet was aligned with a black hole spin so that's the conclusion we drew from that now let me get to my final topic which is primordial black holes black holes produced in the Big Bang and in principle if you imagine the universe at early times it was seeded with density perturbations in homogeneities and if you have a density enhancement of all the unity across the scale of the horizon of the universe the universe it's the horizon of the universe will collapse to make a black hole but since the horizon is very small at early cosmic times you would make a tiny microscopic black hole with a microscopic mass so this could be for example the dark matter you could have some real perturbations that made up the dark matter because we won't be able to tell now Hawking evaporation would eliminate all the black holes with masses less than an asteroid mass but black holes with masses more than 10 to the 15 grams more than the size of an asteroid and the mass of an asteroid have an evaporation time that is longer than the age of the universe so they should still be around if they existed and interestingly enough such a black hole that has an asteroid mass has the size the Schwarzschild radius of the size of a proton ten to the minus thirteen centimeters so if such a black hole passes through a proton it will disintegrate the proton into quarks just due to gravity that's quite remarkable so just like I was talking before about destroying star here we are talking about destroying a proton with a black hole passing through it due to the gravitational tide and a surgical passage of such low mass primordial black holes through the earth is difficult to detect because the only thing it does is excite seismic waves so the question is is the dark matter made of such black holes could it be primordial black holes and we wrote a couple of papers with a postdoc that worked with me Paula pani were ruled out the possibility that the dark matter is made of such black holes and the first part of the argument had to do with black holes with a mass between the mass of the moon and the mass of the Sun okay and it turns out that if you take a black hole and surround it with a mirror and this was argued back in the 70s you take a black hole put a mirror around it a reflecting mirror and let radiation bounce back and forth if the black hole has spin it will turn it turns out that the spin energy of the black hole can be converted into low-frequency electromagnetic radiation with a wavelength comparable or with a frequency comparable or lower than the spin frequency of the black hole and you get a black hole bomb because the the black hole radiates these waves they bounce off the mirror come back just like in a laser they bounce back and forth between the mirror and the black hole and they get amplified every time and so you build up an energy density inside this cavity spherical cavity such that eventually you'll get an explosion all you need to do is surround a black hole with mirrors so is that at all just an academic exercise well for decades people thought but but then it occurred to me that in fact in the early universe you know if you look at these primordial black holes they were so much surrounded by a mirror it's called plasma or ionized gas and it turns out that when you write the dispersion relation for a photon in an ionized gas in a plasma you can think of it as a massive particle the frequency squared is equal to the plasma frequency squared plus the wave number square times the speed of light squared that's similar to having the energy squared of a massive particle equal to its mass squared times the speed of light to the fourth plus its momentum square times speed of light squared so in fact it's as if the photon acquires a mass and if you think about it how does the mirror operate when you look at the mirror you see your reflection the reason you see a reflection is because the plasma frequency inside the metal there is a silver coating to the mirror to the backside of the glass which is basically a metal and that has free electrons in it electrons that are free to move and it has some characteristic plasma frequency related to the density of these free electrons and you are looking at at light where the frequency is smaller than the plasma frequency and therefore the light gets reflected that's what the mirror is so if you look at this primordial black holes and they are surrounded by a dense enough plasma in the early universe they will act that the plasma will act as a mirror and you can extract the spin energy of these primordial black holes it's very difficult to imagine them being formed without any spin they would likely be formed with spin and you can extract this energy and now as time goes on this mirror will eventually disappear because the universe is expanding and the plasma frequency will go down the density of matter would go down and so you will end up with the energy that was stored inside this cavity being dissipated into the radiation field in the universe and so you can end up with the energy distorting the Cosmic Microwave Background and we have limits on that so by using those limits you can actually rule out the possibility this is the fraction of the dark matter that is in the form of primordial black holes as a function of their mass and this mass is roughly the mass of the moon here all the way up to the mass of the Sun or we can rule out the possibility that primordial black holes with even a little bit of spin are the dark matter based on the fact that we haven't seen energy injection into the Cosmic Microwave Background during the later history of the universe so that's one argument then for lower mass black holes that had a mass of the order of an asteroid mass less than the mass of the moon you can rule them out by considering neutron stars so if such a black hole passes through a neutron star very dense star then it turns out that it will excite modes inside the star and eventually get trapped and sink to the center of the neutron star and start eating up the neutron star so turns out if you do the calculation and that's a very detailed calculation that the existence of neutron stars in the Centers of galaxies where there is a lot of dark matter rules out the possibility that the dark matter is made of primordial black holes with masses between the mass of an asteroid and the mass of the moon and once again you know the the limits are quite significant so let me summarize the punchline of my talk and in the first part I talked about the event horizon telescope a very exciting frontier that many of us are involved in and in fact we are now collaborating with and the rominger from the physics department with Peter Galison that was here and with SDI on this project together with a number of astronomers and the goal is to image the silhouette of the black hole at the center of the Milky Way galaxy and in m87 and constrain general relativity or deviations from from general relativity observational ii and then i mentioned the existence of pairs of black holes black hole binaries and that can be looked for in electromagnetic radiation they can also accelerate stars close to the speed of light which is quite remarkable acting as slingshots and when they coalesce they get recoiled and so you can look for offset black holes from the center of galaxies and also for floating star clusters in the Milky Way galaxy and finally primordial black holes probably do not make up the dark matter in the universe thank you I'll be glad to answer questions especially from the students in Andy's class 211 are black holes from A to Z okay go ahead so the question the question was what is the source of the radiation that we see coming from Sagittarius a star this radiation is thought to be emitted by electrons relativistic electrons gyre

Channel: Harvard University

Views: 16,711

Rating: 4.75 out of 5

Keywords: Astronomy (Field Of Study), Black Hole (Celestial Object Category), dark matter, space, Harvard University (College/University)

Id: OBDiXuq0HHg

Length: 74min 55sec (4495 seconds)

Published: Wed Apr 15 2015