The recent detection of gravitational waves from merging binary black hole systems (GW150914 and GW151226) has now opened up the exciting new field of gravitational wave astronomy. However, the signals from these black hole binaries were transient and were only observable in our LIGO detectors for the last second, or less, before they merged. The sources were also more than a billion light years' distant, and so lay far beyond our own Milky Way Galaxy. The signals displayed a characteristic "chirping" form, in which the frequency, or pitch, and amplitude increased over the short duration of the signal. But, we are also searching for signals that could look quite different from that chirp pattern - for example sources that are constantly "on" (i.e. continuous) and emitting at an almost fixed (or monochromatic) frequency, like a pure audio tone.
One possible source of gravitational waves that could be much more local and would provide a continuous signal is a rapidly-rotating compact object known as a neutron star. We have known these objects exist ever since they were first observed as pulsars. They are the collapsed cores of massive stars that have run out of fuel and undergone a supernova explosion. With a mass of slightly more than the Sun's (∼2.8×1030 kg) packed into a sphere of radius ∼10 km, neutron stars are about 40 trillion times denser than lead. A teaspoon of neutron star material would weigh about 10 million metric tons, roughly equivalent to the weight of a small mountain on Earth. Neutron stars are also spinning very rapidly, and for some their surfaces are rotating at up to ∼10% of the speed of light. So, these stars are very extreme objects! Our best understanding is that their pulsed emission comes from beams of radiation emanating from the magnetic poles of the stars acting like a lighthouse. If the magnetic and rotation axes of the neutron star are not aligned then a pulse is observed as the radiation beam sweeps across the Earth once per rotation.
To generate gravitational waves a pulsar must have some non-symmetric distortion in its shape - e.g. a "mountain" - that is not along its rotation axis. There are various ideas about how such a distorted star could form. The distortion could be "frozen" into the crust or core of the star after it was born in the supernova, or formed from material falling onto the star, or be produced and maintained through extremely large internal magnetic fields. However, due to the huge gravitational pull at the star's surface, the material forming the "mountain" needs to be really strong so as not to be flattened out. A mountain on Earth made of jello, for example, could not get very big before collapsing under its own weight, but one made of solid rock can become as large as, or larger than, Everest. For a pulsar with a crust made up of "normal" neutron star material (highly distorted atomic nuclei, free electrons and neutrons) the maximum deformation that could be sustained before collapsing is about 10 cm, so not very high for a "mountain" (scaling up the relative dimensions this would be equivalent to a ∼50 m hill on Earth). If the star was made up from more exotic materials, e.g. if it were a solid quark star, then it could possibly sustain a "mountain" up to ∼10 m in height. The "mountain" size can also be expressed in terms of the star's ellipticity (ε), which is a rough measure of the distortion's size as a fraction of the star's radius.
Making a few reasonable assumptions we can estimate the maximum amplitude of gravitational waves being emitted by most pulsars. To do this we use the law of conservation of energy. Pulsars are seen to slow down (known as spin-down) over time. This spin-down takes a very long time, and even the most rapidly spinning-down objects only decrease in frequency by less than a hundredth of a Hertz (or equivalently, increase their periods by less than ten microseconds) over a year. But, given the huge moment of inertia that the stars possess, this still represents a very large loss in rotational energy, corresponding to a power of ∼1031 Watts, or well over ten thousand times the Sun's luminosity. If we assume that all of this energy is being lost by emission of gravitational waves we can calculate the amplitude with which we would observe those waves at the Earth. This is called the "spin-down limit". When our searches are sensitive enough to reach below this limit we start probing interesting new territory, where gravitational wave signals could be detectable. We do, however, know that the spin-down limit is a naive upper limit, in that a large part of the spin-down can also be attributed to other mechanisms, such as magnetic dipole radiation.
Just as with the "lighthouse" model for their electromagnetic emission, gravitational wave signals are expected at a frequency related to the rotation rate, typically at twice this value. There are just over 430 known pulsars (see the Australia Telescope National Facility pulsar catalogue) spinning fast enough for their gravitational wave emission to be in the sensitive frequency band of the current Advanced LIGO detectors (∼20 to 2000 Hz). Our previous searches in LIGO and Virgo gravitational wave observatory data looked for gravitational wave signals from 195 pulsars, with the spin-down limit being surpassed for two of them (the Crab and Vela pulsars).
In this new analysis we have searched for a total of 200 of these pulsars using data from the first observing run of the Advanced LIGO detectors. To help reach the best sensitivity we have used information about these pulsars obtained through radio and gamma-ray observations; these have provided very precise knowledge of the pulsars' positions, rotational frequencies, and how their frequencies change over time. This information has allowed us to accurately track any potential gravitational wave signal in our data over the whole length of the three-month science run (a search method called "coherent integration").
From these searches we were not able to detect evidence for gravitational radiation from any of the pulsars. But, we have produced the most sensitive upper limits yet, and for eight pulsars our observations have produced limits (using three largely independent statistical methods) on the gravitational wave amplitude that are below the spin-down limits. Two of the pulsars that have long been of interest for gravitational wave searches, due to their large spin-downs, are the Crab and Vela pulsars. These are the pulsars for which we have now surpassed the spin-down limit by a factor of 20 and 10 respectively. From this we can say that, respectively, less than ∼0.2% and 1% of their spin-down energy loss is due to gravitational radiation. We can also limit the ellipticity (roughly speaking the relative deformation, or "mountain" size, compared to the star's total size) of the stars, and say that there are no "mountains" on the Crab pulsar greater than ∼10 cm in height, and none on Vela greater than ∼50 cm. Among the other pulsars, we found 32 more that are within a factor of ten of the spin-down limit. From the gravitational wave data alone we can limit the "mountain" size for some of these to less than ∼0.1 mm, although the spin-down limit is more stringent for those pulsars.
Future science runs of the Advanced LIGO and Advanced Virgo gravitational wave detectors will provide even greater sensitivity for known pulsar searches, and, at the very least, should allow us to surpass the spin-down limits for ten-or-more sources. Searches are also underway for continuous signals that are not associated with any currently known pulsars. These have to search the whole sky and a broad range of frequencies and spin-down values, making the searches computationally intensive, but opening up the possibility of observing previously unknown objects.
Tuesday, January 31, 2017
Thursday, June 16, 2016
So, is this signal different from the first one? Well, like GW150914 it appears to be the result of two black holes inspiralling in to each other and merging, although the two merging black holes are smaller at roughly 14 and 8 times the mass of the Sun. A nice illustration of where these black holes sit, in terms of mass and radius, compared to other known black holes is shown here. However, unlike GW150914 we can pretty definitively say that at one of the merging black holes is spinning. Another thing to note is that if you look at Figure 1 from our detection paper for GW151226 you can't really see the signal in the data time series (whereas GW150914 stuck out like a sore thumb!) and it pretty much looks like noise. As the system was less massive (but at a similar distance to) GW150914 the amplitude of the signal was intrinsically smaller. The saviour to this was that it also lasts longer in the detector's sensitive frequency bands (see Figure 1 in this paper that discusses all the detection's together) which means that you can integrate (basically sum together) over the longer signal and still "see" it in the noise.
Given that we'd already announced the detection you may be wondering what's important about this new one. The main thing is that we are now starting to reveal a population of objects rather than a single one. From looking at the population you can start to understand the distribution of source properties and investigate how they form. Admittedly with just two (and a bit) sources you really can't say much - it would be hard to work out the distribution of everyone's height by measuring just two people, but you at least get a rough idea of the likely range. It also allows us to be sure that the first signal wasn't a fluke, and suggests that we'll see many more of these objects in our upcoming observing runs (the next one, O2, should start this autumn with slightly better sensitivity than O1, and hopefully include the Virgo detector).
We often say that these gravitational waves are opening a new astronomical window on the Universe. And they really are! Imagine that the sky had always been covered in cloud, so you'd never been able to see the Moon, planets or stars (although in this scenario assume that you had a pretty good theory that the diffuse light coming through the clouds was being emitted by very distant objects called "stars".). Then, imagine that one night there's a slight chink in the clouds and through that you see a black sky with a single shining point of light in it. Wow! Your theory about "stars" was right! As the nights go on the clouds clear even more and reveal even more stars and other astronomical objects and the wonders of the Universe (and the exciting physics they reveal(!)) open up to you. It's a slightly tortured analogy, but you can kind of see that we're just seeing the first few points of light as the clouds are just starting to clear.
Some further information/reading:
- The science summary of these results can be found here.
- The GW151226 detection paper is here and a paper detailing all the binary black hole events detected in O1 is here.
- The data, and tutorials on using it (with ipython/jupyter notebooks), for GW151226 can be found here.
- A (probably non-exhaustive) list of blog posts by other LVC members about this detection (in no particular order):
- The Wave that Stole Christmas by Daniel Williams
- Merry Christmas, LIGO: Another Gravitational Wave! by Amber Stuver
- The Cosmic Classroom on Boxing Day by Shane Larson
- The Boxing Day Event by Christopher Berry
- Gravitational waves found again: here’s how they could whisper the universe's secret by Graham Woan
- Black holes rule! by Mark Hannam
*The eagle-eyed of you may have know that amongst all the papers produced about our detection announcement there was also mention of a candidate gravitational event that was within the originally analysed dataset. We've estimated that this candidate, dubbed LVT151012 (for LIGO-Virgo Trigger), has a roughly 90% chance of being a real astrophysical signal, but we like to be far more certain than that to claim it as a definite signal.
Thursday, February 11, 2016
|Fig. 1. The effect of a passing gravitational wave on an alligator (as found around the LIGO Livingston observatory), a tumbleweed (as found in plentiful supply around the LIGO Hanford observatory) and myself (as found in the School of Physics & Astronomy at the University of Glasgow). Note that there is no discernible effect on any of these, except maybe as slight noticeable increase in my happiness at the prospect of the last 13 years of my working life having not been futile!|
|Fig. 2. The GW150914 gravitational wave signal observed in the two LIGO detectors (this is figure 1 from the discovery paper, Abbott et al., Phys. Rev. Lett., 116, 061102 (2016)) (Credit: The LIGO Scientific Collaboration and the Virgo Collaboration)|
I was attracted to the field of gravitational wave research due to the promise that we would be entering exciting times with several large scale projects bringing in unprecedented amounts of new data. Given this the discovery of gravitational waves would be just round the corner, opening up gravitational wave astronomy for real. Little did I know that this has been exactly what’s been said for around 30 years! Despite this I do actually believe that I’ve entered the field at a prime time and finding gravitational waves is just around, if not the first corner, then the next one.So, ten years later, we have now turned that "next corner" and gravitational wave astronomy is finally with us! Many more detections should now be forthcoming in our future observation runs, hopefully including other exciting sources as well as more merging pairs of black holes.
Finally, the other rather cool, and timely, thing is that the signal arrived a century after Einstein published his General Theory of Relativity from which the prediction of gravitational waves arises. Einstein's prediction of gravitational waves and also Schwarzschild's solution to Einstein's equations from which predictions of black holes would arise, were both published a century ago in 1916.
The paper describing the detection and analysis of GW150914 has been peer reviewed and is now published (Abbott et al, Phys. Rev. Lett., 116, 061102, 2016) and further papers detailing the detectors, analyses and science results can be found here. Also, summaries (at a less detailed level) of the main science we've obtained from the signal can be found here. The data containing the signal and some example codes showing how to view, and hear(!), it are available here, so you should go ahead and take a look yourself.
More information, reactions and opinions about this amazing discovery (and the time-line of how the detection happened5) can be found in blog posts by several fellow collaboration members linked below and within a special edition of the LIGO Magazine:
- Amber Stuver (Post-doc, LIGO Livingston Observatory)
- Andrew Williamson (PhD student, Cardiff University)
- Bangalore Sathyaprakash (Professor, Cardiff University)
- Brynley Pearlstone (PhD student, University of Glasgow)
- Christopher Berry (Post-doc, University of Birmingham)
- Chris North (Lecturer, Cardiff University)
- Daniel Hoak (Post-doc, Virgo)
- Daniel Williams (PhD student, University of Glasgow)
- Mark Hannam (Professor, Cardiff University)
- Rebecca Douglas (PhD student, University of Glasgow)
- Roy Williams (Research Scientist, Caltech)
- Sean Leavey (PhD student, University of Glasgow)
- Shane Larson (Research Associate Professor, Northwestern University)
P.S. If you want to know what I was doing when GW150914 passed by it probably involved nappies (diapers for those in the US), feeding a child/cleaning bottles, or doing laundry, as I was on the final day of paternity leave following the birth of my second child (here's my first child one simulating a gravitational wave chirp). I didn't see the growing emails about the signal until early that afternoon when I thought I should try clearing out my inbox before returning to work the following day. It definitely made going back to work that bit more exciting. However, all the work to get the analyses of this event checked has slightly eaten into my main job, which is to search for gravitational waves from pulsars.
1 Don't worry, gravity is very weak. The forces keeping your various constituent bits and bobs together are far more than enough to overcome any piddling gravitational wave that passes through you. Any displacement (stretching or squeezing) is only noticeable (if you have an exquisitely sensitive gravitational wave detector at least) between freely falling objects in the same local frame, i.e. if there are effectively no other external forces acting on the objects.
2 Note that another detector called Virgo is also due to start taking data later this year, but wasn't operational at the time, and that a smaller (and unfortunately less sensitive, but still important) detector called GEO600 was operational, but not observing when the event passed by.
3 Prior to this direct detection (some quibbles over the "directness" of detection can be found here) many gravitational waves have obviously continuously been impinging on the Earth and passing through us, but this is the first time we've had the technology to catch one in the act.
4 There are very good reasons why they've not been seen until now (basically boiling down to us not having been able to build sensitive enough detectors), but that hasn't made us any less impatient.
5 The signal was first "detected" about three minutes after it arrived by online analysis software that looked for generic transient (short-duration) coherent signals, i.e. blips in the data that appeared at the same time in both detectors and looked similar. The first reasonably detailed estimates of the source parameters (i.e. that is was two black holes merging) were with us within about a day. After a couple of days we release our estimate of the location of the source in the sky and released it to selected astronomy groups to point their telescopes at. Following that full and proper detailed studies of the signal, and very careful checks on the performance of the detectors, have taken many months of painstaking work and placed great strain6 on the collaboration. But, given the general inertia that you get within a large collaboration (which we've experienced releasing results that didn't contain any signals) we've actually turned around a finished detection paper (after 14 draft iterations), and twelve(!) companion papers in remarkably short time.
6 This is a hilarious gravitational wave pun.
Disclaimer: everything on this blog is my own personal opinion and any mistakes are my own.
Monday, March 24, 2014
Family constraints have meant I’ve been off the conference circuit for a bit, so the 3rd Gravitational Wave Physics & Astronomy Workshop (GWPAW, formerly the Gravitational Wave Data Analysis Workshop, GWDAW, which ran on 14 occasions) seemed like a good opportunity to get back into the swing of conference attendance. Plus, its location at the Inter-University Centre for Astronomy & Astrophysics (IUCAA) in Pune, India presented the chance to visit a new country. Due to the location of the meeting, many of the other non-local attendees were able to experience a bit of India, including a group that organised a tour round Mumbai (and subsequent train journey to Pune), a couple who started their trip with a holiday in the backwaters of Kerala, and others visiting family or friends. While it would have been a great opportunity for me to see India, I was unable to bookend my trip with any site-seeing, so my experience of India outside of the confines of IUCAA mainly came from my taxi ride from Mumbai to Pune. The taxi ride itself was an interesting insight into travel in India - the first half of the approximately three and a half hour ride (it’s about a 170km journey) was just in leaving Mumbai, where the roads that are about as chaotic as they come. The system seems to be to spot a gap in the traffic, even if it looks too small for the mode of transport you are in, and then squeeze into it. Astonishingly this method (accompanied by liberal application of the horn) got us through the traffic unscathed. The freeway between Mumbai and Pune is apparently one of the best roads in India, and can supposedly offer great views as you climb up into the rocky hills, but a combination of jet lag and low clouds/smog meant that I couldn’t appreciate the trip/views fully (from the plane on my flight back from Pune to Mumbai I was able to see the views I'd previously missed).
In Pune I stayed at the very pleasant Seasons Apartment Hotel, which as the name suggests offered large apartments with a lounge and kitchenette (and free bottled water, which is a must for travellers there). Not feeling very adventurous on my arrival I just opted for dinner at the hotel, but it was definitely worthwhile as the open air rooftop bar/restaurant offered great views of the city. The hotel was just about within walking distance of IUCAA, where the meeting was held (which I had briefly considered as a travel option), but the organisers had put on a taxi service to and from the hotel every day. On travelling to IUCAA I was thankful for this as negotiating the roads, many of which lacked pavements, may have proved daunting. IUCAA itself is situated on the Pune University campus, but is fairly self-contained with its own “housing colony” for guests, students and postdocs to stay. During the meeting we didn’t have to go far between talks in the Chandrasekhar auditorium, coffee breaks (which consisted of strong black tea really) breaks and meals.
As well as our taxi service the organisers provided breakfast, lunch and dinner within IUCAA under a large marquee. The food was great, although you may have been hard-pressed if you didn’t like curry - not a problem for me though! Some of the dishes were pretty spicy, but I suspect they were they were probably still toned down from their usual standard heat levels. We also had freshly made roti cooked in a tandoor oven by the side of the marquee.
On the first evening we had entertainment put on in the form of a Kathak Dance Recital in the meeting auditorium. The singing and musical accompaniment was mesmerising. Afterwards Sathya presented the dancers and musicians with houseplants, which I can only assume is the standard thank-you gift.
Kathak dance recital
And what about the science? The meeting was weighted towards compact binary coalescences (CBC) and electromagnetic follow-up, but that’s not surprising given that these are the most likely sources of the first advanced detector observations. In fact it was good to have a GWPAW where many of talks were about things that could be done in the near future, rather than having to look ahead decades, further cementing the idea that gravitational wave detections are on the horizon! A couple of standout talks were Parameswaran Ajith's overview of the status and prospects for modelling CBC waveforms and Jocelyn Read’s talk on the potential for measuring neutron star equations of state with advanced detectors. Most sessions had lively discussions following the talks, with one particular participant always ready to provide some vigorous questioning.
The breaks and poster sessions in the grounds of the auditorium (which amongst other things contained a giant sundial and a set of swings connected as a coupled harmonic oscillator) were always buzzing with conversation, which for me yielded a potential future collaboration with an IUCAA postdoc. There were many interesting posters, but I particularly liked a couple: one was Chris Messenger’s describing a method to extract redshift information from neutron star mergers by observing modes of a potentially short-lived post-merger hyper-massive neutron star; and another was Shaon Ghosh’s on electromagnetic follow-up of CBC signals. During the meeting my own poster was upgraded to a talk (due to passport related issues for one of the invited speakers causing him to miss the meeting), so I had to quickly put together my own slides.
The meeting turned out to be incredibly productive and fascinating, as well as welcoming and well-organised. The organisers and IUCAA staff were really friendly and helpful. It was a great chance for many Indian students and postdocs to attend the meeting and share their work, and for people from the LVC to interact with them. This was particularly useful because the distance means many collaborators in the USA and Europe got to discuss topics in person, and allowed us to develop these relationships in the run-up to LIGO India. This will be good for bringing through new local people into the field in the run up to LIGO India. There was a great deal of enthusiasm from the IUCAA director Ajit Kembhavi to keep up the efforts with the suggestion that IUCAA and other Indian institutions host summer school-type events in the future. The next GWPAW to look forward to will be in Osaka, Japan in June 2015, closely followed by Amaldi in South Korea.
It’s a shame I didn’t get to experience more of the country, but I did I get to discover a taste for the Indian Coca-Cola equivalent, “Thums-Up”, while discussing exciting science halfway around the world.
Friday, March 21, 2014
I should note that on BICEP2's FAQ the word "direct" gets used in the answer to the question "Have you detected a gravitational wave?" to which they answer "The frequency of the cosmic gravitational waves is very low, so we are not able to follow the temporal modulation. However, we are indeed directly observing a snapshot of gravitational waves through their imprints on matter and radiation over space." Whether this fits into my description of direct or indirect below is another question!
What do I mean by indirect or direct detection? Well in 1993 Hulse and Taylor won the Nobel Prize in Physics for their earlier observation of a pulsar in a neutron star binary system, which was losing energy exactly as predicted through the emission of gravitational waves. This has always been said to be an indirect detection of gravitational waves, i.e., it wasn't physically measuring the waves themselves, but was inferring their presence through the energy they carry away as observed by the binary system's evolution (since their original observations this effect has been measured in many other binary neutron star systems, which also provide other tests of general relativity). With the gravitational wave detectors (such as the aforementioned LIGO, Virgo and GEO600) they aim to directly detect the waves by actually seeing their effect in stretching and squeezing the distance between parts of the detectors. So, the former uses some observations to measure the properties of a source (the orbital evolution of a binary system) and from that infer the presence of gravitational waves, whilst the later directly measures their effect within a detector system. [On a slight aside there could be much discussion on the semantics of "direct" observation/detection - in pretty much all observations (including a persons senses) you could say that you're variously removed/abstracted by a number stages from directly measuring/experiencing the effect of something. In scientific observations it's pretty much always the case that you're having to use proxies to convey some information to you. In most astronomy photons are counted by a CCD, processed by a computer and then displayed, whilst in particle physics you're often measuring the decay of one particle through the products it produces, which themselves are relayed to you through tracks left on silicon detectors, or energy deposited in calorimeters. However, in most cases using "direct" observation/detection is probably a fair term.]
So, in the case of the BICEP2 results, where they're measured the imprint of gravitational waves in the cosmic microwave background (CMB), where does that fit on the scale (if there is some scale in between!) of direct or indirect detection? Initially I was biased against calling this a direct detection. As mentioned above this is mainly due to working as part of a collaboration hoping to soon directly detect gravitational waves with ground-based detectors. I (not wanting to speak for the rest of the collaboration) would like us to be the first to claim a direct detection, so there's a level of guardianship (or unjustified feeling of ownership!) over that claim. However, I think (obviously I'm not the sole arbiter) the CMB measurements deserve the right to be called more than an indirect detection, so for now I'll go with the compromise of semi-direct detection (as used by Andrew Jaffe here).
So, why not indirect? Well, the gravitational waves that are observed in the CMB have (redshifted) frequencies of order 10-17 Hz, which corresponds to wavelengths of ~1 Gigaparsec. To measure such waves you'd need a detector about the size of the Universe. There's obviously no way you could build a physical detector to measure that, so using the CMB's the only way to do it - it is the only "detector" you could have available. In this sense they don't seem to fit with the indirect pulsar binary system paradigm above. [Note that there are also efforts to measure gravitational waves with frequencies around 10-9 Hz using astrophysical objects (in this case pulsars) as the components of a "detector".]
But, why only semi-direct then? This is maybe a technicality that could be argued over, but I suppose it comes down to the basic fact that despite the CMB being the only way to perform the measurement of ultra-low frequency waves you still aren't physically measuring the wave in a detector on Earth (another example might be dark matter, who's effects are imprinted in various astronomical observations, but you still want to see them in a detector on Earth to claim detection). You're also having to use the effect of the gravitational waves on density perturbations, which in turn affect the light intensity, which then affects the CMB polarisation signal received; in a laser interferometric detector the gravitational wave affects the position of mirrors, which in turn effect the phase of reflected and detected light, which you could argue (an I may be pushing it here) is a step less removed than the case with the CMB. There's also the case (which may not be entirely relevant in a direct/indirect argument) that given that the CMB polarisation signal (by the very nature of how it had to be formed during a short period in recombination when photons could diffuse far enough that they would encounter different temperature regions, but that there were still enough free electrons to scatter off and give a polarisation signal) was imprinted within a short space of time, it is just a single snapshot of the gravitational wave signal. Gravitational wave detectors on the other hand (including those using pulsars) are able to measure the variations as the waves pass them, so give a complete time series of the signal. My hand wavy analogy (also implied on the BICEP2 FAQ) is that the CMB measurement is like seeing a photograph of the shadows of water waves on a ripple tank, whereas gravitational wave detectors are like continuously measuring the position of a cork floating on top of the tank.
|Shadows of waves on a ripple tank. Analogous to the imprints of gravitational waves in the CMB polarisation? [Credit]|
Anyway, that's my view. What do you think?
Thursday, January 30, 2014
Carbon is the fourth most abundant element in the Universe (after hydrogen, helium and oxygen) and is the sixth lightest element. To understand it's origins and relative abundance we first have to go back to the origin of the Universe itself.
By the mid-20th Century Edwin Hubble's observations of an expanding Universe suggested that it had started out from an extremely dense and hot initial state: a "cosmic fireball" produced by the Big Bang. However, a question for the Big Bang model was how it produced the known elements in their currently observed abundances (called Big Bang nucleosynthesis). In 1948 a PhD student called Ralph Alpher, working with the renowned physicist George Gamow, published a paper called "The Origin of Chemical Elements" claiming to solve this problem. But, the title slightly overstated the outcome of their work. It was ground-breaking and correctly predicted that in this "comsic fireball" the three lightest elements (hydrogen, helium and lithium) would be made in the abundances that are observed today. However, their work couldn't produce any heavier elements and it was in fact the problem of making carbon that was the stumbling block. The basic process of forming elements is that you take nucleons (protons and neutrons) and fuse them together to create heavier atomic nuclei. You can then fuse further nucleons, or atomic nuclei, together to produce heavier and heavier elements. This is complicated by several facts: the rates that fusion reactions take place can differ enormously for different nuclei; the rates depend very strongly on temperature and density; and, certain nuclei are unstable to radioactive decay and are very short-lived. To create carbon you require six protons and six neutrons, so it can be made by fusing two helium nuclei (two protons and two neutrons) to give a beryllium nucleus and then sticking on another helium nucleus to give carbon. However, Alpher and Gamow found that because the beryllium nuclei only has a lifetime of ~10-16 seconds there wasn't enough time during the hot and dense early stages of the Universe for it to fuse with another helium nucleus and produce carbon. They were therefore left with a Universe containing only the three lightest elements, which was contrary to all observational evidence!
This problem with Big Bang nucleosynthesis was jumped upon by opponents of the Big Bang as a failure of the model. One such person was Sir Fred Hoyle, a forthright theoretical astrophysicist at Cambridge, who, along with others, put forward Steady State models of the Universe (i.e. an infinite Universe with no beginning). However, his models still required that there was some way that elements could be produced, so the problem of creating carbon from lighter nuclei still needed to be solved. In the calculations for trying to fuse three helium nuclei (called the triple alpha process, since helium nuclei are also known as alpha particles) he still found that only insignificant amounts of normal carbon could not be produced during the short life of beryllium, but the production rate would dramatically increase if carbon nuclei were created in an "excited" state i.e. a nucleus with additional potential energy in it. There was no theoretical reason why such an "excited" state should exist (in fact it is still unknown [sorry for the non-open access article link] why this state exists!), but Hoyle argued that because we exist and we require carbon for our existence, then if this is the only way significant amounts of carbon can be produced then this state must be possible. His calculations gave him a precise number for the amount of energy in this state, but he had to convince someone to run an experiment to see if it was true. While visiting the California Institute of Technology in 1953 he persuaded the nuclear experimental groups led by Willy Fowler and Ward Whaling to look for this excited state and soon after it was confirmed that it did indeed exist1.
This didn't mean that Big Bang nucleosynthesis could now produce carbon and the heavier elements as the process was still far too slow given the expansion of the Universe, but there were other environments where it could take place - the cores of massive stars. Hoyle and Fowler, along with the married couple of Margaret and Geoffrey Burbidge, were able to show how all the elements from beryllium up to iron were synthesised in the cores of stars (called stellar nucleosynthesis). In these massive stellar cores there is a high enough temperature and density of helium nuclei so that even though the beryllium produced from fusing two helium nuclei is extremely short-lived there is enough of it that some will fuse with another helium nuclei to form the excited state of carbon. Since carbon was required as the starting point for production of all the heavier elements this allows the large variety we see today. The deaths of these massive stars in supernova explosions has since seeded the Universe we the huge quantities of carbon we see today.
The evidence now shows that the lightest elements were indeed produced during the Big Bang and the Universe has had enough time to produce all other elements (including Carbon) in their observed abundances, via processing in stars.
1A more detailed account of this and the many other people actually involved in the work can be found in H. Kragh, (2010)
When is a prediction anthropic? Fred Hoyle and the 7.65 MeV carbon resonance.
Tuesday, October 01, 2013
Einstein's General Theory of Relativity predicts that the motion of masses can lead to the emission of gravitational radiation, commonly called gravitational waves. These waves, which are distortions in the fabric of space-time, ripple out from their sources at the speed of light. Far away from the source their effect is tiny. The distortions from even the strongest sources (which are some of the most violent events in the Universe) stretch and squeeze the distance between any objects they pass by a fractional amount (called the strain) of order 10-23. That is equivalent to a change in distance between the Earth and the Sun of just a few times an atomic radius! However, scientists have built detectors, based on laser interferometry, to perform very high precision distance measurements that are capable of measuring these extremely small distortions. In the US there are two such detectors called the Laser Interferometer Gravitational-wave Observatory (LIGO), in Italy there is the Virgo detector and in Germany there is the GEO600 detector. These are operated, and their data analyzed, by hundreds of scientists from across the world as part of the LIGO Scientific Collaboration and Virgo Collaboration.
One of the ways we are taking advantage of the fantastic sensitivity of these detectors is to search for continuous gravitational waves from pulsars. Pulsars were first observed in 1967 at the University of Cambridge by the radio astronomers Jocelyn Bell and Antony Hewish. They are neutron stars, which are the collapsed cores of massive stars that have run out of fuel and gone supernova (up until this discovery they had just been theoretical objects first proposed by Walter Baade and Fritz Zwicky in 1934). They are very rapidly spinning, with rotation periods ranging from a few seconds to a few milliseconds, so their surfaces are rotating at up to ∼10% of the speed of light! With a mass of slightly more than the Sun (∼2.8×1030 kg) packed into a sphere of radius ∼10 km, they are about 40 000 billion times denser than lead (this is equivalent to squashing the entire population of the Earth into a thimble). They also have magnetic fields a billion to a few thousand billion times that of the Earth. So, these are very extreme objects! The pulsed emission comes from beams of radiation emanating from the magnetic poles of the stars acting like a lighthouse. If the magnetic and rotation axes are not aligned then pulses are observed as the radiation beam sweeps across the Earth once per rotation.
An artist's impression of a pulsar. Image credit: Michael Kramer (JBCA, Unversity of Manchester).
To generate gravitational waves a pulsar must have some non-symmetric distortion that is not along its rotation axis, i.e. a "mountain". This distortion could have been: frozen into the crust or core of the star after it was born in the supernova; formed from material falling onto the star; or, be produced and maintained though extremely large internal magnetic fields (larger even than the external fields described above). However, due to the huge gravitational field at the star's surface the material forming the "mountain" needs to be really strong to not be flattened out (a mountain on Earth made of jello would not get very big before collapsing under its own weight, but one made of solid rock can become as large as, or larger than, Everest). For a pulsar with a crust made up of normal neutron star material the maximum deformation that could be sustained before collapsing is about 10 cm, so not very high for a "mountain" (scaling up in height only this would be equivalent to a ∼50 m hill on Earth). If the star was made up from more exotic materials, e.g. if it were a solid quark star, then it could possibly sustain a "mountain" up to ∼10 m in height. The "mountain" size can also be expressed in terms of the star's ellipticity (ε), which is a measure of its size as a fraction of the star's radius.
Making a few reasonable assumptions we can estimate the maximum amplitude of gravitational waves being emitted by most pulsars. To do this we use the law of conservation of energy. Pulsars are seen to slow down (spin-down) over time. This spin-down takes a very long time, and even the most rapidly spinning-down objects only decrease in frequency by less than a hundredth of a Hertz (or equivalently, increase their periods by less than ten microseconds) over a year. But, given the huge moment of inertia of the stars this still represents a very large loss in rotational energy, corresponding to a power of ∼1031 Watts, or well over ten thousand times the Sun's luminosity. If we assume that all of this energy is being lost by emission of gravitational waves we can calculate the amplitude with which we would observe them at Earth. This is called the "spin-down limit". If we can achieve detector sensitivities that allow searches to reach below this limit then we are probing interesting new territory, where gravitational wave signals could be detectable.
There are just over 350 pulsars (see the Australia Telescope National Facility catalog) spinning fast enough for their gravitational wave emission to be in the sensitive frequency band of the current detectors (∼20 to 2000 Hz). We have searched for a total of 195 of these pulsars using data from the LIGO, Virgo and GEO600 science runs, with the most up-to-date results for 179 of them coming from the most recent LIGO S6 and Virgo VSR2 and VSR4 runs. To help reach the best sensitivity we have used information about these pulsars obtained through radio, X-ray and gamma-ray observations; these have provided very precise knowledge of the pulsars' frequencies, positions and how their frequencies change over time. This information has allowed us to accurately track any potential signal in our data over the whole length of the science run (called coherent integration).
From these searches we were not able to detect evidence for gravitational radiation from any of the pulsars. But, we have produced the most sensitive upper limits yet, and for seven pulsars we are starting to probe an interesting regime within a factor of five of the spin-down limit. For the Crab pulsar and Vela pulsar we have surpassed the spin-down limit. From this we can say that, respectively, less than ∼1% and 10% of their spin-down energy loss is due to gravitational radiation. We can also say that there are no "mountains" on the Crab pulsar greater than ∼1 meter, and none on Vela greater than ∼10 meters. Among the other pulsars, we found eight more within a factor of ten of the spin-down limit. From the gravitational wave observations alone we can limit the "mountain" size for some of these to less than ∼1 mm, although the spin-down limit is more stringent for those pulsars.
When the current upgrades to the LIGO and Virgo detectors are complete we expect to be able to beat the spin-down limit for many more pulsars. This includes pulsars where we could limit the maximum mountain size to less than a few tenths of a millimeter! It also means we will be in a regime where we can make the first direct detections of gravitational waves from pulsars.