Gravitational Waves in the Cosmic Microwave Background

Earlier today, astronomers and physicists working on the BICEP2 collaboration announced results from their three year long experiment. Polarization measurements of the Cosmic Microwave Background radiation have revealed signs of gravitational waves. The experiment also provides some of the strongest evidence yet to support the inflation hypothesis first proposed by Alan Guth.

Unfortunately, I’ve been a little short on time this semester (as evidenced by the lack of activity on the blog over the past few months), so I don’t have too much time to dive into this exciting discovery. But I do at least want to point to some of the best explanations of the newly announced results:

  • Physicist Sean Carroll provides an excellent (and technical) overview of the significance of the results here and here.
  • Astrobites also provides a technical but good overview of the results here.
  • The Guardian has a much more accessible article that highlights the significance of the results here.
  • The actual data and results (and pretty plots!) from the BICEP2 collaboration are available here.
Earlier this year, a second reaction wheel (out of the total four) failed in the Kepler spacecraft. Reaction wheels are like gyroscopes, and provided the stability for the precise pointing of the Kepler spacecraft. Three reaction wheels were required to provide the necessary high amount of precision in pointing to enable much of the spacecraft’s exoplanet detection. Without the third reaction wheel, the spacecraft’s primary mission was thought to be finished.

Since then, the (very creative) engineers at NASA have proposed a plan to use photons from the Sun in place of the third reaction wheel. Photons colliding with the surface of the Kepler spacecraft result in a force being applied to the spacecraft, and the resulting radiation pressure could be used to provide the necessary stability for the spacecraft to continue with further exoplanet detection work. The graphic above provides a simple overview of the procedure (click for full size).

Earlier this year, a second reaction wheel (out of the total four) failed in the Kepler spacecraft. Reaction wheels are like gyroscopes, and provided the stability for the precise pointing of the Kepler spacecraft. Three reaction wheels were required to provide the necessary high amount of precision in pointing to enable much of the spacecraft’s exoplanet detection. Without the third reaction wheel, the spacecraft’s primary mission was thought to be finished.

Since then, the (very creative) engineers at NASA have proposed a plan to use photons from the Sun in place of the third reaction wheel. Photons colliding with the surface of the Kepler spacecraft result in a force being applied to the spacecraft, and the resulting radiation pressure could be used to provide the necessary stability for the spacecraft to continue with further exoplanet detection work. The graphic above provides a simple overview of the procedure (click for full size).

FRBs: Mysterious Pulses in Radio

Fast Radio Bursts (FRBs1) are exactly what their name implies: very quick and bright signals visible in the sky at radio wavelengths. Just by that description alone, though, these signals sound a little boring. But when we start to dig a little bit deeper into what makes up a FRB, we find something much more exciting, possibly even originating from very bright cataclysmic events far away.

Dispersion Measure

An especially useful way to look at FRBs is through the lens of the quantity called “dispersion measure”.

The light from any astrophysical source takes a finite amount of time to reach to the Earth. Simply, that time is due to the finite speed of light. However, there can be an additional delay, accounted by the fact that the space that the light travels through is not quite a perfect vacuum. By modeling the space between stars, the interstellar medium, as a cold and ionized plasma, we discover that a signal’s group velocity travels slower than the speed of light. Therefore, a signal traveling through the interstellar medium cannot travel as fast as the speed of light.

This effect can be described in the following equation detailing the time delay that a signal experiences due to dispersion:

$$\Delta t \simeq 4.15 \times 10^6 \text{ ms} \times (f_1^{-2} - f_2^{-2}) \times \text{DM}$$

The DM stands for dispersion measure, and is given by:

$$\text{DM} = \int_0^d n_e dl$$

The main takeaway from these equations is that the time delay is dependent on frequency. Signals at lower frequencies, and therefore at longer wavelengths, arrive later than signals at higher frequencies. This is why this effect becomes important for radio waves, which have long wavelengths. At shorter wavelengths, like optical or even infrared wavelengths, the delay due to dispersion becomes negligible. The time delay is also dependent on the dispersion measure (DM), which in turn is essentially the sum of electrons along our line of sight to the object emitting the signal. If there are more electrons along the way, the DM will be higher, and we expect a longer time delay in the signal.

If there is a short and bright broadband (visible across a wide range of frequencies) signal, the dispersion gives rise to a very characteristic pattern. We see the larger frequencies, or shorter wavelengths, arrive first at the Earth. The shorter frequencies, which have a longer time delay, arrive later. An example is shown in the plots below for DM = 125 and 250 pc cm-3:

Broadband Signal DMs

If there was no dispersion, our broadband signal would just look like the dotted line: all the frequencies would arrive at the Earth at the same time. But since there are electrons in the way, we get dispersion, and the signals we measure start looking like that curved solid line.

The dispersion measure becomes more powerful when you start thinking of it as an analog to distance. Since objects further away emit signals that travel through more of the interstellar medium, they encounter more electrons along their journey to a telescope on the Earth and therefore have higher values for their DM. For example, since pulsars emit quick broadband pulses in radio, we can use their DMs to get a rough estimate of their distances from the Earth.

The dispersion measure is also different when we look out at different areas of the sky. Since the Milky Way is a flat spiral galaxy, most of the dust in the galaxy is confined in a thin plane. When we look at objects in the plane of the galaxy, we expect their DM to be higher because signals emitted by these objects have to travel through more dust, and therefore more electrons that cause dispersion, to reach us. Conversely, looking at objects outside the plane of the galaxy, we expect the DM to be lower since there is not as much dust in the way. We can see this by mapping the DMs of all the pulsars we know of in terms of their positions relative to the galactic plane (or in other words, their galactic latitude):

Pulsars plotted against DM, B

As expected, we can see a peak at a latitude of 0, where the galactic plane is located. Looking away from the plane, the dispersion measures of the pulsars fall away quickly, since there is less dust in the way. The only exception is two small peaks near -30 and -45 degrees latitude: those correspond to the two Magellanic clouds.

The artist formerly known as Lorimer Burst

So now that we understand DMs, we can now properly dive into FRBs. The first FRB was discovered in 2007, and was called a Lorimer Burst. While searching through old archival data of the Small Magellanic Cloud from the Parkes Radio Telescope in Australia, a group of astronomers led by Duncan Lorimer discovered a single very bright burst in radio lasting less than 5 milliseconds. What made the burst notable was its large power, short duration, and especially its high dispersion measure. The burst was located low below the galactic plane, a few degrees away from the Small Magellanic Cloud, yet it still had a DM of 375 pc cm-3.

What this suggested was that the signal was not originating from our Milky Way galaxy. If the signal had originated from within the galaxy, it would likely have had a smaller DM, matching that of those pulsars near the signal. In fact, models of the dust distribution in the Milky Way indicate that only 25 pc cm-3 would be expected for an object located at that particular position in the sky. Instead, the higher DM means that the signal passed through a larger number of electrons before being detected, suggesting much further distances. In the original discovery paper, the authors estimated a maximum distance of about 1 Gpc, which would place it in another distant galaxy. The large distance also suggests that the power of the event that generated the signal would also have to be very large in order to be detected so far away. Unfortunately, no other events in that area of the sky were recorded at the time in other observations. Another simultaneous observation of an event in x-ray or gamma ray, for example, could provide more clues about what caused the burst and where it’s located.

While this burst was fascinating and mysterious on its own, it was still only one event. Without more similar bursts, we could only say a limited amount about what the objects emitting the burst might be. Five more bursts have since been detected and reported: one in 2011 and four more in 2013. Along the way, these bursts lost their original “Lorimer Burst” name and instead gained the name “Fast Radio Burst”. All of these bursts share similar characteristics to the original Lorimer Burst.

The high values for the DM of these bursts is especially notable. Plotting the DM of these FRBs (in red) on our pulsar DM plot from before highlights how much these bursts don’t fit in with the pulsars in the galaxy:

Pulsars plotted against DM, B, with FRBs

The high dispersion measures of these bursts is very convincing in suggesting that FRBs are not from within our own galaxy. This raises many interesting theoretical possibilities. To generate pulses that are powerful enough to be detected over the large distances predicted would require very energetic mechanisms that we do not yet know of or understand.

Currently, the only things visible at radio wavelengths outside our own galaxy include sources like gamma ray bursts and active galactic nuclei. None of them, however, can generate the fast and bright signals that we see for FRBs. FRBs could be leading us towards discoveries of very exciting astronomical phenomena, something that we cannot yet explain theoretically.

A little closer to home?

But throughout this post so far, I may have been a little misleading… When looking at the FRBs, we have been assuming so far that the large DM has been caused by the interstellar medium. Although this is usually the primary cause of the dispersion observed in astronomical objects, it does not necessarily have to be the only cause or even the largest contributor to the dispersion. Any ionized plasma with electrons could theoretically cause the same effect to happen. We cannot necessarily say that the high dispersion measure on FRBs is due to the interstellar medium.

Just a few weeks ago, a group of astronomers proposed that flaring stars within the Milky Way might in fact be the source of FRBs. Examples of small dwarf stars that produce flares in radio with the necessary brightness and time scale have already been found. In order to explain the high DM we observe for FRBs, the astronomers modeled these flaring stars to include a plasma “blanket” surrounding them. Coherent emission in radio could be generated at the bottom of the coronae of the stars, and once it passes through the plasma blanket, a time delay is added on due to dispersion. So if this model turns out to be correct, what astronomers thought might be an effect of the interstellar medium over billions of parsecs may instead just be due to a thick blanket of plasma surrounding flaring stars2.

Small Sample Size

The end of the story about FRBs is that there really is no end right now. We’re just getting started. FRBs are a very new discovery and we haven’t found many examples of them to make convincing statements about what causes them or even where they’re located. We’re working with a very small sample size of 6, and we cannot say very much until we find more examples and perhaps discover interesting events coincident with a FRB at other wavelengths.

The recent discovery of four FRBs allowed astronomers to estimate a rate at which these events may be occurring: about 10000 per day over the whole sky. That’s a big number and you may wonder why we haven’t been able to find more if they’re that frequent. The answer is that the telescopes big enough to detect these signals can only look at small areas of the sky. We have only started to detect FRBs because of large scale surveys searching for pulsars and other radio transients. As we increase these transient surveys over the coming years, we should find more examples of FRBs, and these examples can help us better understand what is actually behind these bright mysterious pulses.

Sources and Further Exploration

  • Keane, E. F., M. Kramer, A. G. Lyne, et al. “Rotating Radio Transients: new discoveries, timing solutions and musings”, 13 April 2011, Monthly Notices of the Royal Astronomical Society, 415, 3065–3080.
  • Keane, E.F., B. W. Stappers, M. Kramer, and A. G. Lyne. “On the origin of a highly-dispersed coherent radio burst”, 19 June 2011, Monthly Notices of the Royal Astronomical Society (pre-print), arXiv:1206.4135v1.
  • Loeb, Abraham, Yossi Shvartzvald, and Dan Maoz. “Fast radio bursts may originate from nearby flaring stars”, 9 October 2013, Monthly Notices of the Royal Astronomical Society (pre-print), arXiv:1310.2419v1.
  • Lorimer, D. R., M. Bailes, M. A. McLaughlin, et al. “A Bright Millisecond Radio Burst of Extragalactic Origin”, 2 November 2007, Science, 318, 777–780.
  • Lorimer, D. R., A. Karastergiou, M. A. McLaughlin, and S. Johnston. “On the detectability of extragalactic fast radio transients”, 25 July 2013, Monthly Notices of the Royal Astronomical Society (pre-print), arXiv:1307.1200v3.
  • Lorimer, Duncan, and Michael Kramer. “Handbook of Pulsar Astronomy”, 2007, Cambridge University Press.
  • Thornton, D., B. Stappers, M. Bailes, et al. “A Population of Fast Radio Bursts at Cosmological Distances”, 5 July 2013, Science, 341, 53–56.

  1. Trust me, it’s a lot more fun if you pronounce FRBs as “Furbies”. Extra points if you imagine small furry/creepy toys actually being responsible for these signals. 

  2. Another way to think of this: These are sick stars that sometimes sneeze. They’re covered in thick plasma blankets in order to stay warm and get better. (My imagination might be a little too active right now…) 

→ The life and death of Buran, the USSR shuttle built on faulty assumptions

Some fascinating details and background about the Soviet shuttle program.

Launching up to 60 times per year with the capacity to lift nearly 25,000 kg into low-Earth orbit meant that the United States could put a lot of hardware into space each year. It seemed plausible that the Americans were planning to launch experimental laser weapons into orbit—and with the shuttle’s capacity to bring 15 tons back from space, these weapons could be tested in orbit and then be brought back for modification. In the long term, this capability would let the Americans build a functioning orbital battle station.

→ An Ode to Kepler, the Planet Hunter

We know trillions of stars, millions of galaxies, and only this one place with this strange accident of self-replicating chemistry. When that sense of singularity ends, as it very well might, how might humans see the cosmos differently? The real space age will have begun.

Alexis Madrigal writes a beautiful tribute to the Kepler spacecraft.

→ Quantum quest

Interesting look at attempts to find more fundamental origins of quantum mechanics.

The lesson, says Fuchs, isn’t that Spekkens’s model is realistic — it was never meant to be — but that entanglement and all the other strange phenomena of quantum theory are not a completely new form of physics. They could just as easily arise from a theory of knowledge and its limits.

The ISS Expedition 36 crew arrived back on Earth on September 10 aboard a Soyuz capsule. This picture in particular beautifully captures the retrorockets being fired to slow down the capsule before its landing.

Soyuz landings are very photogenic.

The ISS Expedition 36 crew arrived back on Earth on September 10 aboard a Soyuz capsule. This picture in particular beautifully captures the retrorockets being fired to slow down the capsule before its landing.

Soyuz landings are very photogenic.

Accreting on to Sgr A*

Active galactic nuclei are exciting in that they produce large amounts of energy from a very small and efficient “engine”. They are small and compact regions at the center of some galaxies that emit large amounts of energy. The engines powering the active galaxies are thought to be made up of the same supermassive black holes that are observed to be residing in the center of most galaxies.

The most efficient way to generate the large amounts of energy that we can see originating from these active galactic nuclei is through a process called accretion. Accretion essentially gives a way to release the large amounts of gravitational potential energy of the objects in orbit around the supermassive black hole. Just dropping some matter straight into a black hole does not release much energy, since there is no surface on the black hole where the matter can collide and release energy. Instead, when matter falls into a black hole through an accretion disk, friction within the disk can help convert gravitational potential energy into heat and radiation that can be observed.

A little closer to home

Although our own galaxy, the Milky Way, does not possess an active nucleus, it does still possess a central supermassive black hole, called Sgr A*. It provides a fantastic testing ground for some models of active galactic nuclei much closer to the Earth, where we can more easily conduct observations.

Just as the Sun has a stellar wind, the young and massive stars surrounding Sgr A* provide a steady source of particles from their stellar winds. These particles are predicted to provide a constant resource of mass which the central black hole can accrete from. About 10-5 solar masses, or about 3 times the mass of the Earth, are predicted to be accreted every year by the supermassive black hole through mass primarily provided by these stellar winds.

A discrepancy in x-rays

Using what we know from other active galactic nuclei we can make a prediction of the luminosity, or the energy per time given off, by the x-ray radiation. The surprising part is that the predicted luminosity for Sgr A* is about 100 million times larger than what we actually see1! This leads to two possibilities: either the matter from the stellar winds of stars surrounding the black hole isn’t reaching the black hole or that the accretion process is extremely inefficient for these particles, giving off very little energy.

Recently published observations of Sgr A* in x-ray using the Chandra X-ray Observatory have shown to favor RIAF (Radiatively Inefficient Accretion Flow) models. A key part of these models is that much of the mass is ejected along its way to the black hole. It results in a very small portion of the gravitational potential energy possessed by the inflowing particles to be converted into radiation. This would be consistent with the low luminosity that we measure in the x-ray portion of the spectrum for Sgr A*.

That’s all fine and good, but what about magnets?

Obviously the next step to go from here would be to see how magnetism can make this entire situation more fun. In all seriousness, though, magnetic fields make accretion onto Sgr A* more dynamic. The presence of a strong magnetic field around the central black hole can provide a way to remove the angular momentum of gas, help direct matter through relativistic jets, and emit radiation. If the central black hole is rotating, the magnetic field can even help use energy from the rotation of the black hole to emit radiation through the Blandford-Znajek mechanism.

In order to better understand the accretion mechanism around Sgr A* we need to be able to measure the magnetic field in order to provide constraints on accretion models, like the RIAF model. Measuring the magnetic field can be difficult, but conveniently enough, the recently discovered galactic center magnetar can come to the rescue. Through the Faraday rotation phenomenon, we know that linearly polarized light is rotated when passing through a magnetic field. The angle of rotation can be given by \(\Delta\phi\):

$$\Delta\phi = \text{RM}\lambda^2$$

Importantly, the rotation is dependent on the wavelength of the radiation, \(\lambda\), and the rotation measure, \(\text{RM}\). The rotation measure is given by, in the CGS unit system2:

$$\text{RM} = \frac{e^3}{2\pi m^2 c^4}\int_0^d n_e(s)B_{||}(s) ds$$

This equation essentially shows that the rotation measure is an effect proportional to the strength of the magnetic field, \(B_{||}\), summed over the path the radiation takes to get to the observer. Since much of the radiation from the magnetar is linearly polarized, we can compare the polarizations of the pulsar radiation at different wavelengths. This would give us the rotation measure, which in turn would give us the strength of the magnetic field along the path of the radiation. This can provide a good idea of the strength of the magnetic field near the magnetar’s immediate environment, around Sgr A*.

The big picture

Overall, what I find fascinating about studying accretion onto Sgr A* is that it illustrates very nicely two techniques or methods that astronomers often employ to better understand the universe. One is the tick-tock relation between making theoretical models and conducting observations. New models are made using existing observations as constraints and making their own predictions. Then, new observations are conducted, providing new constraints and supporting or disproving existing models. Models are then tweaked or new ones are made, and the cycle keeps continually iterating.

The second is bringing a problem closer to home. Due to the large scales of the universe, we can’t always be lucky enough to have the technology that makes it possible to observe the interesting phenomena at the resolution we want. Things are often just too far away, and therefore too small to be able to see. What we can do, and frequently do do, is find an analog much closer that we can study more easily. For active galactic nuclei, we can sometimes use our galaxy’s center. Another fantastic example is using Saturn’s rings as an analog to other astrophysical disk systems, like circumstellar disks. When you can’t interact with what you’re studying, the next best thing is to be able to have it as close as possible.

Sources and Further Exploration

  • Bondi, H. “On spherically symmetrical accretion”, 1952, Monthly Notices of the Royal Astronomical Society, 112, 195–204.
  • Carroll, Bradley W. and Dale A. Ostlie. “An Introduction to Modern Astrophysics”, 2007 (2nd Ed.), Pearson Education, Inc, 1108–1121.
  • Eatough, R. P., H. Falcke, R. Karuppusamy, et al. “A strong magnetic field around the supermassive black hole at the centre of the Galaxy”, 14 August 2013, Nature.
  • Genzel, Reinhard, Frank Eisenhauer, and Stefan Gillessen. “The Galactic Center massive black hole and nuclear star cluster”, 20 December 2010, Reviews of Modern Physics, 82, 3121–3195.
  • Narayan, Ramesh, and Insu Yi. “Advection-dominated accretion: A self-similar solution”, 10 June 1994, The Astrophysical Journal, 428, L13–L16.
  • Schnittman, Jeremy D. “The Curious Behavior of the Milky Way’s Central Black Hole”, 30 August 2013, Science, 341, 964–965.
  • Wang, Q. D., M. A. Nowak, S. B. Markoff, et al. “Dissecting X-ray-Emitting Gas Around the Center of Our Galaxy”, 30 August 2013, Science, 341, 981–983.
  • Yuan, Feng, Eliot Quataert, and Ramesh Narayan. “Nonthermal electrons in radiatively inefficient accretion flow models of Sagittarius A*”, 20 November 2003, The Astrophysical Journal, 598, 301–312.

  1. This is assuming a Bondi accretion flow model, which relies on a spherically symmetric accretion. This model assumes that there is no angular momentum involved, meaning no rotation. 

  2. Not at all subjectively the best unit system. 

→ How Curiosity Became an Astronaut

Because what’s notable about the six-wheeled Martian robot is that it, too, is an extension of NASA’s emphasis on manned space travel.

Megan Garber presents an interesting argument that the Curiosity rover has changed how we perceive manned space missions. The personification of Curiosity and its adventures on Mars appears natural.