NOTES

Preface

1. See http://www.ssl.berkeley.edu/ipn3/bibliogr.html for an updated list, maintained by Kevin Hurley at the Space Sciences Laboratory, Berkeley, CA.

Chapter 1. Introduction

1. Derived from the Spanish word velar, meaning “to guard” or “to watch over with vigilance.”

2. S. Singer, Proceedings of the IEEE, 53 (12), 1935 (1965).

3. A suspicious event from September 22, 1979 was found to be unlikely of nuclear-detonation origin by a blue-ribbon panel of physicists. That report was declassified in 2006. See F. Press et al., Ad Hoc Panel Report on the September 22 Event. See http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB190/09.pdf in particular and the archive of the Vela September 22 Event at the National Security Archive, http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB190/1980.

4. J. Bonnell, A Brief History of the Discovery of Cosmic Gamma-Ray Bursts. http://antwrp.gsfc.nasa.gov/htmltest/jbonnell/www/grbhist.html (1995).

5. R. W. Klebesadel, I. B. Strong, and R. A. Olson, ApJ (Letters) 182, L85 (1973).

6. Long retired, but still a participant in some scientific meetings, Ray Klebesadel amusingly refers to the events without the word ray (“gamma bursts”) perhaps out of modesty.

7. The 1965 journal paper about the Vela program (S. Singer, Proceedings of the IEEE, 53 (12), 1935 [1965]), for instance, discussed only events from the Sun and Earth as possible cosmic contaminants to a nuclear-detonation signal.

8. That physical model was proposed by Sterling Colgate (Canadian Journal of Physics 46, 476 [1968]). It involved the production of gamma rays in the outskirts of a supernova explosion. This is now not the preferred theory for the production of gamma rays in most GRBs we discover.

9. This is a quote from Klebesadel et al. We now know why the search for an SN counterpart failed: most GRBs detected occur at distances that are much farther away than the typical distances of SNe discovered in the 1960s and 1970s.

10. I. B. Strong, R. W. Klebesadel, and R. A. Olson, ApJ 188, L1 (1974).

11. W. A. Wheaton et al., ApJ 185, L57 (1973).

12. Angular area on the sky, Ω, has units of angular distance squared. For wide areas, Ω is given in steradians. There are 4 π steradians on the celestial sphere and one steradian = 3,283 square degrees.

13. J.-L. Atteia et al., ApJ Supplement Series 64, 305 (1987).

14. Using the rise time (or, more generally, variability time) to infer source size is the “light travel time” argument. Since the entire surface emitting photons cannot “know” precisely when to light up, the propagation of the information to turn on can travel only as fast as the speed of light. The surface size that participates in the radiation cannot be larger than l = δt ×c, where δt is the timescale for appreciable change. If δt ≈ tens of milliseconds, then l ≈ 6,000 km.

15. After a star explodes as an SN, the ejected material continues to propagate outward, first plowing through circumstellar material, then sweeping up the comparably less dense gas and dust that lies between stars (the interstellar medium [ISM]). Over time the remnant expands to many light-years in size. The accumulated material glows across the electromagnetic spectrum. Individual SN remnants are readily detected in the Milky Way and nearby galaxies.

16. The LMC is a small satellite of the Milky Way and, despite its small mass, is a prodigious factory of supernovae.

17. In the case of a spinning NS, there is an appreciable amount of “rotational” energy available related to the spin of the star. This energy is roughly proportional to the spin rate of the star squared, times the radius squared, times the mass.

18. A list of SGR candidates is currently maintained at http://www.physics.mcgill.ca/~pulsar/magnetar/main.html.

19. C. Kouveliotou et al., Nature 393, 235 (1998).

20. 10¹⁴–10¹⁶ Gauss, more than thousands of times most other pulsars observed. R. C. Duncan and C. Thompson, ApJ 392, 9 (1992).

21. In the late 1910s, Harlow Shapley had argued that the Sun was not at the center of the Galaxy by noting that globular clusters appeared to be distributed around the constellation Sagittarius (see figure 1.3), which is indeed the direction of the recognized center of the Milky Way.

22. This is the one reason why it is colder in the winter: light from the Sun hits the Earth more obliquely, so over a given area and given time, less energy is absorbed. The intensity of light falls as the cosine of the angle between the plane of the detector and the incident angle.

23. All GRB detectors have “blind spots,” where events coming from certain directions are less likely to be detected. Moreover, satellites in low-Earth orbit cannot detect a GRB when it occurs on the opposite side of the Earth. The curators of BATSE carefully kept track of the efficiency for detecting GRBs as a function of time and location on the sky. Just as a national census uses the statistics of replies to determine the total number of citizens, the BATSE efficiency map was used to reconstruct a blind-spot-free map of the rate of events over the entire sky.

24. Buttons were handed out before the Great Debate so that people could display their scenario preferences. One said “Gamma-Ray Bursts Are from the Galaxy.” Another said “Gamma-Ray Bursts Are Extragalactic.” Just to hedge the bets, another set was passed around that claimed “Gamma-Ray Bursts Are Other.” I still have all three buttons.

25. That night, for my M. Phil thesis project at Cambridge University, Nial and I were engaged in a project to image the locations of well-positioned GRBs from the IPN. Getting images of the new well-localized GRB 970228 seemed like a good thing to do!

26. There was also another intervening gaseous system along the line of sight at a lower redshift.

27. See http://www.pbs.org/newshour/forum/may98/bang_5-14.html/.

28. The redshift was a measly z = 0.0085, and the distance to that galaxy is about 39 Megaparsec (Mpc).

29. There is no hard-and-fast distance that distinguishes a source from being in the “local universe” and being of “cosmological” origin. But here I will take a source beyond ~ 400 Mpc (z ≈ 0.1) to be at a truly cosmological distance.

30. See S. E. Woosley and J. S. Bloom, ARA&A 44, 507 (2006) for an extensive review.

31. Many physics and astronomy experiments, like BATSE, are acronyms, but Swift is not. The observatory was so named given its ability to swiftly repoint on new GRB positions—in less than one minute—with its sensitive X-ray and ultraviolet cameras. It was launched in November 2004.

32. J. S. Bloom et al., ApJ 638, 354 (2006).

Chapter 2. Into the Belly of the Beast

1. Integral, a European mission launched in 2002, localizes about one GRB per month to an accuracy of a few arcminutes in radius.

2. This is named after the author David Band who introduced the functional form in D. Band et al., ApJ, 413, 281 (1993). A small minority of GRBs appear to have an additional emission component at very high energies (above a few MeV extending to GeV energies) (K. Hurley et al., Nature 372, 652 [1994]; see for review J. Granot et al., GRB Theory in the Fermi Era. arXiv/0905.2206 [2009]). There are also suggestions that some GRBs have two breaks in the spectra—the one usually seen in the gamma-ray bandpass (E_peak) and another in the X-ray bandpass.

3. E. E. Fenimore, J. J. M. in ’t Zand, J. P. Norris, J. T. Bonnell, and R. J. Nemiroff, ApJ 448, L101 (1995).

4. Our gamma-ray detectors are like our ears, sensitive to only a range of energy (or pitch). For an orchestra moving very fast away from us, the flute melody would be redshifted in frequency, sounding to have as low a pitch as a cello. The low pitches of the cello part might be redshifted outside of our sensitivity range, inaudible to us. Likewise, for GRBs at high redshift, we detect high-energy light that has been redshifted into our sensitivity range, and we do not detect low-energy light that has between redshifted out of our sensitivity range.

5. See D. Lazzati and M. C. Begelman, ApJ 700, L141 (2009) for a review of the observations and implications of polarization.

6. Just as the sky changes brightness throughout the day and night, there are times in the orbit of a satellite when the background brightness of the sky is much higher than at other times. This is due both to a combination of persistent astrophysical sources in the field of view of the detector and the changing flux of charged particles entrapped in the Earth’s magnetic field.

7. These definitions are found in T. Sakamoto et al., ApJ 679, 570 (2008).

8. And indeed individual pulses in a given event could be classified among these three groups.

9. E. P. Mazets et al., Ap&SS 80, 3 (1981); J. P. Norris, T. L. Cline, U. D. Desai, and B. J. Teegarden, Nature 308, 434 (1984).

10. C. Kouveliotou, C. A. Meegan, G. J. Fishman, N. P. Bhat, M. S. Briggs, T. M. Koshut, W. S. Paciesas, and G. N. Pendleton, ApJ (Letters) 413, 101 (1993).

11. Think about the decision process before eating berries you find in the woods.

12. Radioactive material loses energy “exponentially,” meaning that most of the energy loss happens very quickly after the material is synthesized; then the rate of loss decreases with time. The half life of a radioactive element dictates how fast the activity declines with time.

13. Correct: you heat up just a bit when you get an X-ray at the dentist office.

14. Blackbody-only fits are not statistically consistent with average GRB spectra. However, a combination of blackbody plus a nonthermal powerlaw has been shown to be consistent with some GRB spectra (e.g., A. Pe’er, F. Ryde, R. A. M. J. Wijers, P. Mészáros, and M. J. Rees, ApJ 664, L1 [2007]), though “Band plus powerlaw” models also appear to fit GRB spectra as well (e.g., A. A. Abdo et al., ApJ 706, L138 [2009]).

15. See E. E. Fenimore, R. I. Epstein, and C. Ho, A&AS 97, 59 (1993).

16. M. Ruderman, Annals of the New York Academy of Sciences 262, 164 (1975).

17. See R. Sari and T. Piran, ApJ 485, 270 (1997) for an extended discussion of the implications of observed variability in the context of relativistic motion.

18. See for review, J. Granot et al., Highlights from Fermi GRB Observations. arXiv/1003.2452 (2010).

19. See n. 16 above.

20. Weakly interacting particles, like neutrinos, could escape this opaque fireball and carry away energy. Indeed, it is believed that more energy is carried by neutrinos than is confined in the photon/particle soup. We return to neutrinos in §6.4.2.

21. When the particle is at rest, Γ = 1 and this formula reduces to the well-known equation E = mc². The mass m is called the restmass of the particle. When the object is moving with low speeds (υ c), then E ≈mc ² + (1 / 2)mυ²;that is, the total energy associated with the particle is the restmass plus the traditional value for the kinetic energy of a moving particle of mass m.

22. The most natural interactions at this scale would be Coulomb interactions (that is, via forces between charged particles), which causes scattering. This is the dominant interaction that transforms kinetic energy into heat when a car smashes into a brick wall.

23. P. Mészáros and M. J. Rees, MNRAS 257, 29P (1992).

24. M. J. Rees and P. Mészáros, ApJ 430, L93 (1994).

25. This is the so-called Schwartzchild radius, which is not a physical surface like that of a rocky planet but instead represents an important boundary. Inside this radius, nothing can escape the black hole (not even light); outside the boundary, radiation from mass accreting into the black hole can be detected by distant observers. For a black hole of mass M that is not spinning, this radius is R_s = 2 GM/c².

26. Following from M. Rees. See A. M. Beloborodov, in American Institute of Physics Conference Series, ed. M. Axelsson, vol. 1054, 51 (2008) and W. H. Lee and E. Ramirez-Ruiz, New Journal of Physics 9, 17 (2007) for reviews.

27. B. D. Metzger, E. Quataert, and T. A. Thompson, MNRAS 385, 1455 (2008).

28. R. Blandford and D. Eichler, Physics Reports 154 (1), 1 (1987) provide a general overview.

29. Light, of course, is an electromagnetic wave. To start the propagation of this wave (i.e., emit light), a changing magnetic field or a changing electric field must be produced. The simplest way to do this is to accelerate a charged particle. In fact, if you wave an empty soda can around, the free charges in the metal will be accelerated, and you will generate light. In this case, you would generate long-wavelength radio waves. If someone nearby had a sensitive-enough receiver, they could listen to your soda music.

Chapter 3. Afterglows

1. A. C. Fabian, V. Icke, and J. E. Pringle, Ap&SS 42, 77 (1976) appear to have first used the term “afterglow” to describe delayed emission following a GRB (from a Galactic neutron star); see also D. Eichler and A. F. Cheng, ApJ 336, 360 (1989); J. E. Grindlay and S. S. Murray, in X-ray Astronomy in the 1980’s, ed. S. S. Holt (Greenbelt, MD: NASA, 1981), 349–366.

2. N. Gehrels, Bulletin of the American Astronomical Society 26, 1332 (1994).

3. J. I. Katz, ApJ (Letters) 432, L107 (1994); P. Mészáros and M. J. Rees, ApJ (Letters) 418, L59 (1993); P. Mészáros, M. J. Rees, and H. Papathanassiou, ApJ 432, 181 (1994).

4. B. Paczyski and J. E. Rhoads, ApJ (Letters) 418, L5 (1993).

5. To maximize the error-box coverage in the least amount of time, searches were conducted at longer wavelengths where the effective field of view on the sky of radio receivers is larger. Unfortunately, as we later learned, the long-wavelength light of radio afterglows is systematically suppressed relative to shorter wavelengths due to a process called “synchrotron self-absorption.”

6. P. Mészáros and M. J. Rees, ApJ 476, 232 (1997).

7. B. J. McNamara, T. E. Harrison, and C. L. Williams, ApJ 452, L25 (1995) provide a good overview of the counterpart searches before the beginning (1997) of the afterglow era.

8. This X-ray pulse was similar to the events detected by Ginga for years; such X-ray events in Ginga were considered to be part of the prompt emission.

9. See M. de Pasquale et al., A&A 455, 813 (2006) for a review of BeppoSAX afterglow observations.

10. L. Piro et al., ApJ 623, 314 (2005).

11. This is especially true in the first ~1 day after trigger. At later times, a powerlaw behavior is often allowed in fits to sparsely sampled X-ray light curves.

12. D. B. Fox et al., Nature 437, 845 (2005).

13. See M. Sako, F. M. Harrison, and R. E. Rutledge, ApJ 623, 973 (2005) for an excellent review and a systematic reanalysis of all available X-ray data before Swift.

14. V. Connaughton, ApJ 567, 1028 (2002).

15. T. W. Giblin, J. van Paradijs, C. Kouveliotou, V. Connaughton, R. A. M. J. Wijers, M. S. Briggs, R. D. Preece, and G. J. Fishman, ApJ 524, L47 (1999).

16. See, for example, P. Kumar and R. Barniol Duran, External forward shock origin of high energy emission for three GBRs detected by Fermi. arXiv/0910.5726 (2009).

17. With sufficiently rapid observations of arcminute-sized localizations, optical afterglows can be found independently of an X-ray afterglow discovery: it is of course possible to find optical afterglows without X-ray localizations, but the search, more laborious because a wider part of the sky must be searched, is not as consistently fruitful as when an X-ray afterglow is found.

18. The actual number of “dark bursts” is a matter of definition of what dark means. This is discussed more fully in §6.2.

19. This was the so-called naked eye GRB because the afterglow could have been seen with the unaided human eye. No one actually reported seeing this event by eye: only robotic telescopes recorded the very bright afterglow. Still, GRB 080319b smashed the distance record as the farthest object that could be seen with the naked eye.

20. C. H. Blake et al., Nature 435, 181 (2005).

21. The early optical light curve morphologies are discussed in A. Panaitescu and W. T. Vestrand, MNRAS 387, 497 (2008); A. Melandri et al., ApJ 686, 1209 (2008); E. S. Rykoff et al., ApJ 702, 489 (2009).

22. S. R. Oates et al., MNRAS 395, 490 (2009).

23. In the Solar System, small dust grains less than 1 mm in size (called “meteoroids”) entering the Earth’s atmosphere at high velocities burn up and make streaks of light called “meteors.” Single-molecule grains called “micrometeoroids” reflect and reemit sunlight; they are responsible for the Zodiacal light you can see at a dark observing site at night when the Moon is below the horizon. Dust grains in the very early days of the Solar System are thought to be the sites around which larger bodies are formed: comets, asteroids, moons, and planets. Shakespeare’s Hamlet aptly called man and woman the “quintessence of dust.” Attempting to understand this basic building block, the NASA mission Stardust collected dust from the tail of a comet and returned the samples back to Earth.

24. There is a wide range of values of α and β, even for different afterglows at the same stage in their evolution. See D. A. Kann, S. Klose, and A. Zeh, ApJ 641, 993 (2006) (β values) and A. Zeh, S. Klose, and D. A. Kann, ApJ 637, 889 (2006); S. R. Oates et al., MNRAS 395, 490 (2009) (α values).

25. Dale Frail, the discover of GRB radio afterglows at the National Radio Astronomy Observatory (NRAO), has noted that most radio afterglows are detected within about a factor of ten of the sensitivity of the Very Large Array (VLA), whereas optical afterglows are generally detected several order of magnitude above the optical detection limits. The expanded VLA (eVLA) and the international facility Atacama Large Millimeter Array (ALMA) are expected to improve vastly the detection success at radio and millimeter wavebands, respectively.

26. See J. Goodman, New Astronomy 2, 449 (1997).

27. See D. A. Frail, S. R. Kulkarni, L. Nicastro, M. Feroci, and G. B. Taylor, Nature 389, 261 (1997).

28. G. B. Taylor, D. A. Frail, E. Berger, and S. R. Kulkarni, ApJ 609, L1(2004).

29. P. Mészáros and M. J. Rees, ApJ 476, 232 (1997).

30. R. A. M. J. Wijers et al., MNRAS 288, L51 (1997).

31. The relationship between the observer time, Γ and r is t_obs =r/ 2Γ²c under the assumption that Γ is not changing. Since we are considering what happens during a decelerating blastwave, the constant 2 in the denominator is not exact and should be replaced by ~4–6, depending on how the blastwave decelerates.

32. Carrying through the calculation keeping E_γ, the deceleration time t_dec, and n as free parameters, we see that

So the longer the onset time for an afterglow, the lower the initial Lorentz factor.

33. With only a few facilities in the world with sufficient sensitivity to detect typical afterglows, radio, mm, and submm data are the most difficult to obtain.

34. See E. Nakar and T. Piran, ApJ 619, L147 (2005) for a summary.

35. Dale Frail noted at the early turn of the century the parallel of this concern with the worrying addition of “epicycles” to explain the improving data on planetary motion in the Ptolemaic model of the Solar System. Of course, the Keplerian explanation eventually emerged as a more elegant formalism. We hope the Johannes Kepler of GRB afterglows has been born, but it’s possible he or she has not yet!

36. Note, however, that a wide range of p values from 1.8 to > 3 have been inferred in some events. See M. C. Nysewander et al., ApJ 651, 994 (2006); A. Panaitescu, MNRAS 362, 921 (2005); A. Zeh, S. Klose, and D. A. Kann, ApJ 637, 889 (2006).

37. A classical example of an afterglow that is well fit by the sort of nonuniform medium expected around massive stars is GRB 011121. See P. A. Price et al., ApJ 572, L51 (2002).

38. See R. Sari, T. Piran, and R. Narayan, ApJ (Letters) 497, L17 (1998).

39. See D. A. Frail et al., ApJ (Letters) 562, L55 (2001) and a review by S. B. Cenko et al., ApJ 711, 641 (2010).

40. E. Berger, S. R. Kulkarni, and D. A. Frail, ApJ 612, 966 (2004).

41. See D. A. Frail, A. M. Soderberg, S. R. Kulkarni, E. Berger, S. Yost, D. W. Fox, and F. A. Harrison, ApJ 619, 994 (2005).

42. See S. E. Woosley and J. S. Bloom, ARA&A 44, 507 (2006) for a review.

Chapter 4. The Events In Context

1. The ISM is certainly clumpy but the typical scales of clumpiness are much larger than 10¹⁷ cm, the scale over which GRB blastwaves are propagated and afterglows are generated.

2. Interstellar dust grains are generally thought to be either carbon- or silicon-based molecules and exist in a range of sizes (from < 0.1 µm to ~0.1 mm). Dust is formed in the final stages of the lives of ordinary stars and also in the ejected material of supernova explosions. See §6.1.

3. Dust destruction has been suggested as the cause for the late turn-on of GRB 030418 (E. S. Rykoff et al., ApJ 601, 1013 [2004]), but there are a number of alternative models. Dust destruction has specific observable signatures, namely the decrease in the opacity at optical wavebands and the commensurate dereddening of the afterglow. Interestingly, one event (GRB 061126) showed some evidence for “gray dust,” where significant absorption existed in the UVOIR bands but without the expected reddening. Here the interpretation was that the GRB afterglow was effective at destroying small dust grains but did not manage to destroy the largest grains. If only the largest grains survive, they serve to block all wavelengths of light by the same amount. That is τ (λ) ≈ constant.

4. Some high-velocity lines seen in absorption in GRB 021004 were initially taken to be due to fast-moving outflow from a massive-star progenitor. But some of the telltale atomic transitions that could not have persisted given the required intensity from the afterglow were seen. The more mundane interpretation, that the GRB 021004 afterglow absorption lines were actually due to a gas system physically disconnected from the host galaxy, seems to be much more favored. See H. Chen, J. X. Prochaska, E. Ramirez-Ruiz, J. S. Bloom, M. Dessauges-Zavadsky, and R. J. Foley, ApJ 663, 420 (2007) for a review of the spectroscopic signatures in the CBM.

5. J. X. Prochaska et al., ApJ 691, L27 (2009).

6. The inference came from observations of UV-excited lines of H₂. See Y. Sheffer, J. X. Prochaska, B. T. Draine, D. A. Perley, and J. S. Bloom, ApJ 701, L63 (2009).

7. GRB 020813 (M. Dessauges-Zavadsky, H. Chen, J. X. Prochaska, J. S. Bloom, and A. J. Barth, ApJ 648, L89 [2006]) and GRB 060418 (P. M. Vreeswijk et al., A&A 468, 83 [2007]) are the first cases of temporal variation.

8. OK, perhaps that is a stretch!

9. Recall that SNe arise from the death of evolved stars, marking (in many scenarios) the end of life of stars more massive than about 8–10 M. For most of the lifetime of massive stars, they fuse light elements into heavier elements (i.e., metals). Upon explosion, those synthesized elements are ejected and strewn into the immediate environment of the supernova.

10. Metallicities for nearby GRB galaxies are almost exclusively required to be measured by looking at some atomic lines in emission (rather than absorption).

11. Think about the alternative, that only a few photons from a faint afterglow are collected on average per wavelength bin of our spectrograph system. In this scenario, in the presence of normal detection-related noise, if there were no collected photons from a certain wavelength, we could not be certain that the deficit was due to a statistical fluctuation or true absorption from intervening gas.

12. See M. J. Michaowski et al., ApJ 693, 347 (2009) for a review of the environments inferred for low-redshift GRBs.

13. Determining, in practice, where a GRB occurs around a galaxy amounts to comparing an image of the afterglow and its surroundings while it is still bright with an image taken much later. Aligning (or “registering”) the stars and galaxies in the two images is straightforward conceptually but is a bit of a black art when the highest precision is required.

14. In many cases, like with the first X-ray afterglow of a shortduration burst GRB 050509b, the location of the event could be whittled down to “only” tens of square arcseconds. Yet in the deepest images obtained by the Hubble Space Telescope, there can be dozens of faint galaxies inside error boxes of such a size. In such cases, there is no way to know for sure which galaxy to “assign” as the true host galaxy. This is where probability theory comes in. We can treat each location as a fuzzy boundary of where the event could have occurred on the sky. Knowing also the density of galaxies on the sky (units of [galaxy arcsec^-2]) of a certain brightness, for any possible host we can use a series of statistical statements about the likelihood of that galaxy being physically associated. When we have spectroscopic redshifts, we gain more information, since galaxies at a lower redshift than the highest redshift system inferred in the afterglow spectrum cannot be physically associated.

15. Stars are born with a variety of masses, from ~0.08 M to several tens (or more) solar masses. Even though there are far fewer massive stars than less massive stars, the light from those massive stars outshines the collective light of the less-massive stars. Since massive stars are also (generally) hotter, they appear more blue than less-massive stars. The result is that young clusters of stars will appear blue. However, massive stars die away more quickly than less-massive stars; so over time, clusters tend to appear more and more red.

16. See J. S. Bloom et al., ApJ 638, 354 (2006).

17. You can play around with other combinations of redshift, time and distance using an on-line calculator hosted at the University of California, Los Angeles (UCLA): http://www.astro.ucla.edu/~wright/CosmoCalc.html.

18. We have argued (E. M. Levesque et al., MNRAS 401, 963 [2009]) that the only GRB with observed T₉₀ < 2 seconds and an absorption-line redshift (z = 2.6) has some nonnegligible probability (~5%) of belonging to the long-duration class. Many high-redshift GRBs do appear to be “short” after a correction for cosmological time dilation is applied but their physical origin appears to be more likely from massive stars. See §5.4 for discussion.

19. Nearby, volume increases like distance cubed (as you might have suspected!), but its growth at larger distances is more complicated due to cosmological effects. Indeed, since the Universe has a finite age and light takes a finite time to reach us, there is a finite volume of the Universe we can see.

20. Emission-line redshifts of GRB host galaxies can be obtained, in principle, on a more relaxed schedule, well after the GRB has faded. But in practice, emission lines from z > 1 hosts become increasingly more difficult to detect at higher redshifts. Almost all spectroscopic redshifts obtained in the Swift era are afterglow absorption-line redshifts.

21. Here, we assume a nominal optical spectrograph with good sensitivity at wavelengths between λ₁ = 4000 Å and λ₂ = 9000 Å. The available redshift range given is determined using the redshift equation in the footnote on page 27.

22. See D. Guetta, T. Piran, and E. Waxman, ApJ 619, 412 (2005) and references therein.

23. See I. Leonor, P. J. Sutton, R. Fray, G. Jones, S. Márka, and Z. Márka, Classical and Quantum Gravity 26, 204017 (2009) for a summary.

Chapter 5. The Progenitors of Gamma-Ray Bursts

1. This is called “magnetic dipole radiation.”

2. To be sure, a WD in a binary system will undergo changes if mass is transferred from its companion. In the most extreme case, it is thought that a Type Ia SN occurs when a WD accretes so much mass that electron degeneracy pressure is insufficient at holding up the star, causing it to explode.

3. S. E. Woosley, ApJ 405, 273 (1993).

4. A. I. MacFadyen and S. E. Woosley, ApJ 524, 262 (1999).

5. See S. E. Woosley and J. S. Bloom, ARA&A 44, 507 (2006) for a review.

6. See K. Iwamoto et al., Nature 395, 672 (1998), and the review article by Woosley and Bloom, ARA&A 44, 507 (2006).

7. J. S. Bloom et al., Nature 401, 453 (1999).

8. See R. Vanderspek et al., ApJ 617, 1251 (2004), and references therein.

9. See the discovery papers (J. Hjorth et al., Nature 423, 847 [2003]; K. Z. Stanek et al., ApJ 591, L17 [2003]) of SN 2003dh associated with GRB 030329.

10. J. P. U. Fynbo et al., Nature 444, 1047 (2006).

11. With so many GRBs observed, we certainly expect some number of such coincidences. The main challenge is in determining what the chance of such alignments might be for a given set of observations. See B. E. Cobb and C. D. Bailyn, ApJ 677, 1157 (2008) for review.

12. And there may be more of them, such as GRB 051109b. See D. A. Perley, R. J. Foley, J. S. Bloom, and N. R. Butler, GRB 051109B: Bright Spiral Host Galaxy at Low Redshift. GCN Circular 5387 (2006).

13. This is akin to a fast-spinning ice skater, with arms tucked in, suddenly throwing his or her arms out wide. He or she will slow up quickly because of the mass placed at larger distances from the center of rotation.

14. See some of the earlier papers advancing this idea: D. Eichler, M. Livio, T. Piran, and D. N. Schramm, Nature 340, 126 (1989); R. Narayan, B. Paczyski, and T. Piran, ApJ 395, L83 (1992).

15. There is a possibility of a fourth class, a quark star, more compact than a neutron star and supported by pressures at the subnucleon scale. There is no convincing evidence to date that such objects exist in nature.

16. For instance, the other star may start dumping mass onto the NS and create an accretion disk, visible at X-ray wavelengths.

17. V. Kalogera, R. Narayan, D. N. Spergel, and J. H. Taylor, ApJ 556, 340 (2001). See also R. O’Shaughnessy, K. Belczynski, and V. Kalogera, ApJ 675, 566 (2008) for review.

18. There is certainly a possibility that this could be a collapsar leading to a GRB. A second GRB could then follow millions of years later!

19. This is the so-called escape velocity that depends on the galaxy mass and the birthplace of the progenitors. For big spiral galaxies like the Milky Way, the escape velocities can be ~100–200 km/s. For puny (“dwarf”) galaxies, it can be a few tens of kilometers per second.

20. This is not to suggest that such a life path is unromantic or unfulfilling!

21. See A. Panaitescu, P. Kumar, and R. Narayan, ApJ 561, L171 (2001).

22. L.-X. Li and B. Paczyski, ApJ (Letters) 507, L59 (1998).

23. B. D. Metzger et al., MNRAS 406, 2650 (2010).

24. Short-burst afterglows, generally fainter than long bursts, are more difficult to localize in X-rays. Moreover, only ~25 percent of short bursts have optical afterglows (compared to ~50 percent of long bursts) making the subarcsecond localization of short bursts relatively rare. With “large” error regions of a few arcseconds, there can be several potential host galaxies, especially at faint depths.

25. I am not a fan of cats, especially ones running loose in a crowd.

26. See J. S. Bloom et al., ApJ 654, 878 (2007).

27. D. A. Perley et al., ApJ 696, 1871 (2009).

28. There is some disconfirming evidence as well. For instance, it appears that short-duration bursts have roughly the same ratio of X-ray afterglow luminosity to GRB energy as long-duration bursts. Since X-ray afterglow luminosity should scale as the ambient density to the one-half power, if the mergers were happening preferentially in more tenuous circumburst environments, we would expect this ratio in short-duration bursts to be less than in long-duration bursts. So at face value, we would conclude that, absent some unmodeled biases, the circumburst densities of long-duration and short-duration bursts are about the same. (The subtlety of this interpretation is that we are assuming that the prompt event arises from internal shocks and the afterglow from external shocks.)

29. See D. A. Perley et al., ApJ 696, 1871 (2009) for a review.

30. GRB 050906 (A. J. Levan et al., MNRAS 384, 541 [2008]) may be a local-universe short-duration event found by Swift, but its association with a nearby galaxy is tenuous.

31. The notion that magnetars could be produced from an older population of binary white dwarfs has been advanced. See A. J. Levan, G. W. Wynn, R. Chapman, M. B. Davies, A. R. King, R. S. Priddy, and N. R. Tanvir, MNRAS 368, L1 (2006).

32. The origin of GRB 070601 has been advanced as due to a BH binary undergoing a specific transition in accretion phase, a new regime of flaring from a magnetar, and planets smashing into white dwarfs.

Chapter 6. Gamma-Ray Bursts as Probes of the Universe

1. A. Wolszczan and D. A. Frail, Nature 355, 145 (1992).

2. Hulse and Taylor won a Nobel Prize in Physics (1993), using precise timing of a pulsar–NS system to establish observational evidence for gravitational waves. See R. A. Hulse and J. H. Taylor, ApJ 195, L51 (1975); J. H. Taylor and J. M. Weisberg, ApJ 345, 434 (1989).

3. “Killer apps” is used colloquially here. While usually associated with popular and transformative computer applications, in this context I mean to capture the unique applications of GRBs in broader aspects of physics and astrophysics inquiry.

4. Most galaxy studies use emission-line diagnostics to determine metallicities, giving a view of the chemical enrichment in regions where stars are formed. But GRB afterglow measurements (especially from events in the distant universe) use absorption diagnostics, giving access to the enrichment history in the interstellar medium of GRB hosts. The difference in techniques is not thought to dominate the overall comparative trends seen between the two methods.

5. H. Chen et al., ApJ 691, 152 (2009).

6. The physical origin of the 2175 Å bump is not well known.

7. While not the first suggestion (R. Maiolino, R. Schneider, E. Olivia, S. Bianchi, A. Ferrara, F. Mannucci, M. Pedani, and M. Roca Sogorb, Nature 431, 533 [2004]) of “supernova-smoke”-dominated dust, given the simplicity of the underlying afterglow spectrum, this is the least assumption-dependent statement about such dust. D. A. Perley et al., MNRAS 406, 2473 (2010).

8. Strangely, there appears to be a higher incidence of strong Mg II absorbers along GRB sightlines than along quasar sightlines; see G. E. Prochter et al., ApJ 648, L93 (2006). It is not clear whether this tells us more about quasars and GRB emission or something more fundamental about the size and structure of Mg II clouds in the halos of galaxies.

9. Such studies have been done for decades with quasars but suffer from a bias due to the persistence of the quasar: faint galaxies and galaxies near the line of sight are clearly missed in such studies.

10. The adjective “instantaneous” is used loosely here. On cosmological timescales of billions of years, a measurement of the rate of star formation over the past 10–50 million years is an appropriately short snapshot of the recent activities in a galaxy.

11. P. Jakobsson, J. Hjorth, J. P. U. Fynbo, D. Watson, K. Pedersen, G. Björnsson, and J. Gorosabel, ApJ 617, L21 (2004).

12. GRB 080320. GRB 090423 also had no optical detection of a host galaxy. See §6.3.

13. This is a preference, not a hard-and-fast rule. Use this rule of thumb as a last resort if you are lost in the woods (better to use the stars as a compass!). Note that in the Southern Hemisphere, moss prefers to grow on the southern side of surfaces.

14. In principle, we could “see” to even higher redshift by observing gravitational waves and neutrinos from this early time in the Universe. However, detecting these primordial signals is exceedingly difficult.

15. A cup of your favorite energy drink is ≈ 10²⁹ times more dense than the average density of the Universe today. It is left as an exercise to you to determine what fraction of the total types of atoms in that drink were formed in SNe explosions.

16. The technical term for this is “hierarchical structure formation,” which, despite its many syllables, flows rather trippingly off the tongue at cocktail parties.

17. Most spectrographic setups these days require that we have precise knowledge (at the < 1 arcsecond level) of the afterglow position. Spectrographs made of “integral field units”—contiguous groupings of small but independent inputs each with an individual spectrum output (e.g., from bundles of fiber-optic cable)—would allow a less refined afterglow position to be studied spectroscopically. But few large telescopes today currently have such units to be deployed rapidly.

18. Such as the GROND camera, which can take images of GRB positions in seven filters simultaneously (J. Greiner et al., PASP 120, 405 [2008]).

19. Think of Population III stars as the first generation of stars, formed from primordial distributions of elements (mostly hydrogen and helium). Population II is the second generation of stars, sufficiently polluted with first-generation metals. Population I are all the stars that are formed after Pop II stars have had a chance to pollute their surroundings.

20. For instance, we might want to get a constraint on the mass of the galaxy (or protogalaxy) hosting the GRB using a specific emission line whose observed wavelength we could predict knowing the redshift of the GRB. We might also look for telltale emission signatures of Pop III stars, such as emission from ionized helium.

21. The fractional space-time compression that is now possible to detect is comparable to the change of the distance from here to the nearest star by an amount about the thickness of a human hair. It seems as though this sensitivity is still not good enough.

22. J. Abadie et al., Class. Quantum Grav. 27, 173001 (2010).

23. We have not yet been able to determine how matter behaves (the so-called equation of state) at the densities and pressures in the cores of NSs.

24. See A. Dietz, Searches for Inspiral Gravitational waves Associated with Short Gamma-ray Bursts in LIGO’s Fifth and Virgo’s First Science Run. arXiv/1006.3393 (2010) and references therein.

25. Though not moving very fast, they have enough energy to ionize atoms in the Earth’s atmosphere, giving rise to the Aurora Borealis (Northern Hemisphere) and the Aurora Australis (Southern Hemisphere).

26. M. Vietri, ApJ 453, 883 (1995); E. Waxman, Physical Review Letters 75, 386 (1995).

27. E. Waxman and J. Bahcall, Physical Review Letters 78, 2292 (1997).

28. E. Waxman and J. N. Bahcall, ApJ 541, 707 (2000).

29. One big problem is that there is no single LIV theory to be tested. So tests of LIV are stabbing at some small part of an otherwise only weakly constrained parameter space.

30. S. Nissanke, S. A. Hughes, D. E. Holz, N. Dalal, and J. L. Sievers, Exploring Short Gamma-ray Bursts as Gravitationalwave Standard Sirens. arXiv/0904.1017 (2009).