Detectors _ 217 216 _ Astrophysical Techniques

Exerc ise 1.14 natural deposits. This is a fu nction of the half-life of the product and the neutrino fllLx in th e recent past, assuming that a state of eqUlltbnum has If Davis' ch lo rille-37 neutrino detector were allowed to reach equilibrium, bee n reached. Poss ibl e candidate elements are tabulated below. what would be the total number of atoms to be expected? (Hint: see Exercise 1.1 2, and note th at 2:: : 1 G)"= 0.693). Product Energy Threshold Half· life (Years) (MeV) Element React ion 3 x 10 0.046 1.6 GRAVITATIONAL RADIATION Thallium ' 2.6 x 106 8.96 1.6"1 Introduc ti on Molybdenum + /Ie - + II + e- 2. 1 X lOS 0.490 When the first edition of this book was written 25 years ago, this section Bromine + IIf - e- 8 X 10" 2.36 Potassium + /Ie + e- began "This section differs from the prev ious o nes beca use none of the techniques th at are di scussed have yet indisput3bly detected gravitational rad iation." That is still the case. It is possibl e that the upgrades to some of the cu rrent interferometric gravity wave detectors (see Secti on 1.6.2) will Exercise 1.1 2 be se nsitive enough to make the first detections by 2010 to 2012. It has Show that if an element and its rad ioactive reaction product are in an also been stated that a third-generat ion interferometric gravity wave equilibrium state with a steady flux of neutrinos. then the number of detector (tentatively called the Einstein telescope) would have a "guaran- decays per second of the reaction product is give n by teed" discovery rate of thousands of events per yea r. Thus, we ma y hope that perhaps a sixth, seventh, or eighth edition may finally be able to 00 I (I)" b -;; 2: change the opening statement of this section. One change to th e introduction to this section from those in previous editions is possib le though. No gravitational waves may have been when detected, but nonetheless LlGO (Laser Interferometer Gravitational- I" l'» I s N is the number density of the reaction product wave Observatory) (see Section \.6.2.2) has produced a result. On the p February 1,2007 a short GRB occurred whose position aligned with one of I" l' is its half-life the Andromeda galaxy's (M3 1) spiral arms. No gravitational wave wa s Hence, show that the equilibrium ratio of product to original element is picked up from this event, but if the GRB resulted fro m the merger of two given by compact objects (neutron stars and/ or black holes) as man y astronomers surm ise, then it should easily have been detected by Ll GO. A nega ti ve result therefore implies either that the GRB originated via some other process, if it was indeed located within M31 , such as being a soft '(-ray repeater, or the alignment with M3 1 was just due to chan ce and th e GRB where was actually at the usual distance of hundreds to thousands of mega par- N is the number density of the original element sees away from us. e . aI' is the neutrino ca pture cross section fo r the reaction The basic concept of a gravity wave'" is simple; if an object with mass FI' is th e neutrino fhc{ chan ges its position then, in general, its gravitational effect upo n another

Exercise 1.13 ... . t· 'Ii C "K c 8 B solar neutrinos . The term gravity ..... ave is also used to describe oscillations in the earth's atmosphere arisin g Calculate the equilibrium ralio 0 20 a to 19 lor 5 _ -'16 - 2 010 - 2 1) from quite different processes. There is not usually much of confusion. (T,/,=80,000years, u ,,= 1.45 X IO m ,F,,=3 x l m s . 218 • ASl rophys ica l Techniques Delectors • 219 object will change, and the information on Ihat changing gravitational Thus, fo r a typical dwarf nova syslem with field propagates outward through the space-time continuum at the speed of light. The propagation of the changi ng field obeys equations analogous M, = M, = 1.5 X 10'0 kg (1.1 21) 10 those for electromagnetic radiation provided Ihat a suitable adaptation e=O (1. 122) is made for the lack of anything in gravitation that is equivalent to positive and negative electric charges. Hence, we speak of gravitational radiation P = IO·l s (1.1 23) and gravitational waves. Their frequencies for astronomical sources are anticipated to run fro m a few kilohertz for coll aps ing or explod ing objects we have to a few microhertz for binary star systems. A pair of binary stars 24 coalescing into a Single object will emit a burst of waves whose frequency LG = 2 X 10 W ( 1.124) rises rapidly with lime: a characteristic "chirp" if we could hear it. But for an equally typical distance of 250 pc, the flux at the earth is only Theoretical difficulties with gravi tational radiat ion arise from the multi- tudinous metric, curved space-time theories of gravity th at are currentl y FG = 3 X 10- 15 W m- 2 ( 1.125) extant. The best known of these are due to Einslein (general relalivity), Bra ns and Dicke (scalar-tensor theory), and Hoyle and Narlikar (C-field This energy will be radiated predominantly at twice the fundamenlal theory), but there are many others. Einstein's theory forbids dipole radi- frequency of the bi nary wilh hi gher harmonics becoming important as ation, but this is allowed by most of the other theories. Quadrupole th e orbital eccentricity increases. Even for a nearby cl ose binary such as 30 30 radiation is thus the first allowed mode of gravitational radiation in L Boo (distance 23 pc, MI = 2.7 x 10 kg, M , = 1.4 X 10 kg, e = 0, gene ral relativity. and will be about two orders of magnitude weaker P = 2.3 X 10' s), the flux only rises 10 than the dipole radiation from a binary system that is predicted by the - 14 W - , other th eories. Furthermore, there are only two polarization states fo r the FG = 5 X 10 m (l. 126) radiation as predicted by general relativity, compared with six fo r most of Ihe other theories. The possibility of decisive lests for general relativity is ROlaling elli ptical objecls radiale quadrupole radiation with an intensity thus a strong motive fo r as piring gra vity wave observers, in addition to the given approximately by inform ation that may be contained in th e waves on such matters as GM'w6r4 (A + 1)6(A - I)' collapsing and colliding stars, supernovae, close bina ries, pulsa rs. early LG'" _ W ( 1.127) stages of the Big Bang, etc. 64c' The detection prob lem for gravity waves is best app reciated with th e aid where of a few order-of-magn itud e calculations on their expected inte nsities. The NT is the mass quadrupole gravitational radiation from a bi nary system of moderate w the angular velocity eccentricity (e :0; 0.5), is given in ge neral rela tivity by r the minor a..'{ is radius A the ratio of the major and min or ax is radii ( 1.1 20) So that for a pulsa r wilh

where w = 100 rad S- I ( l.1 28) 1\111 and NT z are the masses of the components of the binary system r = 15 km ( 1.129) e is the orb ital eccent ricity P is the orbital period A = 0. 99998 ( 1.1 30) 1 De tectors _ 221 220 _ Astrophysical Techniques

system. This used a massive (> I t) alwninum cylinder, which was isolated we obtain by all possible means fro m any ex ternal di sturbance, and whose shape was ( 1.1 31) LG = 1.5 X 10' 6 W monitored by crystals attac hed aro und its equato r. Two such cylinders separated by up to 1000 kill we re utilized, and o nl y which fo r a distance of 1000 pc leads to an estimate of the fllLX at the co incident events were regarded as signi fican t to eliminate any remainin g earth of external in terference. vV ith this system , vVeber could detect a strain of 16 21 (1132) 10 - (cf. 5 x 10- for the detection of, Boo). Since hi s cyl inders had a natu ral vib rat ion frequency of 1.6 kHz, thi s wa s al so the frequency of the Objects coll apsing to form black holes within th e galaxy or nearby globular grav itatio nal radiation that they wo ul d detec t most efficientl y. Weber cl usters or coalescing binary systems may perh aps produce transient flu xes detected about three pu lses per day at this freq uency with an apparent up to three orders of ma gnitude higher than these continuous flu xes. si derea l co rrelation and a direc tion corresponding to th e ga lactic center or Q Now these flLLxes are relatively large compared with , say. th ose of a point 180 away fro m th e center. If origi nating in th e ga lactic center, interest to radio astronomers, whose faintest sources may have an inten- some 500 solar masses would have to be totally conve rted into sity of 10--2• W m 2 Hz- I. But the gravitational detectors built to date and tio nal radiation each year to provide the energy fo r the pul ses. Unfortu- those planned for the fu ture have a\l relied upon detecting the strain nately (or perhaps fort unatel y fro m the point of view of the continuing ('O x/x) produced in a test object by the tides of the gravitational wave existen ce of the gaia..x y), the results were not confirmed even by workers rath er than the absolu te gravitational wave flux, and thi s in practice means using identical equipment to Weber's, and it is now ge nerally agreed that that measurements of changes in the length of a I m long test object of there have been no defi nite detections of gravitat io nal waves to date. onl y 5 x 10- 21 m, or about 10- 12 times the diameter of the hydrogen Adaptations of Weber's system have been made by Aplin, who used atom, mu st be obtained even for the detection of the radiation from t. Boo. t...-\,o cylinders with the pi ezo-electric crystals sa nd wiched in between them , In spite of the difficulties that the detection of such small changes must and by Papini , who used large crystals with very low damping constants so obviously pose, a detector was built by Joseph Weber that appea red to that the vibrations woul d continue for days following a dist urbance. The have detected gravity waves from the center of the galaxy early in 1969. Expl orer detector at CERN near Ge neva, and the NAUTILUS detector Unfo rtu nately, other worke rs did not confirm this, and the source of near Ro me use 2300 kg bars of aluminwn cooled to 2 and 0.1 K, respect- Weber's pulses remains a mystery, although they are not now generally ively. T hey have reso nant fre quencies around 900 Hz. Other systems attributed to gravity waves. The pressure to confirm Weber's results, based upon niobium bars have also been used. Ultimately, bar detectors 21 22 however, has led to a wide variety of gravity wave detectors being pro- might achi eve strain sensitivities of 10 - or 10 - . At Leid en, a detector posed and built. The detectors so fa r built, under construction or proposed based upo n a spherica l mass of copper-alu minul1'l all oy, know n as are of two types: direct detectors in which there is an attempt to detect the Mi niGRA IL is currentl y worki ng at a tempera ture of 5 K and a strain 20 radiation experimentall y, and indirect detectors in which the existence of sensitivity of 1.5 x 10- at a resonant frequency of 3 kHz. It is expected to the radiation is inferred from the changes that it incidentally produces in reach a strain sensitivity of 4 x 10- " when operated at 0.05 K, and has the other observable properties of the object. The former group may be advantage of being equall y sensitive to gravity waves from any direction. fur ther subdivided into resonant, or narrow bandwidth detectors, and nonresonant or wideband detectors. 1.6.2. 2 Direct, Nonresonant Detectors The direct, nonresonant detectors are of two types and have the potential 1 .6.2 Detectors adva ntage of be ing capable of detecting gravity waves with a wide ran ge of 1.6.2. 1 Direct Resonant Detectors frequenCies. The first uses a Michelson type interferometer (Section 2.5) The vas t majo ri ty of the early working grav ity wave telescopes fall into this to detect th e relative changes in the positio ns of two or more tes t ma sses. category. They are similar to, or improvements on, Weber's original A poss ible la yout for the system is shown in Figure 1. 94, usually, however, 222 • Astroph ys ical Techniques Detectors _ 223

Test disturba nces are likely to have comparable effects on the two machines. mass The light beams make 75 round trips along the arms before recombination so that the arms are in effect 600 km long. When no gravitational disturbance is present there is destructive interference between the two beams at the detector (i.e., no signal) and the light can be returned to the arms of the inte rferometer. thus increasing th e power ava ilable-a tech- nique ca lled power or signal recycling. It is marginal whether LI GO will initially be sensitive enough to detect gravity waves and as of2007 had not 2 1 done so. although it achieved its designed strain sensitivity of 10 - in 2005. Upgrades of LI GO are planned-Enhanced LIGO in 2008 wh ich Laser Test among other improvements will lise more powerful lasers and improve light mass sourc e 8eam the strain sensitivity by a factor of two or three, and Adva nced LlGO whic h wi iJ start constructio n in 2008 and should achieve a stra in sensitiv- 22 ity of 10- . Anyone with a computer and an Intern et link can help with FIG URE 1.94 Possible la yout for an interferometric gravity wave detector. the data processing part of LI GO and GE0600 through the Ei nstein@- home project. This curre ntly has some 180.000 volunteers whose com- the path length will be amplified by up to a factor of 300 by multiple puters process data fo r the project when they would otherwise be idle. An reflections fro m the mirro rs though these are not shown in the figure to Internet search for ei nslein@home wiJI ta ke anyo ne interested in joining preserve simplicity. The mirror surfaces have to be nat to 0.5% of the the project straight to its home page. operating wavelength. The light sources are high-stabi li ty neodymiulll- Also currently starting to operate or nearing completion are the ltalia n- ytt rium-garnet lasers with outputs of 100 W or mo re. The mirrors are French VIRGO with 20 multiple renections along its 3 km arms. It is sited mounted on test masses on pendulum suspensions. and the whole system. near Pisa and had its first science run in 2007. The German-Brit ish including the li ght paths, operates in a vacuum. Path length changes are GE0600 at Hanover with 600 m arms started to operate jOintly with detected by looking at the interference pattern between the two o rthogonal LlGO in 2005. Like Ll GO it also uses power recycling to enhance its beams. Ultimate strain sensitivities of 10 - 22 over a bandwidth of I kHz are sensitivity. The Japanese TAMA near Tokyo has arms 300 m long and predicted for these systems. enabling detecti o ns of coll apSing neutro n plans are being considered fo r the large-scale cryogenic gravity wave stars, supernovae, and coa lescing binaries to be made out to distances of telescope (LCGT) that wi ll have two se ts of 3 km long anns, be situated L07 to 108 pc. Terrestrial detectors are li mited lo frequencies above about in the Kamioka mine, and perhaps be operati onal by 2009 . The distribu- LO Hz because of noise. A proposed space-based system, LISA, whi ch will tion of these detectors over the earth will not only provide confirmat ion of be able to detect much lower frequencies. is discussed below. detections but also enable th e arr ival directions of the waves to be pin- Two Michelson-interferometer type gravity wave detectors. known as pointed to a few minutes of arc. Considerati on is just starting to be given LIGO, have recently been completed in the Un ited States. Their interfer- to the third generation of interferometric gravity wave detectors with the ometer arms are 4 km long and they are si ted 3000 km apart in Washington recent start of the European Einstein telescope feasibi li ty study. However. slate. and in Louisiana. so lhat gravity waves may be distinguished fro m at the time o f writing. liale progress has been made beyond identifying a other disturbances th ro ugh coincidence techniques. The Washington name for the project. machine has a second interferometer with 2 km arms that will also help There is also a proposal for a space-based interferometer system called to separate out gravity wave disturbances from other effects. This is LI SA. This wo uld employ three drag-free spacecraft (Figure 1.96) at the because the gravity wave should induce cha nges in the 2 km machine corners of an equilateral triangle with 5,000,000 km sides. Eac h spacecraft that have half the amplitude of those in the 4 km machine, whereas other would be able to operate as the vertex of th e interferometer. and as the 224 _ Ast rophys ical Techniques Delectors _ 225

proof mass for the other spacecraft. LISA would thus have three separate Vernier rocket motors interferometer systems. It would orbit at I AU fro m the Sun, but so me 20· behind the earth. It s sensitivity would probably be comparable with Optical pOSition sensors the best of the terrestrial gravity wave detectors. but its low noise would enable it to detect th e importan t low-frequency waves from binary stars, etc. LI SA is currently planned as a joint ESA-NASA mission fo r 2018 with a smaller scale LISA pathfinder mission perhaps by 20 II. Beyond this, there may be th e Big Bang Observer which is enVisaged to comprise four in struments like LISA and be ab le to detect gravity waves from soon after the Big Bang. An ingenious idea underlies the second method in this class. An artificial satellite and the earth wi ll be independently inAuenced by gravity waves whose wavelength is less than the ph ys ical separation of the two objects. If an accurate frequency source on the ea rth is broadcast to the satellite, and then returned to the earth (Figure 1.95), its frequency will be changed by the Doppler shift as the ea rth or sateHi te is moved by a gravity wave. Each gravity wave pulse will be observed three times enabli ng the reliability of the detection to be improved. The three detecti ons will correspond to the effect of the wave on the tran smitter, external satellite and in fluenced only the satellite, and the receiver, although not necessarily in that order. by gravitational fields A drag-free satellite (F igure 1.96) would be required to reduce external perturbations arising from the solar wind, radiation pressure, etc. A lengthy FIGURE 1.96 Sc hematic cross section through a drag-free sa tellite. The series of X-band observations using the Ulysses spacecraft aimed at detect- position of the massive test object is sensed optically and the ex ternal ing gravity waves by this method have been made recently, but so far satell ite driven so that it keeps the test object centered. with out any successful detections. 7.6.2.3 Indirect Deleclors Satellite Proposals for these so far only involve binary star systems. The principle of the method is to attempt to observe the effect on the period of the binary of the loss of angular momentum due to the gravitational radiation. A loss of angular momentum by some process is required to explain the present separations of dwarf novae and other close binary systems with evolved components. These separations are so small that the white dwarf Source would have completely absorbed its companion during its ea rli er giant stage, thus the separation at that time must have been greater than it is Receiver now. Gravitational radiation can provide an adequate orbital angular momentum loss to explain the observations, but it is not th e onl y possible Earth mechanism. Ste ll ar winds, turbulent mass transfer, and tides may also FIGURE 1.95 Arrangement for a satelli te -based Doppler tracking gravity operate to reduce th e separation, so that these systems do not provide wave detector. unequivocal evidence for gravitational radiation. 226 _ Astrophys ical Techniques Detectors _ 227

The prime ca ndidate for study for evid ence of gravitational radiation is Coma galaxy cluster showed that they were too high fo r the galaXies to be th e bi nary pulsar (PSR 19 13 + (6). Its orbital period is 2.8 x 10" s, and it retained by the cluster's gravitational field. Over a few hundred million was found to be decreasing at a rate o f 10- 4 s yea r- t soon after the years, the cluster would evaporate and the galaxies move away as inde· system's di scovery. This was initially attributed to gravitational radiation. pendent entities. However. the existence of many clusters of gala.xies and the 1993 Nobel physics prize was awarded to Russell Hulse and suggests that they are stable ove r much longer periods of ti me. Zwicky Joseph Taylo r, for th ei r d iscovery of the pulsar and their interpretation therefore theorized th at there must be additional material, within the of its o rbital decay. However, it now appears that a helium star may be a cluster o r gaia.xies or both. whose presence meant th at th e gravit atio nal part of the system. and so tides or other interactions could aga in ex plain field of the cluster was sufficient for the cluster to be stable. Si nce this the observations. On the o ther hand, the effect of a rapid pulsar on the matter was not directly visibl e it became known as dark matter. Zwicky local int erstellar medium might mimic the appearance of a heliunl star found that the amount of dark matter needed to stabilize th e Coma cluster when viewed from a distance of 5000 pc. Thus, the detection of gravity was 400 times the amount of visible matter. However, subsequent meas- waves fr om the binary pulsa r, and indeed by all other methods remains urements by many astronomers ha ve brought this figure down to the not proven at th e time of writing. quantity of dark matter required generally being fi ve to six times that of th e visible matter. Exercise 1.15 Three-quarters o f a century have passed si nce Zwid..-y's observatio ns Show that the gravitational radiation of a planet o rbiting th e Sun is and although the existence of dark matter is confirmed by many other approxim ately given by circumstantial observations-such as the rotatio n curves of ga laxies-th e nature of dark matter is still a m ys tery: Suggestions for what it might be rIO Lc '" 7 x 102lM' t /l W made up from have included mini black holes. brown dwarfs. large planets (together known as MACHOs, massive astrophysical compact halo where objects), neutrinos, and WIMPs (weakl y interacting massive particles). /vi is the planet's mass in units of th e solar mass The current front runner is a variety of W IMP call ed a neutralino that is P the planet's orbital period in days predicted by the particle physicists' supersymmetry theory to be produced in large numbers at the energies prevalent during the earl y stages o f the Exerc ise 1.1 6 Big Bang. Despite the plentiful secondary evidence fo r the existence of Ca lcu late the gravitational radiation for each planet in the solar system dark matter, three* quarters of a century is a long time for no direct and show that every planet radiates more energy th an th e combined total evidence of its existence to have been found and some workers now radiated by th ose planets whose individual gravitational luminosities are question its existence at all-suggesting lhat some modificatio n to th e lower than its own. way in which the force of gra vity operates could explain the observatio nal discrepancies in stead. Much effort is therefore currently bei ng put int o experiments th at might detect the particles, whatever they ma y be, making 1.7 DARK MATTER AND DARK ENERGY DETECTION up dark matter. 1.7. ·1 Inlroduction The ex.istence o f dark energy, like that of dark matter, has yet to be Main stream cosmology currently suggests that the visibl e portion of the proven. There are two main ci rcumstantial lines of evidence for its universe (stars, nebulae, planets. ga laxies, etc.) makes up onl y about 4% of existence-the mean density of the uni verse and the brightness of Type th e total content of the universe. Dark matter makes up about another Ia supern ovae. The critical density of the universe is th e density that would 22% and dark energy the remaining 74%.

The ex.istence of dark matter was first suggested by Fritz Zwicky ( 1898- • A similar situation though existed for the neUl rino- it s existence was predicted by vVolfgang 1974) in 1933. Hi s observations of the velocities of the galaxies within the Pauli in 1930, but it wa s nol found experimelltally until \956.