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I (I) 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.
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