Astronomy Letters, Vol. 27, No. 4, 2001, pp. 207–212. Translated from Pis’ma v Astronomicheskiœ Zhurnal, Vol. 27, No. 4, 2001, pp. 243–249. Original Russian Text Copyright © 2001 by Dubrovich. Formation Mechanisms of “Negative”-Intensity Spots in the Cosmic Microwave Background Radiation and Distant Objects V. K. Dubrovich* Special Astrophysical Observatory, Russian Academy of Sciences, pos. Nizhniœ Arkhyz, Stavropol kraœ, 357147 Russia Received June 2, 2000; in final form, October 2, 2000 Abstract—We consider the formation mechanisms of “negative”-intensity spots in the radio band for various astrophysical conditions. For wavelengths λ < 1.5 mm, the regions of reduced temperature (relative to the cos- mic microwave background radiation, CMBR) are shown to be produced only by high-redshift objects moving at peculiar velocities. The main processes are CMBR Thomson scattering and bremsstrahlung. We show that the effect δT/T can be ~ 10–5 in magnitude. We derive simple analytic expressions, which allow the redshifts, electron densities, and linear sizes of these regions to be estimated from observed spectral and spatial parame- ters. Additional observational methods for refining these parameters are outlined. © 2001 MAIK “Nauka/Inter- periodica”. Key words: theoretical and observational cosmology INTRODUCTION only two formation mechanisms of the “glow.” One of In the last 30 years, much attention has been given them is the Doppler distortion of external, equilibrium, to the search for and a detailed analysis of spatial fluc- and isotropic radiation (CMBR). For this to occur, the tuations in cosmic microwave background radiation object must have a peculiar velocity Vp and some non- zero opacity. (CMBR) temperature Tr . This is attributable to the fun- damental information about the structure and parame- In cool, weakly ionized matter, free electrons and ters of the Universe that can be obtained from these primordial molecules can be the source of opacity studies. Theoretically, one of the most important prob- (Sunyaev and Zel’dovich 1980; Dubrovich 1977, lems is to analyze statistical parameters of the fluctua- 1997). Molecules scatter CMBR only in narrow spec- tions: the correlation function and power spectrum of tral bands. In the standard evolutionary model of matter spatial scales. after hydrogen recombination, the residual degree of ≈ ionization ne/nH at z 100 in the absence of additional New experimental possibilities enable a complete –4 mapping of the sky to the level of the presumed primor- energy sources does not exceed 10 , where ne and nH dial fluctuations. From the viewpoint of the theory of are the number densities of free electrons and hydrogen atoms, respectively. This implies that the continuum the initial fluctuation spectrum, this information is not τ fundamentally new, and it can be used only as an addi- optical depth T due to Thomson scattering by free elec- tional guarantee that we actually observe CMBR trons is very small. anisotropy. Another opacity mechanism in the presence of free electrons and protons is free–free absorption and emis- The subject of our study is precisely this map. We τ will show that observational data obtained from its sion. However, for this channel, the optical depth ff is analysis can be used to search for protoobjects and also small. Below, we numerically estimate the above allow their redshifts to be estimated. They yield the depths. Note only that the mechanism of free–free coordinates of areas that can be used for more detailed absorption and emission will give additional emission studies. if the temperature of matter Tm is higher than the CMBR temperature and will result in the absorption of Since we are interested in high-redshift objects, the energy from CMBR for T < T . main problem is to determine the sources of their lumi- m r nosity and to estimate their power. At the prestellar evo- lutionary stage of protoobjects, there are essentially “NEGATIVE INTENSITIES” Let us now explain what we mean by “negative intensity” (NI). Usually, when the possibility of observ- * E-mail address for contacts: [email protected] ing an object is considered, the energy that this object 1063-7737/01/2704-0207 $21.00 © 2001 MAIK “Nauka/Interperiodica” 208 DUBROVICH can emit is estimated. Clearly, in this case, we have in Tm lower than the radiation temperature. As matter mind energy release. In the presence of external radia- cools down in the Universe, there comes a stage when tion, the object can also manifest itself by the absorp- the matter temperature ceases to be approximately tion of this radiation. Thus, for example, foreground equal to the radiation temperature. This is variously gas clouds on the line of sight to a point source produce estimated to occur after z = 150. This stage lasts until absorptions in resonance atomic and molecular lines. the so-called secondary heating attributable to the out- At the same time, their intrinsic emission can be very bursts of primordial stars. However, the number density weak, so they can ultimately be considered as “nega- of free electrons at this epoch is very low, and, conse- tive-intensity” objects. In this case, we observe the NI quently, the possible CMBR distortions are small. effect in narrow spectral bands. In broad bands, the NI effect is well known from the absorption of starlight by We are interested in individual objects rather than in the dust component in galaxies. the homogeneous component of the medium. The time of a protoobject’s passage to a nonlinear evolutionary It is difficult to obtain the NI effect for uniform and stage should be considered for them. For different isotropic background radiation. The point is that, in objects, this occurs at different times (Puy and Signore view of the optical theorem, simple scattering does not 1996; Dubrovich 1999). In this case, both the degree of change the CMBR isotropy and intensity. The absorp- ionization and the temperature of matter can differ tion and emission of photons by matter when their tem- markedly from the mean values. Below, we will assume peratures are equal also changes nothing in view of the that T > T . principle of detailed balancing. Therefore, as was m r already mentioned above, we can detect an object if the The specific mechanism that gives rise to NI is the system isotropy is broken in some way or if the matter well-known Sunyaev–Zel’dovich effect (SZ) (Zel’do- and radiation temperatures are not equal. vich and Sunyaev 1969; Sunyaev and Zel’dovich 1972). Anisotropy arises, for example, from the presence Its peculiarity is that a reduction in radiation tempera- of peculiar velocities of primordial objects. The ampli- ture results from a frequency redistribution of CMBR tude of the CMBR temperature distortion through the photons through Compton scattering by very hot elec- Doppler effect is given by trons. This is consistent with the general laws, because the total radiation energy increases, while the decrease V in intensity is only the effect of frequency redistribution δT /T = -----pτ . (1) D r c T of CMBR photons and manifests itself only in the Ray- leigh–Jeans part of the spectrum. In the Wien wing, the For the Planck spectrum, the flux deviation δF can intensity increases (for more details, see below). be written as Let us now consider what the intensity of protoob- δ δ ( –x)–1 T jects’ radiation can be under various conditions. The F/Fr = x 1 – e ------, (2) expression for τ is T r T where τ σ × –6 T = ne T L = 2.0 10 ne Lpc, (5) ν ( ) x = h /kTr, T r = 2.73 1 + z K, (3) where Lpc is the linear size of the protoobject in parsecs, and n is in cm–3. For free–free emission, we can write 3( x )–1( )3 e Fr = F0 x e – 1 1 + z . (4) 2 –1/2 –αx ( )( 24 ) × –15 –2 –1 –1 –1 Fff = 1.07F0ne T m e g x L/10 cm , (6) F0 = 2.71 10 erg cm s sr Hz , h is the Planck constant, ν is the frequency, and k is the Boltz- mann constant. The fact that the effect is linear in where δ velocity implies that the observed TD/Tr can be posi- ( ) ≈ [ ( 3 )3/2( )–1 –1 ] tive and negative. It is important to note that this asser- g x ln 28 T m/10 K 1 + z x + 3 , (7) tion is valid for any frequency. Here, the point is not that the Thomson scattering cross section does not α ( ) –1 depend on frequency; the sign of the temperature devi- = 2.73 1 + z T m . (8) ation is determined only by the sign of the object’s radial velocity. This is a fundamental property of the All physical quantities are taken in a comoving Doppler effect. Thus, the NI effect can be produced in frame of reference, i.e., at the corresponding z. The CMBR only by simple scattering without the true total observed flux δF from the protoobject is the sum absorption of energy. of these two quantities, Doppler and bremsstrahlung δ As was noted above, the NI formation mechanism F = Fff + FD: can be the true absorption of CMBR photons. As fol- –2 V lows from general laws of thermodynamics, this F = 1.6F x4e–x(1 – e–x) (1 + z)3-----pn (L/1024 cm),(9) requires that the absorbing matter have a temperature D 0 c e ASTRONOMY LETTERS Vol. 27 No. 4 2001 FORMATION MECHANISMS OF “NEGATIVE”-INTENSITY SPOTS 209 α –2 δF = δF [e– xg(x)/γ – x4e–x(1 – e–x) ] 10 0 (10) γ = 0.5 δ ( ) 8 γ = 1 = F0 f x , γ = 10 6 δ ( )3V p( 24 ) F0 = 1.6F0ne 1 + z ----- L/10 cm , (11) c 4 ) x ( V p 1/2 –1 3 f 2 γ = 1.4-----T n (1 + z) .