附录 G 符号和缩略语

G.1 希腊字母符号

Symbol Definition Reference

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$\alpha$ fine - structure constant Equation7.141 magnetic inclination angle Section6.1.4 pitch angle Section5.2.3 right ascension Figure6.1 spectral index Equation4.55${\alpha }_0$ initial spectral index Equation5.127${\alpha }_H$ hydrogen recombination coefficient Equation4.7$\beta$ $\equiv v/c$ EquationC.11 ecliptic latitude Section6.3$\gamma$ $Lorentzfactor\equiv {(1-{\beta }^2)}^{-1/2}$ EquationC.10$\delta$ declination Section5.6.4 Doppler factor Equation5.179 phase difference (polarization) Equation2.51 phase error caused by reflector surface error Equation3.119 power law slope of electron energies Equation5.70${\delta }_0$ initial power law slope of electron energies Equation5.126$\mathrm{\Delta }x$ change in a quantity x $\mathrm{\Delta }\nu$ bandwidth line profile FWHM Figure7.4$ϵ$ reflector surface error Section3.3.4${ϵ}_0$ permittivity of free space EquationF.4$\eta$ antenna efficiency Section3.1.3 baryon / photon ratio Section2.6.3 ion / electron energy ratio Equation5.100${\eta }_A$ aperture efficiency Equation3.111${\eta }_B$ main beam efficiency Equation3.58${\eta }_H$ H i column density Equation7.154${\eta }_s$ reflector surface efficiency Equation3.129$\theta$ angle, polar angle ${\theta }_{HPBW}$ half power beam width Figure3.15${\theta }_m$ angle for maximum superluminal motion Equations5.170, 5.171$\kappa$ linear absorption coefficient Equation2.18$\lambda$ ecliptic longitude Equation6.50 wavelength Section1.1.1${}_{\lambda }$ $subscript\lambda \equiv perunitwavelength$ Equation2.4${\lambda }_c$ waveguide cutoff wavelength Equation3.141${\lambda }_D$ Debye length Equation4.46

Symbol Definition Reference

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$\mu$ mean electric dipole moment Equation7.129 plasma refractive index Equation6.39${\mu }_0$ permeability of free space EquationF.5${\mu }_B$ Bohr magneton Equation7.144$\mu Jy$ $microjansky\equiv {10}^{-6}Jy$ AppendixF.4$\mu m$ $micrometer=micron\equiv {10}^{-6}m$ AppendixF.4$\nu$ $frequencyinHz=cycles{s}^{-1}=\omega /(2\pi )$ AppendixF.3${}_{\nu }$ $subscript\nu \equiv perunitfrequency$ Equation2.4${\nu }_0$ line center frequency Figure7.4${\nu }_{10}$ H i line frequency Equation7.141${\nu }_c$ critical frequency Equation5.67 waveguide cutoff frequency Equation3.142${\nu }_e$ frequency in the source frame ${\nu }_g$ group velocity EquationD.18${\nu }_G$ electron gyro frequency Equation5.7${\nu }_o$ frequency in the observer's frame ${\nu }_p$ plasma frequency Equation6.40$\mathrm{\Pi }$ unit rectangle function Equation3.74$\rho$ mass density $\sigma$ cross section root mean square (rms) Stefan - Boltzmann constant Equation2.90 surface area element ${\sigma }_c$ rms confusion Section3.6.3${\sigma }_S$ rms fluctuation in peak flux density Section3.7.6${\sigma }_T$ rms image brightness fluctuation Section3.7.6 rms noise temperature fluctuation Equation3.154${\sigma }_T$ Thomson cross section Equation5.33$\tau$ duration, lifetime, smoothing time $opacity=opticaldepth$ Equation2.23 pulsar characteristic age Equation6.31${\tau }_g$ geometric delay (time) Equation3.172${\tau }_L$ line opacity at the line center frequency Equation7.96${\tau }_s$ synchrotron lifetime Equation5.111${\tau }_z$ atmospheric zenith opacity Section1.1.2$\varphi$ angle azimuth angle Section1.2 fringe phase Equation3.176 pulsar pulse phase Section6.3 visibility phase Equation3.185$\varphi (\nu )$ normalized line profile Figure7.4${\chi }_n$ ionization potential of n th energy level Equation7.92$\psi$ free - free interaction angle Figure4.2$\omega$ $angularfrequencyinrad{s}^{-1}=2\pi \nu$ Equation2.50${\omega }_{\odot }$ Sun's Galactic orbital angular velocity Section7.8.1${\omega }_B$ (angular) magnetic orbital frequency Equation5.21${\omega }_G$ $(angular)gyrofrequency(rad{s}^{-1})$ Equation5.4$\mathrm{\Omega }$ rotation angular velocity solid angle ohm AppendixF.3${\mathrm{\Omega }}_A$ beam solid angle Equations3.42, 3.34${\mathrm{\Omega }}_{MB}$ main beam solid angle Equation3.57

G.2 其他符号和缩写

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$\equiv$ is defined as $\propto$ is proportional to $\dot{f}$ time derivative of f $\ddot{f}$ second time derivative of f $⟨x⟩$ average value of x $|x|$ magnitude of x $\hat{x}$ unit vector in the x - direction $\overrightarrow{x}$ vector quantity x $\bar{x}$ complex conjugate of x $\iff$ is the Fourier transform of EquationA.1$\ast$ convolution operator EquationA.14$\star$ cross - correlation operator EquationA.16$\leftrightarrow$ numerical conversion between units AppendixF.3$a$ acceleration dimensionless scaling factor EquationA.11 dust grain diameter Section2.8 radiation constant Equation2.94 scale factor of the expanding universe Equation2.128$a(\nu )$ absorption coefficient of an opaque body Section2.2.4$a_0$ Bohr radius AppendixF.1$a_n$ Bohr radius of n th energy level Equation7.6$A$ geometric area of an aperture Section3.3 visibility amplitude Equation3.184$A_0$ antenna peak collecting area Equation3.43$A_{10}$ H i line emission coefficient Equation7.146$A_e$ effective collecting area Equation3.35$A_{n,n-1}$ $spontaneousemissionrate,levelntoleveln-1$ Section7.2.2$A_{UL}$ Einstein coefficient of spontaneous emission Figure7.5 Å $angstrom\equiv {10}^{-10}m$ AppendixF.4 AGN active galactic nucleus Figure5.22 ALMA Atacama Large Millimeter Array Figure8.5 ASKAP Australian SKA Pathfinder Figure8.6$au$ astronomical unit AppendixF.2$b$ baseline length Figure3.41 free - free scattering impact parameter Figure4.2 Galactic latitude Section1.3$\overrightarrow{b}$ baseline vector Figure3.41$B_{\lambda }$ blackbody spectral brightness per unit wavelength Equation2.88$B_{\nu }$ blackbody spectral brightness per unit frequency Equation2.86$B$ blackbody total brightness Equation2.89 magnetic field strength AppendixF.3$B_{LU}$ Einstein coefficient of absorption Figure7.5$B_{UL}$ Einstein coefficient of stimulated emission Figure7.5

Symbol Definition Reference

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$c$ vacuum speed of light AppendixF.1$c_{12}$ minimum magnetic energy function Equation5.109$c_{13}$ minimum total energy function Equation5.110$C_{LU}$ collisional excitation rate coefficient Equation7.71$C_{UL}$ collisional de-excitation rate coefficient Equation7.71 C band $4\le \nu (GHz)\le 8$ AppendixF.5 CARMA $CombinedArrayforResearchinMm\lambda Astronomy$$cm$ centimeter AppendixF.3 CMB (R) cosmic microwave background radiation Section2.6$d$ distance $\overrightarrow{p}$ electric dipole moment Equation7.120$d_H$ Hubble distance Equation2.123$D$ diameter directivity Section3.1.3$D$ $1debye\equiv {10}^{-18}statcoulombcm$ AppendixF.4$dB$ decibel AppendixF.4$DC$ Direct Current DFT discrete Fourier transform AppendixA.2$DM$ dispersion measure Equation6.46$e$ eccentricity Section6.1.9 electron charge (magnitude) AppendixF.1${Euler}^{\prime }snumber=2.71828\dots$$e(\nu )$ emission coefficient of an opaque body Section2.2.4$E$ electric field strength AppendixF.3 energy $\dot{E}$ spin - down luminosity Equation6.20$⟨E_{\gamma }⟩$ mean photon energy of blackbody radiation Equation2.101$EM$ emission measure Equation4.57 EOR Epoch of Reionization Section7.8.3$eV$ electron volt AppendixF.1$f$ electric field on an aperture Section3.2.3 focal length Figure3.7 pulsar pulse frequency Section6.3 f(v) nonrelativistic Maxwellian velocity distribution Equation4.34 f(x) (inverse) Fourier transform of F(s) EquationA.2$f/D$ focal ratio Section3.2.1$\overrightarrow{F}$ force F(s) (forward) Fourier transform of f(x) EquationA.1$F_{\nu }$ spectral power / area from an isotropic radiator Equation2.107$F_n$ noise factor Equation3.169 FFT fast Fourier transform AppendixA.2$FR$ Fanaroff - Riley Section5.6.1 FR I edge - dimmed source morphology Section5.6.1 FR II edge - brightened source morphology Section5.6.1 FWHM full width between half - maximum points

Symbol Definition Reference

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$g$ electric field strength on an aperture Section3.2.3 statistical weight of an energy state Section7.3.1 g gram AppendixF.3$⟨g_{ff}⟩$ free - free Gaunt factor Equation4.59$G$ gravitational constant AppendixF.1 antenna power gain Section3.1.3 receiver power gain Section3.6.3$G_0$ antenna peak power gain Section3.1.3 GBT Green Bank Telescope Figure8.1 GeV $GigaeV\equiv {10}^{9}eV$ AppendixF.1 GHz $Gigahertz\equiv {10}^{9}Hz$ AppendixF.4 GMRT Giant Metre wave Radio Telescope $h$ height Planck's constant AppendixF.1$\hslash$ $reduced{Planck}^{\prime }sconstant\equiv h/(2\pi )$$H$ atomic hydrogen $H_0$ Hubble constant AppendixF.2$H_2$ hydrogen diatomic molecule H i neutral atomic hydrogen H ii $ionizedhydrogen{H}^{+}$ HPBW Half Power Beam Width $Hz$ $hertz=frequencyincyclespersecond(s^{-1})$ AppendixF.3$i$ inclination angle $\sqrt{-1}$$I$ electric current Equation3.4 moment of inertia Section6.1.5 total intensity Equation2.6$I_{\lambda }$ specific intensity (per unit wavelength) Equation2.3$I_{\nu }$ specific intensity (per unit frequency) Equation2.2$I_p$ polarized flux density Equation2.57$IC$ inverse Compton Section5.5$IF$ intermediate frequency Section3.6.4 III shah function Equation5.61 IMF initial mass function Section4.2$IR$ infrared ISM interstellar medium $j_{\nu }$ (spectral) emission coefficient Equation2.26$J$ angular momentum quantum number Section7.7.1$J$ joule AppendixF.3$Jy$ $jansky\equiv {10}^{-26}W{m}^{-2}{Hz}^{-1}$ AppendixF.4

Symbol Definition Reference

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$k$ Boltzmann's constant AppendixF.1$\overrightarrow{k}$ wave vector Equation2.49$K$ kelvins AppendixF.3 K band $18\le \nu (GHz)\le 26.5$ AppendixF.5 Ka band $26.5\le \nu (GHz)\le 40$ AppendixF.5 Ku band $12\le \nu (GHz)\le 18$ AppendixF.5$kg$ kilogram AppendixF.3 kpc $kiloparsec\equiv {10}^{3}pc$ AppendixF.2$l$ Galactic longitude Figure7.18$(l,m,n)$ direction cosines in (u,v,w) coordinates Figure3.45$L$ angular momentum luminosity Equation2.16 L band $1\le \nu (GHz)\le 2$ AppendixF.5$L_{\nu }$ spectral luminosity Equation2.15$L_{\odot }$ solar luminosity AppendixF.2$L_E$ Eddington luminosity Equation5.117$LO$ local oscillator Section3.6.4 LOFAR LOw Frequency Array for Radio astronomy Figure8.8 LTE local thermodynamic equilibrium Section2.2.2$ly$ light year AppendixF.2$m$ meter AppendixF.3$m$ mass reduced mass Equation7.105$m_{\mathrm{\perp }}$ perpendicular magnetic moment Section6.1.4$m_e$ electron mass AppendixF.1$m_p$ proton mass AppendixF.1$M$ subreflector magnification factor Equation3.147$M_{\odot }$ solar mass AppendixF.2$M_{Ch}$ Chandrasekhar mass limit Equation6.6$M_H$ H i mass Equation7.166 MJy $megajansky\equiv {10}^{6}Jy$ mJy $millijansky\equiv {10}^{-3}Jy$$mm$ $millimeter\equiv {10}^{-3}m$ AppendixF.3 MHz $megahertz\equiv {10}^{6}Hz$ AppendixF.4 Mpc $megaparsec\equiv {10}^{6}pc$ AppendixF.2 MWA Murchison Widefield Array Figure8.7$n$ electronic quantum number Figure7.1 pulsar braking index Section6.1.8$n^{\ast }$ critical density Equation7.135$n_{\gamma }$ photon number density Equation2.95$n_b$ baryon number density Section2.6.3$n_e$ electron number density $n_H$ number density of neutral hydrogen atoms ${\dot{n}}_H$ hydrogen recombination rate Equation4.6$n_i$ ion number density

Symbol Definition Reference

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$n_L$ number density in lower energy state Equation7.42$n_n$ number density of atoms in n th energy level Equation7.92$n_p$ proton number density $n_U$ number density in upper energy state Equation7.42$N$ number $N_{\nu }$ number of modes per unit frequency Equation2.72$N_e$ electron column density Section1.1.4${\dot{N}}_{IC}$ photon scattering rate per electron Equation5.158$NF$ noise figure Equation3.171 NRAO National Radio Astronomy Observatory $p$ pressure degree of polarization Equation2.58$P$ power probability pulsar rotation period Section6.1.2 P band $0.25\le \nu (GHz)\le 0.50$ AppendixF.5$\dot{P}$ pulsar period derivative Equation6.17$P_{\nu }$ power per unit frequency P(x) probability distribution of x $P_{IC}$ inverse Compton power Section5.5$P_n$ normalized antenna power pattern $P_{syn}$ synchrotron power Section5.2$pc$ parsec AppendixF.2 PDBI Plateau de Bure Interferometer pwv precipitable water vapor Section1.1.2$q$ electric charge AppendixF.3$Q_H$ $productionrateofLy\alpha photons$ Equation4.10 Q band $33\le \nu (GHz)\le 50$ AppendixF.5 QSO quasi - stellar object $r$ radial coordinate or distance $r(\nu )$ reflection coefficient of an opaque body Section2.2.4$r_e$ equilibrium interatomic distance Figure7.12$R$ resistance Equation3.21 correlator response Equation3.175$R_0$ radiation resistance of space Equation3.29$R_{\mathrm{\infty }}$ Rydberg constant Equation7.10$R_{\mathrm{\infty }}c$ Rydberg frequency Equation7.11$R_{\odot }$ distance from the Sun to the Galactic center Figure7.18 solar radius AppendixF.2$R_{ff}$ far - field distance Equation3.64$R_M$ Rydberg constant for nuclear mass M Equation7.12$R_S$ $Str\ddot{o}mgrensphereradius$ Figure4.1 rad radian AppendixF.4$RF$ radio frequency RFI radio frequency interference rms root mean square

Symbol Definition Reference

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$s$ second of time AppendixF.3$s$ coordinate from source to detector Figure2.7$\hat{s}$ unit vector in source direction Figure3.41${\hat{s}}_0$ phase reference direction Figure3.45$S$ flux or flux density Equation2.14 S band $2\le \nu (GHz)\le 4$ AppendixF.5$S_{\nu }$ flux density Equation2.9$\overrightarrow{S}$ Poynting flux Equation2.138 sinc (x) $sincfunction\equiv \sin (\pi x)/(\pi x)$ Equation3.77 SKA Square Kilometer Array SMA SubMillimeter Array SMBH supermassive black hole $sr$ steradian $t$ time $t$ dispersion delay Equation6.43$t_{\star }$ age of universe at recombination Section2.6.2$T$ temperature total time $T_A$ antenna temperature Section3.1.6$T_0$ CMB temperature at redshift zero Section2.6$noisefactorreferencetemperature=290K$ Equation3.169$T_{atm}$ kinetic temperature of the atmosphere $T_b$ brightness temperature Equation2.33$T_C$ continuum brightness temperature Section7.6.1$T_{cmb}$ cosmic microwave background temperature $T_{cmb}\approx 2.73K$$T_e$ electron temperature $T_L$ line brightness temperature at the line center Section7.6.1$T_{min}$ minimum kinetic temperature Equation7.119$T_N$ noise temperature Equation3.149$T_r$ radiometer noise temperature Section3.6.1$T_s$ H i spin temperature Equation7.148 system noise temperature Equation3.150$T_x$ excitation temperature Equation7.70$TE$ thermodynamic equilibrium Section2.2.2 THz $terahertz\equiv {10}^{12}Hz$ AppendixF.4 TOA pulsar pulse Time Of Arrival Section6.3$u$ atomic mass unit AppendixF.1$dimensionlesscoordinate,e.g.,u\equiv x/\lambda$ Equation3.72 total radiation energy density Equation2.92$\bar{u}$ line profile weighted radiation energy density Equation7.39$u_{\nu }$ spectral energy density of radiation Equation2.76$(u,v,w)$ dimensionless coordinates for interferometers Figure3.45 U band $40<\nu (GHz)<60$ AppendixF.5$U_B$ magnetic energy density Equation5.35$U_e$ electron energy density Equation5.93$U_{rad}$ radiation energy density Section5.5$UV$ ultraviolet

Symbol Definition Reference

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$v$ $dimensionlesscoordinate,e.g.,v\equiv y/\lambda$ Figure3.45 velocity $v_g$ group velocity Equation6.41 waveguide group velocity Equation3.143$v_r$ radial velocity $v_{rot}$ rotational velocity Equation7.167$V$ voltage Equation3.20 volume $V_o$ square law detector output voltage Section3.6.2$\mathcal{V}$ complex visibility Equation3.182 V band $50\le \nu (GHz)\le 75$ AppendixF.5 VLA Very Large Array Figure8.4 VLBA Very Long Baseline Array Figure1.5 VLBI Very Long Baseline Interferometry $w$ $dimensionlesscoordinate,e.g.,w\equiv z/\lambda$ Figure3.45 W band $75\le \nu (GHz)\le 110$ AppendixF.5$W$ free - free pulse radiated energy Equation4.24 WMAP Wilkinson Microwave Anisotropy Probe WSRT Westerbork Synthesis Radio Telescope Figure8.3$x$ Cartesian coordinate $(x^{\prime },y^{\prime },z^{\prime },t^{\prime })$ coordinates in moving frame FigureC.1$x_j$ $(inverse)discreteFouriertransformof{X}_k$ EquationA.5$X_{CO}$ $COto{H}_{2}conversionfactor$ Equation7.140$X_k$ $(forward)discreteFouriertransformof{x}_j$ EquationA.4 X band $8\le \nu (GHz)\le 12$ AppendixF.5$y$ Cartesian coordinate $yr$ year AppendixF.2$Y$ Y factor Equation3.167$z$ Cartesian coordinate redshift Equation2.127 zenith angle Figure2.10$Z$ number of electrons removed from an ion