附录 G 符号和缩略语

G.1 希腊字母符号

Symbol Definition Reference

$\alpha$ 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 $\gamma$ ${{Lorentz}{factor}} \equiv {({1 - \beta^{2}})}^{- {1/2}}$ 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 $\Delta x$ change in a quantity x $\Delta\nu$ bandwidth line profile FWHM Figure7.4 $\epsilon$ reflector surface error Section3.3.4 $\epsilon_{0}$ 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 $_{\lambda}$ ${{subscript}\lambda} \equiv {{per}{unit}{wavelength}}$ Equation2.4 $\lambda_{c}$ waveguide cutoff wavelength Equation3.141 $\lambda_{D}$ Debye length Equation4.46

Symbol Definition Reference

$\mu$ 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 $\nu$ ${{frequency}{in}{Hz}} = {{cycles}s^{- 1}} = {\omega/{({2\pi})}}$ AppendixF.3 $_{\nu}$ ${{subscript}\nu} \equiv {{per}{unit}{frequency}}$ 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 $\Pi$ 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 $${opacity} = {{optical}{depth}}$$ 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 $\phi$ angle azimuth angle Section1.2 fringe phase Equation3.176 pulsar pulse phase Section6.3 visibility phase Equation3.185 $\phi{(\nu)}$ normalized line profile Figure7.4 $\chi_{n}$ ionization potential of n th energy level Equation7.92 $\psi$ free - free interaction angle Figure4.2 $\omega$ ${{angular}{frequency}{in}{rad}s^{- 1}} = {2\pi\nu}$ Equation2.50 $\omega_{\odot}$ Sun's Galactic orbital angular velocity Section7.8.1 $\omega_{B}$ (angular) magnetic orbital frequency Equation5.21 $\omega_{G}$ ${({angular})}{gyro}{frequency}{({{rad}s^{- 1}})}$ Equation5.4 $\Omega$ rotation angular velocity solid angle ohm AppendixF.3 $\Omega_{A}$ beam solid angle Equations3.42, 3.34 $\Omega_{MB}$ main beam solid angle Equation3.57

G.2 其他符号和缩写

Symbol Definition Reference

$\equiv$ is defined as $\propto$ is proportional to $\overset{˙}{f}$ time derivative of f $\overset{¨}{f}$ second time derivative of f $\langle x\rangle$ average value of x $$|x|$$ magnitude of x $\hat{x}$ unit vector in the x - direction $\overset{\rightarrow}{x}$ vector quantity x $\overline{x}$ complex conjugate of x $\Leftrightarrow$ 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 $A_{n,{n - 1}}$ $${{spontaneous}{emission}{rate}},{{{level}n{to}{level}n} - 1}$$ 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 $\overset{\rightarrow}{b}$ 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

$$c$$ 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 $4 \leq {\nu{({GHz})}} \leq 8$ AppendixF.5 CARMA ${Combined}{Array}{for}{Research}{in}{Mm}\lambda{Astronomy}$ $$cm$$ centimeter AppendixF.3 CMB (R) cosmic microwave background radiation Section2.6 $$d$$ distance $\overset{\rightarrow}{p}$ electric dipole moment Equation7.120 $d_{H}$ Hubble distance Equation2.123 $$D$$ diameter directivity Section3.1.3 $$D$$ ${1{debye}} \equiv {10^{- 18}{statcoulomb}{cm}}$ 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 ${{Euler}'s{number}} = {2.71828\ldots}$ $e{(\nu)}$ emission coefficient of an opaque body Section2.2.4 $$E$$ electric field strength AppendixF.3 energy $\overset{˙}{E}$ spin - down luminosity Equation6.20 $\langle E_{\gamma}\rangle$ 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 $\overset{\rightarrow}{F}$ 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

$$g$$ electric field strength on an aperture Section3.2.3 statistical weight of an energy state Section7.3.1 g gram AppendixF.3 $\langle g_{ff}\rangle$ 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 ${{Giga}{eV}} \equiv {10^{9}{eV}}$ AppendixF.1 GHz ${Gigahertz} \equiv {10^{9}{Hz}}$ AppendixF.4 GMRT Giant Metre wave Radio Telescope $$h$$ height Planck's constant AppendixF.1 $\hslash$ ${{reduced}{Planck}'s{constant}} \equiv {h/{({2\pi})}}$ $$H$$ atomic hydrogen $H_{0}$ Hubble constant AppendixF.2 $H_{2}$ hydrogen diatomic molecule H i neutral atomic hydrogen H ii ${ionized}{hydrogen}H^{+}$ HPBW Half Power Beam Width $$Hz$$ ${hertz} = {{frequency}{in}{cycles}{per}{second}{(s^{- 1})}}$ 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 $$Jy$$ ${jansky} \equiv {10^{- 26}Wm^{- 2}{Hz}^{- 1}}$ AppendixF.4

Symbol Definition Reference

$$k$$ Boltzmann's constant AppendixF.1 $\overset{\rightarrow}{k}$ wave vector Equation2.49 $$K$$ kelvins AppendixF.3 K band $18 \leq {\nu{({GHz})}} \leq 26.5$ AppendixF.5 Ka band $26.5 \leq {\nu{({GHz})}} \leq 40$ AppendixF.5 Ku band $12 \leq {\nu{({GHz})}} \leq 18$ 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 $1 \leq {\nu{({GHz})}} \leq 2$ 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 $m_{\bot}$ 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 $n^{*}$ 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 ${\overset{˙}{n}}_{H}$ hydrogen recombination rate Equation4.6 $n_{i}$ ion number density

Symbol Definition Reference

$n_{L}$ 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 ${\overset{˙}{N}}_{IC}$ 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 $0.25 \leq {\nu{({GHz})}} \leq 0.50$ AppendixF.5 $\overset{˙}{P}$ 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 $Q_{H}$ ${production}{rate}{of}{Ly}\alpha{photons}$ Equation4.10 Q band $33 \leq {\nu{({GHz})}} \leq 50$ 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 $R_{\infty}$ Rydberg constant Equation7.10 $R_{\infty}c$ 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 $R_{S}$ ${Str}\overset{¨}{o}{mgren}{sphere}{radius}$ Figure4.1 rad radian AppendixF.4 $$RF$$ radio frequency RFI radio frequency interference rms root mean square

Symbol Definition Reference

$$s$$ 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 $2 \leq {\nu{({GHz})}} \leq 4$ AppendixF.5 $S_{\nu}$ flux density Equation2.9 $\overset{\rightarrow}{S}$ Poynting flux Equation2.138 sinc (x) ${{sinc}{function}} \equiv {{\sin{({\pi x})}}/{({\pi x})}}$ 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 $${{noise}{factor}{reference}{temperature}} = {290K}$$ 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 ${dimensionless}{coordinate},e.g.,u \equiv x/\lambda$ Equation3.72 total radiation energy density Equation2.92 $\overline{u}$ 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

$$v$$ ${dimensionless}{coordinate},e.g.,v \equiv y/\lambda$ 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 $50 \leq {\nu{({GHz})}} \leq 75$ AppendixF.5 VLA Very Large Array Figure8.4 VLBA Very Long Baseline Array Figure1.5 VLBI Very Long Baseline Interferometry $$w$$ ${dimensionless}{coordinate},e.g.,w \equiv z/\lambda$ Figure3.45 W band $75 \leq {\nu{({GHz})}} \leq 110$ 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 $$(x',y',z',t')$$ coordinates in moving frame FigureC.1 $x_{j}$ ${({inverse})}{discrete}{Fourier}{transform}{of}X_{k}$ EquationA.5 $X_{CO}$ ${CO}{to}H_{2}{conversion}{factor}$ Equation7.140 $X_{k}$ ${({forward})}{discrete}{Fourier}{transform}{of}x_{j}$ EquationA.4 X band $8 \leq {\nu{({GHz})}} \leq 12$ 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

附录 G 符号和缩略语 ​

G.1 希腊字母符号 ​

G.2 其他符号和缩写 ​

附录 G 符号和缩略语

G.1 希腊字母符号

G.2 其他符号和缩写