Essential Radio Astronomy F Constants, Units, and Dimensions H References and Links

Appendix G Symbols and Abbreviations

G.1 Greek Symbols

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$\alpha$	fine-structure constant	$\mathrm{Equation~{}}$ 7.141
	$\mathrm{magnetic~{}inclination~{}angle}$	$\mathrm{Section~{}}$ 6.1.4
	$\mathrm{pitch~{}angle}$	$\mathrm{Section~{}}$ 5.2.3
	$\mathrm{right~{}ascension}$	$\mathrm{Figure~{}}$ 6.1
	$\mathrm{spectral~{}index}$	$\mathrm{Equation~{}}$ 4.55
$\alpha_{0}$	$\mathrm{initial~{}spectral~{}index}$	$\mathrm{Equation~{}}$ 5.127
$\alpha_{\mathrm{H}}$	$\mathrm{hydrogen~{}recombination~{}coefficient}$	$\mathrm{Equation~{}}$ 4.7
$\beta$	$\equiv v/c$	$\mathrm{Equation~{}}$ C.11
	$\mathrm{ecliptic~{}latitude}$	$\mathrm{Section~{}}$ 6.3
$\gamma$	$\mathrm{Lorentz~{}factor}\equiv(1-\beta^{2})^{-1/2}$	$\mathrm{Equation~{}}$ C.10
$\delta$	$\mathrm{declination}$	$\mathrm{Section~{}}$ 5.6.4
	$\mathrm{Doppler~{}factor}$	$\mathrm{Equation~{}}$ 5.179
	$\mathrm{phase~{}difference~{}(polarization)}$	$\mathrm{Equation~{}}$ 2.51
	$\mathrm{phase~{}error~{}caused~{}by~{}reflector~{}surface~{}error}$	$\mathrm{Equation~{}}$ 3.119
	$\mathrm{power~{}law~{}slope~{}of~{}electron~{}energies}$	$\mathrm{Equation~{}}$ 5.70
$\delta_{0}$	$\mathrm{initial~{}power~{}law~{}slope~{}of~{}electron~{}energies}$	$\mathrm{Equation~{}}$ 5.126
$\Delta x$	$\mathrm{change~{}in~{}a~{}quantity~{}}x$
$\Delta\nu$	$\mathrm{bandwidth}$
	$\mathrm{line~{}profile~{}FWHM}$	$\mathrm{Figure~{}}$ 7.4
$\epsilon$	$\mathrm{reflector~{}surface~{}error}$	$\mathrm{Section~{}}$ 3.3.4
$\epsilon_{0}$	$\mathrm{permittivity~{}of~{}free~{}space}$	$\mathrm{Equation~{}}$ F.4
$\eta$	$\mathrm{antenna~{}efficiency}$	$\mathrm{Section~{}}$ 3.1.3
	$\mathrm{baryon/photon~{}ratio}$	$\mathrm{Section~{}}$ 2.6.3
	$\mathrm{ion/electron~{}energy~{}ratio}$	$\mathrm{Equation~{}}$ 5.100
$\eta_{\mathrm{A}}$	$\mathrm{aperture~{}efficiency}$	$\mathrm{Equation~{}}$ 3.111
$\eta_{\mathrm{B}}$	$\mathrm{main~{}beam~{}efficiency}$	$\mathrm{Equation~{}}$ 3.58
$\eta_{\mathrm{H}}$	$\mathrm{H\textsc{i}~{}column~{}density}$	$\mathrm{Equation~{}}$ 7.154
$\eta_{\mathrm{s}}$	$\mathrm{reflector~{}surface~{}efficiency}$	$\mathrm{Equation~{}}$ 3.129
$\theta$	$\mathrm{angle,~{}polar~{}angle}$
$\theta_{\mathrm{HPBW}}$	$\mathrm{half~{}power~{}beam~{}width}$	$\mathrm{Figure~{}}$ 3.15
$\theta_{\mathrm{m}}$	$\mathrm{angle~{}for~{}maximum~{}superluminal~{}motion}$	$\mathrm{Equations~{}}$ 5.170, 5.171
$\kappa$	$\mathrm{linear~{}absorption~{}coefficient}$	$\mathrm{Equation~{}}\ref{eqn:kappanu}$
$\lambda$	$\mathrm{ecliptic~{}longitude}$	$\mathrm{Equation~{}}$ 6.50
	$\mathrm{wavelength}$	$\mathrm{Section~{}}$ 1.1.1
${}_{\lambda}$	$\mathrm{subscript~{}}\lambda\equiv\mathrm{~{}per~{}unit~{}wavelength}$	$\mathrm{Equation~{}}$ 2.4
$\lambda_{\mathrm{c}}$	$\mathrm{waveguide~{}cutoff~{}wavelength}$	$\mathrm{Equation~{}}$ 3.141
$\lambda_{\mathrm{D}}$	$\mathrm{Debye~{}length~{}}$	$\mathrm{Equation~{}}$ 4.46

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$\mu$	$\mathrm{mean~{}electric~{}dipole~{}moment}$	$\mathrm{Equation~{}}$ 7.129
	$\mathrm{plasma~{}refractive~{}index}$	$\mathrm{Equation~{}}$ 6.39
$\mu_{0}$	$\mathrm{permeability~{}of~{}free~{}space}$	$\mathrm{Equation~{}}$ F.5
$\mu_{\mathrm{B}}$	$\mathrm{Bohr~{}magneton}$	$\mathrm{Equation~{}}$ 7.144
$\mu\mathrm{Jy}$	$\mathrm{microjansky~{}}\equiv 10^{-6}\mathrm{~{}Jy}$	$\mathrm{Appendix~{}}$ F.4
$\mu\mathrm{m}$	$\mathrm{micrometer~{}=~{}micron~{}}\equiv 10^{-6}\mathrm{~{}m}$	$\mathrm{Appendix~{}}$ F.4
$\nu$	$\mathrm{frequency~{}in~{}Hz~{}=~{}cycles~{}s}^{-1}=\omega/(2\pi)$	$\mathrm{Appendix~{}}$ F.3
${}_{\nu}$	$\mathrm{subscript~{}}\nu\equiv\mathrm{~{}per~{}unit~{}frequency}$	$\mathrm{Equation~{}}$ 2.4
$\nu_{0}$	$\mathrm{line~{}center~{}frequency}$	$\mathrm{Figure~{}}$ 7.4
$\nu_{10}$	$\mathrm{H\textsc{i}~{}line~{}frequency}$	$\mathrm{Equation~{}}$ 7.141
$\nu_{\mathrm{c}}$	$\mathrm{critical~{}frequency}$	$\mathrm{Equation~{}}$ 5.67
	$\mathrm{waveguide~{}cutoff~{}frequency}$	$\mathrm{Equation~{}}$ 3.142
$\nu_{\mathrm{e}}$	$\mathrm{frequency~{}in~{}the~{}source~{}frame}$
$\nu_{\mathrm{g}}$	$\mathrm{group~{}velocity}$	$\mathrm{Equation~{}}$ D.18
$\nu_{\mathrm{G}}$	$\mathrm{electron~{}gyro~{}frequency}$	$\mathrm{Equation~{}}$ 5.7
$\nu_{\mathrm{o}}$	frequency in the observer’s frame
$\nu_{\mathrm{p}}$	$\mathrm{plasma~{}frequency}$	$\mathrm{Equation~{}}$ 6.40
$\Pi$	$\mathrm{unit~{}rectangle~{}function}$	$\mathrm{Equation~{}}$ 3.74
$\rho$	$\mathrm{mass~{}density}$
$\sigma$	$\mathrm{cross~{}section}$
	$\mathrm{root~{}mean~{}square~{}(rms)}$
	Stefan–Boltzmann constant	$\mathrm{Equation~{}}$ 2.90
	$\mathrm{surface~{}area~{}element}$
$\sigma_{\mathrm{c}}$	$\mathrm{rms~{}confusion}$	$\mathrm{Section~{}}$ 3.6.3
$\sigma_{S}$	$\mathrm{rms~{}fluctuation~{}in~{}peak~{}flux~{}density}$	$\mathrm{Section~{}}$ 3.7.6
$\sigma_{T}$	$\mathrm{rms~{}image~{}brightness~{}fluctuation}$	$\mathrm{Section~{}}$ 3.7.6
	$\mathrm{rms~{}noise~{}temperature~{}fluctuation}$	$\mathrm{Equation~{}}$ 3.154
$\sigma_{\mathrm{T}}$	$\mathrm{Thomson~{}cross~{}section}$	$\mathrm{Equation~{}}$ 5.33
$\tau$	$\mathrm{duration,~{}lifetime,~{}smoothing~{}time}$
	$\mathrm{opacity~{}=~{}optical~{}depth}$	$\mathrm{Equation~{}}$ 2.23
	$\mathrm{pulsar~{}characteristic~{}age}$	$\mathrm{Equation~{}}$ 6.31
$\tau_{\mathrm{g}}$	$\mathrm{geometric~{}delay~{}(time)}$	$\mathrm{Equation~{}}$ 3.172
$\tau_{\mathrm{L}}$	$\mathrm{line~{}opacity~{}at~{}the~{}line~{}center~{}frequency}$	$\mathrm{Equation~{}}$ 7.96
$\tau_{\mathrm{s}}$	$\mathrm{synchrotron~{}lifetime}$	$\mathrm{Equation~{}}$ 5.111
$\tau_{\mathrm{z}}$	$\mathrm{atmospheric~{}zenith~{}opacity}$	$\mathrm{Section~{}}$ 1.1.2
$\phi$	$\mathrm{angle}$
	$\mathrm{azimuth~{}angle}$	$\mathrm{Section~{}}$ 1.2
	$\mathrm{fringe~{}phase}$	$\mathrm{Equation~{}}$ 3.176
	$\mathrm{pulsar~{}pulse~{}phase}$	$\mathrm{Section~{}}$ 6.3
	$\mathrm{visibility~{}phase}$	$\mathrm{Equation~{}}$ 3.185
$\phi(\nu)$	$\mathrm{normalized~{}line~{}profile}$	$\mathrm{Figure~{}}$ 7.4
$\chi_{n}$	$\mathrm{ionization~{}potential~{}of~{}}n\mathrm{th~{}energy~{}level}$	$\mathrm{Equation~{}}$ 7.92
$\psi$	free–free interaction angle	$\mathrm{Figure~{}}$ 4.2
$\omega$	$\mathrm{angular~{}frequency~{}in~{}rad~{}s}^{-1}=2\pi\nu$	$\mathrm{Equation~{}}$ 2.50
$\omega_{\odot}$	Sun’s Galactic orbital angular velocity	$\mathrm{Section~{}}$ 7.8.1
$\omega_{B}$	$\mathrm{(angular)~{}magnetic~{}orbital~{}frequency}$	$\mathrm{Equation~{}}$ 5.21
$\omega_{\mathrm{G}}$	$\mathrm{(angular)~{}gyro~{}frequency~{}(rad~{}s}^{-1}\mathrm{)}$	$\mathrm{Equation~{}}$ 5.4
$\Omega$	$\mathrm{rotation~{}angular~{}velocity}$
	$\mathrm{solid~{}angle}$
	$\mathrm{ohm}$	$\mathrm{Appendix~{}}$ F.3
$\Omega_{\mathrm{A}}$	$\mathrm{beam~{}solid~{}angle}$	$\mathrm{Equations~{}}$ 3.42, 3.34
$\Omega_{\mathrm{MB}}$	$\mathrm{main~{}beam~{}solid~{}angle}$	$\mathrm{Equation~{}}$ 3.57

G.2 Other Symbols and Abbreviations

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$\equiv$	$\mathrm{is~{}defined~{}as}$
$\propto$	$\mathrm{is~{}proportional~{}to}$
$\dot{f}$	$\mathrm{time~{}derivative~{}of~{}}f$
$\ddot{f}$	$\mathrm{second~{}time~{}derivative~{}of~{}}f$
$\langle x\rangle$	$\mathrm{average~{}value~{}of~{}}x$
$\|x\|$	$\mathrm{magnitude~{}of~{}}x$
$\hat{x}$	$\mathrm{unit~{}vector~{}in~{}the~{}}x\mathrm{-direction}$
$\vec{x}$	$\mathrm{vector~{}quantity~{}}x$
$\overline{x}$	$\mathrm{complex~{}conjugate~{}of~{}}x$
$\Leftrightarrow$	$\mathrm{is~{}the~{}Fourier~{}transform~{}of}$	$\mathrm{Equation~{}}$ A.1
$\ast$	$\mathrm{convolution~{}operator}$	$\mathrm{Equation~{}}$ A.14
$\star$	cross-correlation operator	$\mathrm{Equation~{}}$ A.16
$\leftrightarrow$	$\mathrm{numerical~{}conversion~{}between~{}units}$	$\mathrm{Appendix~{}}$ F.3
$a$	$\mathrm{acceleration}$
	$\mathrm{dimensionless~{}scaling~{}factor}$	$\mathrm{Equation~{}}$ A.11
	$\mathrm{dust~{}grain~{}diameter}$	$\mathrm{Section~{}}$ 2.8
	$\mathrm{radiation~{}constant}$	$\mathrm{Equation~{}}$ 2.94
	$\mathrm{scale~{}factor~{}of~{}the~{}expanding~{}universe}$	$\mathrm{Equation~{}}$ 2.128
$a(\nu)$	$\mathrm{absorption~{}coefficient~{}of~{}an~{}opaque~{}body}$	$\mathrm{Section~{}}$ 2.2.4
$a_{0}$	$\mathrm{Bohr~{}radius}$	$\mathrm{Appendix~{}}$ F.1
$a_{n}$	$\mathrm{Bohr~{}radius~{}of~{}}n\mathrm{th~{}energy~{}level}$	$\mathrm{Equation~{}}$ 7.6
$A$	$\mathrm{geometric~{}area~{}of~{}an~{}aperture}$	$\mathrm{Section~{}}$ 3.3
	$\mathrm{visibility~{}amplitude}$	$\mathrm{Equation~{}}$ 3.184
$A_{0}$	$\mathrm{antenna~{}peak~{}collecting~{}area}$	$\mathrm{Equation~{}}$ 3.43
$A_{10}$	$\mathrm{H\textsc{i}~{}line~{}emission~{}coefficient}$	$\mathrm{Equation~{}}$ 7.146
$A_{\mathrm{e}}$	$\mathrm{effective~{}collecting~{}area}$	$\mathrm{Equation~{}}$ 3.35
$A_{n,n-1}$	$\mathrm{spontaneous~{}emission~{}rate,~{}level~{}}n\mathrm{~{}to~{}level~{}}n-1$	$\mathrm{Section~{}}$ 7.2.2
$A_{\mathrm{UL}}$	$\mathrm{Einstein~{}coefficient~{}of~{}spontaneous~{}emission}$	$\mathrm{Figure~{}}$ 7.5
Å	$\mathrm{angstrom~{}}\equiv 10^{-10}\mathrm{~{}m}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{AGN}$	$\mathrm{active~{}galactic~{}nucleus}$	$\mathrm{Figure~{}}$ 5.22
$\mathrm{ALMA}$	$\mathrm{Atacama~{}Large~{}Millimeter~{}Array}$	$\mathrm{Figure~{}}$ 8.5
$\mathrm{ASKAP}$	$\mathrm{Australian~{}SKA~{}Pathfinder}$	$\mathrm{Figure~{}}$ 8.6
$\mathrm{au}$	$\mathrm{astronomical~{}unit}$	$\mathrm{Appendix~{}}$ F.2
$b$	$\mathrm{baseline~{}length}$	$\mathrm{Figure~{}}$ 3.41
	free–free scattering impact parameter	$\mathrm{Figure~{}}$ 4.2
	$\mathrm{Galactic~{}latitude}$	$\mathrm{Section~{}}$ 1.3
$\vec{b}$	$\mathrm{baseline~{}vector}$	$\mathrm{Figure~{}}$ 3.41
$B_{\lambda}$	$\mathrm{blackbody~{}spectral~{}brightness~{}per~{}unit~{}wavelength}$	$\mathrm{Equation~{}}$ 2.88
$B_{\nu}$	$\mathrm{blackbody~{}spectral~{}brightness~{}per~{}unit~{}frequency}$	$\mathrm{Equation~{}}$ 2.86
$B$	$\mathrm{blackbody~{}total~{}brightness}$	$\mathrm{Equation~{}}$ 2.89
	$\mathrm{magnetic~{}field~{}strength}$	$\mathrm{Appendix~{}}$ F.3
$B_{\mathrm{LU}}$	$\mathrm{Einstein~{}coefficient~{}of~{}absorption}$	$\mathrm{Figure~{}}$ 7.5
$B_{\mathrm{UL}}$	$\mathrm{Einstein~{}coefficient~{}of~{}stimulated~{}emission}$	$\mathrm{Figure~{}}$ 7.5

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$c$	$\mathrm{vacuum~{}speed~{}of~{}light}$	$\mathrm{Appendix~{}}$ F.1
$c_{12}$	$\mathrm{minimum~{}magnetic~{}energy~{}function}$	$\mathrm{Equation~{}}$ 5.109
$c_{13}$	$\mathrm{minimum~{}total~{}energy~{}function}$	$\mathrm{Equation~{}}$ 5.110
$C_{\mathrm{LU}}$	$\mathrm{collisional~{}excitation~{}rate~{}coefficient}$	$\mathrm{Equation~{}}$ 7.71
$C_{\mathrm{UL}}$	$\mathrm{collisional~{}de}$ - $\mathrm{excitation~{}rate~{}coefficient}$	$\mathrm{Equation~{}}$ 7.71
$\mathrm{C~{}band}$	$4\leq\nu\mathrm{(GHz)}\leq 8$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{CARMA}$	$\mathrm{Combined~{}Array~{}for~{}Research~{}in~{}Mm~{}}\lambda\mathrm{~{}Astronomy}$
$\mathrm{cm}$	$\mathrm{centimeter}$	$\mathrm{Appendix~{}}$ F.3
$\mathrm{CMB(R)}$	$\mathrm{cosmic~{}microwave~{}background~{}radiation}$	$\mathrm{Section~{}}$ 2.6
$d$	$\mathrm{distance}$
$\vec{p}$	$\mathrm{electric~{}dipole~{}moment}$	$\mathrm{Equation~{}}$ 7.120
$d_{\mathrm{H}}$	$\mathrm{Hubble~{}distance}$	$\mathrm{Equation~{}}$ 2.123
$D$	$\mathrm{diameter}$
	$\mathrm{directivity}$	$\mathrm{Section~{}}$ 3.1.3
$\mathrm{D}$	$1\mathrm{~{}debye}\equiv 10^{-18}\mathrm{~{}statcoulomb~{}cm}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{dB}$	$\mathrm{decibel}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{DC}$	$\mathrm{Direct~{}Current}$
$\mathrm{DFT}$	$\mathrm{discrete~{}Fourier~{}transform}$	$\mathrm{Appendix~{}}$ A.2
$\mathrm{DM}$	$\mathrm{dispersion~{}measure}$	$\mathrm{Equation~{}}$ 6.46
$e$	$\mathrm{eccentricity}$	$\mathrm{Section~{}}$ 6.1.9
	$\mathrm{electron~{}charge~{}(magnitude)}$	$\mathrm{Appendix~{}}$ F.1
	$\textrm{Euler's~{}number}=2.71828\ldots$
$e(\nu)$	$\mathrm{emission~{}coefficient~{}of~{}an~{}opaque~{}body}$	$\mathrm{Section~{}}$ 2.2.4
$E$	$\mathrm{electric~{}field~{}strength}$	$\mathrm{Appendix~{}}$ F.3
	$\mathrm{energy}$
$\dot{E}$	spin-down luminosity	$\mathrm{Equation~{}}$ 6.20
$\langle E_{\gamma}\rangle$	$\mathrm{mean~{}photon~{}energy~{}of~{}blackbody~{}radiation}$	$\mathrm{Equation~{}}$ 2.101
$\mathrm{EM}$	$\mathrm{emission~{}measure}$	$\mathrm{Equation~{}}$ 4.57
$\mathrm{EOR}$	$\mathrm{Epoch~{}of~{}Reionization}$	$\mathrm{Section~{}}$ 7.8.3
$\mathrm{eV}$	$\mathrm{electron~{}volt}$	$\mathrm{Appendix~{}}$ F.1
$f$	$\mathrm{electric~{}field~{}on~{}an~{}aperture}$	$\mathrm{Section~{}}$ 3.2.3
	$\mathrm{focal~{}length}$	$\mathrm{Figure~{}}$ 3.7
	$\mathrm{pulsar~{}pulse~{}frequency}$	$\mathrm{Section~{}}$ 6.3
$f(v)$	$\mathrm{nonrelativistic~{}Maxwellian~{}velocity~{}distribution}$	$\mathrm{Equation~{}}$ 4.34
$f(x)$	$\mathrm{(inverse)~{}Fourier~{}transform~{}of~{}}F(s)$	$\mathrm{Equation~{}}$ A.2
$f/D$	$\mathrm{focal~{}ratio}$	$\mathrm{Section~{}}$ 3.2.1
$\vec{F}$	$\mathrm{force}$
$F(s)$	$\mathrm{(forward)~{}Fourier~{}transform~{}of~{}}f(x)$	$\mathrm{Equation~{}}$ A.1
$F_{\nu}$	$\mathrm{spectral~{}power/area~{}from~{}an~{}isotropic~{}radiator}$	$\mathrm{Equation~{}}$ 2.107
$F_{\mathrm{n}}$	$\mathrm{noise~{}factor}$	$\mathrm{Equation~{}}$ 3.169
$\mathrm{FFT}$	$\mathrm{fast~{}Fourier~{}transform}$	$\mathrm{Appendix~{}}$ A.2
$\mathrm{FR}$	Fanaroff–Riley	$\mathrm{Section~{}}$ 5.6.1
$\mathrm{FR~{}I}$	edge-dimmed source morphology	$\mathrm{Section~{}}$ 5.6.1
$\mathrm{FR~{}II}$	edge-brightened source morphology	$\mathrm{Section~{}}$ 5.6.1
$\mathrm{FWHM}$	full width between half-maximum points

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$g$	$\mathrm{electric~{}field~{}strength~{}on~{}an~{}aperture}$	$\mathrm{Section~{}}$ 3.2.3
	$\mathrm{statistical~{}weight~{}of~{}an~{}energy~{}state}$	$\mathrm{Section~{}}$ 7.3.1
g	$\mathrm{gram}$	$\mathrm{Appendix~{}}$ F.3
$\langle g_{\mathrm{ff}}\rangle$	free–free Gaunt factor	$\mathrm{Equation~{}}$ 4.59
$G$	$\mathrm{gravitational~{}constant}$	$\mathrm{Appendix~{}}$ F.1
	$\mathrm{antenna~{}power~{}gain}$	$\mathrm{Section~{}}$ 3.1.3
	$\mathrm{receiver~{}power~{}gain}$	$\mathrm{Section~{}}$ 3.6.3
$G_{0}$	$\mathrm{antenna~{}peak~{}power~{}gain}$	$\mathrm{Section~{}}$ 3.1.3
$\mathrm{GBT}$	$\mathrm{Green~{}Bank~{}Telescope}$	$\mathrm{Figure~{}}$ 8.1
$\mathrm{GeV}$	$\mathrm{Giga~{}eV~{}}\equiv 10^{9}\mathrm{~{}eV}$	$\mathrm{Appendix~{}}$ F.1
$\mathrm{GHz}$	$\mathrm{Gigahertz~{}}\equiv 10^{9}\mathrm{~{}Hz}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{GMRT}$	$\mathrm{Giant~{}Metre~{}wave~{}Radio~{}Telescope}$
$h$	$\mathrm{height}$
	Planck’s constant	$\mathrm{Appendix~{}}$ F.1
$\hbar$	$\textrm{reduced~{}Planck's~{}constant~{}}\equiv h/(2\pi)$
$\mathrm{H}$	$\mathrm{atomic~{}hydrogen}$
$H_{0}$	$\mathrm{Hubble~{}constant}$	$\mathrm{Appendix~{}}$ F.2
$\mathrm{H}_{2}$	$\mathrm{hydrogen~{}diatomic~{}molecule}$
$\mathrm{H\textsc{i}}$	$\mathrm{neutral~{}atomic~{}hydrogen}$
$\mathrm{H\textsc{ii}}$	$\mathrm{ionized~{}hydrogen~{}H}^{+}$
$\mathrm{HPBW}$	$\mathrm{Half~{}Power~{}Beam~{}Width}$
$\mathrm{Hz}$	$\mathrm{hertz~{}=~{}frequency~{}in~{}cycles~{}per~{}second~{}(s}^{-1}\mathrm{)}$	$\mathrm{Appendix~{}}$ F.3
$i$	$\mathrm{inclination~{}angle}$
	$\sqrt{-1}$
$I$	$\mathrm{electric~{}current}$	$\mathrm{Equation~{}}$ 3.4
	$\mathrm{moment~{}of~{}inertia}$	$\mathrm{Section~{}}$ 6.1.5
	$\mathrm{total~{}intensity}$	$\mathrm{Equation~{}}$ 2.6
$I_{\lambda}$	$\mathrm{specific~{}intensity(per~{}unit~{}wavelength)}$	$\mathrm{Equation~{}}$ 2.3
$I_{\nu}$	$\mathrm{specific~{}intensity~{}(per~{}unit~{}frequency)}$	$\mathrm{Equation~{}}$ 2.2
$I_{\mathrm{p}}$	$\mathrm{polarized~{}flux~{}density}$	$\mathrm{Equation~{}}$ 2.57
$\mathrm{IC}$	$\mathrm{inverse~{}Compton}$	$\mathrm{Section~{}}$ 5.5
$\mathrm{IF}$	$\mathrm{intermediate~{}frequency}$	$\mathrm{Section~{}}$ 3.6.4
$\mathrm{III}$	$\mathrm{shah~{}function}$	$\mathrm{Equation~{}}$ 5.61
$\mathrm{IMF}$	$\mathrm{initial~{}mass~{}function}$	$\mathrm{Section~{}}$ 4.2
$\mathrm{IR}$	$\mathrm{infrared}$
$\mathrm{ISM}$	$\mathrm{interstellar~{}medium}$
$j_{\nu}$	$\mathrm{(spectral)~{}emission~{}coefficient}$	$\mathrm{Equation~{}}$ 2.26
$J$	$\mathrm{angular~{}momentum~{}quantum~{}number}$	$\mathrm{Section~{}}$ 7.7.1
$\mathrm{J}$	$\mathrm{joule}$	$\mathrm{Appendix~{}}$ F.3
$\mathrm{Jy}$	$\mathrm{jansky~{}}\equiv 10^{-26}\mathrm{~{}W~{}m}^{-2}\mathrm{~{}Hz}^{-1}$	$\mathrm{Appendix~{}}$ F.4

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$k$	Boltzmann’s constant	$\mathrm{Appendix~{}}$ F.1
$\vec{k}$	$\mathrm{wave~{}vector}$	$\mathrm{Equation~{}}$ 2.49
$\mathrm{K}$	$\mathrm{kelvins}$	$\mathrm{Appendix~{}}$ F.3
$\mathrm{K~{}band}$	$18\leq\nu\mathrm{(GHz)}\leq 26.5$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{Ka~{}band}$	$26.5\leq\nu\mathrm{(GHz)}\leq 40$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{Ku~{}band}$	$12\leq\nu\mathrm{(GHz)}\leq 18$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{kg}$	$\mathrm{kilogram}$	$\mathrm{Appendix~{}}$ F.3
$\mathrm{kpc}$	$\mathrm{kiloparsec~{}}\equiv 10^{3}\mathrm{~{}pc}$	$\mathrm{Appendix~{}}$ F.2
$l$	$\mathrm{Galactic~{}longitude}$	$\mathrm{Figure~{}}$ 7.18
$(l,m,n)$	$\mathrm{direction~{}cosines~{}in~{}}(u,v,w)\mathrm{~{}coordinates}$	$\mathrm{Figure~{}}$ 3.45
$L$	$\mathrm{angular~{}momentum}$
	$\mathrm{luminosity}$	$\mathrm{Equation~{}}$ 2.16
$\mathrm{L~{}band}$	$1\leq\nu\mathrm{(GHz)}\leq 2$	$\mathrm{Appendix~{}}$ F.5
$L_{\nu}$	$\mathrm{spectral~{}luminosity}$	$\mathrm{Equation~{}}$ 2.15
$L_{\odot}$	$\mathrm{solar~{}luminosity}$	$\mathrm{Appendix~{}}$ F.2
$L_{\mathrm{E}}$	$\mathrm{Eddington~{}luminosity}$	$\mathrm{Equation~{}}$ 5.117
$\mathrm{LO}$	$\mathrm{local~{}oscillator}$	$\mathrm{Section~{}}$ 3.6.4
$\mathrm{LOFAR}$	$\mathrm{LOw~{}Frequency~{}Array~{}for~{}Radio~{}astronomy}$	$\mathrm{Figure~{}}$ 8.8
$\mathrm{LTE}$	$\mathrm{local~{}thermodynamic~{}equilibrium}$	$\mathrm{Section~{}}$ 2.2.2
$\mathrm{ly}$	$\mathrm{light~{}year}$	$\mathrm{Appendix~{}}$ F.2
$\mathrm{m}$	$\mathrm{meter}$	$\mathrm{Appendix~{}}$ F.3
$m$	$\mathrm{mass}$
	$\mathrm{reduced~{}mass}$	$\mathrm{Equation~{}}$ 7.105
$m_{\bot}$	$\mathrm{perpendicular~{}magnetic~{}moment}$	$\mathrm{Section~{}}$ 6.1.4
$m_{\mathrm{e}}$	$\mathrm{electron~{}mass}$	$\mathrm{Appendix~{}}$ F.1
$m_{\mathrm{p}}$	$\mathrm{proton~{}mass}$	$\mathrm{Appendix~{}}$ F.1
$M$	$\mathrm{subreflector~{}magnification~{}factor}$	$\mathrm{Equation~{}}$ 3.147
$M_{\odot}$	$\mathrm{solar~{}mass}$	$\mathrm{Appendix~{}}$ F.2
$M_{\mathrm{Ch}}$	$\mathrm{Chandrasekhar~{}mass~{}limit}$	$\mathrm{Equation~{}}$ 6.6
$M_{\mathrm{H}}$	$\mathrm{H\textsc{i}~{}mass}$	$\mathrm{Equation~{}}$ 7.166
$\mathrm{MJy}$	$\mathrm{megajansky~{}}\equiv 10^{6}\mathrm{~{}Jy}$
$\mathrm{mJy}$	$\mathrm{millijansky~{}}\equiv 10^{-3}\mathrm{~{}Jy}$
$\mathrm{mm}$	$\mathrm{millimeter~{}}\equiv 10^{-3}\mathrm{~{}m}$	$\mathrm{Appendix~{}}$ F.3
$\mathrm{MHz}$	$\mathrm{megahertz~{}}\equiv 10^{6}\mathrm{~{}Hz}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{Mpc}$	$\mathrm{megaparsec~{}}\equiv 10^{6}\mathrm{~{}pc}$	$\mathrm{Appendix~{}}$ F.2
$\mathrm{MWA}$	$\mathrm{Murchison~{}Widefield~{}Array}$	$\mathrm{Figure~{}}$ 8.7
$n$	$\mathrm{electronic~{}quantum~{}number}$	$\mathrm{Figure~{}}$ 7.1
	$\mathrm{pulsar~{}braking~{}index}$	$\mathrm{Section~{}}$ 6.1.8
$n^{*}$	$\mathrm{critical~{}density}$	$\mathrm{Equation~{}}$ 7.135
$n_{\gamma}$	$\mathrm{photon~{}number~{}density}$	$\mathrm{Equation~{}}$ 2.95
$n_{\mathrm{b}}$	$\mathrm{baryon~{}number~{}density}$	$\mathrm{Section~{}}$ 2.6.3
$n_{\mathrm{e}}$	$\mathrm{electron~{}number~{}density}$
$n_{\mathrm{H}}$	$\mathrm{number~{}density~{}of~{}neutral~{}hydrogen~{}atoms}$
$\dot{n}_{\mathrm{H}}$	$\mathrm{hydrogen~{}recombination~{}rate}$	$\mathrm{Equation~{}}$ 4.6
$n_{\mathrm{i}}$	$\mathrm{ion~{}number~{}density}$

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$n_{\mathrm{L}}$	$\mathrm{number~{}density~{}in~{}lower~{}energy~{}state}$	$\mathrm{Equation~{}}$ 7.42
$n_{n}$	$\mathrm{number~{}density~{}of~{}atoms~{}in~{}}n\mathrm{th~{}energy~{}level}$	$\mathrm{Equation~{}}$ 7.92
$n_{\mathrm{p}}$	$\mathrm{proton~{}number~{}density}$
$n_{\mathrm{U}}$	$\mathrm{number~{}density~{}in~{}upper~{}energy~{}state}$	$\mathrm{Equation~{}}$ 7.42
$N$	$\mathrm{number}$
$N_{\nu}$	$\mathrm{number~{}of~{}modes~{}per~{}unit~{}frequency}$	$\mathrm{Equation~{}}$ 2.72
$N_{\mathrm{e}}$	$\mathrm{electron~{}column~{}density}$	$\mathrm{Section~{}}$ 1.1.4
$\dot{N}_{\mathrm{IC}}$	$\mathrm{photon~{}scattering~{}rate~{}per~{}electron}$	$\mathrm{Equation~{}}$ 5.158
$\mathrm{NF}$	$\mathrm{noise~{}figure}$	$\mathrm{Equation~{}}$ 3.171
$\mathrm{NRAO}$	$\mathrm{National~{}Radio~{}Astronomy~{}Observatory}$
$p$	$\mathrm{pressure}$
	$\mathrm{degree~{}of~{}polarization}$	$\mathrm{Equation~{}}$ 2.58
$P$	$\mathrm{power}$
	$\mathrm{probability}$
	$\mathrm{pulsar~{}rotation~{}period}$	$\mathrm{Section~{}}$ 6.1.2
$\mathrm{P~{}band}$	$0.25\leq\nu\mathrm{(GHz)}\leq 0.50$	$\mathrm{Appendix~{}}$ F.5
$\dot{P}$	$\mathrm{pulsar~{}period~{}derivative}$	$\mathrm{Equation~{}}$ 6.17
$P_{\nu}$	$\mathrm{power~{}per~{}unit~{}frequency}$
$P(x)$	$\mathrm{probability~{}distribution~{}of~{}}x$
$P_{\mathrm{IC}}$	$\mathrm{inverse~{}Compton~{}power}$	$\mathrm{Section~{}}$ 5.5
$P_{\mathrm{n}}$	$\mathrm{normalized~{}antenna~{}power~{}pattern}$
$P_{\mathrm{syn}}$	$\mathrm{synchrotron~{}power}$	$\mathrm{Section~{}}$ 5.2
$\mathrm{pc}$	$\mathrm{parsec}$	$\mathrm{Appendix~{}}$ F.2
$\mathrm{PDBI}$	$\mathrm{Plateau~{}de~{}Bure~{}Interferometer}$
$\mathrm{pwv}$	$\mathrm{precipitable~{}water~{}vapor}$	$\mathrm{Section~{}}$ 1.1.2
$q$	$\mathrm{electric~{}charge}$	$\mathrm{Appendix~{}}$ F.3
$Q_{\mathrm{H}}$	$\mathrm{production~{}rate~{}of~{}Ly}\alpha\mathrm{~{}photons}$	$\mathrm{Equation~{}}$ 4.10
$\mathrm{Q~{}band}$	$33\leq\nu\mathrm{(GHz)}\leq 50$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{QSO}$	quasi-stellar object
$r$	$\mathrm{radial~{}coordinate~{}or~{}distance}$
$r(\nu)$	$\mathrm{reflection~{}coefficient~{}of~{}an~{}opaque~{}body}$	$\mathrm{Section~{}}$ 2.2.4
$r_{\mathrm{e}}$	$\mathrm{equilibrium~{}interatomic~{}distance}$	$\mathrm{Figure~{}}$ 7.12
$R$	$\mathrm{resistance}$	$\mathrm{Equation~{}}$ 3.21
	$\mathrm{correlator~{}response}$	$\mathrm{Equation~{}}$ 3.175
$R_{0}$	$\mathrm{radiation~{}resistance~{}of~{}space}$	$\mathrm{Equation~{}}$ 3.29
$R_{\infty}$	$\mathrm{Rydberg~{}constant}$	$\mathrm{Equation~{}}$ 7.10
$R_{\infty}c$	$\mathrm{Rydberg~{}frequency}$	$\mathrm{Equation~{}}$ 7.11
$R_{\odot}$	$\mathrm{distance~{}from~{}the~{}Sun~{}to~{}the~{}Galactic~{}center}$	$\mathrm{Figure~{}}$ 7.18
	$\mathrm{solar~{}radius}$	$\mathrm{Appendix~{}}$ F.2
$R_{\mathrm{ff}}$	far-field distance	$\mathrm{Equation~{}}$ 3.64
$R_{M}$	$\mathrm{Rydberg~{}constant~{}for~{}nuclear~{}mass~{}}M$	$\mathrm{Equation~{}}$ 7.12
$R_{\mathrm{S}}$	Strömgren sphere radius	$\mathrm{Figure~{}}$ 4.1
$\mathrm{rad}$	$\mathrm{radian}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{RF}$	$\mathrm{radio~{}frequency}$
$\mathrm{RFI}$	$\mathrm{radio~{}frequency~{}interference}$
$\mathrm{rms}$	$\mathrm{root~{}mean~{}square}$

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$\mathrm{s}$	$\mathrm{second~{}of~{}time}$	$\mathrm{Appendix~{}}$ F.3
$s$	$\mathrm{coordinate~{}from~{}source~{}to~{}detector}$	$\mathrm{Figure~{}}$ 2.7
$\hat{s}$	$\mathrm{unit~{}vector~{}in~{}source~{}direction}$	$\mathrm{Figure~{}}$ 3.41
$\hat{s}_{0}$	$\mathrm{phase~{}reference~{}direction}$	$\mathrm{Figure~{}}$ 3.45
$S$	$\mathrm{flux~{}or~{}flux~{}density}$	$\mathrm{Equation~{}}$ 2.14
$\mathrm{S~{}band}$	$2\leq\nu\mathrm{(GHz)}\leq 4$	$\mathrm{Appendix~{}}$ F.5
$S_{\nu}$	$\mathrm{flux~{}density}$	$\mathrm{Equation~{}}$ 2.9
$\vec{S}$	$\mathrm{Poynting~{}flux}$	$\mathrm{Equation~{}}$ 2.138
$\mathrm{sinc}(x)$	$\mathrm{sinc~{}function~{}}\equiv\sin(\pi x)/(\pi x)$	$\mathrm{Equation~{}}$ 3.77
$\mathrm{SKA}$	$\mathrm{Square~{}Kilometer~{}Array}$
$\mathrm{SMA}$	$\mathrm{SubMillimeter~{}Array}$
$\mathrm{SMBH}$	$\mathrm{supermassive~{}black~{}hole}$
$\mathrm{sr}$	$\mathrm{steradian}$
$t$	$\mathrm{time}$
$t$	$\mathrm{dispersion~{}delay}$	$\mathrm{Equation~{}}$ 6.43
$t_{\star}$	$\mathrm{age~{}of~{}universe~{}at~{}recombination}$	$\mathrm{Section~{}}$ 2.6.2
$T$	$\mathrm{temperature}$
	$\mathrm{total~{}time}$
$T_{\mathrm{A}}$	$\mathrm{antenna~{}temperature}$	$\mathrm{Section~{}}$ 3.1.6
$T_{0}$	$\mathrm{CMB~{}temperature~{}at~{}redshift~{}zero}$	$\mathrm{Section~{}}$ 2.6
	$\mathrm{noise~{}factor~{}reference~{}temperature}=290\mathrm{~{}K}$	$\mathrm{Equation~{}}$ 3.169
$T_{\mathrm{atm}}$	$\mathrm{kinetic~{}temperature~{}of~{}the~{}atmosphere}$
$T_{\mathrm{b}}$	$\mathrm{brightness~{}temperature}$	$\mathrm{Equation~{}}$ 2.33
$T_{\mathrm{C}}$	$\mathrm{continuum~{}brightness~{}temperature}$	$\mathrm{Section~{}}$ 7.6.1
$T_{\mathrm{cmb}}$	$\mathrm{cosmic~{}microwave~{}background~{}temperature}$	$T_{\mathrm{cmb}}\approx 2.73\mathrm{~{}K}$
$T_{\mathrm{e}}$	$\mathrm{electron~{}temperature}$
$T_{\mathrm{L}}$	$\mathrm{line~{}brightness~{}temperature~{}at~{}the~{}line~{}center}$	$\mathrm{Section~{}}$ 7.6.1
$T_{\mathrm{min}}$	$\mathrm{minimum~{}kinetic~{}temperature}$	$\mathrm{Equation~{}}$ 7.119
$T_{\mathrm{N}}$	$\mathrm{noise~{}temperature}$	$\mathrm{Equation~{}}$ 3.149
$T_{\mathrm{r}}$	$\mathrm{radiometer~{}noise~{}temperature}$	$\mathrm{Section~{}}$ 3.6.1
$T_{\mathrm{s}}$	$\mathrm{H\textsc{i}~{}spin~{}temperature}$	$\mathrm{Equation~{}}$ 7.148
	$\mathrm{system~{}noise~{}temperature}$	$\mathrm{Equation~{}}$ 3.150
$T_{\mathrm{x}}$	$\mathrm{excitation~{}temperature}$	$\mathrm{Equation~{}}$ 7.70
$\mathrm{TE}$	$\mathrm{thermodynamic~{}equilibrium}$	$\mathrm{Section~{}}$ 2.2.2
$\mathrm{THz}$	$\mathrm{terahertz~{}}\equiv 10^{12}\mathrm{~{}Hz}$	$\mathrm{Appendix~{}}$ F.4
$\mathrm{TOA}$	$\mathrm{pulsar~{}pulse~{}Time~{}Of~{}Arrival}$	$\mathrm{Section~{}}$ 6.3
$u$	$\mathrm{atomic~{}mass~{}unit}$	$\mathrm{Appendix~{}}$ F.1
	$\mathrm{dimensionless~{}coordinate,~{}e.g.,~{}}u\equiv x/\lambda$	$\mathrm{Equation~{}}$ 3.72
	$\mathrm{total~{}radiation~{}energy~{}density}$	$\mathrm{Equation~{}}$ 2.92
$\bar{u}$	$\mathrm{line~{}profile~{}weighted~{}radiation~{}energy~{}density}$	$\mathrm{Equation~{}}$ 7.39
$u_{\nu}$	$\mathrm{spectral~{}energy~{}density~{}of~{}radiation}$	$\mathrm{Equation~{}}$ 2.76
$(u,v,w)$	$\mathrm{dimensionless~{}coordinates~{}for~{}interferometers}$	$\mathrm{Figure~{}}$ 3.45
$\mathrm{U~{}band}$	$40<\nu\mathrm{(GHz)}<60$	$\mathrm{Appendix~{}}$ F.5
$U_{B}$	$\mathrm{magnetic~{}energy~{}density}$	$\mathrm{Equation~{}}$ 5.35
$U_{\mathrm{e}}$	$\mathrm{electron~{}energy~{}density}$	$\mathrm{Equation~{}}$ 5.93
$U_{\mathrm{rad}}$	$\mathrm{radiation~{}energy~{}density}$	$\mathrm{Section~{}}$ 5.5
$\mathrm{UV}$	$\mathrm{ultraviolet}$

$\mathrm{Symbol}$	$\mathrm{Definition}$	$\mathrm{Reference}$
$v$	$\mathrm{dimensionless~{}coordinate,~{}e.g.,~{}}v\equiv y/\lambda$	$\mathrm{Figure~{}}$ 3.45
	$\mathrm{velocity}$
$v_{\mathrm{g}}$	$\mathrm{group~{}velocity}$	$\mathrm{Equation~{}}$ 6.41
	$\mathrm{waveguide~{}group~{}velocity}$	$\mathrm{Equation~{}}$ 3.143
$v_{r}$	$\mathrm{radial~{}velocity}$
$v_{\mathrm{rot}}$	$\mathrm{rotational~{}velocity}$	$\mathrm{Equation~{}}$ 7.167
$V$	$\mathrm{voltage}$	$\mathrm{Equation~{}}$ 3.20
	$\mathrm{volume}$
$V_{\mathrm{o}}$	$\mathrm{square~{}law~{}detector~{}output~{}voltage}$	$\mathrm{Section~{}}$ 3.6.2
$\mathcal{V}$	$\mathrm{complex~{}visibility}$	$\mathrm{Equation~{}}$ 3.182
$\mathrm{V~{}band}$	$50\leq\nu\mathrm{(GHz)}\leq 75$	$\mathrm{Appendix~{}}$ F.5
$\mathrm{VLA}$	$\mathrm{Very~{}Large~{}Array}$	$\mathrm{Figure~{}}$ 8.4
$\mathrm{VLBA}$	$\mathrm{Very~{}Long~{}Baseline~{}Array}$	$\mathrm{Figure~{}}$ 1.5
$\mathrm{VLBI}$	$\mathrm{Very~{}Long~{}Baseline~{}Interferometry}$
$w$	$\mathrm{dimensionless~{}coordinate,~{}e.g.,~{}}w\equiv z/\lambda$	$\mathrm{Figure~{}}$ 3.45
$\mathrm{W~{}band}$	$75\leq\nu\mathrm{(GHz)}\leq 110$	$\mathrm{Appendix~{}}$ F.5
$W$	free–free pulse radiated energy	$\mathrm{Equation~{}}$ 4.24
$\mathrm{WMAP}$	$\mathrm{Wilkinson~{}Microwave~{}Anisotropy~{}Probe}$
$\mathrm{WSRT}$	$\mathrm{Westerbork~{}Synthesis~{}Radio~{}Telescope}$	$\mathrm{Figure~{}}$ 8.3
$x$	$\mathrm{Cartesian~{}coordinate}$
$(x^{\prime},y^{\prime},z^{\prime},t^{\prime})$	$\mathrm{coordinates~{}in~{}moving~{}frame}$	$\mathrm{Figure~{}}$ C.1
$x_{j}$	$\mathrm{(inverse)~{}discrete~{}Fourier~{}transform~{}of~{}}X_{k}$	$\mathrm{Equation~{}}$ A.5
$X_{\mathrm{CO}}$	$\mathrm{CO~{}to~{}H}_{2}\mathrm{~{}conversion~{}factor}$	$\mathrm{Equation~{}}$ 7.140
$X_{k}$	$\mathrm{(forward)~{}discrete~{}Fourier~{}transform~{}of~{}}x_{j}$	$\mathrm{Equation~{}}$ A.4
$\mathrm{X~{}band}$	$8\leq\nu\mathrm{(GHz)}\leq 12$	$\mathrm{Appendix~{}}$ F.5
$y$	$\mathrm{Cartesian~{}coordinate}$
$\mathrm{yr}$	$\mathrm{year}$	$\mathrm{Appendix~{}}$ F.2
$Y$	$Y\mathrm{~{}factor}$	$\mathrm{Equation~{}}$ 3.167
$z$	$\mathrm{Cartesian~{}coordinate}$
	$\mathrm{redshift}$	$\mathrm{Equation~{}}$ 2.127
	$\mathrm{zenith~{}angle}$	$\mathrm{Figure~{}}$ 2.10
$Z$	$\mathrm{number~{}of~{}electrons~{}removed~{}from~{}an~{}ion}$