Essential Radio Astronomy

Appendix G Symbols and Abbreviations

G.1 Greek Symbols

Symbol Definition Reference
α fine-structure constant Equation7.141
magneticinclinationangle Section6.1.4
pitchangle Section5.2.3
rightascension Figure6.1
spectralindex Equation4.55
α0 initialspectralindex Equation5.127
αH hydrogenrecombinationcoefficient Equation4.7
β v/c EquationC.11
eclipticlatitude Section6.3
γ Lorentzfactor(1-β2)-1/2 EquationC.10
δ declination Section5.6.4
Dopplerfactor Equation5.179
phasedifference(polarization) Equation2.51
phaseerrorcausedbyreflectorsurfaceerror Equation3.119
powerlawslopeofelectronenergies Equation5.70
δ0 initialpowerlawslopeofelectronenergies Equation5.126
Δx changeinaquantityx
Δν bandwidth
lineprofileFWHM Figure7.4
ϵ reflectorsurfaceerror Section3.3.4
ϵ0 permittivityoffreespace EquationF.4
η antennaefficiency Section3.1.3
baryon/photonratio Section2.6.3
ion/electronenergyratio Equation5.100
ηA apertureefficiency Equation3.111
ηB mainbeamefficiency Equation3.58
ηH Hicolumndensity Equation7.154
ηs reflectorsurfaceefficiency Equation3.129
θ angle,polarangle
θHPBW halfpowerbeamwidth Figure3.15
θm angleformaximumsuperluminalmotion Equations5.1705.171
κ linearabsorptioncoefficient Equation2.18
λ eclipticlongitude Equation6.50
wavelength Section1.1.1
λ subscriptλperunitwavelength Equation2.4
λc waveguidecutoffwavelength Equation3.141
λD Debyelength Equation4.46
Symbol Definition Reference
μ meanelectricdipolemoment Equation7.129
plasmarefractiveindex Equation6.39
μ0 permeabilityoffreespace EquationF.5
μB Bohrmagneton Equation7.144
μJy microjansky10-6Jy AppendixF.4
μm micrometer=micron10-6m AppendixF.4
ν frequencyinHz=cycless-1=ω/(2π) AppendixF.3
ν subscriptνperunitfrequency Equation2.4
ν0 linecenterfrequency Figure7.4
ν10 Hilinefrequency Equation7.141
νc criticalfrequency Equation5.67
waveguidecutofffrequency Equation3.142
νe frequencyinthesourceframe
νg groupvelocity EquationD.18
νG electrongyrofrequency Equation5.7
νo frequency in the observer’s frame
νp plasmafrequency Equation6.40
Π unitrectanglefunction Equation3.74
ρ massdensity
σ crosssection
rootmeansquare(rms)
Stefan–Boltzmann constant Equation2.90
surfaceareaelement
σc rmsconfusion Section3.6.3
σS rmsfluctuationinpeakfluxdensity Section3.7.6
σT rmsimagebrightnessfluctuation Section3.7.6
rmsnoisetemperaturefluctuation Equation3.154
σT Thomsoncrosssection Equation5.33
τ duration,lifetime,smoothingtime
opacity=opticaldepth Equation2.23
pulsarcharacteristicage Equation6.31
τg geometricdelay(time) Equation3.172
τL lineopacityatthelinecenterfrequency Equation7.96
τs synchrotronlifetime Equation5.111
τz atmosphericzenithopacity Section1.1.2
ϕ angle
azimuthangle Section1.2
fringephase Equation3.176
pulsarpulsephase Section6.3
visibilityphase Equation3.185
ϕ(ν) normalizedlineprofile Figure7.4
χn ionizationpotentialofnthenergylevel Equation7.92
ψ free–free interaction angle Figure4.2
ω angularfrequencyinrads-1=2πν Equation2.50
ω Sun’s Galactic orbital angular velocity Section7.8.1
ωB (angular)magneticorbitalfrequency Equation5.21
ωG (angular)gyrofrequency(rads-1) Equation5.4
Ω rotationangularvelocity
solidangle
ohm AppendixF.3
ΩA beamsolidangle Equations3.42, 3.34
ΩMB mainbeamsolidangle Equation3.57

G.2 Other Symbols and Abbreviations

Symbol Definition Reference
isdefinedas
isproportionalto
f˙ timederivativeoff
f¨ secondtimederivativeoff
x averagevalueofx
|x| magnitudeofx
x^ unitvectorinthex-direction
x vectorquantityx
x¯ complexconjugateofx
istheFouriertransformof EquationA.1
convolutionoperator EquationA.14
cross-correlation operator EquationA.16
numericalconversionbetweenunits AppendixF.3
a acceleration
dimensionlessscalingfactor EquationA.11
dustgraindiameter Section2.8
radiationconstant Equation2.94
scalefactoroftheexpandinguniverse Equation2.128
a(ν) absorptioncoefficientofanopaquebody Section2.2.4
a0 Bohrradius AppendixF.1
an Bohrradiusofnthenergylevel Equation7.6
A geometricareaofanaperture Section3.3
visibilityamplitude Equation3.184
A0 antennapeakcollectingarea Equation3.43
A10 Hilineemissioncoefficient Equation7.146
Ae effectivecollectingarea Equation3.35
An,n-1 spontaneousemissionrate,levelntoleveln-1 Section7.2.2
AUL Einsteincoefficientofspontaneousemission Figure7.5
Å angstrom10-10m AppendixF.4
AGN activegalacticnucleus Figure5.22
ALMA AtacamaLargeMillimeterArray Figure8.5
ASKAP AustralianSKAPathfinder Figure8.6
au astronomicalunit AppendixF.2
b baselinelength Figure3.41
free–free scattering impact parameter Figure4.2
Galacticlatitude Section1.3
b baselinevector Figure3.41
Bλ blackbodyspectralbrightnessperunitwavelength Equation2.88
Bν blackbodyspectralbrightnessperunitfrequency Equation2.86
B blackbodytotalbrightness Equation2.89
magneticfieldstrength AppendixF.3
BLU Einsteincoefficientofabsorption Figure7.5
BUL Einsteincoefficientofstimulatedemission Figure7.5
Symbol Definition Reference
c vacuumspeedoflight AppendixF.1
c12 minimummagneticenergyfunction Equation5.109
c13 minimumtotalenergyfunction Equation5.110
CLU collisionalexcitationratecoefficient Equation7.71
CUL collisionalde-excitationratecoefficient Equation7.71
Cband 4ν(GHz)8 AppendixF.5
CARMA CombinedArrayforResearchinMmλAstronomy
cm centimeter AppendixF.3
CMB(R) cosmicmicrowavebackgroundradiation Section2.6
d distance
p electricdipolemoment Equation7.120
dH Hubbledistance Equation2.123
D diameter
directivity Section3.1.3
D 1debye10-18statcoulombcm AppendixF.4
dB decibel AppendixF.4
DC DirectCurrent
DFT discreteFouriertransform AppendixA.2
DM dispersionmeasure Equation6.46
e eccentricity Section6.1.9
electroncharge(magnitude) AppendixF.1
Euler’s number=2.71828
e(ν) emissioncoefficientofanopaquebody Section2.2.4
E electricfieldstrength AppendixF.3
energy
E˙ spin-down luminosity Equation6.20
Eγ meanphotonenergyofblackbodyradiation Equation2.101
EM emissionmeasure Equation4.57
EOR EpochofReionization Section7.8.3
eV electronvolt AppendixF.1
f electricfieldonanaperture Section3.2.3
focallength Figure3.7
pulsarpulsefrequency Section6.3
f(v) nonrelativisticMaxwellianvelocitydistribution Equation4.34
f(x) (inverse)FouriertransformofF(s) EquationA.2
f/D focalratio Section3.2.1
F force
F(s) (forward)Fouriertransformoff(x) EquationA.1
Fν spectralpower/areafromanisotropicradiator Equation2.107
Fn noisefactor Equation3.169
FFT fastFouriertransform AppendixA.2
FR Fanaroff–Riley Section5.6.1
FRI edge-dimmed source morphology Section5.6.1
FRII edge-brightened source morphology Section5.6.1
FWHM full width between half-maximum points
Symbol Definition Reference
g electricfieldstrengthonanaperture Section3.2.3
statisticalweightofanenergystate Section7.3.1
g gram AppendixF.3
gff free–free Gaunt factor Equation4.59
G gravitationalconstant AppendixF.1
antennapowergain Section3.1.3
receiverpowergain Section3.6.3
G0 antennapeakpowergain Section3.1.3
GBT GreenBankTelescope Figure8.1
GeV GigaeV109eV AppendixF.1
GHz Gigahertz109Hz AppendixF.4
GMRT GiantMetrewaveRadioTelescope
h height
Planck’s constant AppendixF.1
reduced Planck’s constant h/(2π)
H atomichydrogen
H0 Hubbleconstant AppendixF.2
H2 hydrogendiatomicmolecule
Hi neutralatomichydrogen
Hii ionizedhydrogenH+
HPBW HalfPowerBeamWidth
Hz hertz=frequencyincyclespersecond(s-1) AppendixF.3
i inclinationangle
-1
I electriccurrent Equation3.4
momentofinertia Section6.1.5
totalintensity Equation2.6
Iλ specificintensity(perunitwavelength) Equation2.3
Iν specificintensity(perunitfrequency) Equation2.2
Ip polarizedfluxdensity Equation2.57
IC inverseCompton Section5.5
IF intermediatefrequency Section3.6.4
III shahfunction Equation5.61
IMF initialmassfunction Section4.2
IR infrared
ISM interstellarmedium
jν (spectral)emissioncoefficient Equation2.26
J angularmomentumquantumnumber Section7.7.1
J joule AppendixF.3
Jy jansky10-26Wm-2Hz-1 AppendixF.4
Symbol Definition Reference
k Boltzmann’s constant AppendixF.1
k wavevector Equation2.49
K kelvins AppendixF.3
Kband 18ν(GHz)26.5 AppendixF.5
Kaband 26.5ν(GHz)40 AppendixF.5
Kuband 12ν(GHz)18 AppendixF.5
kg kilogram AppendixF.3
kpc kiloparsec103pc AppendixF.2
l Galacticlongitude Figure7.18
(l,m,n) directioncosinesin(u,v,w)coordinates Figure3.45
L angularmomentum
luminosity Equation2.16
Lband 1ν(GHz)2 AppendixF.5
Lν spectralluminosity Equation2.15
L solarluminosity AppendixF.2
LE Eddingtonluminosity Equation5.117
LO localoscillator Section3.6.4
LOFAR LOwFrequencyArrayforRadioastronomy Figure8.8
LTE localthermodynamicequilibrium Section2.2.2
ly lightyear AppendixF.2
m meter AppendixF.3
m mass
reducedmass Equation7.105
m perpendicularmagneticmoment Section6.1.4
me electronmass AppendixF.1
mp protonmass AppendixF.1
M subreflectormagnificationfactor Equation3.147
M solarmass AppendixF.2
MCh Chandrasekharmasslimit Equation6.6
MH Himass Equation7.166
MJy megajansky106Jy
mJy millijansky10-3Jy
mm millimeter10-3m AppendixF.3
MHz megahertz106Hz AppendixF.4
Mpc megaparsec106pc AppendixF.2
MWA MurchisonWidefieldArray Figure8.7
n electronicquantumnumber Figure7.1
pulsarbrakingindex Section6.1.8
n* criticaldensity Equation7.135
nγ photonnumberdensity Equation2.95
nb baryonnumberdensity Section2.6.3
ne electronnumberdensity
nH numberdensityofneutralhydrogenatoms
n˙H hydrogenrecombinationrate Equation4.6
ni ionnumberdensity
Symbol Definition Reference
nL numberdensityinlowerenergystate Equation7.42
nn numberdensityofatomsinnthenergylevel Equation7.92
np protonnumberdensity
nU numberdensityinupperenergystate Equation7.42
N number
Nν numberofmodesperunitfrequency Equation2.72
Ne electroncolumndensity Section1.1.4
N˙IC photonscatteringrateperelectron Equation5.158
NF noisefigure Equation3.171
NRAO NationalRadioAstronomyObservatory
p pressure
degreeofpolarization Equation2.58
P power
probability
pulsarrotationperiod Section6.1.2
Pband 0.25ν(GHz)0.50 AppendixF.5
P˙ pulsarperiodderivative Equation6.17
Pν powerperunitfrequency
P(x) probabilitydistributionofx
PIC inverseComptonpower Section5.5
Pn normalizedantennapowerpattern
Psyn synchrotronpower Section5.2
pc parsec AppendixF.2
PDBI PlateaudeBureInterferometer
pwv precipitablewatervapor Section1.1.2
q electriccharge AppendixF.3
QH productionrateofLyαphotons Equation4.10
Qband 33ν(GHz)50 AppendixF.5
QSO quasi-stellar object
r radialcoordinateordistance
r(ν) reflectioncoefficientofanopaquebody Section2.2.4
re equilibriuminteratomicdistance Figure7.12
R resistance Equation3.21
correlatorresponse Equation3.175
R0 radiationresistanceofspace Equation3.29
R Rydbergconstant Equation7.10
Rc Rydbergfrequency Equation7.11
R distancefromtheSuntotheGalacticcenter Figure7.18
solarradius AppendixF.2
Rff far-field distance Equation3.64
RM RydbergconstantfornuclearmassM Equation7.12
RS Strömgren sphere radius Figure4.1
rad radian AppendixF.4
RF radiofrequency
RFI radiofrequencyinterference
rms rootmeansquare
Symbol Definition Reference
s secondoftime AppendixF.3
s coordinatefromsourcetodetector Figure2.7
s^ unitvectorinsourcedirection Figure3.41
s^0 phasereferencedirection Figure3.45
S fluxorfluxdensity Equation2.14
Sband 2ν(GHz)4 AppendixF.5
Sν fluxdensity Equation2.9
S Poyntingflux Equation2.138
sinc(x) sincfunctionsin(πx)/(πx) Equation3.77
SKA SquareKilometerArray
SMA SubMillimeterArray
SMBH supermassiveblackhole
sr steradian
t time
t dispersiondelay Equation6.43
t ageofuniverseatrecombination Section2.6.2
T temperature
totaltime
TA antennatemperature Section3.1.6
T0 CMBtemperatureatredshiftzero Section2.6
noisefactorreferencetemperature=290K Equation3.169
Tatm kinetictemperatureoftheatmosphere
Tb brightnesstemperature Equation2.33
TC continuumbrightnesstemperature Section7.6.1
Tcmb cosmicmicrowavebackgroundtemperature Tcmb2.73K
Te electrontemperature
TL linebrightnesstemperatureatthelinecenter Section7.6.1
Tmin minimumkinetictemperature Equation7.119
TN noisetemperature Equation3.149
Tr radiometernoisetemperature Section3.6.1
Ts Hispintemperature Equation7.148
systemnoisetemperature Equation3.150
Tx excitationtemperature Equation7.70
TE thermodynamicequilibrium Section2.2.2
THz terahertz1012Hz AppendixF.4
TOA pulsarpulseTimeOfArrival Section6.3
u atomicmassunit AppendixF.1
dimensionlesscoordinate,e.g.,ux/λ Equation3.72
totalradiationenergydensity Equation2.92
u¯ lineprofileweightedradiationenergydensity Equation7.39
uν spectralenergydensityofradiation Equation2.76
(u,v,w) dimensionlesscoordinatesforinterferometers Figure3.45
Uband 40<ν(GHz)<60 AppendixF.5
UB magneticenergydensity Equation5.35
Ue electronenergydensity Equation5.93
Urad radiationenergydensity Section5.5
UV ultraviolet
Symbol Definition Reference
v dimensionlesscoordinate,e.g.,vy/λ Figure3.45
velocity
vg groupvelocity Equation6.41
waveguidegroupvelocity Equation3.143
vr radialvelocity
vrot rotationalvelocity Equation7.167
V voltage Equation3.20
volume
Vo squarelawdetectoroutputvoltage Section3.6.2
𝒱 complexvisibility Equation3.182
Vband 50ν(GHz)75 AppendixF.5
VLA VeryLargeArray Figure8.4
VLBA VeryLongBaselineArray Figure1.5
VLBI VeryLongBaselineInterferometry
w dimensionlesscoordinate,e.g.,wz/λ Figure3.45
Wband 75ν(GHz)110 AppendixF.5
W free–free pulse radiated energy Equation4.24
WMAP WilkinsonMicrowaveAnisotropyProbe
WSRT WesterborkSynthesisRadioTelescope Figure8.3
x Cartesiancoordinate
(x,y,z,t) coordinatesinmovingframe FigureC.1
xj (inverse)discreteFouriertransformofXk EquationA.5
XCO COtoH2conversionfactor Equation7.140
Xk (forward)discreteFouriertransformofxj EquationA.4
Xband 8ν(GHz)12 AppendixF.5
y Cartesiancoordinate
yr year AppendixF.2
Y Yfactor Equation3.167
z Cartesiancoordinate
redshift Equation2.127
zenithangle Figure2.10
Z numberofelectronsremovedfromanion