Introduction to Radio WavesVincent L. Fish

source: Windows to the Universe (UCAR) Image courtesy of NRAO/AUI

Waves

Light is a transverse wave phenomenonElectric and magnetic fields are perpendicular to direction of travel (and each other)

Waves can be characterized by a few parameters:Amplitude AWavelength λ (or frequency f, also called ν)Phase φ

Wavelength and frequencyare related

λ · f = v (velocity of wave)

For light, v = c =2.99792458 x 1010 cm s-1

2.99792458 x 108 m s-1

2.99792458 x 105 km s-1

Energy of light

Quantum mechanics tells us that we can think of light as a particle

Energy of a photon: E = h νh = 6.626068 x 10-27 erg s = 6.626068 x 10-34 J s (Planck's constant)

We can equivalently talk about wavelength, frequency, or energy

Radio waves

Radio waves are the longest wavelength (lowest frequency, lowest energy) portion of the electromagnetic spectrum

Wavelength > 0.3 mmFrequency < 1 THz (1012 cycles s-1)

No sharp cutoff to definition of “radio” – usually defined by hardware/technique or atmosphere

Radio

1 THz1 GHz1 MHz

Blackbody radiation

Thermal emission shows a characteristic spectrum

Peak of emission (per unitwavelength) is atλ

max = 2.9 mm / T[K]

Room temperature300 K: λ

max = 10 μm

(ν = 30 THz)

Cosmic microwavebackground3 K: λ

max = 1 mm

(ν = 300 GHz)

Radio can see colder thingsthan can other wavelengths

source: Giro720, wikipedia

Rayleigh-Jeans approximation valid

“Classical” behavior

Planck's law required

Atmospheric transmission

The atmosphere is transparent to most radio waves

Water vapor is a problem at millimeter wavelengths – requires going to very dry (usually very high) site

Polarization

Polarization can be linear, circular, or elliptical

The two linear polarization modes (horizontal and vertical) are orthogonal – if you have two crossed polarizers, no light will get through

The two circular modes (left and right circular) are orthogonal

However, linear and circular modes are not orthogonal

Terrestrial radio signals are usuallypolarized

Some astronomical radio signalsare polarized also

Radar

Doppler effect

The apparent frequency of a soundwave is shifted when the sourcemoves relative to the observer

The same is true for light

Source moving away:lower frequencyredshift

Source approaching:higher frequencyblueshift

Image courtesy Windows to the Universe

Doppler effect

If v << c, ∆λ/λ ~ ∆ν/ν ~ v/c

Rule of thumb: The fractional Doppler shift in frequency (or wavelength) is the speed in relativistic units (c = 1)

source: TxAlien, Wikipedia

Applications of Doppler effect

The Doppler shift gives the line-of-sight velocity of an object

Examples:radar (reflection off moving object)exoplanet detection (through reflex motion of star)

Spectral lines

Energy levels of atoms and molecules are quantized

Energy can only be absorbed or emitted atspecific frequencies – a “fingerprint” of theatom or molecule

Doppler effect on spectral lines

Spectral lines give velocity information

Rest frequency (wavelength) is knowna priori – every atom and molecule hasa fingerprint

Measuring the frequency (wavelength)of emission or absorption line givesDoppler shift

Doppler shift is proportional to velocity

Direction of Doppler shift tells us whetherthe source is moving toward or awayfrom us

At radio frequencies, the frequency (thus, velocity) can be measured very precisely

Not moving

Moving toward receiver

Moving away from receiver

frequency

Mapping Galactic structure

Milky way has fairly well known rotation curve – far away material is Doppler shifted, and line-of-sight velocity can be used as proxy for distance

Map of galaxy in CO (115.271203 GHz rest frequency) observed with 0.0005 GHz resolution (1.3 km s-1)

CO is abundant in molecular clouds, which trace the spiral arms of the Milky Way – these stand out in the longitude/velocity plot

Dame, Hartmann, & Thaddeus (2001)

Communications

Radio waves are frequentlyused for communications

Example: AM and FM radio

AM = amplitude modulation

FM = frequency modulation

Remember, even thougha car radio produces soundwaves, the information is broadcastusing light waves (radio waves)

Phil Erickson will talk more about AM/FM

source: Berserkus, Wikipedia

Standing wavesConsider a wave travelling in a cavity(e.g., sound in an organ pipe,radio wave in a waveguide)

In general, allowed propagation modeswill have one of two boundary conditions:node (zero) oranti-node (maximum displacement)

Reflection off surface causes wavesto travel in both directions

Peaks at multiples of λ/2

Source: Brews ohare, wikipedia

Phasing and interference

Many radio stations have antenna arraysto allow directional broadcasting

Altering power and phase at each antennachanges the beam (broadcasting pattern)

AM stations may have different beampatterns (and power) for day and night

KMTI photo: smeter.net reception maps: radio-locator.com

Interferometers

Radio astronomy uses arrays of telescopes called interferometers

These are analogous to phased broadcasting arrays, except that they receive radiation

Altering the delays (phases) between telescopes changes the reception pattern

Image courtesy of NRAO/AUI source: rigel.org.uk