Download Week_2_EM_waves

ASTR 2020
Space Astronomy
Week 2
Clicker Test:
The number of arc-seconds in a radian is:
1) 1
2) 200
3) 206,265
4) 2x106
The Golden Age:
• Seeing what we can’t see (with our eyes)
- Electronics & silicon technology
=> sensors at all wavelengths
- Large telescopes (Diameters up to 10 meters now;
37 meter in 10 yrs)
- Space telescopes (to 6 meters)
=> No atmosphere
=> Sharp images
=> Access to all wavelengths
Fermi Chandra Hubble
-ray
X-ray UV/visual
Spitzer Herschel ALMA (Chile)
IR
sub-mm
radio
- Powerful computers
=> Model cosmic evolution, stars, atoms, …
NEW DISCOVERIES!
Understanding nature => Enables technology, economy
Hubble Space Telescope
Very Large Array 27 x 25 m (radio)
Green Bank
100 m
(radio)
Kitt Peak (visual)
CXO
(X-ray)
Fermi (-ray)
GRO
(-ray)
Chandra (X-ray)
Hubble
2.4 m
(visual)
James Webb Space Telescope
6.5 - meter diameter
Earth-Sun L2 (~106 km from Earth): 2018
The Electromagnetic Spectrum
Electromagnetic Waves
What’s “waving”?
- Electric fields induce Magnetic fields
- Magnetic fields induce Electric fields
What is a “field”?
- the force
experienced
by a charge (+,-)
e.g. electrons
protons
but not neutrons
Star
A large, glowing ball of gas that generates heat and light through
nuclear fusion
Visual wavelength
UV & X-ray wavelengths
The Winter sky ….
Infrared view of winter sky (10 - 120 mm)
Electromagnetic (EM) Waves
- Properties of light: it’s a wave … and a particle!
- Wave like properties (EM waves) : frequency, wavelength
[frequency] x [ wavelength] = [speed of light]
f
x
=
c

x
=
c
 = f = c
c = 2.998 x 1010 cm/sec
- Particle like properties (photons) : energy, momentum
[energy] = h f = h 
h = Planck constant
= 6.626 x 10-27 in (c.g.s)
[momentum] = E/c = h f / c = h  / c = h / 
because f = c /  )
How can we know what the
universe was like in the past?
Z Light travels at a finite speed
Z c = 300,000 km/s = 3 x 1010 cm/sec.
Destination
Light travel time
Moon
1 second
Sun
8 minutes
Sirius
8 years
Andromeda Galaxy 2.5 million years
Z Thus, we see objects as they were in the past:
The farther away we look in distance,
the further back we look in time.
No Calculators!
Z A photon has
wavelength =1.5x108cm
what is the frequency?
a) 4x10-2 s-1
b) 5x109 s-1
c) 6x1018 s-1
d) 2x102 s-1
e) 6x102 s-1
No Calculators!
Z A photon has
wavelength =1.5x108cm
what is the frequency?
a) 4x10-2 s-1
b) 5x109 s-1
c) 6x1018 s-1
d) 2x102 s-1
e) 6x102 s-1
The Winter sky ….
Infrared view of winter sky (10 - 120 mm)
Star
A large, glowing ball of gas that generates heat and light through
nuclear fusion
Visual wavelength
UV & X-ray wavelengths
ASTR 2020
Space Astronomy
Week 2: Thursday
Electromagnetic (EM) Radiation
• Light:
-
wavelength,
 = frequency
 = c = 2.998 x 1010 cm/s (in vacuum)
E = h 
Photon energy (erg)
1 erg sec-1 = 10-7 Watt
h = 6.626 x 10-27 (c.g.s)
1 eV = 1.602 x 10-12 erg
-
p = E / c = h /  Photon momentum
 = h / p = h / mv
Wavelength of a particle
• Black-body Planck Function: B(T)
Properties of Thermal Radiation
1. Hotter objects emit more light at all frequencies per unit
area.
2. Hotter objects emit photons with a higher average
energy.
1 nm
“nano meter”:
= 10-9 m
= 10-7 cm
= 10 Angstroms
= 10-3 mm
Thermal (Black-body) radiation:
[peak wavelength] = 0.3 cm / [Absolute Temperature (Ko )]
Wien
Rayleigh-Jeans
The Planck Function: Black-body radiation
(erg s-1 cm-2 Hz-1 2 p sr-1)
Wien:
B(,T) = (2 ph3 / c2) e-h/kT
Rayleigh-Jeans:
B(,T) = 2 p kT / 2
Luminosity & Flux
- Luminosity: Energy given off each second
energy is measured in ergs
luminosity is an erg/second
1 Watt = 107 erg /sec
- Flux: flow or energy though a unit area.
[erg sec-1 cm-2]
Example: Flux of energy from the Sun:
Sun’s luminosity = 4 x 1033 erg sec-1
Sun’s mass = 2 x 1033 grams)
Distance between Earth & Sun D = 1.5 x 1013 cm
= 1 Astronomical Unit
= 1 A.U.
Flux = L / 4 p D2 = 4 x 1033 / (4 x 3.14 x 1.5x1013*2)
= 1.4 x 106 erg s-1 cm-2 = 1.4 x 1010 erg s-1 m-2
= 1400 Watts m-2 = 1.4 kW m-2
Review of Some Basics
•
Angular resolution:
q = 1.22  / D ~  / D radians
206,265” in a radian
• Flux
F = L / 4 p d2
• Flux density (per Hz) 1 Jansky = 10-26 (W m-2 Hz-1)
= 10-23 (erg s-1 cm-2 Hz-1)
Constants:
c = 3 x 1010 cm/sec,
k = 1.38 x 10-16
h = 6.626 x 10-27
mH ~ mproton = 1.67 x 10-24 grams
me = 0.91 x 10-27 grams
eV = 1.602 x 10-12 erg
Luminosity of Sun = 4 x 1033 erg/sec
Mass of the Sun = 2 x 1033 grams
The Doppler Effect
Motion changes wavelength & frequency:
Let:
fobserved - frest = f = “change in frequency”
observedrest =  = “change in wavelength”
f/f =  V / c
= “velocity in units of speed of light”
Fractional change in frequency & wavelength
= [velocity along line-of-sight] / [speed of light]
Spectra of Galaxies:
(Calcium H+K lines)
Spectrum of
Comparison lamp
(He + Ne + Ar)
Spectrum of galaxy
Example:
Freflect = ftrans +/- f
f = 2 f (V/c)
f = 10 GHz = 1010 Hz
Police
V = 100 km/h = 27.8 m /s = 2.78 x 103 cm/s
Radar: c = 3 x 1010 cm/s = 3 x 105 km/s
f = 2 f V / c
= 2 [1010 Hz][2.78x103 cm/s] / [3x1010 cm/s]
= [2 x 2.78 / 3] [10 10+3-10]
= [5.56 / 3] x 103 Hz = 1.85 x 103 Hz = 1,850 Hz
Freflect = f trans + / - f
f trans
f = 1850 Hz
frequency of `beat wave’ (envelope)
Mixers
signal in
w1
local oscillator
w2
signal out
w1+w2
and
w1w2
LO
A mixer takes two inputs:
the signal and a local
oscillator (LO).
The mixer outputs the sum
and difference frequencies.
In radio astronomy, we
usually filter out the high
frequency (sum) component.
Single sideband mixer:
Local oscillator
Down-converted signal
f = 10 GHz
F + f =
10 GHz + 1850 Hz
1850 Hz
f = fIF
Frequency
Band-pass of amplifier:
Intermediate frequency = IF
Observing in the Radio
Z i.e. The NRAO GBT (D ~ 100 m)
at 21cm = 1.420 GHz
l
21cm
q= »
= 7.2'
D 10000cm
at 0.3 cm = 100 GHz
l
0.3cm
q= »
= 0.10' = 6.2' '
D 10000cm