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Transcript
```1B11
Foundations of Astronomy
The Electromagnetic Spectrum
Liz Puchnarewicz
[email protected]
www.ucl.ac.uk/webct
www.mssl.ucl.ac.uk/
1B11 The electromagnetic spectrum
When an electric charge is accelerated, electromagnetic
energy is produced. This energy can be thought of as
propagating as a wave – or, equally as a particle.
The waves are usually referred to as light waves or radiation.
The particles are known as photons.
1B11 EM waves
Electromagnetic waves are transverse sine waves. For a
wave travelling in the x direction, the electric field at time t is
given by:
c= speed of light
 2

E  E0 sin   x  ct 


 = wavelength
E
E0
x
0

1B11 The electromagnetic spectrum
Travelling at right angles to the electric field but in the same
direction, is the magnetic field, B.
electric field
magnetic field
EM waves are self-propagating, ie they need no medium.
c = speed of light in m s-1
 = wavelength in m
c=2.998x108 ms-1
n = frequency in Hz
c  n
1B11 Wave-like properties of light
• Refraction – the direction of travel of light changes when
light crosses the boundary from one medium to another.
• Diffraction – where light waves bend when they strike the
end of a barrier.
• Interference – complex pattern forms when two or more
wave systems combine
• Polarization – where the planes in which the waves vibrate
lie preferentially in one direction
• Doppler Effect – where the observed wavelength, 0, is
different from the emitted wavelength, , due to the velocity
of the emitter, v.
  0  v  = obs wavelength

0

0

c
0=rest wavelength
v=velocity of source
1B11 Quantum nature of light
Alternatively, light can be thought of as packets (or “quanta”)
of energy called photons.
Photon energy, E:
E  hn  hc
n = frequency (Hz)
high frequency
 short wavelength
 high energy

h = Planck’s constant (6.63x10-34 Js)
Examples of particle nature
can be seen in:
• Photo-electric effect
• Atomic spectra
1B11 Units
Wavelength: SI units – metre, m
Optical/UV: Angstrom, A
Infra-red:
1A = 10-10 m = 10-8 cm = 0.1nm
nanometre, nm
1nm = 10-9 m
micron, mm
1mm = 10-6 m
Frequency: SI units – Hertz, Hz
1GHz = 109 Hz
Energy: SI units – Joules, J
X-ray: electron volts, eV 1eV = 1.6x10-19 J
1keV = 1.6x10-16 J
1B11 “Map” of the EM spectrum
Log frequency (Hz)
24
22
20
g-rays
-16
-14
18
16
UV
X-rays
-12
-10
14
-8
12
IR
-6
-4
10
8
microwave
-2
0
6
4
2
2
4
6
Log wavelength (m)
Atmosphere transparent
Atmosphere opaque
Opaque with
narrow “windows”
visible
1B11 Spectroscopy
Spectra were first seen due to the effects of refraction – ie
the bending of light as it passes through a transparent
medium, which is wavelength-dependent.
White
light
prism
Blue light is bent the most, red light the least.
Spectroscopy is the astrophysical technique which is key to
our understanding of astronomical objects.
1B11 Kirchoff’s Rules (1824-1887)
1. A hot, dense object emits a continuous spectrum
2. A hot, transparent gas produces a spectrum of emission
lines. The lines depend on the elements in the gas.
3. If a continuous spectrum passes through a transparent
gas at a lower temperature, the low-T gas will
superimpose dark absorption lines on the spectrum.
1B11 Continuous spectra
Hot, dense objects emit a continuous blackbody spectrum.
Surfaces of stars, for example, are very good “blackbodies”.
Planck (1900) showed that the intensity of radiation emitted
by a blackbody is:
1
hc
2
kT
5
2hc 
I   
e
 

 1

Units: W m-2 (unit wavelength) -1 sr-1
h - Planck’s constant
k – Boltzmann’s constant
T – temp in Kelvin
c – speed of light
sr – steradian (unit of solid angle, 4 sr in a sphere)
1B11 Blackbody curves
Log I
15000K
Rayleigh-Jeans
tail
10000K
5000K
3000K
Wien tail
200
500
1000
 (nm)
1B11 Key BB relations
Wien’s Law:
Wavelength of peak intensity, max = 2.898 x 10-3 / T m
or
MAX  3000 / Tmm
Stefan-Boltzmann Law:
Total flux emitted by a blackbody, F = sT4 W m-2
where s = Stefan’s constant = 5.67 x 10-8 W m-2 K-4
For astronomers:
Colour Index, (B-V) = -0.71 + 7090 / T
where T is in Kelvin
1B11 Absorption and emission lines
Where do absorption and emission lines come from?
The production or absorption of energy when an electron in
an atom changes its level.
Taking the simple case of

a hydrogen atom. It has
one proton in the nucleus
4
and one orbiting electron.
3
In its stable state, the
2
electron orbits in level 1
(the ground state). There
1
are an infinite number of
discrete levels, converging
to n= , the ionization
potential.
1B11 Transitions
Electron moves up
n=
from 2 to 3

Electron moves
down from 4 to 2
n=

n=6
n=5
n=4
n=6
n=5
n=4
n=3
n=3
4861A
6562A
n=2
n=1
Absorption line at 6562A
n=2
n=1
Emission line at 4861A
1B11 Energy levels
n=

n=6
n=5
n=4
Excited states
Ionization potential
Atoms have an infinite
number of energy levels,
converging to a finite value
(the ionization potential). If an
electron gains more energy
than the ionization potential
then it is no longer bound to
the atom. Only the lowest
level (the ground state) is
generally stable. Excited
states (when an electron is in
level 2 or higher) have
lifetimes of ~10-8 seconds.
n=3
n=2
Ground state
n=1
1B11 Transitions
Only certain discrete
energy levels are allowed
for electrons in atoms.
Transitions between
levels are accompanied
by the emission or
absorption of photons.
The photon energy
(emitted or absorbed)
corresponds to the energy
lost or gained in the
transition.
Eb
Ea
Photon energy, hn = Eb - Ea
1B11 Emission lines
To produce emission lines, an excited state must first be
populated – when the electron in an excited state falls by
one or more levels, an emission line is produced.
To populate the excited levels:
(a) Collisional excitation
I()
(b) Photo-excitation
(c) Recombination
  hc E
wavelength, 
These all produce emission lines and explain Kirchoff’s 2nd
rule.
Kirchoff’s Rules
1B11 Collisional excitation
n=

n=5
n=4
n=3
n=2
n=1
Collisions with electrons/ions/atoms can knock electrons
into higher energy levels. The energy comes from the
kinetic energy of the colliding particle. The electron falls
back to lower levels and this energy is radiated away.
1B11 Photo-excitation
n=

n=5
n=4
n=3
n=2
n=1
If a photon with exactly the right energy interacts with an
atom or ion, an electron can be moved up to a higher level
for a short while, before it falls back down to the ground
state.
1B11 Ionization + recombination
n=
OR

n=1
If a photon or particle with sufficient energy interacts with an
atom so that an electron is stripped away completely, it is
said to be ionized. A free electron can recombine with an
ion, falling into an excited state – it will then cascade down
to ground level producing line emission at it falls.
1B11 Absorption lines
When atoms/ions in a gas are illuminated, they will absorb
those photons at wavelengths which will move electrons in
the atoms/ions from one level to another.
F
F


1B11 Absorption lines (cont.)
Atoms or ions in a gas will absorb photons whose energy
corresponds exactly to the energy that an electron in that
atom/ion needs to move into a higher level.
After about 10-8 seconds, the electron will fall back down to
the most stable state, emitting a photon with an energy
corresponding to the difference between the levels, but in a
random direction.
So if you look through the gas at a source, you will see much
few photons at that energy because these are being reemitted in random directions. This produces an absorption
line and explains Kirchoff’s 3rd rule.
Kirchoff’s rules
1B11 Spectrum of the hydrogen atom

13.6eV
Paschen
series
(IR) 12.1eV
Pg Pb Pa
n=2
Lyman
series
(UV)
Lyg Lyb Lya
1.9mm
Balmer
series
(optical)
Hg Hb Ha
1216A
n=1
6562A
4340A
n=3
4861A
n=4
10.2eV


En  13.60 1  1
dg b

eV
n
2
a
6x10-6 eV
=>21cm
0eV
1B11 Astrophysical applications
• Chemical composition – different atoms/molecules have
different lines; line strengths indicate abundances
• Ionization state – different atoms have different ionization
potentials; different ions have different spectra
• Temperature and density – collisional excitation in high
densities; lines broadened in high-T gas
• Pressure – high pressure broadens lines
• State of motion – Doppler effect
• Magnetic fields – in a high-B field, energy levels split due to
the Zeeman effect.
I
I
B=0
B>>0


1B11 Sources of absorption lines
Stellar
atmospheres
star
Interstellar ISM cloud
gas
star
Intergalactic
Lya systems
quasar
outer layers absorb
blackbody emission
from star
1B11 Sources of emission lines
Hot
ionized
nebulae
eg HII regions
Active galactic
nuclei
quasar
```
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