Module 3 Basic Physics for astrophysics.ppt

Basics of Astrophysics

1. 6B15PHY
ASTRONOMY & ASTROPHYSICS
MODULE 3

2. Module 3 - Syllabus
Planck’s theory of Blackbody radiation—Pressure
of radiation—Continuous, Absorption & Emission
spectra—Kirchoff’s laws—Doppler effect—
Zeeman effect
(Minimum marks: 6)
Ref: An Introduction to Astrophysics -
Baidyanath Basu - Chapter 2

3. Planck’s theory of Blackbody radiation
•The ratio of emissive power to absobtivity at
any temperature Tis same for all bodies,
irrespective of the material – Kirchhoff
•A blackbody is one that absorbs all the
radiation falling on it and is able to emit
radiations at all possible wavelengths.
•The absorbtivity of a blackbody is unity.
•The graph between intensity and frequency
(or wavelength) of radiation emitted by a
blackbody is called blackbody spectrum.

4. Planck’s theory of Blackbody radiation

5. Wien’s law of Blackbody radiation
•In order to explain the observed BB spectrum, Wien
proposed a law in 1895:
•The energy density of a blackbody in the frequency
range from ν to ν +d ν is given by:
•This law agrees well with the BB spectrum in the high
frequency (UV) region but fails in the low frequency
region.


deAdU
kT
h
-
3
)( 

6. Wien’s Displacement Law
•It states that the wavelength of the maximum intensity of
the BB radiation is inversely proportional to the
temperature of the BB. i.e.,
λ
maxT = b, a Constant
b = 2.898 x 10
– 3
m K
•For higher T, the peak of the curve will shift towards
shorter waavelength and vice versa.
•The temperature of stars can be estimated using this law
assuming them to be BB – known as colour temperature.

7. Rayleigh –Jeans Formula
•It states that the energy density of the BB
Radiation in the frequency range from ν to ν+dν :
U(ν )d ν =
•
or, U(λ)dλ = 8πkTλ
4
dλ
•This law agrees well with experimental results only
at low frequency region but fails at the high
frequency or UV region of the spectrum - U V
Catastrophe!
2
3
8πkT
νdν
c

8. Planck’s law of BB Radiation
•Empirically derived in 1901.
•It states that the energy density of the BB
Radiation in the frequency range from ν to ν+d ν :
U(ν )d ν =
•This law agrees well with experimental results at
all regions of the spectrum.
•Later derived by S N Bose using Statistical Physics.
3
3 hν
kT
8πh ν
dν
c
e 1
 
 
 

9. Various Laws of BB Radiation
- A comparison

10. Stefan-Boltzmann law
•Total energy radiated by a BB per unit area of its
surface per unit time at a given temperature is
given by:
E = σ T
4
Where σ is the Stefan’s constant.
•σ = 5.6687 x 10
 8
watt m
2
K
4
.

11. Pressure of radiation
•Photoelectric effect – Proof of particle nature
of radiation
•Photons –quanta of em radiation
•Possess momentum and hence can exert
pressure on the objects they fall upon!
•Important in the hydrostatic equilibrium of
stars- balance between gravity and outward
pressure.
•

12. Pressure of radiation
•The radiation pressure is given by SM as:
P
r = U/3 = 1/3 σ’ T
4 ,

σ’ is a constant of radiation density.

U is the total energy density at the point.
•The gas Pressure is given by
•The total pressure that balances gravity is the
sum of radiation pressure and gas pressure.
•RP drives out streams of particles from stellar
surfaces at high temperatures - Cosmic Rays.

kT
P
g


13. Types of Spectra
•The spectra obtained from different sources
are classified as:
1. The Continuous Spectrum
2. The Emission- line or Bright-line Spectrum
3. The Absorption-line or Dark-line spectrum.
•The formation of these spectra are explained
by Kirchhoff’s laws:

14. Kirchhoff’s laws
•1. When the source is an incandescent solid, liquid or a
compressed gas, the radiation given out is a continous
emission in all wavelengths, producing a continuous
spectrum.
•2. When the source is a glowing gas under low pressure,
the radiation emitted is selective. The spectrum consists of
discrete bright lines or emission lines superposed on a faint
continuous spectrum- Emission Spectrum.
•3. If the source is a hotter source emitting radiation
continuously and if, observed through a comparatively
cooler gas, the latter may absorb some wavelengths of the
radiation from the actual source.The spectrum obtained
consists of dark lines or absorption lines superposed on a
continuous background – absorption spectrum

15. Types of Spectra

16. Absorption Spectrum

17. Fraunhofer lines
•Series of Dark lines/absorption lines observed
in solar spectrum.
•Now used for absorption spectrum of any
source!

18. DOPPLER EFFECT
•The phenomenon of apparent change in the
frequency (or wavelength) of light emitted by
a source due to the relative motion between
the source and observer.
•Relative motion along the line of sight is
relevant - Radial component of the motion
between S and O is considered.
•Apparent frequency increses as the source or
observer approaches each other and decreses
as they recede.

19. DOPPLER SHIFT
•The entire spectrum of the source will be shifted
towards violet in the case of an approaching
source, causing Blue shift.
•The entire spectrum of the source will be shifted
towards red in the case of a receding source,
causing Red shift.
•The amount of Doppler shift depends on the
radial velocity of the source and the frequency
being observed as:
for non relativistic case.
λ , the natural wavelength, v
r, the radial velocity.
V
r
+ve, when source recedes from observer.
c
v
r





20. DOPPLER SHIFT
•For relativistic case,
•∆λ = λ’ - λ
c
v
-1
1
1
r
c
v
r







21. DOPPLER SHIFT

22. Doppler effect

23. ZEEMAN EFFECT
•Splitting of spectral lines into several
components in the presence of magnetic field.
•Amount of splitting depends on the
frequency(or wavelength ) of radiation and the
strength of the applied magnetic field.
•The component lines are polarized in different
ways while the original/central line remains un
polarised.
•An experimental proof of the space
quantization of angular momentum of atoms
•Normal & Anomalous ZE

24. NORMAL ZEEMAN EFFECT
•Zeeman Shift
, g is the Lande’ factor ( g=3 for Sun), H in
gauss, λ in cm.
•In frequency,
Hg
2-5
1067.4  
me
eH
o


4


25. ASTROPHYSICAL SIGNIFICANCE OF ZEEMAN EFFECT
•Since the Zeeman shift depends on the
strength of the applied magnetic field, it can be
used to estimate the magnetic field of sun and
other stars.
•Analysis of Zeeman splitting gives valuable
information about the strength and structure
of magnetic field in astronomical bodies.

26. ZEEMAN EFFECT