Transcript Slide 1

Luminosity and Colour of Stars
Michael Balogh
Stellar Evolution (PHYS 375)
The physics of stars
A star begins simply as a
roughly spherical ball of
(mostly) hydrogen gas,
responding only to gravity
and it’s own pressure.
To understand how this simple
system behaves, however,
requires an understanding
of:
X-ray
ultraviolet
infrared
radio
1.
2.
3.
4.
5.
6.
7.
Fluid mechanics
Electromagnetism
Thermodynamics
Special relativity
Chemistry
Nuclear physics
Quantum mechanics
Course Outline
Part I (lectures 1-5)
 Basic properties of stars and electromagnetic radiation
 Stellar classification
 Measurements of distance, masses, etc.
Part II (lectures 6-13)
 Chemical composition of stars (interpretation of spectra)
 Stellar structure (interiors and atmospheres)
 Energy production and transport
Part III (lectures 14-22)
 Stellar evolution (formation, evolution, and death)
 White dwarfs, neutron stars, black holes
The nature of stars
Betelgeuse
• Stars have a
variety of
brightnesses and
colours
• Betelgeuse is a red
giant, and one of the
largest stars known
• Rigel is one of the
brightest stars in
the sky; blue-white
in colour
Rigel
Apparent brightness of stars
The apparent brightness of stars depends on both:
• their intrinsic luminosity
• their distance from us
Their colour is independent of distance
The five brightest stars
Star name
The five nearest stars
Relative
Distance
brightness (light years)
Star name
Relative
Distance
brightness (light years)
Proxima
Centauri
0.0000063 4.2
Sirius
1
8.5
Canopus
0.49
98
Alpha
Centauri
0.23
4.2
Alpha Centauri 0.23
4.2
0.000040
5.9
Vega
0.24
26
Barnard’s
star
Wolf 359
0.000001
7.5
Arcturus
0.25
36
0.00025
8.1
Capella
0.24
45
Lalande
21185
The Astronomical Unit
Astronomical distance scale:
 Basic unit is the Astronomical Unit (AU), defined as the
semimajor axis of Earth’s orbit
How do we measure this?
 Relative distances of planets from sun can be determined
from Kepler’s third law:
2
3
P a
2
 E.g. given Pearth, Pmars:
 PEarth   aEarth 

  

 PMars   aMars 
1AU = 1.49597978994×108 km
3
Parallax
p
d
1 AU
The “parallax” is the apparent shift in position of a nearby star, relative to
background stars, as Earth moves around the Sun in it’s orbit
This defines the unit 1 parsec = 206265 AU = 3.09×1013 km ~ 3.26 light years
Measuring Parallax
The star with the largest parallax is Proxima
Centauri, with p=0.772 arcsec. What is its
distance?
These small angles are very difficult to
measure from the ground; the
atmosphere tends to blur images on scales
of ~1 arcsec. It is possible to measure
parallax angles smaller than this, but only
down to ~0.02 arcsec (corresponding to a
distance of 1/0.02 = 50 pc).
 Until recently, accurate parallaxes were
only available for a few hundred very
nearby stars.
A star field with 1” seeing
Hipparcos
The Hipparcos satellite (launched 1989) collected
parallax data from space, over 3 years
 120,000 stars with 0.001 arcsec precision astrometry
 More than 1 million stars with 0.03 arcsec precision
 The distance limit corresponding to 0.001 arcsec is 1
kpc (1000 pc).
 Since the Earth is ~8 kpc from the Galactic centre it is clear
that this method is only useful for stars in the immediate
solar neighbourhood.
Parallax: summary
1.
2.
3.
4.
A fundamental, geometric measurement of distance
Can be measured directly
Limited to nearby stars
Is used to calibrate other, more indirect distance
indicators. Ultimately even our estimates of
distances to the most remote galaxies rests on a
reliable measure of parallax to the nearest stars
Break
The electromagnetic spectrum
Different filters transmit light of
different wavelengths.
Common astronomy filters are
named:
U B V R I
•
The Earth’s atmosphere blocks
most wavelengths of incident
radiation very effectively. It is
only transparent to visual light
(obviously) and radio wavelengths.
•
Observations at other wavelengths
have to be made from space.
Blackbodies
The energy radiated from a surface element dA is given by:
B (T )d dA cos  d  B (T )d dA cos  sin dd
Units of B(T): W/m2/m/sr
Blackbodies
The energy radiated from a surface element dA is given by:
B (T )d dA cos  d  B (T )d dA cos  sin dd
Units of B(T): W/m2/m/sr
Energy quantization leads to a
prediction for the spectrum of
blackbody radiation:
c
B (T ) 
u (T ) 
4
2hc 2
 hckT 
  e  1


5
Planck’s law
Calculate the luminosity of a spherical blackbody:
 Each surface element dA emits radiation isotropically
 Integrate over sphere (A) and all solid angles ()
L d 
2  / 2
   B d dA cos sin dd
0 0
A
 AB d
Properties of blackbody radiation
1. The wavelength at which
radiation emission from a
blackbody peaks decreases with
increasing temperature, as given
by Wien’s law:
max T  0.290 cm K
2. The total energy emitted (luminosity) by a
blackbody with area A increases with
temperature (Stefan-Boltzmann equation)
This defines the effective temperature of a star
with radius R and luminosity L
L  4R 2Te4
Examples
The sun has a luminosity
L=3.826×1026 W and a radius
R=6.96×108 m. What is the
effective temperature? At what
wavelength is most of the energy
radiated?
max T  0.290 cm K
L  4R 2Te4
Example
Why does the green sun look yellow?
 The human eye does not detect all wavelengths of light
equally
Examples
Spica is one of the hottest stars
in the sky, with an effective
temperature 25400 K. The peak
of its spectrum is therefore at
114 nm, in the far ultraviolet, well
below the limit of human vision.
We can still see it, however,
because it emits some light at
longer wavelengths
max T  0.290 cm K
L  4R 2Te4
Apparent magnitudes
The magnitude system expresses fluxes in a given
waveband X, on a relative, logarithmic scale:
 f 

m X  mref  2.5 log 
f 
 ref 
 Note the negative sign means brighter objects
have lower magnitudes
 Scale is chosen so that a factor 100 in brightness
corresponds to 5 magnitudes (historical)
The magnitude scale
 f 

m X  mref  2.5 log 
f 
 ref 
One common system is to measure relative to Vega
 By definition, Vega has m=0 in all bands. Note this does not mean Vega is
equally bright at all wavelengths!
 Setting mref=0 in the equation above gives:
mX  2.5 log  f   2.5 log  fVega, X 
 2.5 log  f   m0, X
• Colour is defined as the relative flux between two different
wavebands, usually written as a difference in magnitudes
Apparent magnitudes
The faintest (deepest) telescope image
taken so far is the Hubble Ultra-Deep
Field. At m=29, this reaches more than
1 billion times fainter than what we can
see with the naked eye.
 f 

m X  mref  2.5 log 
f 
 ref 
Object
Apparent
mag
Sun
-26.5
Full moon
-12.5
Venus
-4.0
Jupiter
-3.0
Sirius
-1.4
Polaris
2.0
Eye limit
6.0
Pluto
15.0
Reasonable telescope limit (8-m
telescope, 4 hour integration)
28
Deepest image ever taken
(Hubble UDF)
29
10( 296) / 2.5  1046 / 5  109