Download The colour-magnitude diagram

Starlight
• The electromagnetic spectrum
• Characteristics of stars
• The HR diagram
The electromagnetic spectrum
1663: Newton buys an astrology book and a glass prism at Sturbridge
fair
1666: in Woolsthorpe family manor, Newton discovers that the prism
decomposes solar light in the same colors as the rainbow
→ shows that white light is composed of different colors
He postulates that each
monochromatic radiation is composed
of particles → photons
That hypothesis will be abandoned
until the 20th Century, with the
discovery that light presents both
wave and particle aspects
The electromagnetic spectrum - 2
Invisible light
Around 1800, Herschel discovers infrared radiation and Ritter
ultraviolet radiation
Scientists progressively realize that visible radiation represents only a
tiny part of the electromagnetic spectrum, corresponding to
freaquencies detected by the human eye
The visible part of the spectrum
corresponds to:
• maximum of solar emission
• excellent transparency of Earth
atmosphere
→ natural selection (Darwin)
Herschel
Ritter
The electromagnetic spectrum - 3
Spectral domains
Historical – also correspond to different processes
Frequency ν – wavelength λ:
  c /
Velocity of light: c = 3 × 108 m/s
Energy:
E  h
Planck constant: h = 6.63 × 10−34 J·s
The electromagnetic spectrum - 4
The black body (1)
Perfectly absorbing body → only radiation emitted by the objet,
because of its temperature, is detected (no reflexion)
Hotter body → emission peak λmax at higher frequency
Wien’s displacement law:
max
C

T
C ≈ 3 × 10−3 m·K ≈ 3000 μm·K
Examples:
Sun: T ≈ 5800 K → λmax ≈ 0.5 μm
Earth: T ≈ 300 K → λmax ≈ 10 μm
The electromagnetic spectrum - 5
The black body (2)
Stefan-Boltzmann’s law:
Total flux = total energy emitted per unit surface and time
Ftot   T 4
Stefan’s constant: σ ≈ 5.7 × 10−8 W·m−2K−4
Planck’s law:
Emitted flux per unit frequency:
2πh 3
1
F (T ) 
c 2 e h kT  1
Jozef Stefan
The electromagnetic spectrum - 6
The black body (3)
Planck’s law:
Emitted flux per unit wavelength:
F (T ) 
2πhc 2
1
5
e hc kT  1
Or:
F (T ) 
c1 ≈ 3.7 × 10−16 J·m2s−2
Conservation of energy
c1
1
5 e c
2
T
1
c2 ≈ 0.0144 m·K
→
F d  F d
Max Planck
The electromagnetic spectrum - 7
Types of spectra
Light bulb → continuum spectrum
Hot gas → emission lines (1)
Cool gas in front of light bulb → continuum + absorption lines (2)
E
e–
(1)
(2)
e–
Characteristics of stars
Stellar spectra
Generally: continuum + absorption lines
Stellar interior very hot and opaque
→ continuum spectrum
Outer layers more transparent and cooler
→ absorption lines
Remark:
Astronomers often measure
wavelength in Angström (Å)
1 Å = 10−10 m = 0.1 nm
Characteristics of stars - 2
Spectral types
Classification according to spectrum (ex : strangth of hydrogen lines)
→ O B A F G K M sequence (Oh be a fine girl kiss me…)
Characteristics of stars - 3
Appearance of stellar spectra
Spectrum appearance depends on gas properties:
• temperature
• pressure
• chemical composition
Temperature is the dominant factor
→ spectral types correspond to a classification according to
température of outer layers (stellar atmosphere)
Remarks: • stellar is not a precisely defined concept as gas pressure
gradually increases with depth
• spectral types are divided into sub-types (0 to 9) → ex: A0, G2
Characteristics of stars - 4
Effective temperature
Surface température is not a well defined concept
→ one introduces effective temperature Teff
Teff = temperature of a black body emitting the same flux as the star
Teff
 Ftot 
 




1
4
Bolometric luminosity
Lbol = total energy emitted by unit of time (power)
Lbol  4πR 2 Ftot  4πR 2Teff4
(R = radius of the star)
Characteristics of stars - 5
Influence of distance
Radiation emitted by the star is spread over a sphere of radius R
If d is the distance between the star and the observer, the same energy
is spread over a sphere of radius d (→ surface 4πd 2)
Conservation of energy → geometrical dilution:
R
d
R2
Frec  2 Fem
d
Characteristics of stars - 6
Distance to stars
Distances of nearby stars can be obtained by triangulation
Motion of Earth around the Sun allows to measure parallax
In the course of a year, a nearby star seems to move with respect to
background stars along an ellipse of semi major axis:
  arctga d   a d
1 parsec = distance of a star whose parallax θ = 1″
1 parsec (pc) = 1 UA × nr of seconds / radian
1 pc = 206265 UA ≈ 3.26 light-years (L.Y.)
≈ 3×
1016
m
d
θ
a
Characteristics of stars - 7
Stars in the solar neighborhood
Larger parallaxes
< 1″
→ d > 1 pc
117 stars known at
less than 20 L.Y.
(in 2006)
Mean distance
1
R  3
20
117
d  2 R  8A.L.
3D sketch of solar neighborhood
Characteristics of stars - 8
Nearest stars
The 117 stars at less than 20 L.Y., by spectral type:
O
B
A
F
G
K
M
br.dw. w.dw.
0
0
2
1
6
16
78
8
6
Our nearest neighbors:
The Sun
(G2)
8 light-minutes
Proxima Centauri
(K5)
4.2 L.Y.
Alpha Centauri A
(G2)
4.4 L.Y.
Alpha Centauri B
(K0)
4.4 L.Y.
Barnard star
(M5)
5.9 L.Y.
Characteristics of stars - 9
Magnitudes
Hipparcos classified the naked-eye stars according to their apparent
brightness, from 1st magnitude – brightest ones – to 6th – faintest ones
Eye sensitivity follows a logarithmic law
To stick as much as possible to Hipparcos system, astronomers defined
the apparent magnitude of a star:
m  2.5 log Frec  C te
Sirius :
m = –1.5
Vega :
m = 0.0
Canopus :
m = –0.7
Capella :
m = 0.0
Arcturus :
m = –0.1
Rigel :
m = 0.1
Characteristics of stars – 10
Absolute magnitude and distance modulus
Apparent magnitude is not an intrinsic property of a star as it depends
on its distance
 R2

m  2.5 log  2 Fem   C t
d

 m  5 log d  5 log R  2.5 log Fem  C t
R is generally unknown → one defines absolute magnitude M
M = apparent magnitude the star would have at a distance of 10 pc
 M  5  5 log R  2.5 log Fem  C t
Distance modulus:
M  m  5  5 log d
Characteristics of stars – 11
Photometry
In modern astronomy, on always observe through filters which
transmit only part of the electromagnetic spectrum
→ measurement of flux received in a given spectral band
→ the choice of filters determine the photometric system
→ a magnitude is always given
with reference to a filter
Ex : mB, mV, MB, MV,…
The additive constant Ct is
fixed with reference to
standard stars
ex: mi(Vega) = 0 in all filters
Transmission curves of UBVRI filters
Characteristics of stars – 12
Colours
To quantify the colour of a star (or another celestial body), colour
indices are defined
Ex: mB–mV = MB–MV independent of distance as geometric dilution
does not depend on wavelength
Colour indices are written B–V,
V–R, etc…
Remark: they are intrinsic
properties of stars if nothing
modifies the spectrum in
between source and observer
(ex: absorption by dust)
Transmission curves of UBVRI filters
Characteristics of stars – 13
Spectral types and colours
Different effective temperatures correspond to:
• different spectral types
• different colours
B–V
1.5
→ relation between spectral
type and colour of a star
• approximative since both
depend on other parametersf
(ex. pressure and chemical
composition)
1.0
0.5
0.0
O
B
A F G K M
Spectral type
The HR diagram
Around 1910, Ejnar Hertzsprung and Henry Norris Russell plot stars
in an `absolute magnitude – spectral type´ diagram
They realize that stars do not
appear at random but into specific
areas:
• most stars are located along the
main sequence
• a minority appear in the red
giant area
• a few are located in the white
dwarf region
MV
−5
red
giants
0
+5
white
dwarfs
+10
O
B
A F G K M
Spectral type
The HR diagram - 2
The theoretical HR diagram
absolute magnitude ↔ luminosity in spectral band considered


M V  2.5 log 4πR 2 FV  C t  2.5 log LV  C t
M bol  2.5 log Lbol  C t
spectral type ↔ effective temperature
log Lbol
→ theoreticians use a theoretical HR
diagram in which bolometric luminosity
is plotted as a function of effective
temperature
(in logarithmic scale)
log Teff
The HR diagram - 3
Influence of radius
Lbol  4πR 2σTeff4
 log Lbol  2 log R  4 log Teff  C t
→ straight lines of constant radius in HR diagram
• stars located to the upper right of
the main sequence are giants and
supergiants
• main sequence stars are generally
called dwarfs
• stars located below the main
sequence are subdwarfs and white
dwarfs
log (L/L )
+4
100R
+2
10R
0
R
−2
1.0
0.5
0.0
log (Teff /Teff, )
The HR diagram - 4
Luminosity classes
Beside spectral types, luminosity classes have been introduced
For a givan Teff, a ≠ luminosity corresponds to a ≠ radius
Classes :
I, II : supergiants
III : giants
IV : subgiants
V : dwarfs
Ex :
Sun: G2V
Canopus: F0II
The HR diagram - 5
The colour-magnitude diagram
If stars belong to a same cluster
→ they are approximately at the same distance
→ we can use apparent magnitude instead of absolute magnitude
A colour index is often use to measure Teff
(more easily obtained than a spectrum)
V
→ the observational HR diagram is often a
colour-magnitude diagram
V−R
E.H.N.
Hertzsprung
Russell
The HR diagram - 6
Colour-magnitude diagram of a globular cluster
Very useful tool to study
stellar evolution
Sample of stars at:
• same distance
• same age
• same chemical
composition
• different masses
→ study stellar evolution
Colour-magnitude diagram of M13 cluster
The HR diagram - 7
Colour-magnitude
diagram of nearby stars
Parallaxes determined by
Hipparcos satellite (most
accurate to date)
• majority of dwarfs (on main
sequence)
• minority of giants
• a few subdwarfs
• a few white dwarfs
c-m diagram of nearby stars