Classical Stellar Evolution
The Sun – best studied example
Stellar interiors not directly observable
Neutrinos emitted at core and detectable
Helioseismology - vibrations of solar surface can be used to probe density structure
Must construct models of stellar interiors – predictions of these models are tested
by comparison with observed properties of individual stars
Observable properties of stars
Basic parameters to compare theory and observations:
• Mass (M)
• Luminosity (L)
– The total energy radiated per second i.e. power (in W)
𝐿 = න
0
∞
𝐿 𝜆 𝑑𝜆
• Radius (R)
• Effective temperature (Teff)
– The temperature of a black body of the same radius as
the star that would radiate the same amount of energy
L = 4 R2  Teff
 3 independent quantities
Basic definitions
Measured energy flux depends on distance to star
(inverse square law)
𝐹 =
𝐿
4𝜋𝑑2
Hence if d is known then L determined
We can determine distance if we measure parallax
Classical astrometric approach
Now: Gaia
Stellar radii
Angular diameter of sun at distance of 10 pc:
 = 2R/10 pc = 5 10-9 radians = 10-3 arcsec
Compare with Hubble resolution of ~0.05 arcsec
 very difficult to measure R directly
Radii of stars measured with techniques such as
interferometry and eclipsing binaries
JMMC Stellar Diameters Catalogue - JSDC. Version 2:
about 470 000 stars, median error of the diameters is
around 1.5%
Stellar radii
The Hertzsprung - Russell diagram
M, R, L and Teff do not vary
independently
Two major relationships
– L with Teff
– L with M
The first is known as the
Hertzsprung-Russell (HR)
diagram or the
colour-magnitude diagram
Colour and Teff
• Measuring accurate Teff for stars is an intensive task – spectra
needed and model atmospheres
• Magnitudes of stars are measured at different wavelengths
• Colours => Calibration => Teff
• The Asiago Database on Photometric Systems (ADPS) lists
about 200 different systems
Colour and Teff
Various calibrations can be
used to provide the colour
relation:
(B – V) = f(Teff)
Remember that observed
(B - V) must be corrected for
interstellar extinction to
(B - V)0
Absorption = Extinction = Reddening
• AV = k1 E(B-V) = k2 E(V-R) = …
• General extinction because of the ISM characteristics
between the observer and the object
• Differential extinction within one star cluster because
of local environment
• Both types are, in general wavelength dependent
Reasons for the interstellar extinction
• Light scatter at the interstellar dust
• Light absorption => Heating of the ISM
• Depending on the composition and density of the
ISM
• Main contribution due to dust
• Simulations and calculations in Cardelli et al. (1989,
ApJ, 345, 245)
Cardelli et al., 1989, ApJ, 345, 245
Important parameter:
RV = AV/E(B - V)
Normalization factor
Standard value used
is 3.1
Be careful, different
values used!
Depending on the
line of sight
Absolute magnitude and bolometric
magnitude
• Absolute Magnitude M defined as apparent magnitude of a
star if it were placed at a distance of 10 pc
m – M = 5 log(d/10) - 5
where d is in pc
• Magnitudes are measured in some wavelength. To compare
with theory it is more useful to determine bolometric
magnitude Mbol – defined as absolute magnitude that would
be measured by a bolometer sensitive to all wavelengths. We
define the bolometric correction to be
BC = Mbol – MV
Bolometric luminosity is then
Mbol – Mbol, = -2.5 log L/L
Bolometric Correction
BC from Flower, 1996, ApJ, 469, 355
Bolometric Correction
The Hertzsprung - Russell diagram - Gaia
The Hertzsprung - Russell diagram - Gaia
H and He-rich cores
of White Dwarfs
Masses measured in binary systems
Heuristic mass-luminosity relation
L  Ma
Where a = 2 – 5; slope less steep for low and
high mass stars
This implies that the main-sequence (MS) on the
HRD is a function of mass, i.e. from bottom to
top of MS, stars increase in mass
Mass – Luminosity Relation
The lifetime on the Main-Sequene