Preliminaries Part II. Stars

The radiation from stars is approximately thermal (black-body).

F = �T 4 = 4�R2 L

The effective temperature, Teff, of a star is the temperature of a blackbody of some radius that emits the measured luminosity:

Te� =�

L4��R2

�1/4

The effective temperature also determines the ionization and excitation states of elements in stellar atmospheres. Gives rise to spectral differences versus effective temperature.

Stars have a range of Metallicity, approximately just mean heavy element abundance, Z, relative to solar (X+Y+Z=1).

Approximate by Fe abundance:

[Fe/H] = log10(NFe/NH)� log10(NFe/NH)�

Stars with [Fe/H] > 0 have a higher metal fraction than the Sun. Stars with [Fe/H] < 0 have a lower metal fraction.

Tuesday, August 7, 12

Spectral Lines

StellarClassification

Spectral Classification of Stars

Spectral Type Characteristics

O Hottest blue-white stars, few lines. Strong He II (He+) absorption lines. He I (neutral helium) stronger).

B Hot blue-white. He I (neutral Helium), strongest at B2. H I (neutral Hydrogen) stronger.

A White stars. Balmer absorption lines strongest at A0 (Vega), weaker in later-type A stars. Strong Ca II (Ca+) lines.

F Yellow-white stars. Ca II lines strengthen to later types. F-stars. Balmer lines strengthen to earlier type F-stars.

G Yellow stars (Sun is a G5 star). Ca II lines become stronger. Fe I (neutral iron) lines become strong.

K Cool orange stars. Ca II (H and K) lines strongest at K0, becoming weaker in later stars. Spectra dominated by metal absorption lines.

M Cool red stars. Spectra dominated by molecular absorption bands, e.g., TiO (titanium oxide). Neutral metal lines strong.

LVery cool, dark red (brown dwarfs). Brighter in Infrared than

visible. Strong molecular absorption bands, e.g., CrH, FeH, water, CO. TiO weakening.

T Coolest stars. Strong methane (CH4), weakening CO bands.

Hotter

Cooler

Henry Norris Russell’s first diagram

Hertzsprung-Russell

Diagram

Enormous Range in Stellar Radii.

Hypothesis that stars cool over time as they contract, there should be a relation between their temperatures and luminosities.

R = L1

T2 4πσ√Hertzsprung (1873-1967) found that stars of Late type (G and later)

have a large range in luminosity. If two stars of the same spectral type (same Temperature) then more luminous star is larger.

Giants: Stars with big radii & Dwarfs: Stars with small radii.

Our Sun is a G2 star dwarf.

Spectral Classification of StarsStars with much larger radii for their mass have lower

surface gravity, g.

Giants and supergiant stars have very large, R, and thus, lower surface gravity. Can measure this from line broadening in spectra.

But, because L ~ R2 T4, supergiants have very large luminosities.

This leads to Luminosity Classes of stars (depends on metallicity).

Class I = SupergiantsClass II = bright Giants

Class III = GiantsClass IV = sub-Giants

Class V = dwarfs (main sequence stars)Class VI = sub-dwarfs

Our Sun is a therefore a G2V star.

g = GMR

Spectral Classification of StarsHertzsprung-Russell Diagram

Temperature: Hotter

Brighter

TextHR diagram where data points

show measurements from 22,000 real stars from the

Hipparcos satellite.

30,000 K 10,000 K 7500 K 6000 K 5000 K 4000 K 3000 K

(Lines are Theoretical, expected luminosities and

temperatures of stars)

Color Index: B-V

Spectral Classification of StarsMass-Luminosity relation

LL��

�3.5

Nuclear Fusion releases energy. It converts mass into energy. Recall Relativity, E=mc2. 1 u = 931.494013 MeV/c2.

Note that the mass of hydrogen in the ground state, mH = 1.00782503214 u. This says that mH < mp + me = 1.00783. The difference is actually -13.6 eV.

The Sun is fusing He from H. A He-4 nucleus has a mass of 4.0026 u.

4 Hydrogen atoms have a mass of 4.0313 u.

Δm = 0.028697 u, or 0.7% of the total energy.

This is an energy of E=Δmc2 = 26.731 MeV. This is the binding energy of a He-4 nucleus. To break apart a He-4 nucleus takes this much energy.

Stellar Radiation Powered by Nuclear Fusion

Preliminaries Part II. Stellar Evolution

Example: How much nuclear energy is available in the Sun.

Assume the Sun was 100% Hydrogen initially and that only 10% of the inner mass is involved in fusion (gas in the nucleus of the Sun).

0.7% of the hydrogen mass is converted to energy, so :

Enuclear = 0.1 x 0.007 x M c2

t = ΔEnuclear / L⊙ ≈ 1010 yr.

For the sun, we can calculate a timescale for Hydrogen burning by:

Stellar Radiation Powered by Nuclear Fusion

Preliminaries Part II. Stellar Evolution

But, note that ΔEnuclear ~ M. And L ~ M3.5.

Therefore, t ~ M / M3.5 ~ M-2.5.

Hydrogen burning lifetime for stars is strongly dependent on Mass.

Log Teff [K]

Log L [L⊙]

Preliminaries Part II.Stellar Evolution

Shaded regions mark phases in which evolution proceeds slowly.

Therefore, most stars are found in these areas.

Preliminaries. Stellar Abundances.

Now define mass fraction, the fractional abundance (by mass) of an element. Fraction of hydrogen is X. Fraction of Helium is Y, Fraction of everything else is Z.

X = (total mass of H) / (total Mass)

Y = (total mass of He) / (total Mass)

Z = (total mass of Li through Uuo) / (total Mass) = Metallicity.

And X + Y + Z = 1

For the Sun, X=0.70, Y=0.28, and Z=0.02

For the Big Bang Composition, X=0.77, Y=0.23, and Z=0.001

Most Abundant Elements in the Solar Photosphere.

Element Atomic # Log Relative Abundance

H 1 12.00

He 2 10.93 ± 0.004

O 8 8.83 ± 0.06

C 6 8.52 ± 0.06

Ne 10 8.08 ± 0.06

N 7 7.92 ± 0.06

Mg 12 7.58 ± 0.05

Si 14 7.55 ± 0.05

Fe 26 7.50 ± 0.05

S 16 7.33 ± 0.11

Al 13 6.47 ± 0.07

Ar 18 6.40 ± 0.06

Ca 20 6.36 ± 0.02

Ng 11 6.33 ± 0.03

Ni 28 6.25 ± 0.04

Most abundant cosmic elements are H, He, O, C, Ne, N, Mg, Si, Fe. True for

cosmos and the Sun.

Preliminaries. Stellar Abundances.

Abudance of X is X = Log10(NX/NH) + 12

M13 Globular Cluster

Star Clusters

M13 Globular ClusterHST IMAGE

The Pleiades, Galactic ClusterTuesday, August 7, 12

Stars of early spectral types only found for young stellar populations

O B A F G K M

Log t [yr]

Spectral Type

Allowed area

(No Data)

Stars Evolved Away

Star Clusters

Because Star Clusters were formed all at once, they give us a way of seeing “snapshots” of stellar evolution. All the stars have (very, very nearly) the same distance modulus, so we only need their apparent magnitudes.

Color-magnitude diagram of M3, an old globular cluster.

From Renzini & Pecci, 1988, ARAA, 26, 199

Star Clusters

Color-magnitude diagram for NGC 2362, a very young open cluster. Shows Main sequence and pre-main sequence stars (on left).

main sequence

pre-main sequence

Moitinho et al. 2001, ApJ, 563, L73

We can construct theoretical HR (color-magnitude) diagrams for stellar populations as a function of the cluster age. The model for a fixed time is

an isochrone. This lets us determine the age of the star cluster and study stellar evolution (are our models correct ?!)

Age (yrs) at M

ain Sequence turnoff

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

Log Temperature [K]

2.6 M⊙

1.0 M⊙

0.7 M⊙

We can construct theoretical HR (color-magnitude) diagrams for stellar populations as a function of the cluster age. The model for a fixed time is an isochrone. This lets us determine the age of the star cluster and study stellar evolution (are our models correct ?!)

Kalirai et al. 2001, AJ, 122, 266

Color-Magnitude Diagram for NGC 6819

Models are for ages of t= 2, 2.5, 3.2, 4, 5 x 109 yrs.

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