Straling

Reynier PeletierKapteyn Astronomical Institute

Groningen

Blackbody Radiation(thermal radiation):

Converting this to the intensity as a function of frequency:

For low frequencies ( ), we have:

Here h is the constant of Planckand k the constant of Boltzmann

h ν ≪ kT

(Rayleigh-Jeans law = the classical approximation)

Blackbody Radiation:

Hotter B.B. emitters “emit” more total radiation per unit area.However, a big cold object can emit the same or more energy (depending

on how big it is) than a small, hotter one

Cold Hot

Integrating the radiation of a blackbody gives: Stefan-Boltzmann Law: Emitted power per square meter = σ T4

σ = 5.7 x 10-8 W/(m2K4)

Total emitted power: E = 4 R2 σ T4

Two Laws of Black Body Radiation

2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases.

Wien’s displacement law:

max ≈ 3,000,000 nm / TK

(where TK is the temperature in Kelvin).

1. The hotter an object is, the more luminous it is.

The Color Index (I)B band

V bandThe color of a star is measured by

comparing its brightness in two different wavelength bands:

The blue (B) band and the visual (V) band.

We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter

star).

The Color Index (II)

We define the Color Index

B – V(i.e., B magnitude – V magnitude)

The bluer a star appears, the smaller the color index B – V.

The hotter a star is, the smaller its color index B – V.

Stars come in different colors

Color and Temperature

Orion

Betelgeuse

Rigel

Stars appear in different colors,

from blue (like Rigel)

via green / yellow (like our sun)

to red (like Betelgeuse).

If the spectra of stars are black bodies, then these colors tell us about the star’s temperature.

M 51 – HST ACSDistance: 8 Mpc

A Galaxy: Messier 51

In spiral arm

Between spiral arms

M 330.9 Mpc

M33 -Distance 700 kpc

Near a spiral arm

NGC 2050.8 Mpc

NGC 205

The Andromeda Galaxy (M31) with its 2 satellites

M 32

NGC 205

M 32

NGC 89110 Mpc

NGC 891

NGC 891 – thick disk

M51 - In spiral arm

Baade (1944)'s stellar population paradigm:

- Population I is a stellar population similar to the population of stars in the solar neighbourhood, with bright red and blue stars

- Population II is a stellar population similar to stars in globular clusters, where the brightest stars are red.

POP II

POP I

What do we know about colours of stars?

The HR (Hertzsprung-Russell) diagram

B - V

Lum.

Stars populate distinct regions of this plane, corresponding to a particular evolutionary phase.

Terminology:

HRD is “theory” plane: temp. vs. bolometricluminosity.CMD (colour-magnitudediagram) is its emipiricalanalogue.

Stellar Evolutionary Phases

Main Sequence (MS)

Core Hydrogen burning. Longest phase.

Red Giant Branch (RGB)

Hydrogen burning in shell around He core. He core is growing.

When He core is massive and hot enough, it will ignite, starting He-burning (He-flash).

Stellar Evolutionary Phases

Horizontal Branch (HB)

Core He burning. Position stronglymetallicity-dependent.

Asymptotic Giant Branch (AGB)

He-burning in shell around inert CNO core (+ H-burning). Evolution dependenton mass-loss. Pulsating phase.

White Dwarf Sequence (WD)

Remains of the star after envelopehas been ejected (low-mass stars)

Tracks & Isochrones

Tracks:

trajectories of individual stars in the HRD.

Depend on initial mass.

Examples:

BaSTIPadovaGenevaYonsei-Yale

Tracks & Isochrones

Isochrones:

Loci on the HRD populated by stars of the same age, butwith different masses.

(Padova example, Marigo)

Tracks & Isochrones

Isochrone comparison – Bertelli (Padova) vs. BaSTI

Globular Clusters

De-populated upper MS. Strong RGB and HB.

1,000s to 100,000s of stars.

Open Clusters

Open cluster: MS dominant, few RGB or other evolved stars. Only few 100s or 1000s of stars.

Globular cluster: de-populatedMain Sequence, Strong HB and RGB.1000s to 1.000.000s of stars.

Spectra

Encoded in an object’s spectrumis information about the emitter/absorber. This is how we learn what the Universeis made of!

Kirchhoff’s Laws of Radiation (I)

1. A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum.

Kirchhoff’s Laws of Radiation (II)2. If light comprising a continuous spectrum passes

through a cool, low-density gas, the result will be an absorption spectrum.

Light excites electrons in atoms to higher energy states

Frequencies corresponding to the transition energies are absorbed from

the continuous spectrum.

Kirchhoff’s Laws of Radiation (III)3. A low-density gas excited to emit light will do so at

specific wavelengths and thus produce an emission spectrum.

Light excites electrons in atoms to higher energy states

Transition back to lower states emits light at specific frequencies

The Spectra of StarsInner, dense layers of a star produce a continuous (black

body) spectrum.

Cooler surface layers absorb light at specific frequencies.

=> Spectra of stars are absorption spectra.

Most prominent lines in many astronomical

objects: Balmer lines of hydrogen

Lines of Hydrogen

The Balmer Lines

n = 1

n = 2

n = 4

n = 5n = 3

H H H

The only hydrogen lines in the visible wavelength range.

Transitions from 2nd to higher levels of hydrogen

2nd to 3rd level = H (Balmer alpha line)2nd to 4th level = H (Balmer beta line)

…

Absorption spectrum dominated by Balmer lines

Modern spectra are usually recorded digitally and represented as plots of

intensity vs. wavelength

Emission nebula, dominated by the red H line.

The Balmer Thermometer

Balmer line strength is sensitive to temperature:

Measuring the Temperatures of Stars

Comparing line strengths, we can measure a star’s surface temperature!

Spectral Classification of Stars (I)

Tem

pera

ture

Different types of stars show different characteristic sets of absorption lines.

The Spectrum of a star (the Sun)

There are similar absorption lines in the other regions of the electromagnetic spectrum. Each line exactly corresponds to chemical elements in the stars.

The spectrum of a star is most determined by

1. The temperature of the star’s surface

2. The star’s distance from Earth

3. The density of the star’s core

4. The luminosity of the star

Spectral type• Sequence is: O B A F G K M• O type is hottest (~25,000K), M type is coolest (~2500K)• Star Colors: O blue to M red• Sequence subdivided by attaching one numerical digit,

for example: F0, F1, F2, F3 … F9 where F1 is hotter than F3 . Sequence is O … O9, B0, B1, …, B9, A0, A1, … A9, F0, …

• Useful mnemonics to remember OBAFGKM:– Our Best Astronomers Feel Good Knowing More– Oh Boy, An F Grade Kills Me– (Traditional) Oh, Be a Fine Girl (or Guy), Kiss Me

Spectral Classification of Stars (II)

Oh Oh Only

Be Boy, Bad

A An Astronomers

Fine F Forget

Girl/Guy Grade Generally

Kiss Kills Known

Me Me Mnemonics

Mnemonics to remember the spectral sequence:

Stellar spectra

OB

A

F

G

KM

Surface tem

pera ture

The Composition of StarsFrom the relative strength of absorption lines (carefully

accounting for their temperature dependence), one can infer the composition of stars.

Examples of the use of colours in stars and galaxies

1. Multiple main sequences

2. Star formation histories of Local Group dwarf galaxies

3. Galaxies at various wavelengths

4. Redshifts of galaxies

1. Multiple main sequences

Multiple main sequencesMilone et al. (2007)

Multiple main sequence in NGC 2808, Omega Cen, and a double SGB in NGC 1851 (Mackey & Broby Nielsen) impliesthat globular clusters don't have single age/metallicities!

NGC2808 Piotto et al. (2007)

2. Star formation histories of Local Group dwarf galaxies

Determining Star Formation Histories of

Local Group dwarfs

Mateo et al. 1998

Determining Star Formation Histories of Local Group dwarfs

Tucana – Gallart (part of LCID project)

All work based on Hubble Space Telescope data

Draco (from Dolphin 2005)

Some examples:

M32

NGC 147

Charts from Dolphin 2005

The Magellanic Clouds

LMC SMC

SMC

dIrr SFHs – Summary

All dIrrs have an old population. Continuous star formation over

the entire lifetime of the galaxy. Recent star formation often

dominates. No two histories look the same. Different regions can have

different star formation histories (Hodge et al 1991).

3. Galaxies at various wavelengths

4. Redshifts of galaxies

The Doppler Effect: stars/galaxies that move away from us become redder.

Galaxies

What happens to colors of redshifted galaxies?

HUDF–JD2 (z=6.5) (Mobasher et al. 2005)

i > 30.88 z > 30.26

B > 30.61V > 31.02

HST/ACS

VLT/ISAAC

SST/IRAC

Example of a very redshifted object

0.45 0.55 0.70 0.90

2.101.601.20

JD2 (J-dropout) in HUDF (z=6.5)