The Stars and the Sun I. Colors of stars

The Stars and the Sun I.Colors of stars

http://www.phy.cuhk.edu.hk/gee/mctalks/mcpdp.html

Chu Ming-chung 朱明中

Department of Physics

The Chinese University of Hong Kong

[email protected]

M37

Capella 五車二

Binary stars in Cygnus

M20

M42

M8M57All taken in CUHK

What information are carried in star light?

Colors of Stars

1.1 Starlight1.2* Light-matter interaction1.3* Stellar spectrum1.4 Doppler effect1.5 Stellar luminosity1.6 H-R Diagram 1.7 H-R Diagrams for star clusters

1.1 Starlight What is light?

When the velocities of moving charged

particles are changed, electromagnetic

radiation (EM radiation) 電磁輻射 (light

is a kind of EM radiation) is emitted in the

form of waves ( EM waves 電磁波 ).

Thermal motion of particles in a star → light

+

+

http://www.colorado.edu/physics/2000/applets/fieldwaves.html

Different bands of EM waves

3,000oC6,000oC Higher temperature

Why do hot materials give out light?

What happens if temperature rises further?

Charged particles in a hot gas (e.g. inside a star) move

around rapidly and undergo many collisions

their velocities are changed in the collisions

light (EM waves in general) is emitted

Why are the colors of light different for different

temperature?

Violent collisions high-energy light (short wavelength,

high frequency, e.g. violetviolet)

Gentle collisions low-energy light (long wavelength, low

frequency, e.g. redred)

In a star, the temperature is very high, both violent and gentle collisions occur it gives out electromagnetic radiation of all

wavelengths

starlight can be decomposed into a continuous spectrum 連續光譜 (like a rainbow)

Spectrum 光譜 : decomposing light into different colors

Red: lower frequency, longer wavelength

blue: higher frequency, shorter wavelength

Sun’s spectrum

As temperature rises: 1. light intensity increases, 2. the color of light shifts towards high frequency (blue) side

Blue stars are hotter than red stars

1)exp(

125

2

kThc

hcI

= Energy of EM wave with wavelength per unit time per unit area emitted by a body at T. Boltzmanns constant Plancks constant

Intensity peak (Wien’s law)Blue stars are hotter than red stars (higher surface T)

Planck’s distribution

-123 JK1038.1 kJs1063.6 34h

mK109.2 3max

T

for blackbody radiations 黑體輻射

Just for reference!

Cooler stars are dimmer and redderTotal radiation power for all ’s = = energy per unit time per unit

area emitted by a body at temperature TStefan-Boltzmanns const.

Luminosity of a blackbody sphere

Color:

4

0TdI

-4-283245 KWm1067.5152 hck

424 TRL

max 1/T

‘colors’ emitted by different ‘stars’. Eg. Sun’s radiation peaks at ~ 0.5 microns

You emit light too! What ‘color’ is the light you emitted?

Ans.: Body temperature ~ 300 K ~ 1/20 Sun’s surface temperature. Therefore, human’s radiation peaks at 20x 0.5=10 microns.

Spectral classification ( 光譜分類 )

spectral classes Approximate surface

temperature (K) O 40,000 B 20,000 A 10,000 F 7,500 G 5,500 K 4,500 M 3,000

Eg.: Sun: G Vega ( 織女星 ): A

OOh! BBe AA FFine GGirl (Guy)! KKiss MMe!

Group stars with similar spectra (temperature, elements) into same classes.

M20

M42

M8M57

All taken in CUHKWhat information are carried in star light?http://apod.nasa.gov/apod/ap010729.html

http://www.spitzer.caltech.edu/Media/releases/ssc2005-09/ssc2005-09b.shtmlIllustration courtesy NASA/Spitzer Infrared Space Telescope

Use infrared telescopes to detect planets directly – 2 found already so far!

Examples of using non-visible light

http://www.spitzer.caltech.edu/Media/releases/ssc2005-09/ssc2005-09b.shtmlIllustration courtesy NASA/Spitzer Infrared Space Telescope

Planetary Eclipses in Infrared

http://www.spitzer.caltech.edu/Media/releases/ssc2005-10/ssc2005-10b.shtmlIllustration courtesy NASA/Spitzer Space Telescope

Found even asteroid belt around HD 69830 using Infrared telescope


Positron Clouds near the galactic center

How do we know there are positrons ？


2 ,

511 keV.

e e

E

Gamma ray telescope

1.2* Light-matter interaction

http://www.colorado.edu/physics/2000/index.pl

Bohr’s model of atomsElectrons have wave properties (de Broglie)de Broglie wavelength Bohr: circular orbits

only standing wave orbits are stable

Only discrete energies allowed radius ＝ n²ao ao= 5x10-11 m Bohr’s radius

/h p

2n r 2 2 2/ /mv r e r

21 /nE E n

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html

E1 →E2E1 →E3

E1 →E4

E1

E2

E3

E4Hydrogen atom:En= -13.6eV/n²Transitions: emission or absorption of light at specific energiesAbsorption spectrum

吸收光譜

Different elements emit different spectral lines

Emission spectrum 放射光譜

E2 →E1E3 →E1

E4 →E1 E1

E2

E3

E4

http://www.colorado.edu/physics/2000/index.pl

1.3* Stellar Spectrum

Light source emitting a continuous spectrum

Atoms in the atmosphere absorb light of particular frequencies

Dark linesAbsorption spectrum 吸收光譜

Grating and CCD C11 + spectrograph + CCD

Stellar Spectrum

Photos taken by Lee Wing Kit and Chan Wing Hang

Stellar atmosphere colder than interior

Stellar light absorbed

selectively by atoms in

stellar atmosphere

http://apwww.smu.ca/~ishort/Astro/

Spectrum of Vega 織女星

Photos taken by Lee Wing Kit and Chan Wing Hang in CUHK

Hydrogen Alpha line (6563Å)All are H lines !!

1Å=10-10m

red

H lines

violet

Spectrum of Sirius 天狼星光譜

Both are Type A Stars

Compared with Vega’s Violet

RED

紅


Spectral Class 恆星光譜型Type Color

Surface Temperature

O Blue > 25,000 K

B Blue 11,000 - 25,000

A Blue 7,500 - 11,000

F Blue/White 6,000 - 7,500

G White/Yellow 5,000 - 6,000

K Orange/Red 3,500 - 5,000

M Red < 3,500

Spectrum of Betelgeuse 參宿四光譜violet

Hydrogen Alpha line (6563Å) No H lines??

red

A typical Type M star (Red Giants)

Metal lines TiO


Orion 獵戶座

參宿四 Betelgeuse

獵戶座大星雲 Orion Nebula


Spectrum of Orion Nebula

emission spectrum

H lines

What are these?~ 5890Å

violetred


O2+ (Earth’s atmosphere)

4959Å, 5007Å

violet

red

Light pollution!!

Street lamp (sodium)


Spectra of Planets 金星 Venus

red

violet

土星 Saturn

Why are they so similar?

H

different


Atmospheric Absorption大角 Aldebaran

心宿二 Antares

參宿四Betelgeuse

天狼 Sirius

織女 Vega

金星 Venus

土星 Saturn

七姊妹星團Pleiades

獵戶座大星雲

Telluric Lines H HPhotos taken by Lee Wing Kit and Chan Wing Hang

Absorption lines => elementsIntensity peak position => surface temperatureStrengths of absorption lines => also surface

temperature Hydrogen as an example: Very high temperatures

=> electrons leave the atoms (ionized) ; low temperatures, electrons stay at the ground state.

Low High Very High

Measure the absorption line intensities of Balmer lines ( 巴耳末線 ) [electrons transit from the 2nd level to higher levels]

We can know the number of atoms in which the electrons are at the 2nd level

Hence get an estimate of the surface temperature

2nd level

Intensities depend on the number of electrons at the 2nd level

Taken from NOAO/AURA/NSF webpage http://www.noao.edu/image_gallery/html/im0649.html

Spectrum of Sun

Transit method: observe the planetary transit →small periodic dimming of star light, new absorption lines →elements in the planetary atmosphere

Photo and animation courtesy NASA/STScI

Eg. HD209458: Na detected in planetary atmosphere

Examples of Spectral Method

1.4 Doppler effect ( 多普勒效應 )

v=0 v=0.4 v=1

stationary source

moving source

moving source

http://www.tmeg.com/esp/p_doppler/doppler.htm

http://www.tmeg.com/esp/p_doppler/doppler.htm

Light emitted by the source will have wavelength decreased (blue shifted) in front of its motion and increased (red shifted) behind it.

Blue shifted藍移

Red shifted紅移

v

Spectrum of object at rest

Spectrum taken for approaching object

Spectrum taken for receding object

/ / / for ,

wavelength, frequency,

speed of object, speed of light.

f f v c v c

f

v c

http://sci.esa.int/content/doc/16/28950_.htm

Doppler effect demonstration

http://sci.esa.int/content/doc/16/28950_.htm

Width of a spectral line may be affected byNatural broadening - quantum effect, very smallDoppler broadening - Doppler shifts due to random

thermal motions of atoms.

For

Total width

cv

c

vr

m

kTvv

32rms

m

kT

c

32

E.g., H line of the sun

1000 times > natural broadeningK,5770T ,A6563

o

kg,1067.1 27mo

A52.0

Rotational broadening - light coming from a rotating star is Doppler shifted

Eg. see different shifts on different sides of Saturn’s ring: rotation speed

1.5 Stellar luminosity ( 恆星光度 )

Magnitudes and LuminosityApparent magnitude m ( 視星等 ): measures the

luminosity (B) of starlight received on earth.5 magnitudes = 100 timesAbsolute magnitude M ( 絕對星等 ): measures

the luminosity a star would have if it was placed at a distance of 10 pc (~33 light years) away.

Luminosity ( 光度 ) B: Total amount of energy that the star radiates in one second. It is determined by a combination of two factors: Surface area Surface temperature

424 TRL

1 2 1 22.5log /m m B B

Convention: mVega= 0

Luminosity ~ 1/r2

Distance modulusComparing apparent and absolute magnitudes gives distance r

Vega Vega2.5log / 2.5log , 2.5log .m B B k B k B

2

2

( ) 10 ( )log 2 2log ,

(10) (10)

2.5log ( ) 2.5log (10)

( ) 2.5log 5 5log .

(10)

B r B rr

B r B

m M k B r k B

B rr

B

Mm

a hot star with a large surface

area must be luminous

a cool star with a small surface

area must be dim

a cool star could be luminous

if it is very large (not much

radiation is emitted per unit

area, but the total radiation

rate is large because its has a

large surface area for light

emission)

Stefan-Boltzmanns law

y = m x + b

Lines of constant R

424 TRL 2 4

L R T

L R T

log 4log

2log

L T

L T

R

R

2logb R R

1.6 Hertzsprung-Russell diagram, H-R diagram ( 赫羅圖 )

Cooler, NOTNOT hotter

主序星

白矮星

超巨星

Main sequence: A belt from upper left to lower right, 90% of all stars Cool stars are faint and small; hot stars are bright

and largeGiants at the upper right corner, they are cool but

luminous must have large surface area ~10-100 supergiants have ~100-1000

White dwarfs lie in the lower left, they are hot but faint must be very small (~ size of Earth)

RR

RR

Figures courtesy HST/NASA

Red Giant

1.7 H-R Diagrams of Star Clusters

Two kinds of clusters: Open clusters ( 疏散星團 ) : contain 10-1000

stars; open, less densely populated, younger, mostly distributed close to the plane of our Galaxy

Star clusters ( 星團 )

M45 Pleiades Open Cluster M37 taken in CUHK七姊妹

M13 taken in NAM3 taken in CC by Delphi

Globular Clusters 球狀星團Globular Clusters 球狀星團

Star clusters Stars in the same star cluster are formed from the

same cloud

they have similar ages and initial chemical

compositions

But the stars differ in luminosity (mass) and surface temperature (color) They are located at different positions on the

H-R diagram

The Pleiades M45七姊妹星團The Pleiades M45七姊妹星團

From CUHKFrom CUHKHow do you explain the turnoff point?How do you explain the turnoff point?

The Pleiades

More massive members

(more luminous) leave the

main sequence and become

giants, while lower mass

members still lie on the

main sequence

confirms the evolution

picture that more massive

stars have shorter lives on

the main sequence

massive stars

Locating the turnoff point of a cluster’s H-R diagram

determines the cluster’s age by stellar evolution

theory; the lower the turnoff point, the older it is

SummaryLight = EM waves, emitted when charges change speed;

frequency, wavelengthStarlight: continuous spectrum, higher temperature

→higher intensity, bluer spectral lines (absorption or emission)

Bohr model: spectral lines correspond to energy level separations

Doppler effect: red/blue shifts, broadening (T, rotation)Spectral classes: OBAFGKMAbsolute/apparent magnitudes, luminosityH-R Diagram: luminosity vs. surface temperature

424 TRL max 1/T

Colors of Stars

1.1 Starlight1.2* Light-matter interaction1.3* Stellar spectrum1.4 Doppler effect1.5 Stellar luminosity1.6 H-R Diagram 1.7 H-R Diagrams for star clusters

The Stars and the Sun I.Colors of stars

http://www.phy.cuhk.edu.hk/gee/mctalks/mcpdp.html

Chu Ming-chung 朱明中

Department of Physics

The Chinese University of Hong Kong

[email protected]

Documents

The Stars and the Sun I. Colors of stars