Slide 1

Slide 2

How to classify a star and to place it on the H-R diagram correctly??

• Need to know its luminosity, but it is difficult, because distance is unknown

• If you can estimate a star’s diameter and/or mass, you can figure out its luminosity

• Then you can also find the distance to this star

Slide 3

The Radii of Stars in the Hertzsprung-Russell Diagram

10,000 times the

sun’s radius

100 times the

sun’s radius

As large as the sun

Rigel Betelgeuse

Sun

Polaris

Slide 4

The Relative Sizes of Stars in the Hertzsprung-Russell Diagram

Slide 5

Is there any spectral signature of giants?

The width of spectral lines!

How to distinguish between main-sequence stars and giants?

Slide 6

Spectral Lines of Giants

=> Absorption lines in spectra of giants and supergiants are narrower than in main sequence stars

Pressure and density in the atmospheres of giants are lower than in main sequence stars.

=> From the line widths, we can estimate the size and therefore, the luminosity of a star.

Distance estimate (spectroscopic parallax)

Slide 7

Luminosity Classes

Ia Bright Supergiants

Ib Supergiants

II Bright Giants

III Giants

IV Subgiants

V Main-Sequence Stars

IaIb

IIIII

IV

V

Slide 8

Luminosity classes

• Ia bright supergiant

• Ib Supergiant

• II bright giant

• III giant

• IV subgiant

• V main-sequence star

Slide 9

Example Luminosity Classes

• Our Sun: G2 star on the Main Sequence:

G2V

• Polaris: G2 star with Supergiant luminosity:

G2Ib

Slide 10

Mass is the most important parameter.

Knowing masses of stars would allow us to calculate their luminosities, lifetime and all other properties.

But how to measure masses??

Measuring masses

Slide 11

Binary StarsMore than 50 % of all stars in our Milky Way

are not single stars, but belong to binaries:

Pairs or multiple systems of stars which

orbit their common center of mass.

If we can measure and understand their orbital

motion, we can

estimate the stellar masses.

Measuring masses

Slide 12

The Center of Mass

center of mass = balance point of the system.Both masses equal => center of mass is in the middle, rA = rB.

The more unequal the masses are, the more it shifts toward the more massive star.

Slide 13

Center of Mass

(SLIDESHOW MODE ONLY)

Slide 14

m1m2

0221

21 rr

mGmFF

1F

2F

0r

1

2

2

1

d

d

m

m

Slide 15

Estimating Stellar Masses

Recall Kepler’s 3rd Law:

Py2 = aAU

3

Valid for the Solar system: star with 1 solar mass in the center.

We find almost the same law for binary stars with masses MA and MB different

from 1 solar mass:

MA + MB = aAU

3 ____ Py

2

(MA and MB in units of solar masses)

Slide 16

Examples: Estimating Mass

Binary system with period of P = 32 years and separation of a = 16 AU:

MA + MB = = 4 solar masses.163____322

How to measure period and separation?

Arbitrary units:

22

324

PG

aMM BA

Slide 17

Visual Binaries

The ideal case:

Both stars can be seen directly, and

their separation and relative motion can be followed directly.

Slide 18

Visual binaries

The Castor system The Sirius system

The two stars are separately visible in the telescope

Slide 19

Detecting the presence of a companion by its gravitational influence on the primary star.

Wobbling motion of Sirius A

Slide 20

Spectroscopic Binaries

Usually, binary separation a can not be measured directly

because the stars are too close to each other.

However:

1) their SPECTRA are different, like different fingerprints;

2) Their spectral lines shift periodically because of Doppler effect. This allows us to measure their orbital velocities

Stars are seen as a single point

Slide 21

The Doppler EffectThe light of a moving source is blue/red shifted by

/0 = vr/c

0 = actual wavelength

emitted by the source

Wavelength change due to

Doppler effect

vr = radial velocity( along

the line of sight)

Blue Shift (to higher frequencies)

Red Shift (to lower frequencies)

vr

Slide 22

Shift z = (Observed wavelength - Rest wavelength)

(Rest wavelength)

Doppler effect: cVc

Vz rad

rad

;0

00

0

z

The Doppler effect: apparent change in the wavelength of radiation caused by the motion of the source

Slide 23

Doppler effect

1c

;c

radial

00

radial

V

f

fV

The Doppler effect: apparent change in the wavelength of radiation caused by the motion of the source

RADIAL velocity!!

Slide 24

The Doppler Effect The Doppler effect allows us to

measure the source’s radial velocity.

vr

/0 = vr/c

Slide 25

Spectroscopic BinariesThe approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum.

Doppler shift Measurement of radial velocities

Estimate of separation a

Estimate of masses

Slide 26

Spectroscopic binaries

Stars are seen as a single point

• Spectra of both stars are distinguishable

• Sometimes spectrum of only one star is seen

Slide 27

Spectroscopic Binaries (3)T

ime

Typical sequence of spectra from a spectroscopic binary system

Slide 28

Determining the orbital period

Slide 29

• Measure the orbital period

• Measure the radial component of the orbital velocities

• Can estimate the orbit size

• Can determine masses!

;2

3

21 P

aMM

Slide 30

1. Below is a radial velocity curve for a spectroscopic binary. Estimate the mass of each star if the mass of the binary system is 6 solar masses.

Time (days)

V (km/sec)r

-15

-20

-25

-10

-5Star A

Star B

MA dA = MB dB

V ~ 2d/P

2

1

A

B

A

B

B

A

V

V

d

d

M

M

6 BA MM

Slide 31

Only the function of masses and inclination anglecan be measured

Slide 32

Slide 33

...BUT

THE PLANET CANNOT BE SEEN

MOTIONS OF THE STAR

BETRAYITS PRESENCE !

Slide 34

X

EARTH

X

JUPITER

150 000 000 km

30 km/s

450 km

9 cm/s

780 000 000 km

13 km/s

750 000 km

13 m/s

Slide 35

2010

2000

2005

1995

1990

2015

2020

0.002”

MOTIONS OF THE SUN VIEWED FROM A STAR 30 LIGHT YEARS AWAY

0.002’’ IS THE ANGULAR SIZE OF A MAN ON THE MOON OR A STANDARD NEWSPAPER FONT 300 KM AWAY Unobservable!

Slide 36

STELLARWOBBLE

RECEDING:

REDDER

APPROACHING:

BLUER

Slide 37

Slide 38

Over 100 planets discovered

Slide 39

EXPECTED:

NEARLY CIRCULARNEARLY CIRCULAR ORBITS ORBITS

BIG PLANETS BIG PLANETS FAR AWAY FROM THE STARFAR AWAY FROM THE STAR

NONO PLANETS BIGGER THAN JUPITER PLANETS BIGGER THAN JUPITER

DISCOVERED:

STRONGLY ELONGATEDSTRONGLY ELONGATED ORBITS ORBITS

BIG PLANETS BIG PLANETS VERY CLOSE TOVERY CLOSE TO THE STARTHE STAR

MANYMANY PLANETS BIGGER THAN JUPITER PLANETS BIGGER THAN JUPITER

Slide 40

Planetary system of And

Solar system

0.06 AU4.5 days0.75 MJ

2.5 AU3.5 years

4 MJ

0.85 AU242 days

2 MJ

0.39 AU89 days

0.73 AU228 days

1 AU1 year 1.54 AU

1.9 years

Source: Harvard-Smithsonian CfA

Slide 41

Habitable zones

Slide 42

Signs of life in the spectrum:

Slide 43

Slide 44

The Puzzle of Algol

Slide 45

John Goodricke 1764-1786

Explained Algol puzzle in 1783

Slide 46

Eclipsing binaries

Slide 47

Eclipsing Binaries

Usually, inclination angle of binary systems is

unknown uncertainty in mass estimates.

Special case:

Eclipsing Binaries

Here, we know that we are looking at the

system edge-on!

Slide 48

The light curve of Algol

Slide 49

Slide 50

Measuring orbital period and diameters

Slide 51

Measuring diameters

D = Vorb (t2 – t1)

Slide 52

Specific segments of the main sequence are occupiedby stars of a specific mass

L~ M3.5 dependence, but Cutoff at masses > 100 M and < 0.08 M

Slide 53

Puzzles of H-R diagram

• Why > 90% of stars are on the main sequence?

• Reason for mass-luminosity dependence and mass cutoff

• Same stars at different stages of life or just different stars?

Slide 54

How can we learn about the life of stars??

• Our life span is ~ 80 years

• Human civilization exists ~ 5000 years

• Our Sun exists at least 4.6 billion years!

Slide 55

Star Clusters – “School Classes” for Stars

They consist of stars of the same age !

Open clusters100’s of stars

Globular clusters100,000 of stars

Slide 56 p. 188

Pleiades

Slide 57

Slide 58

Age of the cluster from turnoff point

Turnoff point: stars of that mass are going to die and move away from the main sequence

Slide 59

Slide 60

Slide 61

Slide 62

Stars spent most of their lives on the Main Sequence. That is why it is so populated!

At the end of its life the star moves away from the Main Sequence

More massive and more luminous stars die faster

Hypothesis: Stars on the Main Sequence live due to nuclear fusion of hydrogen!

• Stars stay on the main sequence until all hydrogen in the core is consumed • Then something should happen

Slide 63

H-R diagram

• 90% of stars are on the main sequence and obey the mass-luminosity dependence L ~ M3.5

• Stars on the main sequence generate energy due to nuclear fusion of hydrogen

• In the end of their lives stars move to the upper right corner of the H-R diagram

Slide 64

Check this hypothesis

• Mass should be most important parameter

• It determines the pressure in the star center and the central temperature

• It determines the surface temperature

5.3

sunsun M

M

L

L

5.3ML

How to get this dependence?

Slide 65

Gravity Holds a Star Together

Stars are held together by gravity. Gravity tries to compress everything to the center. What holds an ordinary star up and prevents total collapse is thermal and radiation pressure. The thermal and radiation pressure tries to expand the star layers outward to infinity.

1. Newton’s gravitation law2. Hydrostatic equilibrium3. Equation of state4. Energy transport

Mass determines all star’s properties

Slide 66

star mass (solar masses) time (years) Spectral type

60 3 million O3

30 11 million O7

10 32 million B4

3 370 million A5

1.5 3 billion F5

1 10 billion G2 (Sun)

0.1 1000's billions M7

Lifetime T ~ M/L ~ 1/M3.5-1 = 1/M2.5 ; p ~ 3.5

M = 4M; 32

15.2

M

M

T

T sun

sun

Lifetime = Amount of hydrogen fuel

Rate of energy loss

T ~ 3x108 years

Slide 67

Slide 68

How to explain the cutoff at masses > 100 M and < 0.08 M

Slide 69

Maximum Masses of Main-Sequence Stars

Carinae

Mmax ~ 50 - 100 solar masses

a) More massive clouds fragment into smaller pieces during star formation.

b) Very massive stars lose mass in strong stellar winds

Example: Carinae: Binary system of a 60 Msun and 70 Msun star. Dramatic mass loss; major eruption in 1843 created double lobes.

Slide 70

Too massive and luminous stars throw off their outerlayers due to radiation pressure

Eta Carinae

High-mass cutoff at M ~ 100 Msun

Slide 71

Minimum Mass of Main-Sequence Stars

Mmin = 0.08 Msun

At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion.

Brown Dwarfs

Gliese 229B

Slide 72

Low-mass cutoff of the main sequence: M ~ 0.08 Msun

Gliese 229B: only 0.02 M

Brown dwarfs: temperature is too low to ignite nuclear fusion

Slide 73

Conclusion Based on this evidence, we conclude: Stars spend most of their lives as main sequence stars. During its lifetime, the surface temperature and luminosity stays almost constant.

Something else could happen in the star birth process. Something else could happen in the star death process.

The star's mass determines what the temperature and luminosity is during the star's main sequence lifetime.

More mass -> hotter. More mass -> more luminous. Also, more mass -> bigger.