My Lecture_HR Diagram

Hertzsprung-Russell diagramHertzsprung-Russell diagram

Lecture: 5

Dr. H. S. Das

Department of Physics

Assam University, Silchar

One of the most useful and powerful plots in astrophysics is the Hertzsprung-Russell diagram (hereafter called the H-R diagram).

It originated in 1911 when the Danish astronomer, Ejnar Hertzsprung, plotted the absolute magnitude of stars against their colour (hence effective temperature).

Independently in 1913 the American astronomer Henry Norris Russell used spectral class against absolute magnitude.

Their resultant plots showed that the relationship between temperature and luminosity of a star was not random but instead appeared to fall into distinct groups.

The HR diagram

• The tool we use to study stars is called the Hertzsprung-Russell diagram.

• It plots two observable quantities: the absolute brightness of a star and the temperature of a star.

• Combined with some laws of physics, the HR diagram provides a way to understand how stars evolve with time.

Temperature

• To measure the temperature of a star we use must measure the spectrum of the star and then apply more physics

• We assume the star is a “black body radiator” and then we can compute the temperature from the spectral shape.

Temperature

Temperature

Temperature

• Looking at individual spectral lines in a star’s spectrum can also reveal the spectral class of the star; spectral class is closely related to the temperature of the star

Reminder: Spectral Classification of the Stars

Class Temperature Color Examples

O 30,000 K blue 10 Lacentra

B 20,000 K bluish Rigel, Spica, Regulus

A 10,000 K white Vega, Sirius, Altair

F 8,000 K white Canopus, Procyon

G 6,000 K yellow Sun, Centauri A

K 4,000 K orange Arcturus, Aldebaran

M 3,000 K red Betelgeuse, Antaris

Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me

Constructing a HR-Diagram• Example: Aldebaran, spectral type K5III,

luminosity = 160 times that of the Sun

O B A F G K M Type… 0123456789 0123456789 012345…

1

10

100

1000

L

Aldebaran

Sun (G2V)

160

H-R Diagram

• A plot of absolute luminosity (vertical scale) against spectral type or temperature (horizontal scale)

• Most stars (90%) lie in a band known as the Main Sequence

Mass and the Main Sequence

• The position of a star in the main sequence is determined by its massAll we need to know

to predict luminosity and temperature!

• Both radius and luminosity increase with mass

HR diagram:

HR diagram:

HR diagram:

HR diagram:

HR diagram:

HR diagram:

HR diagram:

HR diagram:

The HR diagram

• Most stars lie along the “Main Sequence”– Simple relationship between temperature and

luminosity– Stars spend most of their lives converting

hydrogen to helium, and this is what occurs when the star is on the main sequence

• An HR diagram of the closest 16,000 stars shows most lie along MS

The HR diagram

• The HR diagram can be used to determine other parameters of stars, like the radius

• A black-body radiator has a simple relationship between the absolute brightness (Luminosity) and the temperature L=R2T4, which defines lines of constant stellar radius on the HR diagram.

The HR diagram

• Stars in the upper right are very large and stars in the lower left are very small.

• This defines only the SIZE of the star and not the MASS, since the density of stars can be very different.

• So the branch of stars to the upper right of the MS are giant and supergiant stars.

PHYS 3380 - Astronomy

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

100 times smaller than the sun

Rigel Betelgeuse

Sun

Polaris


The Main Sequence (MS)

90% of all stars lie on the main sequence. A star spends most of its lifetime on the main sequence. All stars on the main sequence have hydrogen fusion as their energy source.


Luminosity Classes

Ia Bright Supergiants

Ib Supergiants

II Bright Giants

III Giants

IV Subgiants

V Main-Sequence Stars

IaIb

II

III

IV

VWhite Dwarfs

This classification is based on spectral lines sensitive to stellar surface gravity.

Example Luminosity Classes

• Our Sun: G2 star on the Main Sequence: G2V

• Polaris: G2 star with Supergiant luminosity: G2Ib

Since the radius of a giant star is much larger than a dwarf star while their masses are roughly comparable, the gravity and thus the gas density and pressure on the surface of a giant star are much lower than for a dwarf. These differences manifest themselves in the form of luminosity effects which affect both the width and the intensity of spectral lines which can then be measured. Denser stars with higher surface gravity will exhibit greater pressure broadening of spectral lines.

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 luminosity of a star - certain spectral lines more sensitive to effect

Distance estimate (spectroscopic parallax)

The life track of a 1 solar mass star from main-sequence star to white dwarf. The dashed line represents the rapid transition from planetary nebulae to white dwarf as the ejected outer layers dissipate, revealing the hot core.

Solar Life Track


Blue supergiants:Bluest, most luminous, hottest; moderately large stars; low densities and large masses, very

rare.

Example: Rigel


Red supergiants:Orange to red in color; the largest stars and among the brightest; large masses and extremely low densities; few in number.

Example: Betelguese


Giants:Yellow, orange, and red; considerably larger and brighter than the sun; average to larger than average masses and low densities; fairly scarce.

Example: Arcturus


Middle main sequence stars:White, yellow, and orange; stars higher than the sun on the main sequence are somewhat larger, hotter, more massive, and less dense than the sun; plentiful in number.

Example: Sirius


Middle main sequence stars:

Stars below the sun on the main sequence are somewhat smaller, cooler, fainter, less massive, and denser than the sun; plentiful in number.

Example: Epsilon Eridani


Red dwarfs: Coolest and reddest stars on the low rung of the main sequence; considerably fainter and smaller than the sun; small masses and high densities; the most abundant stars.

Example: Barnard's star


White dwarfs:

Mostly white and yellow; extremely faint and tiny by solar standards; enormously high densities; terminal evolutionary development; quite plentiful.

Example: The binary

companion of Sirius

Hot stars appear bluer than cooler stars - cooler stars are redder than hotter stars.• B-V color index way of quantifying this - determining spectral class - using two different filters

one a blue (B) filter that only lets a narrow range of colors or wavelengths through centered on the blue colors, and a “visual” (V) filter that only lets the wavelengths close to the green-yellow band through.

Hot star has a B-V color index close to 0 or negative, Cool star has a B-V color index close to 2.0. Other stars are somewhere in between. 1. Measure the apparent brightness (flux) with two different filters (B, V). 2. The flux of energy passing through the filter tells you the magnitude (brightness) at the wavelength of the filter. 3. Compute the magnitude difference of the two filters, B - V.

B-V Color Index and Temperature

Hipparcos satellite measured 105 bright stars with

p>0.001" confident distances for stars with d<100 pc

Hertzsprung-Russell diagram for the 41704 single stars from the Hipparcos Catalogue with relative distance precision better than 20% and (B-V) less than or equal to 0.05 mag. Colors indicate number of stars in a cell of 0.01 mag in (B-V) and 0.05 mag in absolute magnitude (MV).

Mass–Luminosity Relation

All main sequence stars fuse H into He in their cores.Luminosity depends directly on mass because:

- more mass means more weight from the star’s outer layers- nuclear fusion rates must be higher in order to maintain gravitational equilibrium

L m3.5

So mass is the single most important property of any star.- at each stage of a star’s life, mass determines…

- what its luminosity will be- what its spectral type will be

Its lifetime on the main sequence is dependent on its mass

Lifetime on the Main Sequence

How long will it be before MS stars run out of fuel? i.e. Hydrogen?

How much fuel is there? M (solar mass)

How fast is it consumed? L M3.5

How long before it is used up?

M/L = M/M3.5 = M-2.5

MS Lifetime = 1010 yrs / M2.5

Our Sun will last 1010 years on the Main Sequence


Masses of Stars in the Hertzsprung-Russell Diagram

The higher a star’s mass, the more luminous (brighter) it is:

High-mass stars have much shorter lives than low-mass stars:

Sun: ~ 10 billion yr.10 Msun: ~ 30 million yr.0.1 Msun: ~ 3 trillion yr.

0.5

18

6

3

1.71.0

0.8

40

Masses in units of solar masses

Low

masses

High masses

Mass

L ~ M3.5

tlife ~ M-2.5

Lifetime on the Main Sequence

So for example:

B2 dwarf (10 M) lasts 3.2 x 107 yr

F0 dwarf (2 M) lasts 1.8 x 109 yr

M0 dwarf (.5 M) lasts 5.6 x 1010 yr

But the Universe is 1.37 x 1010 yr old!

Every M dwarf that was ever created is still on the main sequence!!

No more today!!!

See you in next class……

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My Lecture_HR Diagram