Astro 103 - Lecture 8

Lectures Lecture page Astro103 page

THE PHYSICAL PROPERTIES OF STARS


1. The HR Diagram Revisited:


The Main Sequence

Giants

Super Giants

White dwarfs


Spectral types: O B A F G K M

hot cool

Each has a unique ...

- spectral absorption lines

- temperature


Both temperature (color) and spectrum are distance-independent.


SO?



2. Spectroscopic Parallax


Pick a star, any star ...

(i) measure spectrum and apparent brightness (l)

(ii) deduce spectral type from spectrum

(iii) infer luminosity (L) from spectral type

(iv) infer distance (d) from apparent brightness and luminosity

(Recall from the previous lecture: l = L / 4 d2 )

So we can write:
l L/d2

and then re-arrange terms and take the square-root:

d

Next rung on the distance ladder!

- to about 1-10 Kpc from the ground

- to a few Mpc (maybe!) from HST



3. Fair Samples


Question: What's the relative frequency of different stars?


Remember:   l L/d2

so,

d =

and

volume d3

volume ()3/2

brightness-limited samples biased to bright objects

``Malmquist bias''



4. Stellar Sizes


Can we resolve stars?

Not easily, and not for very many stars

How do we infer sizes?

Recall Stefan's law: energy is proportional to temperature to the 4th power:

E T4

Surface area of a sphere is proportional to radius squared (A=4R2):

A R2

Total luminosity of a spherical blackbody is proportional to the energy times the area:

L E * A

so

L T4 * R2

or



(i) Measure distance

parallax, or ...
spectroscopic parallax

(ii) Use distance and apparent brightness to calculate luminosity.

(iii) Measure T from colors


R



5. Stellar Masses


Use binary star orbits and Kepler's third law:

orbital periods and radii (semi-major axis)



6. Mass - Luminosity - Radius Relations



For the Main Sequence:

Luminosity Mass4

But note your book says L M3

In reality the index is between 3 and 4, higher at higher masses.
The best 'average' value is 3.2, but we will stick with 4 for simplicity.

In general:

Luminosity Radius2

When is this formula valid?

Counter example, on the Main Sequence:

Radius Mass0.7

which implies

Luminosity Radius5.7

... for the Main Sequence ONLY.



7. Lifetimes


Recall how we estimated the age of the sun. In general:

Lifetime Mass/Luminosity Mass-3


Mass
(Solar units)		 Luminosity
(Solar units)		 Lifetime
0.1    
1 1 10 Gyr
10    
100    


The Main Sequence is a mass sequence:

  • Hot stars live for only a short time
  • Cools stars live a lot longer


    • Q8.1 Two stars have the same temperature but radii that differ by a factor of 2. What are their relative luminosities?

    (a) the same, since they have the same temperature

    (b) not possible to estimate

    (c) the bigger star is brighter in proportion to its greater mass

    (d) the bigger star is brighter by a factor of 4, in proportion to its greater surface-area

    (e) the bigger star is brighter by a factor of 6, in proportion to its greater volume


    Q8.2 The Sun will live for 10 Gyr. How long will a 2 solar mass star live if it is 16 times brighter?

    (a) twice as long as the Sun

    (b) twice as short as the Sun

    (c) the same time

    (d) indefinitely

    (e) 8 times shorter than the sun


    Lectures Lecture page Astro103 page
    Last updated: 03 Oct, 2011 Matthew A. Bershady