Astro 1 - Lecture 21


Matthew A. Bershady

Department of Astronomy & Astrophysics

Penn State University


Fall 1996

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© 1995 Matthew A. Bershady

Lectures Lecture page Astro1 page


STARS AND THEIR ENVIRONS


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


l L/d2

so,

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?



volume limited sample





(sketch to be added in class)





apparent brightness limited sample





(sketch to be added in class)





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 R2

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

so

L T4 x 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



6. Mas - Luminosity - Radius Relations



... for the Main Sequence ...


Luminosity Radius2

Luminosity Mass4

7. Lifetimes


Lifetime Mass/Luminosity Mass-3


Mass Luminosity 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



Q21.1 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


Q21.2 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 Astro1 page
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Last updated: Oct 8, 1996 Matthew A. Bershady