Astro 1050 Mon. Feb. 23, 2004

Today: Chapter 8, Properties of Stars

Chapter 8: Properties of Stars

How much energy do stars produce?

How large are stars?

How massive are stars?

We will find a large range in properties!

How to get distances to stars: Parallax

Intrinsic Brightness of Stars

Apparent Brightness: How bright star appears to us

Intrinsic Brightness:   “Inherent” – corrected for distance

How does brightness change with distance?

Flux = energy per unit time per unit area:   joule/sec/m²   = watts/m²

Example: 100 watt light bulb (assume this is 100 W of light energy)
      spread over 5 m² desk gives 20 Watts/m²

Sun’s flux at the Earth

Luminosity = 3.8 ´10²⁶ Watts

It has spread out over sphere of radius 1 AU = 1.5 ´ 10¹¹ m

Surface area of sphere = 4 p R² = 2.8 ´10²³ m²

F_Sun = 3.8 ´10²⁶ Watts / 2.8´10²³ m² = 1,357 W/m²

Inverse Square Law:   Flux falls of as 1/distance²

Inverse-square law for light:

Correcting Magnitudes for Distance

To correct intensity or flux for distance, use Inverse Square Law

Up to now we have used “apparent magnitudes” m_v

Define absolute magnitude M_v as magnitude star would have
if it were at a distance of 10 pc.

This gives us a way to correct Magnitude for distance, or find distance if we know absolute magnitude. Note: the book writes m_v and M_v: The “V” stands for “Visual” -- Later we’ll consider magnitudes in other colors like “B=Blue” “U=Ultraviolet”

Let’s work some examples:

Problem from textbook:

m_V M_V d (pc) P (arcsec)

___ 7 10 _______

11 ___ 1000 _______

___ -2 ____ 0.025

4 ___ ____ 0.040

Let’s work some examples:

Problem #4:

m M_V d (pc) P (arcsec)

7 7 10 0.1

11 1 1000 0.001

1 -2 40 0.025

4 2 25 0.040

How to recognize patterns in data

What patterns matter for people – and how do we recognize them?

Weight and Height are easy to measure

Knowing how they are related gives insight into health

A given weight tends to go with a given height

Weight either very high or very low compared to trend ARE important

Plot weight vs. height and look for deviations from simple line

Example of cars from the book

Note “main sequence” of cars

Weight plotted backwards

Just make main sequence a line
which goes down rather than up

Points off main sequence are
“unusual” cars

Stars: Patterns of L, T, R

The Hertzsprung-Russsell (H-R) diagram

Plot L vs. backwards T. (We can find R given L and T)

How are L, T, and R related?

L = area ´sT⁴ = 4 p R² sT⁴

Stars can be intrinsically bright because of either large R or large T

Use ratio equations to simplify above equation

(Note book’s symbol for Sun is circle with dot inside)

Example: Assume T is different but size is same

A star is ~ 2 ´ as hot as sun, expect L is 2⁴= 16 times as bright

M star is ~1/2 as hot as sun, expect L is 2^-4= 1/16 as bright

B star is ~ 4 ´ as hot as sun, expect L is 4⁴= 256 times as bright

Example: Assume T same but size is different

If a G star 4 ´ as large as sun, expect L would be 4²=16 times as bright

L, T, R, and the H-R diagram

L = 4 p R² sT⁴

The main sequence consists very roughly of similar size stars

The giants, supergiants, and white dwarfs are much larger or smaller

Lines of constant R in the H-R diagram

Slide 14

Different “types” of H-R diagrams

Luminosity Classes

Spectra of Different Luminosity Classes

Spectroscopic “Parallax”

What fundamental property of a star
varies along the main sequence?

Masses of Binary stars

Measuring a and P of binaries

Two types of binary stars

Visual binaries: See separate stars

a large, P long

Can’t directly measure component of a along line of sight

Spectroscopic binaries: See Doppler shifts in spectra

a small, P short

Can’t directly measure component of a in plane of sky

If star is visual and spectroscopic binary get get full set of information and then get M

Masses and the HR Diagram

Main Sequence position:

M:    0.5 M_Sun

G:        1 M_Sun

B:       40 M_sun

Luminosity Class

Must be controlled by something else

The Mass-Luminosity Relationship

L = M^3.5

Eclipsing Binary Stars

System seen “edge-on”

Stars pass in front of each other

Brightness drops when either is hidden

Used to measure:

size of stars (relative to orbit)

relative “surface brightness”

area hidden is same for both eclipses

drop bigger when hotter star hidden

tells us system is edge on

useful for spectroscopic binaries


	How much energy do stars produce?

	How large are stars?

	How massive are stars?

		We will find a large range in properties!


Apparent Brightness: How bright star appears to us
Intrinsic Brightness: “Inherent” – corrected for distance
How does brightness change with distance?
	Flux = energy per unit time per unit area: joule/sec/m² = watts/m²
		Example: 100 watt light bulb (assume this is 100 W of light energy) spread over 5 m² desk gives 20 Watts/m²
	Sun’s flux at the Earth
		Luminosity = 3.8 ´10²⁶ Watts
		It has spread out over sphere of radius 1 AU = 1.5 ´ 10¹¹ m
			Surface area of sphere = 4 p R² = 2.8 ´10²³ m²
		F_Sun = 3.8 ´10²⁶ Watts / 2.8´10²³ m² = 1,357 W/m²

	Inverse Square Law: Flux falls of as 1/distance²


	To correct intensity or flux for distance, use Inverse Square Law



	Up to now we have used “apparent magnitudes” m_v
	Define absolute magnitude M_v as magnitude star would have if it were at a distance of 10 pc.







	This gives us a way to correct Magnitude for distance, or find distance if we know absolute magnitude. Note: the book writes m_v and M_v: The “V” stands for “Visual” -- Later we’ll consider magnitudes in other colors like “B=Blue” “U=Ultraviolet”


	Problem from textbook:
	m_V M_V d (pc) P (arcsec)
	___ 7 10 _______
	11 ___ 1000 _______
	___ -2 ____ 0.025
	4 ___ ____ 0.040


	Problem #4:
	m M_V d (pc) P (arcsec)
	7 7 10 0.1
	11 1 1000 0.001
	1 -2 40 0.025
	4 2 25 0.040



What patterns matter for people – and how do we recognize them?
Weight and Height are easy to measure
Knowing how they are related gives insight into health
		A given weight tends to go with a given height
		Weight either very high or very low compared to trend ARE important
Plot weight vs. height and look for deviations from simple line

Example of cars from the book
	Note “main sequence” of cars
	Weight plotted backwards
		Just make main sequence a line which goes down rather than up

	Points off main sequence are “unusual” cars



	The Hertzsprung-Russsell (H-R) diagram
	Plot L vs. backwards T. (We can find R given L and T)


L = area ´sT⁴ = 4 p R² sT⁴
	Stars can be intrinsically bright because of either large R or large T

	Use ratio equations to simplify above equation
		(Note book’s symbol for Sun is circle with dot inside)




	Example: Assume T is different but size is same
		A star is ~ 2 ´ as hot as sun, expect L is 2⁴= 16 times as bright
		M star is ~1/2 as hot as sun, expect L is 2^-4= 1/16 as bright

		B star is ~ 4 ´ as hot as sun, expect L is 4⁴= 256 times as bright

	Example: Assume T same but size is different
		If a G star 4 ´ as large as sun, expect L would be 4²=16 times as bright



	L = 4 p R² sT⁴
	The main sequence consists very roughly of similar size stars
	The giants, supergiants, and white dwarfs are much larger or smaller


Two types of binary stars
	Visual binaries: See separate stars
		a large, P long
		Can’t directly measure component of a along line of sight
	Spectroscopic binaries: See Doppler shifts in spectra
		a small, P short
		Can’t directly measure component of a in plane of sky
If star is visual and spectroscopic binary get get full set of information and then get M


	Main Sequence position:
		M: 0.5 M_Sun
		G: 1 M_Sun
		B: 40 M_sun

	Luminosity Class
		Must be controlled by something else


System seen “edge-on”
Stars pass in front of each other
Brightness drops when either is hidden

Used to measure:
	size of stars (relative to orbit)
	relative “surface brightness”
		area hidden is same for both eclipses
		drop bigger when hotter star hidden
	tells us system is edge on
		useful for spectroscopic binaries