Astro 1050     Mon. Oct. 7, 2002

   Today: Discuss HW #4

                Finish Chapter 7 -- The Sun

                Start Ch. 8, Properties of Stars

Homework #4

Q1 The moon remains in Aries!

Q2 1 kg of mass transformed into energy:

E = mc² so E=1 kg x (3x10⁸m/s)² = 9x10¹⁶ J

Q3 Sunspot brightness, use E = σT⁴

(T₁/T₂)⁴ = (5800/4200)⁴ = 3.6 times brighter

Q4 Radio Wave same speed as Gamma Ray

Q5 P. 123, flares up to a billion H-bombs so

The Traitor dies like the dog he is!

Fusion Energy Released in Proton-Proton Chain

Use E=mc² to do accounting

Mass is a measure of the energy stored in a system

Loss of mass from a system means release of energy from that system

Compare mass of four ¹H to mass of one ⁴He

6.693 ´ 10^-27 kg - 6.645 ´ 10^-27kg = 0.048 ´ 10^-27 kg drop in mass

E = mc² = 0.048 ´ 10^-27 kg ´ (3 ´ 10⁸ m/s)^{2 =} 0.43 ´ 10^-11 kg m²/s² = 0.43 ´ 10^-11 J (note == a Joule is just shorthand for kg m²/s²)

So 4.3 ´ 10^-12 J of energy released

This is huge compared to chemical energy: 2.2 ´10^-18 J to ionize hydrogen

How long will Sun’s fuel last?

Luminosity of sun: 3.8 ´ 10²⁶ J/s

H burned rate:

H atoms available:

Lifetime:

In reality not all the atoms we start with are H, and only those near the center are available for fusion. The structure of the sun will change when about 10% of the above total have been used, so after about 10 billion years.

Testing solar fusion model

Does lifetime of sun make sense?

Oldest rocks on earth ~4 billion years old

Oldest rocks in meteorites ~4.5 billion years old

Other stars with higher/lower luminosity

Causes for different luminosity

Lifetimes of those stars

Look for neutrinos from fusion

Complicated story – due to neutrino properties

Example of how astronomy presents “extreme” conditions

Neutrinos

Generated by “weak” force during p⁺® n + e⁺ + n

“Massless” particles which interact poorly with matter

In that first respect, similar to photons

Can pass through sun without being absorbed

Same property makes them very hard to detect

Davis experiment at Homestake Mine in Black Hills

100,000 gallon tank of C₂Cl₄ dry cleaning fluid

in Cl nuclei n + n ® p⁺ + e^- so Cl (Z=17) becomes Ar (Z=18)

Physically separate out the Ar, then wait for it to radioactively decay

Saw only 1/3 the neutrinos predicted

Missing Neutrino Problem

Lack of solar neutrinos confirmed by Kamiokande II detector in Japan. (Using different detection method)

Possible explanation in terms of Neutrino physics

3 different types of Neutrinos:

electron, muon, and tau neutrinos

Sun generates and Cl detectors see only electron neutrinos

Can electron neutrinos can change to another type on way here?

These “neutrino oscillations” are possible if neutrino has non-zero mass

Kamiokande II evidence of muon neutrinos becoming electron ones

Read “Window on Science 7-2” on “scientific faith”

Neutrino mass may have implications for “cosmology”

Neutrinos also used to study supernova 1987A

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!

Distances to Stars

Distance:

Parallax: Really just the small angle formula

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

Double distance – flux drops by 4

Triple distance – flux drops by 9

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 #4:

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 you have 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 21

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


	Today: Discuss HW #4
	Finish Chapter 7 -- The Sun
	Start Ch. 8, Properties of Stars


	Q1 The moon remains in Aries!
	Q2 1 kg of mass transformed into energy:
		E = mc² so E=1 kg x (3x10⁸m/s)² = 9x10¹⁶ J
	Q3 Sunspot brightness, use E = σT⁴
		(T₁/T₂)⁴ = (5800/4200)⁴ = 3.6 times brighter
	Q4 Radio Wave same speed as Gamma Ray
	Q5 P. 123, flares up to a billion H-bombs so
		The Traitor dies like the dog he is!



Use E=mc² to do accounting

	Mass is a measure of the energy stored in a system
	Loss of mass from a system means release of energy from that system

Compare mass of four ¹H to mass of one ⁴He
	6.693 ´ 10^-27 kg - 6.645 ´ 10^-27kg = 0.048 ´ 10^-27 kg drop in mass
	E = mc² = 0.048 ´ 10^-27 kg ´ (3 ´ 10⁸ m/s)^{2 =} 0.43 ´ 10^-11 kg m²/s² = 0.43 ´ 10^-11 J (note == a Joule is just shorthand for kg m²/s²)
	So 4.3 ´ 10^-12 J of energy released
		This is huge compared to chemical energy: 2.2 ´10^-18 J to ionize hydrogen


	Luminosity of sun: 3.8 ´ 10²⁶ J/s

	H burned rate:

	H atoms available:

	Lifetime:


	In reality not all the atoms we start with are H, and only those near the center are available for fusion. The structure of the sun will change when about 10% of the above total have been used, so after about 10 billion years.


	Does lifetime of sun make sense?
		Oldest rocks on earth ~4 billion years old
		Oldest rocks in meteorites ~4.5 billion years old

	Other stars with higher/lower luminosity
		Causes for different luminosity
		Lifetimes of those stars

	Look for neutrinos from fusion
		Complicated story – due to neutrino properties
		Example of how astronomy presents “extreme” conditions


	Generated by “weak” force during p⁺® n + e⁺ + n
	“Massless” particles which interact poorly with matter
		In that first respect, similar to photons
		Can pass through sun without being absorbed
		Same property makes them very hard to detect

	Davis experiment at Homestake Mine in Black Hills
		100,000 gallon tank of C₂Cl₄ dry cleaning fluid
		in Cl nuclei n + n ® p⁺ + e^- so Cl (Z=17) becomes Ar (Z=18)
		Physically separate out the Ar, then wait for it to radioactively decay
		Saw only 1/3 the neutrinos predicted


Lack of solar neutrinos confirmed by Kamiokande II detector in Japan. (Using different detection method)

Possible explanation in terms of Neutrino physics
	3 different types of Neutrinos:
		electron, muon, and tau neutrinos
		Sun generates and Cl detectors see only electron neutrinos
		Can electron neutrinos can change to another type on way here?
	These “neutrino oscillations” are possible if neutrino has non-zero mass

	Kamiokande II evidence of muon neutrinos becoming electron ones

Read “Window on Science 7-2” on “scientific faith”

Neutrino mass may have implications for “cosmology”
Neutrinos also used to study supernova 1987A


	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
		Double distance – flux drops by 4
		Triple distance – flux drops by 9


	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 #4:
	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 you have 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