Astro 1050 Fri. Oct. 17, 2003

Today: Extra Credit Articles

Homework

Chapter 8, Properties of Stars

Homework #5

Q1 At what wavelength does the spectrum of a 10000 K type A star peak?
Use Wien’s Law: λ = 3000000 nm/T, so 300 nm.

Q2 The neutral atom of the most common form of hydrogen consists of a proton and an electron.

Q3 Fusion of very light elements to make heavier ones releases energy, as does fission of very heavy elements to make lighter ones. The most "energetically favorable" and stable element from which neither fission nor fusion can release energy is IRON

Q5 In the two page spread you can find the solar flare energy in terms of nuclear weapons (up to a billion H-bombs), and determine that yes, the traitor dies like the dog he is!

Q6 1 kg of mass transformed into energy:

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

Homework #5

Q7 1 kg of H fused into He. How much energy is liberated? Use E = mc², but must determine how much mass is converted. We learned in class that 4.3 ´ 10^-12 J released for each He produced. He masses 6.645 ´ 10^-27kg, so we have 1.5x10²⁶ He in a kg, each producing the above energy. Multiply the energy per He times number of He = 1.5x10²⁶ x 4.3 ´ 10^-12 J = 6.4x10¹⁴ J

Q9 Sunspot brightness, use E = σT⁴

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

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

Starting Ch.9: Interstellar Medium

Since stars die, new ones must somehow be born

They must be made out of material like star:

H, He, plus a little heavier elements

Three types of interstellar “nebulae” or clouds

Emission nebulae -- Glow with emission lines

Reflection nebulae -- Reflect starlight

Dark nebulae -- seen in silhouette

Emission nebulae

The red glow is Hydrogen Balmer a (Ha ) emission

Could be from hot gas but –

relative strength of emission lines not always right

Can also get fluorescence:

UV photon from bright star boosts electron to high level (or ionizes it)

Emission lines created as electron cascades back down through H energy levels

The “horse” is a dark cloud in front of the glowing gas.

Reflection nebulae – The Pleiades

Cluster of new stars

Visible to unaided eye
in western Taurus

Stars form in clusters – most of which slowly spread apart.

Reflection nebula is reflected sunlight

Can see stellar-like spectra with absorption lines

Blue light scattered more efficiently than red

Pleiades didn’t form here – just moving through this cloud of dust.

Dark Nebula

Spectral Measurements

Use spectra of stars

Ignore broad (“high pressure” stellar lines

Very narrow (low pressure) lines from interstellar gas

This one Ca II = Ca⁺¹

Stronger in more distant stars

Stronger when looking through interstellar gas clouds

Hydrogen hard to measure

remember Balmer rules

Measurements at other Wavelengths

Infrared “Cirrus”

really slightly warm dust

X-Rays of hot gas near exploded stars (supernova)

Radio observations of “Molecular Clouds”

Called that because cool and dense enough for molecules to form

H₂ also hard to detect

CO common and easy to detect

Densest have 1000 atoms/cm³

T as low as 10 K

Location of star formation

Collapse of
Molecular Clouds

Barely stable against collapse:

Imagine slightly compressing cloud

Gravity goes up because material is packed more tightly (R in 1/R² is smaller)

Tends to make cloud want to collapse

Pressure goes up because material is packed more tightly (P µ rT) and r higher

Tends to make cloud want to expand

For smaller clouds Pressure wins (stable)

For larger clouds Gravity wins (collapse)

As it collapses and becomes denser, smaller and smaller parts become unstable

Shock wave can trigger collapse

What will a forming star look like in HR diagram?

Temperature changes relatively simple

Starts out large and relatively cool Must be on red side of diagram

It heats up as it contracts Must towards the blue

Luminosity more complicated because it depends on T and R

Not much energy to start with Luminosity must start out low

Collapse releases grav. energy Luminosity will rise

Fusion begins, releases more energy Luminosity at a peak

Collapse slows, only have fusion now Luminosity declines

Finally stabilizes on the main sequence

How does mass affect collapse?

More massive protostars have stronger gravity

Collapse speed will be much faster

Fast collapse and short lifetime means massive stars reach end of lifetime while low mass stars in cloud are just forming

Supernova shocks may come from earlier generation of stars

Sequential Star Formation

Energy from supernova and other effects eventually disrupts cloud – prevents further collapse.

Observations of collapse

Young cluster “NGC 2264”

Few million years old

High mass stars have reached
main sequence

Lower mass stars are still approaching main sequence

T Tauri stars

Naming of classes of stars: Usually named after first star in class: T Tauri

Stars with letters (RR Lyrae) are typically “variable” stars

Earlier stages hidden by dust

More details of stellar structure and energy generation

Alternatives to the proton-proton chain

Fusion of Helium to heavier elements

Proton-proton reaction slow because:

Need two rare events at once

High energy collision of 2 protons

Conversion of p Þn during collision

The CNO Cycle

Gives way around need for p ®n during the collision

Still must happen later – but don’t need to rare events simultaneously

Trade off is need for higher energy collisions (T>16 million K)

Add p to some nucleus where new one is still “stable”

Wait for p ® n while that nucleus just “sits around”

The net effect is still 4 ¹H ® ⁴He

C just acts like a “catalyst”

Heavy Element Fusion

Triple Alpha process

⁴He + ⁴He ® ⁸Be + g

⁸Be + ⁴He ® ¹²C + g

Similar type reactions create heavy elements above 600 Million K

Plot to left gives:

x:   # of neutrons

y:   # of protons

Right one – add neutron

Up     one – add proton

Diagonal – p ® n or reverse

Jumps:        add ⁴He or more

Models of Stellar Structure

Divide star into thin shells,calculate how following vary from shell to shell
(i.e. as function of radius r)

P (Pressure)

T (Temperature)

r (Density)

To do this also need to find:

M (Mass) contained within any r

L (Luminosity) generated within any r

P example:

Numerical Stellar Models

Why don’t stars collapse?

Limiting case: Assume no nuclear fusion so only energy source is gravity.

Star is “almost” in hydrostatic equilibrium

Star radiates energy: If nothing else happened T would drop, P would drop, star would shrink.

Star does shrink, but in doing so gravitational energy is converted to heat, preventing T from continuing to drop.

In fact, since star is now more compact, gravity is stronger and it actually needs higher P (so higher T) to prevent catastrophic collapse

As star shrinks, ½ of gravitational energy goes into heating up star, ½ gets radiated away

Rate at which it radiates energy, so rate at which it shrinks, is limited by how “insulating” intermediate layers are

Why do we get steady fusion rates?

Strange counterintuitive result:

As star radiates away thermal energy it actually heats up
(because as it shrinks gravity supplies even more energy)

Star continues to shrink till it gets hot enough inside for fusion (rather than gravity) to balance energy being radiated away.

Nuclear thermostat

If fusion reactions took place in a “box” with fixed walls:

Fusion Þ more energy Þhigher T Þ more fusion (explosion)

If fusion reactions take place in sun with “soft gravity walls”:

If fusion rate is too high T tries to go up but star expands and actually ends up cooling off – slowing down fusion. (steady rate)

Mass-Luminosity relationship

L µ M^3.5Why?

Higher mass means higher internal pressure

Higher pressure goes with higher temperature

Higher temperature means heat leaks out faster

Star shrinks until T inside is high enough for
fusion rate (which is very sensitive to temperature)
to balance heat leak rate

Lifetime on Main Sequence

L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5

Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun

How about a 0.5 solar mass star?

M = 0.5 M_sun

Time =

Luminosity =

How about a 0.5 solar mass star?

M = 0.5 M_sun

Time = 5.7 times solar lifetime

Luminosity = 0.09 solar luminosity

Width of Main Sequence – and Stellar Aging

As star converts H to He you have more massive nuclei

Pressure related to number of nuclei

Gravity related to mass of nuclei

Pressure would tend to drop unless something else happens

Temperature must rise (slightly) to compensate

Luminosity must rise (slightly) as heat leaks out faster

Orion Nebula: A Star-Forming Region

Red light = Hydrogen emission

Blue light = reflection nebula

Dark lanes = dust

Astronomy Picture of the Day:
http://antwrp.gsfc.nasa.gov/apod

Protoplanetary Disks in the Orion Nebula

Dusty disk seen in silhouette

Central star visible at long wavelengths

Herbig-Haro objects: The angular momentum problem

As clouds try to collapse angular momentum makes them spin faster

A disk forms around the protostar

Material is ejected along the rotation axis

Herbig-Haro 34 in Orion

Jet along the axis visible as red

Lobes at each end where jets run into surrounding gas clouds

Motion of Herbig-Haro 34 in Orion

Can actually see the knots in the jet move with time

In time jets, UV photons, supernova, will disrupt the stellar nursery


	Today: Extra Credit Articles
	Homework
	Chapter 8, Properties of Stars


	Q1 At what wavelength does the spectrum of a 10000 K type A star peak? Use Wien’s Law: λ = 3000000 nm/T, so 300 nm.
	Q2 The neutral atom of the most common form of hydrogen consists of a proton and an electron.
	Q3 Fusion of very light elements to make heavier ones releases energy, as does fission of very heavy elements to make lighter ones. The most "energetically favorable" and stable element from which neither fission nor fusion can release energy is IRON
	Q5 In the two page spread you can find the solar flare energy in terms of nuclear weapons (up to a billion H-bombs), and determine that yes, the traitor dies like the dog he is!
	Q6 1 kg of mass transformed into energy:
		E = mc² so E=1 kg x (3x10⁸m/s)² = 9x10¹⁶ J


	Q7 1 kg of H fused into He. How much energy is liberated? Use E = mc², but must determine how much mass is converted. We learned in class that 4.3 ´ 10^-12 J released for each He produced. He masses 6.645 ´ 10^-27kg, so we have 1.5x10²⁶ He in a kg, each producing the above energy. Multiply the energy per He times number of He = 1.5x10²⁶ x 4.3 ´ 10^-12 J = 6.4x10¹⁴ J
	Q9 Sunspot brightness, use E = σT⁴
	(T1/T2)⁴ = (5800/4200)⁴ = 3.6 times brighter


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


	Since stars die, new ones must somehow be born
	They must be made out of material like star:
		H, He, plus a little heavier elements

	Three types of interstellar “nebulae” or clouds
		Emission nebulae -- Glow with emission lines
		Reflection nebulae -- Reflect starlight
		Dark nebulae -- seen in silhouette


	The red glow is Hydrogen Balmer a (Ha ) emission

	Could be from hot gas but –
		relative strength of emission lines not always right

	Can also get fluorescence:
		UV photon from bright star boosts electron to high level (or ionizes it)
		Emission lines created as electron cascades back down through H energy levels

	The “horse” is a dark cloud in front of the glowing gas.


	Cluster of new stars
		Visible to unaided eye in western Taurus

		Stars form in clusters – most of which slowly spread apart.

	Reflection nebula is reflected sunlight
		Can see stellar-like spectra with absorption lines
		Blue light scattered more efficiently than red

	Pleiades didn’t form here – just moving through this cloud of dust.


	Use spectra of stars
	Ignore broad (“high pressure” stellar lines

	Very narrow (low pressure) lines from interstellar gas
		This one Ca II = Ca⁺¹
	Stronger in more distant stars
	Stronger when looking through interstellar gas clouds

	Hydrogen hard to measure
		remember Balmer rules


	Infrared “Cirrus”
		really slightly warm dust
	X-Rays of hot gas near exploded stars (supernova)
	Radio observations of “Molecular Clouds”
		Called that because cool and dense enough for molecules to form
		H₂ also hard to detect
		CO common and easy to detect
		Densest have 1000 atoms/cm³
		T as low as 10 K
		Location of star formation


Barely stable against collapse:
Imagine slightly compressing cloud
	Gravity goes up because material is packed more tightly (R in 1/R² is smaller)
		Tends to make cloud want to collapse

	Pressure goes up because material is packed more tightly (P µ rT) and r higher
		Tends to make cloud want to expand

	For smaller clouds Pressure wins (stable)
	For larger clouds Gravity wins (collapse)
As it collapses and becomes denser, smaller and smaller parts become unstable
Shock wave can trigger collapse


	Temperature changes relatively simple
		Starts out large and relatively cool Must be on red side of diagram
		It heats up as it contracts Must towards the blue

	Luminosity more complicated because it depends on T and R
		Not much energy to start with Luminosity must start out low
		Collapse releases grav. energy Luminosity will rise
		Fusion begins, releases more energy Luminosity at a peak
		Collapse slows, only have fusion now Luminosity declines

	Finally stabilizes on the main sequence


More massive protostars have stronger gravity
Collapse speed will be much faster

Fast collapse and short lifetime means massive stars reach end of lifetime while low mass stars in cloud are just forming
	Supernova shocks may come from earlier generation of stars
		Sequential Star Formation

	Energy from supernova and other effects eventually disrupts cloud – prevents further collapse.


	Young cluster “NGC 2264”
		Few million years old

	High mass stars have reached main sequence
	Lower mass stars are still approaching main sequence

		T Tauri stars

	Naming of classes of stars: Usually named after first star in class: T Tauri
		Stars with letters (RR Lyrae) are typically “variable” stars

	Earlier stages hidden by dust



Alternatives to the proton-proton chain

Fusion of Helium to heavier elements

Proton-proton reaction slow because:
	Need two rare events at once
		High energy collision of 2 protons
		Conversion of p Þn during collision


	Gives way around need for p ®n during the collision

	Still must happen later – but don’t need to rare events simultaneously

	Trade off is need for higher energy collisions (T>16 million K)

	Add p to some nucleus where new one is still “stable”
	Wait for p ® n while that nucleus just “sits around”

	The net effect is still 4 ¹H ® ⁴He
	C just acts like a “catalyst”


	Triple Alpha process
		⁴He + ⁴He ® ⁸Be + g
		⁸Be + ⁴He ® ¹²C + g

	Similar type reactions create heavy elements above 600 Million K

	Plot to left gives:
		x: # of neutrons
		y: # of protons

		Right one – add neutron
		Up one – add proton
		Diagonal – p ® n or reverse
		Jumps: add ⁴He or more


	Divide star into thin shells,calculate how following vary from shell to shell (i.e. as function of radius r)
		P (Pressure)
		T (Temperature)
		r (Density)
	To do this also need to find:
		M (Mass) contained within any r
		L (Luminosity) generated within any r

	P example:


	Limiting case: Assume no nuclear fusion so only energy source is gravity.

	Star is “almost” in hydrostatic equilibrium
		Star radiates energy: If nothing else happened T would drop, P would drop, star would shrink.
		Star does shrink, but in doing so gravitational energy is converted to heat, preventing T from continuing to drop.
		In fact, since star is now more compact, gravity is stronger and it actually needs higher P (so higher T) to prevent catastrophic collapse

	As star shrinks, ½ of gravitational energy goes into heating up star, ½ gets radiated away

	Rate at which it radiates energy, so rate at which it shrinks, is limited by how “insulating” intermediate layers are


Strange counterintuitive result:
	As star radiates away thermal energy it actually heats up (because as it shrinks gravity supplies even more energy)

Star continues to shrink till it gets hot enough inside for fusion (rather than gravity) to balance energy being radiated away.

Nuclear thermostat
	If fusion reactions took place in a “box” with fixed walls:
		Fusion Þ more energy Þhigher T Þ more fusion (explosion)

	If fusion reactions take place in sun with “soft gravity walls”:
		If fusion rate is too high T tries to go up but star expands and actually ends up cooling off – slowing down fusion. (steady rate)


	L µ M^3.5Why?

	Higher mass means higher internal pressure
	Higher pressure goes with higher temperature
	Higher temperature means heat leaks out faster
	Star shrinks until T inside is high enough for fusion rate (which is very sensitive to temperature) to balance heat leak rate


	L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5
	Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun


	M = 0.5 M_sun
	Time = 5.7 times solar lifetime
	Luminosity = 0.09 solar luminosity


As star converts H to He you have more massive nuclei
	Pressure related to number of nuclei
	Gravity related to mass of nuclei
		Pressure would tend to drop unless something else happens
Temperature must rise (slightly) to compensate
Luminosity must rise (slightly) as heat leaks out faster


	Red light = Hydrogen emission
	Blue light = reflection nebula
	Dark lanes = dust

	Astronomy Picture of the Day: http://antwrp.gsfc.nasa.gov/apod



	Dusty disk seen in silhouette

	Central star visible at long wavelengths



	As clouds try to collapse angular momentum makes them spin faster
	A disk forms around the protostar
	Material is ejected along the rotation axis



	Jet along the axis visible as red

	Lobes at each end where jets run into surrounding gas clouds



	Can actually see the knots in the jet move with time

	In time jets, UV photons, supernova, will disrupt the stellar nursery