Astro 1050 Mon. Mar 1, 2004

Today: Continue (Finish?) Ch. 9, ISM

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, 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


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, 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