Midterm Exam #2 Tuesday, March 23

Midterm Exam #2Tuesday, March 23

• Closed book

• Will cover Lecture 8 (Special Relativity) through Lecture 14 (Star Formation) only

• If a topic is in the book, but was not covered in class, it will not be on the exam!

• Some combination of multiple choice, short answer, short calculation

• Equations, constants will all be given

• Standard calculators allowed

• Cell phones, PDAs, computers not allowed

Outline - March 16, 2010

• Recap: Interstellar Medium

• Recap: How are stars made?

• Stages of star birth

• Protostars, protostellar disks, protostellar jets

Interstellar Medium (ISM)

• Material between the stars (specifically in our own Galaxy)

• Most of space is a better vacuum than can be made in a laboratory!

• About 1/5 as much mass in the ISM as in stars in our Galaxy

• Some regions of space contain clouds gas (some clouds are hot: > 10,000 K, some clouds are very cold: 10 K-30 K)

• Chemical composition of ISM: 70% H, 28% He, 2% other elements (by mass)

Why should you care about the ISM?

• Stars had to come from somewhere (the Big Bang didn’t make stars)

• When stars die, their guts have to go somewhere

• If those “somewheres” weren’t the same place, we wouldn’t be here! (a topic for after Spring Break)

Association Between Cold Clouds and Stars

“Heir ist wahrhaftig ein Loch im Himmel”

Wm. Herschel

Image taken in optical / visible light

Cold clouds are transparent in the infrared and radio

Milky Way: Optical

Cold clouds obscure our view at visible wavelengths, but infrared and radio light penetrates the clouds.

Milky Way: Infrared

Milky Way: Radio

Molecular CloudsStellar Nurseries

• Very, very cold (10K to 30K)

• Typical density is 300 molecules per cubic centimeter (vastly less than the density of air at sea level, but vastly more than the density of the ISM on average in our Galaxy)

• Gas is primarily H2 molecules, but you can’t detect them directly! (Note: Helium does not form molecules because it is chemically inert.)

• Most common “tracer” molecule is CO (carbon monoxide)

• About 1% of the mass in molecular clouds is in “dust”

“Dust” in the ISM

• Not dust bunnies, more like the microscopic particles in smoke

• Size of dust grains is smaller than bacteria (typical size is 1 micron = 10-6m)

• Dust grains made mostly of some combination of carbon, silicon, oxygen, and iron

• Dust blocks wavelengths of light that are smaller than the size of the grains ( < 10-6 m)

• Dust easily blocks UV and visible light, but IR and radio light can (usually) pass right through

Horsehead Nebula (in Orion), optical image

Cloud Structure: Gravitational Equilibrium

A stable cloud has a balance of two forces:

INWARD: Gravity

OUTWARD: Pressure

No net force => No motion

What do we mean by “pressure” in a cloud?

• Why does a balloon maintain its shape?

• What happens to a balloon if you blow it up at room temperature, then put it in the freezer for a couple of hours?

• This is what is known as “thermal” pressure (the common pressure for gasses)

• Easiest place for gravity to “win” over pressure is in a cloud of gas that is very cold (= low pressure)

Collapsing Clouds

This cold, dark cloud is collapsing and forming cores that will eventually become stars

This is a cloud where gravity has won the tug-of-war!

Most Stars are Born Inside Clusters

Pleiades Star Cluster

Most molecular clouds contain MUCH more mass than would make a single star

Most molecular clouds are very LUMPY (not smooth)

Likely scenario is that many lumps (which are more dense than the average) contract to form stars at about the same time

Single star formation is possible but probably very rare (because you need an unusually dense, yet low-mass cloud)

Star Formation

Basic stages:

* Cloud collapses

* Protostar forms

* Disk forms

* Planets form

Cloud Collapse

Collapse to ProtostarIf you compress a gas, it will heat up.

Center of a collapsing cloud becomes denser and hotter.

The energy is gravitational. Half the gravitational energy goes into heating the collapsing clout, the other half escapes as light.

The central object is called a “protostar”, and they are very bright! (Because they have very large radii.)

Protostars are hard to see because they are being formed in very dusty regions of space.

Protostar

Protostars vs. Stars

Main difference between a protostar and a genuine star:

Stars generate power by nuclear fusion, protostars generate power by gravitational collapse.

Note: For the most part, stars are stable (neither expanding nor contracting). Protostars are all contracting.

When does the contraction end?

When the core becomes hot enough and dense enough to start nuclear fusion reactions.

Some Protostars

NGC 6334 IRDC 43

Disk Formation

Conservation Laws

The following quantities are conserved:

1. Total Energy

2. Linear Momentum

3. Angular momentum

The total amount of these quantities never changes

Angular Momentum, L

m v

r

For an object of mass m orbiting with velocity v and

distance from rotation axis r,

the angular momentum L is

L = mvr

Spin-up

If the radius of the orbit decreases, and angular momentum is conserved, the velocity must increase.

Li = mviriLf = mvfrfLi = Lf vf = vi (ri/rf)

rirf

vi

vf

Disk Formation

To conserve angular momentum, an object moving perpendicular to the rotation axis must increase speed, and eventually stop because it has a finite energy.

L = mvr

r

r changes here

Disk Formation

r

L=mvr

To conserve angular momentum, an object moving parallel to the rotation axis need not change speed, and is free to move to the equatorial plane.

r doesn’t change here

Disk Formation

Do disks around stars exist? YES

HST Image of Beta Pictoris: note star itself has been blocked out

More Disks around Protostars

Scale bar shows 1,000 AU

HH-34

HH-30 (image & model)

Jets are perpendicular to the disk = rotation plays a role in their formation. Most likely link of rotation and outflowing gas are magnetic field lines. We’ll see this again when we talk about “active galaxies”.

Planet Formation

It shouldn’t be that hard….

Portion of Orion Nebula showing “Proplyds” = Protoplanetary Disks

Proplyds are ~99% gas, ~1% dust

Beta Pictoris will have many planets around in the future?