Clicker question:How are the lives of stars with close companions different?

Algol is a binary: a 4.3Msun MS star and a 0.7Msun star

just leaving the MS. What’s odd about that?

Noth

ing

0.7

Msu

n is

not e

nou..

A 4

.3M

sun

star

spen

d...

Bin

ary

star

s al

ways

...

3% 5%

56%

36%

1. Nothing

2. 0.7Msun is not enough mass to form a true star

3. A 4.3Msun star spends less time on the MS than a 0.7Msun star

4. Binary stars always have equal masses

How could this strange pairing have come about?

Stars in Algol are close enough that matter can flow from the subgiant (which just left the main sequence) onto the main-sequence star

Left-hand star is now a subgiant (just leaving the MS), but was originally more massive, say 4.5 solar masses, than its companion (which started with, say, 0.5 solar masses). These original-mass stars are shown at top, on MS.

Left-hand star is now a subgiant (just leaving the MS), but was originally more massive, say 4.5 solar masses, than its companion (which started with, say, 0.5 solar masses).

As the left-hand star reached the end of its MS life and expanded, it began to transfer mass to its companion.

Left-hand star is now a subgiant (just leaving the MS), but was originally more massive, say 4.5 solar masses, than its companion (which started with, say, 0.5 solar masses).

As it reached the end of its MS life and expanded, it began to lose mass to its companion.

Now the companion star is more massive (it went from 0.5 to 4.3 solar masses), while the mass-losing star (now a subgiant) went from 4.5 to 0.7 solar masses.

Eventually the mass-losing subgiant star (the star on the left) will become a white dwarf.

What happens after that? Role reversal! When the star on the right becomes a giant, the white dwarf gains matter from it.

Chapter 13The Bizarre Stellar Graveyard

What is a white dwarf?

White dwarfs are the leftover cores of dead stars, usually made mostly of carbon (some are made mostly of helium; others of oxygen or other elements heavier than carbon, up to and including iron).

Their name comes from the fact they are 'born' glowing white-hot with high temperatures (remember that the core of a normal star has a higher temperature than the surface of the star).

In this Hubble space telescope photo we see Sirius A, the visually brightest star in the sky, and the white dwarf Sirius B as a tiny dot at the lower left. (The spikes of light are artifacts of the camera.)

In X-rays (photo at left), Sirius B, the white dwarf, is brighter than its binary companion Sirius A, the visually brightest star in the sky.

Electron degeneracy pressure supports white dwarfs against gravity, and doesn't depend on temperature. So a white dwarf has the same temperature inside as on its surface (unlike normal stars or planets).

White dwarfs cool off and grow dimmer with time

Hubble space telescope photo of white dwarfs in a globular cluster… they’re very dim!

White dwarfs cool off and grow dimmer with time.

So not all white dwarfs are white: they have colours from blue-white (young) to orange-red (old).

A solar-mass white dwarf is about the same size as Earth

White dwarfs shrink when you add mass to them because their gravity gets stronger. Temperature also increases.

Shrinkage of White Dwarfs

• White dwarfs shrink when they get ‘heavier’!

• Quantum mechanics says that electrons in the same place cannot be in the same state

• Adding mass to a white dwarf increases its gravity, forcing electrons into a smaller space

Shrinkage of White Dwarfs

• Quantum mechanics says that electrons in the same place cannot be in the same state

• Adding mass to a white dwarf increases its gravity, forcing electrons into a smaller space

• In order to avoid being in the same state in the same place some of the electrons need to move faster. That increases the temperature, but not the pressure - degeneracy pressure doesn't depend on temperature

• Is there a limit to how much you can shrink a white dwarf? (That is, how much mass a WD can have?)

The White Dwarf Mass Limit

Einstein’s theory of relativity says that nothing can move faster than light. [The speed of limit is the same relative to all observers.]

When electron speeds in a white dwarf approach the speed of light, electron degeneracy pressure can no longer support the white dwarf.

Chandrasekhar found (at age 20!) that this happens when a white dwarf’s mass reaches 1.4 MSun

S. Chandrasekhar

What can happen to a white dwarf in a close binary system?

White dwarf’s gravity pulls matter off of giant companion, but angular momentum prevents the matter from falling straight in; instead, it forms an accretion disk around the white dwarf.

Friction in disk makes it hot, causing it to glow

Friction also removes angular momentum from inner regions of disk, allowing them to sink onto white dwarf

What would gas in an accretion disk do if there was no friction in the disk?

It w

ould o

rbit

fore

ver

It w

ould e

ventu

ally

fall

in

It w

ould b

e blo

wn

out ..

48%

12%

41%1. It would orbit forever

2. It would eventually fall in

3. It would be blown out of the disk

Hydrogen that accretes onto a white dwarf builds up in a shell on the surface

When base of shell gets hot enough, hydrogen fusion suddenly begins and causes a nova

Nova explosion generates a burst of light lasting a few weeks and expels much of the accreted gas into space

What happens to a white dwarf in a binary when it accretes enough matter to reach the 1.4 MSun limit?

It e

xplo

des

It c

olla

pses

into

a n

e...

It g

radu

ally

beg

ins

fu...

Noth

ing s

pecia

l

36%

0%

24%

40%1. It explodes

2. It collapses into a neutron star

3. It gradually begins fusing carbon in its core

4. Nothing special

Two Types of SupernovaMassive star supernova: (Type II)

Iron core of massive star reaches white dwarflimit and collapses into a neutron star; rest of star 'bounces' off neutron star and explodes

White dwarf supernova: (Type Ia)

As white dwarf in close binary system reacheswhite dwarf limit, carbon fusion begins suddenly, throughout the white dwarf (uniform temperature) …complete explosion of white dwarf into space

One way to tell supernova types apart is through their light curves (showing how luminosity changes with time)

Nova or White Dwarf Supernova?

• Supernovae are MUCH, MUCH more luminous (about 10 million times)

• Nova: H to He fusion in a surface layer, white dwarf left intact

• White dwarf Supernova: complete explosion of white dwarf, nothing left behind

Supernova Type: Massive Star or White Dwarf?

• Light curves differ (brightness changes over time are different)

• Spectra differ (exploding white dwarfs don’t have hydrogen absorption lines --- they're made of carbon and some oxygen, but essentially no hydrogen)

What have we learned?• How are the lives of stars with

close companions different?

• When one star in a close binary system begins to swell in size at the end of its hydrogen-burning life, it can begin to transfer mass to its companion. This mass exchange can then change the remaining life histories of both stars.

• Sun

What have we learned?What is a white dwarf?• A white dwarf is the core

left over from a low-mass star, supported against the crush of gravity by electron degeneracy pressure.

• What can happen to a white dwarf in a close binary system?

• It can acquire hydrogen from its companion through an accretion disk. As hydrogen builds up on the white dwarf’s surface, it may ignite with nuclear fusion to make a nova, or compress the white dwarf until carbon fusion creates a supernova.

Activity 25, Special Relativity, p. 83

Parts I, II and IV (skip part III for now)

1. You’re standing in the aisle of a plane flying at constant speed, and drop your headphones.

They

fall

dire

ctly

bel

..

They

fall

dow

n, b

ut l...

They

fall

dow

n, b

ut la.

.

89%

1%10%

1. They fall directly below your hand.

2. They fall down, but land towards the back of the plane.

3. They fall down, but land towards the front of the plane.

2A. According to Einstein, what will Pertti measure for the speed of

the pulse sent by Riitta?

Lig

htspee

d c m

inus

...

Lig

htspee

d c

Lig

htspee

d c p

lus

ro...

33% 33%33%

:10

1. Lightspeed c minus rocket speed V

2. Lightspeed c

3. Lightspeed c plus rocket speed V

2B. What will Pertti (on a rocket skateboard) measure for the speed of light

from a streetlight in front of her?

Lig

htspee

d c m

inus

...

Lig

htspee

d c

Lig

htspee

d c p

lus

sk...

33% 33%33%

:30

1. Lightspeed c minus skateboard speed v

2. Lightspeed c

3. Lightspeed c plus skateboard speed v

2C. What will Pertti (on a rocket skateboard) measure for the speed of a light

pulse sent by Riitta in her rocket ship?

Lig

htspee

d c m

inus

...

Lig

htspee

d c

Lig

htspee

d c p

lus

s...

33% 33%33%

:30

1. Lightspeed c minus skateboard speed v minus rocket speed V

2. Lightspeed c

3. Lightspeed c plus skateboard speed v plus rocket speed V

2D. Velocity = length divided by time. If lightspeed is absolute…

Len

gth a

nd/or t

ime

mu..

Len

gth m

ust b

e re

lativ

e.

Tim

e m

ust b

e re

lativ

e.

Len

gth a

nd/or t

ime

mu..

29%

61%

7%3%

1. Length and/or time must be absolute.

2. Length must be relative.

3. Time must be relative.

4. Length and/or time must be relative.

Part IV, page 85-86

6A: Referring to Fig. 3, in which Graciela is stationary, whose light pulses travel the greater

distance between ticks?

The

light p

ulses

in G

r...

The

light p

ulses

in D

i...

Nei

ther

– b

oth th

eir l

ig..

0% 0%0%

:10

1. The light pulses in Graciela’s clock

2. The light pulses in Dimitris’ clock

3. Neither – both their light pulses travel the same distance between ticks

6C: Graciela perceives that the interval between ticks on Dmitris’ clock …

Is lo

nger th

an th

e in

t...

Is s

horter t

han th

e in

...

Is th

e sa

me

as th

e in

t...

0% 0%0%

:10

1. Is longer than the interval between ticks on her own clock

2. Is shorter than the interval between ticks on her own clock

3. Is the same as the interval between ticks on her own clock

What we know: Lightspeed c is a constant. c=(distance traveled by light)/(travel time). As seen by

Graciela, Dimitris’ light pulses travel a greater

distance. Therefore:

As

seen

by

Gra

ciel

a, t.

.

As

seen

by

Gra

ciel

a, t.

.

0%0%

:10

1. As seen by Graciela, the travel time (time between light pulses) is longer for Dimitris’ clock.

2. As seen by Graciela, the travel time (time between light pulses) is shorter for Dimitris’ clock.

MOVING CLOCKS RUN SLOW

MOVING CLOCKS RUN SLOW

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

MOVING CLOCKS RUN SLOW

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

• From the point of view of someone not moving relative to the clock, you and your watch are moving. So from that person’s point of view, your watch is running slow relative to the clock.

Dmitris perceives that the interval between ticks on Graciela’s clock …

Is lo

nger th

an th

e in

t...

Is s

horter t

han th

e in

...

Is th

e sa

me

as th

e in

t...

0% 0%0%

:10

1. Is longer than the interval between ticks on his own clock

2. Is shorter than the interval between ticks on his own clock

3. Is the same as the interval between ticks on his own clock

6E: Whose clock is keeping the “right” time?

Gra

ciel

a’s

Dim

itris

’

Both

clo

cks

Nei

ther

clo

ck

0% 0%0%0%

:10

1. Graciela’s

2. Dimitris’

3. Both clocks

4. Neither clock

A CLOCK MOVING RELATIVE TO YOU RUNS SLOWER THAN A CLOCK NOT

MOVING RELATIVE TO YOU

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

• From the point of view of someone not moving relative to the clock, you and your watch are moving. So from that person’s point of view, your watch is running slow relative to the clock.