Compact Objects and end points of stars

Means......

Planetary Nebulae
White Dwarfs
SUpernovae
Neutron Stars
Black Holes
SS433

Mass is the critical factor for "normal" stars: the other important parameter is density

ρ =  Mass =    M  
        Volume     4/3πr³

For comparison

Water (by definition) ρ = 1
Lead ρ ∼ 13
Osmium ρ ∼ 22
Air ρ ∼ .001
Earth ρ ∼ 6
Jupiter ρ ∼ 1
Saturn ρ ∼ .7 (yes, it would float!)
Sun ρ ∼ 1 (but about 150 at centre, much less at outside)

(these are old units: if you compare to a modern book, multiply all densities by 1000)

If stars are small ...

When a star as big as the sun reaches the end of its life, it turns into a planetary nebula: outer 1/3 of star is blown away, leaving very hot core as a white dwarf

The classic example is M57: The Ring Nebula

Central star is a white dwarf (50000°)
Hot blue gas at centre
coolest red gas along the outer boundary.

Credit: H. Bond et al., Hubble Heritage Team (STScI /AURA), NASA

The star blows away its outer layers, so almost all the older ones we knew look like this.

or like this. Gas expands slowly (≈10 km/s)

Star radiates in UV, and most of radiation from nebula is fluorescent. Mass of envelope ≈ .1M₀

Consistent with being penultimate stage in the evolution of a medium mass star,

But now we have all sorts of weird shapes.

This is the Cats-eye nebula: looks like successive explosions

Mz3: The Ant Nebula. Probably magnetic field is creating a "focussed" planetary nebula

Credit: R. Sahai (JPL) et al., Hubble Heritage Team, ESA, NASA

Planetary Nebula CRL 618: this was a red giant a few hundred years ago, but it is now expelling jets of gas

Credit: Susan R. Trammell (UNC Charlotte) et al., ESAIC, HST, ESA, NASA

NGC 2440: a very hot white dwarf which is lowing off its outer layers much faster	Credit: H. Bond (STScI), R. Ciardullo (PSU), WFPC2, HST, NASA
IC 4406: a really weird planetary nebula: probably a cylinder that we see side on. How can a round star make a square nebula? IC 4406 is most probably cylindrical, with its square appearance the result of our vantage point.	Credit: H. Bond (STScI), R. Ciardullo (PSU), WFPC2, HST, NASA

the final stage being....

White dwarfs

As seen in planetary nebula: star with about the same mass as sun but size of earth (∼10000 km )

Density: ∼ 10⁶: ∼ 100,000 times as dense as lead.

This shows some in M4 (a rich globular cluster of stars).

temperature very hot: T ∼ 50000°C: since they are small, they cool very slowly.

Credit: NASA, HST, WFPC 2, H. Richer (UBC)

e.g. Sirius B: probably the best studied;
"Found" by Herschel who noticed Sirius was "wobbling". Observed in 1862 by Alvan Clark: very hard to see since it is close to Sirius A but 1/10000 of the brightness, but mass ∼ 1.05 M_o

This implies a very small object:

T =29500 K
L ∼ 0.003 L₀.
Radius= 1500 km ∼ 1/5 R of the earth.

Since it is so hot, it is bright in X-rays: this shows Sirius B bright and a very dim Sirius A!

Two oddities:

the Dogon people of West Africa have the legend that their ancestors came from a star that circled Sirius and one day they will come back.
Both Greek and Chinese records describe Sirius as red: it may have changed in historical times

What Sirius might have looked like: NGC 3132 (the Eight Burst Nebula), a recently formed planetary nebula with a white dwarf and companion, will probably look like Sirius in 100000 years

Credit: Hubble Heritage Team (AURA/STScI /NASA)

Typically, R∼ 4000 km

Why are white dwarfs so dense? Not possible for a normal gas: in fact the star is supported by the "degeneracy" pressure of electrons, predicted by Chandreshekar in 1930

Very hot (typically O or B type) but very dim (M ≈ 10). Mass is large for such a dim star (≈.5-1.4 M₀)

This implies a very small object:

e.g. Sirius B has mass = 1.05M₀,
T =29500 K and
L ≈ 3 × 10^-3 L₀.
What is its radius and density?

φ = Luminosity/Area = L/4πR² = σT⁴
R = (1.2 × 10²⁴/(4π × 5.56 × 10^-8 × 29500⁴))^1/2

= 1.46 × 10⁶ m ≈ 1/5 R of the earth.

ρ = 1.6 × 10¹¹ kg m^-3

(the sun is about 1400).

Typically, R≈ 4000 km

Such a density is not possible for a normal gas: in fact the star is supported by the "degeneracy" (or Fermi) pressure of electronssee later

Supernova

If Stars are large....

we get supernovae. Approx 1/30 yr known in Milky Way 6 visible in recorded history

1006 Type I SN 1006: History's Brightest Supernova. THis shows remnants of the expanding shockwave
Credit: Frank Winkler (Middlebury College) et al., AURA, NOAO, NSF
1054 Type I Crab. Two superimposed pictures show how it is still expanding

Credit & Copyright: Walter Nowotny (U. Wien, Nordic Optical Telescope
1181 Type II. Now seen as radio source 3C58. THis is in X-rays
Credit: P. Slane (Harvard-Smithsonian CfA) et al., CXC, NASA
1572 Type I Tycho Gas is still very hot, so produces X-rays,seen in blue at front of blast wave Credit: SAO, CXC, NASA
1604 Type I Kepler. Temps still in excess of 1000000°C
Kepler's SNR from Chandra, Hubble, and Spitzer Credit: R. Sankrit and W. Blair (JHU) et al., ESA, NASA Graphic: courtesy STScI
1667 Type II Cas.A
Credit: U. Hwang (GSFC/UMD), J.M. Lamming (NRL), et al., CXC, NASA,

All almost in plane of galaxy.

2 Kinds, distinguished by light curves

TYPE I

Decay rapidly for 30 days, exponentially afterwards
In all galaxies

TYPE II

Rapid decay -> Plateau->Rapid decay

The only one we have seen recently is

Supernova Sn 1987a

Photographically February 23rd (unit is fraction of day!)

23rd .042 - .055, not seen.
23rd 059 - .101, not seen
23rd .39, <7m
23rd .443, m = 6.36
23rd .62, m = 6.11
24th Observed visually Sheldon

v. fast initial rise, then increase to plateau

Star could be identified with known one in catalog Sk-69°202 in Lesser Magellanic Cloud (first time we have been able to do this!) Distance ∼ 156000 lys ∼ 50 kpc
⇒ Mv = -16.0

Distance = 156000 lys ≈ 50 kpc
⇒ Mv = -16.0

Progenitor was blue(!) supergiant M ∼ 20M₀
May have companion star but definitely type II. Surrounded by rings before explosion

Can now see blast wave from explosion hitting rings of material previously ejected

Credit: P. Challis, R. Kirshner (CfA), and B. Sugerman (STScI), NASA

Progenitor was blue(!) supergiant
M ≈20M₀
May have companion star but definitely type II

Problem: would expect red giant to be in C burning phase ⇒ supernova

maybe with companion, atmosphere gets stripped off, so star stays relatively small

The latest supernova:

Supernova 2005cs in M51 (see center of right image). Blue supergiant, type II. Discovered by Wolfgang Kloehr, June 28, 2005

Neutron stars

accidentally observed (1968) as pulsars (Jocelyn Bell etc)

Very regular radio pulses,
period of 4 s ⇒ 2 ms
Note that height of pulse is very irregular

All lie close to Milky Way (i.e. in plane of galaxy).

Therefore must be related to stars

Best known is Crab. Known to be remnant from supernova in 1054 (seen by Chinese)

Pulsar at centre has period of ∼ .03 s

Optical pulsing observed by TV or strobe
Pulses at all wavelengths, in synch.

And we can listen to them!

What pulses?
Now known to be neutron star: predicted by Oppenheimer (yes, that one) in 1935. Density

ρ ∼ 10¹⁵:

i.e. 1000000000000000 times as much as water! Magnetic field is very strong: ~ 1 trillion times stronger than earth

Charged particles travel along lines of force, hence can only escape from poles of neutron star. Hence "lighthouse"mechanism: we only see pulsar when mag. pole points towards us

Do we see all the pulsars?

No, because they would have to be oriented so that they point towards us. rotation period will slow down...

Neutron Star forms from supernova, P ∼ 1 ms
P ∼ 30 ms after 1000 years
P ∼ 5 s over 10⁵ years, also magnetic field may weaken, at which stage radio signal is too weak to be seen

Hence probably large number of radio-quiet neutron stars: essentially impossible to see.

Since neutron stars are so hot we see them in X-rays and γ-rays. This shows how a new satellite (GLAST) will see the sky: the brightest object is he Crab and the second brightest.......

Geminga: a pulsar that had only been seen in γ-rays until it was identified as a very faint star

GLAST Gamma Ray Sky Simulation Credit: S. Digel (USRA/ LHEA/ GSFC), NASA

Black Holes

Invented by .....?

Einstein
Hawking?

Well, actually John Michell rector of Thornhill Church in Yorkshire and

geologist?
philosopher?
astronomer?
Seismologist?
Polymath?

presented his ideas to the Royal Society in London in 1783. and astronomer Pierre Laplace, in 1795.

Escape Velocity

How hard would you need to throw something so that it never came back? energy is conserved: ,the gravitational potential energy of any object at a distance r is

P.E. = -GMm
               r

G = 6.67x10^-11 is Newton's constant, M is the mass of the object from which you are launching, so for the earth is 6x10²⁴ kg and m is the mass of the object. Note P. E. = 0 at r=∞ . The kinetic energy is

K.E. = ½mv²

Total energy is conserved, so at Earth's surface

T.E. = P.E. + K.E. or

E = ½mv² - GMm
                      r

and at r= ∞, P.E. = 0, so want K.E. = 0 as well and Remember T.E. = P.E. + K.E. = 0

so for the earth:

R = 6500 km ,
M = 6x10²⁴
so v = (2GM/R)^½ = 110000 m/s = 11 km/s

However we can interpret this differently: what radius would the earth have for a given escape velocity?	R = 2GM v²
In particular, if the escape velocity is the speed of light c, nothing can escape	R = 2GM c²

This is the Schwarzchild radius ( black-hole radius) for any mass. For the earth it is ∼ 3mm

Statutory Warning:This is a fudge: you cannot treat light as a massive particle, nor can you handle a very strong gravitational field as if it were a weak one...... (there are actually two factors of 2 error which cancel out.....weren't we lucky!)

A black hole is the end product of star with > 10 M₀

But black holes are black:

as the bumper sticker says. So how do we see them?

If we are really lucky....(or unlucky) as a gap in the sky

Too Close to a Black Hole Credit & Copyright: Robert Nemiroff (MTU)

But more likely via the "accretion disk" which will have velocity ∼ c at inner edge, so temp well into X-rays

So want binary, with invisible heavy companion with M > 3M₀, emitting X-rays

Prime candidate is Cygnus X-1, which agrees with position of a massive blue star HD 226868

Mass of primary star ∼ 20M₀
Mass of invisible object M∼ 9M₀
puts out 4x10³⁰ W in X-rays (i.e. 10⁴ L₀!!)

Other weird objects include Cyg X-3, Herc X-1 and

SS-433

SS-433 found as star with very unusual spectrum
X-ray source discovered at same position

Spectrum changes with 164 day cycle, corresponding to v ∼ 50000 km/s

This is something new! Narrow jets travelling at 1/5 speed of light are shot out of poles, probably formed by thick accretion disk around neutron star or black hole: "cosmic lawn sprinkler"

Chemical Anomalies:

We have assumed that all stars have the same chemical composition
90% H, 9% He, 1% metals by number
74% H, 24% He, 2% metals by weight

However some stars do not follow this pattern: in particular all globular cluster stars and many Milky Way stars are metal-poor (≈.1%)

Regular stars are Population I
Metal poor stars are known as Population II.

They lie below the main sequence, since the lack of metals makes the star appear bluer (fewer absorption lines in UV).

Hence we could really think of them as MS stars shifted a bit to the left)

These are very old stars: formed before there was much metal created by supernovae

Some stars have a lot of unexpected heavy elements: e.g. Peculiar A have too much Si, Cr, Eu, Sr

Carbon stars have large amounts of C in their atmospheres, even showing C₂ and CN bands

Heavy metal-oxide stars: ZrO, LaO, YO

All of these are very rare and not understood

Magnetic variables:
Very large magnetic fields
Average B ≈ .1-5 T
(B for sun ≈ .01T ≈ 100 Gauss, inside sunspots ≈ .4T)

Fields very variable, spectrum of stars changes with fields

Where variables fit into the scheme of things...

Stellar evolution once over lightly:

We have now seen all the stages in the stellar evolution of both small and larger stars: they can now be fit into a life-cycle:

(note in passing: we talk about stellar evolution, which is stupid, since we don't talk about the evolution of a baby into an adult.)

Also note: ALL stars go through ALL the stages: the reason why we only see (e.g.) 100 or so planetary nebulae vs 10⁸ normal stars is that the lifetime of a planetary nebula is only ≈ 50000 yrs, vs 10¹⁰ yrs for a main sequence star

Solar mass stars:

Times are approximate in years.

Large Mass stars

Endpoint depends on mass of star:
5M₀ ⇒ neutron star
20 M₀ ⇒ black hole

Note lifetimes are much shorter.

Now we want to look at how stars work