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PH507
Astrophysics
Professor Michael Smith
1
Protostar – Young Star evolution is not so well known:
From Protostar to Young Star

Protostars are cool when they begin to shine in the visible so start to the
lower-right of the HR diagram.

Continued gravitational contraction of the protostar.

Decreasing surface area means a reduction of luminosity

Decreasing radius (higher pressure and therefore higher temperature)

Different masses of star will follow different paths to their main
destination on the main sequence.
Protostars shine because they are hotter than their surroundings:

Need an energy source to stay hot, but

Central temperature is too cool for nuclear fusion to ignite
Initial energy source is Gravitational Contraction (aka, the Kelvin-Helmholz
Mechanism):
PH507
Astrophysics
Professor Michael Smith

The Protostar shrinks slowly, releasing gravitational energy

50% goes into photons, and is radiated away as starlight

other 50% goes into heating the Protostar interior
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How long can does this last?
Kelvin-Helmholz Timescale
To understand how long a Protostar can shine by Gravitational Contraction, we
need to compare two numbers

The Energy Source: (M2/R)

The Energy Loss Rate: Luminosity (L)
The ratio is the Kelvin-Helmholz Timescale:
The Kelvin-Helmholz timescale is ~30 Myr for a 1 solar mass protostar.
Consequences:

Shorter K-H time for high-mass protostars

Longer K-H time for low-mass protostars
H-R Diagram of pre-Main Sequence evolution for stars of various masses:
PH507
Astrophysics
Professor Michael Smith
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Note the vertical Hayashi tracks: as a low-mass protostar contracts, convection
transports energy to surface. Opacity at surface determines the surface
temperature. Luminosity falls but temperature is constant.
Later, or for high-mass stars, radiative energy transport becomes effective –
central temperature rises – luminosity increases slightly as surface temperature
rises and contraction continues.
Brown Dwarfs: Failed Stars
• Stars between 1/100 and 1/12 the mass of the Sun may be able to burn
deuterium into helium for a short time, but cannot sustain nuclear
reactions. Such “failed” stars are called brown dwarfs. They are similar
in size to Jupiter with masses of 10-80 times that of Jupiter
• The Lithium Test. At a temperature of 2 million K, a lithium atom can
combine with a proton to form two He atoms. In a star that can sustain the P-P
chain, the core is hot enough to have burned all the Li to He. If Li does appear
in the spectrum, the center of the star must be cooler than 2 million K. In
addition to Li, brown dwarfs show methane and water absorption in their
spectra.
PH507
Astrophysics
Professor Michael Smith
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PH507
Astrophysics
Professor Michael Smith
5
At an age of 1 million years the most massive stars have contracted to the
Main sequence, lived out their hydrogen-burning lifetimes and are evolving
off the Main Sequence. Lower mass stars like the sun are still in the PreMain Sequence phase. The youngest clusters observed in the Milky Way
are estimated to have ages of a few million years.

At 10 million years stars of 1 solar mass are still above the Main
Sequence, just beginning nuclear reactions. They will be observed as TTauri stars. Stars with M ~ 20M are just moving off the Main Sequence.
Such clusters will still be associated with regions of gas & dust from
which they formed.

At 100 million years most stars are on or nearing the Main Sequence,
but stars with M > 5M are now moving off the Main Sequence. The
Pleiades cluster is estimated to have an age of about 100 million years.
PH507
Astrophysics
Professor Michael Smith
6

With an age of a billion years, cluster stars with masses between 2--3 M
are moving off the Main Sequence. The Main Sequence location at
which stars are just beginning to exhaust the hydrogen fuel in their cores
and
move toward the Red Giant region is called the Main Sequence Turnoff

The oldest clusters in the Milky Way, the globular clusters, are estimated
to have ages of the order of 10-15 billion years and show H-R Diagrams
like that at the left. Because the globular cluster stars have very low
abundances of the elements heavier than helium (C,N,O ...) some
corrections need to be made to compare their H-R diagrams to younger
clusters with higher
abundances.
Observed clusters:
After ten million years:
H-R diagram of stars in the cluster NGC 2264

On this diagram the Main Sequence is marked
with a red line.

We don't see the hottest, most luminous (type
O) MS stars since they have evolved out of
the MS stage already.

The cooler stars are still collapsing and
haven't yet reached their MS stage.
PH507
Astrophysics
Professor Michael Smith
7
After one hundred million years

All the O and B MS stars have used up their Hydrogen.

When we look at this cluster's H-R diagram, we shouldn't see O and B
Main Sequence stars.

All of the less massive stars should still be in their MS stage, since they
burn their H slower than the O and B stars.

In this H-R diagram for the Pleiades we don't see any of the hottest Main
Sequence Stars.

The "Turnoff Point" is the hottest temperature MS star which exist in the
cluster.

The temperature can be used to estimate the age of the cluster. The
hotter the turnoff point temperature, the younger the cluster.

The stars found above the red line correspond to the O and B stars
which have left the Main Sequence.
After 3 billion years:

After 3 x 109 years, all of the O, B, and A stars have used up their H.

We won't see O, B, A Main Sequence stars when we plot an old cluster's
H-R diagram.
PH507
Astrophysics
Professor Michael Smith
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
An HR diagram of the Open Cluster M67 is shown below.

Here we see only the cooler main sequence stars.

We also see lots of Red Giants.

This suggests that Red Giants are what the high mass stars look like
when they use up their Hydrogen.
**Mass Dictates the Life of a Star** (Russell-Vogt Theorem)

The early stages of evolution for the medium and high mass stars are
very similar to the low mass stars, but they occur faster.

The life of stars of all masses during the main sequence phase is very
similar.

The main difference is that the higher the mass, the more luminous the
star and the shorter the main sequence lifetime.

What happens after the main sequence phase depends on the mass of
the star.

Define the following mass ranges:
o
Low Mass Stars: M < 4 MSun
o
Medium Mass Stars: 4 MSun < M < 8 MSun
o
High Mass Stars: M > 8 MSun
Medium and High mass stars are not degenerate while red giants.

Low mass stars end up as White Dwarfs composed of mainly Carbon
and Oxygen.
PH507
Astrophysics
Professor Michael Smith
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
Medium mass stars have higher temperatures in their cores.

The higher T allows fusion reactions creating Oxygen, Neon, Sodium
and Magnesium.

Medium mass stars end up as White Dwarfs composed of the higher
mass elements.
High Mass Stars: Mass > 8 MSun

High mass stars can have many successive stages of fusion of higher
mass element in a core and lighter elements in shells around the core

The general trend is for the star's surface to become cooler and to
become a blue giant and later a red supergiant.

If the mass of the white dwarf in the core is larger than 1.4 M Sun (called
the Chandrasekhar limit) the electrons would have to move faster than
the speed of light in order to create enough degeneracy pressure to halt
the gravitational collapse.

Electrons can't move faster than light, so a white dwarf with M > 1.4 M Sun
collapses.

Main sequence stars with mass larger than about 8 MSun eventually form
white dwarf stars with masses larger than the Chandrasekhar limit and
collapse.

This is the beginning of a Core Collapse Supernova also known as a
Type II Supernova
A Supernova in a star with 8 MSun < M < 20 MSun

When the supernova begins the iron core collapses rapidly under freefall and becomes denser.

When the density is very high, protons and electrons can combine
together to form neutrons and neutrinos:
p + e- -> n + nu

This reaction is called inverse beta decay.

The neutrinos escape easily since they don't interact well with matter and
carry off energy.

The resulting neutron gas collapses until the density is extremely high.

The core of neutrons held stable by neutron degeneracy pressure is
called a neutron star.

The outer layers collapse and collide with the hard surface of the newly
formed neutron star.

This collision causes a violent rebound and a shock wave.

This energy can provide the fuel which allows the endothermic fusion
reactions to create very high mass elements such as Uranium. The
PH507
Astrophysics
Professor Michael Smith
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supernovae are responsible for all the elements with masses larger
than iron found on Earth.

Core Collapse Supernovae probably occur about once every 50 years
in our galaxy, but most of them are hidden by the dust of the galaxy.
A Supernova in a star with M > 20 MSun

The evolution of very massive stars is similar with the formation of a
neutron star at the core in a supernova.

However, neutron stars (like white dwarfs) have a maximum mass near 3
MSun, over which neutron degeneracy pressure can't balance gravity.

In the very high mass stars, the neutron star goes over the critical mass,
and the neutron star collapses.

No other sources of pressure are available, and the collapsing material
forms a black hole.
A White Dwarf in a Semi-Detached Binary: Type Ia Supernovae

Suppose that a white dwarf is receiving mass from a companion star.

The White dwarf's mass will slowly increase.

If it receives enough mass, the White Dwarf's mass will approach the
Chandrasekhar limit and collapse.

The collapse causes the degenerate Carbon gas in the White dwarf to
begin fusing together explosively.
This type of supernova is essentially a giant Carbon bomb.
PH507
Astrophysics
Professor Michael Smith
11
The Sun: A Model Star

Our Sun is the nearest star. The fascinating properties and phenomena of
the solar surface layers are easily observed and have been studied
intensely. Unfortunately, models for understanding solar phenomena have
not kept pace with such detailed data. Because the Sun is a fairly typical
star and because it is the only star that spans a large angular diameter as
seen from the Earth, the discussion here serves as the physical basis to
investigate the other stars.
Sun
Earth
Mass (1024 kg)
1,989,100.
5.9736
GM (x 106 km3/s2)
132,712.
0.3986
12
3
Volume (10 km )
1,412,000.
1.083
Volumetric mean radius (km) 696,000.
6371.
Mean density (kg/m3)
1408.
5515.
2
Surface gravity (eq.) (m/s ) 274.0
9.78
Escape velocity (km/s)
617.7
11.2
Ellipticity
0.00005
0.0034
0.015
2
Moment of inertia (I/MR ) 0.059
0.3308
0.178
Visual magnitude V(1,0) -26.74
-3.86
Absolute magnitude
+4.83
24
Luminosity (10 J/s)
384.6
Mass conversion rate (106 kg/s)
4300.
Mean energy production (10-3 J/kg)
0.1937
6
2
Surface emission (10 J/m s)
63.29
Spectral type
G2 V
Model values at center of Sun:
Central pressure:
Central temperature:
Central density:
2.477 x 1011 bar
1.571 x 107 K
1.622 x 105 kg/m3
(Sun/Earth)
333,000.
333,000.
1,304,000.
109.2
0.255
28.0
55.2
PH507
Astrophysics
Professor Michael Smith
12
The Structure of the Sun

1 AU from the Earth with a radius of 6.96 x 10 5 km (109Ro) and a mass of
1.99 x 1030 kg (333,000Mearth), and luminosity, (rate of total radiative
energy output) of 3.86 x 1026 W.

The average density of the Sun is only 1400 kg/m 3 - consistent with a
composition of mostly gaseous hydrogen and helium.

From its angular size of about 0.5° and its distance of almost 150 million
kilometres, we determine that its diameter is 1,392,000 kilometres (109
Earth diameters and almost 10 times the size of the largest planet, Jupiter).

All of the planets orbit the Sun because of its enormous gravity. It has about
333,000 times the Earth's mass and is over 1,000 times as massive as
Jupiter.

The Sun is made of 94% Hydrogen, 6% Helium, - the other elements make
up just 0.13% (the three most abundant ‘metals’ Oxygen, Carbon, and
Nitrogen make up 0.11%).
The Sun's Photosphere and Chromosphere
The Sun can be split into two regions:

The interior is a sphere with radius R = 7x108m

The atmosphere lies on top and has the following layers (from innermost
to outermost):
o
The photosphere is about 300 km thick. Most of the Sun's visible
light that we see originates from this region.
o
The chromosphere is about 2000 km thick. We only see this layer
and the other outer layers during an eclipse.
o
The corona extends outwards for more than a solar radius.
The Photosphere
An image of the Sun's Photosphere shows:

Limb Darkening. Limb darkening is evidence that the temperature of the
Sun's photosphere decreases outwards.

Sunspots
The Sun's Spectrum is an Absorption Spectrum

Since the photosphere is cooler and less dense than the interior region it
allows the continuous blackbody spectrum to flow through it.

Only at the wavelengths at which atoms in the photosphere can absorb
light will photons be impeded in their outward travel.
PH507
Astrophysics
Professor Michael Smith
13
Sunspots:

Sunspots are regions with high magnetic fields (1000 x higher magnetic
field than average)

Typical size of spots is similar to the size of the Earth.

These regions are cooler (redder) than average, so they look darker than
the surrounding hotter region.

Sunspots are related to X-ray flares, mass ejections and the aurora seen
on Earth.
Close-up Picture of a group of Sunspots

The darkest regions (umbra) have the largest magnetic fields and the
coolest temperatures. The outer brighter region is the penumbra.

Sunspots come in pairs: each member of the pair has opposite polarity.
(I.e. one is a north magnetic pole, the other is south.)
PH507
Astrophysics
Professor Michael Smith
14

Each sunspot region lasts for a few days to a few weeks.

The filaments in the penumbra are due to the magnetic lines of force.
Movement of Sunspots

Movements of spots reveal that the Sun rotates with a period close to
one month.

Equator rotates faster than the higher lattitudes. (Differential Rotation)

You can find photos of the Sun in many different wavelengths (updated
daily) at the website: http://umbra.nascom.nasa.gov/images/latest.html
http://science.nasa.gov/ssl/pad/solar/surface.htm
Granules
Close-up Picture of the Photosphere

Granules are the cell-like features seen on the Sun's photosphere that
cover the entire solar surface, except for the sunspot regions..

The granules are the tops of convective cells which lie in the convective
zone just below the photosphere.

Each cell ranges in size from 100 km to 1000 km across and may last up
to half an hour.

The bright regions are zones where hot gas rises They are the tops of
deep gas columns where energy is transported by convection. Spectra of
the centers of the granules shows these regions to be a few hundred
Kelvin hotter than the surrounding darker lanes.

The dark borders are the places where the cool gas sinks.

The gas moves outwards or inwards at speeds up to 7 km/s. (Measured
through Doppler shifts.).
PH507
Astrophysics
Professor Michael Smith
15
The Sun's Chromosphere
A Solar Eclipse

The photosphere is much brighter than the outer parts of the Sun's
atmosphere (the chromosphere and the corona), so regular photos of
the Sun do not show the outer atmosphere.

During a solar eclipse the Moon blocks out the light from the
photosphere and we can only see the light coming from the
chromosphere and corona.
The Chromosphere with a close-up of the spicules.

The Chromosphere is not exactly a sphere: there are many spicules and
prominences which jut outwards.

Magnetic fields help support the spicules and the prominences.

The red colour results from the emission of Balmer-alpha photons:
electrons jumping from the n=3 level to the n=2 level.
The emission lines can only occur if the gas in the chromosphere is very hot
and the density is very low. The chromosphere is hotter (but less dense) than
the photosphere.
In the spicules, which are best observed in H , gas is rising at about 20 to 25
km/s. Although spicules occupy less than 1% of the Sun’s surface area and
have lifetimes of 15 minutes or less, they probably play a significant role in the
mass balance of the chromosphere, corona, and solar wind, and occur in
regions of enhanced magnetic fields
Solar spicules, short-lived narrow jets of gas that typically last mere minutes,
can be seen sprouting up from the solar chromosphere in this H alpha image of
PH507
Astrophysics
Professor Michael Smith
16
the Sun. The spicules are the thin, dark, spikelike regions. They appear dark
against the face of the Sun because they are cooler than the solar photosphere
Prominences

Close-up picture of the chromosphere showing a prominence.
The prominences are loops of gas which arch over sunspot regions.
The quiescent prominences are very stable and can last weeks or months.
Eruptive Prominences

Some of the prominences will erupt, causing gas to be flung outwards.

The gas travels outwards about 70,000 km in the course of a few hours.

Prominences are more likely to erupt when the magnetic fields near the
sunspots are changing. Variation of Temperature in the Sun's
Atmosphere
PH507


Astrophysics
Professor Michael Smith
17
Photosphere: Temperature decreases outwards.
o
At bottom: T = 6400 K
o
At top: T = 4000 K
Chromosphere: Temperature increases outwards.
o
At top: T = 10,000 K

Transition Zone: Temperature shoots up to near 1 million K

Corona: Temperatures increase to about 2 million K

The source of this heat is not well understood. Current theories suggest
that magnetic waves might transport energy from the convective zone to
the corona.
The Transition Zone

The next picture shows the transition zone as seen through a filter which
only sees the light coming from an electronic transition of Sulfur VI at
temperatures of about 200,000ºC. Instead of hydrogen, the light emitted
by the transition region is dominated by such ions as C IV, O IV, and Si
IV (carbon, oxygen, and silicon each with three electrons stripped off).
These ions emit light in the ultraviolet region of the solar spectrum that is
only accessible from space.
PH507
Astrophysics
Professor Michael Smith
18

These emission lines are Ultra-violet. which are only possible when the
gas is very hot, near 100,000 K.

The structures seen here are similar to those seen in the chromosphere.
The Corona

A visible light photograph of the Corona during a solar eclipse.
Photograph of the solar corona during the July, 1991 eclipse, at the peak of the
sunspot cycle. At these times, the corona is much less regular and much more
extended than at sunspot minimum. Astronomers believe that coronal heating
is caused by surface activity on the Sun. The changing shape and size of the
corona are the direct result of variations in prominence and flare activity over
the course of the solar cycle.
PH507
Astrophysics
Professor Michael Smith
19

The Corona emits X-rays.

This image corresponds to an electronic transition of highly ionized iron.
(Iron stripped of 11 of its electrons.)

Iron can only lose 11 electrons and emit this X-ray light if the
temperature is more than one million K.

The dark regions are coronal holes which are lower density than
average.
PH507

Astrophysics
Professor Michael Smith
20
The solar wind originates from the coronal holes.
Coronal Loops
Huge numbers of small, closely intertwined magnetic loops continuously
emerge from the Sun's visible surface, clash with one another and dissolve
within 40 hours.
The loops seem to form a tight pattern that form a magnetic carpet. Their
interaction generates electrical and magnetic short-circuits
(magnetic
reconnection) and releases enough energy to heat the corona to temperatures
hundreds of times higher than those of the solar surface.
PH507
Astrophysics
Professor Michael Smith
21
Coronal loops come in a variety of shapes and sizes, but most are enormous,
capable of spanning several Earth's. Photo: NASA and the TRACE team
Solar Flares

Solar flares are large outbursts similar to eruptive prominences, but
larger and more energetic.

Solar flares increase the amount of particles which escape into the solar
wind.

If the particles ejected from the flare hit the Earth, then we get intense
auroral displays.
A negative effect is that the solar wind particles can disrupt radio transmissions.
Coronal Mass Ejection

When an eruptive prominence or a solar flare occurs, a coronal mass
ejection (CME) can also take place.
A CME is a stream of plasma (charged particles) ejected from the corona.
PH507
Astrophysics
Professor Michael Smith
22
The Solar Wind

UV images show the flow of gas from the Sun.

The solar wind is a stream of charged particles (protons and electrons)
which flow outwards from the coronal holes.

The wind speed is high (800 km/s) over coronal holes and low (300
km/s) over streamers. These high and low speed streams interact with
each other and alternately pass by the Earth as the Sun rotates.

The solar wind particles flow throughout the solar system. The variations
buffet the Earth's magnetic field and can produce storms in the Earth's
magnetosphere
Further Evidence for the Solar Wind

A comet's tail always points away from the Sun, no matter in what
direction it moves.

The particles in the solar wind push outwards on the gas sublimating
from the comet so that the tail points away from the Sun.
Aurora

When solar wind particles hit atoms in the Earth's atmosphere, they
cause atoms excitation.

The electrons in the excited atoms then jump down to a lower state and
give off radiation.

The green and red aurora are usually due to electronic transitions in
Oxygen.
PH507
Astrophysics
Professor Michael Smith
23

There is almost always an auroral oval over the Earth's north and south
magnetic poles.

The size of the auroral oval and the intensityof the emissions depend on
the strength of the solar wind.
The Solar Cycle

The number and location of sunspots and the severity and number of
flares, eruptive prominences and coronal mass ejections are not
constant in time.

The number of sunspots on the Sun varies on an 11-year cycle. The
number increases from zero at solar minimum, to over 100 at solar
maximum, 5 1/2 years later.

Every 11 years the polarity of the Sun's magnetic field flips.

Therefore, the Sun's magnetic field varies on a 22-year cycle.

As the number of sunspots increases, the number of flares and other
forms of activity increase.

The luminosity of the Sun also increases when there are lots of spots!
(Bright plages also increase when sunspots increase.)

The time at which there is a maximum number of spots is called Solar
Maximum.

The most recent Solar Maximum occurred late in 2000.

The period of time from 1645 to 1715, known as the Maunder minimum,
was a time with a very low number of sunspots.

During the Maunder minimum Europe had colder than usual weather.
PH507
Astrophysics
Professor Michael Smith
24
Predictions about the present sunspot cycle from
http://science.nasa.gov/ssl/PAD/SOLAR/sunspots.htm.
Polarity of Sunspots
 The most important characteristic of a sunspot is its magnetic field. The
magnetic field in a typical sunspot is about 1000 times greater than the field
in neighbouring, undisturbed photospheric regions. Typical field strengths
are near 0.1 T, but fields as strong as 0.4 T have been measured.
 Related to the magnetic field is a horizontal flow of gas in the sunspot
penumbra: gas moves out along the lower filaments and inward along the
higher filaments (at speeds up to 6 km/s).

In each sunspot pair, one sunspot is a north pole (green) and the other is
a south pole (yellow).

Note that in the northern hemisphere of the Sun, the north poles are
always to the right of the south poles.

In the southern hemisphere, the south poles are always to the right of
the north poles.
PH507
Astrophysics
Professor Michael Smith
25
Location of Sunspots

At the beginning of each 11-year cycle the sunspots appear at middle
latitudes above and below the Sun's equator. Very few sunspots are ever
found at latitudes greater than ±40.

As the cycle progresses, the sunspots appear closer to the equator .
Most spots are near ±15 at maximum, and the few spots at the end of
the cycle cluster near ±8.

The cycles overlap at the time of sunspot cycle minimum with old cycle
spots near the equator and new cycle spots at high latitudes.

A sunspot dies at the same latitude where it was born

The sunspots follow active latitude belts during the course of a cycle.
Less clear, but just as tantalising, large active regions and spot groups
seem to fall into preferred longitudes during a cycle - active longitude
belts. Concentrations of magnetic fields appear to persist below the
photosphere, so that new spot groups arise from about the same
locations as previous ones. The active longitude belts sometimes
appear about 180 apart
This plot is known as a "butterfly diagram". It shows the number and position of
sunspots over time.
PH507
Astrophysics
Professor Michael Smith
26
At the end of the 11 year cycle the opposite polarity sunspots at the
equator "cancel" each other out and the Sun's polarity flips.
Flux Tube Model for the Sun's Magnetic Activity

The magnetic field lines get "frozen" into the gas of the Sun and
get dragged around when the gas moves.

The differential rotation of the Sun drags the magnetic field
lines into "horizontal" tubes which break out of the surface,
causing sunspots with the observed polarity.