Properties of Stars. Distances to Stars parallaxapparent The distance to a nearby star can be...

Properties ofStars

Distances to Stars

The distance to a nearby star can be measured by observing its parallaxparallax the apparentapparent shift of its

position on the sky relative to more distant stars. Parallax is caused by Earth’s motion around the Sun.

A parsecparsec is the distance at which 1 AU subtends an angle of 1 arcsecond. 1 pc = 3.26 light years.

A star with a parallax p = 1 arcsec must be 1 pc away:

dd (pc) = (pc) = 11//pp

Apparent vs. Intrinsic Brightness

The apparent brightness of a light source depends on:

(a) its intrinsic brightness (a.k.a. luminosityluminosity)

(b) its distance from us.

Inverse-Square Law

The apparent brightness of a star decreases as the distance to the star increases.

Brightness is proportional to 1/d 2.

LLFF = = __________

44dd 2 2

LL = intrinsic luminosity (energy emitted per second)dd = distance to light sourceFF = flux (i.e., apparent brightness)

Luminosities of Stars

• Thus, if we can measure the apparent brightness and distance of a star and can estimate its temperature (from Wien’s Law) we can determine:

LuminosityLuminosity (from apparent brightness and distance)

RadiusRadius (from luminosity and temperature)

LL = 4 = 4RR22TT 4 4

• From the Stefan-Boltzmann Law, the hotter a star is, the more energy it emits per square meterper square meter of surface area per second.

• The larger the radius of a star, the greater its surface area.

• So, we can express a star’s luminosity as:

Stellar Spectra

Recall that the temperature of a star determines:

• the overall shape of its spectrum

• the spectral line features it exhibits

Line Strength vs. Temperature

Stellar Spectra

What do the lettersO, B, A, F, G, K, Mmean?

Spectral Classification

So, the spectral class sequence is really a temperaturetemperature sequence.

The H-R Diagram

Plotting the luminosities of stars vs. their spectral types (i.e., temperatures) we find that stars follow certain well-defined patterns.

The H-R Diagram

Another H-R Diagram:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Recall that

Thus, stars that have the same spectral type (i.e., temperature) but different luminosities must have different radiidifferent radii.

How can stars of the samesame spectral type have differentdifferent luminosities?

LL = 4 = 4RR22TT 4 4

We can estimate the radiiradii of stars. We call them “dwarfs,” “giants,” or “supergiants” according to their sizes. 90% of the stars we observe are dwarfs on the “Main Sequence.”

Sizes of Stars

We divide dwarf, giant, and supergiant stars into various luminosity classesluminosity classes, denoted IV.

Stars that have the same spectral type but different luminosity classes are distinguished by the widths and strengths of the absorption lines in their spectra.

Luminosity Class

Stellar Demographics

There are many more small, faint red dwarf stars on the main sequence than large, luminous blue stars.

There are many more main sequence stars than giant or supergiant stars.

The Formation of Stars

Different types of nebulae:

The Horsehead Nebula in the constellation of Orion

Emission Nebulae

Hot, blue stars emit a lot of ionizing radiation, which excites the gas that surrounds them.

Another example: the Eagle nebulae

Lifetimes of Hot, Luminous Stars

The big, hot, luminous, blue stars on the upper part of the main sequence have relatively short lifetimes.

Star formation and gas clouds

These hot, blue stars are often found associated with gas clouds in the Milky Way. Because of this association, we believe all stars must be born in such gas clouds.

The collapse of a gas cloud

The pressure in the gas increases as the particles in the gas move faster and faster in random directions. This pressure will push outwards against the gravitational forces.

At the same time the gas cloud will be losing thermal energy through radiation so this increase in pressure is usually not enough to halt the collapse.

Stars form from the rapid collapse of a gas cloud due to gravitational forces.

As the cloud collapses, it converts gravitational energy into thermal energy and heats up.

Collapse of a gas cloud

Because of the conservation of angular momentum, any rotation of the cloud will be amplified as it collapses. A protostar will be surrounded by a swirling disk of material.

Early stages of star formation are hidden from our view by the dense cloud of gas still surrounding it.


The Eagle Nebula

Protostar Evolution

The rapid collapse of the gas cloud will slow down as the temperature and pressure increases in its center. The protostar formed at the center of the cloud will then gradually contract and heat up until...

A star is born…

...the gas at the center of the star is hot and dense enough to ignite nuclear fusion.

This will maintain the pressure and temperature of the gas sufficiently to balance the immense gravitational forces and halt the contraction of the protostar.

Protostar Evolution

The more massive a star is, the more quickly it is born.

In stars like the sun, most of the energy is produced via the proton-proton chain, in which 4 H atoms are fused into a single He atom, and energy is released.

Stellar Energy Sources

In higher mass stars, some of the energy produced in the stellar core comes from a different nuclear reaction chain, called the CNO cycle.


Stellar Mass Limits

Young Stars

When a star is very young, the outpouring of energy from nuclear fusion can drive away the remains of the gas cloud surrounding it, but it will usually still be surrounded by a dark disk of material which is in the process of falling onto the star (and may eventually form planets!).

Young Stars

Stellar Structure & Evolution

Hydrostatic Equilibrium

In a stable star, the inward pull of gravity is exactly balanced by the outward force of gas pressure at each level within the star.

This is known as the law of hydrostatic equilibriumhydrostatic equilibrium.

When stars are not in hydrostatic equilibrium, they will either expand or contract.


One key piece of the puzzle is how stars produce energy. Most of the energy is produced in their cores via the fusion of 4 H atoms into a He atom.

Energy Transport in Stars

Another physical process that is important inside stars is the way in which energy gets transported from the core to the surface. For normal stars, this happens by convectionconvection, radiationradiation, or both.

In the sun, energy is transported via radiation in the central regions, but by convection in the outer regions.


Cross sections of main sequence stars of different masses, showing the modes of energy transport the different stars use.


Modeling Stellar Structure

The structure and evolution of stars is accurately modeled with only a few well understood laws of physics. Astronomers use these laws and powerful computers to compute stellar models.

Main-Sequence Lifetime vs. Mass

• All stars, regardless of their mass, spend roughly 90% of their total lifetimes as main sequence stars.

• Stars end their main sequence lives when their supply of hydrogen fuel runs out in the core.

• The most massive stars (O and B types) have very short lifetimes compared to low-mass stars (K and M types).

Main-Sequence Evolution

Stars begin their main sequence lives when they initiate hydrogen burning in their cores. They are located on the zero-age zero-age main sequencemain sequence (ZAMS) at this time. As they age, they evolve slowly away from the ZAMS.

When stars evolve away from the main sequence they become red giantsred giants.

Recall that the equation

L = 4R2T 4

defines lines of constant radius on an H-R diagram.

Red giants are… giant and red.

Post-MS Evolution

Post-MS Evolution

The sun today and the sun as a red giant star.

Post-MS Evolution

H-R diagram showing the evolutionary paths followed by stars that are more massive than the sun. Note how these two tracks pass through the regions occupied by giant and supergiant stars.

Post-MS evolutionary track for a 5 Msun star, including the helium ignition stage, the helium core-burning phase, and the asymptotic giant branch phase.

12

34

56

Post-MS Evolution

A red giant star (cross section), showing the compact helium core, H-burning shell, and bloated outer envelope. Note the size of the present day sun, for comparison.

How can we test stellar evolution models?

H-R diagram for a group of stars all born at the same time: hot, massive stars evolve the most rapidly.

Over time, main sequence stars of progressively lower temps/masses peel away to the giant regions on the diagram.

“Open” Star Clusters

The Pleiades star cluster, a grouping of hundreds of stars all born at roughly the same time and at the same distance

from Earth.

The Jewel Box cluster. This cluster is somewhat older than the Pleiades. Note the presence of at least one red giant star.

“Open” Star Clusters

The globular cluster 47 Tuc, visible only from the southern hemisphere.

Globular clusters contain several hundred thousand stars each!

“Globular” Star Clusters

Theoretical H-R diagram for a star cluster with an age of 1 Myr. The red line is the ZAMS. Note that the lower mass stars are still evolving toward the MS, while some high-mass stars have already evolved off the MS.

Testing Stellar Evolution


Same as the previous panel, but for a cluster age of 10 Myr.


Cluster age = 100 Myr. All lower mass stars have reached the MS, but the stars along the upper half of

the MS have all ended their lives.


Cluster age = 1 billion years.


Cluster age = 10 billion years.

A real H-R diagram for NGC 2264, a nearby cluster with an age estimated at 1 million years.


ZAMS

A real H-R diagram for the Pleiades cluster, which has an estimated age of 100 million years.


The H-R diagram for M 67, a cluster with an estimated age of 4 billion years.


H-R diagram for a globular cluster. The cluster age estimated from these data is over 10 billion years.


H-R diagrams of star clusters verify our models of stellar evolution.

We can then use the locations of cluster turn-off points to determine the ages of clusters.


The Deaths of Stars

Deaths of the Least Massive Stars (M < 0.4 Msun)

• The least massive stars are fully convective: they will burn all of their hydrogen

• Once their hydrogen is gone they contract and heat up, but the contraction and heating are halted by electron degeneracy pressure before helium fusion can ignite

• They will slowly cool as helium white dwarf stars

• The main-sequence lifetimes of these stars are longer than the age of the Universe, so no such white dwarfs yet exist!

Deaths of Medium-Mass Stars (0.44 Msun)

• Medium-mass stars burn H He in their cores while on the main sequence and He C and O while on the horizontal branch

• They are not massive enough to ignite C-burning once their He is gone. Their cores contract and heat up until the contraction is stopped by electron degeneracy pressure

• At the same time, their envelopes expand because of the energy generated by shell H and He burning and they move up the asymptotic giant branch (AGB)

• The envelope of a star on the AGB is thermally unstable; it pulsates as it expands

• Eventually, the entire envelope is ejected as a planetary nebula, leaving behind its hot, degenerate core: a white dwarf

• The expanding envelope is ionized by UV photons from the hot white dwarf; it will glow as an emission nebula for up to 50,000 years

Deaths of Medium-Mass Stars (0.44 Msun)

Planetary Nebulae

Evolutionary track of a sun-like star from red giant to white dwarf.

Planetary Nebulae and White Dwarf Stars

Observed Properties of White Dwarfs

• ~ 25% of nearby stars are white dwarfs

• masses range from ~ 0.4 1.0 Msun

• surface temperatures range from ~ 80,000 5,000 K

• radii range from ~ 0.007 – 0.02 times the sun’s radius

• their densities are very high: > 106 g/cm3

• WDs cool as they age, eventually becoming black dwarfs

• masses of white dwarfs fall in narrow range

• R ~ 1 / M 1/3

• M’s about the same R’s about the same

The sizes of white dwarfs…

Upper Mass Limit of White Dwarfs

Because it is supported by electron degeneracy pressure, the more massive a white dwarf is, the smaller its radius is. White dwarfs cannot exceed the Chandrasekhar Limit of 1.4 Msun.

Deaths of Very High-Mass Stars (M > 8 Msun)

When the core fuel source is exhausted in massive stars, they contract and heat up to temperatures sufficient to ignite fusion in the “ash” left over from the previous core-burning stage. The final burning stage is silicon (Si) to iron (Fe) in the core. Fusion of lighter elements occurs in shells surrounding the core.

• Iron has the most tightly bound nucleus of all elements. It does not produce energy when it is fused.

• Once the core of the star is all iron it can’t produce energy and collapses.

• Electron degeneracy pressure is not enough to halt the collapse because the core mass exceeds the 1.4 Msun Chandrasekhar limit.

• The core becomes extremely dense – far denser than a white dwarf.

Deaths of Very High-Mass Stars

number of nuclear particles

At these immense densitiesthe electrons will smash into the protons to form neutrons.

If the mass of the core is less than ~3 Msun its collapse will be suddenly halted by neutron degeneracy pressure.

The outer layers of the star, still collapsing onto the core, bounce off in a violent supernova explosion.

Deaths of Massive Stars: Supernovae

Supernovae in Galaxies beyond the Milky Way

SN 1999by

Observations of Supernovae

During a supernova explosion a star will shine many billions of times more brightly than the Sun.

Supernovae Type II result from the deaths of massive stars.

Supernovae Type I are explosions triggered when a white dwarf accretes mass from a companion and suddenly exceeds the Chandrasekhar limit.

Origin of Type Ia Supernovae

Accreted material from a companion star causes the mass of a white dwarf to exceed the Chandrasekhar limit… kaboom!

Supernova Remnants

The Crab Nebula

The Gum Nebula

Supernova Remnants

Exploded high-mass stars: supernovae

X-rayOptical

Neutron Stars&

Black Holes

How big is a Neutron Star?

• Recall that RWD ≈REarth (= 0.01 Rsun, or 7000 km)

• Neutron stars must be even smaller!

RNS ≈ 10 km!

M > 1.4 Msun

≈ 1014 g/cm3

Discovery of Pulsars

• first pulsar (source of pulsed radio emission) discovered in 1967.

• “flashes” of radio waves evenly spaced: periods of first pulsars 0.0333.75 sec

• pulse period increases very gradually

• one of the first pulsars was discovered at the center of the Crab Nebula

Pulsars are Neutron Stars!

The Crab Nebula resulted from the supernova explosion of AD 1054.

visible visible (zoomed in) X-ray (zoomed in more)

How do pulsars work?

The “lighthouse” model attempts to explains why pulsars:

• rotate rapidly

• have intense magnetic fields

• emit beams of radiation that spew from their magnetic poles

Chandra X-ray Observatory Hubble Space Telescope

Observations of the region near the Crab pulsar by…

Black Holes

Black holes form when matter collapses to a point a singularity.

Nothing – not even light – can escape from within the event horizon above a black hole.

The event horizon is one Schwarzschild radius (RS) from the singularity.

As the gravitational field of an object increases, the curvature of space-time near its surface increases to the point (for black holes) where not even light can escape.

Light Bending Near a Black Hole

Black Holes

A probe falling into a black hole:

• would be distorted by the immense gravitational forces

• photons leaving the probe would lose more and more energy; they would be “redshifted” to longer wavelengths.

• time on the probe would appear to move slower and slower to the observer who sent it in.

Black Holes…

…are not cosmic vacuum cleaners!

Observing Black HolesWe can “see” accreting black holes in binary star systems via their X-ray emission.

BlackHole

X-rays from hotaccretion disk

X-ray ExoticaCompact objects give rise to a wide variety of phenomena, all of which have associated X-ray emission.

The Black Widow Pulsar

X-ray ExoticaX-ray Exotica

Jets from a black-hole binary

Summary of Stellar Evolution & Death

Initial mass < 0.4 Msun

He white dwarf

0.44 Msun

planetary nebula C-O white dwarf

48 Msun

planetary nebula/ white dwarf likely

Mass 825 Msun

supernova neutron star

> 25 Msun

supernova black hole

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