Stellar properties

Astronomy 100, Fall 2012

Stars are a basic unit of a galaxy

• The Milky Way galaxy (ours) contains about 100 billion stars.

• The Milky Way is one of billions of galaxies.

• The glowing “arms” of the Milky Way are illuminated partly by the glow of numerous stars.

Our Sun is a star, and a conveniently close star to observe

Most photos of the Sun, such as this one, are taken using a filter; otherwise, the light would be too intense for the camera.

In this image, a hydrogen-alpha filter was used, which blocks all light but the red light from glowing hydrogen.

The features on the right limb of the Sun are called solar prominences.

Red R Orange O Yellow Y Green G Blue B Indigo IViolet V

Isaac Newton in Opticks (1704) demonstrated that sunlight could be dispersed into various colors by a prism, and then re-combined by another prism to yield sunlight again.

Herschel Thinks Outside the Box:In 1800 William Herschel made a discovery when he tried to determine the temperature

of light.

• He noticed that a thermometer recorded energy from the Sun`s spectrum even when placed beyond the red end of the visible rainbow.

•He called this emission Calorific Rays and it was the first discovery that light had colors invisible to the human eye.

•These rays are known today as Infrared light.

Herschel’s work color is associated with a temperature

Visible light is just a small part of the electromagnetic (EM) spectrum

Fraunhofer’s Surprise

In 1813, Joseph von Fraunhofer, the owner of a glass manufacturing firm in Munich, made an interesting discovery.

Using a precision dispersing prism, he discovered that the `solar blackbody` was cut by thousands of dark bands.

Fraunhofer’s Surprise

Fraunhofer tried to test whether this effect was real.

1) He tested with different optics.

2) He tested by looking at different objects (moon and planets).

Bunsen and Kirchhoff`s solution:Robert Bunsen (Univ. of Heidelberg) turned pyromania

into one of the great discoveries of modern physics. Bunsen set fire to things in order to figure out their elemental composition.

Iron

A colleague there, Gustav Kirchhoff, suggested using a prism to break the light apart. They quickly discovered (1860) that burning substances produced light in narrow bands with unique patterns.

Blueprint to Composition:Bunsen and Kirchhoff`s trick was the key to finding out the composition of anything from the light it produced.

Many of the lines they found had the same wavelength as those of Fraunhofer`s dark bands. They were seeing the composition of the Sun!

Absorption by (and re-emission from) a cooler gas!

Kinds of Spectra:

Why were Bunsen`s heated gas spectra composed of bright lines while Fraunhofer`s exhibited a continuous spectrum with dark bands?

Bunsen`s fires were stimulating light emissions in the hot gas.

So what are Fraunhofer`s bands?

Bunsen found that he could identify the signature of different elements in the Fraunhofer spectrum of the Sun.

Types of Spectra

Continuous: black body radiation continuous

Absorption: requires a cool object in front of a hot background(ex: Fraunhofer) discrete

Emission: requires a hot object with a cool background (ex: Bunsen) discrete

Basic definitions:• Element: a substance that cannot be broken

down by chemical means (defined by number of protons)

• Atom: the smallest piece of matter that is still an element

• Molecule: two or more atoms that are bound together by chemical bonds

• Nucleus: the protons and neutrons bound together at the center of an atom

Why do elements have the `discrete` interactions that Bunsen saw?

This has to do with the nature of atoms and how they are put together.

Atoms and light

Why do different elements (and molecules) have different interactions?

A brief history of the atomFirst discussion of the nature of matter (~400 BCE): • Leucippus, a Greek philosopher, all matter consisted “tiny and

indivisible bodies called atoms”. • The word atom comes from the Greek word `atomos` (not

divisible). • Democritus, another Greek philosopher, these atoms were not all

alike, but had different shapes and sizes to make different matter. • Opposed (Aristotle): The prevailing view that everything was made

up of four basic elements: earth, fire, air, and water, not atoms. • Views such as Aristotle`s dominated science for many centuries,

until the Renaissance.

Dividing the ‘indivisible’:The plum pudding model

• J. J. Thomson discovers cathode rays are made of electrons (he called them ‘corpuscles’ – 1897). Electrons are shown to have a negative charge

• Thomson proposes model of the atom (1904):– Atom has smaller components– Negatively charged corpuscles/electrons

(plums)– Positive ‘soup’ to balance negative charge

(pudding)

Discovering “nothing”Meanwhile, Ernest Rutherford (Cambridge) discovers two new types of radiation emitted by uranium (1899):

1. Alpha particles (): later found to be the helium nucleus2. Beta particles (): later called the “electron” by Thomson

Positive Nucleus

Negative electron

In 1909, Rutherford fires alpha particles at gold foil.

Expected only small angle scattering due to gold atoms’ “plum pudding”.

Saw mostly no scattering with occasional back scattering

Matter is mostly empty space!!!!

Rutherford’s atom1. Mass is highly concentrated in the positively-

charged nucleus at the center of the atom.2. Electrons (negatively charged) “orbit” the

nucleus.3. Lots of empty space in-between4. Similar to today’s atom– Number of protons determine

the element identity– Number of electrons determine

the chemical properties of the atom

Positive Nucleus

Negative electron

The nucleus is not uniform

James Chadwick (1932): Discovers the neutron. Neither positive nor negative, it has about the same mass as a proton.

Nuclei are made up of protons and neutrons.

Rutherford (1918): Discovers the proton. The proton is about 2000 times as massive as the electron and has a positive charge, exactly the same magnitude as the electronic charge.

Atoms, elements, and isotopesAtoms (below - periodic table (Mendeleev, Meyer, 1867))

– Nucleus• Protons – number determines the element (atomic #)• Neutrons – number determines the isotope (mass #)

– Electrons – number determines the chemical properties

Atoms, elements, and isotopesIsotopes:Atoms with the same number of protons but different numbers of neutrons are called isotopes.

Isotopes have the same chemical properties, but different masses, different emission spectra, and participate in different nuclear reactions.

e-

p+

hydrogen (1H)

p+

e-

deuterium (2H)

n

A stable isotope of hydrogen – 0.02% natural abundance

p+

e-

nn

Radioactive isotope of hydrogen

tritium (3H)

p+

e-

n

n

p+

e-

New element; not an isotope of H

helium (4He)

A stable isotope of hydrogen – 99.98% natural abundance

Bohr atomic model Niels Bohr (Copenhagen Univ.), based

on Rutherford’s work, suggested a quantized structure of electronic orbits in an atom (1913)

Bohr and Werner Heisenberg later (1926) modify structure to account for the wave properties of electrons.

Electron distances and energies are discrete values

p+

e-

Energy States:

E1

E2

E3

p+

e-

Electrons exist in `orbits` (much like planets in the solar system) that are stable at specific separations from the nucleus.

The spacing of these energy levels is not even.

Atoms and light

The distance from the nucleus determines the energy of the electron (lower E is closer).

Energy States:

E1

E2

E3 E1E2 > E2E3 > E3E4 etc…

So what does all of this have to do with Bunsen and Franhofer lines?

Atoms and light

If you heat the atom up to high enough temperatures, the electron will jump to higher orbits (higher energy state).

How does `heating` do this? Collisions

Atoms and light

p+

e-

Energy States:

E1

E2

E3

If you heat the atom up to high enough temperatures, the electron will jump to higher orbits (higher energy state).

How does `heating` do this? Collisions

Atoms and light

p+

e-

Energy States:

E1

E2

E3

Atoms and light

p+

e-

Energy States:

E1

E2

E3

After a time, the electron falls back to the lowest energy state.

A photon is given off.

The energy of the photon is exactly equal to the energy difference between the two energy states.

Atoms and light: absorption

p+

e-

Energy States:

E1

E2

E3

Process of emission is fully reversible.

The energy of the photon must be exactly equal to the energy difference between the two energy states.

Electron can absorb a photon and jump to a higher energy level.

Atoms and light: absorption

p+

Energy States:

E1

E2

E3

Process of emission is fully reversible.

The energy of the photon must be exactly equal to the energy difference between the two energy states.

Electron can absorb a photon and jump to a higher energy level.

e-

Conservation of energyThe energy difference between electron orbital states is exactly equal to the

energy of the photon emitted or absorbed.

E2 – E1 = h f

Where E1 and E2 are the energies associated with the electronic orbital states, f is the frequency of light, and h is Planck’s constant = 6.62 × 10–34 J•s

hydrogen energy level diagram

Quantized energy

• Different frequencies are perceived as different colors

• Atoms of different elements have different allowable energy level transitions and thus emit and absorb different discrete colors.

• Example: Each line in the spectrum of iron is different energy level transition

Iron

Types of spectra

Continuous: black body radiation continuous

Absorption: requires a cool object in front of a hot background(ex: Fraunhofer) discrete

Emission: requires a hot object with a cool background (ex: Bunsen) discrete

e-

What happens if a very energetic photon interacts with an atom?

Ionization:

Such a photon can give enough energy to the electron that it can escape the atom.

The amount of energy necessary to do this is called the binding energy of the atom.

e-

p+

Energy States:

When an atom absorbs light (or thermal) energy greater than the binding energy, the electron escapes.

Ionization:

The atom is left with a positive charge and is called an ion.

Together, ions and free electrons are called plasma.

e-

e-

p+

Energy States:

Plasma is found in stars, space, and parts of our atmosphere.

e-

Molecules are atoms that are connected by bonds (electrons). At a basic level a molecule will behave similarly to an atom.

What about molecules?

e-

p+

-

e-

p+

Molecules also have discrete electron energy levels.

p+ p+

Like atoms, electrons in molecules can absorb a photon and move to a higher energy level

Electronic Energy States:

A photon with enough energy can free an electron by overcoming the binding energy.

What about molecules?e-

p+

e-

p+

p+ p+

This produces a molecular ion.

Plasmas can also contain molecular ions.

Electronic Energy States:

Photo-dissociation

e-

p+

e-

p+

Or overcome the molecular binding energy and break the molecule up (photo-dissociation).

Electronic Energy States:

e-

e-

p+ p+

With molecules there`s an additional complexity.

Vibrational modes

In addition to electronic energy levels, molecules have vibrational energy levels.

p+ p+

p+ p+

p+ p+

t1

Electronic Energy States:

p+

e-

e-

p+

t2

t3

Rotational modesElectronic Energy States:

p+

e-

e-

p+

Moreover, each vibrational state has separate rotational energy sub-levels.

p+p+Mode 1:

(Out of page)

p+ p+Mode 2:

(in plane of page)

The spectra of molecules are more complex than atomic spectra

Eelectronic ~ 103 Evibrational ~ 106 Erotational Vibrational and rotational transitions are triggered by absorption or emission of light at specific energies, just like transmissions in atoms.

This has two consequences: 1) Molecules have many more transitions than atoms.

2) Molecule rotational- vibrational transitions involve light with much less energy than atomic electronic transitions.

The energies differences between electronic, vibrational, and rotational levels are different.

Electron energy levels in molecules

n = 2

n = 1

VibrationalRotational

Eelectronic ~ 103 Evibrational ~ 106 Erotational

So the Sun’s composition was determined and turned out to be relatively simple

Though the composition is relatively uniform, the Sun is layered by density

Working outward, the dense core (where fusion takes place) goes from 0 to 0.25 Rsun, followed by the radiative zone (0.25 to 0.7 Rsun), topped by the convective zone (0.7 to 1 Rsun). The visible surface of the sun is called the photosphere, and the “atmosphere” of the Sun has two layers, the relatively thin chromosphere and the thicker, but less dense, corona.

Energy transfer = moving the energy of fusion at the core to the Solar System

• As the names of the layers imply, it is not the composition of the sun that is interesting, but the manner in which energy is transmitted from layer to layer.

• This difference in manner of energy transfer will be a direct result of the lessening density of the Sun outwards; in fact, the outer edge of the convective zone (the photosphere) is far less dense than the Earth’s atmosphere!

Conduction is heat transfer by…

1. Direct contact2. Material flow3. Photons4. Phase change

Convection is heat transfer by…

1. Direct contact2. Material flow3. Photons4. Phase change

The second law of thermodynamics governs energy (heat) transfer

Convection: heat exchange due to material flow

Conduction: heat exchange due to direct contact

Radiation: heat exchange due to photons (light)

Phase change: heat exchange due to substance changing phase (for example, evaporation or melting)

Heat transfers from a hot body to a cooler body. The transfer can never be stopped, only slowed down.

Evaporation

The solar interior

• Starting Point: We can’t actually get to the interior of the Sun. We have to model it, based on observations.

• Model Basis: We do know (some!) solar physics and we have some boundary conditions that help us.

1) The Sun’s COMPOSITION

2) The Sun’s MASS

3) The Sun’s TEMPERATURE

4) The Sun’s AGE

Summary of the solar interior

The Sun’s interior can be broken down into a few regions based on how energy (heat)

transfers1) Where it is hot and dense enough for fusion

2) Where it is hot and dense enough to prevent electrons from staying with atomic nuclei

3) Where it is not hot and not dense enough to permit electrons to combine with atomic nuclei

These conditions then tell us:

1) how energy escapes from the Sun.

2) how material moves inside the Sun.

Water

Lead

The standard model for the Sun’s properties

Deepest Ocean Trench

The solar core

• Extends out to 0.25 Rsun

• Contains ~50% of the Sun’s mass.

• Is bounded (loosely) by the point where temperature and density are too low to support P-P fusion.

• Contains ~2% of the Sun’s volume.

Core Boundary Core Boundary

Structure of the solar core

Radiative Radiativeconvective convective

The division between the radiative and convective zones

Energy transfer in the core and radiative zone

Radiative diffusion, modeled as a “random walk”

• Occurs in the core and in the radiative zone.

• Light scatters randomly off free electrons and nuclei. This means a photon can bounce back towards the core, as well as go outwards. • This is a SLOW process.

• A photon produced by fusion in the core today will take 105 – 106 YEARS to exit the radiative zone!

The convective zone

• Extends from 0.7-1.0 Rsun

• Contains ~2% of the Sun’s mass.

• The convective zone is bounded by the point where light (photons) directly escapes from the solar atmosphere (photosphere).

• Contains ~66% of the Sun’s volume.

• Contains hot, neutral gases where electrons and nuclei are together but not as atoms. Thus, the energy transfer involves absorbing enough photons to cause an increase in material temperature, which decreases its density, which moves the mass towards the surface.

Rising Rising

FallingFallingFalling

Energy/mass transport in the convective zone

Energy in the convection zone is transported as a property of the matter.

• Hot gas expands and loses density, and so rises from deep in the zone, cooling as it does.

• At the top of the zone, the gas becomes cooler than its surroundings, compacts and sinks back down.

• These rising and falling regions form adjacent convective cells.

• These cells release solar energy to the photosphere in a pattern similar to the surface of a boiling liquid. The lifetime of any given cell is ~10 minutes.

• The cell structure exists on many different sizes within the zone, with the largest regions measuring up to 105 km across.

Time and Size Scales in the Convective Zone:

The blue regions represent cooler, and thus sinking, parts of the convective cell. The red regions represent warmer, and thus rising, parts of the convective cell. Note the rough equivalence in total area between the two colors.

Granules are convection cells about the size of Texas (image shows 1% of the solar surface, 121,000 km2 )

Each granule delivers, in 5 minutes, the equivalent of 1000 yr of electricity produced by the Hoover Dam

Time and size scales in the convective zone:

How long does it take photons created in the core to escape from the Sun?

1. 1 sec2. 1 day3. 1 year4. 100 years5. 105 years

So how applicable is what we know about the Sun to other stars?

After all, even the nearby stars don’t resemble the Sun for the most part!

Stars come in different colors and groupings47 Tucunae

The Pleiades are an example of an open cluster

47 Tucunae is an example of a globular cluster

It was from those differences (mostly color) that stellar classification began

• Charles Edward Pickering directed the Harvard Observatory in the late 19th century.

• Over his lifetime, he took glass plate photographs of over 300,000 stars.

• He also began taking the spectra of stars.

• Much of the equipment he used, he had to invent as he went along

The Draper Catalog of stellar spectra was the data source for star classification

• Annie Jump Cannon was hired in 1896 by Pickering to find similarities and differences in stellar spectra.

• Cannon (1900) invented the “OBAFGKM” system of classification, based on the relative strengths of various hydrogen emission lines.

• Earned 25 cents/hour for this work, but was named to a professorship at Harvard in 1938.

Quick reminder of what spectral “lines” are

hot, multi-species source

hot, few species source

cold, few species sample in front of continuous source

The first mathematical relationship in stars• Henrietta Leavitt was hired

by Pickering in 1893 to study variable stars – stars that vary in intensity over time cyclically.

• Leavitt (1908) found that a certain type of variable star, the Cepheid variable, followed a simple rule: the more luminous the star, the longer the cycle of dimming/brightening (the luminosity period).

• Edwin Hubble would use this to determine the universe’s expansion.

So what did these early astronomers measure about stars?

• Luminosity (absolute brightness)

• Color• Distance

Through mathematical relationships, we can infer other properties of stars

Wien’s Law allows the calculation of a star’s surface temperature based on its spectral maximum intensity wavelength.

The radius (size) of a star can be calculated from its temperature and luminosity

But the most important relationship was the one between luminosity and

temperature• Ejnar Hertzsprung and

Henry Norris Russell, in 1911 and 1913, independently discovered this relationship and plotted it (The H-R diagram).

• Nearly all the stars in the Milky Way fell onto the Main Sequence: the cooler the star’s surface, the less luminous it is.