Class Meets:- Tuesdays 12.00 in LTB Thursdays 10.00 – 12.00 in TB13.

Lecturer:- W.Gelletly Office 13BB03 e-mail:- W.Gelletly@surrey.ac.uk

All diagrams and pictures on slidesAll notes and pictures etc on Physics Intranet – 1IASS-08

Books:- An Introduction to Modern Astrophysics by Carroll and Ostlie Second edition-this has SI units. Universe by Freedman and Kaufmann – Sixth edition.Assessment:- 70% written examination in summer 30% multiple choice test on Thursday 21st,February at 11.00

Milky Way-over Alps with lunar eclipse

M31-Andromeda Galaxy-2.2Mly from Earth, Part of our Localcluster of galaxies. It will collie with the Milky Way in about6 billion years or so.

Photo-mosaic picture of the Sombrero Galaxy taken with theHubble Space Telescope over several orbits.Glowing central bulge of stars surrounded by pancake shaped disc.

M74 Gemini – Spiral galaxy in Pisces - It is about 30Mly away and has 1011 stars

Taken with Gemini North Telescope – Mauna Keau

Helix Nebula-The glowing gas consists of N,O and H ejected by a Solar Mass star in its death throes. Radiation from the remaining central star causes the gas to glow.This star will become a White Dwarf. Dwarf.

Photograph by D. Malin

Cometary knots in the Helix Nebula.

Gaseous objects seen with the HST in the Helix Nebula. The head is about twice the size of the solar system and the tail is of length 1011 km.

They may be formed when hot, low density gas emitted by the dying star collides with cool, higher density gas ejected some 104

years earlier.

Picture taken Aug 1994 with wide-Field planetary camera 2 - HST

Crab-UV

Crab-vis

CRAB-IR

Crab-X-ray

Crab Nebula at X-ray wavelengths

Supernova seen by Chinese in 1054 A.D.

Bright clumps moving outwards at v ~ 0.5c

Filaments have lower mass andhigher velocity than modelswould predict.

There is a pulsar ( = neutron star) at the centre which rotates atabout 30 times per second.

It is about 7 kly away in Taurus

Crab Nebula(7kly away in Taurus)-several exposures with HST.Clear changes in central regions-wisp like structures moving outwards with v=0.5c and halo which is stationary but brightens and weakens.

Coma Cluster - 20Mly across containing thousands of galaxies(300 seen here). It is about 270 Mly away.Two supergiant galaxies seen in centre.

Hubble Deep Field-A very narrow sample of the sky looking as far back as 10 10 years in some cases.Data taken over 10 consecutive days.

Globular Cluster M10 – 16,000 ly away in ORPHIUCUM Diameter is 70 ly. Mainly post-Main sequence stars

Aurora seen over Edmonton on 4/11/2003. We see the Clover Bar Power station on the Saskatchewan river. The auroral light is seen reflected in a small pond.

Isabel Terra (category 5) hurricane passing east of the Bahamas

NASA LONDON

Ngc6240 merging and infrared bright galaxy in Orpiuchus

SN1987A- Supernova in large Magellanic cloud recorded in October 1987. We see the region before and after the supernova.

Supernova 1998bw- scales are different on right (before) and left (after)

Eagle Nebula- 7000ly away

Pillars of H and dust. In pillars gas is contracting to form new stars. Radiation boils away low density material at ends of pillars.

Lagoon nebula 5000ly away, 100 ly across. It is in Sagittarius

Slides 1-121.The milky Way seen over the Alps during a lunar eclipse.2.&3.the Andromeda Galaxy-M31.It lies 2.5Mly away and is orbitted by two small elliptical galaxies M32 and M110.It will collide with the Milky Way in about 6 billion years.4.Sombrero Galaxy about 50 Mly away in Virgo.We see it edge on.We can see the large central bulge and the distinct dust lanes in the edge.This obscures stars behind them but is a region of star formation and there are many bright stars.In the bulge there are many globular clusters.5.M74-a photogenic spiral galaxy in Pisces.It is about 30 Mly away and has about 1011 stars. This is more or less how the Milky Way must look from outside.Picture taken with the Gemini North telescope on Mauna Keau.6.Helix Nebula-the end of a Sun-like star.The It is a planetary nebula with a central White Dwarf Star.Radiation from this star is fluorescing the clouds of H,O and N thrown off in the final unstable stages of the star’s life. Slide which follows shows some detail.7-11.Crab Nebula-In 1054 AD the chinese recorded a bright new star seen in daylight for quite a long time.It was a Supernova and we see the remnants in these pictures.The first four show it as seen in four different regions of the electromagnetic spectrum[UV,visible,IR,X-ray].The final picture shows detail.The bright clumps of light are moving outwards at v = 0.5c.The filaments have lower mass and higher velocity than models would predict.There is a pulsar = neutron star at the centre,the remnant of the original star.It rotates at 30 times per sec.12.Coma cluster-One of the most dense galactic clusters known with about 10,000 galaxies. Each of these galaxies contains more than 1 billion stars.This is a regular cluster about 270 Mly awayand 20 Mly across.Most of the galaxies are elliptical.Two giant ellipticals dominate in the centre of picture and we see a star local to us top right.

Slides 13-17• 13.Hubble Deep Field-a narrow region of the sky viewed by the HST 4 days.We see more and more galaxies no matter how far we go back in time.14.M10 globular cluster with a few hundred thousand stars.It is 16,000ly away in Ophiucum.Diameter is 70 ly.Stars are highly evolved and are mainly Red and Blue Giants.These are post-Main Sequence stars.15.Aurora seen over Edmonton on 4/11/2003.Clover Bar Power station photographed by auroral light from North Saskatchewan River.Small pond reflects green auroral light.16.Isabel Terra-a hurricane,almost category five,passing east of the Bahamas.Huge swirling storms,called typhoons in East,get their energy from warm evaporated ocean water.As water vapour vapour cools and condenses it heats air,lowers pressure and causes cooler air to rush in.Winds can be up to 250 km per hour.17.London at night from orbit.The M25,Heathrow and Gatwick are clearly visible.

Slides 18-22

• 18.NGC6240-I optical and X-ray regions. 19.SN1987A-A supernova in the Large Magellanic Cloud in October 1987.We see before and after.This marks the death of a massive star. 20.Similar picture of another ,much more distant supernova. 21.Eagle Nebula.This region of star formation is 7000ly away. Evaporating gaseous globules emerging from pillars of H and dust. In interior of pillars gas is contracting to form new stars.At the ends of the pillars intense radiation from young stars boils away low density material. 22.Lagoon Nebula[M8].5000ly away,100ly across.It can be seen in Sagittarius with the naked eye.In the detail shown with HST we see two funnel shaped regions where stars are forming.The vast walls of dust hide other hot young stars.

The nature of Astronomy Astronomy relies almost entirely on observation. We rely on radiation and particles emitted by astronomical objects. We can measure radiation intensities, spectra etc - We deduce compositions of stars temperatures of their surfaces total luminosities atmospheres of planets etc. - We can also obtain information on material between us and the emitting object (gas and dust) from absorption and scattering.

How does Astronomy work?

Observations Models of processes PredictionsTest by further observations

To do this we must make a series of assumptions—next slide

Assumptions The Laws of Physics apply. Even although the conditions in the astrophysical objects may be well beyond anything we can explore on Earth.

In particular we assume the Laws are invariant w.r.t. place and time.

Caveats

The evidence to support these assumptions is very limited.

It is also of quite different quality for each of the four forces we know.

There may also be forces or other Laws of which we are unaware. Then our models would be quite inadequate.

Astrophysics is an application of Physics - we must understand Physics.

Electromagnetic Wave-Schematic picture

• Here we see a plane wave propagating in vacuum in the z-direction with velocity v = c where c = 3 x 10 8 m/sec.

• The wave is linearly polarised and the E field oscillates along the y-axis.

• The magnetic field(B) is along the x-axis and is in phase with the E field

• , and c depend on mode of production and medium

• In medium it can be scattered, reflected,refracted and slowed down.

• E and B are always in the same proportion

Consequences of the Finite Velocity of Light

• Velocity c = with c = 3 x 108 ms-1 in vacuum.

Typically visible = c/vis = 3 x 108 / 500 x 10-9 = 6 x 1014 Hz Velocity is reduced by 1% in gas and tens of percent in solids

• Finite velocity means time delay. Thus Time(Sun-Earth) = 1.496 x 1011/ 3 x 108 = 0.5 x 103 8 mins. Time(Moon-Earth) = 4 x 108 / 3 x 108 1.3 s

• From Alpha Centauri 4 years From nearby galaxies 105 - 106 years Across a “typical” galaxy 105 years

•This leads to the definition of the LIGHT YEAR (ly) as the distance travelled by light in vacuum in 1 year. 1 ly = 3 x 108 x 3.15 x 107 m = 9.45 x 1012 km 1013 km = 9.461 x 1012 km

ANALOGY (commonly quoted in textbooks)

If the Universe began at midnight.

Earth formed in mid-afternoon.

Plants began to produce oxygen in early evening.

Humans began 2 mins. from Midnight

Magellan circumnavigated globe 0.003 secs. from Midnight

Each of us lives for < 0.001 secs.

The age of the Earth is 5 x 109 years So if we observe a galaxy 1010 ly away the light was emitted before the Earth was formed.

Electromagnetic Spectrum-Radio waves to gamma rays.Shown as a function of wavelength() and frequency().All such waves have velocity c = .

The Story so far

The Nature of Astronomy

- based on Observation not experiment

- very different from Physics generally

- relies on assumptions, particularly that the laws of Physics are invariant in space and time and can be applied in the very different conditions which may prevail in the astronomical objects we observe.

To proceed we need to be reminded of some of the simple physics we will use to explain what we see.

The Electromagnetic Spectrum

• The figure shows the electromagnetic spectrum over all wavelengths.

• EM radiation exists at all wavelengths and has the same basic properties.In particular they always propagate with velocity v = c in vacuum and can be refracted, reflected, scattered etc

• The various parts of the spectrum are named by the method of production and not by energy or wavelength. For example gamma rays arise from transitions between levels in atomic nuclei.

Blackbody Radiation

• General question:-What is the spectrum of EM radiation emitted by an object of arbitrary temperature T in thermal equilibrum.

We assume that this “blackbody” reflects no radiation at any

•Max Planck showed that the spectrum is given by

ud = 8hc -5.d[exp(hc/kT) - 1]

where ud is the energy density =energy/unit volume

• Although no perfect blackbody exists solids and stars follow Planck’s Law very closely.Note that picture is on log-log scale.

• Spectrum of Blackbody Radiation as a function of wavelength.• Energy emitted by four blackbodies with equal surface areas.• Note that they are plotted on log-log scale.• Area is proportional to total power per unit surface area (PA)• Stefan-Boltzmann Law- PA = .T4

• PA is in Wm-2 and = 5.67 x 10 -8 Wm-2 K-4

Sun-Yellow

Red

Blackbody Radiation

Wien’s Displacement Law

• Doubling T increases P by 16 since PA = .T4

Luminosity = Surface area x PA

• Note that maximum wavelength max

shifts with .This can be quantified in Wien’s Displacement Law.

max.T = const.

= 2.9 x 10-3 mK

• This quantifies the observation that an object changes colour with Temperature e.g.At room temp. spectrum peaks in infra-red.

• Very important since it allows us to obtain a measure of the SURFACE TEMPERATURE of a star from max.For the Sun max is in blue with but a lot of radiation in red so it looks yellow.For stars with T = 3000k max is in infrared but significant amount in red.Red Giants are at this T.

Betelgeuse

Rigel

Bellatrix

Orion nebula

Saiph

Alnitak, Alnilam and Mintaka

Photons

So far everything I have said assumes that EM Radiation is a wave.

Planck’s Law was deduced assuming it is emitted by oscillators with discrete energies. Einstein introduced the idea that it consists of

particles called PHOTONS each with E = h = hc/

where h = 6.6 x 10-34 Js is Planck’s constant

h is a very small number so number of visible photons needed for us to see is very large.

Peak of blackbody spectrum gives surface temperature only. Photons emitted in the centre are scattered and absorbed before they go very far.

They heat the layers outside them. The surface is heated by conduction and convection of the gas.Sun appears to be a blackbody at 5850 K. In centre it is 5 x 107 K

Stellar Spectra and Kirchhoff’s Laws

• Late 18th/early 19th C William Wollaston and others saw dark lines imposed on Sun’s blackbody spectrum. Light was absorbed at these s.

• 1814-Fraunhofer had catalogued 500 lines and noted Na line.

• Kirchhoff showed that the dark lines are due to absorption of light at that by atoms of a particular element.His results are summarised in Kirchhoff’s Laws:-

1)Hot, dense gas or solid emits a continuous spectrum.

2)A hot,diffuse gas produces bright spectral lines.

3)A cool,diffuse gas in front of a source with a cts. Spectrum produces dark spectral lines.• Full explanation had to wait for the Bohr-Rutherford theory of the atom.

Summary of Kirchhoff’s Laws in pictorial form

Stellar Spectra – A digression

• Main features of the Bohr-Rutherford Model - Central atomic nucleus containing Z protons and N neutrons - A = N + Z - Neutral atom has Z electrons - Electrons are held in place by electrostatic force

• - Two main assumptions namely 1) The only orbits are those where the electron’s angular momentum is an integral multiple of h/2 (h = Planck’s constant ) = n h/2 2) Electrons emit no radiation so long as they remain in an allowed orbit. Radiation is emitted or absorbed when an electron makes a transition from a higher(lower) to a lower(higher) state. - States are characterised by Quantum numbers n,l where n is the Principal quantum number and l is the orbital ang. Mom. Quantum no.

Stellar Spectra - 2

• Main results from Bohr-Rutherford Model -The radii of the orbits are given by R = 0.h2.n2 ,where me is the

.me.Ze2

is the electron mass and 0 is the electrical permittivity of free space. -The energies of the orbits are given by En = - me.e4.Z280.h2.n2

• In this simple model n dictates the level energies hence Principal Q.N. -For H(Z = 1) we find that En = - 13.6/ n2 eV -Note that the zero of energy is at infinity.

• Note:-the elements in increasing Z are Helium(He),Lithium(Li), Beryillium(Be),Boron(B),Carbon(C),Nitrogen(N),Oxygen(O), Fluorine(F),Neon(Ne),Sodium(Na),Magnesium(Mg),Aluminium(Al), Silicon(Si),Phosphorus(P),Sulphur(S),Chlorine(Cl),Argon(Ar), Potassium(K),Calcium(Ca),Scandium(Sc),------------------------------

Stellar Spectra-3

• Pauli Principle:-No two electrons can have the same quantum numbers. As a result each level can hold two electrons.The Periodic Table is built up by placing successive electrons in levels two at a time.Noble gases represent atoms with last electron particularly tightly bound.

• If we think of light in terms of photons then E = h.Photons emitted or absorbed in atoms have discrete energies given by h = me.e4.Z2[1/n1

2 - 1/n22]

802.h2.c

from our expression En = - me.e4.Z2 for the level energies.

80.h2.n2

• In general we see series of spectral lines with 1/ = R[1/m2 - 1/n2],where R is a constant and m,n are integers. In H, Balmer series has m = 2,n = 3,4,5---- Paschen series has m = 3,n = 4,5,6,------

Levels and Transitions in Hydrogen

The figure shows the levels in the hydrogen atom.The zero of energy is at infinity.The levels are labelled by the Principal Quantum Number nand by the energy[on the left]

The series of spectral lines thatwere found empirically by variousexperimenters are shown.

Each series ends on a particular level.

Here we see the atomic spectrafor white light,sunlight and a series of elements.Note that the last spectra are forNa in emission and absorption.

These spectra provide clear fingerprints for the chemical elements.

Stellar spectra-4

Molecular Spectra

• Molecular spectra are more complex than those of atoms-in general. In addition to discrete levels molecules may rotate and vibrate as well. The resulting sets of levels mean that a “chunk” of the spectrum is absorbed.

• When molecules join together to form a dust particle the absorption bands broaden until they approach solid matter and blot out the light. Absorption by interstellar dust is a problem-T is low so molecules stay intact.

• Earth’s atmosphere is an intermediate case.T is low enough for CO2, H2O and O3 to hold together.They absorb bites out of the spectrum in the UV and IR regions of the spectrum due to the excitation of vibrational and rotational bands.Stellar atmospheres are much hotter than that of a planet and so molecules generally break up.Thus the Sun has a series of dark absorption lines due to H,Ca,Fe,Na,etc.

Information on Surface Temperature from Spectral Features.

• Stars contain 75% H and 25% He plus small amounts of other elements. • At T = 6000K we have 3/2 kT eVs. This is similar to the binding energies of molecules.At this T they are broken up in collisions.As T rises spectral features related to molecules will disappear. • At low T atoms are neutral.As T increases collisions cause them to be ionised.At even higher T they become doubly then triply ionised etc. The spectra of ions differ from those of atoms. • We get a progression as T increases.At low T we have neutral atoms and molecules.The former disappear and the latter fade as T increases. We then get spectra from singly charged ions. At still higher T we get doubly charged ions.• H line is n = 2 to n =3 absorption line. The n = 2 level is first excited state in H.It is in middle of red part of spectrum. At low T very few H atoms are thermally excited so H is weak. As T increases so does occupation of n = 2 level and H becomes stronger. This absorption line reaches a peak at 10,000K. Beyond this many of the atoms are ionised and it fades again.

• Picture shows absorption of radiation by Earth’s atmosphere. There is strong absorption by N and O in the X-ray and gamma-ray regions,strong absorption by ozone in the UV,absorption of H2O in the infrared.Free electrons in the ionosphere reflect very long radio waves.

Altitude at which atmos.reduces intensity of radn

by one-half.Proportion of lightwhich arrives at sea level

UV

Doppler Shift

Observer A Observer B

Source moving relative to observer. If the source is moving towards you each successive wave is emitted closer to you. Wavelength appears shorter—blue shifted

Opposite is true if it is moving away from you.—red shifted.

Doppler Shift• If v c then the shift in wavelength due to the motion of an object relative to an observer is = v/c.

• If v is +ve then increases and we have a redshift, object looks colder. If v is -ve then decreases and we have a blueshift, object looks hotter.

• If 0 is the wavelength emitted by a stationary source then = ( - 0 )• We now define the Redshift Z as Z = ( - 0 )/ 0 = / 0 = v/c

• We can measure spectroscopically. As a result if we can identify a spectral line and measure then we can measure the relative velocity.

• If v is not much less than c then we must use the full expression Z = [(c + v)/(c - v)]1/2 - 1 = / 0

The Story so far.

The Nature of Astronomy—based on observation

Our information largely comes from electromagnetic radiation emitted - EM radiation has const. vel. in vacuum c = λν - all λ exist - can be polarised

Black Body radiation -Stefan-Boltzmann Law PA = σT4

-Wien’s Law λMAX.T = 2.9 x 10-3 m.K

Atoms can only exist in discrete energy levels. Consequently transitions between levels have discrete energies. The spectrum of lines is then characteristic of the chemical element.

Doppler shift:- Z = [(c + v)/(c - v)]1/2 - 1 = / 0

If v c then we can write = v/c.

Kirchhoff,s Laws:- Summary of observations about BB spectrum and both emission and absorption spectra

Here we see the atomic spectrafor white light,sunlight and a series of elements.Note that the last spectra are forNa in emission and absorption.

These spectra provide clear fingerprints for the chemical elements.

Stellar spectra-4

Molecular Spectra

Molecule can rotate and vibrate so inaddition to the discrete levels we havelevels built on them with energies associated with them.

We end up with closely spaced bands of levels built on each intrinsic level.

[Rotations and vibrations]

Vibrations:- Levels equally spaced

Rotations:- Levels- E = (h/2)2.[I(I + 1)] 2 ζ where ζ is the moment-of inertia

Information on Surface Temperature from Spectral Features.

• Stars contain 75% H and 25% He plus small amounts of other elements. • At T = 6000K we have 3/2 kT eVs. This is similar to the binding energies of molecules.At this T they are broken up in collisions.As T rises spectral features related to molecules will disappear. • At low T atoms are neutral.As T increases collisions cause them to be ionised.At even higher T they become doubly then triply ionised etc. The spectra of ions differ from those of atoms. • We get a progression as T increases.At low T we have neutral atoms and molecules.The former disappear and the latter fade as T increases. We then get spectra from singly charged ions. At still higher T we get doubly charged ions.• H line is n = 2 to n =3 absorption line. The n = 2 level is first excited state in H.It is in middle of red part of spectrum. At low T very few H atoms are thermally excited so H is weak. As T increases so does occupation of n = 2 level and H becomes stronger. This absorption line reaches a peak at 10,000K. Beyond this many of the atoms are ionised and it fades again.

Summary of Stellar classification

Remember-each of the classes is further subdivided 0-9

In the last few years there has been an attempt to introduce two more groups on thelow temperature end. These are faint stars at low temperature, more and more of which arebeing classified. They are L and T. L stars have T between 1300 and 2500K. One sees a lotof metal hydride molecules such as CrH and FeH. T dwarves are even cooler and show a lot of methane. They are, in general, failed stars like Jupiter.

Temperature

[Metals?]

Classification of Stellar Spectra – Harvard SchemeTYPE Colour Approx T Main Characteristics Examples

O Blue >25000K Singly ionised He in emission/absorption 10 LACERTA B Blue 11-25000K Neutral He in absorption RIGEL/SPICA A Blue 7.5-11000K H lines at max. strength for A0, decreasing thereafter SIRIUS/VEGA F Blue/white 6-7500K metallic lines become noticeable CANOPUS G White/yellow 5-6000K Solar-type, Absorption lines of metallic atoms/ions grow SUN K Orange/Red 3.5-5000K Metallic lines dominate ARCTURUS M Red <3500K Molecular bands of TiO noticeable BETELGEUSE

Within each of these broad categories Annie Jump Cannon assigned sub-categories 0 – 9 with 0 being at the high T end.

This is known as the Harvard scheme. It was funded by the wife of a wealthy doctor-Henry Draper and was carried out by a team composed largely of women [see photo of them in Universe, 6 th Ed. Fig 19.10]. They included Williamina Fleming, Antonia Maury and Annie Jump Cannon.

Later Cecilia Payne and Meghnad Saha showed that the catalogue the Harvard group created and classified was anindicator of surface temperature.

Note:- The spectra reflect the temperature and composition of the surface and essentially the composition of the Star prior to formation since no nuclear reactions occur in the surface and there is little mixing with the interior

A full classification should include Luminosity - See YERKES or MMK classification scheme.

Temp.

• Picture shows absorption of radiation by Earth’s atmosphere. There is strong absorption by N and O in the X-ray and gamma-ray regions, strong absorption by ozone in the UV,absorption of H2O in the infrared. Free electrons in the ionosphere reflect very long radio waves.

Altitude at which atmos.reduces intensity of radn

by one-half.Proportion of lightwhich arrives at sea level

UV

N and O

O3

H2OIonosphere