• e.g Sirius (Dog Star) = αCanis Majoris, α CMa, 9 Canis Majoris, 9 CMa, HD 48915, HR 2491, BD -16°1591, GCTP 1577.00 A/B, GJ 244 A/B, LHS 219, ADS 5423, LTT 2638, HIP 32349.

Brightness

Easiest observation about stars is that some are brighter than others. Hipparchus defined brightest to be of first magnitude, down to the dimmest of sixth magnitude.

• Our eyes respond to light logarithmically (100,1000,10000 photons/sec looks to us as 1:2:3 in terms of brightness). Hence the natural scale is a log scale.
• 5 magnitudes = 100 × luminosity
• 1 magnitude = 100^1/5 = 2.512 (∼2.5)
• Given two stars of luminosity l₀ and l₁
  \color{red}{ \delta m = m_0 - m_1 = 2.5\log _{10} \left( {\frac{{I_1 }}{{I_0 }}} \right)}
• Note that the larger magnitude is the dimmer star. (Yes, I know its stupid)
• Note that negative magnitudes are brighter than positive. (Yes, I know its really stupid)
• Dimmest naked eye objects are m ~ 5, dimmest observable m~25.
• This is apparent magnitude, and mixes up distance and the actual brightness:
• To define the absolute magnitude, we must first talk about distances.

Distances

Distance to stars is measured by parallax
Angle of parallax is defined w.r.t. very distant stars. (Why is π used as a symbol of an angle? Stupidity)

• Closest star is Proxima Centauri, which is a binary with α-Centauri, with parallax of .76" What is distance?
• 1 parsec = distance of a star whose apparent change in position would subtend an angle of 1" ∼ 3 × 10¹⁶ m. ∼ 3 light years
• Parallaxes can be determined to ±; .004"
• Hence distances can be measured out to 100pc: very small compared to galaxy size (∼20 kpc)

Absolute Magnitude

• M is absolute magnitude
• m is apparent
• D is actual distance

e.g sun: m = -26.7, M = 4.83

Proper Motion

Apparent motion of stars (due to parallax) gets mixed up with real motion of star. Since proper motion is cumulative, it can be measured much more accurately.

• Rough guide to distance: nearby objects appear to move faster than distant ones
• e.g. 61 Cygni 5.2"/yr (c/f∼.5" parallax)
• Winner is Barnard's star 10"/year ∼ diameter of moon in 200 yrs.

• Note that Doppler measures motion away from us, proper motion measures it perpendicular to our line of sight.

Colour Index

• Bolometric magnitude m_Bol would be measured over all λ, but need correction term/fudge factor
  \color{red}{ m_{bol} = C_{bol} - 2.5\log \left( {F_{bol} } \right)}
• Define sun to have absolute
  \color{red}{ M_{bol} ^ \odot = 4.74}
• then any star would have
  \color{red}{ M_{bol} = 4.74 - 2.5\log \left( {\frac{L}{{L_ \odot }}} \right)}

However can measure the effective temp by sampling at 3 different wavelengths, originally with filters If the V filter has a response \color{red}{S_V \left( \lambda \right)} then the total visual flux is \color{red}{ F_V = \int {F\left( \lambda \right)S_V \left( \lambda \right)} d\lambda }

• M_U = U-V magnitude at \color{red}{\lambda = 365nm}
• M_B = blue magnitude at \color{red}{\lambda = 440nm}
• M_V = visual (not violet!) at \color{red}{\lambda = 550nm}

  roughly agrees with what is seen by eye

• Define B-V colour index
  \color{red}{ B - V = M_B - M_V = m_B - m_V}
• and U-B colour index
  \color{red}{ U - B = M_u - M_B }
• (Note that distance corrections will be the same, so can use app. or abs. mags.)

• Hence for Vega
  \color{red}{ U - B = B - V = 0}
• so if star has T > 10000,
  \color{red}{ F_B > F_V \Rightarrow B - V < 0}
• Then can translate colour index to temp: could be done exactly for BB, but stars aren't BB's so empirical
  \color{red}{ T \approx \frac{{9000}}{{\left( {B - V} \right) + .93}}}

• BC for this temp is -.40, so
• \color{red}{ m_{bol} = 3.73 - .4 = 3.33}
• i.e: Measure flux of star through 2 filters ⇒ temp
• measure parallax ⇒ distance
• Apply BC to m_V ⇒ m_bol
• dist & m_bol ⇒ M_bol

Spectral Types, Sequence

Vega

Aldebaran

Note hotter (bluer) stars show more H, less complicated spectrum

This provides a direct measure of the surface temp of the star. This allows us to classify stars according to their spectra

Stellar Spectral Types: OBAFGKM Credit & Copyright: KPNO 0.9-m Telescope, AURA, NOAO, NSF

Note this is (generalised) combination of Boltzmann & Saha

These are subdivided into 10 smaller classes running from 1 to 10: e.g. the sun is a G2 star.

• A mnemonic

The Hertzprung-Russell Diagram

Having got two quantities (magnitude/luminosity & colour/type) it is natural to plot one against the other.

Note: the HR diagram is crucial to understanding stars

If we look at bright stars, the results are biased, since we see a very few, very distant objects.

General stars show a very distinct pattern

If we look at clusters of stars, they are presumably all at the same distance and the same age: hence expect that we should be able to learn something about how age & luminosity & spectral type are related.

The best known cluster is the Pleiades: (Seven Sisters except we can only see 6 now)

A closer look: the Pleiades are a very young group (∼ 50) of stars, about 107 years old, and very close: about 40 light-years, so light takes 40 years to travel from them. Note the "star-stuff" still blowing away.

Age probably ∼ 30 × 106 years. Note all are on the main sequence

e.g. Hyades ∼ 108 yrs Note four stars which have become red giants.

e.g. M3 which is a very old globular cluster note no bright blue stars at all (these are app. mags)

Morgan-Keene luminosity classes:

bright supergiant (Ia) supergiant (Ib) bright giant (II) giant (III) sub-giant (IV) dwarf (V)

Binary Stars

Many stars occur in multiple groupings: Roughly

single:	binary:	ternary:	quaternary
45%	46%	8%	1%

• A great deal of info about stars comes from these.
• Binaries range from seperations of 10⁸m (<< Mercury's orbit) up to 10¹⁵m (170 × Pluto's orbit)
• periods from a few hours to ≈ 10⁶ years (Pluto's orbital period ≈ 250 years).<
• Optical binaries: stars that just lie in the same direction (e.g. Alcor,Mizar) and hence of no interest.
• Visual binary orbit can be traced out over (usually large) number of years<:
• e.g. Mizar (ζ Ursa Major) itself is a visual binary

  Astrometric Binary (e.g. Sirius) Proper motion show "wobble", which can be put down to unseen attracting body

• Actual orbit can be deduced from path: Sirius B is too close to A for most of its orbit to be seen

Spectroscopic Binary

Only seen as single object, but spectral lines show recurrent doubling due to Doppler shift

Actual changes depend on orientation of orbit w.r.t observer

Note that each component of Mizar is a spectroscopic binary: i.e. it is a double-double

(note that double-doubles can have stable orbits: random sets of four stars almost never do, and usually one star will end up being ejected)

Unfortunately need to extract shape & inclination of orbit from velocity curves which can be difficult: we'll assume they are edge-on and circular.

Can be done for either visual binaries or spect. binaries: \color{red}{ r_1 = \frac{{v_1 P}}{{2\pi }},r_2 = \frac{{v_2 P}}{{2\pi }}} C.o.M must be fixed, so \color{red}{ m_1 r_1 - m_2 r_2 = 0 \Rightarrow \frac{{m_1 }}{{m_2 }} = \frac{{r_2 }}{{r_1 }} = \frac{{v_2 }}{{v_1 }}} Then can use Kepler's 3rd law \color{red}{ P^2 = \frac{{4\pi ^2 }}{{G\left( {m_1 + m_2 } \right)}}r^3 }

• Can be simplified by choosing units so that a is in AU, M in solar masses and P in years
  \color{red}{ P^2 = \frac{{4\pi ^2 }}{{G\left( {m_1 + m_2 } \right)}}r^3 \Rightarrow \left( {m_1 + m_2 } \right) = \frac{{r^3 }}{{P^2 }}}

Mass-luminosity relation

• In fact it is a little more complicated: he was right for very massive stars
  \color{red}{ \frac{L}{{L_ \odot }} = \left( {\frac{M}{{M_ \odot }}} \right)^4 }
  for solar mass stars,
  \color{red}{ \frac{L}{{L_ \odot }} = \left( {\frac{M}{{M_ \odot }}} \right)^{2.3} }
  for red dwarfs.

• Explanation requires detailed modelling of stellar energy processes:

• However roughly available energy
  \color{red}{ E \propto M \Rightarrow \tau \propto \frac{E}{L} \propto \frac{1}{{M^3 }}}

• If primary is bright, secondary could be brown dwarf whose light is swamped
• One case (Cygnus X-1) of large star ≈ 33M₀ in close orbit round invisible object (≈16M₀) Too massive to be normal star.
• Eclipsing Binary (e.g. Algol) where orbit is "side on" to Earth, so that one star can pass in front of another.

• Light curve usually shows two minima: in the case of Algol, luminosites very different

Stellar Radius

Assume

• circular orbit with plane in line of sight
• r is radius of smaller star
• R..................larger
• a is radius of orbit
• P is period

Obviously \color{red}{ 2r = v\left( {t_2 - t_1 } \right) = v\left( {t_4 - t_3 } \right)} and \color{red}{ 2\left( {R + r} \right) = v\left( {t_4 - t_1 } \right),a = \frac{{vP}}{{2\pi }}}

We discover that \color{red}{R \sim M^{1/2} } for a normal star: i.e. densities of large stars are lower

Can use eclipsing binaries to measure stellar rotation ratess Normally, spectral lines come from the whole star: at the moment of eclipse, they come from the edge only

• Some binaries are so close that the stars produce large tidal effects on each other:

• e.g. βLyrae has two components distorted into ellipses,(found by light curve) surrounded by a large gaseous envelope.

Contact binaries

Roche lobes are limits of stability for gas to be bound to one star: if one star fills its Roche lobe, then gas will flow to the other star.

Note that it is usually the smaller (and hence denser) star that pulls in material from the larger.

In summary, what we learn from binaries:

• Masses of stars (and hence densities)
• Radii
• Rotational speeds Processes for transferring energy & matter from one star to another
• Various exotic binaries: e.g. binary pulsars, Cygnus X-1, Centaurus X-3, SS-433.

• Can also get info about radii from interferometers:
  stars are not exactly point sources, so can get destructive or constructive interference by having light take slightly different paths.

• Speckle interferometers take frequent pictures at different wavelengths which change due to random fluctuations in atmosphere: allows radii of large stars to be determined as well as seeing close binaries

  Led to the discovery that Betelgeuse (α Or.) is a ternary system, with B component revolving inside the envelope of A (the red giant)

Variable stars

Divided loosely into Regular (or periodic) variables e.g. Cepheids Irregular e.g. flare stars Catastrophic e.g. novae We are only interested in Cepheids

Regular variables:

Star pulsates a with period of a few days e.g. δ Cephei Period ≈ 5.4 days, Magnitudes changes M ≈ 3.6-4.3 Spectral type changes (i.e. star heats up and cools down). Star actually expands: can be monitored by Doppler

Polaris is much weaker Cepheid: Δm ≈ .1 (Δm actually seems to be -> 0)

Cepheids are giants which have just moved off the main-sequence. Since M ≈ -1 to -6, they act as very useful distance markers: period \color{red}{P \propto M} , so by measuring m and P, one can get distance. RR-Lyrae: similar behaviour, but much smaller objects (.7M₀)

Polaris is much weaker Cepheid: Δm ≈ .1 (Δm actually seems to be -> 0)

Long period variables:

e.g. Ο Ceti (Mira) changes from m = 9 to 3 (!) over period of 11 months Spectral type changes from M5 to M9

• Mechanism not known, but probably connected to strage shape of star (distorted by WD companion)

Irregular Variables

T-Tauri: shows weird spectrum with too much UV, too much IR (i.e. long way from black body) and many peculiar lines (e.g. ice!) Can change magnitude very rapidly, e.g. X-ray flux can change by a factor of 10 in minutes Beleived to be proto-stars about 105 years after collapse of dust-cloud (see later)

Catastrophic Variables

Nova Cygni, Aug 28th-30th 1975 15th magnitude ................................................................. 2nd magnitude. Rapid rise followed by slow decrease

Old photos exist which show m < 16 until July 1975

Large amount of material (say 10-4 M0) thrown off star and ejected into space at v ≈ 100 km/s. Material can sometimes be seen later as nebula surrounding the star. N. Persei . . . . . . . . . . . . . .N Herculis

Some novae are known to have repeated: e.g. N Persei is surrounded by several shells of gas

WIYN Telescope Consortium

Most novae are binaries (rest may be undetected binaries).

• Standard model: Material flows from red giant to dwarf. Extra energy generated by infalling material heats up surface of the star, triggering nuclear burning. Heat in the outside layers blows off much of the material. Explains repeatability of process (evry few hundred years),

e.g. V838 Monocerotis: Not a nova, since star did not lose material, instead went to M~ -7 (brightest star in galaxy) bay expanding and cooling very fast

Lisa Crause (Univ. Cape Town), Warrick Lawson (Australian Defence Force Academy)

See light echoes from old dust clouds

HST

Wolf-Rayet stars

Very unstable supergiant stars: this is "Thor's Helmet"

Star Shadows Remote Observatory and PROMPT/UNC

Mass-loss is so large that outer layer of star is being stripped away continuously, revealing hotter lower layers. M ≈ 20 M0, extremely hot blue stars with narrow absorption lines and broad blue-shifted emission lines: Implies a star with a very extended atmosphere, which is rapidly losing material ΔM ≈ 10-5 M0/yr (i.e. can lose its whole mass in 106 years)

Flare stars:

Red dwarfs, which show very sudden and brief increase in luminosity, along with strong radio burst.

Flare in sun produces ≈ 1% increase in luminosity: if magnetic field was 10 × stronger, and luminosity 10^-3 as large, the same mechanism would give a 5 magnitude increase in luminosity

Chemical Anomalies:

• 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. 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<

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

Fields very variable, spectrum of stars changes with fields

Star Birth

Note Left centre: group of young stars Left lower:: star still blowing away cocoon of gas Right: glowing "lanes" of gas heated by large stars Centre left: dark lanes where stars are about to form

Credit & Copyright: T. Rector (U. Alaska Anchorage), Gemini Obs., AURA, NSF

Eagle Nebula: Cluster of stars just formed in centre of dark shell of dust and gas, taken with the 0.9-meter telescope on Kitt Peak, Arizona, USA. Part of M16

Credit & Copyright: T. A. Rector & B. A. Wolpa, NOAO, AURA,

Eagle close up: pink light is sulphur. Young stars excite the gas so it glows around the "birth pillars". Large stars will go supernova in about 5 million years

Credit: P. Challis (CfA), Whipple Obs., 1.2 m Telescope

The Eagle's EGGs: evaporating gaseous globules (EGGs). Very dense parts of the Eagle contract to form new stars which promptly blow away the surrounding dust and illuminate the columns

Credit: J. Hester, P. Scowen (ASU), HST, NASA

Henize 206: Another star forming region in the Large Magellanic Cloud. Can see left over remnants of old supernova at the top, which compressed the gas and triggered the star formation

Credit: V. Gorjian(JPL) et al., JPL, Caltech, NASA

N81: a group of very young hot stars in the Small Magellanic Cloud heating up the nebula round them

Credit: M. Heydari-Malayeri (Paris Obs.) et al., Hubble Heritage Team, NASA

XZ Tauri consists of 2 very young unstable stars, separated by about Sun-Pluto distance, emitting vast cloud of gas (pictures taken over 5 years)

Credit: John Krist (STScI) et al., WFPC2, HST, NASA

Compact Objects and end points of stars

Means......

1. Planetary Nebulae
2. White Dwarfs
3. Supernovae
4. Neutron Stars
5. Black Holes

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

• Water (by definition) ρ = 1000
• Osmium ρ ∼ 22000
• Air ρ ∼ 1
• Sun ρ ∼ 1000 (but about 1.5x10⁵ at centre, much less at outside)

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.

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

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

White dwarfs

Density: ∼ 10¹¹: ∼ 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

This implies a very small object: mass ∼ 1.05 Mo 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!

Note: 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)

Predicts maximum mass of WD is ∼ 1.4M_o

Supernova

If Stars are large....

Approx 1/30 yr known in Milky Way
6 visible in recorded history

SN 1006

SN 1006: History's Brightest Supernova. Composite view X-ray data in blue from the Chandra Observatory optical data in yellowish hues radio image data in red

THis shows remnants of the expanding shockwave

Credit: Frank Winkler (Middlebury College) et al., AURA, NOAO, NSF

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,

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

Type 1 have a compact object (white dwarf) with a red giant, which expands and spills material onto companion, finally triggering catastrophic collapse. All type 1a seem to be the same (very important for later on!) Material ⇒ Accretion disk onto compact object Triggers explosive burning ⇒ shock wave compresses accretion disk ⇒ more burning ⇒ massive ejection of disk material ⇒ formation of 54Fe (half-life 70 days!) decay provides energy for slow light curve

Drawing Credit: ST ScI, NASA

Type II

Pre-collapse: \color{red}{\rho \sim 10^9 ,T_C > 10^9 K}

SN2005

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

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 fitted into a life-cycle:

Comments

• We talk about stellar evolution, which is stupid, since we don't talk about the evolution of a baby into an adult.)

• 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
• There are intermediate steps that we will discuss later

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.

• In HR terms: