Lecture 13: Stars and Star Clusters

Lecture 13: Stars and Star Clusters
SCI238 W08 Lecture 13: Stars and Star Clusters double star Albireo is a binary system with P~75000yr L13 – Feb 28/08 Stars and Star Clusters

Stars and Star Clusters
This week’s events: the Moon: Last Quarter Feb. 28 Mercury: remains visible in the early morning Venus: visible low in east before sunrise; brightest “morning” star Mars: is visible all night, rises at sunset Jupiter: low in east before sunrise Saturn: rises at 8pm L13 – Feb 28/08 Stars and Star Clusters

Today’s Lecture stars and star clusters colours of stars spectral classification of stars the HR diagram and what it can tell us binary stars lifetimes of stars star clusters → evolution of stars, distances variable stars motions of stars L13 – Feb 28/08 Stars and Star Clusters

The Colours of Stars A star’s “colour” is a direct measure of its temperature red stars are cooler than blue stars (~BB, Wien’s Law…) the reddest stars are probably a few x103K bluest stars are probably a few x104K also, there are processes that can change the colour of the light – especially: dust grains in interstellar space can “redden” starlight. we can measure the brightness in a particular range of wavelengths and compare - say brightness in blue vs. red the measured brightness in two different wavelength ranges gives the colour of the object simplistically: if a star is measured to be brighter in the blue (more energy) than in the red, then we say that the star is blue – it is hotter we can quantify this => colour scale Start here on 28 Feb. L13 – Feb 28/08 Stars and Star Clusters

this HST image shows range of colours of stars in a field near the centre of the Milky Way galaxy the human eye is not very sensitive to colour at low light levels L13 – Feb 28/08 Stars and Star Clusters

BB spectra: reminder hotter sources are brighter (emit more energy) at all λ E=σT4 note: log scales plotted here… max (nm)= /T(K) peak λ is shorter for hotter T L13 – Feb 28/08 Stars and Star Clusters

Photometry, BB spectra, colours
Example: two sources of different T observed through B,V filters 15000K star brighter in B than in V: blue 3000K star brighter in V than in B: red L13 – Feb 28/08 Stars and Star Clusters

Measuring the colours of stars
colour is the ratio of the brightnesses in two wavelengths – or the magnitude difference. example: for a star the brightness in the blue is bB =100, and in the visual bV =80. Another, identical, star is much further away so that the energy received is 10 times less and one measures a bB =10 and bV =8. the difference for the nearby star is bB-bV =100-80=20 the difference for the distant star is bB-bV =10-8=2 for both stars the ratio of bB/bV is 1.25 (100/80 or 10/8) presumably both stars appear the same colour to the observer! the ratio of brightness energies gives the same numerical measure of their colour ( a bluer star would have a higher ratio and a red star would have a lower ratio). and colour is independent of distance! L13 – Feb 28/08 Stars and Star Clusters

Quantifying the colours of stars
the magnitude scale already relates a ratio of actual brightness to a difference. We can use this to describe colours in magnitudes mblue  mred =  2.5 log (bblue / bred) a standard (but not unique!) system of measuring the brightnesses at different wavelengths is called the UBV system, named for the original three wavelength ranges: ultraviolet, blue, and “visible” now extended into the red and infrared: R, I, J, K, L,M,N in this system a star might be described as having B=2.6 and V=2.9 giving it a B-V colour of 0.3 (a blue star) B V colours for most stars range from 0.3 (blue) to 1.5 (red) L13 – Feb 28/08 Stars and Star Clusters

Wavelength response curves for UBV and eye Note: eye’s best response is in red wavelengths, dark eye bluer L13 – Feb 28/08 Stars and Star Clusters

Stars are nearly black bodies but not totally
spectral lines cause a star’s spectral shape to deviate slightly from BB curve – generally more in the red than blue a star’s spectrum tells us more, better L13 – Feb 28/08 Stars and Star Clusters

Stellar Spectra learned about three kinds of spectra (L5) continuous: emission at all wavelengths (e.g. a blackbody) formed by hot solid or hot high pressure gas emission line: each element, as a hot low pressure gas, emits at a unique set of wavelengths (determined by the energy levels occupied electrons) absorption line: each element, as a cool low pressure gas, will absorb at a unique set of wavelengths (the same as above) from a continuous spectrum stars can produce all three kinds of spectra - but most produce an absorption (i.e. a continuous spectrum with absorption lines) spectrum the wavelength patterns in the lines give the elements in the cooler outer layers of the star the strengths of the lines tell us about the density and temperature where the lines are formed and also the amount of the elements present L13 – Feb 28/08 Stars and Star Clusters

classifying the spectra of stars Stars and Star Clusters
originally a scheme whose sequence was ordered by the strength of the hydrogen lines – the system has been re-ordered to be a sequence of temperature L13 – Feb 28/08 the Harvard “girls” Stars and Star Clusters

Spectra of hot stars dominated by H, He lines; cooler metals, molecules… L13 – Feb 28/08 Stars and Star Clusters

More Detailed Spectral Classification
The standard classification (OBAFGKM) was found to be not detailed enough. Subtypes were added as decimal numbers, occasionally with a half step: O5, O6, O8, O9, O9.5, B0, B1, …. M9 Subtle differences in the widths of the spectral lines were found to relate to the luminosity/radius of the stars: stars with very narrow lines were designated I Stars with wider lines: II, III, IV, V Final spectral types such as: G2V (the Sun!) L13 – Feb 28/08 Stars and Star Clusters

Stellar spectra vs. Photometry
show detailed lines and line structure can determine chemical abundances, rotation, magnetic field strength, radial velocity and more spreads star’s light out to see detail => need bigger telescopes Photometry good estimates of temperature chemical abundances – only very roughly can use smaller telescopes, observe more stars For broad surveys => photometry good For more detailed information => spectra better Astronomers use both… L13 – Feb 28/08 Stars and Star Clusters

the abundances of the elements as measured in the Sun For every 1,000,000 hydrogen atoms there are: 85,114 helium 331 carbon 91 nitrogen 661 oxygen 83 neon 26 magnesium 33 silicon 16 sulphur 40 iron (<10 of anything else) L13 – Feb 28/08 Stars and Star Clusters

Absolute Magnitude vs. Spectral Type: the HR Diagram
F K -4 first plotted by Hertzsprung (1905) and Russell (1913) –> now called the HR diagram vertical axis: luminosity (absolute brightness) –> MV absolute magnitude in V horizontal axis: originally spectral type (now also T, colour) Mv +4 +8 +12 +12 L13 – Feb 28/08 Stars and Star Clusters Spectral Type

Modern HR Diagram MV vs. B-V for 4902 stars absolute magnitudes based on parallax distances from Hipparcos satellite colours => density of points; red highest Note: even with this many stars same regions are empty or filled strictly speaking this is a colour-magnitude diagram (CMD) because the x-axis is colour, not spectral type L13 – Feb 28/08 Stars and Star Clusters

schematic HR diagram showing the main features: not a scatter plot; large “empty” areas most stars lie along a main sequence (MS) MS is a mass sequence other major regions: giant, supergiant, white dwarf are different evolutionary stages with a wide range of mass radius lines “diagonal” L T (sp.type/colour) L13 – Feb 28/08 Stars and Star Clusters

HR diagram: stellar L, T, R Remember: luminosity depends on both energy emitted/area and surface area For a spherical BB: L= 4πR2 x σT4 stars are moderately good blackbodies…. stars with same surface temperature (colour) but different luminosities must have different radii; also different densities… L13 – Feb 28/08 Stars and Star Clusters

nearby binary system Sirius A,B radius difference is real Sirius A: hot MS star with R~2RSun Sirius B: hot white dwarf star with R~0.008RSun if Sirius A and B have ~ same T, how much more luminous is Sirius A than B? if Sirius A has a mass ~2.2MSun and Sirius B is ~1MSun how much more dense is Sirius B than Sirius A? L13 – Feb 28/08 Stars and Star Clusters

HR diagram of the nearest stars sample bias = distance nearest stars are mostly faint MS – low mass, less massive than the Sun a few white dwarfs a few brighter MS stars no massive MS stars, no giants or supergiants L13 – Feb 28/08 Stars and Star Clusters

HR diagram of the brightest stars sample bias = apparent brightness brightest stars are mostly luminous stars on MS all much more massive thanthe sun also giants, supergiants no intrinsically faint stars – i.e. low MS, WD why are the nearest and brightest star samples so different? Are most stars high mass and luminous or low mass and faint? L13 – Feb 28/08 Stars and Star Clusters

Binary stars are common – and useful from binaries we get stellar masses, radii… detected “visually”, spectroscopically, and via eclipses L13 – Feb 28/08 Stars and Star Clusters

Binary Stars two (or more) stars in orbit around a common centre of mass. various possible cases: visual binary: both stars visibly orbiting each other astrometric binary: only one star is visible – the one star moves around in the sky in a loop or wave spectroscopic binary: only one star is visible; it shows no visible motion, but from its spectrum one can see a regular periodic motion from doppler shifts; sometimes only brighter star’s spectrum is seen, sometimes both eclipsing binary: one star passes “in front” of the other, blocking some of the light reaching us and causing a change in the system’s brightness L13 – Feb 28/08 Stars and Star Clusters

Kruger 60 is a visual binary with period ~40y m1+m2 ~0.4MSun L13 – Feb 28/08 Stars and Star Clusters

binary star systems: can be used to measure the mass of the stars visual binaries in a visual binary system the stars are resolved period determined from motion of one star about the other mass ratio from relative orbital scales need to know distance to determine “true” masses L13 – Feb 28/08 Stars and Star Clusters

Spectroscopic Binary System in a spectroscopic binary we observe periodic changes in spectral line wavelengths timescale => orbital period amplitude => orbital scale amplitude ratio => mass ratio L13 – Feb 28/08 Stars and Star Clusters

Centre of Mass location of centre of mass depends on relative masses in an equal mass system, CM is midway between in SS MSun >> Mplanet and CM is inside the Sun more general form of KIII (m1+m2)P2 = a3 = (a1+a2)3 L13 – Feb 28/08 Stars and Star Clusters

m1=m2 as centre of mass location depends on mass ratio… m1=2m2 so does relative orbital size m1>>m2 m1/m2 =a2/a1 = v2/v1 L13 – Feb 28/08 Stars and Star Clusters

Spectroscopic Binary star example:
The separation between two stars in a binary system is 0.5AU and the orbital period is 0.1 y What is the sum of their masses? m1+m2 = (0.5AU)3/(0.1y)2 = 12.5MSun Assume we know one star is moving in orbit twice as fast as the other; what are the individual masses of the two stars?? v2/v1 =2=m2/m1 and m2=2m1 => m1+m2=3m1=12.5MSun m1=4.2MSun, m2=8.3MSun m1/m2 =a2/a1 = v2/v1 (m1+m2)P2 = a3 = (a1+a2)3 L13 – Feb 28/08 Stars and Star Clusters

Spectroscopic Binary star example:
The separation between two stars in a binary system is 0.5AU and the orbital period is 0.1 y How do we observe the orbital speeds of the two stars? radial velocity from stars’ spectral lines: How does that give us orbital size? v1=2πa1/P v2=2πa2/P For this example we know a=a1+a2=0.5AU = 7.48x1010m => we know a1, a2 Observationally, if we know v1 and v2 then we can get a1 and a2 assuming circular orbits. It is more complex if orbits are not circular but can be done. In this example the orbital velocities are ~99.2km/s and 49.6km/s – verify for yourself for circular orbit: v=2πa/P m1/m2 =a2/a1 = v2/v1 (m1+m2)P2 = a3 = (a1+a2)3 L13 – Feb 28/08 Stars and Star Clusters

Eclipsing Binary System in an eclipsing binary we observe periodic changes brightness: eclipses timescale => orbital period eclipse timing => ratio of radii eclipse depth + radius => temperature and luminosity ratios if also spectroscopic => true radii; +mass -> densities previous/other knowledge of distance not needed if system is both eclipsing and spectroscopic L13 – Feb 28/08 Stars and Star Clusters

Data on stellar masses tell us: a star’s Main Sequence location is determined by its mass we will use this information to discover that massive stars use up their fuel much faster than do low mass stars L13 – Feb 28/08 Stars and Star Clusters

Stellar radii can be as small as a planet or as big as Mars’ orbit L13 – Feb 28/08 Stars and Star Clusters

≥ 90% of stars have mass < 1MSun => nearest stars sample more “representative” L13 – Feb 28/08 Stars and Star Clusters

M M Luminosities of MS stars span a much greater range (~106) than either their masses (≤102) or radii (≤102). In fact, the “mass-luminosity” relationship is best expressed as a “power-law” → L13 – Feb 28/08 Stars and Star Clusters

the lifetimes of stars depend on 1) the amount of fuel (mass) and 2) the rate at which the star uses up that fuel (luminosity) L13 – Feb 28/08 Stars and Star Clusters

for MS stars the Mass Luminosity relationship => relative numbers of stars on the MS are correlated with MS lifetimes is this also true for stars such as giants, supergiants, white dwarfs? i.e. are # stars related to lifetimes? we will find out L13 – Feb 28/08 Stars and Star Clusters

cluster is a group of stars, held together by their mutual gravity all stars in a cluster are assumed to be of roughly the same age – i.e. formed together at the same time and from the same gas cloud important testbeds for models of stellar evolution three types of clusters “associations” – 100 stars, probably short-lived “open clusters” – many thousands of stars “globular clusters” – ~spherical balls of ~ stars L13 – Feb 28/08 Stars and Star Clusters

Pleiades: a young open cluster; t~108 y gas illuminated by hot stars: shines by reflection L13 – Feb 28/08 Stars and Star Clusters

Two young star clusters: M46 (~3x108 y), M47 (~8x107 y)
which is older? why ? L13 – Feb 28/08 Stars and Star Clusters

M80: a globular star cluster
globular clusters are old (>1010 y) and massive ( MSun) L13 – Feb 28/08 Stars and Star Clusters

HR diagram for Pleiades
MS region for Pleiades populated below ~100LSun, but not above we see a few stars to the right of the MS above this “break” ML prediction: turnoff => age ~108 y L13 – Feb 28/08 Stars and Star Clusters

HR diagram for globular cluster M4
turnoff here at L≤ LSun => age ≥ 1010 y L13 – Feb 28/08 Stars and Star Clusters

4 star clusters plotted on the same H-R diagram wide range of ages of star clusters allows comparison with stellar models over a wide range of mass and evolutionary stage we’ll see what these stages are and how they occur when we look at stellar evolution L13 – Feb 28/08 Stars and Star Clusters

White Dwarfs in a Globular Cluster
L13 – Feb 28/08 Stars and Star Clusters

Deep HR diagram for globular cluster M4 shows lots of white dwarfs…
“rare” stars can be found if you look in the “right place” models tell us white dwarfs are a late stage of stellar evolution and globular clusters are the oldest identifiable stellar population… L13 – Feb 28/08 Stars and Star Clusters

Variable Stars many stars vary in brightness for various reasons – here we look at stars whose luminosity varies on “short” timescales eclipsing binary stars vary, but not intrinsically the most common cause of a (intrinsic) variable star is a pulsation the star increases and then decreases in radius usually the surface temperature also varies during the pulse… since the luminosity depends on both radius and surface temperature this can result in a variety of “light curves” (the luminosity as a function of time). we will look at various types of intrinsic variable stars L13 – Feb 28/08 Stars and Star Clusters

Variable Stars: main types
pulsating: common types are Cepheid: periods of 3 to 50 days, vary by ~0.2 magnitudes, absolute magnitude of -1.5 to -5 (very bright!) RR Lyrae: periods of less than a day, absolute magnitude of 1.0 “long-period” or Mira: periods of 80 to 600 days, large range in brightness eruptive variables: flare stars, novae, supernovae rotating “spotted” stars L13 – Feb 28/08 Stars and Star Clusters

Variable Star light curves
a light curve is a plot of the brightness of the light at different times many different shapes of light curves are found the shape tells us a lot about the kind of variations in radius and surface temperature that the star is undergoing L13 – Feb 28/08 Stars and Star Clusters

some pulsating variables are found in specific parts of the HR diagram – why? models tell us that heat can’t get out… and stars pulsate so it can… L13 – Feb 28/08 Stars and Star Clusters

Period-Luminosity Law of Cepheids
Cepheid variable stars have a very well-behaved, simple relationship between their Period (the time between successive brightest points in their light curve) and their Luminosity This provides us with a “Standard Candle” an object with well determined luminosity of knowing L, b we can find distance (b=L/4πd2) calibrate P/L relation for Cepheids with distances known by other means (mostly cluster members…) then knowing P,L for any Cepheid => we know its distance powerful because P/L relation is “tight” and Cepheids are quite luminous L13 – Feb 28/08 Stars and Star Clusters

pulsation is connected to a star’s internal structure…and the rate of pulsation is related to its luminosity…mainly its radius L P This makes pulsating variables a valuable tool! L13 – Feb 28/08 Stars and Star Clusters

Novae very rarely, but every once in a while a star will become much (~10,000 times) brighter often the original star wasn’t known before the event so… “nova” means “new star” some stars will repeat this behaviour decades or centuries later L13 – Feb 28/08 Stars and Star Clusters

Supernova 1987A in Feb a Canadian observatory night assistant, “playing” on his day off spotted bright new star in a galaxy close to our own. it was a supernova – the first one detected detectable with the naked eye in over 300 years L13 – Feb 28/08 Stars and Star Clusters

Supernovae Supernovae although several had been seen and recorded throughout history. The last (before 1987A) naked eye supernova was in 1604 (described by both Kepler and Galileo). Tycho recorded one in Chinese records show one in 1054. modern study of supernovae (beginning in the late 1920s) are almost entirely based on those seen in other galaxies it is estimated that each large galaxy has one supernova every one to three hundred years a supernova is brighter than all of the rest of the stars in its “parent” galaxy together! L13 – Feb 28/08 Stars and Star Clusters

Supernova 1987A “light curve”
the change in brightness of a supernova also has a pattern L13 – Feb 28/08 Stars and Star Clusters

Supernova Light Curves
because of this predictable pattern, SNIa are also standard candles more on standard candles later… L13 – Feb 28/08 Stars and Star Clusters

Stellar Motions: all stars move
measurable components: radial velocity (Doppler shift) and “transverse” velocity (across the line of sight) can measure transverse velocity only if the star is moving fast and is close to us! (“proper motion”) without motion, gravity acting between all of the stars would bring them together motions of stars tell us something about the gravity acting on the stars – if there is more motion (higher velocities) then there is stronger gravity (more mass) binary star orbits => stellar mass internal motions of stars in clusters => cluster masses motions of stars around the galaxy => galaxy mass statistical studies of the motions of stars are used as well… L13 – Feb 28/08 Stars and Star Clusters

Three clusters of different age
what is different about their CMDs? what do you see in the cluster images that “makes sense” re the CMD? this is stellar evolution: what we observe how it compares with models comes next L13 – Feb 28/08 Stars and Star Clusters

L13 – Feb 28/08 Stars and Star Clusters

Lecture 13: Stars and Star Clusters

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Lecture 13: Stars and Star Clusters

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