Download Spectroscopy Lecture 10

Spectroscopy ­ Lecture 10
Chemical analysis
Stellar radii & temperatures
● Stellar spectra
● Abundances
● The Sun
● Examples: peculiar stars etc. ●
Measuring Radii and Temperatures of Stars
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Direct measurement of radii
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Photometric determinations of radii
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Determining temperatures
– Speckle
– Interferometry
– Occultations
– Eclipsing binaries
– Bolometric flux
– Surface brightness
– Absolute flux
– Absolute flux
– Model photospheres
– Colours
– Hydrogen lines
– Metal lines
Stellar Radii
To calculate R: Observe: ● parallax p => distance d = 1 / p ● spectral type or colour index => T
● apparent magnitude, e.g. V
Stellar Diameters
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Angular diameters typically measured in milli­arcseconds (mas)
Angular diameter (in radians) given by physical diameter divided by distance
Some diameters: Vega (3.2 mas), Sirius (5.99 mas), Aldebaran (21.1mas) Typical radii:
Sun: R = 700000 km
main­ sequence stars: R ~ 0.1 ... 10 RSun
giants: R ~ up to 100 RSun
supergiants: red: R ~ up to 1000 RSun
blue: R ~ 20 – 50 RSun
white dwarfs: R ~ 0.01 RSun
Accurate radii
Most accurate radii ( < 1% ) from eclipsing binary stars
● interferometry (for nearby stars)
● lunar occultations (for a few stars)
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Accurate R improves T via Speckle Diameters
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The diffraction limit of 4­m class telescopes is ~0.02” at 4000A, comparable to the diameter of some stars
The seeing disk of a large telescope is made up of the rapid combination of multiple, diffraction­limited images
2­d Fourier transform of short exposures will recover the intrinsic image diameter
Only a few stars have large enough angular diameters. Speckle mostly used for binary separations
Interferometry
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7.3­m interferometer originally developed by Michelson
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Measured diameters for a few K & M giants
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Until recently, only a few dozen stars had interferometric diameters
Other Methods
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Occultations
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Moon used as knife­edge
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Diffraction pattern recorded as flux vs. time
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Precision ~ 0.5 mas
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A few hundred determined
Eclipsing binaries
Homepage of Joachim Köppen:
http://astro.u­strasbg.fr/~koppen/JKHome.html
Eclipsing binary
Eclipsing binary
Photometry
use filters (e.g. U, B, V, R, I)
measure flux densities: fB, fV, ...
apparent magnitudes: (B, V, ...)
colour indices: absolute magnitudes (d from parallax):
colours => Teff , log g
Bolometric magnitude
Mbol = absolute bolometric magnitude
total flux over the entire spectrum
Difficult to measure Mbol, easy to measure MV.
Why spectra differ
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Line strengths change mainly due to surface temperature
hot: high ionization and excitation
cool: neutral atoms and molecules
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some line widths and ratios change with luminosity
very little range of abundances ( 74% H, 24% He, 2% everything else) ●
... BUT ... some stars show pronounced abundance anomalies ! Curves of Growth
Traditionally, curves of growth are described in three sections
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The linear part: –
The width is set by the thermal width
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Eqw is proportional to abundance
The “ flat” part:
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The central depth approaches its maximum value
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Line strength grows asymptotically towards a constant value
The “ damping” part:
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Line width and strength depends on the damping constant
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The line opacity in the wings is significant compared to κ ν
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Line strength depends (approximately) on the square root of the abundance
Determining Abundances
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Classical curve of growth analysis
Fine analysis or detailed analysis – computes a curve of growth for each individual line using a model atmosphere
Differential analysis
– Derive abundances from one star only relative to another star
– Usually differential to the Sun
– gf values not needed
Spectrum synthesis
– Uses model atmosphere, line data to compute the spectrum
Abundances
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[m/H] = log N(m)/N(H)star – log N(m)/N(H)Sun
• [Fe/H] = ­1.0 is the same as 1/10 solar
• [Fe/H] = ­2.0 is the same as 1/100 solar
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[m/Fe] = log N(m)/N(Fe)star – log N(m)/N(Fe)Sun
• [Ca/Fe] = +0.3 means twice the number of Ca atoms per Fe atom
Solar Abundances (Grevesse and Sauval)
CNO
Log e (H=12)
8
Fe
5
S r , Y, Zr
Sc
2
Ba
Li, Be , B
Eu
-1
10
20
30
40
50
Atomic Number
60
70
80
Recall: Solar abundances
Element
log N
∆NLTE
6 C
8.592+/­0.108
­0.045
7 N
7.931+/­0.111
­0.032
8 O
8.736+/­0.078
­0.028
10 Ne
8.001+/­0.069
…
12 Mg
7.538+/­0.060
~0
14 Si
7.536+/­0.049
­0.010
26 Fe
7.448+/­0.082
+0.000
Holweger, H. (2001), AIP Conference Proceedings
Details of Solar Abundances
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Oxygen
– Variations of 0.1 dex depending on which lines are included or not
– Individual lines vary from 8.697 to 8.921
– NLTE effects generally strengthen the lines
– Also affected by granulation
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Carbon, Nitrogen ­ dito •
Magnesium – Use Mg II as dominant species
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Neon – EUV spectra of emerging active regions
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Iron – still controversial! – Values range from 7.42 to 7.51; ... 7.448 'best' value
– If Fe II is used, NLTE effects very small
– Disagreements about choice of lines, f­values
Summary for the Sun
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Departures from LTE occur in all lines formed above τ c=1
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Cores of lines with well­developed wings show strong departures from LTE
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Weak, low­excitation lines of trace elements are likely to show departures from LTE
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Weak, high­excitation lines of abundant elements are less susceptible to NLTE
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Far wings of strong lines are less susceptible to NLTE
Basic Methodology for “ Solar­Type” Stars
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Determine initial stellar parameters
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Composition
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Effective temperature
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Surface gravity
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Microturbulence
Derive an abundance from each line measured using fine analysis
Determine the dependence of the derived abundances on
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Excitation potential – adjust temperature
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Line strength – adjust microturbulence
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Ionization state – adjust surface gravity
Different spectra ...
what do these spectra have in common ... ?
Different spectra
Examples: peculiar stars etc.
The Lower Main Sequence
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Flare Stars
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M dwarf flare stars
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About half of M dwarfs are flare stars (and a few K dwarfs, too) –
A flare star brightens by a few tenths up to a magnitude in V (more in the UV) in a few seconds, returning to its normal luminosity within a few hours
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Flare temperatures may be a million degrees or more
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Some are spotted (BY Dra variables)
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Emission line spectra, chromospheres and coronae; x­ray sources
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Younger=more active
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Activity related to magnetic fields (dynamos)
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But, even stars later than M3 (fully convective) are active – where does the magnetic field come from in a fully convective star?
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These fully convective stars have higher rotation rates (no magnetic braking?)
Wolf­Rayet Stars
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Luminous, hot supergiants
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Spectra with emission lines
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Little or no hydrogen
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105­106 Lsun
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Maybe 1000 in the Milky Way
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Losing mass at high rates, 10­4 to 10 ­5 Msun per year
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T from 50,000 to 100,000 K
• WN stars (nitrogen rich)
• Some hydrogen (1/3 to 1/10 He)
• No carbon or oxygen
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WC stars (carbon rich)
NO hydrogen
C/He = 100 x solar or more
Also high oxygen
Outer hydrogen envelopes stripped by mass loss
WN stars show results of the CNO cycle
WC stars show results of helium burning
Do WN stars turn into WC stars?
Red Giants
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Miras (long period variables)
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Periods of a few 100 to 1000 days
Amplitudes of several magnitudes in V (less in K near flux maximum)
Periods variable
“ diameter” d epends greatly on wavelength
Optical max precedes IR max by up to 2 months
Fundamental or first overtone oscillators
Stars not round
Pulsations produce shock waves, heating photosphere, emission lines
Mass loss rates ~ 10­7 Msun per year, 10­20 km/sec
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Dust, gas cocoons
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More Red Giants
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Normal red giants are oxygen rich – TiO dominates the spectrum
When carbon dominates, we get carbon stars (old R and N spectral types)
Instead of TiO: CN, CH, C2, CO, CO2
M Dwarf Spectral Types
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Molecular species switch from MgH to TiO
CaOH appears in later M dwarfs
Prominent Na D lines
Spectral types determined in the blue
M Dwarf Spectra Are a Mess
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Observed spectrum of M8 V dwarf VB10
Black body and H­ continuum spectra shown as dashed lines
Real spectrum doesn’t match either
Spectrum dominated by sources of opacity
Later Spectral Classes
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TiO disappears to be replaced by water, metal hydrides (FeH, CrH)
Alkali metal lines strengthen (note K I in the L8 dwarf)
Spectral types determined from red, far red spectra (blue too faint!)
L­type Spectral Sequence
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K I line strength increases with later spectral type
Li I appears in some low mass stars (m < 0.06 solar masses)
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Appearance of FeH, CrH
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Strength of Ca I
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Strength of water
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Disappearance of TiO
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Absence of FeH, CrH in T dwarf, much increased strength of water
Brown Dwarfs
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Many L and T dwarfs have now been found
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Improved IR detectors
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Better spatial resolution (seeing improvements, AO)
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IR and multi­color surveys (2MASS, DENIS, and Sloan)
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Breakthrough in understanding appearance of spectra
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Significant progress in modeling low mass stellar and substellar objects
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Understood in the late ’50s that
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low mass stars must be fully convective
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Electron degeneracy must play a role
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H2 formation also important (change in slope of main seq. at 0.5 MSun)
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early ’60s: a minimum mass is needed for H burning (0.08 Msun)
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early '70s: deuterium burning included in models ●
Recent improvements include better equation of state and grain formation
Li in Brown Dwarfs
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Li I appears in about a third of L dwarfs
EQW from 1.5 to 15 Angstroms
Li I can be used to distinguish between old, cooled brown dwarfs and younger, lower mass dwarfs
History of White Dwarfs
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Bessell (1844)
– Proper motions of Sirius and Procyon wobble
– Suggested they orbited “d ark stars”
Alvan Clark (1862)
– Found Sirius B at Northwestern’s Dearborn Observatory
Procyon B found in 1895 at Lick
– Was it a star that had cooled and dimmed?
Spectrum of 40 Eri B observed – an A star!
– It must be hot
– Must have small radius to be so faint
– The first “w hite dwarf”
Adams found Sirius B is also an A star in 1915
– From luminosity, R~ 2 x Earth (actually ¾)
– From orbit, about 1 solar mass
– Density 105 x water (actually 106)
20th Century History
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Eddington – Gas must be fully ionized so that nuclei could be compacted together
– as the white dwarf cools, the atoms should recombine, but they can’t because the star can’t swell against gravity
R. H. Fowler (1926)
– Recognized the role of degeneracy pressure in supporting the star
Chandrasekhar (1935)
– Upper limit to mass supported by electron degeneracy pressure due to limit of velocity of light (1.4 solar masses)
Zwicky (1930’s) ­ Degenerate Neutron Stars
Schatzman (1958) – chemical diffusion in strong gravity (plus radiative levitation, winds and mass loss, convective mixing, accretion)
Greenstein and Trimble (1967) ­ Gravitational redshift
Hewish and Bell (1967) ­ Pulsars
White Dwarfs
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White Dwarfs – DO, DB, DA, DF, DG, DM, DC
Classifications NOT analogous to MS – reflect compositions, not temperature
– DA – hydrogen lines (no other lines, pure H atmosphere)
– DB – neutral He lines (no hydrogen at all, pure He)
– DO – ionized He lines (no hydrogen at all, hotter DBs)
– DC – continuous spectrum, no lines
– DF, DG, DM ...
Heavier atoms sink in gravitational field
Above 15,000 K, 15% are non­DA, below 15,000 K, half are non­DA. How do the stars do that?
NO DB stars between 30,000 and 45,000 K
Chemically Peculiar Stars of the Upper Main Sequence
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Ap stars
– SrCrEu stars
– Silicon Stars
– Magnetic fields
– Oblique rotators
– Slow rotators
Am­Fm stars
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Ca, Sc deficient
Fe group, heavies enhanced
diffusion
HgMn stars
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The λ Boo stars ... Vega is a l Boo star ! ●
NLTE in O & B Stars
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Low atmospheric density
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High temperature
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LTE not valid
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Methods for NLTE in O stars date from the late ’60’s
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NLTE effects not subtle – observable even at low spectral resolution
Model atoms
O I 29 levels, 71 transitions
(Hempel & Holweger 2003)
Diffusion
... important in B, A, F main­sequence stars and white dwarfs
Diffusion
Pre­condition: atmosphere stable, i.e., no convection, low rotational velocity (meridional circulation!)
gravitational settling <=> selective radiation pressure
radiation pressure is large for ● atoms / ions with many lines near flux maximum
● Elements with complex term structures
● rare earths
small for ● noble gases
● saturated lines
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overabundances of Mn, Sr, Y, Zr, Ba, ...
underabundances of He, Ne, Ca, Sc, ...
timescales 104 – 106 a < main­sequence evolution of a B star
Diffusion in late B­stars – results (Hempel & Holweger 2003)
Effects of weak stellar winds (Landstreet et al.1998)
Certain elements can be used as tracers for weak stellar winds
(10­14 ... 10­12 MSun/yr)
Assumption: outward radial mass flux
Behaviour of abundant elements He, O, C, Fe, Ne, N, ...) :
Ne interesting in the case of late B­type stars (Teff = 11000 ... 16000K)
Ne II from layers below atmosphere is pushed outwards with the stellar wind
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Ne becomes neutral in stellar atmosphere
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Ne I has a smaller cross­section than Ne II
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enrichment of Ne I in stellar atmosphere
Weak stellar winds from late B­stars ­ results
LTE
NLTE
overabundances are artefacts of the assumption of LTE !
necessity of NLTE­calculations Some spectra ...