This page intentionally blank except for the words This page intentionally blank e Interpretation of Stellar Spectra Ian Howarth, UCL
• Quantitative spectroscopy: effective temperature; [plane-parallel] surface gravity; surface abundances;
mass-loss rates, terminal velocities; [winds]
[radii, distances, luminosities, masses – v. weakly; GM/R2 vs √2GM/R]
Two disadvantages....fundamentallityism & pictures . (zoom) What are the less ‘fundamental’ (but still interesting?) O aspects can we investigate? B
[From a viewpoint biassed by a background in hot, luminous A stars.....] F
F and earlier: radiative envelopes
OB: windy, core-collapse finale What are the less ‘fundamental’ (but still interesting?) aspects can we investigate?
Doppler shifts dynamics • Radial velocities • Binary (and higher-order) motion • Rotation • Binary+Rotation Rossiter effect • Pulsation
Polarization • Geometry • Magnetic fields
• First, one really fundamental parameter from spectroscopic dynamics: masses (the fundamental stellar parameter!)
Discovery plates of the first known spectroscopic binary, ζ Uma (E.C. Pickering, Harvard plate collection). Top: Mar 29, 1887, Bottom: Apr 5, 1887. • First, one really fundamental parameter from spectroscopic dynamics: masses (the fundamental stellar parameter!)
• Orbit basics: centrifugal ‘force’ balances 2 2 gravitational force [Gm1m2/R = mv /r]
• Projected velocity amplitudes depend on binary separation and masses (‘closer’, more massive systems need faster orbits)
• Projection factor can be determined for eclipsing binaries: direct stellar mass determination (sin3i dependence). Ratio of eclipse depths ratio of surface brightness
Eclipse width/depth star sizes (wrt orbital septn.) and inclination
RV curve scale stars sizes, masses Ratio of eclipse depths ratio of surface brightness
Eclipse width/depth star sizes (wrt orbital septn.) and inclination
RV curve scale stars sizes, masses +f(T) distance.... !10 Zones of constant projected velocity
sharp edges
We can’t normally separate out projection effects [hence ‘v(e).sin(i)’] If the intensity (as a function of emergent angle) is unaffected by rotation...
VLTI Achernar (α Eri)
Von Zeipel: F \propto g If the intensity (as a function of emergent angle) is unaffected by rotation, then
1. Rotation is an example of ‘macroscopic’ broadening -- velocity displacements occur on length scales greater than the photon mean free path (total line strength [equivalent width] is conserved).
2. The observed spectrum is the convolution of the intrinsic (non-rotating) flux spectrum, and a rotational broadening function
EW conserved We can’t normally separate out projection effects [hence ‘v(e).sin(i)’] Limb darkening matters a little bit Linear: I(μ) = I(0)[1 – u(1 – μ)] , μ=cos(θ) How to measure rotational broadening (~line width)?
• ‘Old school’ – direct analysis in wavelength/velocity domain
Direct line-width measurement e.g., fwhd; calibrate against models. (don’t forget to account for other broadening mechanisms, inc.instrumental); or profile fits.
Okay for ‘simple’ spectra (isolated lines) in ‘slowly’ rotating stars (ω << ωc)
But normally, simple profile fits ok
HD 93521 (O9.5V)
Profile fits vs model calibration of widths • ‘New’ school (Gray): frequency space (individual lines)
u • ‘New’ school (Gray): frequency space
Complications: Single lines (can compare with models) Other broadening mechanisms, differential rotation, limb darkening, etc. have (fairly small) effects.
Need good S:N, but sharp rotational ‘edges’ give reasonably distinct signal
!20
V(e) sin(i) = 170, 385 km/s
HeI 4026 Dufton et al.
V(e) sin(i) = 170, 385 km/s
HeI 4026 Dufton et al. Okay for isolated lines... More complicated spectra? Cross-correlation (and related techniques; e.g. LSD) Do xcorr in pseudo-velocity (log λ) space, not wavelength)
0
0
0 Cross-correlation (and related techniques; e.g. LSD) Do xcorr in pseudo-velocity (log λ) space, not wavelength)
0
0
0
Cross-correlation is functionally equivalent to convolution (can deconvolve to recover broadening function) Real world isn’t ideal.... Cross-correlation (and related techniques; e.g. LSD) Do xcorr in pseudo-velocity (log λ) space, not wavelength)
Treat ccf in similar way as single line Err...why is this worth investigating?
Balona B-stars; observed, error-corrected, intrinsic
(Penny & Gies 2009, O stars)
Err...why is this worth investigating?
Energetically, rotation is negligible (kinetic energy << nuclear!), but is central to dynamo processes in cool stars, and is responsible for mixing processes which influence high-mass stellar evolution.
Rotation also influences outflow characteristics (e.g., is probably of profound significance for the Be phenomenon), and allows investigation of surface morphology (micro-arcsec resolution!) through mapping of velocity to spatial structure
Brott et al.2011
Brott et al.2011 Main-sequence O-type stars: ON vs O-norm
Main sequence Potential of ‘Doppler mapping’’ E.g. effect of dark spots: produces a bright bump in the (normalised) line profile
(Vogt & Penrod) Mapping: equatorial vs temperate spots (polar spots change profile shape)
V410 Tau (K3V HAe/Be; Rice et al. 2011)
Inversion tools typically use maximum entropy methods for image reconstruction Same but different:
Rossiter- -McLaughlin effect
(In reality, usually just a centroid shift) • Rossiter, Anne Arbor (1924, ApJ 60, 15-21) McLaughlin, Anne Arbor (1924, ApJ 60, 15-21)
HD 189733A
WASP 8A
(Mayor et al.)
• Stellar pulsation Cepheid variables: radial pulsators • Delta Cephei (prototype) 1. Integrate radial-velocity curve (dR/dt) absolute change in radius (correction for sphericity)
2. Change in brightness relative change in radius (correction for temperature) 3. OR direct interferometric imaging....
4. Absolute radii; + surface brightness (temperature) absolute magnitude distance (Baade-Wesselink; f(T))
• Non-radial pulsation
l = degree (no. of node lines; 3)
|m| = azimuthal number
l = |m| sectoral mode
(cp. tesseral modes) Doppler imaging... l=3 3 ‘bumps/dips’
(Requires adequate rotation to resolve structure) r b red blue HD 93521 (von Zeipel effect?) HD 93521 P1 = 1.8h, l=10 P2 = 2.9h, l=6 Returning to rotation...
Main-sequence O stars how both more rapid and slower rotation than O supergiants. O-type stars
Main-sequence O stars how both more rapid and slower rotation than O supergiants. This implies a significant non-rotational line-broadening mechanism: ‘turbulence’. HD 191612 Take-aways:
• Rotation is interesting (dynamo action in convective envelopes [hence X-ray emission etc.]; evolutionary & surface-abundance effects in massive stars with radiative envelopes) • Allows (model-dependent) surface mapping in single stars: spots, pulsation... • Rossiter-McLaughlin effect in eclipsing binaries (and exo systems) Part II: SpectroPolarimetry
• Linear spectropolarimetry: geometry • Circular spectropolarimetry: magnetic fields Linearly polarized light is characterized by
(i) the plane (direction) of polarization (ii) the relative strength of the polarized light intensity (compared to total light intensity)
Polarized light has strength and direction -> alternative representation in vector form; vector components as “Stokes’ parameters”, QU (or qu)
In astronomy, we can measure the polarization in integrated light (photopolarimetry),as a function of position (imaging polarimetry), or as a function of wavelength (spectropolarimetry),
Why? Because polarigenic mechanisms disclose astrophysics, and polarization properties disclose geometry
Astrophysically important polarigenic processes: Dichroic absorption (0) reflection (in instrumentation) (polaroid) (i) dipole scattering (electron s) (ii) dichroic absorption (interstellar dust)
And some more familiar situations.... Why is the sky blue? Scattering! Polarized
Haidinger’s brush (dichroic absorption); LED screens, the sky Rainbows? (Internal) reflection
Spectropolarimetry
• Split starlight into two orthogonally polarized beams; feed to spectrograph • Uses ‘birefringent’ crystal (calcite, iceland spar; different refractive index for different polarization) Seyfert galaxies were first identified by Carl Seyfert in 1943.
He defined this class based on observational characteristics:
Much of the luminosity comes from a small (unresolved) region at the center of the galaxy – the (active) galactic nucleus.
Nuclei have MB > -23 (arbitrary dividing line between quasars/seyferts)
NGC 4151
Type 1 spectropolarimetry
Spectropolarimetry reveals “hidden” sources, exemplified by unification of Seyferts (and other AGN)
Stellar spectropolarimetry: geometric information on spatially unresolved scales The ‘line effect’ in early-type emission-line stars
continuum source scattering
line-emitting region Competing mechanisms can give confusing results!
Geometry (& astrophysics) of unresolved sources
Ca. 20% of WR stars have ‘significant’ (bias) intrinsic distortion
Similar effects in unrelated systems with similar geometries: Be stars, young Herbig Ae/Be, etc. A special case: symbiotic stars....
‘Mystery lines’ at 6830 & 7088: broad, unidentified Solution (Hans Schmid): Raman scattering Neutral Hydrogen
E(1032) = hν = hc/λ - OVI (Balmer) Hα = hc/1032
E(1216) = hc/1216 - Lyα
Energy difference = (hc/1032) – (hc/1216) Lyman α => λ=6830! λ=1215.7 (Extreme wing of Hα) Line width
Δλ/λ: 6830/1032
Doppler shifts in OVI are amplified 6x
Cool Star Wind - neutral hydrogen ‘H II region’
Hot Star- OVI photons
Scattering - Polarization?
He2-38
Scattered photons - polarized perpendicular to line of centres
PA rotation is 180 degrees, independent of period Periods of centuries possible in principle (determines mass accretion process) Magnetic-field measurement
Zeeman Effect
No B
With B
1897/1902, a reversal of fortunes Nature 55, 347 (1897) Hale (1908) – sunspot field (above) Earth’s field: 0.5G 1G=10-4T (1913) – general field Sun: (1G) Fridge magnet 50G Sunspots: few kG
Zeeman split lines from sunspots
Swedish solar telescope Splitting is small: of order 1 km/s/kG; what if lines are broad? (OB stars, 100 km/s)
Zeeman Effect
I have since found by means of a quarter- wave plate and an analyser, that the edges of the magnetically-widened lines are really circularly polarised when the line of sight coincides in direction with the lines of force. On the contrary, if one looks at the flame in a direction at right angles to the lines of force, then the edges of the broadened sodium lines appear plane polarised, in accordance with theory. P. Zeeman, “The Effect of Magnetisation on the Nature of Light Emitted by a Substance” Measuring the Zeeman Effect
A quarter-wave plate converts circularly polarized light into linearly polarized light; and vice-versa
Linear polarization Circular polarization Linearly polarized light can be analysed...
‘A quarter-wave plate consists of a carefully adjusted thickness of a birefringent material such that the light associated with the larger index of refraction is retarded by 90° in phase (a quarter wavelength) with respect to that associated with the smaller index.’ Zeeman split + Circular polarization
Stokes V = ↺ - ↻
V/I Babcock 1947:
Rapid rotation implicated; first ‘magnetic star’, 78 Vir, A2V (“field proportional to rotation: 1.5kG. Pure coincidence...”) (1978)
‘Babcock’s star’ – A0 [oblique rotator] Most look like simple dipoles... σ Ori E RRM Model Hα Observations
But not all....
Tau sco NGC 1624-2 (dipole)