1. asteroseismology of pulsating sdB stars
Simon Jeffery (Armagh Observatory)
Vik Dhillon (Sheffield University) Tom Marsh (Warwick University) Ramachandran (Armagh Observatory) Conny Aerts, Paul Groot (Nijmegen)
MNRAS: July 2004

2. subluminous B stars
origin of sdB stars
pulsations in sdB stars
ultracam
colorimetry
nrp mode evaluation

3. faint blue stars in the Galactic halo
Greenstein and Sargent 1974, ApJS 28, 157.
The nature of faint blue stars in the halo. II

4. Green Schmidt and Liebert 1986, ApJS 61, 305
Palomar Green survey of faint blue objects
Green Schmidt and Liebert 1986, ApJS 61, 305
Primarily a qso survey

5. UV excess in giant elliptical galaxies
Excess flux observed in early UV galaxy surveys. Seen as upturn in flux shortward of c A in elliptical galaxies (Burstein et al ApJ 328, 440)
Hypothesized to be due to post-AGB and extreme horizontal branch stars (Greggio & Renzini 1990 ApJ 364, 35)
Demonstrated by Brown et al. (1997 ApJ 482, 685) using HUT data for M60 and other ellipticals.
UV excess in giant elliptical galaxies

6. NGC2808: Brown et al. 2001

7. evolution of sdBs

8. horizontal branch stars and normal stellar evolution
Post-GB and He-flash
He-burning core 0.5 M
H-rich envelope
0.4 M/ metal-rich - red HB
0.2 M/ metal-poor - blue HB
M - EHB / sdB
Problems: How does RGB star lose its entire H envelope? How does it still suffer He-flash?

9. stellar evolution with mass loss on the giant branch
Brown, Sweigart, Lanz, Landsman & Hubeny 2001, ApJ 562, 368
If star reaches within 0.25mag of RG tip, a helium flash will occur.
Final position on ZAHB depends on Menv.
Mass loss could be RLOF as binary on RGB.

10. origin of sdB stars
Binary evolution is important in at least 2/3 of sdBs (Green, Liebert & Saffer, 2001, ASP 226). Key factor is Roche Lobe Overflow in metal-rich low-mass giants near the Red Giant Tip. Group III (composite) sdBs are the key:
i. low-mass binary with initial separation R
ii. secondary has mass M
iii. primary Roche lobe radius = R < RGB tip radius
iv. at initial Roche lobe overflow, secondary accepts 0.3 M dynamical mass transfer without overflowing its own Roche lobe
v. mass ratio inverts, further mass transfer increases orbital separation, no common envelope phase
vi. secondary now a blue straggler with mass M

11. initial secondary  sdB
origin of sdB stars: II
Other binary outcomes depend on initial separation, masses and mass ratio.
initial primary  sdB
sdB + dM (IIB)
sdB + BS (III)
initial primary  HeWD
HeWD + dM (pre-CV)
HeWD + BS
initial secondary  sdB
HeWD + sdB (IIA)
Evolution that produces single sdB stars (I) include: enhanced mass loss from single stars (d’Cruz et al. 1996) merger of two He WDs (Iben 1990, Saio & Jeffery 2000)

12. pulsations in sdBs

13. a comedy of errors...
SAAO: high-speed photometry of pulsating white dwarf candidate EC (Kilkenny et al. 1997)

14. Frequency Period Amplitude
(mHz) (s) (mmag)

15. sdB stars and pulsational instability

16. KPD
Koen 1998, MNRAS
and also
Billères et al. 1998, ApJL

17. sdB stars and pulsational instability
pulsators, non-pulsators and not yet observed sdBs vs. number of unstable l=0 models
from Charpinet et al. 2001, PASP
(now ~ 10 more pulsators)

18. astero-seismology of sdBs
comparison of number of excited frequencies and period ranges for observed and model sdB stars
Charpinet et al. 2001, PASP

19. asteroseismology of PG1047+003
theoretical frequency spectrum compared with an observed power spectrum
adjust the stellar interior model to match the observed frequencies
Charpinet et al. 2001, PASP

20. nonradial oscillations
l=20, m=10
l=4, m=1
l=4, m=0
l=4, m=3

21. nonradial oscillations of stars (simple version)
Nonradial oscillations (nro’s) are waves travelling through the interior of a star. Surface displacement may be characterized by spherical harmonic functions:
s = so Yl,m(,)
l: degree of the spherical harmonic = number of lines of nodes on a spherical surface
m: azimuthal number = number of lines of nodes passing through the polar axis
n: order of the spherical harmonics related to number of nodes along the radial direction
In most non-radially oscillating stars (e.g. the Sun) many modes are superposed. nro’s can affect total light, colour, temperature, radial velocities and line profiles from a star.

22. nro’s: some equations The wavenumber, n, is related to:
the wave frequency, ,
the local sound velocity, vs,
the Lamb frequency, Ll=l(l+1)vs2/r2 ,
the Brunt-Vaïsälä frequency, N2=-g[d ln /dr + g/1P],
by the dispersion relation: n2=(2-Ll2)(2-N2)/  vs2
To propagate, n must be real, hence: 2>Ll2 and 2>N2 (pressure modes) or 2<Ll2 and 2<N2 (gravity modes)
In general:
p-modes are excited near the surface of a star, g-modes in the interior.
p-modes have periods shorter than the radial fundamental
g-modes have periods longer than the radial fundamental

23. information from nro’s
Surface displacement due to spherical harmonic with degree l and azimuthal number m characterized by:
s = so Yl,m(,)
Third number n related to number of nodes in direction of propagation,
For example:
Hot white dwarfs with g-mode nro’s:
1) period spacing: mass of star
2) mode trapping: depth and composition of outer layers
3) 1+2: luminosity
4) rotational splitting: rotation period
5) magnetic splitting: magnetic field
6) period changes: evolution time scales
Mode identification:
l normally small
n from frequencies
m from mode splitting ?
Normally difficult to disentangle n,l,m from light curve alone.
Aim: Obtain additional information from colours, radial velocities and line profiles.

24. Normally difficult to disentangle n,l,m from light curve alone…but:
Mode identification:
l normally small
n from frequencies
m from mode splitting ?
Normally difficult to disentangle n,l,m from light curve alone…but:
If star is not rotating, m value does not alter frequency.
Ratio of photometric amplitude at different wavelengths is independent of i, but sensitive to l.
Aim: Obtain additional information from multicolour light curves to identify n and l, and compare with models.

25. observations 1998 WHT/ISIS high speed spectroscopy (drift mode)
PB8783: 5.3hrs, 1400 spectra, (~8s)
KPD : 5.8 hrs, 1200 spectra (~10s)
Jeffery & Pollacco (2000)

26. coadded spectra
F star spectrum H H

27. radial velocities and frequency analysis
Cross-correlate individual spectra against template to obtain wavelength displacement .
Displacement corresponds to Doppler shift or radial velocity.
v/c
Plot velocities as function of time.
Compute Fourier transform of velocities to identify periods.
Compare peaks with periods identified from photometry.

30. 3 frame transfer CCDs with dual readout: windows optimized to required time resolution

31. observations 2002
4 nights:
1 wiped out
1.2 cloudy
KPD : mB~13 10 hrs, CCD frames ~1s
HS : mB~ hrs, CCD frames ~4s

32. ultracam light curve for KPD2109+4402

33. ultracam light curve for HS0039+4302

34. sampling window functions
KPD HS

35. KPD 2109+4401: light curve and fit, power spectrum + residual

36. 3 new views of KPD
1998 rv
2002 r’
2002 u’-g’

37. HS 0039+4302: light curve and fit, power spectrum + residual

38. colour variations and the amplitude ratio diagram
ax’/au’ 1 r’ g’ u’
l=2
l=1
l=0

39. Amplitude Ratio Diagram

40. Evolution tracks for extended horizontal branch stars (Charpinet et al

41. Linear pulsation models for EHB stars (Charpinet et al. 2002)
Observations:
small v sin i  m splitting ~ 0
n,l pairs unique for each frequency
ax’/au’ l
given l, wave equations  simple cadence in n
Theory:
Linear analysis gives frequencies for each mode in each model
Plotted as l value versus frequency (cf. chirp diagram for solar oscillations)
Lowest frequency is fn of stellar radius (cf models for KPD )
Frequency spacing is fn of envelope structure (cf models for HS )

42. conclusions
ultracam provides outstanding 3-channel light curves for pulsating sdB stars down to 15th mag.
amplitudes measurable to <0.5 mmag and new frequencies identified
g’/u’ persistently larger than r’/u’ - as expected
l = 0,1,2 and 4 modes identified by ranking amp. ratios
n values assigned by demanding realistic cadence from modes of same l
Comparison with theoretical models - pointer to powerful stellar structure diagnostics

43. the future 2004 Autumn: WET campaign on PG0014+067 + WHT/ultracam…

44. quick look ultracam light curve for PG0014+067