Peculiar Magnetic A stars: Exploring Rapid Oscillations

1. Notes: In many of the Fourier transforms the frequency is given in c/d = cycles per day. To convert to mHz multiply numbers by 11.57 HD 101065 has a period of ~12 minutes. If you use Period04 on the data this corresponds to ~118 c/d

2. Rapidly Oscillating Peculiar Magnetic A stars 1. What is an A star? 2. What is a magnetic A star? (Zeeman effect) 3. What is a peculiar magnetic A star? (Doppler imaging) 4. What is rapidly oscillating peculiar magnetic A star? (stellar oscillations)

3. What are A-type stars? Spectral Class O B A F G K M -10 Supergiants -5 1.000.000 10.000 Main Sequence 0 Giants Absolute Magnitude Luminosity (Solar Lum.) 100 +5 1 +10 0.01 White Dwarfs +15 0.0001 +20 20000 14000 10000 7000 5000 3500 2500 Effective Temparature • Effective temperatures: 10000 < Teff < 7500 K • Rotational velocities: 0-250 km/s (Sun = 2 km/s)

4. Convective region Radiative region Structure of A stars A Star The Sun • Dynamo • Magnetic fields • Spots • Flares Boring!

5. No field Magnetic field For a triplet a magnetic field splits a spectral line into 3 components with different circularization states circular circular linear What are Magnetic Ap stars? First: How does one measure a magnetic field?

6. First measure the position of the line in one polarization... … then the position in the second polarization. Dl = 9.34 x 10-7l2 geff Bz Note: The separation scales as the square of the wavelength, thus it is larger in the Infrared. This is why magnetic field measurements is one science case for high resolution spectrographs.

7. Zeeman measurements of some A stars:

8. The Oblique Rotator model of Stibbs (1950) b Magnetic axis Rotation axis

9. The Magnetic Ap stars? • Approximately 15% of all A stars have magnetic field • Field strength is few hundred to a few kilo- Gauss • Global dipole field • Well explained by the oblique rotator model • Origin ??????? • Fossil fields (ohmic dissipation time is long) • Dynamo = field generation • Hybrid : field generated during the star‘s life and becomes fossil The origin of the magnetic A stars is one of the unsolved problems in stellar astrophysics

10. What are peculiar magnetic A stars? • In 1906 spectra of a CVn showed it to be variable. • Magnetic A stars show enhancements of Fe-peak elements. • Enhancements of rare earth elements by factors of 10-10000 over the solar values • Periodic variations in the strength of these lines with the same period as the magnetic variations (i.e. rotation) • The magnetic Ap phenonenon extends from 7400 K (the SrCrEu stars with Sp. Type F0) to 23.000 K (the He-strong stars with spectral type B8)

11. Origin of the anomalous abundances The Ap phenomenon must be a surface phenomenon since the overabundance of rare earth elements (e.g. Eu is overabundant by a factor of up to 104 ) is so great that a signficant fraction of the supply of such elements in the Universe would be contained in Ap stars if this abundance extended throughout the star • Explanations: abnormal model atmospheres, accretion of planetesimals, interior nuclear processes with mixing, surface nuclear processes, or magnetic accretion. • Most accepted hypothesis: Diffusion

12. The Diffusion Theory of Michaud (1970) • A stars have high effective temperatures (high radiation field) • A stars have an outer radiative zone (stable). Magnetic field further stabilizes the atmosphere • If an element has many absorption lines near flux maximum radiation pressure drives it outwards where it can accumulate and become overabundant • If an element has few absorption lines near flux maximum radiation it sinks under its own weight and can become underabundant

13. The Abundance distribution on Ap stars Ions can move along field lines at magnetic poles. Can be ehanced or depleted Ions cannot move across field lines at magnetic equator. Can be enhanced The magnetic field in combination with the diffusion process can result in a patchy distribution of an element across the stellar surface.

14. a CVn at two rotation phases For slowly rotating Ap stars one sees changes in the line strength with rotation For rapidly rotating Ap stars one sees distortions in the spectral line profiles. For these one can use the Doppler imaging technique to derive the distribution of elements on Ap stars

15. Principles of the Doppler imaging technique There is a one-one mapping between location on the star and location in wavelength in the line profile for rapidly rotating stars All locations on the star along constant radial velocity chords are mapped into the same location in the line. An overabundant spot of an element will produce excess absorption (dip) in the line profile. An underabundant spot will produce less absorption (peak).

16. Latitude information: Shape information:

17. The spectral line shapes represents a one-dimensional projection of the 2-dimensional surface of the star at a given instance • As the star rotates one obtains a different projection of the surface • By obtaining a time series of different projections one can reconstruct a two dimentional image of the star similar to the procedure of medical CAT scanning

18. Cr on q Aur Si on BPBoo

19. Cr on q Aur Blue/green regions: less chromium Red/yellow regions more chromium

20. Si on q Aur

21. Si on BP Boo

22. Cr on e UMa

23. Things to keep in mind about Ap stars when we consider their oscillating counterparts: • There are strong dipole magnetic fields inclined to the rotation axis • The surface distribution of elements is inhomogenous • Different elements can have different distributions • The magnetic field dominates everything, and the abundance distributions reflect the magnetic geometry • Because of diffusion there may be vertical stratification of elements as well.

24. What are rapidly oscillating Ap stars? • Discovered by Don Kurtz in 1978 (23 now known) • Occurs among cool magnetic Ap stars (~F0) • Periods range from 5 – 15 min • Photometric Amplitudes are a few milli-magnitudes • p-mode oscillations aligned with the magnetic axis • l = 1,2 m = 0 modes (zonal)

25. roAp stars in the „oscillating“ HR Diagram roAp stars occupy the „cool“ end of the instability strip

26. Phase jump indicates an oblique pulsator:

27. The Oblique Pulsator b Pulsation axis Rotation axis

28. How do we know they are p-modes? nnlm≈ nm,l± mW Equal spacing in frequency => p-mode oscillations For HR 1217 the modes split into a triplet, this means this is most likely an l = 1 mode

29. The Radial Velocity Variations in roAp stars • The light variations should also be accompanied by velocity variations • The radial velocity variations can shed clues as to the nature of the pulsations • e.g. 2K/Dm (RV amplitude to light variations) = 55 km/s/mag for Cepheids • so what is the 2K/Dm for roAp stars?

30. Matthews et al. 1988, ApJ, 324, 1099 tried to measure the RV variations of HR 1217 using a mercury emission line superimposed on the stellar spectrum. They also obtained simultaneous photometry: HR 1217 is one of the brightest roAp stars that is multi-mode and the dominant one having a period of about 6 min

31. Photometric 2K/Dm = 59 km/s/mag (K = 200 m/s), but large night-to-night variations

32. Libbrecht, 1988ApJ, 330, 51L, used an iodine absorption cell on g Equ and found that it was multi-periodic, and determined 2K/Dm = 30 km/s/mag (K = 42 m/s). Note: no simultaneous photometric measurements, used literature values

33. Hatzes & Kürster (1994, A&A, 285, 454) put an upper limit of 36 m/s for RV variations, 2K/Dm < 10 km/s/mag (K < 30 m/s). Again literature values for the photometric amplitude

34. Matthews et al. (1988) for HR 1217 2K/Dm = 59 km/s/mag (K = 200 m/s) Libbrecht (1988) for g Equ 2K/Dm = 30 km/s/mag (K = 42 m/s) Hatzes & Kürster et al. (1994) for a Cir 2K/Dm < 10 km/s/mag (K < 30 m/s) The discrepant photometric-to-radial velocity ratios determined from different investigations was the first hint of radial velocity amplitude variations in roAp stars.

35. The Amplitude Variations in roAp Stars gEqu is a bright, V=4.7, roAp star that pulsates with a period of 12 min. In Dec 2007 Antonio Kannan and I wanted to try using the iodine cell to measure radial velocity measurements. Because we were using an echelle spectrograph, we got large wavelength coverage on a roAp star for the first time. At the time, our radial velocity reduction software could only measure RVs for one spectral order

36. g Equ : Period 12 min The panels show the Fourier amplitude spectrum of 10 spectral orders for g Equ with the wavelength range shown in the panel

37. g Equ : Period 12 min The RV variations for each spectral order phased to the pulsational period.

38. HR 1217 also shows ampitude variations: The numbers show the RV amplitude of the individual spectral lines. Depending on which wavelength region you look at and which lines you look at the RV amplitude can vary by factors of 100 or more. Conclusion: the 2K/Dm ratio for roAp stars is a completely meaningless value that tells you nothing about the stellar oscillations!

39. Savanov, et al. 1999, Astron. Lett., 25, 802 found that the highest amplitude lines were from the elements Pr and Nd with amplitudes reaching up to 1 km/s or more in g Equ!

40. Why do the spectral lines of roAp stars show different radial velocity amplitudes? • We are seeing the vertical structure to the stellar oscillations • We are seeing the effects of the inhomogenous surface distribution on Ap stars

41. 1. The vertical structure: line strength maps in to atmospheric depth. Different depth means a different pulsational amplitude Photosphere t=1 On average weak spectral lines are formed deeper in the stellar atmosphere that stronger spectral lines Intensity EW Note in Ap stars there may be vertical stratification of elements, so there is not always this straight one-to-one mapping between line strength and depth Wavelength

42. The amplitude and phase variations of HD 101065 versus line strength

43. 2. The spotted surface: • Integrated disk observations: large number +/- regions cancel or reduce velocity or light variations • When looking at a spectral line formed in a spot, cancellation is less => higher amplitude • Higher degree modes may be detected as the surface distributions act as a „spatial filter“

44. Periodic Spatial Filter (PSF) concept for NRP mode identification (2-D (l,m) concept)(Mkrtichian 1992, in “Magnetic Stars”, Nauka; 1994 Solar Physics, 152, p.275) Cr abundance spot Si abundance spots Cr pseudo-mask Si pseudo-mask

45. The Power of Spectroscopy! Black represents the oscillation spectrum derived from 324 hours from photometry. With 54 hours of RV measurements we found all photometric frequencies plus the 2 additional frequencies in red.

46. The Phase Variations in roAp Stars Mkrtichian, Hatzes, Kannan, 2003, MNRAS, 345, 781. 33 Lib is a single mode pulsator with a period of 8.7 minutes. These are Fourier amplitude spectra of different spectral regions taken with the McDonald 2.7m telescope

47. The phase variations indicate a radial node in the stellar atmosphere + Radial node r ─ Nd II and Nd II pulsate 180 degrees out of phase.

48. The Concept of a Radial Node and Acoustic Cross-Sections Upper atmosphere Stratified REE elements Nd III Formation of weak lines Lower atmosphere

49. A Tale of 3 roAp stars • 33 Lib • 10 Aql • HD 101065

50. 33 Lib • Single mode (~8.7 min) • Constant Magnetic field +1600 Gauss • Rotation period > 75 years