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

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)

What are A-type stars? Effective temperatures: < T eff < 7500 K Rotational velocities: km/s (Sun = 2 km/s) OBAFG KM Absolute Magnitude Luminosity (Solar Lum.) Effective Temparature Spectral Class White Dwarfs Main Sequence Giants Supergiants

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

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

First measure the position of the line in one polarization... … then the position in the second polarization.  = 9.34 x g eff B z 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.

Zeeman measurements of some A stars:

The Oblique Rotator model of Stibbs (1950) Rotation axis Magnetic axis 

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

What are peculiar magnetic A stars? In 1906 spectra of  CVn showed it to be variable. Magnetic A stars show enhancements of Fe-peak elements. Enhancements of rare earth elements by factors of 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 K (the He-strong stars with spectral type B8)

Origin of the anomalous abundances Explanations: abnormal model atmospheres, accretion of planetesimals, interior nuclear processes with mixing, surface nuclear processes, or magnetic accretion. 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 10 4 ) 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 Most accepted hypothesis: Diffusion

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

The Abundance distribution on Ap stars The magnetic field in combination with the diffusion process can result in a patchy distribution of an element across the stellar surface. 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

 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

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).

Latitude information: Shape information:

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

Cr on  Aur Si on BP  Boo

Cr on  Aur Blue/green regions: less chromium Red/yellow regions more chromium

Si on  Aur

Si on BP Boo

Cr on  UMa

Things to keep in mind about Ap stars when we consider their oscillating counterparts: 1.There are strong dipole magnetic fields inclined to the rotation axis 2. The surface distribution of elements is inhomogenous 3. Different elements can have different distributions 4. The magnetic field dominates everything, and the abundance distributions reflect the magnetic geometry 5. Because of diffusion there may be vertical stratification of elements as well.

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) What are rapidly oscillating Ap stars?

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

Phase jump indicates an oblique pulsator:

The Oblique Pulsator Rotation axis Pulsation axis 

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 How do we know they are p-modes? n l m ≈ m, l ± m 

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

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

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

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

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

Matthews et al. (1988) for HR K/  m = 59 km/s/mag (K = 200 m/s) Libbrecht (1988) for  Equ 2K/  m = 30 km/s/mag (K = 42 m/s) Hatzes & Kürster et al. (1994) for  Cir 2K/  m < 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.

The Amplitude Variations in roAp Stars  Equ 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

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

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

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/  m ratio for roAp stars is a completely meaningless value that tells you nothing about the stellar oscillations!

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  Equ!

Why do the spectral lines of roAp stars show different radial velocity amplitudes? 1. We are seeing the vertical structure to the stellar oscillations 2. We are seeing the effects of the inhomogenous surface distribution on Ap stars

1. The vertical structure: line strength maps in to atmospheric depth. Different depth means a different pulsational amplitude On average weak spectral lines are formed deeper in the stellar atmosphere that stronger spectral lines EW Photosphere  =1 Intensity Wavelength 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

The amplitude and phase variations of HD versus line strength

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“ 2. The spotted surface:

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) Si abundance spots Si pseudo-mask Cr pseudo-mask Cr abundance spot

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. The Power of Spectroscopy!

The Phase Variations in roAp Stars 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 Mkrtichian, Hatzes, Kannan, 2003, MNRAS, 345, 781.

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

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

A Tale of 3 roAp stars 1.33 Lib 2.10 Aql 3. HD

Single mode (~8.7 min) Constant Magnetic field Gauss Rotation period > 75 years 33 Lib

Approximately 15% of the spectral lines pulsate ~180 degrees out of phase in 33 Lib The distribution of pulsational phases for spectral lines in 33 Lib

3 photometric modes (~11.6 min) Lowest photometric amplitude (0.3 mmag) Constant Magnetic field Rotation period ~decades 10 Aql

10 Aql : Integrated Radial Velocity The integrated RV variations of 10 Aql over the 5000 – 6000 Å are constant to within 3 m/s. The dashed lines mark the photometric frequencies.

10 Aql : Spectral Line Variations

HD Almost all the spectral lines of HD pulsate in phase. HD Lib

How to explain: 1. 15% of lines in 33 Lib pulsating out of phase 2. Almost 100% of the spectral lines in HD are in phase 3. Only few lines in 10 Aql with measurable RV variations Most of these can be explained by a radial node in the stellar atmosphere Line forming region of stellar atmosphere: + ─ High amplitude High amplitude, but 180 degrees out of phase Near node, low amplitude 0 = line forming region of star

10 Aql + ─ Special lines of 10 Aql originate away from the node Most spectral lines originate near the node + ─ 33 Lib 15% of spectral lines Line forming region straddles radial node HD ─ Most spectral lines originate away from the radial node

The p- mode spectrum of Przybylski’s star Previous study of pulsation spectrum: Martinez & Kurtz (1990) “HD pulsates with at least 3 frequencies...which cannot all be identified with consecutive overtones”. Tentative large spacing ~58  z was suggested

F0 V F0p Przybylski´s star Why HD is a peculiar star:

Przybylski’s star Most peculiar star in the sky 80% of the spectral lines are unidentified 51 chemical elements identified including Tc, Pb, Bi, Li, and all radioactive elements for Z = 84 to Z = 99 (except At and Fr) Tc with a half life of 17.7 years detected. Either flare activity of decay of Th and Uranium

Spectroscopic RV time series: 2-5 March 2004, ESO 3.6m tel., HARPS, λ Å, R=110,000, N=1074 spectra, T exp = 70 sec “Integral” (λ Å) radial velocities

Mean spacing of modes averaged for all consecutive overtones is equal μHz, due to l = 0,2 and l=1,3 excited modes Oscillation Spectrum of HD

Pre-whitening to find multi- frequencies In the classic „prewhitening“ one: 1. Perform a Fourier transform on your data to find the highest peak 2. Fit the data with a least-squares sine fit 3. Remove the signal from your data 4. Are you at the level of the noise? 5. No, go to step one 6. Yes, stop End result: a list of frequencies, amplitudes and phases in your data

The frequency of modes as a function of magnetic field strength Note: that an l = 0 normally has a lower frequency than an l = 2, but with a strong magnetic field, the opposite is the case!

Asteroseismic Parameters for HD Mass = ± M סּ Age = (1.5 ± 0.01) x 10 –9 Log T eff = ± Luminosity, log L = ± L סּ Surface gravity, log g = 4.06 ± 0.04 Magnetic field, Bp = 8.7 kiloGauss This is the first asteroseismic determination of a magnetic field on a star!

Points: the RV variations of HD Dashed line: the RV variations expected for a normal pulsating star (e.g. Cepheid) Light variations for HD The RV variations are in phase with the light variations. This is 180 degrees out of phase with normal pulsating stars where the light maximum is near the radial velocity minimum.

+ ─ Most likely spectral lines in HD originate a the radial node. If the light variations originate here as well then the RV an photometry will be out of phase with each other The light-to-RV variations again can be explained by a radial node in the atmosphere: But the continuum, where the light variations originate, is formed deeper in the stellar atmosphere, on opposite sides of the radial node.

Velocity Amplitude of Hydrogen Lines For roAp stars, the amplitude variations can be cause by vertical structure and/or the surface distribution (spatial filter). Hydrogen is expected to be uniformly distributed on and throughout the surface.

Back to the „meaningless“ 2K/  m measurement The Hydrogen lines probably are the best measure of the velocity amplitude to compare to the photometric measurements. H  and H  are formed deep in the interior, probably close to the continuum (photometric variations) 2K ~ 420 m/s  m ~ Mag 2K/  m ~ 43 km/s/mag or comparable to Cepheids and  Scuti stars

The Long Term RV Variation of  Cir This complicated RV curve is all due to rotation! The solid line represents a fit using components of P rot, P rot /2, P rot /3, P rot /4. In frequency these are harmonics of the rotation period. Why?

Recall that the surface distribution of elements is inhomogeneous and that different elements can have different distributions. Some concentrated at one magnetic pole, others at both, other elements concentrate at the magnetic equator. In integrated velocities we see the signals of all of theses elements Element concentrated at one magnetic pole: P rot Rotation axisMagnetic axis Element concentrated at two magnetic poles: P rot /2 Element concentrated in 4 spots along the magnetic equator : P rot /4

At least 35 Frequencies have been found in a Cir with a preliminary frequency spacing of 50  Hz using 80 hours of HARPS time Oscillation Spectrum and Echelle Diagram for  Cir

With 2016 hours of observations with the WIRE camera photometry gets 5 modes. f 2 and f 3 come from ground based photometry. Spacing is ≈ 60  Hz Photometry of  Cir (Bruntt et al. MNRAS, , 1189)

Ap star with a reversing magnetic field Rotation period 18.5 days Same effective temperature as other cool roAp stars Abundance anomalies similar to other roAp stars Intensive photometric searches have revealed no variations to level of 0.34 mmag (Kreidl 1991)  CrB: A low amplitude roAp star

Ando et al. (1988, PASJ, 40, 249) detected a possible signal at 6.1 min with an amplitude of 360 m/s in  CrB using a Fabry-Perot Interferometer

Kochukhov et al, (2002, MNRAS, 337, L1) found RV possible RV variations with a period of 11.5 minutes in  CrB, but only in 1 line! I think this result is rubbish because….

..they also found RV variations in 10 Aql with a period of 11 min! They believed the 10 Aql because photometry found a period at These measurements were not made with simultaneous wavelength calibration thus they are most likely instrumental artifacts.

Scargle Periodogram of RV measurements of  CrB made at the McDonald 2.7 m telescope with an iodine absorption cell: Hatzes & Mkrtichian, MNRAS, 204, 351, 663

Period = 16.2 min, amplitude = 3.5 m/s

Our analysis only found one spectral line at 6272 Å which showed pulsations with an amplitude of 138 m/s

The power in a Scargle periodogram is related to the statistical significance of the signal. As the signal becomes more significant the power should increase.

Kurtz was the referee of the Hatzes & Mkrtichian paper and did not believe our result. Until…

Comfirmation comes from Kurtz et al. 2007, MNRAS, 380, 741. Period = 16.2 min!

On the physchology of paper titles: Note: this is a „detection“ and not a „confirmation“

The roAp Stars: Show large variations in the amplitude and phase for individual spectral lines Evidence for radial nodes (vertical structure) Spotted distribution may help us to find higher degree modes (horizontal structure) These modes can be used to probe the interior and may tell us the nature of the magnetic A stars Radial Velocity measurements are a more effective way to study oscillations in roAp stars