SEARCHING FOR NORTHERN ROAP : THE UBC-OAN PHOTOMETRIC SURVEY

By

FRANCOIS CHAGNON B. Sc. (Specialise en Physique) Universite de Montreal (1996)

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in

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DEPARTMENT OF PHYSICS & ASTRONOMY

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THE UNIVERSITY OF BRITISH COLUMBIA September 1998 © FRANCOIS CHAGNON, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.

Department of Physics & Astronomy

The University of British Columbia

129-2219 Main Mall

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Date: Abstract

Because they pulsate in multiple high-overtone p-modes, rapidly oscillating Ap stars

(roAp) represent a very powerful tool to apply the techniques of , which

can lead to the global properties and internal structure of stars. The majority of roAp

stars are in the Southern Hemisphere, beyond the reach of northern observatories like

CFHT and DAO, which have superb coude spectrographs that can help reveal additional modes and clues to the pulsation dynamics. To try to correct this imbalance, we began

a systematic search for roAp stars in the Northern Hemisphere.

The UBC-OAN roAp Survey was conducted with the 84-cm and 1.5-m tele•

scopes at the Observatorio Astronomico Nacional (OAN) in Mexico, equipped with a

single-channel photoelectric photometer and a Johnson B filter. During 28 nights in

July/August 1997 and 16 nights in May/June 1998, we monitored about 50 cool A-Fp

stars with time resolution of less than a minute. The reduced data were Fourier analysed to search for periodic signals and we were generally sensitive to amplitudes as small as

0.3 millimagnitude in the period range of 4-15 min.

We have made one detection, HD 10088, which shows two periods near 9.3 and 10.6

min, and amplitudes of about 1.6 and 1.3 mmag respectively, at the 99% confidence level.

A tentative candidate, HD 3883, with period near 9.2 min and amplitude around 1.35 mmag is highlighted for further study. We also observed the known roAp star 10 Aql (HD

176232) and detected its main pulsation at a period near 11.5 min, the largest amplitude yet observed for this star. Finally, we independently confirm the newly discovered roAp star HD 122970 (Handler & Paunzen 1998) and combine our data with those of a global campaign (Handler et al. 1998) to infer some of the characteristics of this star.

u Table of Contents

Abstract ii

List of Tables v

List of Figures vi

Acknowledgements viii

1 INTRODUCTION 1

1.1 The Ap stars 1

1.2 The roAp stars 3

1.2.1 Driving Mechanism 7

1.2.2 Oblique Pulsator Model 8

1.3 Asteroseismology of roAp stars . 12

1.4 Searching for roAp stars 16

1.4.1 The Cape rapidly oscillating Ap star Survey 17

1.4.2 The Lowell-Wisconsin Northern Survey for rapid variability. ... 17

1.4.3 Why look for the northern roAp stars? 18

2 THE UBC-OAN roAp star SURVEY 20

2.1 Instrumentation and observing technique 21

2.2 The Survey sample 23

2.3 Observing runs 25

m 3 REDUCTION AND ANALYSIS 34

3.1 Photometric Reduction 34

3.2 Flexure Problems 36

3.3 Frequency Analysis 40

4 THE UBC-OAN SURVEY RESULTS 45

4.1 HD 10088 45 4.2 HD 3883 (HR 178): roAp or not roAp, that is the question 51

4.3 HD 176232 (10 Aql) 55

4.4 HD 122970 57

5 DISCUSSION 62

5.1 The Discoveries 62

5.2 HD 122970: a demonstration of asteroseismology 63

5.3 The effectiveness of the UBC-OAN Survey 79

References 83

Appendices 93

A Reduction procedure 93

A.l Dead-Time Correction 93

A. 1.1 A value for the dead-time constant 94

A.1.2 How good is the approximation and is it important? 95

A.2 Dark and Sky Subtraction 96

A.3 Airmass 96

A.4 Heliocentric Correction 98

iv List of Tables

1.1 The Chemically Peculiar stars 3

2.1 Diaphragm Size 23

2.2 UBC-OAN Survey Sample 28

2.2 UBC-OAN Survey Sample (continued) 29

2.2 UBC-OAN Survey Sample (continued) 30

2.3 Journal of Observations 31

2.3 Journal of Observations (continued) 32

2.3 Journal of Observations (continued) 33

4.1 Characteristics of the main peak in the Fourier spectrum of HD 122970

on each of the three nights of observations 59

5.1 The roAp stars and candidates detected in the UBC-OAN Survey .... 63

5.2 Frequency Identification of HD 122970 71

5.3 Frequency spacings in the Fourier spectrum of HD 122970 71

A.l Comparison of 2 dead-time constant values 95

A.2 Validity of the approximation (ip = 100 ns) 95

A.3 Importance of the dead-time correction (tp = 100 ns) 96

v List of Figures

1.1 Light curve of roAp star HR 1217 4

1.2 Amplitude spectrum of HR 1217 5

1.3 Phase and amplitude of pulsation in HR 3831 vs. the rotation phase. . . 9

1.4 The sound speed squared as a function of the radius in the 15

2.1 Colour-colour diagram of the. sample and survey stars 27

3.1 Flexure problems: The relative Am vs. the airmass X 38

3.2 Bouguer's plot for a linear variation with the horizontal distance of the

extinction coefficient. . 41

3.3 Bouguer's plot for a linear variation with time of the extinction coefficient. 41

3.4 Bouguer's plot for an instrumental drift linear with time 42

4.1 A null detection for the star HD 204411 46

4.2 Light curve of HD 10088 on 1997 August 1 48

4.3 Fourier spectra (amplitude and power) of HD 10088 on 1997 August 1. . 49

4.4 Successive filtering of the two periods detected in HD 10088 50

4:5 Power spectra of HD 3883 on two different nights 53

4.6 Fourier amplitude spectra for the star HD 3883 on 1997 August 5. ... 54

4.7 Detection of roAp-type pulsation in the known roAp star 10 Aql 56

4.8 Light curve of HD 122970 on 1998 June 12 58

4.9 Fourier spectrum of the combined three nights of data for HD 122970. . 60

4.10 Successive filtering of the principal frequencies in HD 122970 61

vi 5.1 Data string for HD 122970 from the global campaign 64

5.2 Window function for the frequency vx 65

5.3 Fourier Spectrum of the campaign data set of HD 122970 67

5.4 Fourier spectrum of HD 122970 in the frequency range of interest. ... 68

5.5 Successive filtering of the main frequencies in HD 122970's eigenspectrum. 69

5.6 Subtraction of the window pattern of v\ from the eigenspectrum of HD

122970 72

5.7 Constraints on i and $ for Hd 122970 75

5.8 The asteroseismological H-R diagram showing HD 122970 78

5.9 Line of sight inclination vs projected rotation speed for HD 122970. ... 80

vii Acknowledgements

I wish to take time to thank many people who have helped me throughout this work or during my experience in Astronomy. Je veux particulierement remercier Nicole St-Louis et Gilles Fontaine, professeurs a l'Universite de Montreal, ainsi que Rene Doyon, attache de recherche a l'U. de M., pour m'avoir donne mes premieres chances en astronomic

I gratefully acknowledge the contribution of the Astronomy group at UBC in the development of this work through a few and insightful comments. I especially want to thank Greg Fahlman for the various and helpful comments he provided me after reading this work. Also, I want to acknowledge the help received from Gerry Grieve on computer matters. Part of this work (Flexure Problems) was enlightened by Gordon Walker's comments: it was much appreciated, as much as the various exchanges on translation for

Cassiopeia. Many thanks to the other graduate students (and post-docs) in Astronomy, especially Alexei Razoumov, David Woods, Stephen Holland and Pat Durrell for many discussions and for their companionship.

I would like to offer my sincerest gratitude to Philippe Eenens (Universidad de Gua- najato, Mexico) who made possible our observing at the Observatorio Astronomico Na• cional, Baja California, Mexico. Quisiera exprimir mi gratitud por su ayuda y su collab- oracion. Tambien, quisiera agradecer la Comision de Asignacion de Tiempo de Telescopio del Observatorio de San Pedro Martir por habernos asignado los tiempos de observacion deseados. Su comprension en cuanto a las tempestades de El Nino fue muy apreciada.

Muchas Gracias al equipo de apoyo tecnico a SPM por su ayuda, a veces tarde en la noche, al laboratorio de Electronica y a todos los que encontre en la montafia. Final- mente, quiero agradecer a William Schuster (Instituto de Astronomia, Ensenada, Mexico)

vm por sus commentarios.

Philippe Eenens and Petr Harmanec (Ondfejov Observatory, Czech Republic) are following up on our promising roAp star candidate, HD 10088, at the moment of writing these lines. This effort is really appreciated. I owe many thanks to Gerald Handler

(University of Vienna, Austria) for various discussions and suggestions, and especially for sharing the campaign data on HD 122970 with us.

I am greatly indebted to Jaymie (also known under various cover names), my su• pervisor, for all his help and support throughout this work. I learned a lot from him about science. I am very grateful to him for having observed at OAN, in the Sierra San

Pedro Martir, Mexico, as part of my project. More than anything else, I'll keep the remembrance of a great teacher, a real Habs fan, a generous and helpful man, un ami...

This project was partially supported by a scholarship from the Natural Sciences and

Engineering Research Council of Canada (NSERC) and by operating grants to my su• pervisor from NSERC. I want to acknowledge the large contribution to this work of the Simbad database. We accessed it as Guest Users at the Canadian Astronomy Data

Centre (CADC), which is operated by the National Research Council, Herzberg Institute of Astrophysics, Dominion Astrophysical Observatory.

ix Chapter 1

INTRODUCTION

The discovery of the five-minute oscillations on the surface of the Sun (Leighton et al.

1962), eventually allowed solar astronomers to study the interior of our nearest star, through the approach known as (Christensen-Dalsgaard 1988a, Deubner

& Gough 1984, and Hudson 1988). In fact, eigenfrequencies and wave patterns resolved on the Sun's disk trace the sound speed with depth in the solar interior, and hence help test the physical predictions of the Standard Solar Model.

Some of the techniques of helioseismology can be extended to the case of multi- periodic pulsating stars, opening a new domain of astronomy: asteroseismology. In the last two decades, a new class of pulsating stars, the rapidly oscillating Ap (roAp) stars, has provided some of the best targets for asteroseismology among non-degenerate stars.

Pulsating stars can be used as laboratories to study the physical properties of the physical plasma under extreme conditions and the strong magnetism and chemical anomalies of roAp stars make them particularly interesting labs. To study them we must first find them, and to find them, we must first know what to look for.

1.1 The Ap stars

Among all stars in the spectral type A, about 20% could be described as abnormal

(Bonsack & Wolff 1980), based on spectral lines which are weak or strong compared to the solar spectrum. These stars are referred to as the A peculiar stars, or Ap stars

(actually ranging from B8 to F0). For example, the coolest Ap stars show exceptionally

1 Chapter 1. Introduction 2

strong lines of rare-earth elements like Si, Cr, Sr and Eu, but weak or no He lines. These elements are in typical overabundance of 10-1000 times the solar composition. Radiative diffusion (Michaud 1970, 1976, 1980) appears to be responsible for the presence of rare- earths and the absence of He oh the surface. Elements which are normally abundant and that have ionization potentials larger than 13.6 eV (He, N, Ne, 0) should show marked deficiencies: because they interact less with photons, they are less supported by radiative pressure and they sink deeper in the atmosphere. On the other hand, elements (such as the rare-earths) with appropriate ionization potentials are radiatively supported in the atmosphere and hence show overabundances. Different elements are affected differently depending on the of the star, because the radiation field and the degree of ionization change with temperature.

This could explain the different types of Chemically Peculiar (CP) stars, presented in Table 1.1 (Preston 1974, Maitzen 1984). The second group (CP2) comprises magnetic

Ap stars, which have strong fields of the order of 1 kG (Didelon 1984). In fact, the magnetic field is thought to regulate the distribution of peculiar elements on the surface of the star. In the absence of a magnetic field, particles would diffuse vertically as the results of an imbalance between and radiation pressure. But the magnetic field affects the motion of ionized particles (Michaud et al. 1981). Due to the dipole geometry on Ap stars, the elements tend to gather in spots'or rings centred on the magnetic field axis.

The magnetic Ap stars also show slow magnetic, spectral, and photo• metric variations all with the same period in a given star. These long-term variations can be explained by the Oblique Rotator Model developped by Stibbs (1950). In this model, the magnetic field axis and the rotation axis form an angle 3 (obliquity), in the same manner that Earth's magnetic axis is inclined with respect to its rotation axis. As the star rotates, an observer, seeing different projections of the magnetic field, would notice Chapter 1. Introduction 3

Table 1.1: The Chemically Peculiar stars

CP1 metallic line (Am) CP2 magnetic Ap CP3 HgMn CP4 magnetic He-weak CP5 nonmagnetic He-weak CP6 magnetic He-strong CP7 nonmagnetic He-strong

a variation in its intensity with the same period as the rotation period.

The inhomogeneous distribution on the surface of Ap stars can explain the spectral

variations. As they rotate in and out of the visible disk, the intensities of the absorption lines grow and diminish. At the same time, the difference in brightness between the

spots and the rest of the surface generates photometric and Doppler variations tied to

the rotation. The slow photometric variations have amplitudes from 0.01 to 0.1 mag

(Catalano et al. 1993). All the variations share the rotation period of the star: typical

rotation periods for Ap stars range from a few days to several weeks (Preston 1974).

1.2 The roAp stars

In addition to the above variations due to rotation, a subset of magnetic Ap stars are now

known to have variations caused by pulsation. The rapidly oscillating Ap (roAp) stars

pulsate with short periods about 5-12 min (eigenfrequencies of ~ 100 to 300 cycles/day)

and photometric amplitudes of only a few millimagnitudes (mmag). Figure 1.1 shows

the light curve of roAp star HR 1217 (HD 24712) and its associated Fourier spectrum is

presented in Figure 1.2.

While conducting a search for 8 Scuti stars (pulsating stars with periods of a few Chapter 1. Introduction 4

hours and amplitudes around 0.1 mag) Kurtz (1978, 1980a) discovered the first roAp- type oscillator, Przybylski's star (HD 101065). Since then, most of the class has been discovered by Kurtz (e.g., 1980a,1980b,1982,1983,1984,1985) and by Martinez and collab• orators (e.g. Martinez et al. 1991), as part of The Cape Rapidly Oscillating Star Survey at the South African Astronomical Observatory (SAAO). Based on these early efforts, the roAp phenomenon appears to be restricted to the coolest Ap stars, in the late-A to early-F spectral range. According to model atmospheres by Kurucz (1979,1993), their temperature ranges from 7000 to 8300 K. For excellent and complete reviews on roAp

stars, the reader is referred to Matthews (1991) and Kurtz (1990), and, with a more

theoretical touch, to Shibahashi (1987).

-\ ?n --T'

00 -20 1 1 1 1 1 "~ —'' I f—~i 1 1 r—1 1 ! r—j 1 1 1 1 r— ^ 6.5 7.5 8.5 9-5 10.5

UT (JD 2446779)

Figure 1.1: Light curve of roAp star HR 1217 observed on 1986 Dec 16 UT. Each cross represents an average of 3 consecutive 10-s integrations. (Matthews et al. 1988)

Whereas the long-term variations observed on Ap stars are simply explained by the

rotation of the star, the rapid variations of roAp stars arise from a different phenomenon:

non-radial pulsations. The discovery of radial velocity variations by Matthews et al.

(1988) in the roAp star HR 1217 and later, in 7 Equ (HD 201601) by Libbrecht (1988) Chapter 1. Introduction

Figure 1.2: Amplitude spectrum of HR 1217 based on 324 hours of rapid B photometry from 8 sites over a time span of 46 days. The principal frequencies

v-i to u6 are labelled. (Kurtz et al. 1989) Chapter 1. Introduction 6

confirmed the status of roAp stars as pulsating variables. The roAp pulsators usually exhibit RV variations of the order of 100 m/s (see Scott Sz Matthews 1996, Viskum et al. 1996, Chagnon & Matthews 1998).

These small-amplitude oscillations result from acoustic waves whose restoring force is the gas pressure, so they are called pressure modes or more commonly, p-modes.

Each mode has a dependance on time and on the spherical coordinates (r, 0, ip) and is characterised by the three wave numbers:

• £= spherical degree (number of nodes on the surface)

• m=azimuthal order (number of nodes crossing the pulsation pole)

• n=radial overtone (number of nodes along the radius).

The radial overtone n characterizes the motion in the radial direction whereas £ and m describes the angular pattern of the mode, which is modelled by the spherical harmonics

Y™(Q,(p). The spherical harmonics are related to the Legendre polynomials, P™(9,tp), through the following expression

mv YT(d,

m 2 where Q>m is a normalization constant such that the integral of |y^ | over the whole volume of the star is equal to 1.

The gas displacement for a single mode can be expressed as (Christensen-Dalsgaard

& Dappen 1992)

r)Vm 1 rfYm ^(r^.O^^r)^ (1.2) Chapter 1. Introduction 7

where aT, dg, are the unit vectors in r, 6 and ip directions, 3ff indicates the real part

of the expression in brackets and the quantities £r and £h are the radial and horizontal displacements respectively.

1.2.1 Driving Mechanism

The very nature of the roAp phenomenon is still somewhat obscure as the driving mech• anism is not yet known. Because roAp stars are located on or near the cool edge of the , it was first hypothesized that they share a common driving mechanism with 8 Scuti stars, namely the Hell ionisation K mechanism. It can be rightly argued that the pulsation periods of roAp and 8 Scuti stars have periods too different to be the result of the same physical process: they must differ in some fundamental way. Furthermore,

Ap atmospheres are deficient in He, which is required for the classical K mechanism.

Shibahashi (1983) suggested that magnetic overstable convection could trigger pulsa• tions. In this mechanism, magnetic field lines play the role of the restoring force against convective motions, inducing and maintaining pulsations. Oscillations induced from this mechanism are expected to be linked to modes of very-high overtones and short periods, such as those observed. But, according to Matthews (1988), this mechanism doesn't explain the narrow temperature range in which roAp stars are found. He suggests an• other K mechanism involving an ionisation layer of Si IV, instead of He II. Because of the overabundance of this element and the deficiency of He in the upper atmosphere, this idea provides a natural explanation for pulsational instability. However, is Si enhance• ment sufficient to sustain the pulsations? Matthews (1988) suggests that the degree of

Si enhancement might act as the discriminating parameter that distinguishes roAp star from non-varying Ap stars of similar characteristics.

Recently, Gautschy et al. (1998) have performed nonadiabatic stability analyses on evolutionary models revealing that the « mechanism of H/He ionization may be able Chapter 1. Introduction 8

destabilize short-period roAp-type modes.

1.2.2 Oblique Pulsator Model

An interesting phenomenon of amplitude modulation occurs in roAp stars. The lower panel of Figure 1.3 shows the behaviour of the pulsation amplitude for the roAp star HR

3831 (HD 83368). In this case, the pulsation amplitude goes from its maximum value to a minimum, where it can even be undetectable, twice during one rotation period. The amplitude modulation seems to be correlated to the magnetic field period: maximum amplitudes are observed at moment of magnetic extrema whereas amplitude minima occur near time of magnetic quadrature (Kurtz 1990).

Another uncommon phenomena has been observed on at least 2 known roAp (HD

6532, HR 3831, Martinez Sz Kurtz 1995): at amplitude quadrature, a phase reversal occurs, that is the phase undergoes a jump of n radians, as shown at the top of Figure 1.3.

These two phenomena (phase reversal and amplitude modulation) have been explained by the Oblique Pulsator Model (OPM) (Kurtz 1982, 1990). Here, the pulsation axis is parallel to the magnetic axis, both forming an angle 3 (obliquity) with the rotation axis, which is tilted to the line of sight by an angle i. Thus, as the star rotates, the observer sees different aspects of the pulsation pattern on the visible disk, creating an amplitude modulation caused by rotation. Consequently, the amplitude modulation period is equal to the rotation period. The angles i and 3 can be such that both poles will come into view during one rotation period, which would explain the phase reversal and the presence of two amplitude modulation cycles in one rotation cycle in Figure 1.3 (lower panel). This situation arises when i + 3 > 90°.

Finally, the OPM also takes into account the frequency splitting seen in the Fourier spectrum of many roAp's. A mode of degree I will be split into a multiplet of (21 + 1) frequencies: a central one with frequency u> (pulsation frequency) and symmetric sidelobes Chapter 1. Introduction

ROTATION PHASE

Figure 1.3: Phase (upper panel) and amplitude (lower panel) of pulsation in HR 3831 as a function of the rotation phase (Kurtz 1992). Chapter 1. Introduction 10

with frequencies (a> ± jQ,), where j = (1, 2,£ — 2, t— 1, €) and f2 represents the angular rotation frequency. We can thus infer the rotation period of the star from the frequency multiplet's spacing.

We can study the OPM by looking at the variation which depends on time, as pulsations go on, and on the particular geometry of the OPM, that is:

—— oc Pi(cos a) cos{u>t + ) (1-3) Li where Pi is the appropriate Legendre polynomial. The angle a is the angle between the pulsation pole and the line of sight, which depends on the time-varying geometry of the

OPM as below:

cos a = cos i cos 8 + sin i sin 8 cos Sit (1-4)

If only a single mode with I — 1 is excited, then Pi = cosa and the luminosity variation can be decomposed as the combination of a triplet of frequencies:

^ a A0cos(ujt + 4>) + A^cos^u + Q)t + (/>} + COS[{LO - ft)t + (j)}} (1.5) Li where AQ and A\ represent the amplitude of the central peak and the two sidelobes, respectively. As a matter of fact, they constrain the values of i and 8 by the following relations:

AQ = cos i cos 3

Ax = -sinisinB (1-6) which can be expressed as the following ratio: Chapter 1. Introduction 11

—- = - tan i tan 3

A0 2 (1.7)

However, the axisymmetric multiplet peaks are often found to have different ampli• tudes (Kurtz 1990), which is not predicted by Equation 1.5. This is explained by introduc• ing the competing effects of rotation and magnetic field on the pulsations. Dziembowski

Sz Goode (1985,1986) and Kurtz &; Shibahashi (1986) assume that the perturbation to the frequency by the magnetic field is more important than the perturbation due to the rotation. The perturbed frequency can be expressed as the sum of an unperturbed fre• quency (in the absence of a magnetic field) a/0) and a term including the effects of the

Lorentz force OJ™^:

^^(0) + « (1-8)

For £=1 and m=0, this model still predicts a triplet of frequency. The variation of luminosity is now expressed as:

^ oc A0cos[(JV + uw)t + ^

+ A+1cos[(JV + w™* + tyt + ^]

+ A^cos[(uW + w™« _ ft)t + ft (1.9) where

AQ = cos i cos 3

1 CnlQ A±i = - sini sinB [1 ± —^ (1.10) 2 -ut,o ) Chapter 1. Introduction 12

We can rewrite these constraints as (£ = 1):

1 = tan i tan 8 (1.11)

For £ = 2, the amplitudes of the two innermost sidelobes and of the central peak are related to i and 8 in the following manner:

A+l + A^l 12 sin 8 sim cos 8 cost (1.12) ^(2) (3 cos2 8- l)(3cos2i- 1)

1.3 Asteroseismology of roAp stars

Asymptotic pulsation theory (Tassoul 1980) predicts that the frequency of an observed mode, in the case of pulsation with high overtone and low degree (n ^> £), can be

approximated by

l !/„,/ _ Au0{n + - + e) - + 1) + (1-13)

where i? represents higher-order terms and

Av, = {2J -)-1 (1.14)

with cs being the sound speed.

The variable AVQ is called the fundamental spacing and is the inverse of the travel

time of a sound wave across the diameter of the star. The spacing is a function of the

star's global density p, and thus of its radius and mass. It has been independently shown

by Gabriel et al. (1985), Shibahashi & Saio (1985) and Heller & Kawaler (1988) that

stellar models lead to a relation between p and AVQ which is: Chapter 1. Introduction 13

Ai/0 = (0.205 ±0.011)^^-Hz (1.15) where G is the gravitationnal constant, M is the mass and R, the radius, all in SI units.

The dependence on the radius is stronger than on the mass. To include luminosity L and

temperature Teff, it can be reexpressed (Matthews et al. 1998) in the following way:

16 1/2 3 3/4 Au0 = (6.64 ± 0.36) x 10~ M Teff L~ Hz (1.16)

where Teff is in Kelvin and M and L are in solar masses (M©) and solar

(!<©), respectively. In Equation 1.13 the second term is small. If we neglect it for a while, we realize that modes which have the same value of (n-\-£/2) (e.g. (n,£) and (n± 1,£=(=2)) are degenerate, that is:

Also, for odd or even £, modes of consecutive overtones n will be spaced by Afn, whereas alternating even and odd modes £ are spaced by AUQ/2. For the Sun, the fundamental spacing is AUQ — 135 fiHz (which corresponds to a sound crossing time of about two hours). The roAp stars also appear to pulsate in high-overtone, low-degree p- modes, so that the asymptotic pulsation theory applies. Figure 1.2 shows a good example of an roAp star having the expected equally spaced modes. Rapidly oscillating Ap stars

have observed Au0 values between 30 and 80 fiHz which translate into sound crossing times of ~4 to 9 hrs.

However small the second term may be in Equation 1.13, it is not negligible. In fact, it lifts the degeneracy by introducing a slight separation between the modes of the same

(n + £/2). We express this separation as Chapter 1. Introduction 14

Svn,i = vn%L - Vn-iz+2 (1-18)

where 8vn>i is known as the fine splitting and typical values are around 5 //Hz. From asymptotic analysis, it can be expressed in relation with the second term of Equation

1.13 (Christensen-Dalsgaard & Dappen 1992):

R

Suntl _ -(4£ + 6) 2 x ( f ^-) = (4/ + 6) * A, (1.19) Aw un

(Christensen-Dalsgaard 1993)

c = J^sI (1.20) V Vmu

where 7 _ 5/3, KB is the Boltzmann's constant, mu is the atomic mass unit, \i is the mean molecular weight and T is the temperature. The dependence on the mean

molecular weight makes 8vn>i a measure of (Christensen-Dalsgaard 1988), as central He abundance varies due to ongoing H burning. Therefore, the fine-splitting

8vn>t is directly related to the main-sequence age. By plotting 8un

Dalsgaard 1988), sensitive to mass (or radius) vs. age. This is the only way to estimate directly the age of a single main-sequence star (i.e., not in a cluster).

In addition, eigenfrequency patterns and splitting can provide information on the effective temperature, luminosity, radius, atmospheric structure, rotation rate and mag• netic field's strength and geometry of an roAp star (Kurtz 1990). Moreover, the diversity Chapter 1. Introduction 15

Figure 1.4: The sound speed squared as a function of the radius in the Sun (Shibahashi & Takata 1996). The fine splitting is mostly sensitive to the sound speed gradient in the centre of a star, making a good evolution indicator. The solid curve represents the most likely sound speed profile from inversion (Vorontsov & Shibahashi 1991) of the observational data of the solar p-mode frequencies obtained by Libbrecht et al. (1990) and Jimenez et al. (1988). The dashed curves show the 3

of physical processes acting in roAp stars make them very appealing objects to study.

They can be the "testbed" for such phenomena as radiative diffusion, magnetic fields and their role in the evolution of stars, driving mechanisms, etc.

Because they are high-overtone, low-degree p-mode pulsators, rapidly oscillating stars represent, other than the Sun, the only non-degenerate candidates to apply the techniques of asteroseismology, making them very appealing for asteroseismologists (Matthews 1993).

Although the luminosity amplitudes of roAp oscillations (a few millimagnitudes) are about 1000 times larger than the Sun's, they are still not easy to detect.

1.4 Searching for roAp stars

A number of surveys on rapid variability have been conducted to date. They all shared two major objectives: 1) identify more roAp stars for detailed studies, and 2) define the observational characteristics which distinguish roAp stars from Ap stars without detectable oscillations (i.e., an "roAp Instability Strip"), as proposed and attempted by

Matthews (1990). A few sporadic attempts at finding roAp are reported in the literature

(Matthews Sz Wehlau 1985, Matthews et al. 1988b, Heller Sz Kramer 1988a, Schneider et al. 1992) but we will restrict our discussion to two more comprehensive surveys which influenced this thesis the most: The Cape Survey (Martinez et al. 1991) and The Lowell-

Wisconsin Survey (Nelson Sz Kreidl 1993).

After the first roAp star was discovered by Kurtz (1978, 1980a), new members have been added to the class at an average rate of about one per year. It was recognised early on that the roAp phenomenon seems to occur among the coolest Ap stars, mainly in the spectroscopic subclass Ap(SrCrEu) with late-A to F0 temperature types. This does not appear to be entirely a selection effect, despite the fact that search efforts are less concentrated on hotter Ap stars. Still, not all cool A-Fp(SrCrEu) stars oscillate at Chapter 1. Introduction 17

detectable amplitudes, and after a decade, only 14 roAp stars were known.

1.4.1 The Cape rapidly oscillating Ap star Survey

In 1988, Peter Martinez began The Cape Rapidly Oscillating Ap star Survey (Martinez et al. 1991) for his Ph.D. thesis. The University of Cape Town Photometer attached to the 1.0-m Elizabeth telescope of the South African Astronomical Observatory (SAAO) was used to acquire the data: The observations consisted of continuous 10-s integrations through a Johnson B filter. Martinez monitored a total of 148 ApSrCrEu stars in 3 years. The survey sample contained stars with Stromgren and H/3 indices similar to those of the initial 14 roAp stars. They were chosen among the 629 SrCrEu Ap stars from the Michigan Spectral Catalogue (Houk & Cowley 1975, Houk 1978, 1982, Houk &

Smith-Moore 1988) and Bidelman & MacConnell's (1973) compilation of astrophysically interesting southern stars.

Thanks to the excellent photometric conditions at SAAO, ample telescope time, and

a sample with uniformly consistent spectral classifications, the Cape survey uncovered

10 new roAp stars - almost doubling the size of the class in a third of the time. Martinez used this larger sample to define new (but still poorly defined) limits on the photometric indices of roAp stars:

0.08 <(b-y)< 0.31

0.19 < ml < 0.33

0.46 < cl < 0.88 (1.21) Chapter 1. Introduction 18

1.4.2 The Lowell-Wisconsin Northern Survey for rapid variability.

From 1985 to 1991, Nelson Sz Kreidl (1993) conducted a high-speed photometry survey of 120 Ap stars in the northern hemisphere, searching for rapid variability (P ~ 5-12 min.). Incontestably the largest survey of its kind in the northern sky, it unfortunately identified only one new roAp star, HD134214 (Kreidl Sz Kurtz 1986). The observations were taken either at Lowell Observatory or at Table Mountain Observatory, using either

a single-channel, a dual-channel or a two-star photometer. Johnson V,B or Stromgren

uvby or even narrower filters were used, depending on the intensity of the .

Nelson Sz Kreidl searched stars in a range of spectral types from B8 to F4, which

represents a wider range than the photometric limits inferred by Martinez. Given the low detection rate, however, they were unable to distinguish a well-defined roAp instabil• ity strip. They did emphasise that the anticipated extension of the Michigan Spectral

Catalogue to positive declinations would increase the stock of good northern candidates for future surveys.

1.4.3 Why look for the northern roAp stars?

While we can infer physical properties of the star from the fundamental spacing and the

fine-splitting in the photometric eigenspectrum, spectroscopy can give other clues about

the pulsation dynamics. Recently, Viskum et al. (1996) and Baldry et al. (1997) have

obtained radial velocity (RV) measurements of the known roAp star a Cir (HD 128898)

(Kurtz et al. 1994) and they used them to probe its atmosphere. They found that the

amplitudes and phases of the principal pulsation modes can vary significantly depending

on the lines being measured. They argued that this phase differences among different lines could be caused by different formation depths in the atmosphere and a high-overtone

standing wave with a radial node high in the atmosphere of the star. Chapter 1. Introduction 19

Also, indirect imaging techniques like Doppler Imaging (Rice et al 1989, Hatzes et al. 1989, Wehlau & Rice 1993) have been developed to map the surface abundance and temperature distribution from line profile variations. The metallic absorption lines are primarily broadened by rotation. On pulsating stars, velocity perturbations caused by pulsation modes translate into bumps in the line profile (Kennelly et al. 1991, 1992, and Merryfield & Kennelly 1992). The bumps travel across the line profile following the rotation of the star, so that the profile variations can be considered a one-dimensional map of the surface velocity field. In this way, Doppler Imaging is sensitive to modes of higher degree £, which would not be detected from photometric studies due to cancellation effects.

The results of the surface mapping indicate that the elements gather in annular dis• tributions about the magnetic axis. Accurate and detailed images of the inhomogeneous abundance distribution at the surface of roAp stars can help probe the magnetic field and its structure. It can also increase our understanding of the interaction of radiative diffusion with the magnetic field, which produces these abundance distribution.

Some of the best facilities in the world for high-resolution spectroscopy are located in the Northern Hemisphere: the coude spectrographs of CFHT, DAO, Lick, UWO and

McDonald. The vast majority of roAp stars is beyond the reach of these telescopes.

Despite the efforts of Nelson & Kreidl (1993) and others, only two northern roAp stars were known at the start of this work. Further progress in the understanding of pulsation dynamic and structure of roAp stars depends on finding more candidates in the Northern

Hemisphere.

This became a motivation to undertake a photometric survey of the cool stars in the northern skies. This thesis marks the beginning of an ongoing effort aiming at finding more northern roAp targets for detailed study. Chapter 2

THE UBC-OAN roAp star SURVEY

Ever since the first roAp star was discovered in 1978, a few photometric searches, aiming at identifying more members of this class of pulsators, have been undertaken. Rapidly oscillating Ap star surveys face the combined challenges of the low pulsation amplitudes, amplitude modulation due to rotation and/or beatings, and no well-defined "instability strip". To ensure the best chances of success in a survey for roAp stars, several criteria should be satisfied:

1. excellent photometric conditions to allow for detection of variations with amplitudes

of the order of 1 mmag;

2. a telescope aperture larger than 60 cm to have good photon counting statistics as

well as to reduce photometric noise due to atmospheric scintillation;

3. accurate telescope tracking facilities which keeps the star well centred, to avoid

light loss due to the edge of the star's seeing disk moving outside the diaphragm;

4. a well-maintained and stable photometer; and

5. long observing runs in order to sample an Ap star at various phases of a its rotation

cycle (and hence, possible amplitude modulation cycle) which can last from days

to weeks or more.

The Observatorio Astronomico Nacional (OAN) at San Pedro Martir, Mexico, repres• ents one of the few observatories in the Northern Hemisphere which satisfies these criteria.

20 Chapter 2. THE UBC-OAN roAp star SURVEY 21

The site is located in a remote area where superb photometric conditions (criterion [1]) are encountered. There are two telescopes, with apertures of 84-cm and 1.5-m [2], both equipped with an offset guider [3], and a single-channel photoelectric photometer [4].

The 84-cm telescope in particular is often available for weeks at a time [5]. Moreover

OAN is readily and affordably accessible from UBC for repeated long observing runs, approximating the conditions of the successful southern Cape Survey for roAp stars.

2.1 Instrumentation and observing technique

The UBC-OAN roAp star Survey was conducted at OAN (Observatorio Astronomico

Nacional) (Moreno-Corral et al. 1994), in the Sierra San Pedro Martir, Baja California,

Mexico. Located at an altitude of 2830 m, OAN is known to be an excellent photometric

site, of comparable quality with CFHT in Hawaii and Cerro Tololo and La Silla in Chile

(Alvarez & Maisterrena 1977 and Tapia 1992). We obtained all the survey data from

the 84-cm and 1.5-m1 telescopes, using a single-channel photoelectric photometer known

as Cuentapulsos (Echevarria et al. 1986) equipped with a dry-ice cooled RCA C31034

phototube. Most of the observations were obtained at the 84-cm telescope. The 1.5-m

was reserved for fainter targets or to check possible detections with the smaller telescope.

The larger aperture provided better signal-to-noise and reduced the noise introduced by

atmospheric scintillation.

We performed non-differential photometry: the pulsation periods of roAp stars are so i short that it is impossible to switch from target star to comparison star (and check star) rapidly enough to sample properly the variation cycle of an oscillation. A two-channel photometer is an option, but our candidates are relatively bright, so there are no suitable 1 Harold Johnson, who gave his name to the Johnson UBV filter system, collaborated for many years with UNAM astronomers (Universidad Nacional Autonoma de Mexico). In fact, his filter system was calibrated at the 1.5-m telescope which now bears his name. Chapter 2. THE UBC-OAN roAp star SURVEY 22

comparison stars close enough to lie in the field of the telescope. Fortunately, the experi• ence of previous roAp observers has demonstrated that non-differential rapid photometry can reliably detect low-amplitude oscillations if the sky transparency is sufficiently stable.

As a result, the observing procedure was quite simple and systematic. A typical se• quence of star observation consisted of about 500 - 600 continuous 10-second integrations covering a total of ~ 1.5 hr or about 8 to 15 cycles of a typical roAp pulsation. Before and after each sequence, at least 5 dark and 5 sky integrations of 10-s each were obtained.

If the raw data seemed to show evidence of oscillation, more time was dedicated to that star on following nights. When possible, each star was monitored more than once at an interval of a couple of days to several days, in an attempt to respond to any rotational amplitude modulation (Section 1.2.2)

All the observations were obtained using a Johnson-B filter, because 1) roAp pulsation

amplitudes increase toward shorter wavelengths (Matthews et al. 1996, and references therein) and 2) the broad bandpass gives good photon statistics for stars as faint as V

~10. Target stars brighter than V ~ 6 (on the 84-cm telescope) and V ~ 7 (on the

1.5-m) exceeded the phototube's counting limit of 1.6 x 105 cps. For such stars, a neutral density (ND) filter with a transmittance of 7.5% over the visible range was introduced, reducing the apparent brightness of the star by about 2.8 mag.

The diaphragm used should be a compromise between ensuring that all the light from the target star is enclosed and keeping the background skylight small compared to the starlight. To minimise light losses from the far edge of the seeing disk as a result of guiding errors, a larger diaphragm should be favoured. Table 2.1 lists the available

diaphragms, their physical size and their angular diameters in both telescopes. The seeing

at the OAN site is generally lower than 1".5 arcsecond (Alvarez & Maisterrena 1977),

such that diaphragm #5 is a good compromise. Moreover, even for our faintest stars, this diaphragm keeps the sky background low and the signal-to-noise ratio is still very Chapter 2. THE UBC-OAN roAp star SURVEY 23

large. In some cases, we had to use different sizes of diaphragm. When the candidate star had a visual companion, a smaller diaphragm (#7 or #9) was necessary to isolate the target star. In the cases of smaller angular separation, we preferred a larger diaphragm to safely encompass both stars, and accepted dilution of any oscillation signal in exchange for reducing light losses. On nights of bright moonlight, we used a smaller diaphragm with the fainter targets to reduce the sky contribution.

Table 2.1: Diaphragm Size

Diaphragm Size Angular size (") - (mm) 84-cm 1.5-m 3 3.1 51 33 5 2.0 33 21 7 1.5 25 16 9 1.0 16 11

2.2 The Survey sample

While we always had in mind to choose the best possible candidates to maximise our chances of detecting roAp stars, we also wanted broad enough selection criteria to hope• fully better locate the extent of the roAp instability strip. The selection criteria for target stars evolved with time during the survey, but was guided by the same principles as previous roAp surveys.

In 1997, we compiled a list of targets based on the following criteria:

1. declination: 8 > 0

2. spectral classification: late Ap-early Fp (V-IV), with SrCrEu (if known)

3. (B — V) > 0 and as large as possible (without substantial reddening) Chapter 2. THE UBC-OAN roAp star SURVEY 24

4. (6 — y) > 0 and as large as possible (without substantial reddening)

The brighter targets were taken from The Bright Star Catalogue and Sky Catalogue

2000.0 and the fainter ones, from SAO Catalogue, based on the first three criteria. (The

Stromgren (b-y) index is not given in these references). In addition to these general cata• logues, we identified some targets from previous surveys on Ap stars such as The Lowell-

Wisconsin Survey (Nelson & Kreidl 1993), Malanushenko et al. (1994) and Catalano &

Renson (1984,1988,1991,1993,1997) respecting the same three criteria. These catalogues also provide rotation periods for some stars, a definite asset to planning the observing strategy. After this initial list was compiled, the stars were checked via Simbad2 for their

Stromgren (b-y) indices to confirm that they satisfied criterion 4. We also gave higher priority to stars which were part of the Lowell-Wisconsin Survey (Nelson & Kreidl's 1993) sample list.

In 1998, we expanded and refined the survey sample by including the Stromgren mi and c\ luminosity indices as criteria. In addition to browsing the catalogues used previously, we systematically searched the "Catalogue general des etoiles Ap et

Am" (Renson et al. 1991). We were guided by the limits established by the Cape Survey

(see Section 1.3) but expanded them somewhat so that we might confirm or refine those limits. Our parameter space included stars with:

0.03 < (b - y) < 0.40

0.13 <•, mi < 0.35

0.43

2The Simbad database is based at the Centre de Donnees astronomiques de Strasbourg (CDS). We accessed it as Guest User at the Canadian Astronomy Data Centre (CADC), which is operated by the National Research Council, Herzberg Institute of Astrophysics, Dominion Astrophysical Observatory. Chapter 2. THE UBC-OAN roAp star SURVEY 25

Table 2.2 presents our survey sample, consisting of a total of 82 stars. The firstcolum n gives the star catalogue number; stars in boldface were actually observed in the survey.

The second and third columns give the coordinates of the star, as of epoch 2000.0. The next columns contains the V magnitude, the Stromgren indices [b — y), ml, cl and the spectral type of the star, from the Simbad database and/or Renson et al. (1991). The final column gives the rotation period when it is available.

2.3 Observing runs

The original plan was to have two observing runs covering the summer and winter sky.

On the first run, which occured during 10 July - 10 August 1997, the observations were obtained by Francois Chagnon (FC) with contributions from Drs. Philippe Eenens and

Jaymie Matthews. We observed a total of 35 stars across a range of Right Ascension of 15 - 24 hr. The second run was scheduled for 21 February - 21 March 1998, but

El Nino conditions prevailed atop San Pedro Martir and led to the evacuation of the observatory. Another attempt (30 March - 14 April 1998) was also spoiled by many storms. Finally, FC completed a second observing run during 30 May - 14 June, in which

30 stars were monitored across the RA intervals 12 - 21 hr. The targets for this final run included a known roAp star, HD 176232 (10 Aql) (Heller & Kramer 1990), and a newly detected candidate, HD 122970,'reported to us informally by Gerald Handler (University of Vienna, Austria) based on his observations at the McDonald Observatory.

Fifty-three different stars have been searched for rapid variability so far in the UBC-

OAN roAp Survey. Table 2.3 presents the journal of the observations: star HD number,

UT date and Heliocentric Julian Date, telescope used (84-cm or 1.5-m) and time spent on each star on each night. The column labelled Noise is an eye estimate of the noise level in the Fourier spectrum in the range 100-400 c/d (1.2-4.6 mHz) (roAp star pulsations Chapter 2. THE UBC-OAN roAp star SURVEY 26

have frequencies in the interval 110-300 c/d (1.25-3.5 mHz)). When no noise evaluation is given, the time strings were not analysed due to unusable data.

Figure 2.1 presents three Stromgren colour-colour diagrams of the survey sample. The open circles represent the unobserved stars whereas the filled circles stand for the stars that were actually observed during the two runs. The rectangles mark the limits of the roAp stars known up to and including the Cape Survey. Chapter 2. THE UBC-OAN roAp star SURVEY 27

1.5 ~i 1 1 1—n 1 i 1 1 r EH*" i 1 1 1 1 r 1

0.5 QftP o

0 I I I I I I I I I I I I I I I I I 1 1 1 1 1 1 1 L. 0 0.1 0.2 0.3 0.4 0.5 ml

1.5 n—i—i—r—j- -[ 1 1 r ~i 1 1 r

1

°o <§> 0.5

0 I I I I I I L I I I I I I I I I I 1 1 1— 0 0.1 0.2 0.3 0.4 0.5 (b-y)

-i 1 1 1 1 1 1 1 1 1 1 1 i i i r 0.4 ft • ° 0.2 'o

0 I I I I I I I I I I I L_ _L J I I L 0 0.1 0.2 0.3 0.4 0.5 (b-y)

Figure 2.1: Colour-colour diagram of the sample and survey stars. On each panel the open circles represent our sample stars and the filled ones stand for the stars that we observed. The rectangles show the photometric limits known from the Cape Survey (section 1.4.1). Chapter 2. THE UBC-OAN roAp star SURVEY

Table 2.2: UBC-OAN Survey Sample

star RA DEC V (b-y) ml cl SP. Prot HD 2000.0 2000.0 - - - - - days 573 00:10:13 25:31:36 8.60 - - - FOCrEuIII - 3883 00:41:36 24:37:45 6.00 0.137 0 257 0 931 A5p/A7m - 10088 01:38:56 21:55:07 7.90 0.176 0 225 0 748 AOp - 12573 02:03:12 00:07:42 5.43 0.080 0 188 1 064 A3p - 15089 02:29:04 67:24:08 4.53 0.057 0 232 0 857 A5p 1.74 22374 03:36:58 23:12:40 6.71 0.073 0 173 1 097 A2p 10.6 24546 03:56:35 50:41:49 5.28 0.279 0 159 0 490 F5IV - 25354 04:03:10 38:03:17 8.37 0.033 0 146 0 775 AOp 3.9 30466 04:49:15 29:34:18 7.28 0.039 0 185 0 693 AOp - 34740 05:27:39 74:33:22 7.24 0.073 0 201 0 937 AOp - 43478 06:17:51 32:30:16 7.53 0.248 0 256 0 661 A3 - 62140 07:46:27 62:49:53 6.49 0.143 0 265 0 735 FOpSrEu 4.29 64491 07:55:40 35:24:47 6.23 0.196 0 132 0 669 A3p - 65339 08:01:42 60:19:28 6.01 0.057 0 256 0 760 A2pSrCrEu 8.03 78661 09:09:46 11:33:54 6.48 0.233 0 137 0 506 F2Vp - 82328 09:32:56 51:41:04 3.18 0.314 0 153 0 463 F6IV - 84179 09:45:55 63:39:13 6.34 0.228 0 168 0 643 F2V - 96707 11:09:40 67:12:38 6.1 0.124 0 182 0 969 FOp 0.93 99028 11:23:54 10:31:48 . 3.94 0.267 0 172 0 606 F4IV - 106223 12:13:17 30:16:58 7.40 - - - Fp - 107700 12:22:30 25:50:46 4.81 0.322 0 175 0 779 F2 - 108651 12:28:44 25:53:58 6.65 0.120 0 231 0 833 AOp - 112097 12:53:49 12:25:08 6.25 0.174 0 175 0 750 A7III - 112412 12:56:01 38:18:50 5.60 0.228 0 154 0 575 Fl - 113894 13:06:42 07:08:49 8.10 0.137 0 247 0 794 A7SrCrEu - SA082717 13:12:49 28:56:34 10.30 0.113 0 242 0 892 Al - 115606 13:18:02 13:00:00 8.50 0.166 0 297 0 623 A2SR - 115708 13:18:37 26:21:56 7.81 0.162 0 198 0 746 A2p 5.08 118623 13:37:28 36:17:40 4.80 0.154 0 162 0 923 A7III -

119288 13:42:13 08:23:22 6.16 0.279 0 142 0 466 F3VP - 122970a 14:04:49 05:24:51 8.50 - - - FOp - 126515 14:25:55 00:59:34 7.11 0.044 0 221 0 857 A2p 130 132739 15:00:18 13:19:15 8.40 0.226 0 169 0 703 FO - 134305 15:08:45 12:29:19 7.20 - - - A7p - Chapter 2. THE UBC-OAN roAp star SURVEY 29

Table 2.2: UBC-OAN Survey Sample (continued)

star RA DEC V (b-y) ml cl Sp. Prot HD 2000.0 2000.0 - - - - - days 134214b 15:09:02 13:59:59 7.40 - - - FOp 248*

134793 15:11:34 08:31:03 7.56 0.063 0.217 0.898 A3P 2.78 135631 15:14:57 38:18:02 7.15 - - - FO - 137898 15:28:38 01:50:32 5.20 0.135 0.197 0.847 A8IV - 137909 15:27:50 29:06:16 3.68 0.141 0.257 0.740 FOp 18.5 139478 15:36:04 52:04:07 6.76 0.207 0.169 0.666 F4p - 141988 15:48:29 62:20:37 8.54 0.211 0.190 0.669 A2 - 151199 16:42:58 55:41:21 6.16 0.030 0.213 1.065 A3pSr/A2p 6.14 151604 16:46:35 41:47:33 7.97 0.187 0.273 0.697 AO - 152107 16:49:14 45:59:02 4.82 0.037 0.207 0.942 A2pSrCrEu 3.86 152598 16:52:58 31:42:06 5.32 0.214 0.156 0.635 F1V - SAO2902 17:27:42 85:13:34 11.20 - - - F2 - 162003 17:41:55 72:09:09 4.58 0.293 0.147 0.497 F5IVV - SAO85405 17:46:42 27:58:59 9.30 0.203 0.236 0.840 FOp - 163506 17:55:25 26:03:00 5.50 0.230 0.130 1.361 F5p/F2Ibe - 163929 17:55:23 55:58:10 6.09 0.193 0.187 0.764 F0IV - 163930 17:58:07 15:08:18 7.30 - - - F4IV-V - 164258 18:00:15 00:37:46 6.37 0.087 0.183 1.097 A3pSrCrEu 2.4 165474 18:05:43 .12:00:13 7.45 0.167 0.227 0.832 A7pSrCrEu 23.4 165475 18:05:43 12:00:14 7.04 0.187 0.159 0.954 A7pCrEuSr - 168605 18:19:50 19:10:17 8.10 0.037 0.101 1.089 AOp - 171914 18:37:12 02:58:35 7.93 0.071 0.137 0.613 AOp - 176232b 18:58:46 13:54:26 5.90 0.150 0.208 0.829 FOp 6.5 179259 19:09:49 44:33:28 8.90 0.143 0.195 0.813 A8EuCr - 179367 19:10:11 44:33:35 7.35 0.120 0.250 0.841 A5p - SAO3150 18:41:16 87:09:21 11.00 - - - FO - 180583 19:15:59 27:55:35 6.20 0.398 0.208 0.759 F6SR/F6Ib 1.5 184471 19:33:20 32:34:38 8.80 0.165 0.201 0.845 A9SrCrEu - 186343 19:43:05 22:18:08 8.05 0.120 0.234 0.912 A2 - 186688 19:44:48 29:15:53 6.45 - - - F2pla - 188854 19:55:11 46:39:55 7.59 0.181 0.258 0.727 A7p - 190145 19:58:59 67:28:21 7.57 0.129 0.260 0.838 A2p - 351100 19:59:08 17:58:20 10.00 0.054 0.202 0.724 AOSrCrSi - 191742 20:09:47 42:32:29 8.14 0.114 0.232 0.960 A7p - Chapter 2. THE UBC-OAN roAp star SURVEY 30

Table 2.2: UBC-OAN Survey Sample (continued)

star RA DEC V (b-y) ml cl Sp. Prot HD 2000.0 2000.0 - - - - - days 196524 20:37:32 14:35:44 4 00 0.287 0 174 0.606 F5SR - 197461 20:43:28 15:04:30 4 44 0.194 0 163 0.854 A7IIIpdelDel - 198639 20:50:04 44:03:27 5 04 0.108 0 209 0.897 A5p/A4me - 198920 20:53:29 03:00:06 7 60 0.387 0 196 0.783 F2SrEu - 199942 21:00:04 07:30:58 5 99 0.167 0 168 0.835 FIVp - 202444 21:14:46 38:02:22 3 80 0.256 0 165 0.607 FOSr - 204411 21:26:51 48:50:05 5 31 0.056 0 179 1.202 A6pCrEu 0.73 205924 21:38:31 05:46:16 5 70 0.155 0 180 0.848 A8 - 210221 22:07:25 53:18:26 6 14 0.336 0 002 1.342 A3Ib - L370c 22:12:42 49:34:08 9 77 - - - Ap -

211797 22:18:56 37:46:07 6 17 - - - A9IIIP - 213232 22:28:34 58:32:24 8 00 0.073 0 220 0.994 A5p - 215304 22:43:37 39:39:22 9 10 0.050 0 163 0.912 AO - 217401 23:00:19 14:00:03 8 10 0.187 0 264 0.717 A2p - 220846 23:26:56 25:24:10 7 50 - - - A5p - aRecently discovered roAp star (see Section 5.3) bKnown roAp star cMember of NGC7243 (Maitzen & Pavlovski 1987). The coordinates are the star's and not that of the cluster's centre. The magnitude given in this case is the Chapter 2. THE UBC-OAN roAp star SURVEY 31

Table 2.3: Journal of Observations

star UT Date HJD telescope T noisea HD - 2450000 - (hours) (mmag) SAO85405 14-07-97 643.76 84 1.03 0.40 31-07-97 660.68 1.5 1.54 0.40 12-06-98 976.80 1.5 2.07 0.30 15-06-98 979.79 1.5 1.60 0.20 573 31-07-97 660.93 1.5 1.39 0.25 3883 19-07-97 648.91 84 1.50 0.70 05-08-97 665.93 1.5 1.00 0.75 10088 01-08-97 661.92 1.5 1.45 0.45 12573 11-08-97 671.93 84 1.53 0.40 106223 06-06-98 970.66 84 1.53 0.20 108651 03-06-98 967.68 84 1.53 0.15 14-06-98 978.67 1.5 1.00 0.40 112412 04-06-98 968.67 84 1.53 0.30 113894 10-06-98 974.67 1.5 1.43 0.30 115708 07-06-98 971.68 84 1.21 0.40 119288 02-06-98 966.68 84 0.57 0.40 122970 12-06-98 976.67 1.5 2.46 0.30 13-06-98 977.68 1.5 1:98 0.25 15-06-98 979.67 1.5 1.84 0.30 126515 05-06-98 969.67 84 0.95 0.20 134305 13-07-97 642.75 84 1.51 0.30 29-07-97 658.67 1.5 1.61 0.45 134793 16-07-97 645.72 84 1.33 0.50 18-07-97 647.69 84 1.80 1.00 06-06-98 970.75 84 1.36 0.25 135631 30-07-97 659.67 1.5 0.91 - 137898 11-06-98 975.67 1.5 0.29 - 13-06-98 977.78 1.5 1.02 0.40 137909 15-07-97 645.05 84 1.51 - 04-06-98 968.78 84 1.34 0.15 139478 14-07-97 643.67 84 1.50 0.30 05-06-98 969.75 84 1.53 0.25 151199 21-07-97 650.71 84 1.24 - 08-08-97 668.69 84 0.60 0.40 151604 10-06-98 974.76 1.5 1.52 0.25 152107 17-07-97 646.76 84 1.78 0.40 Chapter 2. THE UBC-OAN roAp star SURVEY 32

Table 2.3: Journal of Observations (continued)

star UT Date HJD telescope T noise HD - 2450000 - (hours) (mmag) 19-07-97 648.71 84 1.40 0.30 20-07-97 649.69 84 1.73 0.20 28-07-97 657.82 1.5 1.30 0.40 02-08-97 662.69 84 1.09 1.00 03-06-98 967.76 84 1.56 0.60 152598 02-06-98 966.78 84 1.52 0.35 07-06-98 971.77 84 0.65 0.80 08-06-98 972.79 1.5 0.74 - 14-06-98 978.74 1.5 2.93 0.15 163929 06-06-98 970.83 84 1.50 0.20 09-06-98 973.82 1.5 1.37 0.20 11-06-98 975.80 1.5 1.49 - 163930 09-08-97 669.67 84 1.51 0.70 163506 15-07-97 644.86 84 1.19 0.50 164258 06-08-97 666.67 84 1.51 0.50 165474b 04-08-97 664.69 84 1.30 0.30 05-08-97 665.67 84 1.50 0.60 11-08-97 671.66 84 1.52 0.15 02-06-98 966.87 84 2.28 0.25 168605 30-07-97 659.73 1.5 1.58 0.40 31-07-97 660.76 1.5 1.58 0.15 01-08-97 661.67 1.5 1.24 0.30 176232 05-06-98 969.86 84 2.70 0.25 179259 10-06-98 974.85 1.5 0.93 0.30 179367 03-06-98 967.85 84 1.44 0.50 . 13-06-98 977.92 1.5 1.07 0.40 15-06-98 979.91 1.5 1.41 0.15 180583 07-06-98 971.86 84 1.06 0.30 184471 01-08-97 661.75 1.5 1.66 0.30 10-06-98 974.93 1.5 0.92 0.35 186343 09-08-97 669.78 84 0.90 0.50 13-06-98 977.84 1.5 1.31 0.25 186688 18-07-97 647.83 84 1.11 0.25 188854 13-07-97 642.85 84 1.00 0.25 20-07-97 649.79 84 1.52 0.20 29-07-97 658.78 1.5 1.52 - 04-06-98 968.86 84 1.52 0.30 Chapter 2. THE UBC-OAN roAp star SURVEY

Table 2.3: Journal of Observations (continued)

star UT Date HJD telescope T noise HD 2450000 - (hours) (mmag) 190145 21-07-97 650.82 84 0.90 - 02-08-97 662.79 1.5 1.53 -

191742 28-07-97 657;82 1.5 1.30 0.40 31-07-97 660.84 1.5 1.56 0.20 11-06-98 975.89 1.5 1.97 0.15 196524 06-06-98 970.92 84 1.30 0.20 197461 04-08-97 664.78 84 1.50 0.40 . 198920 09-06-98 973.91 1.5 1.37 0.15 198639 19-07-97 648.81 84 1.07 0.30 05-08-97 665.75 1.5 1.51 0.50 03-06-98 967.94 84 0.70 0.60 04-06-98 968.95 84 0.27 0.50 07-06-98 971.94 84 0.50 0.50 14-06-98 978.89 1.5 1.39 0.20 199942 13-07-97 642.93 84 1.44 0.20 14-07-97 643.85 84 2.37 0.25 06-08-97 666.75 84 1.58 - 202444 12-06-98 976.90 1.5 1.52 0.15 204411 10-08-97 670.80 84 0.52 0.40 11-08-97 671.75 84 1.40 0.30 210221 04-08-97 664.89 84 1.19 0.30 211797 15-07-97 644.97 84 0.65 - 16-07-97 645.82 84 3.58 0.30 ' 17-07-97 646.87 84 2.56 - 18-07-97 647.90 84 1.89 0.50 30-07-97 659.85 1.5 2.79 0.30 213232 02-08-97 662.89 84 0.57 - 11-08-97 671.83 84 1.51 0.25 217401 28-07-97 657.91 1.5 1.98 0.25 220846 20-07-97 649.89 84 2.02 0.25 05-08-97 665.84 1.5 1.52 0.60 09-08-97 669.84 84 1.47 0.60 L370c 29-07-97 658.90 1.5 1.28 0.45 01-08-97 661.84 1.5 1.65 0.40 aWhen no noise estimation is given, the time strings were not analysed due to unusable dat bHD 165474 refers to visual double HD 165474 and HD 165475 CNGC 7243 cluster member Chapter 3

REDUCTION AND ANALYSIS

3.1 Photometric Reduction

The key steps in the data reduction include dead-time corrections, dark and sky subtrac• tion, conversion of the counts to a magnitude scale, extinction corrections and conversion of the times to Heliocentric Julian Date (HJD). These steps are summarised in this sec• tion; more details are provided in Appendix A. The reduction was performed using my

FORTRAN code REDUCTION, reproduced in Appendix B

Before the raw data were reduced, manifestly bad data were removed by visual inspec• tion. For example, during the first run, the photometer occasionally produced spurious counts; adjusting the preamplifier's discriminator threshold and checking the cable con• nections reduced but did not eliminate completely the problem. Also, if it was obvious that a patch of cirrus or anomalous extinction passed over the telescope on an otherwise stable night, those data were rejected.

First, a dead-time correction was applied to each count. When a photon strikes.the photocathode, it generates an electron cascade which is counted as a pulse. The system photomultiplier-electronics takes some time to register it and is thus unable to respond to other pulses, within this short period of time, the so-called "dead-time". Although the

Cuentapulsos manual (Echevarria et al. 1986) states that this correction is negligible (due to the high gain of the RCA C31034 phototube and its high counting limit of 6.1 x 105

34 Chapter 3. REDUCTION AND ANALYSIS 35

cps), we were conservative in this regard. It turns out that the systematic effect of dead- time is about 5% of the raw counts. The dead-time correction can be accounted for with the following form (see Appendix A):

Ct = (3 1} (i-cl*tD) - where Co represents the observed count rate in counts per seconds (c/s), Ct, the true count rate (c/s) and tp is the dead-time constant. The photometer has a dead-time constant around tr>= 100 ns.

We then subtracted the average dark noise and a background sky count from the , linearly interpolating between sky readings. Then, the star counts d were converted to a magnitude scale by:

-mi = -2.5 * log d (3.2)

To correct for changes in extinction with airmass, we used Bemporad's relation (Har- die 1962) which shows the dependence of the airmass X on the zenith angle z:

X = secz- 0.0018167(secz - 1) - 0.002875(secz - l)2

- 0.0008083(secz - l)3 (3.3)

Although this equation assumes a plane-parallel atmosphere, it leads to an error of only 1% at X ~ 10 (Golay 1974, p. 47) which is adequate for our observations, as we never observed at extreme zenith angles. If m.j is the raw instrumental magnitude of a star, mo the extraterrestrial magnitude (magnitude measured above the Earth's atmosphere) and JSB, the extinction coefficient measured in the blue bandpass, then

mj = mQ + kg * X (3.4) Chapter 3. REDUCTION AND ANALYSIS 36

where kg is the extinction coefficient as measured in the blue bandpass. On a clear night, a typical value for &g is around 0.3 (Golay 1974, p.50, figure 25). However, depending on the atmospheric conditions on a particular night and site, this coefficient can vary significantly.

For most stars on each night, we performed a linear fit of the raw magnitudes m{ vs. airmass X, whose slope is the extinction coefficient fcjg. This extinction correction is then applied to the raw data. In the next section, we present some details about flexure problems between different parts of the telescope, that may introduce a non-linear relation between the instrumental magnitude and the airmass.

Because the data are non-differential, there remain small, slow residual variations in sky transparency which are not removed by the simple airmass correction. Any trends with timescales longer than 30 min (more than twice as long as the longest period ex• pected for an roAp star) were removed by a spline fit or least-squares fits to long-period sinusoids. The residual magnitudes were then normalised to zero for subsequent frequency

analysis. Finally, we converted the central times of each integration to Heliocentric Julian

Date (HJD) so that our data can be related to those of other observers.

3.2 Flexure Problems

The automatic data reduction occasionally led to extreme values of the extinction co• efficient k,B- We realized by inspecting our data that sometimes there was a strongly non-linear relation between the extinction and the airmass. In a normal situation, one expects to measure the same magnitude m at zenith distances z symmetrically distributed on each side of the meridian, that is:

m(z) — m(—z) (3.5) Chapter 3. REDUCTION AND ANALYSIS 37

However,we can see from Figure 3.1, which shows the relation between the relative

magnitude (Am = m — m0, where mo is the magnitude outside Earth's atmosphere) and secz (~ airmass) for the star 10 Aql on the night of 1998 June 5, that this is not always the case. The right end of the lower branch marks the start of the observations.

The magnitude measured at a zenith angle z east of the meridian is diffferent from the magnitude measured at the same z west of the meridian. This behaviour is typical of other stars which crossed the meridian during our observations. We noticed the same behaviour on both runs and on both telescopes. An automatic fit to m^ vs X (Equation

3.4) lies erroneously somewhere between the two branches of the curve, leading to a very poor correlation and an incorrect extinction coefficient.

This problem is believed to "contaminate" the data continuously. Observations which do not cross the meridian are affected in the same way and therefore, the extinction coefficient ks takes extreme values. In the case where a star was monitored east and west of the meridian, we sometimes didn't apply an airmass correction. Instead a spline fit was applied carefully to remove any sky transparency variations. On other times, it seemed preferable to apply an airmass correction: some data contained many spurious or bad counts which were influencing the spline, resulting in large noise, and our spurious counts rejection routine is part of the airmass correction. In these cases, we performed the airmass correction in two time strings: before and after the meridian crossing, which have a different dependence on the airmass. The data set was reunited for the Fourier analysis (see section 3.3).

In a private communication, William Schuster (Universidad Nacional Autonoma de

Mexico, Instituto de Astronomia, Ensenada) suggested an asymmetry in the sky could be responsible for this behaviour. The Observatorio Astronomico Nacional is located in the San Pedro Martir mountain range in Baja California, Mexico, bordered on the east by the Sea of Cortez and on the west by the Pacific Ocean. As Young (1974) points Chapter 3. REDUCTION AND ANALYSIS 38

Figure 3.1: The relative magnitude Am measured as a function of airmass X, for the star 10 Aql on 1998 June 5. The data span 2.7 hrs and the star crosses the meridian about midway through the observations. The right end of the lower branch marks the start of the observations. On the vertical axis, the brightness increases upward. Telescope/instrument flexure is believed to cause the non-linear relation between instrumental magnitude and airmass. Chapter 3. REDUCTION AND ANALYSIS 39

out, a nearby body of water can produce an asymmetry in the atmospheric transparency.

However, an inspection of Schuster's Stromgren photometric data taken on various nights at the 1.5-m telescope didn't appear to show any asymmetry. Moreover, Young (1974, p. 141) estimated that any real asymmetry must be local, within 10 km of the telescope, which is still too close to be explained by the Pacific Ocean or the Sea of Cortez.

Gordon Walker (UBC, private communication) suggested that the culprit could be a flexure problem between different parts of the telescope and/or photometer. Under the influence of gravity, the telescope tube, the mirror supports, the photometer mounting, etc. are all subjected to torques. This would cause the pupil to move relative to the photocathode; an angular misalignment of the optical axis of the telescope with that of the photometer results in a spatial displacement of the image on the cathode. A way to monitor this problem would be to measure photometric standard stars from time to time

during the night (Young 1974).

At first it might seem difficult to distinguish between an east-west sky asymmetry and

an instrumental problem, especially after the fact. But Young (1974, pl42) considered

different models built around factors which would introduce nonlinearity in the relation

between magnitude and airmass. These are:

1. a linear variation with horizontal distance (east-west gradient) of the extinction

coefficient:

Am = m-i — m0 = (Ao + Ai * tan z) * sec z (3-6)

where Ao and A\ are constants;

2. a linear variation with time (but constant all over the sky):

Am = (A0 + Ax * t) * sec z (3.7)

and Chapter 3. REDUCTION AND ANALYSIS 40

3. an instrumental drift linear in time which would result in:

Am = A0secz + A1*t (3.8)

It is possible to distinguish between these three alternatives by the shapes of the

Bouguer1 curves, which represent the three models above. We present in Figures 3.2,

3.3, 3.4 the results of Young's calculations for an observatory located at the equator.

The east-west gradient gives two branches that are convex toward each other, the time- dependent extinction coefficient results in two nearly straight lines and the instrumental

drift gives two lines concave toward each other and joined by a rounded curve. It is not obvious that one of these models can explain exactly the data presented in Figure

3.1. The concavity of the curve close to the meridian suggests that an instrumental drift might be the cause. However, this curve has two main differences with the model in

Figure 3.4: 1) close to the meridian, Figure 3.1 is not smoothly curved like Figure 3.4;

and 2) in the second part of the observations (after the meridian) in Figure 3.1, the

star brightness increases toward larger airmass. We tested the three models for various values of AQ and A^ and realized that both characteristics are explained only by the instrumental drift model, when the A\ gets significantly large compared to AQ, that is when the instrumental drift is important.

3.3 Frequency Analysis

The reduced data were systematically binned into groups of 4, increasing the signal-

to-noise in the Fourier spectrum. The 40-s binned integrations still well sample the expected pulsation periods of roAp stars. We then Fourier analysed both the binned and unbinned time series using Matthews &; Wehlau's (1985) modified version of Deeming's

1 Unfortunately, Young (1974) introduces the Bouguer plots without giving any reference. Chapter 3. REDUCTION AND ANALYSIS 41

0.5h

1.0

1.5

Figure 3.2: Bouguer's plot for a linear variation with the horizontal distance of the extinction coefficient (A0 = 0.2 and Ax = 0.01 in Equation 3.6) (Young 1974, p. 142).

e

Figure 3.3: Bouguer's plot for a linear variation with time of the extinction coefficient

(A) = 0.2 and Ax = 0.01 in Equation 3.7) (Young 1974, p.143). Chapter 3. REDUCTION AND ANALYSIS 42

Figure 3.4: Bouguer's plot for an instrumental drift linear with time (Ao = 0.2 and Ai = 0.05 in Equation 3.8) (Young 1974, p. 144).

(1975) algorithm for computing a Discrete Fourier Transform of unequally spaced data

(see also Kurtz 1985). To encompass the whole period range of roAp stars and to assess the low frequency noise, all stars were searched for frequencies from 0 to 500 c/d (0-5.8 mHz). For any sampling interval Ai, there is a critical frequency, the Nyquist frequency,

UN, which is the maximum frequency at which one can reliably detect a periodic variation.

The critical sampling of a sine wave with the Nyquist frequency is only two sample points per cycle. The Nyquist frequency is given by

(3.9) 2A* None of our searches approach the Nyquist frequency of our data, which is, using At = 10

s, uN = 4320 c/d (50 mHz)

The next step was to filter out the low frequency (0 to ~ 100 c/d (0 to ~1.10 mHz)) noise resulting from small remaining sky transparency variations. The filtering process Chapter 3. REDUCTION AND ANALYSIS 43

was done with PERDET ("multiple PERiod DETermination") (Breger 1989), a program using multiple-frequency least-squares fitting. The best fits are determined by minimizing the squares of the residuals between the measurements and the trial fits.

The frequency resolution (ability to distinguish two closely separated frequencies) has been estimated to be A/ = 1.5/AT, where AT is the length of the data string (Loumos

& Deeming 1978). The error on an individual frequency determination is estimated to be the standard deviation cr of the Gaussian curve associated with the shape of the Fourier peak. The standard deviation a is approximately one-sixth of the frequency resolution

(Kurtz & Wegner 1979), such that:

1 1-5 Ar (7, = -— = —. (3.10) 6 AT 4 v ; If we noticed an apparent oscillation peak in the Fourier spectrum, we performed

a false alarm probability test (Scargle 1982) which measures the probability a that a peak of given amplitude X might arise as the product of white (frequency independent)

noise in the data. To use the false alarm probability as devised by Scargle, we need to

transform the actual amplitude X to a power signal-to-noise ratio z (Scargle 1982):

2 z = N0*[^} (3.11)

where 7Y0 is the number of points in the time series and a is the standard deviation of

the data. The probability a can then be evaluated using (Scargle 1982)

a = 1 - (1 - e~z)Ni (3.12) where Ni is the number of independent frequencies which are searched in the data set.

Based on numerical simulations, Home & Baliunas (1986) evaluated N{ to be Chapter 3. REDUCTION AND ANALYSIS 44

2 Ni = -6.362 + 1.193 * N0 + 0.00098 * iV (3.13)

The Scargle criterion (Equation 3.12) is valid for a data set which contains a single oscillation and white noise. But roAp stars are multi-periodic pulsators and the noise in non-differential photometry increases toward lower frequencies, so results from a false alarm probability test should be considered conservative estimates. Chapter 4

THE UBC-OAN SURVEY RESULTS

Of the fifty-three stars observed, we have detected oscillations in four of them: (1) two detections at the 99% confidence level in HD 10088 (section 4.1); (2) one detection at the

90% level in HD 3883 (section 4.2); (3) one detection of the known roAp star HD 176232

(10 Aql) with a confidence level greater than 99% (section 4.3); and the first independent confirmation of a newly discovered roAp star, HD 122970 (section 4.4). The data didn't reveal any credible signals on a majority of stars even though the noise level was generally as low as ~ 0.3 mmag. For example, we present the Fourier spectrum of a null detection in Figure 4.1. The upper panel shows a typical result for our Survey: a relatively low noise level in the frequency range of interest and a higher noise level at low frequency.

The peak at a frequency of 360 c/d [y — 4.17 mHz or P = 4 sidereal minute) is present in many of the Fourier spectra. It is an artifact of the telescope clock drive which arises from periodic backlashes in the gears. Fortunately, the pulsation modes of roAp stars are not expected to have periods close to 4 min, although harmonics and resonances can occur in this range. The lower panel shows the residuals after filtering the low-frequency noise and removing the 4-sidereal-minute period from the time series.

4.1 HD 10088

Weiss (1983) decided to observe HD 10088 for rapid variability (P ~ 5-15 min) since

Hauck Sz North's (1982) survey indicated that it was a cool Ap star with a temperature around 7300 K. This fell in the expected range for the class of roAp stars, discovered

45 Chapter 4. THE UBC-OAN SURVEY RESULTS 46

n 1 r 1 r

100 200 300 400 500 FREQUENCY (c/d)

Figure 4.1: Null result for the star HD 204411 (V = 5.3). This Fourier spectrum represents the combination of two nights, 1997 August 10 and 11 (JD2450670.5 and 671.5), covering a total of 1.9 hrs. The upper panel shows the data before filtering the low-frequency due to residual sky/instrument variations; the lower panel shows the filtered data. The peak at a frequency of 360 c/d is due to a 4-sidereal-minute tracking artifact in the telescope. Chapter 4. THE UBC-OAN SURVEY RESULTS 47

only a few years before. Weiss obtained non-differential Stromgren v photometry, with the University of Hawaii's 60-cm telescope on Mauna Kea. The data revealed no rapid variability but did however suggest the presence of a 6 Scuti-type variability. Binning the data over intervals of 6 minutes, Weiss detected a variation with a period of lh29m and an amplitude of about 0.03 mag. The results were made more credible by the fact that two other stars were observed on the same nights, immediately after HD 10088. Both showed a constant light curves, implying the atmosphere and the instrument were stable.

The observed period was consistent with the fundamental or first overtone of a S Scuti star (Stellingwerf 1979).

Prompted by Weiss' finding, Kreidl attempted to confirm the variability of HD 10088 but failed to do so in two separate observing runs. In the first (Kreidl 1984a), he obtained observations from Lowell Observatory's 1.1-m and 0.8-m telescopes with single and dual channel photometers1. The second search (Kreidl 1984b) was also at Lowell Observatory's

1.1-m telescope with a dual photometer and B and V filters. The integrations were 10 or 15 seconds. A total of 13.5 hours of differential photometry taken during the 2 runs revealed no periodic signal.

The lack of detectable oscillations could be attributed to: a) damping of the mode since Weiss' observations; b) destructive interference between multiple frequencies (Danzi- gen Sz Dickens 1967; Wehlau Sz Leung 1964; Fitch Sz Wehlau 1965); c) a spurious first detection, since non-differential photometry was used, which is not optimal to look for a period as long as 1.5 hours; d) evolution of the star outside the instability strip as suggested by Kreidl (1984a) based on the location of HD 10088 near the edge of the strip; or e) beating between closely-spaced frequencies which could produce an apparent period of ~1.5 hours.

Nelson Sz Kreidl (1993) observed this star as part of The Lowell-Wisconsin Survey for

1 Kreidl doesn't mention which filter was used during this first run. Chapter 4. THE UBC-OAN SURVEY RESULTS 48

rapid variability (section 1.4.2). They obtained ~ 6.5 hours of data on 3 different nights in an interval of 18 days, using the Table Mountain Observatory 24" telescope. Their data didn't show any evidence of rapid variability higher than the noise level, which they evaluated at ~ 0.2 mmag.

We observed HD 10088 on the night of 1997 August 1 UT (JD2450660.5) with the

1.5-m telescope for ~ 1.5 hrs. The light curve is presented in Figure 4.2. A "quick-look" reduction of the raw data, consisting only of a spline of the data to flatten the light curve, didn't show any obvious signal, so we didn't follow up on this star immediately.

However, the full photometric reduction (chapter 3) and Fourier analysis, revealed a

signal at a frequency vx ~ 155 ± 4 c/d (Vl = 1.79 ± 0.05;( P = 9.29 ± 0.25 min) and an amplitude AB = 1.65 mmag. The uncertainty on the frequency comes from the poor frequency resolution due to the short time series. In Figure 4.3, the Fourier spectra (both power and amplitude) of the unbinned data show the peak at this frequency. The false alarm probability (section 3.3) is less than 1% (based on a search of 750 independent frequencies): the horizontal line in Figure 4.3 represent the 99% confidence level.

40 n r

OS 1 1.5 HOURS

Figure 4.2: Light curve of HD 10088 on 1997 August 1.

Figure 4.3 also shows an unresolved peak on the left shoulder of the main peak.

We filtered the principal frequency and the result is presented in the upper panel of Chapter 4. THE UBC-OAN SURVEY RESULTS 49

FREQUENCY (c/d)

Figure 4.3: Fourier spectra of HD 10088. The relative power is shown in the upper panel, while the lower panel presents the amplitude spectrum. The horizontal line in both plots is the 99% confidence level. Chapter 4. THE UBC-OAN SURVEY RESULTS 50

1.5

<

CQ < 0.5

J I I L_ 100 200 300 400 500 FREQUENCY (c/d)

Figure 4.4: Successive filtering of the two periods detected in HD 10088. The upper

panel shows the amplitude spectrum after removing the main peak vx from Fig 4.3.

The amplitude of u2 is above the 99% confidence level, represented by the horizontal line. After filtering this peak, only noise remains (lower panel). Chapter 4. THE UBC-OAN SURVEY RESULTS 51

Figure 4.4. The secondary peak has a frequency u2 = 136 ±4 c/d (yi = 1.57 ±0.05 mHz;

P = 10.6 ± 0.3 min) and an amplitude AB = 1.30 mmag. We performed a false alarm probability test which yielded a 99% confidence level at an amplitude of 1.1 mmag.

As for Weiss' detection of a 8 Scuti-type oscillation on HD 10088, our data are in•

sufficient to address this question. However, if the secondary peak is confirmed, beating between the two frequencies could produce a beat period around 1.5 hours, which suggests that option (e) above could explain Weiss' detection and Kreidl's non-detection.

HD 10088 has Stromgren indices in the range expected for roAp stars as identified by Martinez (section 1.4.1): V = 7.9, b-y = 0.176, ml = 0.225 and cl = 0.748. Weiss

(1983) derived the of HD 10088 from Breger & Bregman's (1975)

calibration for 8 Scuti stars. He found My = 2.0 ± 0.22, which indicates an evolution off the by about 0.9 mag. However, using Crawford's (1979) calibration,

My = 2.5 is derived, which would bring back HD 10088 closer to the Main Sequence.

Its spectral classification is even more uncertain. It was once classified as a Am, A2-F2

star by Cameron (1966) while Bertaud (1959,1960,1969) and Bertaud & Floquet (1967)

consistently classify it as a SiSr star. Nelson & Kreidl (1993) adopt a spectral type of

A7. Finally, the Simbad database lists a spectral type of AO. On this basis HD 10088

appears to be rather hot compared to other roAp stars, but Hauck & North gave it

an effective temperature around 7300 K. Also, using Breger's (1975) calibration of the

Stromgren indices, a Teff ~ 7500 K is inferred. These values are in good agreement with

the temperature range expected for roAp stars.

4.2 HD 3883 (HR 178): roAp or not roAp, that is the question

We observed HD 3883 on two nights (1997 July 19 and August 5 UT) with the 84-cm telescope for time intervals of 1.5 and 1.0 hr, respectively. We experienced some guiding Chapter 4. THE UBC-OAN SURVEY RESULTS 52

problems on the first night. A Fourier analysis of this first night did not reveal any oscillations above the noise level (other than the 4-sidereal-minute artifact) but a signal was detected on the second night. The power spectra are presented in Figure 4.5: in the lower panel, there is a peak with frequency i/\ = 157 ± 6 c/d = 1.82 ± 0.07 mHz;

P = 9.17 ± 0.35). The corresponding amplitude spectrum is presented in the upper panel of Figure 4.6, where the peak has an amplitude AB 1.38 mmag. This lies slightly above the 90% confidence level which results from a false alarm probability based on 490 independent frequencies. We filtered out this peak and the residuals are presented in the lower panel of Figure 4.6: no peak, rises above the 90% confidence level.

HD 3883 was initially included in the UBC-OAN Survey because its SAO Catalogue spectral classification is A5p. In addition, its Stromgren indices place it within the Cape

Survey limits on the roAp phenomenon. However, we discovered later that van't Veer-

Menneret et al. (1985) did a detailed spectroscopic study of HD 3883 which indicated it has the spectral anomalies of a classical Am ("metallic A") star with effective temperature

about re//=7750 K.

Am stars (Table 1.1) are non-magnetic stars located on the blue side of the classic instability strip. They appear to be somewhat evolved from the Main Sequence (Garrido et al. 1980). Their spectra show chemically peculiar characteristics such as overabund• ances in metallic elements heavier than Fe and deficiencies of He, Ca and Sc. Like Ap stars, they were long thought to be constant stars since pulsation and metallicity were thought to be mutually exclusive, according to surveys and the expectations of theory

(Breger 1970 and Kurtz et al.. 1976). However, Kurtz (1989) found an exception to this rule in the classical Am star HD 1097 which showed 8 Scuti variability.

The strong magnetic fields in rapidly oscillating Ap stars are believed to be strongly related to their pulsations. In fact, the pulsation pattern is aligned with the magnetic axis as predicted by the Oblique Pulsator Model. Also, the magnetic field is suspected Chapter 4. THE UBC-OAN SURVEY RESULTS 53

Figure 4.5: Power spectra of HD 3883 on two different nights: on the first night (1997 July 19), the data didn't reveal any stellar signal whereas a peak at frequency ui is present on the second night (1997 August 5). The peak at 360 c/d in the upper panel is due to a 4-sidereal-minute tracking artifact in the telescope. The horizontal line presents the 90% confidence level. Chapter 4. THE UBC-OAN SURVEY RESULTS 54

Figure 4.6: Fourier amplitude spectra for star HD 3883 on the second night. The

upper panel shows the peak detected at a frequency vx. We filtered out this frequency from the time string and the result is presented in the lower panel. Chapter 4. THE UBC-OAN SURVEY RESULTS 55

to play a role in the mode selection: it would somehow only allow the high overtones ob• served in roAp stars (e.g, Shibahashi 1983). So, if indeed the classical Am star HD 3883 is confirmed to possess roAp-type pulsations, we can reject with certainty Shibahashi's

(1983) suggestion of a "magnetic overstable convection" driving mechanism. More im• portantly, it would have profound implications on the nature and origin of roAp-type pulsations.

4.3 HD 176232 (10 Aql)

After our first run, in which no clear detections were made, it was suggested that we observe a known roAp star to test our ability to detect roAp-type oscillations. We chose

10 Aql as a challenging test since it has the lowest maximum amplitude AB among the class of roAp stars. It was discovered by Heller & Kramer (1988a) as part of their

survey on rapid variability. Their data showed a peak at a frequency v = 1.46 mHz (126

c/d) from 4.7 hours of data over two consecutive nights in July 1987. They observed it

again one year later (Heller & Kramer 1988b), and confirmed the previous detection with

~26 hours of data over 8 nights. They refined the frequency value to v\ — 1.4360 mHz

(124.1 c/d) with an amplitude of 0.44 mmag, and further found two other frequencies:

i/2 = 1.3854 mHz (119.7 c/d) and u3 = 1.2393 mHz (107.1 c/d) (amplitudes of 0.33 and

0.28 mmag, respectively). The frequencies v\ and v

spacing between and u3 is 146.1 /zHz. The former value is consistent with the expected

fundamental spacing (section 1.3) for roAp stars. If Af0 = 50.6/xHz (the second value

is close to 3x this value), then 10 Aql would not be far evolved from the zero-age Main

Sequence. (Shibahashi & Saio 1985 and Heller & Kawaler 1988).

We observed 10 Aql for 2.7 hrs on 1998 June 5 with the 84-cm telescope. This

was enough to unveil a peak at a frequency of 125 ± 2 c/d (v = 1.45 ± 0.02 mHz; Chapter 4. THE UBC-OAN SURVEY RESULTS _ 56

Figure 4.7: Detection of roAp-type pulsation on HD 176232 (10 Aql) at the expected frequency / _ 126 c/d. We observed this star mainly as a way to test our ability to detect roAp variability. The horizontal line marks the 99% confidence. Chapter 4. THE UBC-OAN SURVEY RESULTS 57

P = 11.52 ± 0.18 min) and an amplitude AB = 0.87 mmag, which is larger than any previously reported amplitude for this roAp star. The amplitude spectrum is presented in Figure 4.6. A false alarm probability based on a search of 475 independent frequencies yielded a 99.9999% confidence level for the amplitude measured, so our detection seems quite firm. We then filtered the principal frequency from the time series and no other signal higher than the noise level can be detected, as shown in the lower panel of Figure

4.6.

We cannot say much from this short data string. We can only confirm the main peak at a frequency ~ 1.44 mHz, but with the poor frequency resolution induced from our data, we cannot give an accurate estimate of the frequency, to investigate long-term frequency changes or multi-periodicity. However, this positive detection reaffirms the sensitivity of our observing technique to roAp-type pulsation.

4.4 HD 122970

At the end of January, Gerald Handler announced to us privately the discovery of a new roAp star, HD 122970. The discovery data were 10-s integrations taken with the 0.9- m telescope at McDonald Observatory using a two channel photometer equipped with a Hamamatsu R647 phototube. They consisted of about 3.25 hours in the Johnson B filter, on 3 different nights (Jan 15, 17 and 18 1998).

Responding to this, we made HD 122970 a priority candidate for the second run in our survey. We observed it on 3 nights (1998 June 12, 13 and 15 UT) for a total of 6.25 hours. The light curve of a part of the first night is shown in Figure 4.8. At the time of our observations, we were still unaware of the value of the period(s) and amplitude(s) of the oscillation found by Handler. We reduced and Fourier analysed the three nights separately and they all showed a signal at a period near 11 min which turned out to Chapter 4. THE UBC-OAN SURVEY RESULTS 58

match Handler's discovery of 11.1 min (Handler & Paunzen 1998). Table 4.1 presents the frequency and the amplitude of the main peak on each of the three nights of data we obtained for HD 122970. The amplitude measured varies over the three nights, a sign of amplitude modulation. We combined the three nights of data to improve the frequency resolution and reduce the noise; the Fourier spectrum is presented in Figure 4.9. The

combined data give a frequency of ut = 130.84 ± 0.08 c/d fa = 1.514 ± 0.001 mHz;

P — 11.006 ±0.007 min) an amplitude of almost 1.20 mmag. Handler &: Paunzen (1998)

found a frequency vx = 129.7 c/d fa = 1.5012 mHz; P = 11.1 min). The 99% confidence level is at an amplitude of Ai? = 0.53 mmag, based on a search of 7225 independent frequencies.

T 1 1 I 1 1 1 1 1 1 , 1 1 1 1

O 0.5 1 1.5 HOURS

Figure 4.8: Light curve of the first night (1998 June 12) of obser• vation for HD 122970.

Figure 4.10 magnifies the frequency range of interest. We clearly see the cycle/day alias pattern which arises from gaps in the data string In the upper panel, the identifi• cation of the main peak is somewhat ambiguous as we don't have a way to prefer one peak over another without additional information; we decided to take the frequency of the highest peak as the main one. Because of that pattern, the possible systematic error on the frequency determination is larger than 0.08 c/d.

There is also evidence for another alias pattern centred at a frequency near 120 Chapter 4. THE UBC- OAN SURVEY RESULTS 59

Table 4.1: Characteristics of the main peak in the Fourier spectrum of HD 122970 on each of the three nights of observations

UT Date HJDa v v AB (+ 2450000) (c/d) mHz (mmag) June 12 976.67 130.7 ±2.4 1.51 ± 0.03 1.19 June 13 977.68 129.1 ±3.0 1.49 ± 0.03 1.35 June 15 979.67 130.2 ±3.3 1.51 ± 0.04 1.07

total - 130.84 ±0.08 1.5144 ± 0.0009 1.20 aHJD stands for Heliocentric Julian Date

c/d. When we filter out the principal frequency, the peak remains, as shown in the intermediate panel. This peak, with frequency v?. = 117.36 ±0.08 c/d (yi = 1.358 ±0.001 mHz; P = 12.270 ± 0.008 min) and amplitude AB = 0.44 mmag, has a 95% confidence level. The lower panel of Figure 4.10 presents the residuals after filtering both frequencies

simultaneously. Note that the noise level is quite low. The spacing between the two frequencies is ~ 13.5 c/d (156 /zHz).

We present in chapter 5 our independent analysis of a multi-site campaign data on

HD 122970, which includes our own contribution from this thesis. Chapter 4. THE UBC- OAN SURVEY RES ULTS 60

Figure 4.9: Fourier spectrum of the combined three nights of data for HD 122970. The horizontal line represent the 99% confidence level. Chapter 4. THE UBC-OAN SURVEY RESULTS

2

110 120 130 140

1 1 1 1 1 1 1 c—i 1 1 < 1 ' ' i r~

110 120 130 140 FREQUENCY (c/d)

Figure 4.10: A magnified view of a part of Fig 4.9 in the frequency range of interest. The upper panel presents the main peak at a frequency ui and a

lower amplitude secondary peak at v2, which remains after the filtering of v\ (intermediate panel). The lower panel shows the residuals after subtracting the two frequencies from the data. The presence of aliases makes the frequency determination difficult. The horizontal line marks a confidence level of 99% and 95% in the upper and lower panel respectively. Chapter 5

DISCUSSION

5.1 The Discoveries

Table 5.1 summarises the detections made so far in the UBC-OAN Survey. We have identified two new northern roAp candidates: a strong detection (HD 10088) and an intriguing one (HD 3883). HD 10088 showed evidence of at least two periods near 9.3 and 10.6 min at the-99% confidence level, although this detection is based on a short data string. The published spectral types for HD 10088 are diverse: A2-F2, A7, ApSrSi,

AO. Some of these seem rather hot for the expected range of roAp stars, but, if verified, they might extend that range. In HD 3883, the signal detected at a period near 9.2 min is less certain, with only a 90% confidence level. Moreover, it is classified as an Am star in the literature and Am stars are not expected to pulsate in the roAp period range.

Both stars deserve further photometric and spectroscopic study.

In fact, to follow up our survey results, Drs. Philippe Eenens (Universidad de Guana- jato, Mexico) and Petr Harmanec (Ondfejov Observatory, Czech Republic) have kindly

agreed to contribute some of their observing time'at the OAN 1.5-m telescope in early

September 1998, to attempt to confirm these two detections. If the apparent signs of multi-periodicity in HD 10088 are clearly established, a multi-site observing campaign would be justified to get a more complete eigenspectrum and reduce the aliasing which hampers the frequency determination. As for HD 3883, the confirmation of the roAp-type pulsation would be in itself a major accomplishment as it would be the first of its kind

62 Chapter 5. Discussion 63

for a metallic A star, forcing us to reconsider the role of the magnetic field in exciting high-overtone pulsations. We urge northern observers to get more data on these two stars: their status is intriguing enough to deserve more attention.

Table 5.1: The roAp stars and candidates detected in the UBC-OAN Survey

star V V P AB confidence c/d mHz min mmag %

HD 10088 155 ±4 1.79 ±0.05 9.29 ±0.25 1.65 > 99% 136 ±4 1.57 ±0.05 10.6 ±0.30 1.30 > 99%

HD 3883 157 ±6 1.82 ±0.07 9.17 ±0.35 1.38 > 90%

10 Aql 125 ±2 1.45 ±0.02 11.52 ±0.18 0.87 > 99%

HD 122970 130.84 ±0.08 1.514 ±0.001 11.006 ±0.007 1.20 > 99% 117.36 ±0.08 1.358 ±0.001 12.270 ±0.008 0.44 95%

5.2 HD 122970: a demonstration of asteroseismology

Following the discovery of roAp-type pulsations in HD 122970 by Handler (Handler &:

Paunzen 1998) in 1998 January, it was included as a secondary target for a Whole Earth

Telescope (WET) multi-site campaign on the S Scuti star XX Pyx (Handler & Breger

1997), since XX Pyx was not available all night near the end of the campaign. Our observations independently confirm the principal oscillation near 130 c/d and we have contributed our photometry to this data pool. A total of 121.4 hours were obtained on

31 nights over about 150 days (from JD2450828.99 to JD2450979.74) from 6 different observatories (Handler et al. 1998).

We present here our own independent frequency analysis and interpretation of the Chapter 5. Discussion 64

whole data set, which Handler shared with us. This is a direct application of the tech• niques of asteroseismology described in Chapter 1. Figure 5.1 presents the entire data set. The first group of observations consist of three nights (January 1998) and represents the discovery data (Handler & Paunzen 1998); the intermediate group includes the data obtained during the multi-site campaign (25 nights from end of February to beginning of April) and the third group represents the UBC-OAN Survey contribution, which was

described in Section 4.4. The time gaps, principally the day-night cycle and the large gaps between the three groups of data, introduce strong alias patterns; the window func• tion associated to the principal frequency is shown in Figure 5.2. On the other hand,

such a large time baseline (150.75 days) gives a good frequency resolution, which allowed

additional structure to be detected in the eigenspectrum. Also, the multi-site sampling

suppressed the cycle/day aliases to less than half the central peak amplitude.

We performed a Fourier analysis of the whole data set, the result of which is presented in Figure 5.3. Figure 5.4 presents a magnification in the frequency range of interest:

this spectrum, as well as the others presented in this section (except for Figure 5.3),

was oversampled with a frequency resolution of 0.0001 c/d. The window function of

the principal frequency V\ is obvious and it is clear there is at least one other frequency

present. The main peak has a frequency vx = 129.814±0.002 c/d (Vl = 1.50248±0.00002

mHz; P = 11.0928 ± 0.0002 min) (the uncertainty was evaluated based on the discussion

in Section 3.3) and an amplitude AB = 1.61 ± 0.10 mmag (The noise level in the Fourier

spectrum is about 0.1 mmag, which sets a conservative error on the amplitudes). In

Section 4.4, we found a principal frequency vx = 130.84 ± 0.08, which we now suspect to

be the +1 c/d alias of the main peak.

After filtering the first frequency, an alias pattern is still present around a secondary

peak at v2 = 127.684 ± 0.002 c/d (v2 = 1.47782 ± 0.00002 mHz; P = 11.2778 ± 0.0002 min) with (AB = 0.91 ± 0.10 mmag), as shown in the upper panel of Figure 5.5. We Chapter 5. Discussion 65

Figure 5.1: Data string for HD 122970. The UBC-OAN Survey contribution is indicated on the graph. The first group of data, at the extreme left of the graph, is the set of discovery data. The in• termediate group of data was obtained as part of a WET campaign.

notice a lower amplitude peak, left of i/2, at a frequency near 127.6 c/d. This peak

an remains (middle panel of Fig 5.5) after removing v2, d it has its own accompanying

set of aliases. It has a frequency of v% = 127.595 ± 0.002 c/d {u3 = 1.47679 ± 0.00002 mHz; P = 11.2857 ± 0.0002 min) and an amplitude AB = 0.35 ± 0.10 mmag. Finally, removing this peak gives a flat periodogram consisting only of noise (lower panel, Figure

5.5).

The presence of a closely spaced pair of frequencies at v-i and v$ could mean at least two things:

1. The frequency v2 is an £ > 1 mode split in a frequency multiplet by rotation mod•

ulation (see section 1.2). The frequency 1/3 would be one sidelobe of this multiplet Chapter 5. Discussion

Figure 5.2: Window function for frequency vx- The fine structure in the aliasing pattern is due to the large time gaps between the different groups of observation. Chapter 5. Discussion

1 1 1 1 1 1 —i—i—i—i—i—i—i—i—i—i—i i i III

1 \ _i_JMN_ti_|J __i__-i^ -i A. .i.,u_.__i „UI_iAll 0 100 200 300 400 500 FREQUENCY (c/d)

Figure 5.3: Fourier Spectrum of the campaign data set of the new roAp star HD 122970. Chapter 5. Discussion

Figure 5.4: Fourier spectrum of HD 122970 magnified in the frequency range of

interest. The main and secondary peaks are indicated by labels v\ and u2. Chapter 5. Discussion

Figure 5.5: Successive filtering of vx (upper panel), v2 (intermediate panel) and (lower panel), from the spectrum of HD 122970. Chapter 5. Discussion 70

while the others could have amplitudes lower than the noise level. The spacing

— v2 ^3 is 0.089 c/d (~ 1/iHz). So the symmetric sidelobe on the other side of v2

would be expected at a frequency near v ~ 127.775 c/d [y ~ 1.479 mHz). Coin-

cidentally, this frequency is very close to the frequency of the —2 c/d alias of the

main peak, v_2 — 127.808 c/d (v_2 = 1.479 mHz): it is possible that, if the filtering

of the main peak and its aliases were not exact, it may have obscured this other

sidelobe; and

2. Frequencies v2 and u3 represent two different modes of same (n + 1/2), i.e. (n,£)

and (n ± 1,£ =p 2) (section 1.3), that are almost degenerate but split by the second

order term in Equation 1.13 by about ~ 1/iHz.

The upper panel of Figure 5.6 shows the eigenspectrum of HD 122970. The three

known frequencies are identified as u2 and u3. We indicate by v the expected frequency for the right sidelobe. We then subtract a fraction of the window function associated with the principal frequency v\ (Figure 5.2) from the eigenspectrum, in the frequency

domain (Gray Sz Desikachary 1973). The result is presented in the lower panel of Figure

5.6. The best fraction of the window to subtract is the one that leaves a peak at v\ barely below the noise level, as seen in the figure. However, one notes that the amplitude of

some frequencies is now negative. This suggests that the peak identified as v and the

other ones surrounding it in the upper panel are aliases of vx. Note that v2 and v3 persist

after this subtraction.

We successively performed a least-squares fit in the time domain with the three fre• quencies found and then with the four frequencies, including v = = 127.775 c/d. It appears that the latter case is a better fit to the data as the residuals are lower. More• over, the amplitude of 1/4 is AB ~ 0.21, which is close to twice the noise level (see Table

5.2). As a matter of fact, the alias pattern arising from time gaps in the data hampers Chapter 5. Discussion 71

the identification of the right sidelobe of the frequency multiplet. More observations to increase the frequency resolution and reduce the noise are necessary in order to identify or refute beyond any doubt, the right sidelobe. We present in Table 5.2 the results of the least-squares fit, including It is important to note that Handler (private commu• nication) identified the same four frequencies in his independent analysis. Finally, Table

5.3 presents the frequency spacings among the frequencies of the triplet structure, and between the main peak and the secondary one.

Table 5.2: Frequency Identification of HD 122970

V V P A B (c/d) mHz min mmag ±0.002 ±0.00002 ±0.0002 ±0.10 129.814 1.50248 11.0928 1.62 0.526

v$ 127.595 1.47679 11.2857 0.40 0.993 127.684 1.47782 11.2778 0.86 0.677 V2 127.776 1.47889 11.2697 0.21 0.674

Table 5.3: Frequency spacings in the Fourier spectrum of HD 122970

frequency separation of modes:

Ui - v2 2.130 ±0.004 c/d 24.70 ±0.05 /xHz

frequency multiplet spacing:

v2 — Vz 0.089 ±0.004 c/d 1.03 ±0.05 /xHz

u4 - u2 0.091 ± 0.004 c/d 1.05 ±0.05 /*Hz

Various combinations of modes are possible for the two structures (single peak and

frequency triplet) that we identified in the data. Keeping in mind that some low ampli•

tude peaks could be lost in the noise, we start with the assumption that frequency v2 has Chapter 5. Discussion 72

Figure 5.6: The upper panel shows the eigenspectrum (magnified view of Figure

5.4) of HD 122970, where the frequencies vx, v2 and u3 are identified. The frequency v indicates the expected frequency for the right sidelobe. Chapter 5. Discussion 73

£ > 1, and the single mode, £ > 0. Also, degrees £ > 3 — 4 are not detectable by ground- based photometry due to cancellation effects in integrated light. Finally, as the amplitude and phase modulations have different behaviours (Handler, private communication), the single peak and the frequency triplet must arise from different £.

The separation vx - v2 is 24.70 //Hz. If Av0 = ,24.70/AHZ, HD 122970 would be very evolved from the main sequence. In this case, the two frequencies must arise from modes of the same £ or, at least, of odd or even £ (see Section 1.3). On the other hand, if

= 24.70/xHz so that AVQ = 49.4/iHz, then the star is closer to the main sequence

(Figure 5.7). Modes associated with ux and v2 would likely be consecutive £.

In Section 4.4, we found a second peak at a frequency v = 117.36 ± 0.08 c/d, [y =

1.358 ±0.001 mHz) which does not show up in this combined data set. It is possible that this mode was short-lived or that it was invisible due to beating. Further observations could confirm this peak and determine its frequency more accurately. The frequency

separation with both V\ and v2 could help determine if the fundamental spacing Au0 is

24.7 //Hz or 49.4 //Hz

The best possible combinations of modes for the single peak and the triplet structure are:

1. The principal frequency v\ is a radial mode (£ = 0) and the triplet corresponds to

a dipole mode (£ = 1);

2. The principal frequency is a radial mode (£ = 0) and the triplet is the visible part

of a quintuplet, corresponding to a quadrupole mode (£ = 2);

3. The principal frequency is the central peak of a triplet (£ = 1), with sidelobes be•

neath the noise, and the triplet corresponds to the innermost peaks of a quadrupole

mode (£ = 2); and Chapter 5. Discussion 74

4. The principal frequency is the central peak of a quintuplet (£ = 2) with sidelobes

beneath the noise, and the triplet corresponds to a dipole mode (£ = 1)

According to the value of £, we can use Equations 1.11 and 1.12 to constrain the values of ^ and 8. The amplitudes of the sidelobes in the triplet are such that

AW , A(i) +1 -1 (/) = 0.71 ± 0.15 mmag (5.1)

where the uncertainty is evaluated from the noise level. If the triplet structure arises due

to a dipole mode (£ = 1), we have

tanitand = 0.71 ± 0.15 mmag (5-2)

which yields the following constraints on i and 8

74.0° < i + 8 < 89.5°

i or 8< 37.0° (5.3)

On the other hand, if the triplet comes from a mode £ = 2 (quadrupole), where the

outermost sidelobes are below the noise level, we have

12 sin 8siiii cos 8 cos i n _ , n , _ ,r M (3 cos2 8- l)(dcos2i- 1) - 0.71 ± 0.15 mmag (5.4) and the constraints on % and 8 are:

43.5° < i + 8 < 54.5°

i or 8 < 21.5° (5.5) or Chapter 5. Discussion 75

145.5° < i + 3 < 157.0°

56.0°

These different constraints are presented schematically in Figure 5.7, for both £ — 1 and £ = 2. The second group of constraints in the case £ = 2 can be rejected beforehand as no phase reversal has been observed in the data (Handler, private communication).

The constraints 5.3 and 5.5 apply to cases 1 and 2, respectively. From the third case,

u2 is a triplet tells us that the angle i and 8 are constrained by 5.3. Then, if V\ is a

quintuplet, we can use these values of i and 8 in Equation 1.12 to estimate the sum of

(2} (2) the amplitudes of the sidelobes A\.( + A_{. We find values of the sum larger than 5 mmag,

which is obviously not observed in our data. We can therefore reject this combination.

In the final case, the constraints on i and 8 are those of Equation 5.5 as u2 is a

quintuplet. Then, we insert these values in Equation 1.11 to find an estimation of the

amplitude sum

A{1\ + AW\ < 0.35 mmag (5.7)

The noise level around the principal frequency Ui is about 0.30 mmag, so, it is really

possible that we cannot observe these sidelobes of individual amplitudes ~ 0.15 — 0.20

mmag as they would be below the noise.

We can estimate the radial overtone n of the frequencies presented in Table 5.2: using

Equation 1.13, where we neglect the small second-order term, we express the frequency ratio (Matthews et al. 1987) as

f_ _ v ,t _ n .+ £2/2 n2 2 2 (5.8) Chapter 5. Discussion 76

0 20 40 60 80 0 20 40 60 80

i

Figure 5.7: Constraints on % and 3 for £ = 1 (left side) and £ = 2 (right side), for roAp star HD 122970, calculated from the pulsation amplitudes measured in the Fourier spectrum. The upper panel shows (i + 3) vs i and the lower panel presents 3 vs i. Chapter 5. Discussion 77

Of the four cases discussed, three require ni,n2 — 30 and one «.i,re2 ~ 60, consistent with other roAp stars.

From the triplet structure, we can infer the beating period and hence the rotation period in the context of the Oblique Pulsator Model (see Table 5.3). In our case, we use only the frequency spacing between the left sidelobe and the central peak, as we didn't

identify the right sidelobe v± A rotation period PTot — 11.2 ± 0.5 days is infered from the data, which is typical for Ap stars (Section 1.1).

Following Matthews et al.'s (1998) work, we can locate HD 122970 in the H-R diagram, as Equation 1.15 provides us a good estimate of the radius from the fundamental spacing.

Then, by assuming a mass M = 2.0 ± 0.5M© and an effective temperature Teff = 6930 ±

100 K, computed from model atmospheres calibration by Villa & Breger (1998), we find the asteroseismological luminosity, using Equation 1.16. For a spacing Auo = 24.70/zHz

(Au0 = 49.40/xHz) we find a radius i2„ = 3.01 ± 0.35/2® (R* = 1.90 ± O.22#0) and a luminosity log j% = 1.47 ± 0.15 (log j% = 1.07 ± 0.15).

From the Hipparcos parallax (TT = 7.74 ± 1.01 mas) and the same estimate of tem•

perature, we can find the luminosity using

V-Mv = 5log(-) - 5 + Av (5.9) 7T

Neglecting the reddening, HD 122970 has an absolute visual magnitude My — 2.75 ±

0.30. The bolometric correction was estimated from Matthews et al. (1998) to be 0.07,

such that the bolometric magnitude is Mboi = My — BC = 2.68±0.30 and the luminosity is log -jr^ = 0.816±0.112. Figure 5.7 shows the location of HD 122970 in the asteroseismo• logical H-R diagram, for both values of the fundamental spacing, and for the Hipparcos

value. One can see that a Av0 = 49.4/xHz locates the star closer to the main sequence.

Only in the case Av0 = 24.7/xHz do we find the star in the classic Instability Strip. The Chapter 5. Discussion 78

luminosity obtained from the Hipparcos parallax doesn't agree with either value obtained with asteroseismology. However, it is much closer to the asteroseismological prediction for 49.4/iHz, which would suggest that this is the true fundamental spacing.

The difference between the asteroseismological luminosity prediction and the value calculated from the Hipparcos parallax is common to many roAp stars (Matthews et al

1998). Matthews et al. argue that if both the Hipparcos parallax and the interpretation of p-mode spacings are correct, then roAp stars are systematically cooler than expected from photometric calibrations. A lower temperature would shift some roAp stars beyond

the classical Instability Strip in the H-R diagram. This would strongly suggest that the

Hell ionisation mechanism cannot be responsible for the roAp-type pulsations.

Using the values for the radius and the rotation period Prot found earlier, we estimate

the equatorial rotation velocity to be vrot = 13.71 and 8.66 km/s for Au0 = 24.7 and

AUQ = 49.4/xHz respectively. High-resolution spectra of HD 122970 could determine a

value of its projected rotation velocity, v-sini, which would yield an estimate of i, and

hence 0, from the constraints discussed earlier. Figure 5.8 shows the inclination angle i

vs the projected rotation speed, for the two radii calculated.

5.3 The effectiveness of the UBC-OAN Survey

Figure 2.1 presents three colour-colour diagrams comparing the Stromgren indices of

our Survey sample with the photometric limits of the roAp phenomenon as identified

by The Cape Survey (section 1.4.1). We have covered a large range in each Stromgren

index, which indicates the completeness of our survey. Also, we intentionally selected

targets with Stromgren indices out of the photometric limits in order to test the limits

of the roAp phenomenon. As others before us, we notice that many null detections fall

inside the roAp intervals, too many to be dismissed solely by rotational modulation and Chapter 5. Discussion 79

-•I I I 1 1 1 < 1 1 1 1 1 i 1 i i i i i i i i 1 1 1 1 / / 1.5 1 < j 1 0 > I 24.7 microHz / / / / \ 1 o - b - \ 0 1 \ ' 0

1 - \ / -

V ' - 0 \ o ' > 49.4 microHz \ ' * \ /

— \ °' \ '• \ ' ~ \ / \ / j- Hipparcos - \ ' * - \ ;

-

0.5

1 1 1 1 i , , , , I , , i i i i i i i i i 4.1 4 3.9 3.8 3.7 3.6

log Te„

Figure 5.8: The asteroseismological H-R diagram where we plotted HD 122970 for both values of the fundamental spacing and from the Hipparcos' parallax. Open circles are other roAp stars with estimated p-mode spacings. The line is the Zero-Age Main Sequence and the dashed lines represent the limits of the Instability Strip (adapted from Matthews et al. 1998). Chapter 5. Discussion

0 5 10 15 v sin i (km/s)

Figure 5.9: Line of sight inclination vs projected rotation speed for different radius estimates for HD 122970 (Figure 5.8 is adapted from Figure 15 of Kurtz (1982)). Chapter 5. Discussion 81

photometric noise limits. We thus reach the same conclusions as Matthews (1988) and

Nelson & Kreidl (1993): another parameter other than colours and spectral type must discriminate between roAp and non-roAp stars.

The selection of candidates for a northern roAp star survey is somewhat complicated by the fact that systematic spectral classifications for Northern Hemisphere Ap stars are not yet available. HD 10088 offers a good example of the inaccurate and sometimes contradictory spectral classifications of peculiar stars in the literature. In that sense, southern observers have an extra arrow in: their quiver: the Michigan Spectral Catalogue

(Houk & Smith-Moore 1988). In the future, we hope to use the northern extension of the

Michigan Spectral Catalogue to better identify target stars and select candidates from reliable A-FpSrCrEu spectral types.

The OAN facility itself has proved to be a very good site for an roAp star survey. The detection of a signal in a known low-amplitude roAp star (10 Aql) and an independent confirmation of a new one (HD 122970) verify that our techniques, equipment and site are suitable for such a survey. Our data generally showed a low noise level which would allow us to identify roAp pulsations with amplitudes as low as 0.5 mmag under the best conditions. However, our data revealed a non-linear relationship between instrumental magnitude and airmass which is probably due to an instrumental problem. Tests on photometric standard stars (and maybe an artificial light source) should be conducted to try to identify the cause of the problem and quantify it. However, as this roAp survey is based on non-differential photometry, this problem didn't hinder this work, nor should it seriously affect the continuing Survey.

In light of our results and experience gained throughout this work, we have realized it would be preferable to observe fewer stars in a given observing run, but to dedicate more observing time to each. It is important to repeat observations of stars with null results to circumvent the possible effects of amplitude modulation. This work represents Chapter 5. Discussion 82

the starting stage of an ongoing survey: more time will be attributed to stars observed only once and to unobserved stars from our Survey sample.

As we have seen in the case of HD 122970, aliasing can become a problem in the frequency determination and in our capacity to identify closely spaced low amplitude peaks. Multi-site campaigns are essential to reduce the aliasing in the Fourier spectra.

But, unless the duty cycle is 100%, time gaps in the data will always produce aliases.

The only solution is to go to space, where duty cycles approaching 100 % for weeks at a time are feasible. Moreover, the atmospheric scintillation, which is the dominant source of photometric noise for ground-based observations of oscillation amplitudes of a few millimagnitudes, would be eliminated by going to space.

At the beginning of the next millenium, a Canadian microsatellite will be launched into space (Matthews 1998) to study, among other objects, rapidly oscillating Ap stars.

Led by Mission Scientist J.M. Matthews, MOST (Microvariability & Oscillations of

STars) will be equipped with a 15-cm Maksutov telescope. It will be able to moni• tor stars for up to 7 weeks at a time, and to attain a photometric precision better than a few //mag in stars as faint as V ~ 6 in 10 days of observations. This will allow the

detection and the resolution of fine structure in p-mode eigenspectra of stars such as roAp stars.

As more roAp candidates are discovered every year by this Survey and others, more interesting targets await MOST on its way. to space. The superb frequency resolution

attainable from space along with the powerful techniques of asteroseismology shall help us find more about the dynamics of pulsation and the structure of roAp stars. References

[1] Alvarez, M., k Maisterrena, J., 1977, Rev. Mex. Astron. Astrof., 2, 43

[2] The Astronomical Almanac, Washington, D.C., Government Printing Office. Issued

Annually.

[3] Baldry, I.K., Bedding, T.R., Viskum, M., Kjeldsen, H., k Frandsen, S., 1997,

MNRAS, in press

[4] Bertaud, C, 1959, J.Obs., 42, 45

[5] Bertaud, C, 1960, J.Obs., 43, 129

[6] Bertaud, C, 1969, J.Obs., 48, 211

[7] Bertaud, C. k Floquet, M., 1967, J.Obs., 50, 425

[8] Bevington, P.R., 1969, Data reduction and error analysis for the physical sciences,

McGraw-Hill Book Company, 1969, 336 p.

[9] Bidelman, W.P., k MacConnell, D.J., 1973, Astron. J., 78, 687

[10] Bonsack, W.K, k Wolff, S.C., 1980 Astron. J., 85, 599

[11] Breger, M.', 1970, ApJ., 162, 597

[12] Breger, M., 1975, Dudley Obs. Rep., no. 9, 31

[13] Breger, M., Communications in-Astroseismology, Dec 1989, no. 6

[14] Breger, M. k Bregman, J.N., 1975, ApJ., 200, 343

83 References 84

[15] Cameron, R.C., 1966, Georgetown Obs. Mon., No. 21

[16] Catalano, F.A., and Renson, P.R., 1984, Catalogue des periodes observees pour des

etoiles Ap, A&A Suppl.Ser., 55, 371

[17] Catalano, F.A., and Renson, P.R., 1988, Premier Supplement au catalogue des

periodes observees pour des etoiles Ap, A&A Suppl.Ser., 72, 1

[18] Catalano, F.A., and Renson, P.R., 1991, Second Supplement to the catalogue of

observed periods of Ap stars, A&A Suppl.Ser., 87, 59

[19] Catalano, F.A., and Renson, P.R., 1993, Third Supplement to the catalogue of ob•

served periods of Ap stars, A&A Suppl.Ser., 98, 269

[20] Catalano, F.A., and Renson, P.R., 1997, Fourth Supplement to the catalogue of

observed periods of Ap stars, A&A Suppl.Ser., 121, 57

[21] Chagnon, F. & Matthews, J.M., 1998, JRASC, vol. 92(1), 27

[22] Chagnon, F., Matthews, J.M and Eenens, P., 1998, in preparation (this work)

[23] Christensen-Dalsgaard, J., 1988a, in Advances in Helio and Asteroseismology, IAU

Symp. No. 123 eds. J. Christensen-Dalsgaard & S. Frandsen, p.3

[24] Christensen-Dalsgaard, J., 1988b, in Advances in Helio and Asteroseismology, IAU

Symp. No. 123, eds. J. Christensen-Dalsgaard & Frandsen, p.295

[25] Christensen-Dalsgaard, J., & Dappen,W., 1992, The A&A Rev., 4, 267

[26] Christensen-Dalsgaard, J., 1993, ASP Conf. Ser., vol. 40, in Inside the stars, IAU

Coll. 137, eds. W.W. Weiss & Annie Baglin, p.483

[27] Cox, A.N., 1955, ApJ, 121, 628 References 85

[28] Crawford, D.L., 1979, Astron.J., 84, 1858

[29] Deeming, T.J., 1975, Astrophys. and Space Science, 36, 137

[30] Deubner, F.-L. & Gough, D., 1984 Annu. Rev. A&A, 22, 593

[31] Didelon, P., 1984, A&A Suppl.Ser., 55, 69

[32] Dogget, L.E., Kaplan, G.H., and Seidelmann, P.K., 1978, Almanac for computers

for the Year 1978, Washington D.C., Nautical Almanac Office

[33] Dziembowski, W. & Goode, P.R., 1985, ApJ., 296, L27

[34] Dziembowski, W. & Goode, P.R., 1986, in Seismology of the Sun and Distant Stars,

p.441, eds. Gough, D.O., Reidel, Dordrecht, Holland.

[35] Echevarria, J., Arevalo, V., Rico, R., Wong, L., Alvarez, M. and Valle, C, 1986,

Manual de usuario del fotometro Cuenta Pulsos I, from OAN-UNAM Laboratorio

de Electronica en Ensenada, Reporte Tecnico No. 37

[36] Gabriel, M., Noels, A., Scufflaire, R., and Mathys, G., 1985, A&A, 143, 206

[37] Garrido, R., Lopez de Coca, P., Quintana, J.M., Rolland, A. & Saez, M., 1980,

A&A, 83, 114

[38] Gautschy, A., Hideyuki, S., & Harzenmoser, H., 1998, MNRAS, in press

[39] Golay, M., 1974, Introduction to Astronomical Photometry, ed. Dordrecht-Holland

[40] Gray, D.F., & Desikachary, K., 1973, ApJ., 181, 523

[41] Hall, D.S. & Genet, R.M, 1982, Photoelectric photometry of variable stars, a prac•

tical guide for the smaller observatory, publ. International Amateur-Professional

Photoelectric Photometry (IAPPP) References 86

[42] Handler, G., & Breger, M., 1997, Star Newsletter 11, 10 (University of

Vienna)

[43] Handler, G., k Paunzen, E., 1998, A&A Suppl. Ser., in preparation

[44] Handler, G., Paunzen, E., Hatzes, A.P., Kanaan, A., Garrido, R.,Medupe, R., Shob-

brook, R.R., Guzik, J.A., Beach, T.E., Chagnon, F., Matthews, J.M., 1998, A&A,

in preparation.

[45] Hardie, R.H., 1962, in Astronomical Techniques, ed. by W.A.Hiltner, The University

of Chicago press, chap.8

[46] Hatzes, A.P., Penrod, G.D., Vogt, S.S., 1989, ApJ., 341, 456

[47] Hauck, B., North, P., 1982, A&A, 114 23

[48] Heller, CH. and Kramer, K.S., 1988a, PASP, 100, 583

[49] Heller, CH. and Kramer, K.S., 1988b, IBVS, 3247

[50] Heller, CH. and Kramer, K.S., 1990, MNRAS, 244, 372

[51] HeUer, CH. and Kawaler, S.D., 1988, ApJ., 329, L43

[52] Henden, A.A., & Kaitchuck, R.H., 1982, Astronomical photometry, eds. Van Nos-

trand Reinhold Company, chap.4 and 5

[53] Hensberge, H., Van Rensbergen, W., & Blomme, R., 1991, A&A, 249, 401

[54] Home, J.H., & Baliunas, S.L., 1986, ApJ., 302, 757

[55] Houk, N., & Cowley. A.P., 1975, Michigan Spectral Catalogue of Two-Dimensional

Spectral Types for the HD Stars, Volume 1, Dept of Astronomy, University of Michi•

gan References 87

[56] Houk, N., 1978, Michigan Spectral Catalogue of Two-Dimensional Spectral Types for

the HD Stars, Volume 2, Dept of Astronomy, University of Michigan

[57] Houk, N., 1982, Michigan Spectral Catalogue of Two-Dimensional Spectral Types for

the HD Stars, Volume 3, Dept of Astronomy, University of Michigan

[58] Houk, N., & Smith-Moore, M., 1988, Michigan Spectral Catalogue of Two-

Dimensional Spectral Types for the HD Stars, Volume 4, Dept of Astronomy, Uni•

versity of Michigan

[59] Hubrig, S., & Schwan, H., 1991, A&A, 251, 469

[60] Hudson, H.S., 1988, Annu. Rev. AkA, 26, 473

[61] Jimenez, A., Palle, P.L., Perez, J.C., Regulo, C, Roca Cortes, T., Isaak, G.R.,

McLeod, CP., van der Raay, H.B., 1988, in Advances in Helio and Asteroseismology,

IAU Symp. No. 123, eds. J. Christensen-Dalsgaard & Frandsen, p.205

[62] Kennelly, E.J., Walker, G.A.H., Hubeny, I., 1991, PASP, 103, 1250

[63] Kennelly, E.J., Walker, G.A.H., Matthews, J.M., & Merryfield, W.J., 1992, ASP

Conf. Ser., 42, 359

[64] Kreidl, T.J., 1984a, IBVS, no. 2460

[65] Kreidl, T.J., 1984b, IBVS, no. 2602

[66] Kreidl, T.J. & Kurtz, D.W., 1986, MNRAS, 220, 313

[67] Kurtz, D.W., Breger, M., Evans, S.W., Sandman, W.H., 1976, ApJ, 207, 181

[68] Kurtz, D.W., 1978, IBVS, no. 1436 References 88

[69] Kurtz, D.W., Wegner, G., 1979, ApJ., 232, 510

[70] Kurtz, D.W., 1980a, MNRAS, 191, 115

[71] Kurtz, D.W., 1980b, MNRAS, 193, 29

[72] Kurtz, D.W., 1982, MNRAS, 200, 807

[73] Kurtz, D.W., 1983, MNRAS, 202, 1

[74] Kurtz, D.W., 1984, MNRAS, 206, 253

[75] Kurtz, D.W., 1985, MNRAS, 213, 773

[76] Kurtz, D.W. & Shibahashi, H., 1986, MNRAS, 223, 557

[77] Kurtz, D.W., 1989, MNRAS, 238, 1077

[78] Kurtz, D.W., et al. 1989, MNRAS, 240, 881

[79] Kurtz, D.W., 1990, ARA&A, 28, 607

[80] Kurtz, D.W., 1992, MNRAS, 259, 701

[81] Kurtz, D.W., & Martinez, P., 1993, ASP Conf. Ser., vol. 44, eds. M.M. Dworetsky,

F. Castelli, and R. Faraggiana

[82] Kurtz, D.W., Sullivan, D.J., Martinez, P., & Tripe, P., 1994, MNRAS, 270, 674

[83] Kurucz, R.L., 1979, ApJ Supp.Ser. 40, 1

[84] Kurucz, R.L., 1993, ASP Conf. Ser.,44, 87

[85] Lanz, T., 1984, A&A, 139, 161

[86] Leighton et al, 1962, ApJ., 135, 474 References 89

[87] Libbrecht, K.G., 1988, ApJ., 330, 51

[88] Libbrecht, K.G., Woodard, M.F.,Kaufman, J.M., 1990, ApJ.SuppL, 74, 1129

[89] Loumos, G.L., & Deeming, T.J., 1978, Astrophys. and Space Science, 56, 285

[90] Maitzen, H.M., 1984, A&A, 138, 493

[91] Maitzen, H.M. and Pavlovskiy., 1987, A&ASuppl.Ser., 71,441

[92] Malanushenko, V.P., Polosukchina, N.S., Weiss, W.W., 1994, Catalogue of CP stars

with references to short time scale variability, A&A Suppl.Ser., 105, 125

[93] Matthews, J.M., & Wehlau, W.H., 1985, PASP, 97, 841

[94] Matthews, J.M., Kurtz, D.W. and Wehlau, W.H., 1987, ApJ., 313, 782

[95] Matthews, J.M., 1988, MNRAS, 235, 7

[96] Matthews, J.M., Wehlau, W.H., Walker, G.A.H. & Yang, S., 1988a, ApJ., 324, 1099

[97] Matthews, J.M., Kreidl, T.J. & Wehlau, W.H., 1988b, PASP, 100, 255

[98] Matthews, J.M., 1990, Lecture Notes in Physics, 367,385

[99] Matthews, J.M., 1991, PASP, 103, 5

[100] Matthews, J.M., 1993, ASP Conf. Ser., 42, 303

[101] Matthews, J.M. & Scott, S., 1996, ASP Conf.Ser., 83, 347

[102] Matthews, J.M., Wehlau, W.H., Rice, J. & Walker, G.A.H., 1996, ApJ., 459, 278

[103] Matthews, J.M., Kurtz, D.W. & Martinez, P., 1999, ApJ, to appear 20 Jan References 90

[104] Matthews, J.M., 1998, in Structure and Dynamics of the Interior of the Sun and

Sun-like Stars, eds. S.G. Korzennik & A. Wilson, ESA SP-418, ESA Publications

Division (Noordwijk, Netherlands), in press.

105] Martinez, P., Kurtz, D.W., and Kauffmann, G.M., 1991, MNRAS, 250, 666

106 Martinez, P., PhD dissertation, University of Cape Town

107 Martinez, P. k Kurtz, D.W., 1995, ASP Conf. Ser. 83, 58

108 Megessier, C, 1988, A&A, 206, 74

109 Merryfield, W.J., & Kennelly, E.J., 1992, ASP Conf. Ser., 42, 363

110 Michaud, G., 1970, ApJ., 160, 641

111 Michaud, G., 1976, in Physics of Ap Stars, p.81, eds. Weiss, W.W., Jenner, H.,

Wood, H.J., Universitatssternwarte Wien, Vienna

112 Michaud, G., 1970, Astron. J., 85, 589

113 Michaud, G., Megessier, C, & Charland, Y., 1981, A&A, 103, 244

114 Moreno-Corral, M.A., Costero, R., & Schuster, W.J., 1994, High atop the Baja, The National Astronomical Observatory of Mexico, in Mercury, jan-feb, 29

115 Nelson, M.J., & Kreidl, T.J., 1993, Astron. J., 105(5), 1903

116 Preston, G.W., 1974, Ann.Rev.A&A, 12,257

117 Renson, P., Gerbaldi, M. & Catalano, F.A., 1991, A&A Suppl.Ser.,89,429

118 Rice, J.B., & Wehlau, W.H., 1990, A&A, 233, 503

119 Rice, J.B., Wehlau, W.H., & Khokhlova, V.L., 1989, A&A, 208, 179 References 91

120] Scargle, J.D., 1982, ApJ., 263, 835

121] Schneider, H., Kreidl, T.J., & Weiss, W.W., 1992, A&A, 257, 130

122] Semel, M., A&A, 225, 456

123] Shibahashi, H., 1983, ApJ., 275, L5

124] Shibahashi, H., 1987, Lecture Notes in Physics, 274, 112

125] Shibahashi, H. & Saio, H., 1985, PASJ, 37, 245

126] Shibahashi, H. & Takata, M., 1996, PASJ, 48, 377

127] Stellingwerf, R.F., 1979, ApJ., 227, 935

128] Stibbs, D.W.N., 1950, MNRAS, 110, 395

129] Tapia, M., 1992, Rev.Mex.Astron.Astrof., 24, 179

130] Tassoul, M., 1980, ApJ. Suppl. Ser., 43, 469

131] van't Veer-Menneret, C, Coupry, M.F., & Burkhart, C, 1985, A&A, 146, 139

132] ViUa, P., & Breger, M., 1998, A&A, in press

133] JViskum, M, Baldry, I.K., Kjeldsen, H., Frandsen, S. & Bedding, T.R., 1996, IAU

Symp. 181, p.285

134] Vorontsov, S., k Shibahashi, H., 1991, PASJ, 43, 739

135] Wehlau, W.H. k Rice, J., 1993, ASP Conf.Ser., eds M.M. Dworetsky, F.Castelli,

and R. Faraggiana, vol. 44

[136] Weiss, W., 1983, A&A, 128, 152 References 92

[137] Young, A.T, 1974, in Methods of experimental physics, volume 12, ed N. Carleton

(Academic Press: New York), chap. 1-3 Appendix A

Reduction procedure

A.l Dead-Time Correction

The dead-time equation presented in'section 3.1 is an approximation which we will justify here. We start from the exact expression (Henden 1982)

C0 = Ct * exp(-Ct * tD) (A.l) where Co is the observed count rate in counts per seconds (c/s), Ct, the true count rate

(c/s) and tp is the dead-time constant. This simple formula has a somewhat complicated derivation. To simplify, we can re-express equation A.l in the following manner

H~) = -Ct*tD (A.2) Ct The best way to solve this transcendant equation is by numeric integration, starting from an initial lower value and iterating to a larger one, by steps whose size will limit the

accuracy on Ct- This process can be time-consuming and it is easier to expand Equ. A.2

by using the Taylor series of the natural logarithm:

!„=(-lll + lx( —)2 + .... for x> 1/2 (A.3) x 2 x

where x — Co/Ct. It applies to our case as x ~ 1, since the correction turns out to be

rather small.

So we have

93 Appendix A. Reduction procedure 94

Lt a; which can be written as

^ = 1 - Co x tD (A.5) Ct

And then after inverting, we get the final and simpler-to-solve approximate result of equation (3.1):

°'= (iJ^T)

A.1.1 A value for the dead-time constant

The reference manual for the OAN photometer Cuentapulsos (Echevarria et al. 1986)

doesn't list a value for the dead-time constant tp1. In a private communication with the

staff of the OAN electronics lab, they report that the constant has never been measured,

but they agree to say that its value must be in the range 70-100 nanoseconds. We tested

both values to see the difference in the true count rate Ct and noticed that, indeed, it

is very small. We present these results in table A.l. For Co = 10,000 c/s, we see that

the difference implied is about 0.03%. For larger count rates, the difference increases but

it is still small. Even at the photometer's limiting count rate (Co = 610,000 c/s), the

difference between using tj) = 70 ns and tjj = 100 ns in the dead-time correction is still less than 2%. However, most of our targets were fainter stars, so a difference of less than

1 % is typical. To be conservative, we chose the largest reasonable value to = 100 ns.

*It specifies that due to the RCA C31034 phototube's high gain and to the limit of 6.10 x 105 cps, the dead-time correction is not very important. Appendix A. Reduction procedure 95

Table A.l: Comparison of 2 dead-time constant values

to c c ns Co = 10,00t 0 c/s Co = 610,00t 0 c/s 70 10,007.00 637,209 100 10,010.01 649,267 Axa 0.03 % 1.9 %

a Ai = | Ct(tD = 100) - Ct(tD = 70) \/Ct{tD = 70)

A.1.2 How good is the approximation and is it important?

Using tz> — 100 ns, we calculate the true count rate Ct from both the exact equation A.l and its approximation A.6. The results are presented in Table A.2. Up to the extreme phototube limit, the error introduced by using the approximation is still very small, if not negligible. The approximation is thus valid.

Table A.2: Validity of the approximation [tr> = 100 ns) c Co = 10,000 c/s Co = 610,000 c/s exact t 10,000.00 651,175.00 approx 10,010.01 649,62.7.00

a A2 0.10 % 0.23 %

a A2 = | Ct ,exact Cttapprox \/ct exact

The Cuentapulsos manual states that there is no need to apply the dead-time cor•

rection. We can now do a test to see the relative importance of this correction. Table

A.3 presents the results from the difference between the observed count rate and the true

count rate, calculated from equation A.6.

For a small value of the count rate, the correction is not very important but for

a larger one, it becomes more significant, although not critical. All our stars being

somewhat fainter than the phototube limit, not applying the correction would lead to an

error around 5%. We thus think it is important to include that correction in the reduction Appendix A. Reduction procedure 96

Table A.3: Importance of the dead-time correction (to = 100 ns)

CQ (c/s) 10,000.00 610,000.00

Ct (c/s) 10,010.10 649,627.00

a A3 0.10 % 6.10 % a A3 = Ct - Co/Co

process. However, because the count rate is approximately constant over the time we observe the star, the dead time correction does not vary by much. As a consequence, it doesn't affect the frequency and amplitude determination in the Fourier analysis.

A.2 Dark and Sky Subtraction

An average of all darks obtained before and after a star was subtracted from all star counts. For the sky subtraction, a straight line was fitted through the sky points which were obtained before and after the star. Then, using this linear relationship, we interpo• lated a sky count for every integration time, and subtracted it from the star counts. The sky subtraction is not optimal because, in nature, the sky brightness rarely varies linearly with time. With a rising or setting moon, it would be best described by a power law.

To fit a quadratic curve through the sky points would require at least three measures of the sky at different times, for each star (e.g., before, in the middle and after the program star). This however reduces the efficiency of the observations.

A.3 Airmass extinction

When following a star across the sky, the sky transparency varies in zenith angle and, unless the conditions are absolutely perfect, in time as well. Inherent to any ground- based observation, the airmass extinction is simply the absorption of starlight by Earth's atmosphere. As an example, at the zenith on a clear night and at high altitude the Appendix A. Reduction procedure 97

extinction can be about 15%, or 0.2 mag (Hall & Genet 1982, p.9.1).

The extinction also depends on the wavelength, as the atmosphere does not transmit all wavelengths equally. It is completely opaque at A < 3000 A (ultraviolet and shorter),

A > 10 meters and in many portions of the infrared, between 10, 000 Aand 1 cm. This is why ground-based astro-photometry must be conducted through an atmospheric window: the visible, the radio, or one of the narrow infrared windows (Hall & Genet 1982, p.9.4).

The extinction depends on the airmass X. It is a relative quantity describing the amount of air or the width of the atmospheric layer blocking part of the starlight. The vertical thickness of this layer, on a line along the zenith, is X = 1. We then characterize the airmass of other points on the sky as a function of their distance to the zenith, that is the angle z between the observatory's zenith and a line joining the observatory and the star:

X = secz (A.7)

This equation assumes the atmosphere can be described by a plane-parallel structure, which is a good approximation if z < 60°. For larger z, Equation A.7 would introduce errors of the order of 5% (Golay 1974, p.47). Instead, we have used Bemporad's expression

(Hardie 1962), which leads to an error of only 1% at X ~ 10:

X = sec(z) - 0.0018167(secz - 1) - 0.002875(secz - l)2 - 0.0008083(secz - l)3 (A.8)

A more general expression, valid for a spherical atmosphere, is also presented in Golay

(1974) along with other relevant discussion, but for the scope of this work, the previous

equation is satisfactory.

So if m; describes the raw instrumental magnitude of a star and mo the extraterrestrial magnitude, then we can write Appendix A. Reduction procedure 98

mi — m0 = k\* X (A.9) where k\ is the extinction coefficient valid at wavelength A. A good example of the wavelength dependence of the extinction coefficent is shown in Golay (1974, p.50). This plot shows that k\ varies from 0.6 to 0.1 over the visible region of the spectrum, and from 1.4 to ~ 0.05 from 3,000 to 10,000 A (for a clear atmosphere). Specifically, in the

Johnson B filter (Ao = 4470 Aand AA = 1000 A) the extinction coefficient is about 0.3 mag/airmass (Golay 1974, p.50) on a clear night.

We can derive X from secz, and z from the coordinates of the star, the latitude of the site and the time. The photometer measures a count rate which is converted to a magnitude scale, m,-. Using the previous equation, we can fit a linear relation through the points ra; vs X, which would yield the 2 parameters, ks as the slope, and mo as the zero point (i.e., magnitude at airmass X=0).

Then, the reduction procedure recalculates the extinction coefficient-fcjg, this time rejecting any points 3

A.4 Heliocentric Correction

Our observations were recorded in Universal Time and Date and then converted to Julian

Date. However, for a , two time series obtained a few months apart can be out of phase since the separation between the Earth and the star is not constant throughout the year. On its way around the Sun, Earth's distance to a star varies by a maximum of 2 Appendix A. Reduction procedure 99

Astronomical Units if the star is in the ecliptic plane. Therefore, maximum or minimum light in the pulsation cycle could arrive as much as 16 min before or after the predicted time. This difference can cause artifacts in the frequency analysis of data obtained at different times.

We thus want to transform the Julian Date to a time reference fixed to the Sun: the Heliocentric Julian Date (HJD). The correction to the Julian Date is essentially the

difference in the starlight travel time to the Earth and the Sun, as shown through the following equation:

HJD = JD + At (A.10) where At depends on the stars' coordinates a and 8, obliquity e of the ecliptic (23°27) and

the Sun's rectangular coordinates X, Y on a given date, such that (Henden & Kaitchuik

1982)

Ai = -0.0057755 * [(cos8cosa)X +

(tan e sin 8 + cos 8 sin a)y] (A.11)

The values of X and Y can be obtained from the Astronomical Almanac or from the

trigonometric series given by Dogget et al. (1978).