Optical Studies of X-Ray Peculiar Chromospherically Active Stars

Optical Studies of X-ray Peculiar Chromospherically Active Stars

THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (PHYSICS)

Investigator: Jeewan Chandra Pandey ARIES, Naini Tal

Supervisor: Co-Supervisor: Prof. Ram Sagar Prof. K. P. Singh ARIES TIFR Naini Tal - 263 129 Mumbai - 400 005

Submitted to Kumaun University, Naini Tal August, 2005 DECLARATION

I hereby declare that the work presented in this thesis is a result of the work carried out by me at the Aryabhatta Research Institute of Observational Sciences (ARIES), Naini Tal, under the joint supervision of Prof. Ram Sagar (Aryabhatta Research Institute of observational Seiences (ARIES), Naini Tal) and Prof. K. P. Singh (Tata Institute of Fundamental Research (TIFR), Mumbai). This work has not been submitted for the award of any degree, diploma, associateship, fellowship, etc. of any other University or Institute.

Place : Naini Tal Date : , 2005 Jeewan Chandra Pandey CERTIFICATE FROM THE SUPERVISOR AND CO-SUPERVISOR

This is to certify that

1. The thesis entitled “Optical studies of X-ray peculiar choromospherically active stars” for the award of the degree of Doctor of Philosophy in Physics was ap- proved by the Kumaun University, Naini Tal, as per Academic Council Resolution dated 07 August, 2003, letter number 43/Physics/4/2003.

2. This thesis embodies the work of Mr. Jeewan Chandra Pandey himself.

3. Mr. Jeewan Chandra Pandey worked under us on this thesis for not less than twenty months commencing from the date of his application to Kumaun Uni- versity, Naini Tal for registration as candidate for the Ph. D. degree. He has put up at least 200 days of attendance at the Aryabhatta Research Institute of Observational Sciences (ARIES), Naini Tal during this period.

4. This thesis has not been submitted for the award of any degree, diploma, associateship, fellowship, etc., of any other University or Institute.

Prof. Ram Sagar Prof. K. P. Singh (ARIES, Naini Tal) (TIFR, Mumbai) (Supervisor) (Co-Supervisor)

Place: Naini Tal Place: Mumbai Date : , 2005 Date : , 2005 To

Who always encourage me to do what I love, Support my efforts without question, And only expect one thing in return, That I be a gentle person.

(My parents) Acknowledgements

I express my deep respect and gratefulness to my supervisor Prof. Ram Sagar and co-supervisor Prof. K. P. Singh for their supervision, encouragement, inspiration and motivation. Without their support it would not have been possible to finish this thesis. Prof. Ram Sagar’s ideas and unique way of enthusiasm are gratefully acknowledged. Prof. K. P. Singh has introduced me X-ray astronomy. His valuable criticism and suggestions are gratefully acknowledged. Comments and suggestions given by Dr. S. A. Drake at various stages of this work are highly acknowledged. I am highly grateful to Dr. Vijay Mohan and Dr. A. K. Pandey for the various scientific discussions. I also thank to Drs. B. S. Rautela, G. C. Joshi and B. B. Sanwal for various discussion. Thanks are extended to entire faculty and staff of ARIES, who are directly and indirectly responsible for this work. I am thankful to Prof. A. R. Rao, Prof. H. M. Antia, Dr. D. K. Ojha, Dr. B. Paul and Prof. S. K. Ghosh for the discussions on various issues. I also thank to Prof. A. V. Raveendran for the discussions through mails. I am highly thankful to my seniors Drs. Alok, Nilakshi, Ramakant, Santosh, Stalin and Yogesh for their help and company during initial stage of my research. The discussions on various scientific topics with Dr. Brijesh are sincerely acknowledged. The student seminars organised by him are useful and enjoyable. I greatly appreciate my batch-mate Shashi for the various discussions, helps and fun on many occasions. I am thankful to my friends Bhuwan, Kuntal, Saurabh and Umesh for their cherish company and the discussion on the variety of their research topics. I am also thankful to Dr. Amitesh, Atish, Dr. David, KK, Ramesh, Sneh and Tejbir for their company and discussion on various issues. I thank to my other friends at ARIES particularly Arti, Amitava, Himali, Kumar, Raman, Manash, Prashant and Saurav for the fun we had. Thanks to Dr. Anandmayi, Uddipan and Surajit for their various helps and fun during my TIFR stay. Much thanks to Vikram for his help in X-ray data reduction and other scientific discussions. A special thank to Girish for his various generous helps and making me feel at home at work. I also thank the Department of Astronomy and Astrophysics of TIFR for the facilities given to me during my visits to TIFR. The technical staffs at the 104-cm telescope particularly Nautiyal ji, library, computer section particularly Navin Kishor ji, electronic section and optics section of ARIES are sincerely acknowledged. I am also thankful to technical staff and the observers of Vainu Bappu Observatory for their help during the observations at VBT. This research had made use of many public domain softwares and databases. The entire teams of ROSAT X-ray observatory, 2MAAS, IRAF, FTOOLS and Starlinks are sincerely acknowledged. I would like to take this opportunity to express my deepest gratitude to my parents, my brothers Rajesh and Tribhuwan, sister Mannu, brother in law and all family members for all their love, affection and moral support. Without their constant encouragement I would not have been able to reach here.

(Jeewan Ch. Pandey) List Of Publications

Refereed Journals:

1. Unravelling the nature of HD 81032 - A new RS CVn binary. J. C. Pandey, K. P. Singh, S. A. Drake & R. Sagar, 2005, JAAp, Submitted

2. A Optical and X-ray studies of Chromospherically active stars FR Cnc, HD 95559 and LO Pegasi J. C. Pandey, K. P. Singh, S. A. Drake & R. Sagar, 2005, AJ, 130, 3/asto-ph 0506010

3. ARIES Imaging Polarimeter. B. S. Rautela, G. C. Joshi & J. C. Pandey, 2004, BASI, 32, 159.

4. FR Cnc = BD +16 1753 - A Young Active Main-Sequence Star. J. C. Pandey, K. P. Singh, R. Sagar & S. A. Drake, 2002, IBVS, 5351.

5. Photometric Variability of Four Coronally Active Stars. J. C. Pandey, K. P. Singh, R. Sagar & S. A. Drake, 2002, JAAp, 23, 9.

Proceedings:

6. HD 81032: A newly discovered RS CVn J. C. Pandey , K. P. Singh, R. Sagar & S. A. Drake, 2005, in Proceedings of ASI

7. FR Cnc - A Young Spotted star. J. C. Pandey, 2003, BASI, 31, 329.

8. Photometric Variability of Four Coronally Active Stars. J. C. Pandey , K. P. Singh, R. Sagar & S. A. Drake, 2002, in proceedings of the

i ii

’MULTI COLOUR UNIVERSE’, eds. R. K. Manchanda & B. Paul, 2002, p237[ISBN 81-88513-00-8], p58. Additional Pubilcations

Refereed Journals:

1. SS 433: Results of a Recent Multi-wavelength Campaign S. K. Chakrabarti, B. G. Anandarao, S. Pal, S. Mondal, A. Nandi, A.Bhattacharyya, Samir Mandal, R. Sagar, J. C. Pandey, A. Pati & S. K. Saha, 2005, MNRAS, in press/astro-ph 0501285.

2. Optical observations of the bright long duration peculiar GRB 021004 afterglow. S. B. Pandey, D. K. Sahu, L. Resmi, R. Sagar, G. C. Anupama, D. Bhattacharya, V. Mohan, T. P. Prabhu, B. C. Bhatt, J. C. Pandey, Padmakar Parihar & A. J. Castro- Tirado, 2003, BASI, 31, 19.

3. A ﬂattening in the Optical Light Curve of SN 2002ap. S. B. Pandey, G. C. Anupama, R. Sagar, D. Bhattacharya, D. K. Sahu & J. C. Pandey, 2003, MNRAS, 340, 375.

Non-refereed Journals:

4. Observation of Leonid meteor sower from Naini Tal (India) Nilakshi, K. Upadhyay , S. B. Pandey, J. C. Pandey & Sneh Lata 2000, WGN Journal of the International Meteor Organization, 28, 41. Circular:

1. GRB 011030, R-band observations. V. Mohan, S. B. Pandey, J. C. Pandey et al., 2002, GCN 1120. iii

Abbriviation and Notation Abbriviation

2MASS Two Micron All-Sky-Survey BC Bolometric correction BY Dra BY Draconis CABS Chromospherically Active Binary System CCD Charge Coupled Device CVs Cataclysmic Variables CZ Convective Zone ESS Einstein Slew Survey EW Equivalent Width FK Com FK Comae Berences FR Cnc FR Cancri HWP Half-Wave Plate IRAF Image Reduction and Analysis Facility Jy Jansky LO Peg LO Pegasi MEKAL Mewe-Kaastra-Leidahl mJy milli-Jansky MS Main-sequence NIR Near Infra-red OMR Opto-Mechanic Research PMS Pre-Main-sequence RASS ROSAT All-Sky Survey ROSAT ROntgen SATellite RS CVn RS Cannum Venaticorum PET Photon Event Table PHA Pulse Height Amplitude PI Pulse Invariant PSPC Position Sensitive Proportional Counter W UMa W Ursa Majoris (W UMa) iv

Notation

B Johnson B band magnitude

Fx X-ray Flux

Frad Radio Flux I Cousin I band magnitude

Lbol Bolometric Luminosity

Lrad Radio Luminosity

Lx X-ray Luminosity L Solar Luminosity

Mbol Absolute bolometric magnitude

MV Absolute V band magnitude M Mass of Sun

M Mass of star ∗ P Period p Degree of polarization R Cousin R band magnitude

RV Radial velocity

Sx X-ray surface luminosity

Srad radio surface luminosity R Sun’s radius

R Star’s radius ∗

Teﬀ Eﬀective temperature U Johnson U band magnitude V Johnson V band magnitude λ Wavelength π Parallax

τc Convective turnover time ω Angular velocity Ω Diferential Roattion v

µα Proper motion in RA

µδ Proper motion in DEC

θmin Phase minimum θ Angle of polarization σ Standard deviation Contents

1 Introduction 2 1.1 The Sun and solar activity ...... 2 1.2 Late-type stars ...... 4 1.3 Chromospherically active binary stars (CABS) ...... 5 1.4 Stellar activity ...... 6 1.4.1 Starspots: A photospheric feature ...... 6 1.4.2 Eﬀects of activity on photometric colour ...... 8 1.4.3 Spot cycle and diﬀerential rotation ...... 8 1.4.4 Chromospheric and transition region activity ...... 9 1.4.5 Coronal X-ray emission ...... 11 1.4.6 Coronal radio emission ...... 12 1.4.7 Flares ...... 13 1.5 Various types of active stars ...... 14 1.5.1 RS Cannum Venaticorum (RS CVn) binary stars ...... 14 1.5.2 BY Draconis (BY Dra) ...... 17 1.5.3 FK Comae Berences (FK Com) ...... 17 1.5.4 W Ursae Majoris (W UMa) ...... 18 1.5.5 Algol binaries ...... 19 1.5.6 Cataclysmic Variables (CVs) ...... 20 1.6 Stellar dynamo mechanism ...... 21 1.7 Motivation of thesis ...... 22 1.8 Organisation of thesis ...... 24

vi CONTENTS vii

2 Instruments, Observations, Data Reduction & Analysis Procedure 26 2.1 Overview ...... 26 2.2 Optical Obervations ...... 26 2.2.1 The telescopes ...... 26 2.2.2 The filters ...... 27 2.2.3 The detectors ...... 27 2.2.4 The spectrograph ...... 29 2.3 Optical observations ...... 30 2.4 Optical data reduction ...... 32 2.4.1 Bias subtraction ...... 32 2.4.2 Dark subtraction ...... 33 2.4.3 Flat fielding ...... 33 2.4.4 Cosmic ray removal ...... 33 2.4.5 Photometry ...... 34 2.4.6 Spectroscopy ...... 34 2.5 Differential photometry and selection of comparison stars ...... 35 2.6 ROSAT X-ray observatory ...... 38 2.6.1 The position sensitive proportional counter (PSPC) ...... 40 2.6.2 ROSAT data ...... 42 2.6.3 Coronal plasma model ...... 45 2.7 Near-IR data ...... 46 2.8 Time series analysis ...... 47

3 Main Sequence Active Stars 50 3.1 Overview ...... 50 3.2 Introduction ...... 50 3.2.1 FR Cnc ...... 51 3.2.2 HD 95559 ...... 51 3.2.3 HD 160934 ...... 52 3.2.4 LO Peg ...... 52 3.3 Light curves and period analysis ...... 52 3.3.1 Light curves and period analysis of FR Cnc ...... 52 CONTENTS viii

3.3.2 Period analysis of HD 95559, HD 160923 and LO Peg ...... 56 3.4 Folded light and colour curves ...... 58 3.4.1 FR Cnc ...... 58 3.4.2 HD 95559 ...... 65 3.4.3 HD 160934 ...... 66 3.4.4 LO Peg ...... 67 3.5 Chromospheric emission features ...... 70 3.6 X-ray light curves of HD 95559, HD 160934 and LO Peg ...... 73 3.7 X-ray spectra of HD 95559, HD 160934 and LO Peg ...... 77 3.7.1 HD 95559 ...... 79 3.7.2 HD 160934 ...... 80 3.7.3 LO Peg ...... 80 3.8 Comparison of X-ray properties with similar systems ...... 82 3.9 Stellar parameters from optical data ...... 83 3.10 IR excess and spectral energy distribution (SED) ...... 85 3.11 Kinematics and age ...... 87 3.12 Colour-magnitude diagram (CMD) ...... 88

4 HD 81032: A new long period RS CVn binary 91 4.1 Overview ...... 91 4.2 Introduction ...... 91 4.3 Photometric light curves and period analysis ...... 93 4.4 Photometric variation and phase of minima ...... 93 4.5 Hα and CaII H and K emission lines ...... 99 4.6 Spectral type and physical parameters ...... 100 4.7 SED of HD 81032 ...... 101 4.8 X-ray light curve ...... 102 4.9 X-ray spectra ...... 102 4.10 X-ray and radio properties: comparison with similar systems ...... 106

5 Correlation between various physical quantities of Active Stars 108 5.1 Overview ...... 108 CONTENTS ix

5.2 Our sample and previous studies ...... 109 5.3 HR-diagram of active stars ...... 109 5.4 Bolometric luminosity and stellar diameter ...... 117 5.5 Average X-ray and radio luminosities ...... 118 5.6 Correlation of radio emission with X-ray emission ...... 121 5.6.1 Physical signiﬁcance of the radio to X-ray correlations ...... 123 5.7 Correlation of X-ray and radio emission with rotation ...... 123 5.8 Dependence of stellar radius on rotational period ...... 128 5.9 The (B-V) to X-ray and radio correlation ...... 130

6 Imaging Polarimeter 133 6.1 Overview ...... 133 6.2 Introduction ...... 133 6.3 Polarization sensitive optical elements ...... 134 6.3.1 Half-wave plate (HWP) ...... 134 6.3.2 Wollaston prism ...... 135 6.4 Principle of the instrument ...... 136 6.5 Observations and Data reduction ...... 141 6.6 Performance estimates ...... 141 6.7 Results ...... 142 6.8 Polarization of active stars ...... 143

7 Summary and future work 149 7.1 Summary ...... 149 7.2 Future work ...... 152 List of Figures

1.1 Variation of temperature with height above the convective zone of the Sun . 3 1.2 HR diagram ...... 5 1.3 A schematic diagram to the show the variability in brightness due to inhomogeneities (cool spots) on the surface of a star...... 7 1.4 Ratio of the total transition-region emission ﬂux to the bolometric ﬂux versus Rossby number ...... 11 1.5 Ratio of X-ray to bolometric luminosities as a function of log of Rossby number ...... 12 1.6 A diagram illustrating how the dynamo process works in cool stars . . . . . 22

2.1 Quantum eﬃciency curve of 2k 2k and 1k 1k CCD ...... 29 × × 2.2 Optical identiﬁcation chart ...... 36 2.3 The ROSAT Telescope ...... 40 2.4 A schematic view of the ROSAT PSPC detector ...... 42 2.5 X-ray images of the target source ...... 44

3.1 Light curves and corresponding CLEANed power spectra of FR Cnc . . . . 54 3.2 Power spectra of entire dataset of FR Cnc ...... 55 3.3 CLEANed power spectra of HD 95559 (left panel) and LO Peg (right panel) 57 3.4 BVR light curves and CLEANed power spectrum of HD 160934 ...... 58

3.5 Vc, B, V, R light curves and (B-V), (V-R) colour curves of FR Cnc . . . . . 61 3.6 Plot of the mean epoch vs the phase minimum of light for FR Cnc . . . . . 63

3.7 Vc, B, V, R light curves and (B-V), (V-R) colour curves of HD9559 . . . . . 66

3.8 Vc, B, V, R light curves and (B-V), (V-R) colour curves of HD 160934 . . . . 67

3.9 Vc, B, V, R light curves and (B-V), (V-R) colour curves of LO Peg . . . . . 68

x LIST OF FIGURES xi

3.10 Plot of the mean epoch vs the phase minimum of light for LO Peg . . . . . 69 3.11 Hα spectra of the FR Cnc ...... 72 3.12 Hβ spectra of FR Cnc ...... 73 3.13 Spectra of FR Cnc in CaII H & K region ...... 74 3.14 X-ray light curve of HD 95559 ...... 75 3.15 X-ray light curve of HD 160934 ...... 76 3.16 X-ray light curves of LO Peg ...... 77 3.17 Power density spectra and folded X-ray light curve of LO Peg ...... 78 3.18 X-ray spectra of HD 95559 ...... 80 3.19 X-ray Spectra of HD160934 ...... 81 3.20 X-ray spectra of LO Peg ...... 82 3.21 SED of FR Cnc, HD 95559, HD 160934 and LO Peg ...... 86 3.22 CMD ...... 89

4.1 Light curves and corresponding power spectra ...... 92 4.2 CLEANed power spectra of the entire data set of the star HD 81032 . . . . 94 4.3 Diﬀerential V , B, V, R light curve and (B V), (V R) colour curve of HD c − − 81032 ...... 96 4.4 Plot of mean epoch versus light minima of HD 81032 ...... 97 4.5 Hα spectra of HD 81032. HD 71952 was taken as reference spectra . . . . 98 4.6 Ca II H & K spectra of HD 81032. Spectra of HD 71952 was taken as a reference ...... 99 4.7 Plot of ∆V, Hα and CaII H & K EWs against phase ...... 101 4.8 SED of the star HD 81032 ...... 103 4.9 X-ray light curve of HD 81032 ...... 104 4.10 Spectra of HD 81032 taken with the ROSAT PSPC detector ...... 105

5.1 HR diagram of active stars ...... 110 5.2 A correlation plot between radio luminosity and X-ray luminosity . . . . . 118 5.3 Correlation plot between normalised radio luminosity and noramlised X- ray luminosity ...... 119 5.4 Correlation plot between surface radio ﬂux and surface X-ray ﬂux . . . . . 120 LIST OF FIGURES xii

5.5 X-ray emission vs. rotational period ...... 122 5.6 Radio emission vs. rotational period ...... 122 5.7 Stellar radius of the active star as a function of rotational period ...... 129 5.8 X-ray emission vs. (B-V) ...... 131 5.9 Radio emission vs. (B-V) ...... 131

6.1 A schematic of Wollaston prism ...... 136 6.2 Optical layout of IMPOL ...... 137 6.3 A picture of imaging polarimeter mounted at 104 cm telescope of ARIES . 137 6.4 A block diagram of polarimeter control system ...... 138 6.5 A CCD image of HD 18270 ﬁeld after emerging through the polarimeter. Two orthogonal component (ordinary and extraordinary) of an object are shown ...... 142

6.6 Plot of σp versus V magnitude ...... 143 6.7 The best cosine ﬁt for the 4 values of R(α) for diﬀerent stars ...... 144 6.8 Plot of Q/I versus U/I ...... 145 List of Tables

1.1 Summary of activity indicators of active stars ...... 15 1.2 The sample of active stars ...... 23

2.1 Parameters of Optical Telescope used ...... 27 2.2 Filter glass combination used at ARIES, Naini Tal ...... 28 2.3 Characteristics of the CCDs used in the observations ...... 29 2.4 Log of B, V and R observations and standard deviation (σ) of ’comparison (S) - chaeck (C)’ star...... 31 2.5 Log of spectroscopic observations ...... 32 2.6 Magnitude and colour of program, comparison and check stars ...... 38 2.7 The basic parameters of ROSAT ...... 39 2.8 Log of ROSAT X-ray observation ...... 43

3.1 Photometry of FR Cnc, HD 95559, HD 160934 and LO Peg...... 64 3.2 CaIIH&K, Hα and Hβ data of FR Cnc ...... 71

2 2 3.3 Results of X-ray spectral analysis. χν = χ /ν, where ν is degrees of freedom (DOF) ...... 79 3.4 Physical parameters of stars FR Cnc, HD 95559, HD 160934 and LO Peg . 85

1 3.5 Galactic space-velocity components. All the units are in km s− ...... 88

4.1 Parameters determined from the light curves of the star HD 81032...... 98 4.2 Equivalent widths (EWs) of CaIIH&K and Hα emission lines ...... 100 4.3 Results of X-ray spectral analysis of HD 81032 ...... 104

5.1 Database of active stars with radio and X-ray measurements ...... 111 5.1 Database of active stars with radio and X-ray measurements ...... 112

xiii LIST OF TABLES xiv

5.1 Database of active stars with radio and X-ray measurements ...... 113 5.1 Database of active stars with radio and X-ray measurements ...... 114 5.1 Database of active stars with radio and X-ray measurements ...... 115 5.1 Database of active stars with radio and X-ray measurements ...... 116 5.1 Database of active stars with radio and X-ray measurements ...... 117 5.2 Average and median X-ray and radio luminosities of dwarfs, subgiants and giants ...... 120 5.3 Summary of ML fits, r represents the linear correaltion coefficient...... 126 5.3 Summary of ML fits, r represents the linear correaltion coefficient...... 127 5.3 Summary of ML fits, r represents the linear correaltion coefficient...... 128

6.1 Degree of linear polarization (p) and polarization angle (θ) of polarized standards...... 145 6.2 Noramlised Stokes parameter (Q/I and U/I) of unpolarized standards . . . . 146

Chapter 1

Introduction

Late-type stars (F, G, K, M), also called cool stars show activity phenomenon that appear analogous to features observed on the Sun. Activity and variability in these stars are often explained in terms of processes producing magnetically active regions distributed across the stellar surface. These are indicative of dynamo action within the convective envelopes of these stars. However, there are vast differences regarding the strengths and lifetimes of these structures compared to the solar features. By studying the stellar activity more closely we can investigate how dynamo mechanism are affected by differences in stellar parameters (such as age, mass, rotation etc). This in turn gives us further insight into the evolution of the solar dynamo. On learning more about the magnetic configurations of these stellar atmosphere we can also evaluate how important the magnetic activity is in determining the stellar evolution. Various observational characteristics of stellar activity in cool stars are outlined in this chapter with a particular emphasis on the types/phenomenon that are observed in their atmospheres.

1.1 The Sun and solar activity

The Sun is a typical star of spectral type G2 V. Most of what is observed from the Sun is radiation leaking from the solar surface. The visible solar atmosphere lies above the convective zone and can be divided up into four layers; the photosphere, chromosphere, transition-region and corona (Athay 1976). The photosphere is one of the constituent parts of solar outer atmosphere and has a negative temperature gradient. It is a thin ( ∼

2 1.1. The Sun and solar activity 3

Figure 1.1 Variation of temperature with height above the convective zone of the Sun (reproduced from Sun, Earth and Sky by Kenneth Lang, 1995).

100 km ), dense layer of plasma which emits the major part of solar radiation. The gas

17 3 density in this area is 10 cm− (Priest 1984), where the peak photospheric temperature ≈ is 6600K (decreasing to 4300K at the temperature minimum where photosphere joins the chromosphere). The chromosphere is less dense than the photosphere and extends to about 2500 km above the photosphere. This region is more transparent with temperatures rising monotonically up to 105 K, where the transition-region begins. The chromosphere emits in the ultraviolet and is also detected via narrow bands of emission in optical photospheric line profile. The transition region is a thin region above the chromosphere, where temperatures rise rapidly, from about 20000 to a few million K. This region is characterised by a steep positive temperature gradient. The corona is the outermost area, extended out to several solar radii and reaches temperatures of 106 K. It can be detected at extreme ultraviolet ∼ and X-ray wavelengths. Figure 1.1 illustrates how the temperature varies with height above the solar surface. The Sun follows an approximately 11 year activity cycle, during which the polarity of the global magnetic field is reversed. From observations, we find that there is a period of 1.2. Late-type stars 4

minimum activity . However, structures similar to those seen at high activity level can also be seen at the minimum activity level. During active periods, structures form on the solar surface via interactions between the plasma and changing magnetic field. Observational characteristics of these active regions vary according to which wavelength band is being used to observe the Sun. Different types of the structures form at different heights from the surface of the Sun. At the photospheric level, sunspots and plages can be seen close to the limb of the Sun in optical continuum. Chromospheric features such as plages can be seen at UV and EUV wavelength as well as in strong optical lines, while coronal prominences and flares can be seen at EUV and X-ray wavelengths. Active regions can either occur singly or in group. The active regions are formed by a common surface of magnetic field. They also appear to rotate at different rates from each other. Groups of activity have a longer life time than the single activity, and form at preferred longitudes. Plages are the first structures to be observed in active regions and are also among the last to disappear. Prominences are among the largest structures seen in the solar atmosphere. These are about a hundred times denser than the surrounding corona, and are supported by the magnetic fields around the prominences.

1.2 Late-type stars

The stars in cool half (Teff< 6500K) of the HR diagram are called late-type stars. Right side of the vertical line in the Figure 1.2 shows the location of late-type stars. Solar-like magnetic activity such as photospheric spots, chromospheric emission and flares are observed in these stars. This is to expected on the basis of the dynamo theory of magnetic field generation since such stars have substantial convective envelopes (see 1.6). For ex- § ample solar magnetic flux distribution can give rise to sunspots which cover up to 0.2% of the Sun’s surface but some active stars can have starspots coverage of 10-40% (see Table 1.1). In such stars the energy release during X-ray, UV, and radio flares can be 105 times greater than in the solar flares. 1.3. Chromospherically active binary stars (CABS) 5

Figure 1.2 The HR diagram. Late-type stars are shown to the right side of the vertical line

1.3 Chromospherically active binary stars (CABS)

Binary systems containing at least one late-type companion that must be chromospherically active, where the chromospheric activity is defined by presence of Ca II H and K emission lines, are known as chromospherically active binary stars (CABS) (Starssmeier et al. 1988, 1993). The catalogue of CABS includes only RS CVn (see 1.5.1), BY Dra (see 1.5.2) § § and other binary systems which show strong Ca II H and K emission lines in their spectra (Starssmeier et al. 1988, 1993). It excludes W UMa-type (see 1.5.4) binaries and binaries § containing M-giants because chromosphere of their active component(s) is influenced by other physical processes like pulsation or a common convective envelope . Hall (1976) first identified the special characteristics of the RS CVn group and Bopp & Fekel (1977) defined the BY Dra variables. The RS CVn binaries contain dwarf or subgiant or giant components in the spectral type range F to K, whereas the BY Dra stars are always dK or dM. The class of RS CVn-type binary defined by Hall (1976) contains five subgroups: long-period group 1.4. Stellar activity 6

(1d > P > 14d), short period group (P < 1d), the ﬂare star group (hotter component of spectral type dKe or dMe), the group similar to V471 Tau (hotter component is a white dwarf), and the W UMa group. In current terminology the W UMa-type contact binaries keep their identity as a separate class and are not included with RS CVn stars. RS CVn and BY Dra systems are discussed in 1.5 along with other active stars. § In these active binary systems the companions are forced to rotate rapidly due to tidal interaction and often have rotational periods which are synchronised with the orbital periods. Active binary systems display regular eclipsing behavior, and are important for the study of stellar magnetic activity for several regions. The physical parameters of companion stars, such as mass, radius and luminosity ratios may be independently derived from orbital analysis of eclipsing systems. Tidally induced rapid rotation also maintains a high level of activity throughout most of the system’s lifetime thereby producing the sample of stars whose magnetic characteristics are essentially unaﬀected by the decrease in rotation rate with age. CABSs are therefore a powerful probe for the currently accepted ideas on magnetic activity in the stars.

1.4 Stellar activity

The stellar dynamo produces the magnetic ﬁeld which in turn drives various activities on the star’s surface and also in its atmosphere. The magnetic activity indicators such as starspots analogous to the sunspots, chromospheric and transition region activity, ﬂares, and coronal X-ray and radio emission are some of the common characteristics to be discussed below.

1.4.1 Starspots: A photospheric feature

The local strong magnetic ﬁeld of the active star hinders the convection that brings the energy from interior of the star to its surface (photosphere). This process forms a nearby dark region on the surface of the star, called starspots. These starspots are cooler than the surrounding photosphere of the star. The relative coolness of sunspots is evident by the existence of absorption bands of TiO molecules which would normally be disassociated at photospheric temperatures (Tandberg-Hanssen 1967). Most of the known facts about starspots on active binaries, and other single active stars 1.4. Stellar activity 7

B R I G H T N E S S −180 0 +180

Stellar longitide

Figure 1.3 A schematic diagram to the show the variability in brightness due to inhomogeneities (cool spots) on the surface of a star.

comes from the study of low amplitude quasi-sinusoidal light variation commonly seen in their broad-band light curve. A schematic diagram to show the variability mechanism is shown in Figure 1.3. The initial suggestion that these light variations were caused by starspots was made by Kron (1947) nearly 60 years ago. However, it was not taken se- riously until Hall’s (1976) study. He indicated that the star spots hypothesis is linked to chromospheric activity. The dark starspots in CABS and other active stars are typically 300-1200 K cooler than the star’s photosphere, and cover up to 30-40% (see Table 1.1) of the star’s surface (Eaton & Hall 1979; Dorren et al. 1981; Dorren & Guinan 1982; Rodono´ et al. 1986; Strassmeier et al. 1991). Star spots on tidally synchronized binaries have been observed to display additional modulations at a period close to the binary revolution period. Such wave-like distortions in the light curves of these systems are interpreted as spot migration to higher latitudes and are direct analogous of latitudinal evolution of sunspots. The existence of the starspots has also been veriﬁed and studied spectroscopically using the Doppler imaging technique developed by Vogt and Pernod (1983). With Doppler imaging the presence of dark regions on the surface of a star is determined from the small dis- 1.4. Stellar activity 8

tortions the spot produces on the rotationally broadened line proﬁle. This method permits the reconstruction of the surface brightness distribution of the rotating star. The Doppler imaging method requires high signal-to-noise ratio and high resolution spectroscopy along with good phase coverage.

1.4.2 Eﬀects of activity on photometric colour

The activity of cool stars affects the overall properties of the photosphere of a star in its intrinsic mean colours. Generally, an active star is redder when at its minimum brightness, in agreement with the hypothesis of cool starspots as the cause of the photometric variations. However, evidence of B-V and, more strongly, U-B colour curves being anti-correlated with the V light curve have been provided for very active systems, like UX Ari and HR 1099 (Catalano et al. 1996) and MM Her (Tas et al. 1999) indicating the presence of a distribution of hot spots (plages, fculae, promonances and flares) on the photosphere of the star. One of the most remarkable properties sometimes attributed to CABS is the evidence of infrared (IR) excess related to the presence of diffuse circumstellar matter. The existence of this non-stellar component in the flux distribution of active binaries has been the object of controversy. Some studies discarded this possibility (Antonopoulou & Williams 1984; Berriman et al. 1983), while other argued in favor of it (Verma et al. 1987; Lazaro 1988). Scaltriti et al. (1993a) suggested that IR excess is not modulated by the spot activity but is due to the presence of a circumstellar shell. Also, several RS CVn and BY Dra binaries have small, variable amounts of linear polarization (< 0.1%) at optical wavelengths that are the best interpreted as the result of scattering from cool circumstellar material (Scaltriti et al. 1993b). However, Reglero et al. (1990) find the opposite effect to that found by Scaltriti et al. (1993a) in the proto-type RS CVn binary.

1.4.3 Spot cycle and diﬀerential rotation

Many of the active stars show evidence of a long term variation in the light amplitude and in the mean light level of their light curves that could be similar to the 11 years solar activity cycle (Rodono´ 1981; Evren 1990 ; Ibanoglu˘ 1990). Hall (1990) and Henry et al. 1.4. Stellar activity 9

(1995a) found cyclic alternating changes in the orbital periods of CABS and concluded that this may be due to the solar type magnetic cycle. The change in the orbital periods of close binaries is due to the variation of gravitational acceleration of the companion star, which is induced by a change in angular momentum and the magnetic field distribution. (Appelegate 1992; Lanza 1998). Dorren & Guinan (1990) found an activity cycle in V711 Tau ( G5V+K0IV; P = 2.84d) with a period of 11-14 years. Single late type stars also show the activity cycles. Recently, Jarvinen¨ et al. (2005) found 20 years spot cycle in a single active star AB Dor (K0V; P=0.51479d). Henry et al. (1995a) have proposed other indicators of activity cycle, i.e. the modulation of mean colour indexes. Differential rotation is a fundamental ingredient of the magnetic dynamo theory. It makes the observation of differential surface rotation important (Gilman 1980). In active stars, differential surface rotation provides a consistent explanation of wave migration or changing periods observed in the light curve (Baliunas & Vaughan 1985). Two types of behavior in the time series photometry imply the surface differential rotation. First, a significant change in period from one observing duration to the next. A change in period can also be due to different latitudinal position of the active region from one epoch of the observation to other. Second, two periods can also be present simultaneously in an observing season, which suggests two active areas rotating differentially with respect to each other as they formed at two different latitudes. Using the Doppler imaging technique, Hatzes (1998) concluded that in very active stars the relative amplitude of latitudinal differential rotation is one or two orders of magnitude smaller than in the Sun. Similar conclusions were also drawn by Donati & Cameron (1997) and Vogt et al. (1998), who studied the stars AB Dor and HR 1099, respectively.

1.4.4 Chromospheric and transition region activity

The chromosphere being a narrow part of the atmosphere above the photosphere is not normally visible without special observing techniques. Its main characteristic being a rise in temperature with height and complex temporal changes in structure (see Figure 1.1). One of the distinctive characteristics of the active stars is strong CaII H (λ3968) and K(λ3934) emission and sometimes Balmer Hα (λ6563) and Hβ(λ4861) emission. In the Sun these emissions arise from the plages like region and chromosphere. Solar-type stars showing 1.4. Stellar activity 10

enhancement of these lines are called chromospherically active stars. By analogy with the Sun, it is widely accepted that the CaII emission in late type stars is associated with magnetic structure. The Ca II H and K lines of the active stars often display a modulation in intensity. It is hypothesised that the emission originates in solar-like plage regions and modulation is caused by these features rotating in and out of view on the stellar disk (Buzasi et al. 1987). The other important spectroscopic indicator of the chromosphere in late- type stars include Mg II h (λ2803) and k(λ2796), Lα (λ1216), He I(λ10830, 5876), O I(λ1305, 1355), Si II (λ1808, 1817) and continua in the ultraviolet and infrared (Linsky 1980, Vilhu & Walter 1987). The Ca II and Mg II features are amongst the most readily observed of these diagnostics, consequently the surveys of these chromospheres generally are based on these lines. The presence of C II(λ1334, 1335) and Si III(λ1206, 1892) emission lines, which are likely to form at about 16,500 K temperature when a plateau exists at the top of the chromosphere as appear likely for the sun are indicative of the heated region above the chromosphere. This region is commonly known as transition-region. The other emission feature in this temperature range are C III (λ1175,1909), Si IV (λ1394,1403), C IV (λ1548, 1551), N V(λ1238, 1242) and O V (λ1371). Chromospheric and transition region activity is tightly related to the rotation and convection of active stars and other single G-K stars (Vilhu, 1984). The rotation and convection

are parameterized by the Rossby Number (R0 = P/τc; where P is period and τc is convec-

tive turnover timescale∗). The ratio of the total TR emission ﬂux relative to the bolometric

flux (FTR/Fbol) is plotted against the R0 (see Figure 1.4). As shown, there is a very tight relation between FTR/Fbol and R0 for more slowly rotating single stars (including the Sun) and RS CVn-type binaries for the value R 0.4. For more rapidly rotating active stars 0 ≥ ( R 0.4) the strength of net TR line flux levels off and remains nearly constant at log 0 ≤ (F /F ) 4.4. This upper limit is interpreted as a saturation limit in which stars sur- TR bol ≈ − face is completely filled with emitting structure and active regions (Vilhu & Walter 1987). Ayres et al. (1995) found strong correlation between TR and chromospheric fluxes in the

1.5 1.5 form of FTR/Fbol = 10− (FMgII/Fbol) .

∗τc = vc/2l, where vc is convection velocity and l is characteristic length of convection. The value of τc can be determined empirically from spectral type or (B-V) colours of the star (Noyes et al. 1984; Stepien 1990) 1.4. Stellar activity 11

Figure 1.4 Ratio of the total transition-region emission ﬂux to the bolometric ﬂux (FTR/Fbol) is plotted against the Rossby number ( from Vilhu 1984)

1.4.5 Coronal X-ray emission

Cool stars with convective envelopes generate magnetic fields via an internal dynamo mechanism. Convective motions and differential rotation “wind up” the magnetic field lines. The magnetic field emerges from the stellar surface, traps and heats a tenuous coronal plasma to millions of degrees, which then emits X-rays. The mechanism by which the X-rays are emitted from the coronal plasma is ’Thermal Bremsstrahlung’. The X-ray lu-

29 32 1 2 5 minosity of the active late-type stars ranges from 10 to 10 erg s− , which is 10 − times more than the X-ray luminosity of the Sun. Figure 1.5 from Randich et al. (2000) shows a plot of normalised X-ray luminosity versus Rossby number. As shown in the plot, there is a tight correlation between the normalised X-ray luminosity and Rossby number for the less active, slowly rotating stars up to R 0.2. At fast rotation rates (i.e. R 0.2), X-ray emission reaches maximum level 0 ∼ 0 ≤ value near log (L /L ) h 3.0. However, as discussed by Vilhu (1984, 1987), the leveling x bol − oﬀ of X-ray for the most active RS CVn and BY Dra stars is at R 0.5. 0 ≤ The coronal X-ray emission is well correlated with the transition-region ﬂux and chro- 1.4. Stellar activity 12

Figure 1.5 Ratio of X-ray to bolometric luminosities (logLx/Lbol) as a function of log of Rossby number (log R0), compiled from samples of open cluster stars. Key to the symbols: circle: pleiades, squares: IC 2602 and IC 2391, stars: α Per, triangle: single Hyades stars, crossed triangles: Hyades binaries, diamonds: IC 4665, ﬁlled symbols: ﬁled stars (Randich et al. 2000)

mospheric emission. The standard relation between normalised luminosity from transition- region emission (e.g. C IV) and coronal X-ray luminosities is non linear, with power-law slope of about 1.4-1.5 (Vilhu 1984; Agrawal et al. 1986; Haisch et al. 1990; Ayres et al. 1995). The power-law becomes steeper if the chromospheric lines (e.g. Mg II) are L used. The form of these relation are Lx ( LCIV )1.5 and Lx ( MgII )3.0. The non-linearity Lbol ≈ Lbol Lbol ≈ Lbol in the corona-transition region luminosity-luminosity relation explained by the increasing coronal temperatures with increasing activity, bringing a progressively larger fraction of the emission into the X-ray band ( Ayres et al. 1996).

1.4.6 Coronal radio emission

Since most of the radio emission observed in the sun is a consequence of magnetic activity, it is not surprising to ﬁnd that active stars are radio sources. The possible radio emission mechanism in coronal type stars are: 1.4. Stellar activity 13

i) Free-free emission from chromosphere and coronae: The thermal free-free emission (also called Bremsstrahlung) is one of the emission mechanism that must always be present at some level from a partially ionised plasma. It is the dominant emission process in the absence of relativistic electrons and magnetic field. ii) Gyroresonance emission: When a plasma contains a magnetic field, acceleration due to particle can often be negligible in comparison with those due to gyration around the field lines. In place of Bremsstrahlung, there is gyroresonance (or cyclotron) emission in the case of non-relativistic particles (Lorentz factor γ = 1). iii) Gyrosynchrotron emission: This is the semi-relativistic (γ < 3) extension of cyclotron

7 9 emission process for electrons with temperatures of 5 10 − K, or nonthermal energy of × 10-100 keV (Gudel¨ 2002). The gyrosynchrotron emission from high-energy (nonthermal) particles is only conﬁrmed to be present in the Sun during solar ﬂares. In most of the active stars, gyrosynchrotron emission appears to be a near-continual process rather than the highly sporadic process as it is in the sun (Drake et al. 1992).

14 17 1 1 The radio luminosity of late-type active stars ranges from 10 − erg s− Hz− (Drake et al. 1989, 1992; Gudel¨ 1992) The radio luminosity of CABS is well correlated with the X-ray luminosity. For example, RS CVn (see 1.5.1) and Algol (see 1.5.5) binaries, one § § 1.0 1.4 ﬁnds a correlation between radio and X-ray luminosities, L L − (Drake et al. 1989, rad∝ x 1992; Dempsey et al. 1997; Padmakar et al. 2000), whereas for late-type dwarfs, a rather tight linear correlation appears to apply (Gudel¨ et al. 1993). The most straight forward reason for this correlation is that hot plasma emits both thermal X-ray and nonthermal gyrosynchrotron radiation (Drake et al. 1989, 1992).

1.4.7 Flares

A common feature of all the active type stars is the property of flaring at optical, UV, radio and X-ray ranges. Flares arise as a consequence of a sudden energy release and relaxation process of the magnetic field in stellar atmosphere. Time scales of flares range from a few seconds to minutes for the initial impulsive phase, and from tens of minutes to several hours

2 4 for the decay phase. The average ﬂare duration is 10 − s (Kuijpers 1989). The total energy

34 36 2 4 release during the ﬂare (in all wavelengths) is 10 − erg, i.e. 10 − times more powerful that the solar analogue (Byrne 1989). 1.5. Various types of active stars 14

In most active stars, presence of the He I D3 emission line is the indicative of the optical flare like activity (Zirin 1988; Montes et al. 1996). The highly variable coronal emission in a short time (few minutes to several hours) is indicative of the X-ray flares (Gudel¨ 2004; Favata & Micela 2003). During the X-ray flare the coronal temperature increases to 6 10 107K. During the radio flare the value of radio luminosity reaches to − × 14 18 1 1 10 − erg s− Hz− (Byrne 1989). Flaring presumably provides a reservoir of power-law electrons needed for gyrosynchrotron emission process. The apparent existence of long- lasting nonthermal radio emission in most of active stars may be due to the low-amplitude flaring.

1.5 Various types of active stars

All the common properties of the active stars have been presented in 1.4. The level of the § activity also depends on their evolutionary status. In this section we discuss various types of active stars based on their evolutionary status.

1.5.1 RS Cannum Venaticorum (RS CVn) binary stars

The RS CVn type binaries named after the prototype are a particular class of the active binary systems which were originally deﬁned by Hall (1976). In an RS CVn binary, the two stars are usually tidally locked so that the rotational period of each star is approximately the same as the orbital period; however, the two stars are not undergoing mass transfer (i.e. they form a detached system). One star is generally a spectral type F to G dwarf or a subgiant that is 1000K hotter than its companion, which is usually a G to K type giant ∼ or sub-giant. In the more recent deﬁnition of the RS CVn class, there is no restriction on the spectral type of the secondary star or on the orbital period, except for the evolutionary constraint (Fekel et al. 1986). The prerequisites for membership of this class of stellar systems is that binaries have orbital periods between 1 and 14 days, contain at least one component of spectral type F-G V-IV and the Ca II H and K lines are in emission outside of eclipse. RS CVns have been further subdivided into three groups according to their orbital period: the short period (P 1 d), classical (1d P 14 d), and long period (P 14 ≤ ≤ ≤ ≥ 1.5. Various types of active stars 15

Table 1.1 Summary of activity indicators of active stars. In addition the corresponding properties of the Sun are included for the comparison 4 4 6 6 10 10 10 10 × × 25. 11 2 27 0 0 × × 13 . . . − = − - 0 - 2 4 1 1 10 10 G2 Sun ot ≥ − − − − 10 r ∼ 10 1 2 7 9 P . . 1200-1600 0 0 ∼ ∼ ∼ ∼ 40 32 . − 0 disk 31 - - - - - ? ? ? ? ? − + yes CV 10 06 wd . ∼ 0 semi-detached 7 15 10 10 8 . 30 7 − 10 V 0 6 7 15 1000 7 × − × − − 10 5 29 − − 6 − K 10 10 Uma 10 yes - × − 5 14 dMe 10 10 ∼ ∼ 22 − contact 4 F . 2 W ∼ 500 10 ∼ 0 5 ∼ ∼ ∼ ∼ (UV) 6 7 17 6 10 10 7 31 V 10 800 8) 10 V (X-ray) 10 7 − − − × × (RADIO) 6 20 − − × 29 − (7 K A 10 7 REGION 5 − A − yes 10 2 - 5 15 OSPHERE 10 − Algol ∼ − 1 F − ∼ 500 10 T ON ∼ B5-F2 3 10 5 ∼ ON OMOSPHERE . 1 ∼ 1 ∼ ∼ semi-detached PHO COR COR CHR ANSITION T 7 5 5 . . 0 -III . 10 d 6 7 7 31 15 III IV − − − − × 6 7 5 5 Com – 10 – – . . . — 5 6 . 29 13 10 ∼ Single 5-15% 2 0.5-5 G-K 10 FK G-K 200-1350 10 10 ∼ – 6 no 6 yes 6 7 10 7 31 17 = 10 = 8) × -III 30 1200 − − − -IV 10 − × 5 6 20 − V 29 15 20 − − IV (7 CVn 20 7 − − 5 − − 10 5 > 2 10 10 − < 5 1 . 10 ∼ 10 RS b ∼ detached 3 500 b ∼ 1 ∼ ∼ G-K G-K or ∼ or ∼ ∼ P P 6 6 7 no yes 10 7 14 10 30 9) 20 0 10 = . × = 1000 20 6 − − × 10 2 − 3 − Dra 5 3 29 − − . 10 5 (11 5 6 × − . 2 > − 5 < 10 − ∼ 0 4 0 b dK-dM dG-dM 10 . BY − b ∼ detached 10 300 1 ∼ 1 ∼ or ≥ 8 or ∼ . ∼ ∼ P P 1 (d) ) ) ) ) ) .) 1 1 1 1 b v − − − − ) K bol ype or s s s 1 I 2 2 2 Co T type spot) F P I − Hz V > Period − − − K K x / I x g s sec) - cm 1 / 1 2 6 = C L F T M io g − T T L cm cm cm F s ∆ F ad ot rot. surf. r / r (pri Property g g g (er Starspots g < F P Binary Spectra ( (phot. Synchronized (er (er (er (% (er Orbital 1.5. Various types of active stars 16

d) groups. For the systems with smaller orbital periods the stars almost certainly rotate synchronously and are tidally locked producing high rotation rates. De Campli & Baliunas (1979) and Scharlemann (1981) considered the tidal forces in such a system in relation to both the circularization of the orbit and the spin-up of rotational period resulting in synchronism. In most cases, when orbital period is less then about 20 d, the star rotates synchronously so that the upper limit for the period of classical RS CVn stars should be extended to 20 d (Linsky 1988). ≈ RS CVn systems evolve from normal non-emission main-sequence binaries, acquiring their properties only after entering the Hertzsprung gap (Popper & Ulrich 1977). A related class of the objects are the BY Dra (main-sequence) binaries (see below). More recently, Barrado et al. (1994) and Montesinos et al. (1988) confirmed the evolved stage of RS CVn components. Their location near the base of the giant branch where hydrogen shells can ignite and envelope expansion can occur shows that convection zone can be significantly altered from main-sequence stars. RS CVn stars have low amplitude quasi-sinusoidal light variations due to the presence of large, dark starspots. The starspots are 500-1200 K cooler than the surrounding photosphere, can cover upto 30% of the stellar surface (Doyle et al. 1988). Ramsey (1990) pointed out that most RS CVn binaries have excess TiO absorption in their spectra which may be ascribed to the presence of starspots. Solar-like structure in the RS CVns extends into coronal regions. They are known X-ray (Walter et al. 1980; Caillault 1982; Rengarajan 1983; Schrijver et al. 1984; Dempsey et al. 1997; Drake et al. 1989; Singh et al. 1996a) and radio emitters (Mutel & Lestrade 1985; Moris & Muttel 1988; Drake et al. 1989). The nonthermal radio emissions (gyrosynchrotron) is one of the few direct indicators of magnetic fields. In the soft (0.1 - 2.0 keV) X-ray band, the luminosities of RS CVn bi-

29 32 1 naries typically lie in the range of 10 10 erg s− (Drake et al. 1989), compared to − 25.5 29.5 1 10 10 erg s− for normal late-type stars (Schmitt & Liefke 2004). VLA and ATCA − observations at cm wavelengths have shown that the radio luminosities of RS CVn systems

14.5 18.5 1 1 are in the range from 10 to 10 erg s− Hz− (Drake et al. 1986, 1989, 1993), which

15 1 is also enhanced compared to that found for other late-type stars, typically 10 erg s− ≤ 1 Hz− (Gudel¨ 2002). 1.5. Various types of active stars 17

1.5.2 BY Draconis (BY Dra)

BY Dra stars are a class of late K and M type dwarfs which exhibit photometric rotational modulation of few hundredths to a few tenths of a magnitude (Bopp & Evans 1973). The orbital or rotational period of BY Dra is in the range of 0.5 - 20 d. As originally defined by ≈ Bopp & Fekel (1977), BY Dra types may include active single main-sequence star as well as a members of detached binary system. In alternative definition of active binary systems by Fekel, Moffet & Henry (1986), the systems with F- and G- type dwarfs primaries are now classed as BY Dra binaries rather then the sub-type of RS CVns. BY Dra binaries typically rotate synchronously with their orbital period, but there are more than 40 systems (Glebocki & Stawikoski 1997) which are known to rotate asynchronously, e.g. the prototype K3.5V + K3.5V binary system BY Dra which has a rotational period of 3.84 d and an orbital period of 5.98 d. The late spectral type BY Dra stars tend to more often exhibit Hα emission and more frequent flaring activity than the RS CVn systems, but this is probably mostly due to the greater contrast of their chromospheric lines relative to their weaker photospheric emission. The evolutionary status of the BY Dra is not clear. Vogt & Fekel (1979) suggested that BY Dra systems are in the final stage of pre-main-sequence evolution. Soderblom (1990) assigned an age of 1-2 Gyr for the systems in general. Eker (1992) finds BY Dra systems with kinematic properties comparable to both young and old disk population. The BY Dra systems are weaker X-ray and radio emitters than RS CVn systems. This may be due to the smaller surface area than the RS CVn systems. The X-ray luminosity

28.5 30 1 of the BY Dra systems is of the order of 10 − erg s− (Drake 1993), which is 10-100 times less than the RS CVn systems. The radio luminosity of BY Dra systems ranges from

12.5 15 1 1 10 10 erg s− Hz− (Drake 1993). −

1.5.3 FK Comae Berences (FK Com)

FK Com stars were ﬁrst deﬁned as a new group of active stars by Bopp & Rucinski (1981) and Bopp & Stencel (1981). FK Com stars are late-type (G or K) giants with rotation of period only a few days. Spectroscopic observations reveal rotational velocity of these stars

1 of 50 - 150 km s− . These star do not show any signiﬁcant periodic radial velocity variations 1.5. Various types of active stars 18

and therefore are most likely single stars. The photometric variability in FK Com stars is due to non-uniform surface brightness. The photometric and spectroscopic characteristics of FK Com stars are very similar to those of the very active RS CVn stars ( 1.5.1), with § the exception that RS CVn stars are close binary systems in which the tidal effects produce synchronous rotation and therefore also rapid rotation. The evolution of FK Comae stars is still debated. A few evolutionary scenarios have been proposed for explaining the odd rapid rotation of late-type single stars. According to Bopp & Stencel (1981), FK Com are the final product of the coalesced close binary system such as W Uma i. e. of a binary system where one component has been absorbed by the other through first Lagrangian point to form single rapidly-rotating star surrounded by a disk (Webbink 1976). The Kinematics and age of FK Com support this hypothesis (Guinan & Robinson, 1986). Fekel (1988) and Simon & Drake (1989) have suggested that FK Com originate from early type, rapidly rotating single star as they evolved into giant domain. Fekel & Balchandran (1993) argued that the detection of lithium in these active giants is evidence against binary coalescence. They considered a scenario in which the surface convection zone reaches the rapidly rotating core just as a star begins its first ascent of the giant branch, and dredges both high angular momentum material and freshly synthesises Li to surface. FK Com possess extensive convective zone and are known to be magnetically active. Activity related emission of FK Com has been observed in all accessible bands from X-ray (Walter & Bowyer 1981) to the radio domain (Hughes & McLean 1987).

1.5.4 W Ursae Majoris (W UMa)

W Uma systems are eclipsing contact binaries with spectral types between F and K, and orbital period from 0.2 to 1.5 d (Rucinski 1998) but strongly peaked between 0.25 - 0.6 d. The minima in the light curves are of almost equal depth, indicating similar surface temperature of the components. Because of extremely rapid rotation rates, which are only rarely encountered in single stars, W UMa systems are expected to show high level of chromospheric and coronal activity. The light curve of the W Uma systems frequently show asymmetry and undergo changes in shape, height, and depth with time. These properties are explained in terms of the presence of dark spots on the surface of active component of 1.5. Various types of active stars 19

the W UMa systems. Most W UMa systems are strong X-ray sources with typical X-ray luminosity L x≈ 29 31 1 10 − erg s− (Cruddace & Dupree 1984; Rucinski 1985; McGale at al. 1996; Stepien et

30 1 al. 2001). The average X-ray luminosity of W Uma systems is 1.5 10 erg s− (Stepien et × al. 2001), which is more than the average luminosity of the similar main-sequence BY Dra systems (see above). The radio emission in W Uma type stars seems to be low as compared to the RS CVn-type stars. It appears that the ratios of radio to bolometric luminosity of

12 11 8 7 L /L 10− to 10− much smaller relative to the values of L /L 10− to 10− rad bol' rad bol' observed for active RS CVn and Algol binaries (Drake et al. 1986; Rucinski & Seaquist 1988; Vilhu et al. 1988).

1.5.5 Algol binaries

Algol binaries are interacting semi-detached systems with B-to-early-F primary components and less massive, G-to-K secondary companions that are in contact with their Roche equipotential surfaces. They appear to have formed from previously detached binaries in which the originally more massive star evolves off the main sequence, expands to its Roche lobe limit and is losing as well as transferring mass and angular momentum to its companion and the interstellar medium. Unlike RS CVn and BY Dra, Algol-type binaries have only one of the component of late spectral type that shows chromospheric activity. Chro- mospheric activity in Algol systems is rather difficult to detect because the cooler (=active) component in these system is in contact with Roche lobe and mass loss and mass transfer from the cooler, Roche-lobe filling star frequently produce light variations and spectroscopic features. Since the cooler component of Algol systems have spectral type and rotational characteristics similar to RS CVn stars, it is probable that they have similar level of activity. This contention is supported by X-ray and radio studies of these systems. All the important chromospheric properties of Algol type binaries are summarised in Table 1.1. Similar to other active stars, Algols are also X-ray (Singh et al. 1995, 1996a) and radio (Slee et al. 1987; Stewert et al. 1989) emitters. The X-ray luminosity of Algol binaries is 3 4 times less than the RS CVn systems (Singh et al. 1996a). The radio ∼ − properties of the Algol systems appear similar to the more common RS CVn binary. The

16 1 1 average radio luminosity of 1.6 10 erg s− Hz− found for the Algol systems is similar × 1.5. Various types of active stars 20

to the average luminosity of the RS CVn systems (see above and Moris & Mutel 1988).

1.5.6 Cataclysmic Variables (CVs)

CVs are a diverse class of short-period semi-detached binaries consisting of an accreting white dwarf primary and a low-mass main-sequence secondary star. They are believed to be the results of a common envelope evolution of an initially much wider binary system. During its red giant or asymptotic branch phase the more massive primary component expands to a degree where it engulfs the less massive secondary which is still on the main sequence. Frictional energy and angular momentum loss helps to expel the common envelope and at the same time causes a substantial shrinking of the binary orbit. One of the possible results of this evolutionary phase is a detached white dwarf - red dwarf pair in a close orbit which may further shrink on longer time scales due to angular momentum loss via gravitational radiation and magnetic breaking until the Roche lobe of the secondary gets into contact with the surface of the red dwarf and stable mass transfer from the secondary to the primary is initiated (Bruch & Diaz 1999; Warnar 1995). The orbital periods of CVs typically range from approximately 0.6 day to 0.06 day. These stars generally have rotational periods of 10 times faster than the BY Dra stars. ∼ Because of their tidally induced rapid rotations and late spectral types (implying deep convective zone), the cool components should have extremely high levels of dynamo-related magnetic activity. However, most of the luminosity of a CV binary is produced from the release of gravitational energy of matter transferred from the cooler star to a viscous accretion disk. Because of this, it is diﬃcult to study the direct properties of the cool star. However, observational tests of magnetic activity cycles in the secondary stars of CVs can be performed by accreting the long-term observations of the systems. Such cycles were found by Bianchini (1988, 1990) in long term visual magnitudes of some CVs. Recently, Ak et al. (2001) found the cyclical variation (period = 3- 29 years) in the quiescent magnitudes and outburst intervals of 23 CVs produced by the solar-type cycles of the late-type secondary components. They have found no correlation between cycle parameters (i.e. cycle period, cycle amplitude), and other system parameters such as orbital period, mass of primary and secondary star. Horne & Saar (1991) observed Balmer emission line from accretion disk of some CVs and show similar behavior between emission and period as 1.6. Stellar dynamo mechanism 21

chromospherically active stars. Further evidence in support of magnetic cycles in CV is provided by Warner (1988). He has investigated the changes in orbital periods of some eclipsing CV systems and ﬁnds that the timescales and the magnitude of observed period changes are consistent with magnetic activity cycle hypothesis.

1.6 Stellar dynamo mechanism

A possible correlation between rotation and chromospheric activity in late-type stars was pointed out by Kraft (1967) and this is now interpreted in terms of dynamo theory of magnetic field generation. This hypothesis suggests that late-type stars have a magnetic fields generated by a dynamo mechanism, that field generation depends on differential rotation and cyclonic convection. The key mechanisms of the dynamo, rotation and magnetic activity processes in late-type stars are illustrated in Figure 1.6. Convection appears to be necessary for the evolution of key processes occurring in late-type stars such as angular moment loss and magnetic field generation. As in the sun, stellar dynamo is thought to be located in the layer at the bottom of convective zone (CZ) (Brandenburg et al. 1994). The dynamo at work in a solar-type star is thought to depend on the interaction between the twisting effect on the field induced by the convective eddies (the α effect) and the − shearing of the field’s toroidal component by star’s differential rotation (the Ω effect). − The dynamo can operate in various modes, depending on the relative strengths of the α and Ω processes. It is generally accepted that the α Ω dynamo is most likely to operate in late − type stars, since it can successfully account for many of the observed features in the solar cycle (Parker 1979). The efficiency of the stellar dynamo can be calculated by the Dynamo Number (Parker 1979; Noyes et al. 1984) and defined as

α∆Ωd4 N = (1.1) D η2

Where α is the product of mean helicity in CZ and convective turnover time (τc) at the base of the CZ, ∆Ω is differential rotation, d is the characteristic length scale of CZ and η is turbulent magnetic diffusivity. The efficiency of the dynamo may also be related to both rotation period (P) and convective turnover time (τc) of a star through Rossby number (R0). 2 Furthermore, it can be shown that N R− (Noyes et al. 1984; Weiss 1994), implying D ∝ 0 1.7. Motivation of thesis 22

Stellar Evolution Binary companions

Evolving Tidal spin−orbit moment of inertia interaction Convection

(Differential) Loss of spin angular Rotation momentum

Envelope and surface Atmospheric heating Dynamo Process structure wind

Figure 1.6 A diagram illustrating how dynamo process work in cool stars. The dashed lines show processes affecting binaries and magnetic field effects are represented in the shaded box. This plot has been reproduced from Schrijver & Zwaan (1991)

that surface magnetic ﬁeld production and hence magnetic stellar activity should increase with decreasing Rossby number (increasing stellar rotation). The α Ω dynamo is not expected to operate in fully convective stars (e.g. in the low- − mass pre-main sequence and main sequence star of spectral type later than M5). Another type of dynamo depends slowly on the action of the convective eddies (Durney et al. 1993) - thus called α2 dynamo - and can therefore be at work also in fully convective stars.

1.7 Motivation of thesis

Strong X-ray and non-thermal radio emission in late-type stars are well-known indicators of enhanced coronal activity (Drake et al. 1992). Ayres and collaborators have shown

6 7 (e.g., Ayres et al. 1995) that the emission from coronae (T 10 − K) and chromospheres e ∼ (T 104K) are closely correlated, and thus stars with intense coronae will also have e ∼ strong chromospheric emission. Many active stars have been identiﬁed as such through their above-average X-ray and radio emission. Recently it was found that late type stars 1.7. Motivation of thesis 23

Table 1.2 The sample of active stars 12 Object α δ V Spectral F ( 10− ) F 2000 2000 X × rad 2 1 (mag) type erg cm− s− mJy

h m s FR Cnc 08 32 30 15◦4902600 10.24 K5V 1.7 0.4 - h m s HD 81032 09 22 53 -13◦4902100 08.60 K0IV 3.9 0.4 0.68 0.05 h m s HD 955559 11 02 02 22◦3504600 08.35 K1V 6.6 0.4 - h m s HD 160934 17 38 39 61◦1401600 10.00 K7V 3.8 0.1 - h m s LO Peg 21 31 01 23◦2000700 08.82 K3V 5.5 0.3 3.6 0.5 constitute a signiﬁcant fraction (about 25 - 40 %) of the content of the X-ray surveys with Einstein, EXOSAT and ROSAT. However, the nature of most of these X-ray sources is not fully understood and it is possible that many of them may be chromospherically active. The chromospherically active nature of the stars can be judged from the study of low amplitude quasi sinusoidal light variation commonly seen in their broad band light curve and Ca II H and K line emission. So detailed photometric and spectroscopic study will help us to understanding these sources. The main aims of thesis are:

a) Search for optical variability in a sample of soft X-ray sources at least in three broad band B, V and R and to ﬁnd the periodic nature of their optical variations.

b) Determine the presence and evolution/migration of star spots.

c) Study the chromospheric emission lines (Hα, CaII H and K) , their variability and correlation with photometric light curve.

d) Study the X-ray emission, X-ray light curve and low resolution X-ray spectra and correlation of X-ray emission with radio emission and other physical parameter like rotation.

The details of the sample under study are given in Table 1.2. 1.8. Organisation of thesis 24

1.8 Organisation of thesis

The thesis consists of six chapters including this ﬁrst chapter on the intruducing the subject mtter related to thesis. Chapter 2 contains the description of the instruments, data acquisition, basic data reduction and analysis procedure used in this thesis. Detailed optical photometric, spectroscopic, X-ray and IR studies of the four main sequence stars (FR Cnc, HD 95559, HD 160934 and LO Peg) are presented in chapter 3. The ﬁrst photometric and spectroscopic studies along with the archival X-ray and IR studies of an evolved star HD 81032 are presented in chapter 4. In chapter 5, we present the correlations between various physical quantities of active stars using a larger sample than before. In chapter 6, we present the principle and performance of the newly commissioned imaging polarimeter at ARIES, Nainital. The conclusions are presented in chapter 7.

Chapter 2

Instruments, Observations, Data Reduction & Analysis Procedure

2.1 Overview

This chapter brieﬂy describes the instruments, data acquisition, basic data reduction and analysis used in the thesis. Optical photometric data for the present study are acquired at Aryabhatta Research Institute of observational -sciencES (ARIES), Naini Tal, while optical spectroscopic data are taken from the Vainu Bappu Telescope (VBT) Kavalur. In addition to optical observations, X-ray data from ROSAT and 2MASS NIR data from archive have also been used.

2.2 Optical Obervations

2.2.1 The telescopes

The sources picked up for the present study are observed using the two telescopes listed in Table 2.1. All the photometric observations were taken from the Sampurnanand telescope of ARIES, Naini Tal. It is a 104-cm aperture Veb Carl Zeiss, Jena reﬂector with f/13 Cassegrain. The synchronous motor provided for the hour angle drive of the telescope runs on the output from a 3-phase, 50 Hz ampliﬁer system. A stable frequency of 50 Hz is generated from a quartz oscillator having frequency stability of better than 1 part in

26 2.2. Optical Obervations 27

Table 2.1 Parameters of Optical Telescope used Telescope Sampurnanand Vainu Bappu Telescope Telescope Place ARIES, VBO, Naini Tal, India Kavalur, India

Longitude 79◦2702400(E) 78◦500(E)

Latitude 29◦2104200(N) 12◦340(N) Altitude 1951 m 700m System Ritchey-Chretien Ritchey-Chretien Focal length Cassegrain: f/13 Cassegrain: f/13

Plate scale 15.200/mm 6.800/mm

107. Further details of this telescope are given by Sagar (1999). For optical spectroscopy we used the 234-cm VBT at Kavalur. The details of this telescope has been given by Chinnappan & Bhattacharyya (1985). The basic parameters of both the telescopes are given in Table 2.1.

2.2.2 The ﬁlters

Filters are primarily used for two objectives: (a) to restrict the wavelength band of the incoming light; (b) to reduce the intensity of the light coming from very bright source. Since the detectors have a wider range of wavelength response and sensitivity, filters are important for the flux measurement of the astronomical objects at various wavelengths. These filters provide information like temperature, colour and other properties of a distant source. Johnson B, V and Cousin R filters were used for the present study. The details of the filters used are listed in Table 2.2.

2.2.3 The detectors

The detectors used for the observations were cryogenically cooled 2048 2048 and 1024 × × 1024 pixel2 CCDs. In each CCD a 24 µm square size pixel at f/13 Cassegrain of 104-cm

telescope corresponds to a square of 0.37 arcsec size, covering a total sky are a of 120 × 2.2. Optical Obervations 28

Table 2.2 Filter glass combination used at ARIES, Naini Tal

Filter λe f f Band width Glass combination of Filter Å Å B 4400 980 GG 385(2) + BG 18(1) + BG 12(1) + KG 3(2) V 5500 890 GG 495(2) + BG 18(2) + KG 3(2) R 6530 2200 OG 570(2) + KG 3(2)

120 in case of the larger CCD and 60 60 in case of the smaller CCD. To increase the S/N × ratio, observations were made in 2 2 binning. A brief description of the CCD camera is × given below. A typical CCD camera used for astronomical purpose consists of a two-dimensional array of photon detectors in a layer of semi-conducting material silicon. Each individual detector in the array is referred to as pixel. Its size is of 24 µm for both the CCDs used in the presents observations. Each individual pixel is capable of collecting the photons and storing the produced electrons, which can be read out from the CCD array to a computer to produce a digital image of the varying intensities of light detected by the CCD. As photons come in contact with CCD surface and electrons build up in the wells (pixels) over the period of its exposure to light (the integration), a digital image is built up consisting of the pattern of electrical charge (intensity) present in each pixel. At the end of the integration period when light is no longer allowed to reach the CCD detector, the accumulated charge in each pixel is transferred to the on-chip ampliﬁer, pixel by pixel. During the read out process of the array, charge must be moved out of the imaging region of the array to a location where the amount of charge can be measured. Rows of pixels are moved in parallel down to a single row (the serial register) which is read out sequentially by Analog to Digital (A/D) converter where it is measured and then recorded. The measuring device is emptied and once again the rows of pixels are moved in parallel to the serial register, then each pixel is read out sequentially. This process continues until all of the pixels have been measured (read out). At a room temperature and for a longer integration time (more than hundred milliseconds) thermal noise is created by the random generation of dark current. Therefore, to avoid the self generated dark signal, CCD must be cooled down to such a low temperature 2.2. Optical Obervations 29

Table 2.3 Characteristics of the CCDs used in the observations

CCD chip size pixel gain read out Dark Current Operating Field of 1 (pixels) size (µ) e−/ADU noise e− /pixel/sec Temperature view Tektronix 1024 1024 24 24 11.98 7e 1 < 5 10 -110 C 6 6 × × − − ◦ ∼ 0 × 0 Wright 2048 2048 24 24 13.7 10e 1 < 5 10 -140 C 12 12 × × − − ◦ ∼ 0 × 0

3000 4000 5000 6000 7000 8000 9000

Figure 2.1 Quantum eﬃciency curve of 2k 2k and 1k 1k CCD × ×

where thermal noise becomes negligible in comparison to the signal received from the astronomical source. Both 1k 1k and 2k 2k CCDs used in our observations were therefore × × cooled to about -110◦C and -140◦C, respectively in a liquid nitrogen dewar to minimize the eﬀect of thermal noise. The characteristics of the CCDs used for our observation are given in Table 2.3. One of its important characteristic is quantum eﬃciency (QE), which is a function of wavelength, and is shown in Figure 2.1. The peak of QE lies at about 7000Å and 6500Å for 1k 1k and × 2k 2k CCDs, respectively. ×

2.2.4 The spectrograph

The intermediate resolution spectroscopic observations were obtained from Vainu Bappu telescope at Kavalur, using the OMR spectrograph designed and built by the Opto-Mechanics 2.3. Optical observations 30

Research (OMR) Inc., Vail, Arizona, USA. It has a 2.5-mm long slit with a minimum and maximum width of 40 µ and 950 µ, respectively. The jaws of the slit are polished in order to help centering and guiding on the object. The collimator is an oﬀ-axis paraboloid

of focal length 1-m, clear aperture of 110-mm and tilt of 6◦. There are four manually in- terchangeable gratings of 150 lines/mm, 300-lines/mm, 600-lines/mm and 1200 lines/mm. Two cameras are available, both are having a clear aperture of 100-mm. The short camera is a semi-solid folded Schmidt of eﬀective focal length 150-mm. The long camera is a folded Schmidt of eﬀective focal length 420-µm. We have used a grating of 1200 lines/mm for intermediate resolution spectroscopy which yields a dispersion of 1.25 Å per pixel.

2.3 Optical observations

Late-type stars FR Cnc, HD 81032, HD 95559, HD 160934 and LO Peg were observed in Johnson B, V and Cousins R filters at the Aryabhatta Research Institute of observational- sciencES (ARIES). The observations were made with the 104-cm Sampurnand telescope to which a 2k 2k CCD in the years 2000 - 2003 and 1k 1k CCD during the seasons 2003- × × 2004, were attached. A log of observations is given in Table 2.4. A number of CCD frames were taken on each night with different exposure times ranging from 2 to 120 s depending upon the seeing conditions and the filter used. Several bias and twilight flat frames were also taken during the observing run ( for detail see the 2.4). § Spectroscopic observations were carried in 2002 - 2003 at the Vainu Bappu Observa- tory, Kavalur with OMR spectrograph fed by the 234-cm Vainu Bappu Telescope (VBT). The data were acquired with a 1k 1k CCD camera of 24 µm square pixel size, cover- × ing a range of 1200 Å and having a dispersion of 1.25 Å/pixel. Several bias, dome flats and arc spectra were also taken for further processing (see below). A log of spectroscopic observations is given in Table 2.5. 2.3. Optical observations 31

Table 2.4. Log of B, V and R observations and standard deviation (σ) of ’comparison (S) - chaeck (C)’ star.

Date Of No.of data σ of S-C Date Of No.of data σ of S-C observations points B V R observations points B V R

FR Cnc FR Cnc 03-05/2/2001 9 0.003 0.006 0.007 19/12/2003* 31 0.008 0.008 0.007 10-12/3/2001 21 0.006 0.008 0.009 21/12/2003* 21 0.006 0.008 0.006 03-07/4/2001 19 0.006 0.010 0.008 22/12/2003* 19 0.004 0.009 0.005 27/11/2001 18 0.004 0.004 0.003 15/01/2004* 10 0.010 0.010 0.006 28/11/2001 19 0.004 0.004 0.005 16/01/2004* 16 0.006 0.007 0.009 29/11/2001 14 0.005 0.010 0.005 17/01/2004* 6 0.008 0.005 0.005 05/12/2001 24 0.005 0.003 0.006 18/01/2004* 17 0.007 0.009 0.004 11/12/2001 25 0.003 0.004 0.007 12/12/2001 9 0.009 0.007 0.005 HD 81032 28/12/2001 13 0.006 0.004 0.008 05/12/00-08/04/01 19 0.011 0.011 0.011 29/12/2001 30 0.007 0.006 0.006 01/11/01-13/03/02 54 0.011 0.009 0.010 01/01/2002 32 0.016 0.015 0.018 17/11/02-06/01/03 24 0.011 0.011 0.010 23/01/2002 14 0.005 0.003 0.006 27/11/03-13/03/04* 25 0.014 0.011 0.010 24/01/2002 28 0.008 0.010 0.010 31/01/2002 12 0.005 0.003 0.008 HD 95559 01/02/2002 26 0.005 0.006 0.010 03/02/2001 8 0.002 0.009 0.008 02/02/2002 27 0.006 0.007 0.008 04/02/2001 9 0.005 0.005 0.007 03/02/2002 27 0.005 0.006 0.005 05/02/2001 10 0.006 0.005 0.006 04/02/2002 16 0.009 0.007 0.009 31/03/2001 5 0.003 0.008 0.008 17/11/2002 22 0.009 0.008 0.007 03/04/2001 7 0.003 0.003 0.004 18/11/2002 18 0.005 0.005 0.010 04/04/2001 6 0.009 0.007 0.004 19/11/2002 22 0.008 0.007 0.006 05/04/2001 9 0.011 0.004 0.011 20/11/2002 23 0.007 0.005 0.008 06/04/2001 8 0.010 0.005 0.010 22/11/2002 18 0.011 0.005 0.010 07/04/2001 8 0.008 0.006 0.009 06/12/2002 16 0.010 0.006 0.007 07/12/2002 11 0.004 0.004 0.005 HD 160934 10/12/2002 14 0.010 0.007 0.009 17/02/01-25/04/01 23 0.011 0.010 0.013 21/12/2002 25 0.007 0.004 0.007 25/12/2002 27 0.008 0.003 0.007 LO Peg 01/01/2003 24 0.007 0.005 0.008 28/09/2001 10 0.008 0.007 0.007 02/01/2003 25 0.007 0.004 0.005 10/10/2001 17 0.010 0.006 0.005 05/01/2003 27 0.006 0.005 0.005 15/10/2001 10 0.004 0.005 0.004 06/01/2003 29 0.005 0.005 0.006 28/09/2002 12 0.010 0.013 0.012 14/12/2003* 17 0.006 0.013 0.011 30/09/2002 7 0.012 0.015 0.006 17/12/2003* 18 0.015 0.009 0.007 01/10/2002 12 0.011 0.005 0.006 18/12/2003* 14 0.006 0.007 0.005 02/10/2002 14 0.011 0.013 0.010 03/10/2002 6 0.012 0.013 0.011

Observations were carried out using 1k 1k CCD ∗ × 2.4. Optical data reduction 32

Table 2.5 Log of spectroscopic observations Object Date of Observation Spectral Range Exposure Time Observation Time Signal-to-noise ratio Å (seconds) (UT in HH:MM:SS) FR Cnc 2002 November 15 3600 - 4800 2400 21:29:00 9.0 3600 - 4800 2400 22:22:00 10.1 2003 January 20 4700 - 5900 1800 17:37:00 12.1 4700 - 5900 1800 18:11:00 14.0 5700 - 6900 1800 16:29:00 25.4 5700 - 6900 1800 17:02:00 29.4 2003 January 21 3700 - 4900 1800 17:47:00 9.0 4700 - 5900 1800 17:13:00 11.0 5700 - 6900 1800 16:39:00 27.1 5700 - 6900 1800 21:46:00 27.7 2003 January 22 3700 - 4900 1800 17:58:00 8.9 4700 - 5900 1800 17:22:00 12.0 5700 - 6900 1800 16:47:00 23.7 5700 - 6900 1800 21:06:00 24.5 2003 January 23 3700 - 4900 2400 17:13:00 8.8 4700 - 5900 1800 16:39:00 13.9 5700 - 6900 1800 16:03:00 25.4 5700 - 6900 1800 17:57:00 26.3 5700 - 6900 1800 20:55:00 25.4 2003 January 24 4700 - 5900 1800 18:05:00 12.0 5700 - 6900 1800 18:42:00 22.6 HD 81032 2003 January 20 3700 - 4900 1800 21:31:00 12.5 4700 - 5900 1800 22:05:00 14.5 2003 January 21 3700 - 4900 1800 18:49:00 14.0 4700 - 5900 1800 19:27:00 18.0 5700 - 6900 1800 20:04:00 34.1 2003 January 22 3700 - 4900 1800 20:15:00 11.0 4700 - 5900 1800 19:38:00 13.5 5700 - 6900 1800 18:59:00 31.5 2003 January 23 3700 - 4900 2400 20:05:00 11.1 4700 - 5900 1800 19:31:00 16.2 5700 - 6900 1800 18:56:00 31.8 2003 January 24 5700 - 6900 1800 19:23:00 24.5

2.4 Optical data reduction

Pre-processing of the images as well as the photometry and spectroscopy were performed using the IRAF ∗ software. The various steps carried out in the processing of the images are summarized below.

2.4.1 Bias subtraction

An image generated from several raw CCD frames taken with no light incident upon the detector and of zero exposure time is a bias frame. Bias in the context of CCDs is the term for the signal added before digitization, in order to avoid the noise creating negative

∗IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Associ- ation of Universities for research in Astronomy, Inc. under co-operative agreement with the National Science Foundation 2.4. Optical data reduction 33

values at the readout of a pixel. The bias level of the CCD is determined from several bias frames (generally more than five) taken intermittently during observations in the course of a night. In general, the bias frames were not found to vary during the night. An average bias frame was formed using the zerocombine task in IRAF and applying the minmax clipping algorithm, which was then subtracted from all the image frames, i.e., both target frames and the flat-field frames.

2.4.2 Dark subtraction

Subtraction of a dark frame from each target frame was not carried out for the observations

reported here, as the CCDs used in the observations were cryogenically cooled to 120◦ C − at which the rate of accumulation of thermal charge is negligible for the exposure used in the present observations.

2.4.3 Flat ﬁelding

Since all the pixels in a CCD do not possess the same response, so, it is necessary to correct for pixel-to-pixel variations in the CCD. This was accomplished by taking several twilight sky frames. They were median combined using the task flatcombine in IRAF employing the average sigma clipping algorithm. The combined flat-field frame was then normalized by mode and all the bias-subtracted target frames were then divided by this normalized flat-field frame. This works fine in the case of direct imaging, however in the spectroscopic flat fields the spectrum of the sky or lamp and transmission variations with wavelength are a part of the observations. Therefore, the wavelength dependence of the combined flat is corrected using the responce task, then divided form the target spectra.

2.4.4 Cosmic ray removal

The ﬁnal step involved in the pre-processing of the images is the removal of cosmic ray strikes on pixel(s). Cosmic ray events are typically single-pixel event and easily distinguish

such against clearly broader stellar point spread function†. Cosmic ray hits seen in the ﬂat ﬁelded target frames were removed using cosmicray task in CRUTIL package of IRAF.

†The point spread function (PSF) is a two dimensional brightness distribution proﬁle produced in the detector by the point source object. 2.4. Optical data reduction 34

2.4.5 Photometry

After pre-processing, aperture photometry was performed on both the object and the comparison stars present in each frame. For this, the task apphot in IRAF was used for com- puting the instrumental magnitudes of the objects. The chip co-ordinates of both the target object and its comparison stars, found by the task daofind, were used by phot in order to properly center the apertures over them. A critical input to be specified under phot was the radius of the aperture to perform the photometry. The phot allows us to specify a series of increasing aperture from a optimal small aperture (FWHM of the stellar profile) to larger aperture ( seven times of the FWHM). At the same time care was also taken that the neighboring stars should not start influencing the sky background of the program star. The increment of the aperture was 0.5 pixel. The larger the aperture, the more of the flux from the star is within the aperture. But with larger aperture, the error introduced due to sky subtraction is also large. Thus, the optimal aperture is one which is large enough to enclose most of the flux, but otherwise is as small as possible. The correction for the finite size of the aperture is called the aperture correction. It is computed from a growth curve, i.e. a plot of magnitude within a given aperture versus aperture size. The aperture correction is simply the magnitude difference between the asymptotic magnitude and the magnitude at the given aperture. The most straightforward way to determine the aperture correction is to measure it directly from a number of growth curves. A more advanced method is the DAOGROW algorithm (Stetson 1990), imple- mented in the task mkapfile in digiphot.photcal. It fits a five parameter (with usually only 3 of them free) stellar profile model to the growth curves for one or more stars in one or more images. It then computes the aperture correction from a given aperture to the largest aperture. One of the five parameters in the model, Ri, represent the seeing radius for the individual images. The other four parameters are global for all the images.

2.4.6 Spectroscopy

After debiasing and flat fielding, we converted the two dimensional spectrum of the object into one dimensional spectrum. This was done with the help of aperture selection. An aperture is selected and counts in it are summed together to represent a single pixel. Cor- 2.5. Differential photometry and selection of comparison stars 35

rection for atmospheric extinction is applied in all the spectra. The one dimensional spectra are extracted using apall task, which is based on the extraction algorithm by Horne (1986). This task makes sky subtraction, delivers maximum possible signal-to-noise ratio and takes care of the effects of moderate geometric distortion and cosmic ray hits. The one dimensional spectrum is in the form of intensity versus pixel number. In order to calibrate the pixel-number in the terms of wavelength, it is necessary to take spectra of a laboratory standard source such as an arc-lamp (e.g. Fe-Ar, Fe-Ne), for which wavelength of different spectral features such as emission are known. The wavelength calibration is done using identify, hedit and dispcor task of IRAF. The spectral resolution was determined by using emission lines of arc lamps taken on the same nights. Spectral resolution (δλ) of 2.7 Å at 6300 Å and 3.7 Å at 4000 Å was achieved. After wavelength calibration, we have normalised the spectra by fitting lower order polynomial to a region of continuum judged to be free of the absorption line. Normaliza- tion of the spectra was performed by continuum task of IRAF. The equivalent widths for emission lines were computed using task splot. The error in the measurements of EWs of the Hα, Hβ and CaII H and K lines was computed by measuring the EWs of 4 moderate absorption features at 6494, 6163, 6122 and 6103 Å in each spectra. The standard deviation for each absorption feature was computed from the spectra available. The mean of the standard deviations thus obtained was taken as the error in the measurement of the EWs of all the absorption as well as the emission line features (see also Padmakar et al. 2000).

2.5 Diﬀerential photometry and selection of comparison stars

There are two main methods for doing photometric measurements of the stars: i) All-sky and ii) Differential. In differential photometry one measures the difference between the program and comparison stars. Differential photometry is easier than All-Sky photometry, and provides the maximum accuracy when measuring small variations. With a modest CCD field of view, the process becomes very simple and very effective as the comparison stars are often within the field of the program star at all times. To see any variation in the differential light curve of target star, selection of the comparison stars is very important. 2.5. Differential photometry and selection of comparison stars 36

Figure 2.2 Optical identiﬁcation chart. C1 and C2 in each ID chart represent the comparison and check star. P stands for program star. C3 in the ID chart of the FR Cnc is the comparison star taken during the observing season 2003-2004 2.5. Diﬀerential photometry and selection of comparison stars 37

The comparison star is chosen as close in the brightness and the colour to the target star, and another star called check star is also chosen to check the variability of comparison star (Howell et al. 1988). The V magnitudes and B-V colours of all the program and comparison stars corresponding to the target star are given in Table 2.6 (see also Figure 2.2 for ID chart). The atmospheric extinction and colour of the comparison stars may aﬀect the variability of the program star. The standard equation which is used to correct the observations for both the atmospheric extinction and the colour of the star is

mλ0 = mλ + Kλ0 X + Kλ00cX (2.1)

where mλ0 is the true magnitude, mλ is the observed magnitude, Kλ0 is the principle extinction coefficient, Kλ00 is the colour dependent extinction coefficient, c is the colour index, and X is the airmass. An advantage of performing differential photometry between the target and comparison stars in the same CCD frame is that extinction effects can be ignored as both the comparison stars and the target are seen through nearly identical atmospheric layers. However, second order extinction coefficient can have an effect on the differential magnitude. From equation (2.1) the differential magnitude between two comparison stars of colour index c1 and c2 is given by

∆mλo = ∆mλ + Kλ00X∆c (2.2)

where ∆c = c1 c2 is the difference in colour indices. The principal extinction term − cancels off as both the comparison stars have same airmass. From linear least square fitting of the above relation (equation 2.2) to observations, the second order extinction coefficient

(Kλ00) is found to be negligible (0.003) as compared to the real variability (see also Stalin 2002). The standard deviation (σ) of the ’comparison - check light curve’ is used to assess the photometric precision of the observations. The σ of diﬀerent measures of comparison and check stars are listed in Table 2.4, and indicate that the comparison stars are indeed constant during the observations. 2.6. ROSAT X-ray observatory 38

Table 2.6. Magnitude and colour of program, comparison and check stars

Program Star Comparison Star Check Star V B-V V B-V V B-V

FR Cnc TYC 1392 2110 1 USNO A2.0 1050-05766589 10.24 1.11 10.95 1.10 12.25 0.60

BD +16◦1751 9.51 0.71 HD 81032 TYC 6471 1345 1 USNO A2.0 0750-06845737 8.93 1.04 10.42 0.66 12.55 1.25

HD 95559 HD 95467 BD +33◦2294 8.92 0.85 9.32 1.03 10.20 0.90 HD 160934 TYC 4199 652 1 TYC 4199 590 10.18 1.32 11.10 1.10 12.10 1.30

LO Peg BD +22◦4405 TYC 2188 1288 1 9.24 1.02 9.63 0.50 11.09 1.02

2.6 ROSAT X-ray observatory

ROntgen¨ SATallite (ROSAT) was a soft X-ray observatory built in a co-operative program between Germany, the United States, and the United Kingdom (Trumper¨ , 1990). It was launched into a near Earth orbit on 1 June 1990. It operated for almost nine years until 12 February 1999. One of the main goals of the ROSAT mission was to perform the ﬁrst all sky survey (1990 August to 1991 January) with an imaging X-ray telescope in the energy band of 0.1 - 2.4 keV, possessing an X-ray sensitive factor of about 1000 higher than that of UHURU (Voges et al. 1992, Snowden et al. 1990). During the mission phase, the satellite scanned the sky continuously along great circles roughly perpendicular to the Earth-Sun direction. The ROSAT rotation period was synchronized to the orbital period in such a manner that no Earth occultation occurred. About 6000 sources have been detected in the survey, thereby increasing the number of known X-ray sources by an order of mag- 2.6. ROSAT X-ray observatory 39

Table 2.7 The basic parameters of ROSAT (source: ROSAT Users Handbook) The Satellite: Launch 1990 June 1 Initial Altitude 580 km Inclination 53 deg Period 96 min. X-ray Telescope: Mirrors 4 pairs of Wolter-I mirrors Maximum aperture 83.5 cm Geometric area 1141 cm2 Focal length 240 cm

Grazing angle 1 - 2◦ PSPC: Window size 8 cm (diameter) Entrance window 1 µ m polypropylene

FOV 2◦(diameter) Gas mixture 65 % Ar + 15 % Methane + 20% Xe

Spatial resolution 2500at 1 keV (FWHM) Energy resolution 43% at 1 keV (FWHM) Temporal resolution 130µs ∼ Dead time 250µs

nitude. The survey was followed by a Pointed Observation Phase, where the observatory investigated selected target regions over the entire sky. Usually the target observing time during the pointed phase was appreciably longer than that during the survey. In very deep exposures this resulted in point source sensitives that were a factor 10 higher than those achieved by deep exposure in the Einstein observatory and with appreciably better spatial and spectral resolution in the 0.1 - 2 keV energy band. The ROSAT X-ray payload consisted of an X-ray telescope (XRT) in conjunction with one of the two focal plane instruments - Position Sensitive Proportional Counter (PSPC) and High Resolution Imager (HRI). ROSAT provides a 2◦diameter ﬁeld of view with the 2.6. ROSAT X-ray observatory 40

Figure 2.3 The ROSAT Telescope

PSPC in the focal plane and 380diameter ﬁeld of view with HRI in the focal plane. The basic parameters of the ROSAT X-ray observatory are listed in Table 2.7. A schematic view of the ROSAT XRT is shown in Figure 2.3. The XRT consisted of 4 nested grazing incidence Wolter-I mirror (Wolter 1952) with a maximum aperture of 83.5 cm and a focal length of 240 cm. All of the 8 mirror shells (4 pairs each of paraboloid and hyperboloid mirrors) were constructed of Zerodur ( a glass ceramic with an almost negligible thermal expansion coeﬃcient). The grazing angles the range of 1◦- 2◦, depending upon the sub-shell considered. The collimation of the incoming X-rays leads to a circular

ﬁeld of view with a diameter of 2◦.

2.6.1 The position sensitive proportional counter (PSPC)

The PSPC was a gas-filled multiwire proportional counter (Pfefermann et al. 1987). A schematic diagram showing the arrangement of anodes and cathods is shown in Figure 2.4. It consisted of essentially two separate counters: the first anode (with two cathodes) acted as a position sensing, X-ray sensitive counter, and the second anode as the anti-coincidence counter for background rejection. The mutually perpendicular cathode grids (K1 and K2) were of gold-plated molybdenum wires with a 0.5 mm spacing used to determine the position of events. The A1 anode grid consisted of gold-plated tungsten wires of 1 mm sepa- 2.6. ROSAT X-ray observatory 41 ration used to determine energy of events. The A2 anode was of identical construction as A1 (expect with 2mm wire separation) and used as anti coincidence counter. The anode and cathode grids were contained in a gas-filled counter housing, containing a mixture of 65% Argon, 20% of Xenon and 15% of Methane. X-ray photons enter the PSPC through

2 a 1 µm thick polypropylene ([C3H6]n) window which was coated with 50 µg cm− graphite 2 and 40 µg cm− of lexan ([C12H14O3]). Lexan decreases the UV transmission. The window was essentially opaque at energies just above the carbon edge at 0.286 keV, but transmitted at about 50% level below the edge. The X-ray absorption of the counter gas was close to 100% almost up to 2.4 keV where the X-ray mirrors cut off. An X-ray photon, passing through the entrance window, is absorbed by counter gas producing a photo-electron. The primary electron is thermalized and in the process causes the ionization of other gas atoms forming a secondary electron cloud. The positive ions can also add to this cloud by Auger effect when energetically allowed. The number of electron contained within the secondary electron cloud is approximately proportional to the energy of incident photon. The secondary electron cloud drifts through the K1 cathode grid toward the A1 anode grid. When the electrons of the charge cloud approach close enough to an anode, the electric field strength becomes sufficiently high for the secondary electrons to ionize additional gas atoms (i.e., the energy that the electron gains from the electric field between collisions is greater then the ionization energy of the gas) causing the charge cloud to be amplified by a (gain) factor of 5 104. The avalanche of charge on to the anode leads × to a charge pulse at the anode and an induced signal at the cathodes, which are all processed by charge sensitive pre-amplifiers. The spatial information is determined by measuring the center of gravity of the charged electron cloud at the cathode wires, K1 and K2. The point response function (PRF) of the PSPC plus XRT depends on the off axis angle and the energy as well. It is in the 2000 - 5000 range for energy between 0.2 to 1.5 keV for on-axis sources. It increases to 40 - 50 for a source located 500 off-axis. The PSPC ∼ 0.5 has a spectral resolution of ∆E/E = 0.43(E/0.93)− (FWHM, E in keV) and operates in the energy range 0.1 - 2.4 keV. The PSPC has a dead time of 0.25 ms and a temporal ≈ resolution of 0.13ms. 2.6. ROSAT X-ray observatory 42

POTENTIAL DISTANCE WINDOW [kV] [mm] 1 µ m POLYPROPYLEN 0 + 40 µ g/cm2 LEXAN µ 2 8 +50 g/cm CARBON

+0.3 K1 FRONT CATHODE

4.2

+3.1 A1 ANODE

4.2

+0.3 K2 BACK CATHOD

5.5

+2.9 A2 ANTI−COINCIDENCE ANODE

5.5

+0.3 K3 MONITOR CATHOD (For High Energy Events)

0 GROUND PLATE

Figure 2.4 A schematic view of the ROSAT PSPC detector (Based on ROSAT Users Hand- book

2.6.2 ROSAT data

The raw data obtained from the pointed/survey ROSAT observations with the PSPC have been archived at the High Energy Astrophysics Research Center (HEASARC‡), and are publically available. A set of the data corresponding to a single observation contains basic file (photon event table, PET) which contains the calibrated science data, essential for performing standard scientific analysis. The basic data generally consist of times which define the length of observation, and the photon event list which gives time arrival, sky position, detector position, and the pulse invariant (PI) channel for each photon. The ROSAT data sets corresponding to the objects studied in the thesis are listed in Table 2.8, and were obtained from the HEASARC. The stars HD 95559 and LO Peg were observed serendipitously in pointed observations of the ROSAT PSPC detector, while the stars FR Cnc, HD 81032 and HD 160934 were observed and detected by the ROSAT PSPC detector during the ROSAT All-Sky-Survey (RASS) phase. The X-ray images for all the objects are shown

‡http://heasarc.gfsc.nasa.gov 2.6. ROSAT X-ray observatory 43

Table 2.8 Log of ROSAT X-ray observation Object Sequence Instrument Oﬀ-set Start Time End Time Exposure No. arcmin Y,M,D Y,M,D Time(s) FR Cnc rs931423n00 PSPC 68.1 1990,10,09 1990,10,29 384 HD 81032 rs932025n00 PSPC 187.8 1990,11,02 1990,11,22 501 HD 95559 rp200987n00 PSPC 38.4 1993,06,02 1993,06,09 4874 HD 160934 rs930625n00 PSPC 240.2 1990,07,11 1991,08,13 4620 LO PEG rp201753n00 PSPC 0.3 1993,11,11 1993,11,11 5968 rp201753a01 PSPC 0.3 1993,12,07 1993,12,08 14012

in the Figure 2.5.

Extraction of light curve and spectra

Firstly we create an image from a basic event ﬁle. Source spectra and light curve for each source were accumulated from on-source counts obtained from a circular region on the sky centered on the X-ray peak. The background was accumulated from several neighboring regions at nearly the same oﬀset from the source. Then the light curve and the spectra for the source and background were extracted using the xselect package for the PSPC 0.1 - 2.4 keV energy band which contains all the X-ray photons.

X-ray spectral ﬁtting

X-ray spectrum is computed by histogramming of PI values of all the photons within an extraction region. Source and background spectra are constructed separately. An observed X-ray spectrum is distribution of photon counts over the PI channels. The photon count

1 rate (in count s− ) in PI channel is given by

∞ C(I) = R(I, E) f (E)A(E)dE (2.3) Z0 where R(I,E) is probability of observing a photon with energy E in channel I, f(E) is photon

2 1 ﬂux density at energy E (source spectrum, in photons s1 cm− keV− ), A(E) is the eﬀective area of the telescope and the detector system (Davis 2001). Usually it is not possible to 2.6. ROSAT X-ray observatory 44

Figure 2.5 X-ray images of the target sources. The corresponding X-ray source of the program star is encircled 2.6. ROSAT X-ray observatory 45

determine the source spectrum f(E) by inverting the above equation. Therefore, a model source spectrum describable in terms of a few parameters, f(E,p1,p2,....), is chosen and a

model source count rates CP(I), are predicted which is compared to the observed data. This is usually done by varying the parameters and minimizing the χ2 fit statistic. For this purpose, X-ray spectral fitting package xsepc (Arnaud 1996) is used. The effective area is input into this program via a file called the ancillary file (ARF) and the energy resolution of the detector is specified by the redistribution matrix file (RMF). The parameters corresponding to the minimum χ2 are referred to as the best-fit parameters. χ2 is defined as

2 2 2 χ = (Cp(I) )/(σ(I) ) (2.4) X The χ2 statistics provides a well-known goodness-of-ﬁt criterion for a given number of degree of freedom or dof(ν). If χ2 exceeds a critical value (Bevington 1969) one can

conclude that fb(E) is not adequate to model for C(I). A general rule for an acceptable model is that reduced χ2 (χ2/ν) must be approximately one or χ2 ν for an acceptable ∼ model.

2.6.3 Coronal plasma model

Coronal plasma models have been used extensively to model the solar coronal spectrum and the spectra of stellar coronae. A coronal plasma model is an ’ideal’ where plasmas, viz: the plasma (i) is collisionally ionized and radiatively cooled, (ii) is in ionization equilibrium, (iii) is optically thin at all energies to its radiation, (iv) has electron and ion components with Maxwellian energy distribution, and (v) is not aﬀected by any external radiation through like photoionization. Conditions close to these are often found in low density

10 3 6 8 (N 10 cm− ), high temperature (T = 10 − K) plasma such as solar corona. Given e ≤ e these assumptions and assuming that the atomic physics for line and continuum is accurately described, for any speciﬁed Te and Ne, and adopted set of elemental abundances, the emissivity per unit volume of the model plasma as function of energy can be calculated (Drake 1997). The Mewe & Kaastra (or MEKA) , Raymond & Smith, and Landini & Monsignori Fossi codes are most commonly used plasma codes. Since there are thousands of lines of 2.7. Near-IR data 46

astrophysically abundant elements in the ultraviolet, EUV, and soft X-ray spectral regions that contribute, together with continuum processes such as free-free, bound-free, atomic data. The primary sources of uncertainty in these coronal models are probably (i) the particular ionization equilibrium that has been adopted, and (ii) error and emission in tabulated lines, their predicted energies and collisional strengths. This later problem is particularly acute in the Fe L-shell region of 0.5 to 1.5 keV (8 to 20 Å) which contains a large number of lines, principally the n=3 and n=4 to n=2 ’L-shell’ line complexes from a variety of ionization stages of Fe (Fe XVII - XIV), analogous to Ni L-shell complexes, as well as the resonance lines of the He- and H- like ions of N, O, Ne, and Mg. Recent version of these codes MEKAL ( Mewe et al. 1995) have incorporated these updated atomic data. The standard way in which the spectra of astrophysical plasmas are compared with those predicted by coronal plasma models is to use global ﬁtting procedures such as those incorporated into xspec (see above).

2.7 Near-IR data

We have also used the near-IR data for our study. The near-IR data are taken from the digital Two Micron All Sky Survey (2MASS) available at web site http://www.ipac.caltech.edu/. This survey is being carried out with two identical highly-automated 1.3-meter aperture, open-tube, equatorial fork-mount telescopes. One is the northern telescope which is located at 2306 meters elevation in Arizona (N 31◦ 400 5000.8, W 110◦ 520 4100.3) and second one is the southern telescope which is at 2171 meters elevation in Chile (S 30◦ 100 300.7, W 70◦

480 1800.3). Both telescopes have Cassegrain focus mount for the infrared cameras. During survey mode the telescope moves continuously in declination at approximately 5700/second, while tracking in hour angle at the sidereal rate. Each telescope is equipped with a three-channel camera. Each camera consists of a liquid nitrogen cryostat which contains three NICMOS3 arrays. During the observations each array views the same region of the sky. The detailed description of the 2MASS camera optical design is given in Milligan et al. (1996). In the 2MASS survey three band passes are used namely J(1.11-1.36 µ), H (1.50-1.80 µ) and Ks (2.00-2.31 µ). When camera mounted on the 2MASS telescopes each pixel subtends approximately 200.0 on the sky. 2.8. Time series analysis 47

2.8 Time series analysis

Fourier transform is the most useful analytical tool to identify periodic variations in a time-series data, which yields a discrete power density spectrum representing the variations present in the light curve. In particular, a dominant periodicity may be present at the rotation period of the light curve due to surface inhomogeneities in photosphere of a star. The ideal case of a pure sinusoidal light curve is only produced by a rotating star if one hemisphere is uniformly darker than the other and the star is observed along its equatorial plane. A star with a single small surface feature (spot) would show a sinusoidal pattern only when a spot is present in the observable hemisphere. A star with two spots shows yet more complex light curve, as two, one or both spots are observable at any one time. While these light curve are periodic, they will not be a sinusoidal, as additional sine waves are required to reconstruct the light curve. The power spectrum picks out the rotational period despite the noise and despite the fact that the light curve is not sinusoidal (Blair-Jones & Mundt 2001). Single, coherent frequencies yield a single spike in the spectrum whose height is proportional to the power (or amplitude) of the signal and whose width (resolution) is determined by the length of the data. But large gaps in the data set lead to complications in the power density spectrum as the true frequencies in the source are further modulated by the irregular and infrequent sampling deﬁned by window function of the data. Therefore, the calculation of the discrete power density spectrum from the light curve was followed by deconvolution of the window function from the data using one dimensional CLEAN (Roberts et al. 1987)

algorithm in Starlink’s§ PERIOD package. The cleaned power spectrum is a frequency domain representation of light curve, g(t), using the sinusoids of amplitude A (not peak-to-peak), frequency ν and a phase φ, determined by CLEAN. The power P at a certain frequency is related to the amplitude by A = 2 √P in the noiseless case. For evenly spaced data, the noise in the power spectrum ¯ 2 ¯ 2 is approximately δmd/K, where δmd is average photometric error and K the number of points in the light curve. For a light curve with large occasional gaps, the result needs to be multiplied by a factor 1 (t /t ), where t is total duration of the light curve and − gaps max max tgaps is the sum of the duration of gaps. Peaks which are not more than several times this

§http://star-www.rl.ac.uk/ 2.8. Time series analysis 48

noise level should not be considered signiﬁcant. Note that it is possible to detect a sinusoid of amplitude less than the photometric errors, because the noise is spread over many frequencies in the power spectrum. The uncertainty in a period is set by the ﬁnite resolution of

the spectrum. This is determined by the duration of the observations (tmax), which makes it impossible to distinguish between two closely separated frequencies, giving rise to an error

2 in a period τ of τ /(2tmax) (Roberts et al. 1987). However, at very short periods it is good to place a lower limit on a temporal resolution due to the ﬁnite integration time.

Chapter 3

Main Sequence Active Stars

3.1 Overview

Main-sequence late-type (& F5V) stars constitute the most common class of the object in our Galaxy. These are capable of exhibiting rotational velocities and magnetic activity manifestations. For lower main-sequence star rotation, mass and chemical composition controls the magnetic activity. Observations have shown that younger (. 100 Myr) the star, faster the rotation and high level of the chromospheric and coronal activity in it. On the other hand, somewhat older (& 500 yrs) solar-type stars appears to rotate much slower and exhibit lower level of the chromospheric and coronal emission. The commonly known dwarf active stars are BY Dra occuring either as a single stars or as binaries. In this chapter we present a detailed study based on our extensive optical observations and archival X-ray and IR data of four young main-sequence chromospherically active stars selected on the basis of the their strong X-ray and radio ﬂuxes. They are FR Cnc, HD 95559, HD 160934 and LO Peg.

3.2 Introduction

An introduction on the objects under study is given in the following sub-sections.

Major part of this chapter is published in Pandey et al. (2005a, 2002a, 2002b)

50 3.2. Introduction 51

3.2.1 FR Cnc

The star FR Cnc = BD +16◦1753 (= MCC 527) first came to be noticed as a potential active star when it was identified as the likely optical counterpart of a soft X-ray source in the Einstein Slew Survey (ESS), 1ES 0829+15.9, with an observed X-ray flux of ≈ 11 2 1 1.8 0.6 10− erg cm− s− (Elvis et al. 1992; Schachter et al. 1996). This X-ray source × was rediscovered in the RASS at a somewhat weaker (but more statistically significant)

12 2 1 level of 2 10− erg cm− s− , and dubbed as 1RXS J083230.9+154940 in the RASS × Bright Source Catalogue (Voges et al. 1999). In the photometric notes annex of Hipparcos catalogue (Perryman et al. 1997), it was regarded as an unsolved variable star and given the name FR Cnc. It was recently classiﬁed as a BY Draconis type in the 74th special Name-List of the variable stars (Kazarovets et al. 1999). The implied X-ray luminosity of

29 1 3.3 2 12 10 erg s− and ratio of X-ray to bolometric luminosity f / f of 10− both − × x bol ≥ 3 show that FR Cnc has an active corona at or near the saturation limit of f / f of 10− x bol ≈ (Schachter et al. 1996). Recently, Upgren et al. (2002) have given two measurements of the radial velocity of FR Cnc (see Table 3.4) which diﬀer only by an amount of the order of the measurement error, and the authors thus conclude that it is not a binary system.

3.2.2 HD 95559

HD 95559 (= BD 23◦2287) has recently been shown to be a double lined spectroscopic binary with an orbital period of 1.5260 days. The photometric period of 1.5264 days is tightly synchronized to the orbital motion (Fekel & Henry 2000). Earlier observations indicate that this system has 2.9 day photometric period (Jeﬀries et al. 1994a; Strassmeier et al. 2000; Pandey et al. 2002a). This appears to be detection of the 1 day alias of the 1.526 day orbital period. HD 95559 is a pair of K1 V stars with a Li-based age younger than the Hyades cluster. Fekel & Henry (2000) conclude that optical variability in this system is due to the rotational modulation of the star spots and thus identify it as belonging to the (binary) BY Dra type. HD 95559 was detected as an X-ray source in the RASS observations with

12 2 1 a ﬂux of 3.03 0.21 10− erg cm− s− . This indicates the presence of corona in the star. × 30 1 Using Hipparcos parallax the implied X-ray luminosity of 1.07 0.07 10 erg s− indicates × that HD 95559 has an active corona. 3.3. Light curves and period analysis 52

3.2.3 HD 160934

The K7V type star HD 160934 was detected as an X-ray source 1ES 1737+61.2 in the ESS

11 2 1 (Elvis et al. 1992; Schachter et al. 1996) with an X-ray flux of 0.7 0.3 10− erg cm− s− . × An X-ray source at this position was later detected in the RASS at a weaker level of 3.8 12 2 1 0.1 10− erg cm− s− . This star was also identified as an extreme ultraviolet source RE × J1738+6122 (Pounds et al. 1993) and shows flares of the UV Cet-type (Gershberg et al. 1999). Follow-up spectroscopy by Mulliss & Bopp (1994) resulted in the detection of a strong Hα emission. Periodigram analysis by Henry et al. (1995b) shows that HD 160934 is a periodic variable with a period of 1.82 0.005 d.

3.2.4 LO Peg

LO Peg (=BD+22◦4409) is a single young K5V - K7V type star and is a member of the local association (Jeffries & Jewel 1993; Montes et al. 2001). It is an active star showing strong Hα and Ca II H and K emission lines (Jeffries et al. 1994b). Jeffries et al. (1994b) proposed six probable rotational periods, and stated that the periods of 0.3841 d and 0.42375 d are more likely. Subsequently, Robb & Cardinal (1995) eliminated completely the possibility of the 0.38417 d period. Evidence of an intense downflow of material and optical flaring on LO Peg have been presented by Eibe et al. (1999). Recently, Zucker- man et al. (2004) has identified LO Peg as a member of a group of 50 Myr old stars that ∼ partially surround the Sun. LO Peg was identified as an X-ray source 1ES 2128+230 in the

2 1 ESS with a ﬂux of 1.4 0.5 erg cm− s− . During RASS observation it was rediscovered as 12 2 1 an X-ray source with a ﬂux of 5.5 0.3 10− erg cm− s− . ×

3.3 Light curves and period analysis

In this section we discuss the period analysis of the star FR Cnc, HD 95559 and LO Peg.

3.3.1 Light curves and period analysis of FR Cnc

FR Cnc was observed in broad band B, V, and R ﬁlters during the years 2001-2004. We obtained nine light curves, with each light curve corresponding to an observational run that 3.3. Light curves and period analysis 53

JD = 245000.0 + cont..... 3.3. Light curves and period analysis 54

Figure 3.1 Light curves and corresponding CLEANed power density spectra (insets) of FR Cnc at diﬀerent epochs. The epoch is mentioned at the top of each panel, and the period is written at the top of inset. The bottom right panel (j) shows the Hipparcos light curve along with its power spectrum was nearly continuous. Figure 3.1 shows the light curves of FR Cnc for each epoch. The mean epoch of the light curves, the observed maximum (∆Vmax) and minimum (∆Vmin) in the V band, peak to peak amplitude (∆V = ∆V ∆V ), and phase minima (θ ) are max − min min listed in Table 3.1. θmin was determined by a linear least square ﬁtting of the second order polynomial at the minimum of each light curve. It appears that the shape and the amplitude of the light curves are changing during the observing season. The comparison and the check stars for the star FR Cnc were TYC 1392 2110 1 (= S1) and USNO-A2.0 1050-05766589 (= C), respectively during the observing season 2001-

2003. BD +16◦1751 (= S2) of the spectral type G0 was taken as the comparison star 3.3. Light curves and period analysis 55

Present data (Febraury 2001 to January 2004) 0.0004

0.0002

0.8

0.4

0.00012

0.8 1.6 2.4 3.2

Figure 3.2 Power spectra of FR Cnc from the entire photometric data taken during 2001- 2004. Top: Dirty power density spectrum; Middle: corresponding window power; Bottom: CLEANed power density spectrum . during the observing season 2003-2004 (see Figure 2.2). The mean difference between the (S2-C) and (S1-C) in each BVR filter was added to each BVR data of 2003-2004 season before plotting. No significant light variation was detected between the different measures of comparison and check stars (∆Vc) (see the bottom panels of Figure 3.5 (a to i)) indicating that the comparison stars are constant during the present observations. The nightly mean of the standard deviation (σ) of different measures of comparison and check stars in B, V and R filter was 0.007,0.007 and 0.008 mag, respectively. Similarly, σ determined for ∆(B V) − c and ∆(V R) was 0.006 and 0.01 mag, respectively. The nightly σ of the different measure − c of comparison and check stars are given in the Table 2.4. We have used the CLEAN algorithm for the period analysis. This algorithm is discussed in 2.8. The CLEANed power spectra presented here were obtained after 100 iterations § with a loop gain of 0.1. Data for each epoch were analysed separately for the periodicity by using the CLEAN algorithm. Inset in each panel of Figure 3.1 shows the corresponding 3.3. Light curves and period analysis 56

CLEANed power spectrum. The epoch and the period are mentioned inside each panel of Figure 3.1. The period is found to be constant, within the uncertainty, for each epoch. The entire data were also analysed together using the CLEAN algorithm to improve the period determination. The top panel of Figure 3.2 shows the discrete power spectra, with the corresponding window and CLEANed power spectra shown in the middle and the bottom panel. The highest peak in the CLEANed power spectrum corresponds to a period of 0.8267 0.0004 d.

Hipparcos light curve of FR Cnc

The light curve based on the Hipparcos photometric data is shown in Figure 3.1 (j). The total number of measurements with Hipparcos is 70 during three years of observations (from March 1990 - November 1992). We have also analysed the Hipparcos data using the same algorithm as used for our photometric data. The CLEANed power spectrum is shown in the inset of Figure 3.1 (j). The highest peak here corresponds to a period of 0.815 0.002 d, which is close to the period determined above from the present data.

3.3.2 Period analysis of HD 95559, HD 160923 and LO Peg

Star HD 95559 was observed twice in an observing season 2001, ﬁrst, from 03 to 05 Feb 2001 and second, from 31 March to 07 April 2001, while the star LO Peg was observed in two observing seasons, ﬁrst, from 28 September to 28 October 2001, and second, from 28 September to 03 October 2002 (see Table 2.4). We have analysed the light curves of HD 95559 and LO Peg using the CLEAN algorithm. The CLEANed power spectra of HD 95559 and LO Peg are shown in left and right panel of Figure 3.3. The highest peak in the CLEANed power spectrum of HD 95559 corresponds to a period of 0.75 0.02 d, which is half of the period determined by Fekel & Henry (2000). The period determination of Fekel & Henry (2000) was based on their long term spectroscopic observations. So, their period determination is more reliable. We assume that our period determination is mainly due to

the presence of two similar size of spots separated by 180◦ in longitude. A rotating star ∼ with two spots separated by 180◦ in longitude can give rise a sinusoidal variation with a period of half of the rotational period, as a result of single rotation, two minima are visible in the light curve. Such eﬀects is clearly seen in the folded light curve of HD 95559 (see 3.3. Light curves and period analysis 57

Figure 3.3 CLEANed power spectra of HD 95559 (left panel) and LO Peg (right panel)

Figure 3.7b) The highest peak in the CLEANed power spectrum of LO Peg corresponds to a period of 0.424 0.003 d. This period is consistent to the period determined by Jeffries et al. (1994b) and Robb & Cardinal (1995). Star HD 160934 was observed from 17 February 2001 to 25 April 2001. The observed points shown in left panel of Figure 3.4 are not sufficient for finding a reliable period, however, a sinusoidal curve was fitted using the method of the least square deviations for each of the B, V and R light curves. The best period found in B, V and R light curves is 43.918 0.0154, 43.931 0.012 and 41.719 0.0035 respectively, giving a mean value of 43.182 .040 days (Pandey et al. 2002a) . A similar period appears to be present in the X-ray light curve of HD 160934 (see 3.6). The inferred period seems rather long for § an active late K dwarf considering that vsin i = 16.4 km/s for this star (Fekel, 1997), and assuming that R = 0.6R , the maximum period (for sin i = 1.0) is 1.85 days. We have

also analysed the data of HD 160934 for the periodicity using CLEAN algorithm. Right panel of Figure 3.4 shows the CLEANed power spectrum of HD 160934. The highest peak corresponds to the period of 1.89 0.05 d, which is consistent with the above estimated period of 1.85 d. A similar period of 1.842 d was determined by Henry et al. (1995b). Long run observations are needed to see the 43.18 d periodicity (if any) in HD 160934. 3.4. Folded light and colour curves 58

0.2

0.0

-0.2

0.0

-0.2

0.0

-0.2

0.0

-0.2

1640 1660 1680 (JD - 2450000 +)

Figure 3.4 Left panel: Light Curve of HD 160934 in B V and R ﬁlter. Dotted line represent the best ﬁt sine curve to the data. Right panel: CLEANed power spectra of HD 160934. Vertical dash line indicates the period values of 43.182 d.

3.4 Folded light and colour curves

Based on the present observations, folded light and colour curves are obtained for all the objects under study. The parameters determined from these are given in the following subsections.

3.4.1 FR Cnc

The data were folded using the period of 0.8267 d, and an arbitrary epoch of JD 2451943.1980. Figure 3.5 shows the plot of ∆V , ∆B, ∆V, ∆R, ∆(B V) and ∆(V R) as a function of phase c − − at diﬀerent epochs. The mean epoch is mentioned at the top of each panel of Figure 3.5. As can be seen from Figure 3.5, the phase coverage is fair to reasonably good in most of

the light curves. The value of ∆Vmax was nearly constant during most of the epochs indi- 3.4. Folded light and colour curves 59

0.16 0.16

0.24 0.24 0.16 0.16

0.24 0.24

-0.84 -0.84

-0.72 -0.72

-0.60 -0.60

-0.48 -0.48

-0.36 -0.36

-1.20 -1.20

-1.08 -1.08

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase

0.16 0.16

0.24 0.24 0.16 0.16

0.24 0.24

-0.84 -0.84

-0.72 -0.72

-0.60 -0.60

-0.48 -0.48

-0.36 -0.36

-1.20 -1.20

-1.08 -1.08

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase cont.... 3.4. Folded light and colour curves 60

0.16 0.16

0.24 0.24 0.16 0.16

0.24 0.24

-0.84 -0.84

-0.72 -0.72

-0.60 -0.60

-0.48 -0.48

-0.36 -0.36

-1.20 -1.20

-1.08 -1.08

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase

0.16 0.16

0.24 0.24 0.16 0.16

0.24 0.24

-0.84 -0.84

-0.72 -0.72

-0.60 -0.60

-0.48 -0.48

-0.36 -0.36

-1.20 -1.20

-1.08 -1.08

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase cont...... 3.4. Folded light and colour curves 61

0.16

0.24 0.16

0.24

-0.84

-0.72

-0.60

-0.48

-0.36

-1.20

-1.08

0.0 0.4 0.8 1.2 1.6 2.0 Phase

Figure 3.5 Vc, B, V, R light curves and (B-V), (V-R) colour curves of FR Cnc folded using a period of 0.8267 d, and shown for nine different epochs. The epoch (JD=2400000.0+ is marked at the top of each panel. The bottom panel in each Figure represents the plot of different measures between the comparison (TYC 1392 2120 1 for Figure a to g and BD +16◦1751 for Fig h and i) and the check (USNO-A2.0 1050-05766589) stars with phase. cating that the brightness of the unspotted photosphere was constant from epoch to epoch. During the epoch ’b’ it went to its minimum value. At the same time a smaller variation (∆V = 0.063 mag) during this epoch is probably associated with a continuous reduction of the spot coverage. Light curve during the epoch ’b’ has two maxima whereas during the epoch ’c’ it has one flat maximum and one minimum indicating the formation of a new group of spots that further separate into two groups of spots during the epoch ’d’ and ’e’. An increase in the amplitude by 0.05 mag during the epoch ’e’ indicates an increase in the spot coverage on the surface of the star that remained constant during epoch ’f’. However, poor phase coverage during the epochs ’f’, ’g’ and ’i’ does not allow us to follow this progress of spots properly. The activity level in our observation became very high during the epoch ’h’, where the amplitude of variation became 0.21 mag and appeared to remain 3.4. Folded light and colour curves 62

the same during the epoch ’i’. Variable size of the spot (or a group of spots) are indicated by the variable depth of the light minimum in the light curves. The minimum of the light changed by 0.1 mag from epoch ’a’ to epoch ’h’ (see Table 3.1). Comparing the light curves of FR Cnc from epoch ’a’ to epoch ’i’, a shift in the phase of the minimum and a variable amplitude is quite evident. Such cycle-to-cycle variation of both the amplitude and phase of the minimum has been seen for some rapidly rotating stars like LO Peg (Dal & Tas 2003), Speedy Mic (Barnes et al. 2001), AB Dor (Bos 1994; Donati & Collier-Cameron 1997) and PZ Tel (Innis et al. 1990). Variation in the colour of the star is correlated with its magnitude i.e. the star becomes redder when fainter, and bluer when brighter, supporting the starspot hypothesis. The signiﬁcance of correlation has been calculated by determining the linear correlation coeﬃcient, r, between the magnitude and the colours. The value of r between V and (B-V), V and (V-R) and (B-V) and (V-R) was found to be 0.11, 0.35 and 0.581 with corresponding

25 probability of no correlation being 0.00181, 1.51 10− and 0, respectively. ×

Phase of minima

The phase minimum of light (θmin) for the nine light curves in V band were plotted against the mean epoch listed in Table 3.1 and shown in the Figure 3.6. To illustrate the spot

motions over several longitudinal cycles, we deﬁne the longitude as longitude + n*360◦or

(θmin + n*1), where n is the cycle number. The phases of the light minima directly indicate the mean longitude of the dominant groups of the spots. The presence of two spots is clearly established by two well separated straight lines. Both the spots are closer to each other during the epoch ’g’, with a longitudinal separation of 830. Both the spots are visible ∼ during all the epochs, except during the epoch ’c’. Poor phase coverage during the epoch ’f’ could not establish the presence of the second spot. It is interesting to see the variable separation of the two spots. This could be due to the different latitudinal positions of the two spots and the presence of differential rotation in the star. Due to differential rotation,

spots at different latitudes would give rise to a different migration rate for associated θmin (Raveendran & Mohin 1995). The following relation was fitted to the data by the method of the least squares: 3.4. Folded light and colour curves 63

Figure 3.6 Plot of the mean epoch vs the phase minimum of light for FR Cnc. Vertical bar shows the associated error in the determination of phase minimum and horizontal bar shows the length of epoch.

θ = ω(t t ) + θ (3.1) min − 0 0 where ω = 2π/P is the angular velocity of the spot or the rate of phase shift (degrees/day), P is the corresponding period in days, t is time in days, t0 is reference time, and

θ0 is the reference spot longitude in degree. Applying the above relation, the rate of phase shift for the spots A and B are determined as 1.02 0.02 degree/day and 1.06 0.02 degree/day, respectively. The corresponding migration period for the spot A and B are found to be 0.97 0.03 years and 0.93 0.02 years, respectively. These migration periods, being so close to each other, indicate that the spots that are located at diﬀerent longitudes rotate with almost the same angular velocity. It thus appears that the observed phase minima of FR Cnc are well arranged in two permanent strips with approximately the same slope (i.e. same migration period), which can be interpreted as two long-lived active longitudes. 3.4. Folded light and colour curves 64

Table 3.1. Photometry of FR Cnc, HD 95559, HD 160934 and LO Peg.

Mean epoch Amplitude ∆Vmax ∆Vmin phase minima 240000.0+ ∆V I II

FR Cnc

(a) 51984.75 0.106 -0.716 -0.610 0.33 0.75 (b) 52245.50 0.063 -0.670 -0.607 0.29 0.66 (c) 52267.00 0.108 -0.683 -0.575 0.27 - (d) 52308.75 0.100 -0.697 -0.597 0.23 0.58 (e) 52598.00 0.153 -0.725 -0.572 0.44 0.75 (f) 52626.25 0.158* -0.738 -0.580 - - (g) 52643.75 0.128* -0.728 -0.600 0.39 0.62 (h) 52992.00 0.210 -0.721 -0.511 0.25 0.54 (i) 53022.25 0.181* -0.736 -0.555 0.21 0.53

HD 95559

(a) 51945.40 0.051 -0.435 -0.384 0.00 - (b) 52003.80 0.076 -0.481 -0.405 0.00 0.53

HD 160934

(a) 52003.40 0.050 -1.115 -1.064 0.20 -

LO Peg

(a) 52190.80 0.081 -0.483 -0.402 0.50 - (b) 52548.00 0.050 -0.495 -0.445 0.66 -

∗Because certain phases were not covered fully during the observations, therefore minima and/or maxima at the epoch f, g and i could not be determined accurately 3.4. Folded light and colour curves 65

3.4.2 HD 95559

Stars HD 95467 and BD +33◦2294 were observed for the differential photometry of the program star HD 95559. The data were folded using the following ephemeris for HD 95559: JD = 2450359.094 + 1.52599775E, where the epoch E corresponds to a time when the more massive star is in front of the less massive star and period is spectroscopic orbital period (Fekel & Henry 2000). Variation in the B V R magnitude and colours of the program star with respect to the comparison star are shown in Figure 3.7a and 3.7b. The nightly mean of σ of the different measures of comparison and check stars was determined 0.006 mag in each B and V filter, and 0.007 mag in R filter ( see Table 2.4). The comparison star was constant during the observations as shown in the bottom panel of Figure 3.7a and 3.7b. We have divided our observations into two epochs, namely, epoch ’a’ ( 2001 February 3-5) and epoch ’b’ (2001 March 31 - April 7). The amplitude and the phase of the minima with the mean epoch of the observations of this star are shown in Table 3.1. It is interesting to examine the light curves of HD 95559 during the observing season 2001. During the epoch ’a’ the light curve has a flat topped maximum and only one minimum (Figure 3.7a). During the epoch ’b’ that flat topped maximum developed into a minimum at a phase = 0.5. At the same time, the amplitude of the variation increased by 0.025 mag. The position of the minimum during the epoch ’a’ however, did not change from the phase 0.0. This directly indicates the formation of a new group of spots at phase 0.5. Light curves of HD 95559 during the observing season 1995-1997 had only one minimum and a sharp maximum (Fekel & Henry 2000). It appears that the colours remain nearly constant during our observations in HD 95559. A larger amount of scatter is, however, seen during the epoch ’b’. This may be due to the formation of the new group of spots on the surface of the active star. The lack of brightness- colour relation may be due to the presence of bright faculae or plages like regions accom- panied by dark spots in any one or both components of this binary system. 3.4. Folded light and colour curves 66

(a) 51945.4 (b) 52003.8

-0.06 -0.06

0.00 0.00

-0.24 -0.24

-0.18 -0.18

-0.50 -0.50

-0.40 -0.40

-0.50 -0.50

-0.40 -0.40

-0.70 -0.70

-0.60 -0.60

-1.50 -1.50

-1.40 -1.40

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase

Figure 3.7 Vc, B, V, R light curves and (B-V), (V-R) colour curves of HD 95559 folded using a period of 1.52599775 d, and shown for two diﬀerent epochs. The epoch (JD=2400000.0+) is marked at the top of each panel. Bottom panel in each Figure represents the plot of diﬀerent measures between the comparison (HD 95467) and the check (BD +33◦2294) stars with phase.

3.4.3 HD 160934

The differential photometry was done as both the comparison (TYC 4199 652 1) and the check (TYC 4199 590) stars were in the same CCD frame. The comparison star was found to be constant during our observations (see Bottom panel of the Figure 3.8). The σ of different measures of comparison and check stars in each B, V, and R filter was 0.011, 0.01 and 0.012 mag, respectively. The data were folded using the ephemeris HJD 2449400.0 + 1.842E ( Henry et al. 1995b). Figure 3.8 shows the folded light and colour curves of the star HD 160934. The amplitude of the variation of 0.05 mag in V band was obtained during our observations, which was 0.01 mag more than the observations by Henry et al. (1995b). All the parameters 3.4. Folded light and colour curves 67

(a) 2452003.8341

0.24

0.16

-1.28

-1.36

-1.04

-1.12

-0.88

-0.96

-0.88

-0.96 0.0 0.4 0.8 1.2 1.6 2.0 Phase

Figure 3.8 Left panel:Vc, B, V, R light curve of HD 160934. The solid line represent the best ﬁtted sine curve to the data. Right panel: Vc, B, V, R light curves and (B-V), (V-R) colour curves of HD 160934 folded using a period of 1.842d. The mean epoch of the observation is JD 2452003.4 obtained from the light curve are given in Table 3.1. It is clear from Figure 3.8 that the colour is correlated with brightness, which further supports the star spot hypothesis.

3.4.4 LO Peg

Photometric data of LO Peg were folded using the following ephemeris as given by Dal & Tas (2003): HJD = 2448869.93 + 0.42375E. The folded light curves are shown in Figure 3.9. The observations separated by a year were divided into two diﬀerent epochs namely ’a’ and ’b’. The epoch ’a’ has observations from 2001 September 28 to October 15, and epoch ’b’ has the observations from 2002 September 28 to October 3. The ’b’ epoch observations partly coincide with one set of 3.4. Folded light and colour curves 68

0.33 0.33

0.36 0.36

0.60 0.60

0.63 0.63

-0.80 -0.80

-0.72 -0.72

-0.48 -0.48

-0.40 -0.40

0.16 0.16

0.24 0.24

-1.44 -1.44

-1.36 -1.36

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 Phase Phase

Figure 3.9 Vc, B, V, R light curves and (B-V), (V-R) colour curves of LO Peg folded using a period of 0.42375 d, and shown for two different epochs. The epoch marked at the top of each panel is JD = 2400000.0+ . The bottom panel in each Figure represents the plot of different measures of the comparison (BD +22◦4405) and the check (USNO-B1.0 1133- 0542608) stars with phase. observations (2002 October 1-31) of Dal & Tas (2003). Table 3.1 shows the parameters determined from the light curves of the LO Peg. Phase minimum computed from our photometry at epoch ’b’ differs by 0.26 from that of Dal & Tas (2003) photometry. This may be due to the larger span of their observations, as phase minimum changed significantly within a couple of rotational periods, probably as a result of change in the spot configuration. As in the case of FR Cnc no two light curves of LO Peg are similar in shape, size and amplitude, which is seen quite commonly in the BY Dra type of stars. A plot of the phase minima as a function of the mean epoch of the observations of LO Peg is shown in the Figure 3.10. The solid circles represent the observations made by Dal & Tas (2003) and the solid triangles represent our observations. Two large groups of spots are clearly seen. We have fitted the equation (3.1) by the linear least squares deviation 3.4. Folded light and colour curves 69

Figure 3.10 Plot of the mean epoch vs the phase minimum of light for LO Peg. The open circle was not used in the ﬁtting. Vertical bar shows the associated error in the determination of phase minimum and horizontal bar shows the length of epoch.

method for the group of spots A and computed the rate of phase shift. The open circle in the Figure 3.10 was not used in the ﬁtting. The rate of the phase shift for the group of spots A was determined 0.85 0.03 degree/day. The corresponding migration period is 1.12 0.05 years. From Figure 3.9, it is clear that the colour curves are strongly correlated with light curves, i.e. bluer at light maximum and redder at light minimum. This indicate that the variability is due to the dark spots present on the surface of the star.

We have also checked whether the comparison star (BD +22◦4405) is variable or not. Star USNO-B1.0 1133-0542608 was used as a check star. The σ was computed between the different measures of comparison and check stars. Nightly mean of the σ was 0.010, 0.009 and 0.007 mag in B, V, and R filter, respectively (see Table 2.4). Lower panels of Figure 3.9a and 3.9b show the plot of different measures of comparison and check stars and indicate that the comparison stars were indeed constant during the observations. 3.5. Chromospheric emission features 70

3.5 Chromospheric emission features

In late type dwarfs, Hα emission is a good indicator of chromospheric activity. It has been suggested that the detection of Hα emission above the continuum or even a filled- in emission is sufficient to indicate that K - M dwarf is a BY Dra variable (Bopp et al. 1981). Spectrum of FR Cnc in the Hα region is shown in Figure 3.11. Spectrum of the star HD 26794 (V = 8.81 mag and Spectral type - K3V) is also shown in Figure 3.11 for comparison. Hα is in emission at all phases in FR Cnc. The measured equivalent width of the Hα emission feature and the corresponding JD and phase of FR Cnc are listed in Table 3.2. The phase is determined using the photometric period of 0.8267 d and an epoch of JD 2451943.1980 for phase 0. The equivalent width is seen to vary from 1.2 to 1.8 Å. Such a significant change in the Hα profiles and the equivalent width on a time scale as short as few hours has also been reported for the active K5 V star LO Peg (Jeffries et al. 1994b). A strong Hα emission feature was also found in HD 160934 (Mullis & Bopp 1994). Hβemission in late type stars is another indicator of enhanced chromospheric activity. Figure 3.12 shows the spectra of FR Cnc and the comparison star HD 26794 in the Hβ region. Hβ is seen clearly in emission, while it is in absorption in the comparison star. The ratio of excess emission EHα with the correction given by Hall & Ramsey (1992) was also EHβ calculated for FR Cnc using the following equation.

EHα EW(Hα) (B R) = 0.2444 2.512 − (3.2) EHβ EW(Hβ) ∗ ∗ This yields a value of 5.34 for the mean values of the equivalent widths of Hα and Hβ. According to Hall & Ramsey (1992), values of EHα > 3 are indicative of the line emission EHβ likely arising from an extended region viewed oﬀ the limb, perhaps a stellar ‘prominence’. Figure 3.13 shows a comparison of spectrum of FR Cnc with that of HD 26794 in the region near the Ca II H and K lines. One can see that these lines have strong central emission components in the spectra of FR Cnc due to its active chromosphere. The spectrum of the Ca II H and K region taken on 15 November 2002 (φ =0.72 and 0.76) was obtained close to the photometric epoch ’e’. The photometric light minima during this epoch are at phase of 0.44 and 0.75. The equivalent widths of the Ca II H and K lines in the 15 November 2002 spectra were found to be at a maximum during the photometric light minimum. Such 3.5. Chromospheric emission features 71

Table 3.2. CaIIH&K, Hα and Hβ data of FR Cnc

JD Phase EWs (Å) 240000+ CaIIK H Hα Hβ

52594.400 0.73 6.45 5.70 - - 52594.431 0.77 5.39 4.58 - - 52660.197 0.32 - - 1.51 - 52660.220 0.35 - - 1.21 - 52660.463 0.64 - - - 0.40 52660.486 0.67 - - - 0.33 52661.204 0.54 - - 1.498 - 52661.251 0.59 5.19 4.59 - - 52661.417 0.79 - - 1.32 - 52661.446 0.83 - - - 0.36 52662.199 0.74 - - 1.82 - 52662.248 0.80 5.06 4.86 - - 52662.379 0.96 - - 1.39 - 52662.452 0.05 - - - 0.40 52663.168 0.91 - - 1.55 - 52663.217 0.97 5.67 4.22 - - 52663.247 0.01 - - 1.36 - 52663.371 0.16 - - 1.64 - 52663.422 0.22 - - - 0.31 52664.253 0.23 - - 1.62 - 52664.508 0.53 - - - 0.31 3.5. Chromospheric emission features 72

HD 26794

FR Cnc

6500 6550 6600

Figure 3.11 Hα spectra of the FR Cnc and the comparison star HD 26794. The phase is mentioned at the top of each spectrum

a correlation is seen quite commonly among chromospherically active stars and is typically interpreted as evidence that, as in the solar case, the plage regions responsible for the Ca II emission are adjacent to the spotted regions responsible for the photometric modulation. The equivalent widths of the Hα and Ca II H and K lines in FR Cnc are in the range of 1.2 to 1.8 Å and 4.2 to 6.4 Å, respectively. This is similar to the equivalent width found in most BY Dra type stars (e.g., see Bopp 1987). 3.6. X-ray light curves of HD 95559, HD 160934 and LO Peg 73

HD 26794

FR Cnc

4800 4850 4900

Figure 3.12 Spectra of FR Cnc showing Hβ in emission, while spectrum of HD 26794 shows Hβ in absorption. The phase is mentioned at the top of each spectrum of FR Cnc

3.6 X-ray light curves of HD 95559, HD 160934 and LO Peg

The stars HD 95559 and LO Peg were observed serendipitously in pointed observations of the ROSAT PSPC detector. FR Cnc and HD 160934 were not observed in any of the point- ings made by ROSAT. However, FR Cnc and HD 160934 were observed in the ROSAT All-Sky Survey phase. The ROSAT observational parameters are given in Table 2.8. The light curve for the source and background were extracted using the xselect package for the PSPC 0.1 - 2.4 keV energy band which contains all the X-ray photons. The source region were accumulated from on-source counts obtained from a circular region on the sky centered on the X-ray peak having a radius 4.5, 3.8 and 3.3 arcmin for HD 95559, HD 160934 and LO Peg, respectively. The background region was accumulated from the several neighboring at nearly the same oﬀset from the source. The star FR Cnc was observed for a short 3.6. X-ray light curves of HD 95559, HD 160934 and LO Peg 74

HD 26794

FR Cnc

3950 4000 4050 4100

Figure 3.13 Spectra of FR Cnc and the comparison star HD 26794 near the Ca II region. The phase is mentioned at the top corner of each spectrum of FR Cnc exposure of 380 s. So, we did not produce a light curve for FR Cnc. The X-ray observations of HD 95559 consisted of two short exposures in 1993 June separated by a week. The background subtracted light curves of HD 95559, with a bin size of 64.0 s does not show any significant variability (see Figure 3.14). A ’constant + linear’ count rate fit to the light curve of HD 95559 gives minimum value of χ2 of 123.1 for 79 degrees of freedom. A remarkable variability in the soft X-ray flux from HD 160934 can be seen in Figure 3.15 with a bin size of 256 s. A χ2 of 770.0 for 209 degrees of freedom for a fit of ’constant + linear’ count rate shows a remarkable variation in X-ray flux of HD 160934. Visual inspection of the light curve shows a sinusoidal variation with a long periodicity. Although 3.6. X-ray light curves of HD 95559, HD 160934 and LO Peg 75

Figure 3.14 Background subtracted ROSAT PSPC light curve of HD 95559 observed during 2 to 9 June 1993. The bin size of the light curve is 64 s the data are not sufficient to dertemine the period, however, we have fitted sine curves to the light curve (see top panel of Figure 3.15). From the best fit sine curve a period of 43.47 0.5 d was determined. This period is similar with the period determined by sine curve fitting to the optical light curve of HD 160934 (see 3.3.2). It appears from the optical and X-ray § light curves of HD 160934, there is a signature of the presence of 43.47 d periodicity. The lower panel of Figure 3.15a shows ’observed - computed’ X-ray light curve of HD 160934. It is easily interpreted from the light curve of HD 160934 that a flare occurred

1 during the RASS observations with a peak about 0.20 cts s− (compared to its mean count level) at approximately JD = 2448123.12 (1990/08/19 14:52:48). Figure 3.15b shows same data folded with the ephemeris HJD 2449400.0+ 1.842E (Henry et al. 1994). Rotational modulation appears to be present to some extent, but with some ﬂuctuations superimposed. LO Peg was observed on two occasions. The light curves of LO Peg generated are shown in Figure 3.16 during 11 - 13 November 1993 (upper panel) and during 7 - 8 Decem- ber 1993 (lower panel). As can be seen in upper panel of Figure 3.16, the X-ray emission was steady during the observations. However, the observations during 7 -8 December 1993 shows remarkable variability. A ’constant + linear’ count rate ﬁt to the light curve of LO Peg gives the minimum value of χ2 of 369 for 117 degrees of freedom. X-ray light curve of LO Peg is analysed for the periodicity using the CLEAN algorithm. The top panel of the Figure 3.17a shows the discrete power spectra, with the corresponding window and CLEANed power spectra shown in the middle and the bottom panels. The highest peak in the CLEANed power spectrum corresponds to a period of 0.192 0.003 d. This period is 0.5 times of the rotational period (see 3.3.2). The dash line in lower ∼ § 3.6. X-ray light curves of HD 95559, HD 160934 and LO Peg 76

0.4 (a)

Bin time 256 s

0.2

-0.2 8110 8120 8130 8140 8150 JD = 2440000.0+

0.4 (b)

0.2

0 0.4 0.8 1.2 1.6 2 phase

Figure 3.15 (a) upper panel: Background subtracted ROSAT PSPC light curve of HD160934 observed during 11/071990- 13/08/1991. The bin size of the light curve is 256 s. The solid line represent the best ﬁt sine curve to the data (lower panel: Observed - ﬁtted light curve. Flare can bee seen easily at JD2448123.12. (b) X-ray data folded with rotational period and plotted versus the phase.

panel of Figure 3.17a shows the rotational period values of 0.4237 d. Rotational period of LO Peg is established very well (Jeﬀries et al. 1994b; Robb & Cardinal 1995; Dal & Tas 2003), so, the period of 0.192 0.003 d obtained from the power spectra may not show the true rotational period. We assume that this period determination is mainly due to the

two highly active regions separated by 180◦in longitude. A similar eﬀect was also seen ∼ in the period analysis of the optical light curve of the star HD 95559 (see 3.3.2). Upper § panel of Figure 3.17a shows the folded light curve with the period of 0.192 d. The best ﬁt

2 sine curve (shown by solid line) gives the high value of χν of 2.4. In order to conﬁrm that modulation of the X-ray emission is due to rotation we have folded the X-ray light-curve 3.7. X-ray spectra of HD 95559, HD 160934 and LO Peg 77

Figure 3.16 ROSAT PSPC light curve of LO Peg observed on 11 to 13 November 1993 (upper panel) and 7 to 8 December 1993 (lower panel). The time bin size is 128 s

with the photometric rotational period as shown in lower panel of Fig. 3.17b. Phase-related variability is clearly evident. A combination of two sine curves was ﬁtted to the data. The

2 2 best ﬁt sine curves give a χν of 2.1. The high value of χν could be due to the presence of ﬂuations that are superimposed in the X-ray light curve. The two minima in the X-ray light curve of LO Peg are clearly seen (lower panel of Figure 3.17b), and could be due to the two active regions present in its corona.

3.7 X-ray spectra of HD 95559, HD 160934 and LO Peg

The X-ray spectra of the HD 95559, HD 160934 and LO Peg are shown in Figures 3.18, 3.19 and 3.20, respectively. We created response matrices based on the available off axis calibration of the PSPC and using the appropriate ancillary response files. We used the xspec (version 11.2) spectral analysis package to fit the data with spectral model for thermal equilibrium plasma known as the Mewe-Kaastra-Liedahl or MEKAL model (Liedahl et al. 1995; Mewe et al. 1995). The coronal plasma models have been discussed in 2.6.3. The § background subtracted X-ray spectra were fitted with 1T and 2T plasma models assuming 3.7. X-ray spectra of HD 95559, HD 160934 and LO Peg 78

2 (b)

1.6

1.2

0.8

0.4

1.6

1.2

0.8

0.4

0 0.4 0.8 1.2 1.6 2 Phase

Figure 3.17 (a) Power spectra of LO Peg from the entire X-ray data. Top: Dirty power density spectrum; Middle: Corresponding window power; Bottom: CLEANed power density spectrum, vertical dash line indicates the rotational period values of 0.4237 d. (b) Top: Folded X-ray light curve of LO Peg using a period of 0.1817d obtained from CLEANed power spectra; Bottom: Folded light curve using a period of 0.4237 d. The solid line represent the best fit sine curve to the data. the solar photospheric abundances given in Anders & Grevesse (1989) and allowing the abundance of every element other than H to vary by a common factor relative to their solar (photospheric) values. In each of the above models we assumed that interstellar absorption follows the absorption cross-sections given by Morrison & McCammon (1983) and we allowed the total intervening hydrogen column density NH to vary freely. The best fit parameters were determined using the χ2 minimization technique as discussed in 2.6.2. § Table 3.3 summarizes the best fit values obtained for the various parameters along with

2 2 minimum χν = χ /ν (ν= degrees of freedom), and the 90% conﬁdence error bars estimated from minimum χ2 + 2.71. Further discussion on each objects under study is given below. 3.7. X-ray spectra of HD 95559, HD 160934 and LO Peg 79

2 2 Table 3.3. Results of X-ray spectral analysis. χν = χ /ν, where ν is degrees of freedom (DOF)

a 2 Object Model Abundances NH kT1 EM1 kT2 EM2 χν DOF 1020cm 2 (keV) 1052cm 3 (keV) 1052cm 3 − − −

HD 95559 MEKAL 1T 1.0(fixed) 0.00 0.31 5.7 - - 28.3 10 < . . +0.4 . +0.08 . +8 MEKAL 1T 0 02 0 6 0.4 0 69 0.06 33 7 7 - - 1.7 9 − − − MEKAL 2T 1.0(fixed) 0.00 0.26 4.1 1.16 5.8 2.5 8 . +0.3 < . . +0.19 . +3.1 . +4.4 . +3.1 MEKAL 2T 0 25 0.2 0 45 0 45 0.18 10 9 2.1 1 27 0.5 12 3 4.9 1.6 7 − − − − − HD 160934 MEKAL 1T 1.0(fixed) 0.00 0.32 0.73 - - 9.45 10 +0.08 +1.3 MEKAL 1T < 0.02 < 0.9 0.60 0.07 3.9 1.1 - - 0.9 9 − − < . . +0.10 . +5.6 . +0.2 < . MEKAL 2T 1.0(fixed) 2 9 0 13 0.02 7 1 1.5 0 7 0.1 0 5 1.6 8 − − − . +0.04 . +2.0 > . . +1.4 . +0.14 < . MEKAL 2T 0 1 0.04 2 1 1.1 0 1 9 94.7 0 6 0.5 5 3 1.1 7 − − − LO Peg MEKAL 1T 1.0(fixed) 0.00 0.31 1.6 - - 37.7 23 MEKAL 1T 0.01 0.5 0.58 7.6 - - 2.0 22 < . . +0.01 . +0.06 . +0.04 . +0.04 MEKAL 2T 1.0(fixed) 0 1 0 21 0.02 0 91 0.06 0 85 0.04 0 93 0.04 1.8 21 − − − − < . < . . +0.04 . +1.0 . +0.1 . +0.1 MEKAL 2T 0 15 4 1 0 30 0.05 2 5 0.6 1 0 0.2 1 9 0.1 1.3 20 − − − −

aCommon value of abundances for all the elements with respect to the solar photosphere values; 2 2 Notes: 1. Errors are with 90 % conﬁdence based on χmin + 2.71; No errors or upper limits are derived when χν is > 2. 2. Distance = 54.3 pc (HD 95559), 24.5 pc (HD 160934), 25.1 pc (LO Peg).

3.7.1 HD 95559

Single-temperature MEKAL models with abundances ﬁxed to the solar values gave a high

2 value of χν (=28.3) for the star HD 95559 (see Figure 3.18 a). However, single-temperature MEKAL models with abundances < 0.02 times the solar abundances and with plasma temperatures in the range of 0.63-0.77 keV were found acceptable (3.18b). Two-temperature plasma models with the abundances fixed to the solar values were not found to be acceptable (see Table 3.3 and Figure 3.18c). Acceptable MEKAL 2T fits were achieved when the abundances were allowed to depart from the solar values. The best fit two-temperature plasma model with sub-solar abundances along with the significance of the residuals in terms of the ratio of observed counts to the predicted counts from the model for the HD 95559 is shown in Figure 3.18d. For HD 95559 an acceptable fit was obtained for abun-

+0.3 dances that were only 0.25 0.2 times the solar values and with plasma components at tem- − peratures of 0.45 keV and 1.27 keV. Based on the best ﬁt 2T MEKAL model a source ﬂux

12 2 1 of 6.46 10− erg cm− s− was obtained. × 3.7. X-ray spectra of HD 95559, HD 160934 and LO Peg 80

Figure 3.18 Spectrum of HD 95559 with ROSAT PSPC detector, along with (a) 1T MEKAL model and solar abundances, (b) 1T MEKAL model and sub-solar abundances, (c) 2T MEKAL model and solar abundances, and (d) 2T MEKAL model and sub-solar abundances. The lower panel in each Figure represents the ratio of the observed counts to the counts predicted by the best-ﬁt model

3.7.2 HD 160934

Figure 3.19 shows the X-ray spectrum of the star HD 160934. Keeping abundances ﬁxed to

2 the solar values 1T MEKAL model gave unacceptably high values of χν (see Table 3.3 and Figure 3.19a). However, 1T MEKAL model with abundances < 0.1 times solar abundances

+0.08 were found acceptable for the plasma temperature 0.60 0.07 keV as shown in Figure 3.19b. − 2T plasma models with solar abundances were not found to be acceptable (see Table 3.3

+0.14 and Figure 3.19c). The best fit plasma temperature of > 0.08 keV and 0.6 0.5 keV were − obtained with abundances 0.1 0.04 times solar values (Figure 3.19d). A source flux of 12 2 1 3.47 10− erg cm− s− was obtained from the best fit 2T MEKAL model. ×

3.7.3 LO Peg

For LO Peg there were two dataset corresponding to two observations (see Table 2.8). Spectrum was accumulated for each dataset and ﬁtted above mentioned models individually 3.7. X-ray spectra of HD 95559, HD 160934 and LO Peg 81

Figure 3.19 Spectrum of HD 160934 with ROSAT PSPC detector, along with (a) 1T MEKAL model and solar abundances, (b) 1T MEKAL model and sub-solar abundances , (c) 2T MEKAL model and solar abundances, and (d) 2T MEKAL model and sub-solar abundances. The lower panel in each Figure represents the ratio of the observed counts to the counts predicted by the best-ﬁt model

as well as jointly. The values of fitted parameters were found to be similar. The best fitted parameter are summarized in the Table 3.3. The X-ray spectrum of LO Peg along with the MEKAL models along with the ratio of observed count to the counts predicted by best fit model are shown in Figure 3.20. 1T MEKAL models with solar and sub-solar abundances

2 gave unacceptably high value of the χν (see Figure 3.20a and 3.20b). As shown in Figure 3.20c Two-temperature plasma model with abundances ﬁxed to the solar values was also found to be unacceptable (see Table 3.3). Departing the abundances from the solar values 2T plasma models were found acceptable. The best ﬁt two-temperature model with sub-

+0.04 solar abundances is shown in Figure 3.20d. The best fit plasma temperatures were 0.300.05 +0.1 keV and 1.0 0.2 keV, with abundances that were only < 0.15 times the solar values for both − 12 2 1 plasma components. A flux of 6.97 10− erg cm− s− was obtained from the best fit 2T × MEKAL model. 3.8. Comparison of X-ray properties with similar systems 82

Figure 3.20 Spectrum of LO Peg with ROSAT PSPC detector, along with (a) 1T MEKAL model and solar abundances, (b) 1T MEKAL model and sub-solar abundances , (c) 2T MEKAL model and solar abundances, and (d) 2T MEKAL model and sub-solar abundances. The lower panel in each Figure represents the ratio of the observed counts to the counts predicted by the best-ﬁt model

3.8 Comparison of X-ray properties with similar systems

A sample of 35 BY Dra systems were studied spectroscopically with ROSAT by Dempsey et al. (1997) assuming that their coronae had solar abundances. The average value of the low temperature (kT1) and the high temperature (kT2) components for these BY Dra systems are 0.19 0.03 keV and 1.31 0.04 keV, respectively. The value of kT derived 1 using the solar abundances (see Table 3.3) is found to be consistent for all three stars to that of the average value for the other BY Dra systems in Dempsey et al. (1997). The value of kT2 derived using solar abundances for the star HD 95559 was found to be constient with

the average value of similar system. But, the value kT2 using solar abundances for the stars HD 160934 and LO Peg was found to be smaller than the average value of similar systems. However, 2T plasma model using the solar abundances failed to ﬁt the data with high

2 signal-to-noise ratio and gave an unacceptable high value of χν for these stars. The value

of the kT1 derived using sub-solar abundances for the stars HD 95559 and LO Peg (see 3.9. Stellar parameters from optical data 83

Table 3.3) is found to be more than the mean value of the BY Dra systems. However, the

value of kT1 derived using the sub-solar abundances for the star HD 160934 is consistent

with the average value of the similar systems. The values of kT2 derived using the sub- solar abundances are consistent with that of the other BY Dra systems for the stars HD

95559 and LO Peg. However, the value of kT2 derived using sub-solar abundances for the star HD 160934 is found to be less than the average value of the BY Dra systems. The

average volume emission measures EM1 and EM2 for the BY Dra systems in Dempsey 52 52 3 et al. (1997) are 1.4 0.4 10 and 7.6 2.9 10 cm− , respectively. The volume × × emission measures EM for the stars HD 95559 and HD 160934 are found to be 7 8 1 ∼ − times more than the average value of BY Dra systems. However, the value of EM1 for LO

Peg is consistent with that of the BY Dra systems. The values of EM2 of the stars HD 95559 and HD 160934 using sub-solar abundances are consistent with those of the other BY Dra systems. However, the value of EM for LO Peg is 2 3 times less than the 2 ∼ − average value of the other BY Dra systems. For the sample of 101 dwarfs (Padmakar et al. 2000 and literature; see Table 5.1)

1 the average and the median X-ray luminosity (log L ) are 29.6 0.7 and 29.63 erg s− , x respectively. The inferred log Lx for FR Cnc, HD 95559, HD 160934 and LO Peg are 1 29.4 - 30.1, 30.3, 29.4 and 29.7, where Lx is in units of erg s− , respectively, which are all close to the average value of active dwarf systems. Out of 101 dwarfs only 82 have radio ﬂux measurements ( Padmakar et al. 2000 and literature; see Table 5.1). The average and

1 1 median log L for a sample of 82 dwarfs are 14.8 0.7 and 14.9 erg s− Hz− , respectively. rad LO Peg has been detected as a radio source of 3.6 0.5 mJy (Condon et al. 1998). However, FR Cnc, HD 95559 and HD 160934 do not have any radio observations. Using a distance

1 1 25.1 pc, the radio luminosity (log Lrad) of LO Peg is found to be 15.43 erg s− Hz− , which is again close to the typical value for BY Dra type.

3.9 Stellar parameters from optical data

The value of the total Galactic reddening E(B V) in the direction of FR Cnc is estimated − from Schlegel et al. (1998) to be 0.03 mag. However, given that the Hipparcos parallax of this star implies a distance of only 33 parsec, it is likely that its light suﬀers little if any 3.9. Stellar parameters from optical data 84

reddening, and for the remaining discussion, we assume E(B V) = 0.00 mag. Using − the Hipparcos parallax of 30.24 2.03 mas and the value of V = 10.24 mag from our photometry, the absolute magnitude MV of FR Cnc is 7.64 mag. (The Hipparcos V-band

measurements and the V magnitude of Weis (1993) lead to similar values for MV = 7.7 mag and 7.5 mag, respectively). This value is consistent with a luminosity class V for this star. The colour (B V) of FR Cnc derived from our photometry is 1.11 0.02, compared − to a redder, but less precise, value of 1.62 0.20 given in the Hipparcos Catalogue. The 1.11 value of (B V) is best matched with a spectral class of K5 V. While this is three − subclasses earlier than the spectral class (K8) given in the Hipparcos Catalogue, the latter appears to be derived from a fairly crude spectral classification by Vyssotsky (1956) and thus the difference is likely not significant. Observations of the star LO Peg by Jeffries et al. (1994b) showed it to be a single K5-K7 dwarf, while Bowyer et al. (1996) had reported it to be a K8 type star. Assuming negligible reddening, and from the present photometry the

absolute magnitude (MV = 6.8) and colour (B-V = 1.04) of the star LO Peg are consistent with the spectral type of K3V. We have also calculated the Spectral Energy Distribution (SED) of the stars FR Cnc, HD 95559, HD 160934 and LO Peg (see below). The well matched synthetic SED with

observed SED gives the value of T ﬀ of 4250 250, 5250 250, 3750 250 and 4750 250K e for FR Cnc, HD 95559, HD 160934 and LO Peg, respectively. The value of log g for all the four stars was found to be 4.5 0.5. We have determined values of M /M , R /R , L /L for all the four stars using the ∗ ∗ ∗ Hipparcos parallax, the inferred Te f f and log g values, and the following empirical relations (Schaifers & Voigt 1982)

M ∗ = 0.46 0.10M (3.3) M − bol R ∗ = 0.2M 2logT + 8.47 (3.4) R − bol − e f f L M ∗ = 3.8log (3.5) L M

These well-determined parameters along with the MV , Mbol are given in Table 3.4. 3.10. IR excess and spectral energy distribution (SED) 85

Table 3.4. Physical parameters of stars FR Cnc, HD 95559, HD 160934 and LO Peg

Parameter FR Cnc HD 95559∗ HD 160934 LO Peg

Sp. Type K5V K1V K7V K3V V 10.24 0.01 8.93a 10.28 8.82 0.01 M (mag) 7.60 0.01 6.04 8.33 6.80 0.01 V M (mag) 6.83 0.01 5.67 7.32 6.30 0.01 bol T (K) 4250 250 5250 250 3750 250 4750 250 e f f log g 4.5 0.5 4.5 0.5 4.5 0.5 4.5 0.5 L /L 0.13 0.02 0.54 0.03 0.10 0.25 0.02 ∗ M /M 0.60 0.02 0.81 0.01 0.51 0.66 0.02 ∗ R /R 0.70 0.08 0.77 0.10 0.68 0.72 0.10 ∗ µ (mas/y) 98.93 1.99a 140.79 1.24a 31.25 11.57a 132.06 1.01a α − − − µ (mas/y) 97.39 1.44a 4.91 0.87a 59.44 14.15a 144.83 0.93a δ − − π(mas) 30.24 2.03a 18.43 1.19a 40.75 12/06a 39.91 1.18a R (km/s) 27.0 2.3b 3.81 0.11c 26.7 0.1 17.4 1.0 V − − 24.0 4.0b · · · · · · · · ·

∗Parameters are determined for individual component of the binary system, aHipparcos, bUpgren et al. 2002, c Fekel & Henry 2000

3.10 IR excess and spectral energy distribution (SED)

Assuming negligible reddening and the 2MASS JHK magnitudes (Cutri et al 2003), we have determined the intrinsic (J K) and (H K) colour for FR Cnc, HD 95559, HD − 0 − 0 160934 and LO Peg. The intrinsic (J K) and (H K) colour for K1V, K3V, K5V and − 0 − 0 K7V type of the stars are 0.54 and 0.11, 0.62 and 01.4, 0.7 and 0.16, and 0.80 and 0.17 mag, respectively (Koornneef 1983). The intrinsic (J-K) and (H-K) colours of FR Cnc are 0.74 0.03 mag and 0.14 0.03 0 0 mag imply a colour excess of 0.03 0.05 mag and 0.02 0.03 mag in (J-K) and (H-K) colour, respectively. The intrinsic (J K) = 0.539 0.03 mag and (H K) = 0.111 0.03 − 0 − 0 3.10. IR excess and spectral energy distribution (SED) 86

Figure 3.21 Spectral energy distribution of the stars (a) FR Cnc, (b) HD 95559, (c) HD 160934 and (d) LO Peg. The solid lines represents the model SEDs from Kurucz (1993) as expected from the intrinsic properties of the star. The vertical bars show the uncertainty associated due to the distance and the radius of the star. mag colours of HD 95559 give the colour excess 0.00 0.03 in each (J-K) and (H-K) colour. Assuming HD 160934 is a K7V spectral type star and (J K) = 0.81 0.03 − 0 mag and (H K) = 0.19 0.02 mag. The colour excess in HD 160934 is found to be − 0 0.01 0.03 mag and 0.01 0.02 mag in J-K and H-K colour, respectively. The intrinsic (H K) and (J K) for the star LO Peg is 0.02 0.04 mag and 0.00 0.03 mag, respectively. − 0 − 0 Assuming the LO Peg as K3V type star the (J-K) and (H-K) colour excess is 0.02 0.04 mag and 0.00 0.03 mag, respectively. The values of the colour excess for each stars are consistent with zero to within the uncertainties, indicating that all these three stars have no signiﬁcant colour excess in the 3.11. Kinematics and age 87

JHK bands, which is also supported from the matching of the model SEDs as shown in Figure 3.21 (also see below). The presence of circumstellar material, their geometry and the nature of the radiation is best studied by SEDs covering NIR region. We have determined the spectral energy distribution (SED) of FR Cnc, HD 95559, HD 160934 and LO Peg using broad band UB- VRI (present photometry and literature) and 2MASS JHK (Cutri et al. 2003) ﬂuxes. The broad band optical (UBVRI) and NIR (JHK) ﬂuxes were determined using the following equations:

2 D 0.4mλ F(λ) = f (λ)10− (3.6) R2 0 ∗

where D is distance of the star, R is radius of the star, f0(λ) is a broad band zero point ﬂux ∗ of at central wavelength λ and mλ is a broad band magnitude. Distances and radii of all the program stars are given in Table 3.4. Thus, the obtained SEDs of all the four stars are shown in Figure 3.21 (a to d). The synthetic SEDs from Kurucz (1993), predicted from the intrinsic properties of the stars are plotted over the observed SEDs (see Figure 3.21). The well matched synthetic SEDs with the observed SEDs do not show any signiﬁcant near IR excess in the JHK bands for each star.

3.11 Kinematics and age

FR Cnc, HD 95559, HD 160934 and LO Peg are inside the boundaries for the young disk population in the (U,V) and (W,V) diagrams (Montes et al. 2001). The (U,V,W) components of FR Cnc are close to that of the IC 2391 supercluster (-20.6, -15.7, -9.1) which is estimated to have an age of 35 to 55 Myrs, and for which several dozen possible late-type members have been previously identiﬁed. We have also calculated the UVW

1 components for the star HD 95559 using the radial velocity 3.81 0.11 km s− (Fekel & Henry 2000) and the parallax and proper motion given in the Hipparcos Catalogue. The UVW components of this star (see Table 3.5) indicate that it is possible member of the 600 Myr Hyades supercluster, although as already noted its strong Li I absorption lines are more consistent with a Pleiades-type age of 100 Myrs (Fekel & Henry 2000). The UVW components of the star HD 160934 indicate the it is a possible member of the Local 3.12. Colour-magnitude diagram (CMD) 88

1 Table 3.5. Galactic space-velocity components. All the units are in km s−

R σ U σ V σ W σ V σ V RV U V W total Vtotal

FR Cnc

27.0 2.3 25.2 1.7 23.4 0.9 4.3 1.4 34.7 2.0 − − − 24.0 4.0 23.0 3.1 22.2 1.7 5.7 2.2 32.5 3.7 − − − HD 95559

3.81 0.11 32.9 0.4 10.9 0.2 11.2 0.1 36.4 05 − − − HD 160934

26.7 0.1 6.9 1.7 24.5 0.7 11.2 1.2 27.8 1.6 − − − − LO Peg

17.4 1.0 5.2 0.29 23 0.95 23.86 0.95 29.0 − − − −

Association (-11.6,-21.0,-11.4). The star LO Peg has also been identiﬁed as a young star previously: as either a member of the 100 Myrs old Local Association (Montes et al. 2001) or of the 50 Myr old AB Dor moving group (Zuckerman et al. 2004).

3.12 Colour-magnitude diagram (CMD)

In order to further constrain the age of FR Cnc, HD 95559, HD 160934 and LO Peg we have used pre-man sequence isochrones from Siess et al. (2000). Figure 3.22 shows the colour- magnitude (B V vs M ) for pre-main sequence isochrones. The continuous line − V shows the ZAMS and dotted lines are 5, 10, 35 and 80 Myrs isochrones (from top to bottom). The error bars shown in B V and M are deviation of one subclass from the − V spectral type of the star. The position of FR Cnc in the HR Diagram is right on the ZAMS, but it is also consistent to within 1 σ with the upper range age of 55 Myrs for stars in the IC 2391 supercluster. The position of the star HD 95559 is left to the ZAMS imply that 3.12. Colour-magnitude diagram (CMD) 89

Figure 3.22 B V vs M diagram. Dotted lines are 5, 10, 35 and 80 Myrs isochrones from − V top to bottom and continuous line corresponds to ZAMS. this is younger than 80 Myrs. Which supports the conclusion drawn by Fekel & Henry (2000), that this system has just reached to the ZAMS. HD 160934 is located to the left of the ZAMS, indicates that this star is older than 80 Myrs. Position of LO Peg in colour- magnitude diagram indicates that this star is younger than 80 Myrs.

Chapter 4

HD 81032: A new long period RS CVn binary

4.1 Overview

Evolved active stars (e.g. RS CVn and FK Comae) are amongst the most commonly known type of active stars. Popper & Ulrich (1977) argue that the RS CVn systems evolve from normal non-emission main-sequence binaries, acquiring their properties only after entering the Hertzsprung gap. As the evolved active stars have larger surface area, they are more X-ray and radio luminous than the dwarfs. This indicate that evolved active stars are much more coronally active than dwarf active stars. In this chapter, we present extensive optical photometric and spectroscopic observations, as well as an analysis of archival X-ray and IR data of an evolved active star HD 81032 and show that it is an RS CVn binary. This is the ﬁrst detailed optical photometric and spectroscopic study of this star.

4.2 Introduction

The K0 IV star HD 81032 (Houk & Smith-Moore 1988) was first noticed as an X-ray active star when it was identified as the likely optical counterpart of a soft X-ray (0.2-4.0 keV) source in the Einstein Slew Survey, 1ES 0920-13.6, with an X-ray flux of 2.1 0.9 × Major part of this chapter is published in Pandey et al. (2002a) and communicated in Pandey et al. (2005b)

91 4.2. Introduction 92

-3.0 -3.0

-2.8 -2.8

0.006 0.010 0.004 -2.6 -2.6 0.005 0.002

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4

1900 1950 2000 2250 2300

-3.0 -3.0

-2.8 -2.8

0.0010 0.0010 -2.6 -2.6 0.0005 0.0005

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4

2600 2620 2640 2980 3000 3020 3040 3060 3080

Figure 4.1 V band light curves and corresponding CLEANed power spectra of the star HD 81032 at diﬀerent epoch

11 2 1 10− erg cm− s− (Elvis et al. 1992, Schachter et al. 1996). An X-ray source at this position was later detected in the RASS at a weaker (but statistically more signiﬁcant) level

12 2 1 of 3.9 0.4 10− erg cm− s− , named 1RXS J092253.7-134919 in the RASS Bright × Source Catalogue (Voges et al. 1999). Given its spectral type and luminosity class, and its V-magnitude of 8.91 (Wright et al. 2003), the spectroscopic distance of HD 81032 is

31 1 140 45 pc, implying an X-ray luminosity of 0.92 0.45 10 erg s− (based on the RASS × value), where the distance uncertainty is the dominant contributor to the large errors in the luminosities. These values clearly show that the star HD 81032 has an active corona. 4.3. Photometric light curves and period analysis 93

4.3 Photometric light curves and period analysis

The broad band B, V and R observations of HD 81032 have been carried during the years 2000 - 2004 (see Table 2.4). Photometric light curves corresponding to the four observing runs are studied. Differential light curves are obtained as all the program, comparison, and check star are on the same CCD frame (see Figure 2.2). Figure 4.1 shows the V band differential light curves of the star HD 81032 at different epochs. We did not find any significant variations in the comparison star. Lower panel of Figure 4 (a to e) shows the differential light curves of the comparison star in the sense of comparison minus check star. The yearly mean of the standard deviation(σ) between the different measures of comparison and check stars in the B, V and R filters was found to be 0.011, 0.01 and 0.01 mag (see Table 2.4), respectively. Each light curve shown in Figure 4.1 was analysed for periodicity. To find a period from unequally spaced data, we used the CLEAN algorithm (see 2.8). The power spectrum § obtained using this method is shown in the inset of each panel of Figure 4.1 along with the period determined. The CLEANed power spectra presented were obtained after 100 iterations with a loop gain of 0.1. The period is found to be constant within error for each epoch. To improve the period determination of the star HD 81032, the entire data from 2000 - 2004 were analysed using the same algorithm. Figure 4.2 shows the CLEANed power spectrum from the entire dataset. The highest peak in the CLEANed power spectrum corresponds to a period of 18.802 0.074d. The 18.802 d period is much more plausible than the 57 d period reported by Pandey et al. (2002a). This determination was mainly due to observational limitations as our early data were too sparse and highly uneven. Besides a subgiant like this one is unlikely to be synchronized in a of 57-days period binary.

4.4 Photometric variation and phase of minima

The Julian days of the observation were converted to the phases using the ephemeris: Phase(θ) = JD2452307.761 + 18d.802E where the initial epoch ’E’ corresponds to the conjunction with the first minimum observed. Figure 4.3 shows the differential B, V, R and Vc, light curves and, (B-V) and (V-R) colour curves of the star HD 81032. Here Vc stands for the differential V band light curve 4.4. Photometric variation and phase of minima 94

0.0002

0.0001

0.1 0.2 0.3 0.4

Figure 4.2 CLEANed power spectra of the entire data set of the star HD 81032

of the comparison and the check stars. Each point in the light curves is mean of 3 - 4 independent observations taken over a night. The light curve during the observing years 2001-2002 has a dense temporal coverage. We, therefore, divided this light curve into two diﬀerent epochs to see any variation in the θmin and the amplitude. The mean epoch of the light curves, the observed maximum (∆Vmax) and minimum (∆Vmin) in the V band, peak to peak amplitude (∆V = ∆V ∆V ), and phase of minima(θ ) are listed in Table max − min min 4.1. The value of ∆Vmax was constant during each epoch indicating that the brightness of unspotted photosphere was constant from epoch to epoch. However, the value of ∆Vmin was reduced by 0.14 mag from epoch ’a’ to epoch ’b’, and remained constant during the epoch ’c’, ’d’ and ’e’. The RS CVn systems usually show one or two well deﬁned minima, thereby indicating that the rotational modulations caused by one or two prominent spots or groups of spots.Additional spots may be present at other longitudes, or in the circumpolar regions but contribution to the overall rotational modulation may not be appreciable.The phase of the

light minimum (θmin) directly indicates the mean longitude of the dominant groups of spots. A sharp minimum was observed during the epoch ’a’ (see Figure 4.3a). At the same time the amplitude of the V band light curve was found to be 0.288 mag, which was maximum during our observations. The sharpness of the minimum indicate that it is the latitudinal extent of the groups of spots that may be responsible rather than the longitudinal extent. 4.4. Photometric variation and phase of minima 95

0.24 0.24

0.32 0.32

0.48 0.48

0.56 0.56

-3.20 -3.20

-3.00 -3.00

-2.80 -2.80

-2.60 -2.60

-2.40 -2.40

-0.80 -0.80

-0.60 -0.60

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 PHASE PHASE

0.24 0.24

0.32 0.32

0.48 0.48

0.56 0.56

-3.20 -3.20

-3.00 -3.00

-2.80 -2.80

-2.60 -2.60

-2.40 -2.40

-0.80 -0.80

-0.60 -0.60

0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.4 0.8 1.2 1.6 2.0 PHASE PHASE 4.4. Photometric variation and phase of minima 96

0.24

0.32

0.48

0.56

-3.20

-3.00

-2.80

-2.60

-2.40

-0.80

-0.60

0.0 0.4 0.8 1.2 1.6 2.0 PHASE

Figure 4.3 Differential V , B, V, R light curve and (B V), (V R) colour curve of HD 81032. c − − ∆Vc stands for the differential magnitude between comparison and check stars. The light curve is folded using the period 18.802 d. The epoch of each light curve is mentioned at the top. The lower panel in each figure represents the plot of different measures of comparison and check stars

Broad minima during the epochs ’b’,’c’ and ’d’ indicate that the spots were spread over an appreciable longitudinal range (Figure 4.3 b to d). It is interesting to see the light curve of the star HD 81032 during the epoch ’e’. Here a single large spot, characterized by a broad minimum during the epochs ’b’, ’c’ and ’d’ separated into two groups of spots. This can be easily seen by two well separated minima (see Figure 4.3 e). Significant change in θmin (see Table 4.1) is probably associated with a change in the spot configuration on the surface of the star. Variation in the colour of the star HD 81032 is correlated with its magnitude (see top two panels of Figure 4.3 a to e) i.e. the star becomes redder when fainter, and bluer when brighter, supporting the starspot hypothesis. The significance of the correlation has been calculated by determining the linear correlation coefficient, r, between the magnitude and 4.5. Hα and CaII H and K emission lines 97

Figure 4.4 Plot of mean epoch versus light minima. The solid line represents the linear least square ﬁt of the equation (3.1). The open circles were not used in the ﬁt.

the colours. The value of r between V and (B-V), V and (V-R) and (B-V) and (V-R) was found to be 0.20, 0.55 and 0.40, with the corresponding probability of no correlation being

12 6 0.0253, 6.157 10− and 2.443 10− , respectively. The conventional starspot model × × assumes that the spots are cooler than the surrounding photosphere, and hence one would expect the star to be the reddest at the light minimum, although ﬂaring activity can lead an opposite eﬀect being observed as seen in UX Ari (Ulvås & Henry 2003; Padmakar & Pandey 1999; Ravindran & Mohin 1995).

Figure 4.4 shows the plot of the mean epoch versus phase minima (θmin) of the V band light curves. The following relation was ﬁtted to the data by the method of linear least squares to determine the rate of the phase shift. The equation (3.1) when ﬁtted to the data by the method of linear least squares yields the rate of phase shift for the group of spot as 0.1348 0.002 degree/day, which corresponds to a migration period of 7.32 0.04 years. The arrangement of groups of spots in one permanent strip can be easily interpreted as a long lived active group rotating with the same velocity. The open circles in the Figure 4.4 are not following that strip, and may be due to the formation of a new group of spots on the surface of the star. 4.5. Hα and CaII H and K emission lines 98

Table 4.1 Parameters determined from the light curves of the star HD 81032.

Mean epoch Amplitude ∆Vmin ∆Vmax phase minima 245000.0+ I II (a) 1946.3350 0.288 -2.739 -3.027 0.01 (b) 2245.8599 0.160 -2.893 -3.053 0.12 (c) 2322.6527 0.156 -2.896 -3.052 0.15 (d) 2621.4426 0.152 -2.890 -3.042 0.07 (e) 2983.8913 0.175 -2.891 -3.066 0.89 0.40

HD 71952

HD 81032

6200 6400 6600

Figure 4.5 Hα spectra of HD 81032. HD 71952 was taken as reference spectra 4.5. Hα and CaII H and K emission lines 99

HD 71952

1ES 0920-13.6

3900 4000 4100 4200

Figure 4.6 Ca II H & K spectra of HD 81032. Spectra of HD 71952 was taken as a reference 4.5 Hα and CaII H and K emission lines

As in the case of dwarf active stars, the Hα and CaII H & K emission lines are important indicators of chromospheric activity in evolved active stars. But, in dwarf active stars the strength of Hα emission feature is more than in the evolved active stars. In very active evolved stars like II Peg, V711 Tau, UX Ari the Hα emission is seen clearly above the continuum, whereas in less active stars only a ﬁlled in absorption line is observed. Figure 4.5 shows spectra of HD 81032 in the Hα region. Spectrum of the star HD 71952 (V = 6.25 mag; spectral type = K0IV) is shown for comparison. Hα emission line can be seen clearly in the star HD 81032 (Figure 4.5). It has been suggested that in the RS CVn systems at least one star must also show the intense emission in the H and K lines of CaII (Fekel et al. 1986). As shown in Figure 4.6, CaII H and K lines are above the continuum at all the phases observed. The measured equivalent widths (EWs) of the Hα, CaII H and K emission 4.6. Spectral type and physical parameters 100

Table 4.2 Equivalent widths (EWs) of CaIIH&K and Hα emission lines JD Phase EWs (Å) 245000+ CaIIK H Hα 2659.626 0.71 1.828 1.037 - 2660.513 0.76 - - 0.980 2661.520 0.82 4.393 2.661 1.178 2662.518 0.87 5.012 2.949 1.651 2663.536 0.92 - - 1.680 feature, the corresponding JD and phase are listed in Table 4.2. The photometric observations during the epoch ’d’ were close to the spectroscopic observations. Figure 4.7 shows the plot of EWs of Ca II H, K and Hα against phase, along with the V band light curve of the epoch ’d’. It appears that Hα, Ca II H, and K emission features are variable and anti-correlated with the photometric phase i.e. the maximum at photometric minimum and minimum at photometric maximum. This could be due to the presence of active cool spots on the surface of the star.

4.6 Spectral type and physical parameters

The value of the total galactic reddening E(B-V) in the direction of HD 81032 is estimated to be 0.04 mag from the reddening map given by Schlegel et al. (1998). However, the star HD 81032 suﬀers negligible reddening at a distance of 140 pc, and we assume E(B- V) = 0 for the remaining discussion. Using the Tycho parallax (Hog 1997) and the value of V(= 8.63 mag) mag from the present photometry the absolute magnitude MV of HD

81032 is 3.04 mag. The value of MV is consistent with the luminosity class IV for this star. The (B V) colour of HD 81032 derived from our photometry is 1.02 0.01 consistent − with the value of 0.98 0.05 given in the Tycho catalogue (Wright et al, 2003). The (B-V) colour is best matched with the spectral class K0IV, and is consistent with the spectral class identiﬁed by Wright et al, (2003). Applying the bolometric correction -0.4 (Schaifers & Voigt 1982) for K0IV star, the bolometric magnitude of HD 81032 is 2.65 mag. 4.7. SED of HD 81032 101

-3.0

-2.9

1.8

1.2

4.0

2.0

2.4

1.2

0.0 0.2 0.4 0.6 0.8 1.0 phase

Figure 4.7 (I) V light curve of the HD 81032 during the epoch ’d’, (II) variation of EW of Hα emission feature, (III) CaII K EW and (IV) Ca II H EW. Phases are reckoned from JD 2452307.761 and the period 18d.802.

4.7 SED of HD 81032

We have determined the SED of HD 81032 using broad band UBVRI (present photometry), 2MASS JHK (Cutri et al. 2003) and 12, 25, 60 and 100 µ IRAS (Moshir 1989) fluxes using the equation (3.6). However, only upper limits are available at 25, 60 and 100 µm. We have assumed negligible reddening towards the direction of HD 81032. The observed SED of HD 81032 along with the synthetic SED is shown in Figure 4.8. The synthetic SED is expected from the intrinsic properties of the star. We have overplotted the synthetic SED for the different Teff and log g combinations. The values of Teff and logg which best match the observed SED are 5000 250 K and 3.5 0.5, respectively, and are consistent within 4.8. X-ray light curve 102 one subclass of the inferred K0IV spectral type of the star HD 81032 (see 4.6). The § continuum of HD 81032 is in good agreement with the normal values for the spectral type of K0IV up to JHK band but deviates in all bands longer than 25µm (see Figure 4.8). The difference between the observed and the expected (J-K) and (H-K) colours are 0.06 0.04 and 0.005 0.03 mag, respectively. This indicates that there is no significant colour excess in J, H and K band. The expected (J-K) and (H-K) colours were taken from the spectral type of the star (Koorneef, 1983). The 12 µm magnitude (m12) of the star HD 81032 was found to be 6.09 0.17 mag using the relation m = 2.5logf +3.63 (Mitrou et al. 1996). 12 − 12 The intrinsic [K 12] colour of the star HD 81032 is determined to be 0.03 0.17 mag. − The expected [K 12] colour of 0.14 mag for the K0IV type star (Verma et al. 1987) gives − the colour excess of 0.11 mag, which is consistent with the ideal value of 0.0 0.2 mag (Mitrou et al. 1996).

4.8 X-ray light curve

The light curve for the source and background were extracted using the ”xselect” package for the PSPC 0.1 - 2.4 keV energy band which contains all the X-ray photons. The background-subtracted X-ray light curve of HD 81032 is shown in Figure 4.9 plotted with a time bin size of 64 s. It appears from the light curve that a moderate ﬂare occurred during

1 the RASS observations, with a peak of about 0.6 ct s− (compared to a pre-ﬂare level of 0.2

1 - 0.3 ct s− ) at approximately JD = 2448206.95 (1990/11/11 10:48:0.0) and a half-decay time of 2.6 104 s. ×

4.9 X-ray spectra

The X-ray spectrum of HD 81032 as observed with the ROSAT PSPC is shown in Fig- ure 4.10. Response matrices based on the available off-axis calibration of the PSPC and using the appropriate ancillary response files were created and data were fitted using the xspec (version 11.3.1) spectral analysis package. Spectral models for thermal equilibrium plasma known as the MEKAL model (Liedahl et al. 1995; Mewe et al. 1995) were used (for more detail see 2.6.3). The background-subtracted X-ray spectra were fitted with § 4.9. X-ray spectra 103

-6.0

-8.0

-10.0

-0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4

Figure 4.8 SED of the star HD 81032. The solid line represents the best matched model SEDs from Kurucz as expected from the intrinsic properties of the star.

1-temperature (1T) and 2-temperature (2T) plasma models, either assuming solar photospheric abundances as given by Anders & Grevesse (1989) or allowing the abundance of every element other than H to vary by a common factor relative to the solar (photospheric) values. In each of the above models the interstellar absorption was assumed to follow the absorption cross-sections given by Morrison & McCammon (1983), and the total intervening hydrogen column density NH was allowed to vary freely. The results of different model fits are summarized in Table 4.3. Single-temperature MEKAL models with abundances fixed to the solar values gave unacceptably high values

2 for χν, and thus can be rejected (see Figure 4.10a). However, single-temperature plasma +0.14 +0.17 models with abundances of 0.19 0.08 times solar and plasma temperature of 0.84 0.20 were − − found acceptable (see Figure 4.10b). Alternatively, two-temperature MEKAL models with 4.9. X-ray spectra 104

Figure 4.9 Background subtracted RASS PSPC X-ray light curve of HD 81032. The bin size in the light curve is 64 s

Table 4.3 Results of X-ray spectral analysis a 2 Model Abundances NH kT1 EM1 kT2 EM2 χν Degrees of 20 2 52 3 53 3 10 cm− (keV) 10 cm− (keV) 10 cm− freedom . 0.22 . +0.29 . +2.2 MEKAL 1T 1.0 (fixed) 0 21 0.16 0 85 0.10 5 2 2.5 1.87 17 − − − . 0.14 . +1.0 . +0.20 . +14.7 MEKAL 1T 0 19 0.08 1 5 1.0 0 84 0.17 18 9 9.9 1.53 16 − − − − . +5.4 . +0.2 . +5.7 . +0.52 . +1.1 MEKAL 2T 1.0 (fixed) 1 4 1.1 0 2 0.1 2 9 1.5 1 12 0.36 1 8 1.6 1.4 15 a Common value of abundances for all the elements− respect−to the solar photosphere− v−alues; Errors−are with 90% confidence for single 2 parameter based on χmin + 2.71; distance = 140 pc.

+0.2 fixed solar abundances were also found to be acceptable; the two temperatures being 0.2 0.1 − +0.52 keV and 1.12 0.36 keV. Multi-temperature variable abundance models would also produce − acceptable fits to the PSPC spectrum, but the small number of accumulated counts does not warrant such complex models. The PSPC spectrum and the best-fit two-temperature plasma model with solar abundances are shown in Figure 4.10 along with the significance of the residuals in terms of their χ2. 4.9. X-ray spectra 105

Figure 4.10 Spectra of HD 81032 taken with the ROSAT PSPC detector, along with 1T MEKAL model and solar abundances, (b) 1T MEKAL model and sub-solar abundances and (c) 2T MEKAL model and solar abundances. The lower panel in each ﬁgure shows the χ2 for each bin. 4.10. X-ray and radio properties: comparison with similar systems 106

4.10 X-ray and radio properties: comparison with similar systems

+0.9 12 2 1 Based on the best ﬁt 2T MEKAL model a source ﬂux of 9.1 1.6 10− erg cm− s− was − × obtained. At a distance of 140 pc the X-ray luminosity of HD 81032 is calculated to be

+0.2 31 1 2.1 0.4 10 ergs− , similar to that of known subgiants RS CVn binaries (Drake et al. 1989, − × Singh et al. 1996 a, 1996b; Dempsy et al. 1997; Padmakar et al. 2000; Pandey et al. 2005c). The derived X-ray luminosity is about a factor of 2 bigger than the earlier estimate

20 2 given in 4.2. This may be due to the non-trivial column density of 1.4 10 cm− inferred: § × objects with a high column density will typically have a higher count rate to ﬂux conversion factor than the standard one which assumes a low column density. The values of kT1 and kT2 of HD 81032 (see Table 4.3) are consistent with those of other RS CVn systems studied by Dempsey et al. (1997), who found an average value of 0.18 0.01 keV and 1.37 0.04 keV for a sample of 28 RS CVn systems.The volume emission measures EM1 and EM2 of HD 81032are also found to be consistent with those of the other similar systems, where the average volume emission measures EM and EM are 1.2 0.3 1053 and 5.7 1.2 1053 1 2 × × 3 cm− , respectively (Dempsey et al. 1997). The average and median radio luminosity of a sample of 64 subgiants is 16.3 0.7 1 1 and 16.33 erg s− Hz− , respectively (see Table 5.1). The star HD 81032 was detected on 1993 February 12 as a radio source, with a 3.6 cm ﬂux of 0.68 0.05 mJy (Drake, S. A. private communication). The inferred radio luminosity (log Lrad) of HD 81032 is 16.2 1 1 erg s− Hz− is consistent with the average value for similar systems.

Chapter 5

Correlation between various physical quantities of Active Stars

5.1 Overview

Most of the active stars are strong X-ray and radio emitters. The radio emission is attributed to a persistent population of mildly relativistic electrons (see 1.4.6). There is considerable § interest in correlating radio-emission with X-ray emission. The standard ﬂare models in- volve electron beam (visible at radio wavelengths) that heat the plasma to X-ray emitting temperatures. So, signiﬁcant correlation between Lx and Lrad has been shown by various authors (Drake et al. 1989; Padmakar et al. 2000). As discussed in 1.6 the dynamo is § inversely proportional to the square of Rossby number hence the square of rotation period. So, it is inferred that these emissions are also correlated with the rotation period. Previ- ously, such correlations were shown by Walter & Bowyer (1981), Vilhu (1984), Drake et al. (1989) and Dempsy et al. (1997) with smaller number of sample. In this chapter we discuss the correlations between the optical, X-ray, radio emission and colours, and their interpretation. The correlations of X-ray and radio emission with rotation and (B-V) colour are also discussed.

108 5.2. Our sample and previous studies 109

5.2 Our sample and previous studies

Based on our perusal of the literature we find that at present X-ray flux measurements exist for a sample of 248 active stars. On the basis of Simbad∗ spectral classification and the catalogue of CABS we have divided the sample into 101 dwarfs, 65 subgiants, and 82 giants. A significant correlation has been shown to exist between X-ray and radio luminosities for active binaries by Drake et al. (1989), Dempsey et al. (1993, 1997) and Padmakar et al. (2000). Drake et al. (1989) used a sample of 71 (26 out of which have radio upper limits), Dempsey et al. (1993) used a sample of 80 (23 of which have radio upper limits), Dempsey et al. (1997) used a sample of 101 (36 of which have radio upper limits), and later on Pad- makar et al. (2000) used a larger sample of 202 (101 of which have radio upper limits). Our larger sample (compared to that of Dempsey et al. 1997), when subdivided into different types of stars provides us nearly 2-3 times bigger sample for each type when compared to the earlier samples mentioned above. It contains 82 dwarfs (inclusive of 52 radio upper limits), 64 subgiants (inclusive of 22 radio upper limits), and 80 giants (inclusive of 47 radio upper limits). The entire sample used for the present study is given in Table 5.1. It lists the name, spectral type, V band magnitude, period, distance, radio luminosity, X-ray luminosity, (B-V) colour and radius of the active star. For comparison we noted that the sample of Dempsey et al. (1997) contained only 27 dwarfs, 28 subgiants and 38 giants. Therefore, we have re-examined the correlations between various quantities for the three stellar types. All the correlations are computed using the maximum likelihood (ML) algorithm of Drake et al. (1989), which accommodates censored data in one variable.

5.3 HR-diagram of active stars

The positions of 248 active stars on a Hertzsprung-Russell Diagram (HRD, brightness MV vs. colour B-V) are shown in Figure 5.1 The dwarfs are represented by open circles, the subgiants are represented by open squares and the giants are represented by open triangles.

The absolute magnitude MV was calculated from the apparent magnitude mV by reducing

∗The SIMBAD database is operated at CDS, Strasbourg, France; http://simbad.u-strasbg.fr/Simbad 5.3. HR-diagram of active stars 110

Figure 5.1 The Hertzsprung-Russel diagram of 248 active stars. Here open triangle represents giants, open square represents subgiants and circle represents dwarfs. All the classi- ﬁcation has been done on the basis Simbad spectral classiﬁcation. Solid lines from bottom to top represent the main-sequence, subgiant and giant branch, respectively the unit distance of r = 10 pc, so that

M = m + 5 5log(r) A (5.1) V V − − V where r is distance in pc and AV is interstellar absorption. In our sample most of the stars are nearby, it is likely that their light suﬀers negligible reddening, we assume E(B-V) =0.00 mag. The solid lines from bottom to top in Figure 5.1 represent main-sequence, subgiants and giant branch, respectively. 5.3. HR-diagram of active stars 111

Table 5.1. Database of active stars with radio and X-ray measurements

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

Systems containing a dwarf companion

ADS 48A DK6 8.23 3.04 11.0 < 14.16 27.60 1.44 0.72* V471 TAU WD/K2V 9.71 0.52 59.0 15.62 29.76 0.87 0.74 YY GEM DM1E/DM1E 9.07 0.81 13.7 14.35 29.42 1.35 0.62 UX FOR G5-8V/(G) 7.99 0.96 35.0 15.12 30.09 0.73 0.92 DF UMA DM0E/(DM5) 10.14 1.03 22.7 < 14.54 29.23 0.69 0.6/0.27 DH LEO K0V/K7VK5V 7.75 1.07 32.0 14.98 30.09 0.88 0.97/0.67 CM DRA M4VE/M4VE 12.90 1.27 14.5 < 14.13 28.48 1.60 0.252/0.23 CC ERI K7VE/WDM4 8.76 1.56 12.0 < 14.03 29.26 1.39 0.7/–* TZ PSA G5VP 7.59 1.65 46.0 < 15.01 29.63 0.71 0.92 V833 TAU DK5E 8.16 1.90 16.7 14.86 29.62 1.12 0.92 V837 TAU G2V/K5V 8.10 1.89 55.0 16.14 31.00 0.70 1.0/0.72 FF AND DM1E/DM1E 10.38 2.17 23.8 < 14.67 29.53 1.38 0.55/0.55 BD+23 635 DK0/DM0: 9.34 2.39 40.0 < 14.98 29.90 1.09 0.85/0.60 CP-32 5229 K5VE 10.40 2.45 40.0 15.01 29.64 1.18 0.72 KZ AND DK2/DK2 7.98 3.03 23.0 14.62 29.86 0.89 0.74 V1396 CYG M2V/M4VE 10.13 3.28 15.9 14.01 29.23 1.52 0.4/ BD-00 4234 K3VE/K7VE 9.87 3.76 50.0 < 14.92 29.48 0.98 0.8/0.7 FK AQR DM2E/DM3E 9.05 4.39 8.3 13.63 29.11 1.50 0.55/0.4 V818 TAU G6V/K6V 8.31 5.61 44.7 < 14.70 29.51 0.77 0.92/0.72 BY DRA K4V/K7.5V 8.07 3.83 15.6 14.57 29.45 1.22 1.2 *.4/ OU GEM K3V/K5V 6.79 7.36 12.0 < 13.60 29.23 0.95 0.8/0.72 MS SER K2V/K6V 8.36 9.60 30.0 < 14.40 29.23 1.08 0.8/0.72 V1285 AQL M3.5VE/M3.5V 10.10 4.00 10.8 13.90 29.00 1.75 0.44/0.44 GL 268 DM5E/DM5E 11.47 10.43 5.9 < 12.92 28.00 1.71 0.27/0.27 V808 TAU K3V/K3V 9.67 6.28 42.0 < 14.93 29.00 1.06 0.8/0.8 ADS 11060C K7V/K7V 10.62 9.00 41.7 < 14.70 30.45 1.36 0.7/0.7 HR 7578 K2-3V/K2-3V 6.16 3.24738 15.0 < 13.91 28.60 1.05 0.72/0.72* V775 HER K0V/(K5-M2V) 8.04 2.879395 24.0 < 14.55 28.85 0.91 0.85/ TZ COL G1V 9.05 2.27 85.0 < 15.44 29.92 0.60 1.07 XY UMA G3V/(K4-5V) 9.62 0.4789944 100.0 < 15.56 30.46 0.58 0.98/0.73 BI CET G5V/G5V 8.08 0.515782 60.0 16.14 30.60 0.72 0.9/w0.9 SV CAM G2-3V/K4V 8.40 0.593071 74.0 < 15.42 30.20 0.67 1.11/0.74 RT AND F8V/K0V 8.95 0.6289298 95.0 < 15.24 30.11 0.48 1.17/0.84 CG CYG G9.5V/K3V 9.97 0.6311434 63.0 < 15.04 29.48 0.86 0.88/0.87 ER VUL G0V/G5V 7.27 0.6980951 46.0 15.84 30.57 0.57 1.07/1.07 XY LEO B M1V/M3V 9.67 0.8050 58.0 15.34 29.48 1.03 0.6/0.5* UV PSC G4-6V/K0-2V 8.99 0.861048 125.0 16.22 31.07 0.67 1.21/.91 V772 HER G0V/M1VG 7.02 0.879504 41.7 15.31 30.61 0.62 1.0/0.6 IL COM F8V/F8V 8.08 0.9616 86.0 < 15.18 30.46 0.49 1.1/1.1 5.3. HR-diagram of active stars 112

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

SIGMA2 CRB F6V/G0V 5.70 1.139791 21.0 16.05 30.49 0.51 1.22/1.21 IM VIR G5V/(K-M) 9.00 1.3086 60.0 < 14.98 29.92 0.64 0.92* V815 HER G5V/(M1-2V) 7.66 1.809837 31.0 15.26 30.38 0.70 0.97/ 13 CET A F7V/G4V 5.20 2.08200 21.3 < 13.91 29.00 0.60 1.3/0.9 V478 LYR G8V/(DK-DM) 7.68 2.130514 26.0 14.74 30.06 0.74 0.9/ AG DOR K1VP 8.67 2.562 32.0 15.91 29.81 1.00 0.8* HR 8170 F8V/WK5V 6.40 3.243347 29.0 < 14.21 29.72 0.53 1.11/0.74 BF LYN K2V/(DK) 7.70 3.80406 29.0 14.85 30.29 0.99 0.78/0.7 XI UMA B G5V 4.87 3.9805 7.9 < 13.48 29.43 0.76 0.92* BD+14 690 G0V 7.00 4.00000 45.0 < 15.34 29.51 0.50 1.1* SZ PIC G8V 7.90 4.96 30.0 14.60 29.52 0.76 0.88* AS DRA G4V/G9V 8.00 5.412514 29.4 < 14.19 29.30 0.73 0.9/0.8 V1423 AQL G5V/G5V 7.79 5.43435 34.0 < 14.37 29.45 0.66 0.92/0.92* WZ ARI G4V/G6V 8.36 6.15 50.0 < 14.76 28.71 0.67 0.9/0.9 KT PEG G5V/K6V 7.04 6.201986 25.0 < 14.22 29.18 0.74 0.93/0.72 LR HYA K0V/K0V 7.58 6.86569 34.0 < 14.48 28.30 0.86 0.8/0.8 V918 TAU K0V 8.59 0.99 35.0 < 14.87 28.73 0.72 0.90 DE BOO K2V 5.97 0.81 11.9 < 13.88 28.72 0.83 0.8* V819 Her F2V/G0G 5.51 69.0 < 15.12 29.48 0.63 1/10 · · · HR 9038 K3V 6.39 11.90 10.8 13.58 28.31 0.96 0.8* HD 16287 K2V 8.11 11.78 27.0 < 14.24 28.42 0.95 0.8* HD 284303 K1V/K5V 9.56 1.887 45.0 < 15.08 30.07 0.86 0.82/0.72* KZ PAV F6V 7.26 0.9498768 110.0 < 16.03 30.51 0.39 1.3* DY LEO F9V/K0:V 7.59 3.39 53.0 < 14.87 29.84 0.60 1.1/0.85 LN PEG G8V/K5V 8.40 1.84 55.0 15.53 30.09 0.81 0.88/0.72* V368 CEP G9V 7.54 2.74 29.0 < 14.40 30.43 0.86 0.85* HD 286898 G0V/K1V 8.94 1.868 45.0 < 14.56 29.49 0.53 1.1/0.82* VV CRT G0V/G5V 9.42 2.296 115.0 < 15.50 29.99 0.62 1.1/.92* BY CET G9V/K4V 9.55 7.655 55.0 < 15.34 29.63 0.70 0.88/0.72* HD 71208 F8V 8.62 6.951 87.0 < 15.13 29.37 0.50 1.2* V838 Cen K0 *VP 8.97 1.848 41.5 < 15.62 30.10 0.91 0.85* LO Peg K5V 9.24 0.424 25.2 15.430 29.70 1.10 0.72* EP Eri K1V 6.00 10.4 < 13.41 27.84 0.91 0.85* · · · WY Cnc G5V 9.47 0.82937 85.0 15.60 30.45 0.70 0.92* UV Leo G0V 8.98 0.60 92.0 < 15.56 30.56 0.62 1.1* SZ Crt K4/K5V 8.61 11.58 13.2 < 14.32 29.12 1.36 0.72/0.72* BH Vir G0V 9.68 0.81687161 126.0 < 15.53 30.34 0.61 1.1/1.2 QY Aur M4.5V 11.47 6.4 < 13.16 27.94 1.72 0.27* · · · KSI Boo G8V 4.55 10.137 6.7 < 13.03 27.84 0.76 0.88* BU 163 G0V 7.03 50.0 < 14.87 29.75 0.56 1.1* · · · 5.3. HR-diagram of active stars 113

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

V1430 Aql K0V 10.5 0.8 93: < 15.13 30.06 0.90 0.85 DS Leo M1V 9.69 11.7 < 14.21 27.66 1.31 0.55 · · · CF TAU F8V 10.03 2.75589 200.0 16.61 30.30 0.90 1.18 BE Psc G2V 8.24 91.9 350.0 31.39 0.96 1.0 · · · BB Scl K3V 7.14 6.29 24.0 30.09 0.91 0.8* · · · BD+17 703 G5V 7.53 46.0 29.29 0.65 0.92* · · · · · · V988 Tau K2V 9.37 63.0 28.11 0.95 0.8* · · · · · · HZ Com G8:V 9.76 79.0 29.87 0.82 0.88* · · · · · · SAO 240653 G0V 6.20 40.0 30.01 0.54 1.1* · · · · · · SAO 235111 G0V:e 6.63 26.0 28.30 0.56 1.1* · · · · · · BK Psc K6V 10.57 33 29.55 1.16 0.72* · · · · · · QU And F8V 7.29 45 29.66 0.78 1.2* · · · · · · MR Del K5V 11.01 44 30.18 0.70 0.72* · · · · · · V1358 Ori G0V 7.96 50 30.10 0.54 1.1 · · · · · · V1082 Tau G8V 8.2 37 29.20 0.50 0.9 · · · · · · HP Aur G0V 11.25 1.4228132 224 30.34 0.65 1.1 · · · FK UMa G0V 9.29 108 29.90 0.62 1.1 · · · · · · TV Crt K0V 9.11 47 30.08 1.16 0.85 · · · · · · PZ MON K2Ve 9.03 530.0 < 16.91 30.90 1.19 0.8 · · · BD+36 2193 G5V 9.89 92 28.29 0.67 0.92 · · · · · · FR Cnc K5V 10.16 0.82695 33.0 30.10 1.16 0.70 · · · HD 95559 K1V/K1V 8.96 1.526 54.2 30.30 1.00 0.78/0.78 · · · Systems containing a subgiant companion

W92/NGC2264 K0:IVP 11.69 0.74479 900.0 < 17.27 31.71 0.86 5.5 CABS 128 K5V-IV 13.50 500.0 < 17.48 31.51 0.85* · · · · · · V1198 ORI G5IV 7.12 4.55 60.0 15.53 30.85 0.68 1.5 V824 ARA G5IV/K0V-IV 6.63 1.682 39.0 16.89 30.44 0.78 1.23 EI ERI G5IV 6.96 1.945 75.0 16.43 31.14 0.63 1.9/ AR LAC G2IV/K0IV 6.09 1.98319204 47.0 16.21 31.02 0.72 1.8/3.1 BH CVn F2IV/K2IV 4.93 2.6131738 53.0 16.24 30.74 0.38 3.10/2.85 CF TUC G0V/K4IV 7.41 2.79786 54.0 16.40 30.53 0.71 1.67/3.32 V711 TAU G5IV/K1IV 5.70 2.83774 36.0 16.67 31.38 0.85 1.3/3.9 PW HER F8-G2/K0IV 9.90 2.88100 285.0 16.88 30.93 0.81 1.4/3.8 AD CAP G5-8IV-V/G5 9.67 2.9600 250.0 < 16.29 31.40 0.86 /3.3 TY PYX G5IV/G5IV 6.83 3.19858 55.0 15.67 30.67 0.67 1.59/1.68 BD+36 2975 G6V/K1IV 8.00 3.30443 83.0 < 15.42 30.82 0.85 0.91/ GK HYA F8/G8IV 9.32 3.587033 220.0 16.78 30.89 - 0.22 1.51/3.39 UX COM G2/K1(IV) 9.93 3.642386 350.0 17.20 31.31 0.85 1.0/2.5 SZ PSC F8IV/K1IV 7.20 3.965866 125.0 17.70 31.30 0.75 1.50/5.1 Z HER F4V-IV/K0IV 7.23 3.992801 100.0 < 15.33 30.16 0.56 1.85/2.73 5.3. HR-diagram of active stars 114

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

BD+11 2910 G8IV 8.28 4.28549 110.0 < 15.48 30.62 0.78 6.93* BD+10 4514 F9V/G0VGIV 7.02 3.966031 50.0 < 14.86 29.48 0.56 3.55 WW DRA G2IV/K0IV 8.22 4.629617 180.0 < 16.59 31.19 0.70 2.12/3.9 RS CVN F4IV/G9IV 7.93 4.797851 180.0 17.25 31.07 0.56 1.99/4.00 SS CAM F5V-IV/K0IV- 10.10 4.824246 255.0 < 16.49 30.48 0.84 2.2/6.4 RT LAC G5:/G9IV 8.84 5.074015 205.0 16.58 30.62 1.07 4.2/3.4 RT CRB G2/G5-8IV 9.40 5.117159 360.0 < 16.42 30.53 0.73 2.6/3.0 V841 CEN K1IV 8.50 5.998 63.0 16.92 30.45 1.07 8.9* VV MON G2IV/K0IV 9.44 6.05056 380.0 17.44 31.16 0.78 1.75/6.0 II PEG K2-3V-IV 7.20 6.724183 29.4 15.88 30.78 1.01 2.2 RW UMA F8IV/K0IV 10.16 7.328223 150.0 < 15.66 30.85 0.51 2.31/4.24 SS BOO G0V/K0IV 10.24 7.606133 220.0 < 16.02 30.32 0.790 1.31/3.28 MM HER G2/K0IV 9.51 7.960322 190.0 16.99 30.55 0.780 1.58/2.83 LX PER G0IV/K0IV 8.14 8.038207 130.0 15.98 30.77 0.728 1.64/3.05 AW HER G2/G8IV 9.65 8.800760 315.0 17.01 31.06 0.734 2.4:/3.2 FF AQR SDO-B/G8IV-I 9.34 9.207755 300.0 17.13 31.49 0.884 0.1/6.12 RU CNC F5IV/K1IV 10.03 10.17299 300.0 < 16.36 30.64 0.56 1.9/4.9 HU VIR K0IV 8.57 10.3876 220.0 16.89 31.40 0.96 5.7 CQ AUR F5/K1IV 9.00 10.62148 220.0 16.55 31.12 0.54 1.9/8.7 RV LIB G8IV/K3IV 9.00 10.72216 270.0 17.04 31.06 0.76 6.8 54 CAM F9IV/G5IV 6.50 11.06803 38.0 15.32 30.18 0.59 3.14/2.64 EZ PEG G5V-IV/K0IV: 9.49 83.0 15.26 30.45 0.72 0.92/7.9 · · · CD-38 7259 G5V/K1IV 7.95 11.710 62.0 15.62 30.39 0.91 0.92/8.9 42 CAP G2IV 5.17 13.1740 34.0 < 14.42 29.57 0.65 3.2 VY ARI K3-4V-IV 6.90 13.198 21.0 15.37 30.37 0.96 0.9 UV FOR K0IV 7.97 15.05 100.0 < 15.68 30.03 0.93 4 LU HYA K1IV 7.34 16.537 95.0 < 15.64 30.23 0.94 5 RZ ERI AM/K0IV 7.70 39.2826 143.0 16.75 31.45 0.64 2.83/7.0 LS TRA K2IV/K2IV 7.31 49.431 54.0 16.43 30.37 1.04 9.9* PS SER F8IV* 8.15 134.0 16.30 30.29 0.60 3.5* · · · HD 192785 K2IV/K3IV 7.74 129.0 17.19 30.88 1.05 9.9/10.9* · · · HD 191179 G2V/K0IV 8.42 117.0 16.48 30.91 0.75 1/7.9* · · · IN VIR G7V/K4IV 9.19 8.40 162.0 15.73 30.86 1.15 0.89/11.9* HS LUP G5IV/G5IV 7.73 116.0 < 16.11 30.14 0.71 5.46/5.46 · · · HS AQR F8V/K1IV-V 9.22 123.0 < 15.60 30.25 0.53 1.18/8.9* · · · TY COL F7V/G8IV 9.57 3.62 65.0 15.17 30.33 0.64 1.22/6.9* V858 CEN G/K1IV 10.49 290.0 < 16.31 31.21 1.00 8.9* · · · V991 SCO G5-6IV 9.70 222.0 16.28 31.15 0.64 5.4* · · · EZ ERI F9V/K2IV 10.24 9.08 285.0 < 16.29 30.79 1.00 1.14/9.9* BG PSC F6V/G8IV 8.71 120.0 15.81 30.30 0.63 1.26/6.93* · · · 5.3. HR-diagram of active stars 115

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

HD 61396 K0IV 8.02 31.95 257.0 17.88 31.83 1.24 7.9* HD 81032 K0IV 8.61 18.81 151.0 16.26 31.03 1.02 7.9* SAO 234181 F7IV 5.95 127 < 16.14 30.95 0.61 3.0* · · · BQ Hyi G1:IVp 8.30 18.66 214 16.62 31.26 0.92 3.9* STT 82 AB F8IV 7.12 47 < 14.89 29.56 0.50 3.5* · · · V1355 Ori K1IV 9.13 129 31.11 0.92 8.9* · · · · · · BD+15 4053 G8IV 8.43 117 16.48 30.91 0.75 6.9* · · · UX ARI G5V/K0IV 6.5 6.43 50.0 17.12 31.08 0.90 0.93/¿4.7 CS Cet G5IV 7.79 14.8 132.0 31.68 0.84 0.92 · · · Systems containing a giant companion

BD-04 3419 K2IV-III 8.27 165.0 < 16.36 30.57 1.12 1.0/2.5 · · · 3 CAM K0III 5.05 85.0 < 15.34 29.64 1.07 15* · · · V1430 Aql G5V/K0III-IV 10.00 95.0 < 15.15 30.24 0.90 0.92/15* · · · IN COM G5IV-III 8.00 1.2001 125.0 < 16.10 29.00 0.79 1.76/0.58 1E1848+3305 K0III-IV 10.00 229.0 < 16.30 30.81 - · · · UZ LIB WA8/K0III 9.30 4.767885 550.0 18.02 31.81 1.01 1./21. RS UMI G0/G-K 10.07 6.16860 546.0 < 16.77 30.67 0.84 4.31/7.9 DM UMA K0 *IV-III 10.14 1.033824 130.0 16.78 31.09 1.00 3.8 1E1937+3027 K0III-IV 10.00 9.527 229.0 < 16.30 30.65 - 7.9 GX LIB (G-KV)/K1III 7.29 11.1345 219.0 < 16.02 30.43 1.04 7 V344 PUP K1III 6.88 11.761 190.0 < 16.24 30.94 1.03 17.0* V851 CEN K2IV-III 7.81 11.989 80.0 16.97 30.61 1.05 3.5 IL HYA K1III 7.25 12.908 263.0 17.24 31.41 1.01 6 V4138 SGR K1III 6.57 13.048 210.0 < 16.63 30.01 1.01 9 TZ PIC K1IV-IIIP 7.59 13.637 60.0 < 15.50 29.85 1.15 8.9* 6 TRI F5/K0III 4.94 14.7339 75.0 15.13 31.06 0.78 13 V4091 SGR K0III 8.38 16.887 340.0 < 16.46 31.02 1.16 6 V350 LAC K2III 6.41 69.0 < 15.14 30.38 1.17 11 · · · ZETA AND /K1III 4.06 17.7692 31.0 < 14.48 30.15 1.10 0.7/13.4 UV CRB K2III 7.20 18.6651 230.0 < 16.03 30.36 1.27 15.5 BL CVN G-KIV/K0III 8.13 18.6917 300.0 < 16.24 30.81 1.12 14.8 CP-77 196 K1IIIP 7.57 19.310 82.0 15.80 30.25 1.05 17.0* SIGMA GEM K1III 4.14 19.60447 59.0 15.41 31.43 1.12 21.5 λ AND G8IV-III 3.82 23.0 15.37 30.57 1.08 7.5 · · · BM CVN K1III 7.21 20.625 250.0 < 16.02 31.84 1.17 6 AR MON G8III/K2-3II 8.62 21.20812 525.0 17.33 31.37 1.05 10.8/14.2 V492 PER K1III 6.72 21.2902 50.0 < 15.05 30.81 1.07 10 RZ CNC K1III/K3-4II 8.69 21.64303 395.0 < 16.70 31.03 1.12 10.2/12.2 BH IND K1IIICNIVP 8.70 22.349 417.0 18.20 31.75 0.98 0.98 CD-32 9477 K2IIIP 9.13 22.740 760.0 17.44 31.66 1.22 1.22 5.3. HR-diagram of active stars 116

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

AT CAP K2III 8.87 23.206 99.0 16.06 29.70 1.10 10 HK LAC F1V/K0III 6.52 24.4284 150.0 17.09 31.49 1.05 15* IM PEG K2III-II 5.60 24.65 50.0 16.10 30.79 1.14 12 V792 HER F2IV/K0III 8.10 27.5368 310.0 16.36 31.36 0.91 2.58/12.2 TW LEP F6IV/K2III 7.00 28.344 220.0 17.09 31.79 1.06 9 HR 7275 K1IV-III 5.81 28.5895 250.0 17.05 31.98 1.08 8 V965 SCO F2IV/K1III 8.52 30.969 400.0 < 17.06 30.60 0.99 5.5/14 BD CET K1III 7.89 35.100 71.0 < 14.96 29.34 1.11 10 BD+31 4046 K0III 7.90 38.787 275.0 16.43 31.46 1.01 9 *0 UMI A8-F0V/G5III 4.23 39.4809 71.0 < 15.01 30.66 0.88 1.7/12 V1764 CYG F/K1III: 7.69 40.1418 390.0 16.97 30.76 1.22 22 HR 3385 K0III 6.32 45.130 135.0 < 15.94 30.98 0.93 3 V4139 SGR K2-3III 8.40 45.180 417.0 < 16.92 31.23 1.21 17* EL ERI G8IV-III 7.92 48.263 146.0 17.54 31.77 1.13 7.6 IN VEL K2IIIP 8.83 52.270 500.0 < 16.98 31.35 1.21 19* V1149 ORI K1III 6.58 53.580 164.0 16.34 31.20 1.12 11 AY CET WD/G5III 5.47 56.824 66.7 < 15.03 31.00 0.87 0.012/15 HR 4492 A0/K2-4III 5.08 61.360 140.0 17.78 31.65 0.80 21* BN MIC K1IIIP 7.72 63.09 265.0 17.57 31.44 1.12 12 HR 4665 K1III/K1III 6.14 64.44 130.0 16.55 31.56 1.13 13/13 93 LEO A6:V/G5IV-II 4.50 71.6900 36.0 < 14.42 29.99 0.51 1.7/5.9 33 PSC K0III 4.61 72.93 111.0 < 15.51 28.66 1.04 20 12 CAM K0III 6.10 80.895 134.0 16.13 30.94 1.11 16 HR 2054 G8III 6.47 83.19 140.0 16.10 31.06 0.98 13* 5 CET WF/K1III 6.07 96.439 140.0 < 15.58 29.42 1.36 50 HR 6626 K3III 6.68 99.557 250.0 < 16.02 30.50 1.39 32 αAUR G1III/K0III 0.08 104.0214 13.0 13.61 30.58 0.80 8.7/12.6 TY PIC F/G8-K0III 7.61 106.74 110.0 < 15.95 30.40 0.97 15* HR 7428 A2V/K2III-II 6.32 108.854 302.0 < 16.34 30.83 1.12 62 BD+26 2976 G5III 8.60 122.56 350.0 < 16.28 30.57 0.82 10* OMICRON DRA G9III 4.64 138.420 67.0 < 14.96 29.40 1.17 37 CD-26 11634 K0III 8.10 314.0 300.0 16.75 30.26 1.1 10 29 DRA WD/K0-2III 6.55 905.9 87.9 15.91 30.91 1.04 0.012/5 HR 1176 F2:V/G8III 5.66 962.8 100.0 < 15.86 29.91 0.75 13* V832 ARA WD/G8III 7.08 3.0784 170.0 < 17.30 30.67 0.98 /13* α2 HER F2V/G5III 5.40 117.0 < 15.47 30.77 1.70 1.3/10* · · · V356 PUP K1-2IIIP 8.20 380.0 < 17.97 30.87 1.16 17* · · · V340 GEM G4III 7.53 230.0 16.97 31.10 0.77 9* · · · η AND G8III 4.40 74 < 15.16 30.33 0.94 15.91 · · · BC PHE G6/G8III/IVe 8.86 118 < 16.07 30.76 0.72 6.9* · · · 5.4. Bolometric luminosity and stellar diameter 117

Table 5.1 (cont’d)

Object Spectral type V Period d log Lrad log Lx (B-V) Radius 1 1 1 (mag) (days) (pc) (erg s− Hz− ) (erg s− ) (mag) (R )

IX PER F2III-IV 6.68 1.326363 68 15.93 30.23 0.41 3.0* YZ MEN K1IIIp 7.77 180 16.55 31.01 1.05 17* · · · EE UMA K2IIICN 6.31 195 < 15.98 29.55 1.27 25.155 · · · 26 AQL G8III 4.99 266.54 47 < 14.87 29.39 0.92 7.0735 AS CAP K0IIIp 7.70 204 < 16.00 31.06 1.04 15* · · · δ CAP A7IIIm 2.87 1.0227688 11.5 < 13.42 29.35 0.29 2.0 KU PEG G8II 7.66 188 < 15.71 30.71 1.13 13* · · · V510 Per G5III 7.18 177 30.04 1.02 10* · · · · · · BD+42 1790 K2III 9.07 530 < 16.75 0.83 19* · · · · · · BD +40 2194 K0III 6.67 155 30.99 0.90 15* · · · · · · V846 Her K2III 8.95 480 0.88 19* · · · · · · · · · BD+44 2760 K2III 8.22 350 30.86 0.91 19* · · · · · · AZ PSC K0III 7.30 147.4 < 15.65 31.22 1.01 11 · · · V1379 Aql sdB/K0IV-III 8.32 235.3 16.98 31.08 1.11 7.5 · · ·

5.4 Bolometric luminosity and stellar diameter

The bolometric luminosity of the star was calculated using the following relations given in Landolt-Boirnstein¨ (Schaifers & Voigt 1982)

M = M BC (5.2) bol V −

Mbol = 2.5log(L/L ) + 4.64 (5.3) − where BC is bolometric correction. Radii of the active stars were taken from the catalogue of CABS (Strassmeier et al. 1993) except in some cases where data is not available. For these cases we used the Barne-Evans (Barnes & Evans 1976, Barnes et al. 1978) relation to estimate the angular diameter. Barne & Evans (1976) deﬁned the visual surface-brightness parameter FV is :

F = 4.2207 0.1V 0.5logφ0 (5.4) V − 0 −

V0 is unreddened apparent magnitude in the Johnson’s UBVRI photometric systems and 5.5. Average X-ray and radio luminosities 118

subgiants 18 giants

dwarfs

28 30 32

(a)

Figure 5.2 Correlation plot between radio luminosity (log Lrad) and X-ray luminosity (log Lx). Radio upper limits have been indicated with arrows.

φ0is stellar angular diameter expressed in milliseconds of arc. The relations FV and (B-V) are given by the following equations

F = 3.897 1.010(B V) , 0.32 (B V) = 0.10 (5.5) V − − 0 − ≤ − ≤ − F = 3.964 0.333(B V) , 0.10 (B V) = 1.35 (5.6) V − − 0 − ≤ − ≤

5.5 Average X-ray and radio luminosities

The average and median X-ray and radio luminosities of the three stellar systems are summarised in Table 5.2 For the sample of 101 dwarfs the average and the median X-ray lumi- 5.5. Average X-ray and radio luminosities 119

-16 subgiants giants

dwarfs

-18

-20

-22 -8 -6 -4 -2

(b)

Figure 5.3 A correlation plot between normalised radio luminosity (log Lrad/Lbol) and noramlised X-ray luminosity (log Lx/Lbol). Radio upper limits have been indicated with arrows.

1 nosity (log L ) are 29.6 0.7 and 29.63 erg s− , respectively. The average and median X-ray x luminosity for the 65 subgiant and, the 82 giant active systems are found to be 30.8 0.5 1 and 30.83; 30.7 0.7 and 30.8 erg s− , respectively. The average and median luminosity for a sample of 81 dwarfs, 64 subgiants and 80 giants are found to be 14.8 0.8 and 1 14.9 , 16.3 0.7 and 16.2, and 16.3 0.9 and 16.1 erg s− , respectively. This indicates that the evolved systems (subgiants and giants) are more X-ray/radio luminous than the dwarf systems, as expected since these stars have larger surface areas from which to radiate X-rays/radio. 5.5. Average X-ray and radio luminosities 120

Figure 5.4 Correlation plot between surface radio ﬂux (log Srad) and surface X-ray ﬂux (log Sx). Radio upper limits have been indicated with arrows.

Table 5.2. Average and median X-ray and radio luminosities of dwarfs, subgiants and giants

1 1 1 Stellar class X-ray luminosity (erg s− ) Radio lunimosity (erg s− Hz− ) Average value Median value Average value Median value

Dwarfs 29.6 0.7 29.63 14.8 0.8 14.9 Subgiants 30.8 0.5 30.83 16.3 0.7 16.2 Giants 30.7 0.7 30.80 16.3 0.9 16.1 5.6. Correlation of radio emission with X-ray emission 121

5.6 Correlation of radio emission with X-ray emission

Our sample is only slightly larger than the largest previous sample of Padmakar et al. (2000), and we do not ﬁnd any appreciable changes in the correlations reported in the

1.37 0.07 previous studies. The slope is unchanged from L L for 202 active stars in Pad- rad ∼ X 1.38 0.08 makar et al. (2000) to L L for all 226 active stars in our sample. In order to rad ∼ X demonstrate that most of this correlation was not spuriously introduced by a systemic error due to distance scale, we have also examined the correlation of the distance-independent quantities (L /L ) and (L /L ). The slope of the ML fit is 1.15 0.07. The slope deter- rad bol X bol mined by our sample is indicated to be slightly more than the previously determined slope of 1.03 0.12 by Dempsey et al. (1997), but is well within 1σ error bar of the old value. Figure 5.2 shows the correlation plot between log Lradand log Lx. A significant correlation with linear correlation coefficient of 0.79, 0.75 and 0.60 is found for dwarfs, subgiants

and giants, respectively. We found no appreciable change in the slope between Lrad and LX for dwarfs and subgiants from Dempsey et al. (1997). However, the slope is slightly steeper for the giants, but the change in slope corresponds to a diﬀerence of only 1.4σ. We found a

systematic trend in the slope between Lrad and Lx for diﬀerent types of the stars. The slope is found to be steeper in the giants compare to that for the dwarfs and the subgiants. The

slope between Lrad/Lbol and Lx/Lbol for the three kinds of the systems are consistent within 1σ to that determined by Dempsey et al. (1993) (see Figure 5.3 and Table 5.3).

We have also looked at the correlation between the X-ray surface ﬂux (SX) and the

corresponding radio surface ﬂux (Srad). The SX and Srad for the stars were derived assuming 2 that these luminosities are mostly from the surface of the active stars, thus S = L/4πRa,

where Ra is the radius of active star in binary, S is surface ﬂux and L is luminosity. Radii were taken from catalogue of CABS (Strassmeier et al. 1993) except in few cases where data are not available. For these cases we used the Barnes-Evans relation to estimate the angular diameter (Barnes & Evans 1976; Barnes et al. 1978 and see 5.4). We have found § 1.21 0.16 the signiﬁcant correlation between these two quantities of the form S S for rad ∝ X 1.22 0.15 1.50 0.17 dwarfs, S S for subgiants and S S for giants (see Figure 5.4 and rad ∝ X rad ∝ X Table 5.3). This indicates that the correlation is also independent of the surface area of the active star in the system. 5.6. Correlation of radio emission with X-ray emission 122

Figure 5.5 Left panel: normalised X-ray luminosity (log Lx/Lbol) versus rotational period (log P), right panel:Surface X-ray ﬂux (log Sx) versus rotational period (log P). Symbols are similar to the Figure 5.1

Figure 5.6 Left panel: normalised radio luminosity (log Lrad/Lbol) versus rotation period (log P),right panel:Surface radio ﬂux (log Srad) vs. rotational period (log P). Symbols are similar to Figure 5.1. Radio upper limits have been indicated with arrows. 5.7. Correlation of X-ray and radio emission with rotation 123

5.6.1 Physical signiﬁcance of the radio to X-ray correlations

The level of radio continuum emission produced by nonthermal process is well correlated with the level of presumably thermal X-ray emission from the coronae of all three stellar systems. The underlying cause for this is not clear. Many active stars show a constant sign of radio circular polarization throughout (Gibson 1983; White et al. 1986; Mutel et al. 1987, 1998; Kundu & Shevgaonkar 1988; White & Franciosini 1995). This has been generally interpreted as due to the gyrosynchrotron radiation by mildly relativistic electrons of few MeV energy spiraling in magnetic fields of 10 - 100 G (e.g. Dulk 1985; Gudel¨ 2002). On the other hand, the soft X-ray observed by Einstein and ROSAT are presumably due to a Maxwellian distribution of the electron at coronal temperature. Thus, one should explore, why the radio emission is well correlated with thermal X-ray emission. Drake et al. (1989) propose that the close correlation between the low-level (i.e. nonflare) radio emission and the hot component of X-ray emission is due to both emission being produced by the same T = 5 107 K thermal electrons. Later, Linsky (1996) argued that thermal and nonthermal × electrons coexist in the same volume of quasi statistical steady state. Thus, there is continual exchange between the reservoirs of thermal and nonthermal electrons by acceleration and thermal ionization process (primarily collision at lower energy and gyrosynchrotron radiation at higher energy). The most straight forward interpretation of this correlation is in terms of the chromospheric evaporation of frequent, unresolved flares that produce the radio emission and at the same time heat the plasma to coronal temperature. Slope for the radio/X-ray correlation is significantly greater than unity, suggesting that there is not a simple one-to-one relation between the emission at these different energies.

5.7 Correlation of X-ray and radio emission with rotation

Surface activity of rapidly rotating, deeply convective stars is thought to be governed by a magnetic dynamo. So, it is important to look for the correlation of rotation with stellar activity. A correlation between stellar rotation and activity level was firstly noticed in the early Einstein observations, by Walter & Bowyer (1981), and by Pallavicini et al. (1981) on larger sample of star of different types. Similar correlation was shown by Drake et al. (1989, 1992) and Dempsey et al. (1993, 1997). There is a practical difficulty in do- 5.7. Correlation of X-ray and radio emission with rotation 124 ing the correlation between the rotation and fluxes as many systems do not have rotation period. In many systems, particularly those with orbital period 20 d, the stars almost ≤ certainly rotate synchronously because of tidal coupling (Zahn 1977, Linsky 1988) and hence we use Prot = Porb. In practice, as for most of the correlations it makes negligible difference whether one use P or P (Drake et al. 1989) since few systems ( 40) ro- orb rot ∼ tate asynchronously (Glebocki & Stawikowski 1997). Although many of them are slightly asynchronous, presumably because stellar rotation rates vary with latitude across the stellar surface. The results of the correlation of rotation with X-ray and radio emissions are given in Table 5.3.

Using the entire sample we found the positive correlation between Lx and P with a slope of 0.34 0.09 and a linear correlation coefficient of 0.25. We did not found any appreciable change in the slope between Lx and P for subgiants and giants (Table 5.3) from Dempsey et al. (1997). However, the slope is steeper for dwarfs, and the change in slope corresponds to a difference of 2σ. The normalised X-ray luminosity is well correlated with the rotation for all the three stellar systems. The linear correlation coefficients are -0.42, -0.33 and -0.44 for dwarfs, subgiants and giants, respectively. Left panel of the Figure 5.5 show the dependency of the normalised X-ray luminosity on the rotation. It is clear from the Figure 5.5 that faster the rotation more is the X-ray emission. But, the X-ray luminosity of the star above a given value of rotation period (P . 0.5) remains constant

3 around the maximum allowed value of Lx corresponding to a ﬁxed fraction (10− ) of the star’s bolometric luminosity and known as saturation limit. The physical cause of saturation is not well understood. Vilhu & Walter (1987) suggested that internal dynamo saturates i.e. it produces no more magnetic ﬂux if the rotation period increases.

The plot of Sx versus P for all the systems is shown in the right panel of Figure 5.5. The solid lines in the right panel of the Figure 5.5 represent the best ﬁt to the dwarfs, subgiants

1.29 0.47 and giants. The measured slope for the dwarf population is S P− , compared to x∼ 0.42 0.20 the slope S P− given in Dempsey et al. (1997). For the subgiant stars, the x∼ 0.47 0.33 0.39 0.21 slopes changed from S P− in Dempsey et al.(1997) to S P− , while a x∼ x∼ 0.77 0.16 0.48 0.20 similar change from S P− to S P− is observed for the giants. Using the x∼ x∼ 0.76 0.13 entire sample, we derived Sx= P− . It is well within the 1σ error bar of the value determined by Dempsey et al. (1987). 5.7. Correlation of X-ray and radio emission with rotation 125

We have also determined the correlation of the radio emission with rotation period for all the three stellar systems. Table 5.3 summarise the results of ML ﬁt. The ML ﬁt gives

0.41 0.19 the slope of log L P for the entire sample. The linear correlation coeﬃcient rad∼ of this ﬁt is 0.25 with probability of no correlation being 0.0004. Previously, Drake et al.

(1989) found no correlation between Lrad and P for a sample of 122 active stars. Morris & Mutel (1988) obtained a marginal positive correlation (slope = 0.29 0.14) between P and Lrad for 45 radio-detected active stars. Excluding the radio upper limits we found the slope of 0.49 0.15 with r = 0.31. We found a signiﬁcant correlation between L and rad P for dwarfs in the form of log L = (14.8 0.2) (1.77 0.34)P with r = -0.56. A rad − similar correlation was also found by Gudel¨ (1992) with a slope of 1.74 0.48 for a − sample of 13 dwarfs. However, Drake et al. (1989) found a slope of 0.39 0.38 with − linear correlation coeﬃcient of -0.2. The slope for subgiants and giants is found to be - 0.44 0.4 and 0.3 0.4, respectively. Which is within a 1σ level of the slope determined − by Drake et al. (1989). These correlations are not very tight, as expressed in the large error range for the slope. The correlation plot between normalised radio luminosity (log

Lrad/Lbol) and rotation period (log P) is shown in left panel of the Figure 5.6 (see Table

5.3 for slope and linear correlation coefficient). The slope between log Lrad/Lbol and P is found well with in the 1σ level of the slope determined by Drake et al. (1989) for subgiants and giants. However, the slope determined by our sample of dwarfs is indicated to more than the previously determined slope of 0.42 0.40 by Drake et al. (1989). Right panel − of Figure 5.6 shows the correlation plot between surface radio flux (log Srad) and rotation period (log P), radio upper limits have been indicated by arrows. We find a significant

1.6 0.3 0.99 0.41 correlation between S and P in the form of S P− for dwarfs, S P− rad rad∼ rad∼ 1.01 0.40 for subgiants and S P− with linear correlation coeﬃcients of -0.56, -0.42 and rad∼ -0.38, respectively. 5.7. Correlation of X-ray and radio emission with rotation 126

Table 5.3. Summary of ML ﬁts, r represents the linear correaltion coeﬃcient.

Variable No/ULa r Slope intercept

All Systems

logL logL 226/121 0.82 1.38 0.08 26.6 2.5 rad − X − log(L /L ) log(L /L ) 226/121 0.80 1.15 0.07 14.5 0.3 rad bol − X bol − logS logS 226/121 0.81 1.27 0.08 16.4 0.6 rad − X − (B V) - log L 246/0 -0.05 0.19 0.21 30.4 0.2 − x − (B V) - log L /L 246/0 -0.04 0.17 0.23 3.8 0.2 − x bol − − (B V) - log S 246/0 -0.25 0.17 0.90 7.4 0.2 − x − (B V) - log L 224/120 -0.04 0.39 0.46 15.2 0.4 − rad − (B V) - log L /L 224/120 -0.01 0.18 0.45 19.2 0.4 − rad bol − − (B V) - log S 224/120 -0.17 0.84 0.45 8.0 0.4 − rad − − P - log L 194/0 0.65 1.03 0.08 33.4 0.1 bol P - log L 194/0 0.25 0.34 0.09 30.0 0.1 x P - log L /L 183/0 -0.55 0.77 0.24 3.3 0.1 x bol − − P - log S 194/0 -0.36 0.76 0.13 7.3 0.1 x − P - log L 182/93 0.25 0.41 0.19 14.6 0.2 rad P - log L /L 182/93 -0.40 0.75 0.19 18.7 0.2 rad bol − − P - log S 182/93 -0.46 0.79 0.16 8.0 0.2 rad − Dwarfs only

logL logL 82/52 0.79 1.19 0.14 21.0 4.1 rad − X − log(L /L ) log(L /L ) 82/52 0.78 1.10 0.13 14.9 0.5 rad bol − X bol − logS logS 82/52 0.71 1.21 0.16 16.9 1.2 rad − X − (B V) - log L 101/0 -0.39 1.04 0.24 30.5 0.2 − x − (B V) - logL /L 101/0 0.27 0.68 0.24 4.4 0.2 − x bol − (B V) - log S 101/0 -0.09 0.22 0.24 7.1 0.2 − x − (B V) - log L 82/52 -0.51 0.99 0.49 14.9 0.5 − rad − (B V) - log L /L 82/52 0.24 0.73 0.52 19.9 0.5 − rad bol − 5.7. Correlation of X-ray and radio emission with rotation 127

Table 5.3 (cont’d)

Variable No/ULa r Slope intercept

(B V) - log S 82/52 -0.19 0.21 0.48 8.4 0.5 − rad − − P - log L 81/0 0.02 0.04 0.17 33.3 0.1 bol P - log L 81/0 -0.47 0.91 0.19 29.9 0.1 x − P - log L /L 77/0 -0.42 0.79 0.19 3.4 0.1 x bol − − P - log S 81/0 -0.28 1.29 0.47 7.3 0.2 x − P - log L 76/46 -0.56 1.77 0.34 14.8 0.2 rad − P - log L /L 76/46 -0.56 1.56 0.35 18.6 0.2 rad bol − − P - log S 76/46 -0.41 1.60 0.30 7.8 0.1 rad − − Subgiants only

logL logL 64/22 0.75 1.34 0.18 25.1 5.4 rad − X − log(L /L ) log(L /L ) 64/22 0.76 1.03 0.15 14.5 0.5 rad bol − X bol − logS logS 64/22 0.71 1.22 0.15 16.2 1.1 rad − X − (B V) - log L 64/0 0.26 0.59 0.26 30.1 0.2 − x (B V) - logL /L 64/0 0.24 0.80 0.40 4.2 0.3 − x bol − (B V) - log S 64/0 0.19 0.58 0.37 6.5 0.6 − x (B V) - log L 64/22 0.31 1.18 0.60 15.1 0.5 − rad (B V) - log L /L 64/22 0.33 1.45 0.65 19.4 0.6 − rad bol − (B V) - log S 64/22 0.19 0.64 0.55 8.3 0.4 − rad − P - log L 51/0 0.35 0.45 0.16 34.0 0.1 bol P - log L 48/0 -0.25 0.40 0.20 30.1 0.2 x − P - log L /L 51/0 -0.33 0.58 0.23 3.1 0.2 x bol − − P - log S 48/0 -0.48 0.87 0.23 7.6 0.2 x − P - log L 48/16 -0.21 0.44 0.40 16.4 0.4 rad − P - log L /L 48/16 -0.32 0.81 0.38 17.7 0.3 rad bol − − P - log S 48/16 -0.42 0.99 0.39 7.0 0.3 rad − − Giants only 5.8. Dependence of stellar radius on rotational period 128

Table 5.3 (cont’d)

Variable No/ULa r Slope intercept

logL logL 80/47 0.60 1.65 0.24 35.2 7.5 rad − X − log(L /L ) log(L /L ) 80/47 0.76 1.21 0.14 14.3 0.6 rad bol − X bol − logS logS 80/47 0.76 1.50 0.17 18.3 1.3 rad − X − (B V) - log L 80/0 0.14 0.53 0.39 30.2 0.4 − x (B V) - logL /L 80/0 -0.03 0.16 0.58 4.5 0.6 − x bol − (B V) - log S 80/0 -0.22 1.11 0.54 7.0 0.6 − x − (B V) - log L 79/46 0.25 1.00 0.98 14.3 1.0 − rad (B V) - log L /L 79/46 0.08 0.26 1.23 20.5 1.3 − rad bol − (B V) - log S 79/46 -0.07 0.60 1.26 9.1 1.3 − rad − − P - log L 62/0 0.32 0.37 0.12 34.8 0.2 bol P - log L 57/0 0.17 0.24 0.19 30.5 0.3 x P - log L /L 55/0 -0.44 0.90 0.24 3.2 0.4 x bol − − P - log S 57/0 -0.28 0.54 0.23 6.7 0.3 x − P - log L 59/32 -0.11 0.26 0.36 15.8 0.7 rad − P - log L /L 48/16 -0.25 0.71 0.54 19.1 0.8 rad bol − − P - log S 59/32 -0.38 1.01 0.40 8.1 0.7 rad − − aNumber of data points/number of radio upper limits

5.8 Dependence of stellar radius on rotational period

As shown in Figure 5.7, stellar radius is a strong function of rotational period. It shows the similar relationship with period, including the leveling oﬀ for log (P) . 0.5, as does

Lx/Lbol or Sx. We found for the stellar radius of 1R , the rotational period is always . 3 d, where most of the dwarfs lie. The radii of dwarfs is independent of period and the slope results almost exclusively from giants. Including the sample for log (P) . 0.5, we ﬁnd the following relation between stellar radii and rotational period of active stars. 5.8. Dependence of stellar radius on rotational period 129

Figure 5.7 Stellar radius of the active star as a function of rotational period

log(R /R ) = (0.57 0.04)log(P) 0.03 (5.7) ∗ − while excluding the sample for log (P) . 0.5, the relation obtained is

log(R /R ) = (0.65 0.06)log(P) 0.12 (5.8) ∗ − The linear correlation coefficients of 0.64 and 0.75 for the relations (5.7) and (5.8), respectively, show the high significance of the correlation. For both the relations the confidence level for linear correlation is > 99%. From these correlations we reconfirm the conclusion of Rengarajan & Verma (1983) and Dempsey et al. (1993), based on smaller sample, that period-activity relation follows from the dependence of radius on period. 5.9. The (B-V) to X-ray and radio correlation 130

5.9 The (B-V) to X-ray and radio correlation

We have also investigated the correlation of X-ray and radio emission with B-V colour. The results of correlation are given in Table 5.3. For the entire sample we found no signiﬁcant correlation of B-V colour with Lx, Lx/Lbol and Srad. The X-ray luminosity as a function of

B-V colour is displayed in left panel of the Figure 5.8. A slope between log Lxand B-V was found to be 1.04 0.24 for dwarfs, 0.56 0.26 for subgiants and 0.53 0.39 for giants − with linear correlation coefficients of -0.39, 0.26 and 0.14, respectively. In all cases the confidence of the linear correlation is found to be less than 82%. Similar to the Lx - (B-V) correlation we did not find any significant correlation between Sx and B-V and Lx/Lbol and

(B-V). The correlation plot between Sx and B-V for all kinds of stellar systems is shown in right panel of Figure 5.8. The slope of the correlations along with the linear correlation coeﬃcients are given in Table 5.3. Further, we did not ﬁnd any of correlation between

Sx and (B-V), and Lx/Lbol and (B-V) for all three stellar types. From this discussion it appears that X-ray emission does not depend on the spectral type of the cool stars.

The left and right panel of Figure 5.9 show the correlation plot between Lrad and B-V, and Srad and B-V, respectively. For the entire sample we ﬁnd a lack of correlation of (B-V) with Lx, Lx/Lbol and Sx. The correlation of (B-V) with Lrad and Lrad/Lbol for dwarfs and subgiants are found to be signiﬁcant (see Table 5.3). These correlation were found to be -ve for dwarfs and +ve for subgiants. However, for giants the B-V colour was found to be uncorrelated with Lrad, Lrad/Lboland Srad. 5.9. The (B-V) to X-ray and radio correlation 131

Figure 5.8 Left panel: log Lxversus (B-V) and right panel: log Sxversus (B-V). Symbols are similar to the Figure 1.1

Figure 5.9 Left panel: log Lradversus (B-V) and right panel: log Sradversus (B-V). Symbols are similar to the Figure 1.1. Radio upper limits have been indicated by arrows

Chapter 6

Imaging Polarimeter

6.1 Overview

In this chapter, we present the characterization of an imaging polarimeter (IMPOL) , which has been fabricated for use with liquid-Nitrogen cooled CCD camera and is designed to suit 104-cm Sampurnanand telescope at ARIES, Naini Tal. The instrument measures the linear polarization in broad B, V and R band, and has a ﬁeld of view 20 20. Towards the ∼ × end, we also summarised the possible uses of this instrument for the studies of active stars.

6.2 Introduction

Polarization measurements act as a very good diagnostic tools in understanding various physical phenomenon. There are several processes which produce polarizations in astronomy. For example i) synchrotron emission from crab nebula, ii) scattering by aligned dichroic grains, irregularly shaped grains and electrons on the inter stellar medium, circuimstellar disk and photosphere of Be stars, respectively, iii) Zeeman splitting of lines by magnetic field on white dwarfs and iv) resonance fluorescence in late type stars and comets. Polarization measurement in principle involves measurement of incoming photon flux by some detectors, through different orientations of some optical devices, whose transmission depends upon the state of polarization of incoming beam. The properties of such optical device (usually dichroic, birefringence plates) can be characterised by a (4 4) × A part of this chapter is published in Rautela et al. (2004)

133 6.3. Polarization sensitive optical elements 134

matrix, called Muller matrix. Light with a set of Stokes parameters S = (I, Q, U, V), when transmitted out of an optical device will have a diﬀerent set of Stokes parameters

S 0 = (I0, Q0, U0, V0) given by

S 0 = M.S (6.1)

where M represents Mullar matrix. The electromagnetic radiation reaching us from celestial objects consists of two orthogonal components of vibration:

Ex(λ) = Ex0(λ)exp(i(k.z + ω.t + δx))

Ey(λ) = Ey0(λ)exp(i(k.z + ω.t + δy)) where the notations have their usual meanings. The Stokes parameters are deﬁned as

2 + 2  I   Ex0 Ey0           Q   E2 E2     x0 y0    =  −  (6.2)          U   2Ex0Ey0cos(δx δy)     −           V   2Ex0Ey0 sin(δx δy)     −      The transmitted light out of an optical device will have the modified intensity according to equation (6.1). The elements of the Mullar matrix in this equation are functions of the angle α between some reference direction (say celestial N-S axis) and fast axis of the optical device. The angle α defined in this way is also called the position angle of fast axis of optical device. Thus, an optical device or a suitable combination of them placed at a different values of α, can in principle determine all the four Stokes parameters.

6.3 Polarization sensitive optical elements

6.3.1 Half-wave plate (HWP)

A plate of doubly refracting uniaxial crystal cut with its optic axis parallel to the refracting faces and capable of producing a path diﬀerence of λ/2 between ordinary and extraordi- 6.3. Polarization sensitive optical elements 135 nary rays, acts as a half-wave plate (see Serkowski 1974 for more discussion). The path diﬀerence (λ/2) between ordinary and extraordinary ray for a HWP is given by

λ (µo µe) t = (6.3) − × 2 where µo and µe are the refractive indices of the ordinary and extraordinary rays and t is the thickness of the plat. Thus, the two orthogonally polarized components (parallel and perpendicular to the fast-axis of the HWP), acquire a phase difference of π radian, when light passes through the HWP. If the incident light is plane-polarized at an angle θ with respect to the fast-axis of the HWP, since one of the polarization components acquire an additional phase difference of π radian, the emerging light will be polarized at an angle θ − with respect to fast-axis. This property is quite useful, since allows to rotate the plane of polarization of light through a known angle. For example, if HWP is rotated through an angle α the emergent light will rotate through and angle 2α. The plate introduces a relative retardance of π between the two components at a particular wavelength (see equation (6.3)). Plates which retarded by π at at-least two different wavelengths could be made by gluing together two plates of different birefringent materials with appropriate thickness. To prevent the reflection from interfaces of the plates, the birefringent materials should have same refractive indices. Crystalline quartz and magne- sium fluoride (both are positive crystals) are commonly used material for making HWP. Pancharatnam (1955a, 1955b) proposed a novel kind of achromatic retarder. It consists of three half-wave plates glued together in such a way that the first and last plates have their corresponding optic axes parallel and that of the central one at an angle of 57.2◦ with the other two. Such a system is almost perfectly achromatic from 400 to 780 µm.

6.3.2 Wollaston prism

The Wollaston prism consists of two orthogonal calcite prisms which are cemented together on their base. Their optical axes lie perpendicularly to each other and perpendicular to the direction of propagation of the incident light (see Figure 6.1). Light striking the surface of incidence at right angles is refracted in the ﬁrst prism into an ordinary and an extraordinary ray. However, these two rays continue to propagate in the same direction. As the optical 6.4. Principle of the instrument 136

ψ O

Figure 6.1 A schematic of Wollaston prism. The dots represent directions normal to the plane of the paper axis of the second prism is perpendicular to that of the ﬁrst, the ordinary ray becomes an extraordinary ray at the boundary surface. Its refractive index changes from µo to µe and µe < µo (for positive crystal) the extraordinary ray is refracted away from the axis of incidence. The opposite applies to the original extraordinary ray, now an ordinary ray. Both these rays deviate away from the normal as they emerge from the surface of the Wollaston prism. The total separation between the beams depends on the two refractive indices (µo and µe) as well as the angle ψ.

6.4 Principle of the instrument

The principle of the instrument is similar to that of IUCAA polarimeter by Ramaprakash et al. (1998) (hereafter IUIMPOL), which is based on the principle given by Sen & Tandon (1994), which again has taken into consideration the ideas suggested by the various authors (e.g. Ohman 1939; Appenzeller 1967 etc). These ideas have emerged out, mainly taking into considerations the advantages of aperture polarimetry as against imaging polarimetry. We have a plan to use the polarimeter at the Cassegrain end of 104 cm Sampurnanand telescope. We use a guiding unit mounted at the eye piece end of 8 inch ﬁnder telescope. A schematic diagram of the optical system of IMPOL is shown in Figure 6.2 and a picture 6.4. Principle of the instrument 137

Wollaston Prism Nicon Main 85 mm, f/1.8 CCD Rotatable Housing

f/13 O

Half−Wave Field Lens Plate Filter Assembly 320 mm 82.5 mm 81.5 mm

Figure 6.2 Optical layout of IMPOL

Figure 6.3 A picture of imaging polarimeter mounted at 104 cm telescope of ARIES 6.4. Principle of the instrument 138

CCD Controller

Control RS − 232 Image data

CCD Polarimetry Telescope Dewar Optics

Controller for HWP Motor Drive

Figure 6.4 A block diagram of polarimeter control system of IMPOL mounted at 104 cm telescope of ARIES is shown in Figure 6.3. As illustrated in Figure 6.2, a f/13 beam from the telescope falls on the field lens ( 50 mm, f/6 Karl Lambrecht part no. 322305 ) which in combination with the camera lens ( 85 mm, f/1.8 ) makes the image of the object at the CCD chip. The camera lens acts as a focal reducer that reimages the telescope focal plane on the surface of the CCD. In between the camera lens and the field lens a rotatable HWP and a Wollaston prism are mounted. HWP gives components of electric vector polarized orthogonally of varying intensities after emerging out of the Wollaston prism. The axis of the Wollaston prism is aligned to north - south axis of the telescope and the HWP is placed in such a way that the fast axis of the plate is aligned to the axis of the prism. Fast axis of the plate and axis of the prism are kept normal to the optical axis of the system. Once the light passes through the Wollaston prism, it is split into two orthogonal polarization components parallel and perpendicular to the axis of Wollaston prism. These two components (usually called the ordinary and the extraordinary components) travel slightly different directions. This results in two images being produced on the CCD for every point at the telescope focal plane. The ratio (R(α) = (I I )/(I + I )) of the difference be- o − e o e tween the intensities in the ordinary (Io) and extraordinary (Ie) images to their sum is the normalised Stokes parameter (Q/I) , defines a coordinate system aligned with the axes of Wollaston prism. In order to determine the degree of linear polarization p and its position 6.4. Principle of the instrument 139

angle θ, it is necessary to measure the above ratio for two orientation of Wollaston prism, for example 0◦ and 45◦. Equivalently, the same is accomplished by placing HWP on a rotatable mount preceding the Wollaston prism and keeping the Wollaston prism itself fixed with respect to the instrument axes. The property of the HWP is to add an additional phase shift of 180◦ to the polarization eigen vector parallel to its fast axes. Thus, effectively when the HWP is rotated through an angle α, the electric vector rotates through an angle 2α. In this arrangement, the first Stokes parameter I is the total intensity of the light, the second stokes parameter Q is the difference of the intensities between two orthogonal linear polarization component measured in the reference coordinate system. The third parameter U is similar to Q, but measured in the coordinate system rotated by 45◦(22.5◦in case of HWP) with respect to the first one. Q and U are related to the linear polarization p and its position angle θ by the relations,

Q = I p cos(2θ) and U = I p sin(2θ) (6.4)

It can be further shown that p and θ are derived from the above relations in the following manner:

2 2 (Q + U ) 1 1 Q p = and θ = tan− (6.5) p I 2 U The Mullar matrices corresponding to HWP and Wollaston prism are expressed as:

1 0 0 0 1 cos2β sin2β 0              0 cos4α sin4α 0   cos2β cos22β (1/2)sin4β 0      M1 =   , M2 =   (6.6)        2   0 sin4α cos4α 0   sin2β (1/2)sin4β sin 2β 0   −             0 0 0 1   0 0 0 0          where α and β are the position angle of fast axis of HWP and that of the direction of principle plane of Wollaston prism. Therefore, S 0 = M1.M2.S , where S and S 0 are the matrices representing Stokes parameters of the beam entering the polarimeter and the beam 6.4. Principle of the instrument 140

incident on the CCD detector, respectively. If we choose β = 0 (i.e. keeping ﬁxed the Wollaston prism) then the relative intensity diﬀerence (R(α)) can be expressed as:

R(α) = (Q/I)cos4α + (U/I)sin4α

using the equation (6.4) the above equation can be written as

R(α) = pcos(4α 2θ) (6.7) −

So, the basic equation of the instrument which relates the measured quantities (Io, Ie) to the parameter determined (p, θ) is given by

I /I 1 R(α) = e o − = pcos(2θ 4α) (6.8) Ie/Io + 1 −

The values of position angle at 0◦ and 22.5◦ of HWP directly measure the normalised stokes parameter Q/I and U/I. The linear polarization (p) and position angle of the polarization vector (θ) are determined by using the equation (6.5). Additional two values are measured at α = 45◦ and 67.5◦ due to non-responsivity of the system (see the 6.5). § The detector is a Tektronix 1kX1k CCD camera cooled by liquid-nitrogen ( see 2.2.3 § and Table 2.3 for details). For each object within the field of view, two images (see Figure 6.5) formed are separated by 15 pixels in the CCD frame. In case of overlap of the ordinary and extra ordinary images, we are aiming to place a grid of parallel obscuring strips at focal plane of the telescope. For the preliminary testing of the polarimeter, we have observed only the isolated stars brighter than 13 mag. So, the images were not overlapped. Simultaneous measurements of two orthogonal components take care of the atmospheric effects. All the components have anti reflection coating to minimize the polarization due to reflection and the inside of the polarimeter has been painted black to avoid stray light. We find that some of the components have got their anti reflection coating slightly damaged,

which may cause some polarization due to reﬂection. The uncertainty (σα) in the position of HWP gives a maximum uncertainty in polarization σ = p σ (Serkwoski 1974), p ∗ α where α is expressed in radians. An uncertainty of 0.1 degree in position of HWP (a typical

value if rotated by stepper motor) will give σp = 0.002p%. The instrument measures linear polarization in the wavelength region 400-780 nm. 6.5. Observations and Data reduction 141

6.5 Observations and Data reduction

Polarimetric observations were made at ARIES using 104-cm telescope. All the measurements were taken in the white/V light for testing the instrument. Three to four CCD frames of same exposure time at each position of the HWP have been taken for each object. The exposure time is ranging from 1 to 120 s depending on the source brightness. Number of bias and twilight flat frames were also taken during the observing run. We have observed nine polarized stars, (see Table 6.1). Unpolarized standards were also observed to check the instrumental polarization (see Table 6.2). IRAF was used for the data reduction. Bias was subtracted from target image and then resulting image was divided by normalised bias subtracted flat field image. Cosmic hits were removed using the crutil package in IRAF (see 2.4 for details). A daofind task under § apphot package finds the center of the star. Then through the phot task we have determined the flux of ordinary and extraordinary images (see 2.4.5 for details). § Even after the flat fielding the responsivity of the CCD frame to the two orthogonal images may not be same and may be a function of its surface. So, the actual flux ratio may differ from observed one and related by the following formula (Ramaprakash et al. 1998)

I (α) F I0 (α) e = o e (6.9) Io(α) Fe × Io0 (α)

1/4 F I0 (00) I0 (450) I0 (22.50) I0 (67.50) o = o o o o 0 0 where F 0 0 0 0 , and Ie(α) and Io(α) are actual measured e Ie0 (45 ) × Ie0 (0 ) × Ie0 (67.5 ) × Ie0 (22.5 ) fluxes. To get the best values of p and θ we have fitted equation (6.8) to the four values of R(α) determined using equation (6.8) and (6.9) by linear least square deviation method. Figure 6.7 shows the best fit of these four points for the stars mentioned in Table 6.1. The results of the best fit are given in Table 6.1.

6.6 Performance estimates

The typical observing conditions and telescope parameters are:

2 Back ground sky 20.5 mag asrsec− at V band, ∼ 1 plate scale = 15.5 arcsec mm− (f/13 beam of 104-cm telescope), light collecting area of the telescope = 3.2 104 cm2 × 6.7. Results 142

Figure 6.5 A CCD image of HD 18270 ﬁeld after emerging through the polarimeter. Two orthogonal component (ordinary and extraordinary) of an object are shown

For small value of p the number of photoelectrons corresponding to ordinary and extra ordinary images are approximately equal. So, the error in the measurement of p and θ due to photon noise are given by (Ramprakash et al. 1998)

√(N + N ) σp σ = b 100% and σ = 0.5 rad (6.10) p N × θ × p

where N and Nb are number of photoelectrons corresponding to the source and background. For the star of the apparent visual magnitude m = 13 the value of σ is 0.18% v p ∼ with an exposure time of 120 s. Figure 6.6 shows the plot between visual magnitude and the theoretically estimated error in the measurements of the polarization, due to photon statistics alone. Actual measured error is also plotted against the visual magnitude in the same ﬁgure. In Figure 6.6, solid circles and triangles represent the theoretically estimated error and the actual measured error, respectively.

6.7 Results

This section describes the performance of our instrument. We have measured the polarization of nine standard polarized stars. The measured value of p and θ in V band along with the standard values are given in Table 6.1. The observed unpolarized stars are given in 6.8. Polarization of active stars 143

actual observed error error due to photon noise

Figure 6.6 Plot of σp versus V magnitude. Solid circle represents theoretically estimated error due to photon noise and triangle represents the actual error obtained

Table 6.2. Figure 6.8 shows the plot of Q/I = R(0◦) against U/I = R(22.5◦) for unpolarized standards in white light. The low value of linear-correlation coeﬃcient (r = 0.103) between Q/I and U/I with probability of no correlation 55 % is indicative of the low instrumental polarization. The average value of Q/I(= 0.032%) and U/I(= 0.024%) gives the value of instrumental polarization 0.040%. ∼

6.8 Polarization of active stars

Magnetically active late-type stars have inhomogeneities on their surfaces that cause various observable eﬀects in the spectral lines and light curves. These variations are partly caused by rotational modulation due to more or less permanent inhomogeneities in stellar surface (see 1.4) , or change in visibility of the atmosphere of a multiple star. It is § expected that the polarization of the integrated stellar light may change along with stellar activity phenomenon. As discussed in chapter 1, several RS CVn and BY Dra binaries have small, variable amounts of linear polarization (< 0.1%) at optical wavelengths that are the 6.8. Polarization of active stars 144

HD 29647 HD 43384 HD 213789 0.03

0.00

-0.03

HD 25330 HD 28170 HD 29333 0.03

0.00

-0.03

HD 7927 HD 14433 HD 15642 0.03

0.00

-0.03

0 20 40 60 0 20 40 60 0 20 40 60

Figure 6.7 The best cosine fit for the 4 values of R(α) for different stars. The star name is mentioned inside of each panel best interpreted as the result of scattering from cool circuimstellar material (Scaltriti et al. 1993b). Liu & Tan (1987) show that for most of the RS CVn binaries the optical polarization is weak, generally below 0.45% , averageing about 0.20%. Pfeiffer (1979) found 0.32% polarization in proto-type RS CVn and concluded that the polarization is attributed to scattering from cool, transient, circuimstellar material probably ejected in clouds. In BH CVn the polarization in U band varied synchronously with the binary period with a peak- to-peak amplitude of 0.03%. It was attributed to reflection of light coming from the bright primary by the envelope of the secondary star (Barbour & Camp 1981). There are several other mechanism which can produce linear polarization in late-type 6.8. Polarization of active stars 145

Table 6.1. Degree of linear polarization (p) and polarization angle (θ) of polarized standards.

Object V Our measured values Standard Values Ref. (mag) p(%) θ(degree) p(%) θ(degree)

HD 7927 5.0 3.23 0.03 90.0 0.8 3.23 0.20 94.0 0.5 a HD 14433 6.4 4.08 0.12 109.4 0.8 3.87 0.20 112.0 1.5 a HD 15642 8.5 3.26 0.12 112.0 0.6 3.13 0.20 115.0 1.8 a HD 25330 5.7 1.55 0.02 128.7 0.4 1.52 0.03 134.4 0.7 a HD 28170 8.9 2.11 0.02 88.8 0.2 2.03 0.03 89.4 0.7 a HD 29333 8.5 5.29 0.01 66.1 0.1 5.25 0.02 70.9 1.5 b HD 29647 8.4 2.10 0.01 66.5 0.1 2.30 0.02 71.4 7.3 b HD 43384 6.3 3.08 0.08 161.4 2.3 3.05 0.04 170.6 1.3 c HD 213789 5.9 0.53 0.01 130.7 0.5 0.53 0.04 133.7 1.9 a

aHeiles 2000, b Whittet et al. 2001 and c Ramprakash et al. 1998

0.1

-0.1

-0.1 0 0.1 Q/I (%)

Figure 6.8 Plot of Q/I versus U/I 6.8. Polarization of active stars 146

Table 6.2. Noramlised Stokes parameter (Q/I and U/I) of unpolarized standards

Object V(mag) Q/I(%) U/I(%) Object V(mag) Q/I(%) U/I(%)

HD 21447 5.10 0.011 0.029 HD 10476 5.20 0.027 -0.020 HD 100623 6.00 0.022 0.027 HD 102438 6.50 0.026 -0.027 HD 125184 6.50 0.043 0.004 HD 42807 6.50 -0.051 -0.020 HD 42807 6.50 0.096 0.012 HD 90508 6.50 0.128 0.050 HD 103095 6.50 0.031 0.016 HD 90156 6.95 0.005 -0.002 HD 9540 7.00 0.059 0.022 HD 65583 7.00 0.063 -0.086 HD 97343 7.04 -0.025 0.085 HD 65583 7.00 0.033 0.067 HD 144287 7.10 0.068 0.018 HD 98281 7.30 0.067 0.080 HD 98281 7.30 -0.090 -0.026 HD 109055 8.82 0.068 0.089 HD 94851 9.10 0.073 -0.113 BD +33 2642 10.84 0.041 0.140 G 191B2B 11.78 -0.017 0.163

active stars. These are i) magnetic areas of star spots and plages, ii) inhomogeneous circuimstellar gas or dust, iii) non-isotropic stellar winds in interacting binaries, and iv) tidal and rotational deformations in rapidly rotating close binaries. The most popular mechanism that have been suggested as a source of linear polarization in these cases are Rayliegh, Thomson or Mei scattering in an optical thin medium (e.g. Tuominen et al. 1989) . Also synchrotron radiation has been proposed as a possible source of polarization, but it should require magnetic ﬁeld and electron energies several order of magnitude larger than the observed in the Sun to be eﬀective in the optical region (Ginzberg & Syrovatskii 1964). Mullan (1975) concludes that the polarization in late-type Main-sequence active stars is most likely not due to synchrotron radiation. So, the polarimetric studies of late-type active stars give the information about the various phenomenon in it. For example, wavelength dependent polarization give the information about Rayleigh scattering in optical thin gases, while Thomson scattering introduces wavelength independent polarization. Multi-band polarimetry represents a powerful tool 6.8. Polarization of active stars 147 for investigating scattering circuimstellar envelopes. Keeping view of these above reasons, we are planning to measure the polarization of active stars in future.

Chapter 7

Summary and future work

This chapter summarizes the main results of this thesis. It also discusses possible future extension of this work.

7.1 Summary

In this thesis we have presented a multiwavelength study of ﬁve active stars namely FR

Cnc (=BD +16◦1753), HD 81032, HD 95559, HD 160934 and LO Peg. The study is based on newly obtained photometry, low-resolution spectroscopy for FR Cnc and HD 81032, as well as archival IR, X-ray and radio observations. We have selected these stars on the basis of their X-ray (Elvis et al. 1992; Schachter et al. 1996) and radio (Drake, S. A. private communication) luminosities. The nature of some of these stars ( FR Cnc and HD 81032) as being chromospherically active binaries has been elucidated for the ﬁrst time. A summary of main results is as follows

The BVR photometry carried out during the years 2000 - 2004 has found a signiﬁ- • cant photometric variability to be present in all ﬁve stars. We have used a CLEAN algorithm for the period search Roberts et al. (1987). For FR Cnc, a photometric period 0.8267 0.0004 d has been established. The strong variation in the phase and amplitude of the FR Cnc light curves when folded on this period implies the presence of evolving and migrating spots or spot groups on its surface. A photometric period of 18.802 0.074d has been discovered in the star HD 81032. The amplitude and the phase of the photometric light curves of HD 81032 are observed to be changing from

149 7.1. Summary 150

one epoch to another. The amplitude of variation in HD 81032 is found to be maximum (0.29 mag) during the observing year 2000-2001. For the star HD 160934, we did not ﬁnd any appreciable change in the amplitude of variation from the one reported in the light curve obtained by Henry et al. (1995).

The shape and amplitude of the photometric light curves of FR Cnc, HD 81032, HD • 95559 and LO Peg are observed to be changing from one epoch to another. The change in the amplitude is mainly due to a change in the minimum of the light curve, and this may be due to a change in the spot coverage. This indicates that photometric variability is due to the presence of dark spots on the surface of active star.

Two groups of spots are identiﬁed for FR Cnc and LO Peg. The spots are found to • migrate, and migration periods of 0.97 year and 0.93 year are determined from the 4 years of data. A migration period of 1.12 years for one group of spots in LO Peg is also determined. Formation of a new group of spots in the star HD 95559 was also seen during our observations. A single large group of spots is found to migrate, and a migration period of 7.32 0.04 years is determined for HD 81032. The photometry of HD 95559 suggests the formation of a spot (group) during the interval of our observations.

The stars FR Cnc, HD 81032, HD 160934 and LO Peg are seen to be redder at • the light minimum and we interpret this as due to the relatively cooler temperature of the darker regions present in the visible hemisphere. It appears that the colours remain nearly constant during our observations in HD 95559. A larger amount of the scatter is, however, seen during 2001 April 3 -7. This may be due to the formation of new group of the spots on the surface of active stars. The lack of colour-brightness correlation in the star HD 95559 may be due to the presence of bright faculae and plages like regions accompained by dark spots in any one component of the this binary system.

The optical spectroscopy of FR Cnc and HD 81032 carried out during 2002-2003, re- • veals the presence of strong and variable Ca II H and K, Hβ and Hα emission features indicative of high level of chromospheric activity. The chromospheric line emission for both stars seems to correlate with the photometric light curve, i.e. maximum 7.1. Summary 151

at the light curve minimum, or minimum at the light curve maximum. The value

of 5.3 for the ratio of the excess emission in Hα to Hβ, EHα/EHβ for the star FR Cnc, suggests that the chromospheric emission may arise from an extended oﬀ-limb region.

The spectral types of FR Cnc and LO Peg were determined to be K5V and K3V type, • respectively. A spectral type of K0IV was determined for HD 81032. The synthetic SED predicted from the spectral type of the star are well matched with the observed SED in each the ﬁve stars. No color excesses in the near-IR JHK bands of these stars have been found using 2MASS and IRAS data.

The kinematics of FR Cnc suggest that it is a very young (35 - 55 Myrs) main- • sequence star and a possible member of the IC 2391 supercluster. LO Peg also has young disk-type kinematics and has been previously suggested to be a member of the 100 Mys old Local Association (Pleiades Moving Group). The kinematics of HD 95559 indicate it is a possible member of the 600 Myrs old Hyades supercluster.

The archival X-ray observations of HD 81032, HD 95559, HD 160934 and LO Peg • carried out by with the ROSAT observatory were also analysed. We did not find any significant variability in the X-ray light curve of the stars HD 95559. However, it appears from the X-ray light curve of HD 81032 that a moderate flare occurred

1 during the RASS observations, with a peak of about 0.6 ct s− at approximately JD=244806.95 and half decay time of 2.6 104 s. A similar flare was also observed × 1 in HD 160934 with a peak about 0.2 ct s− (above its mean level) at JD = 2448123.12. A significant variability was found in the X-ray light curve of LO Peg. Rotational modulation appears to be present in the X-ray light curve of LO Peg. The best fit models to their X-ray spectra imply the presence of two coronal plasma components of differing temperatures and with sub-solar metal abundances. The inferred emission measures and temperatures of HD 95559 and LO Peg are similar to those found for other active dwarf stars. The observed X-ray spectrum and the inferred coronal plasma parameters for HD 81032 are typical of those seen in active stars such as RS CVn binaries.

All of the optical and X-ray properties found for FR Cnc, HD 95559, HD 160934 7.2. Future work 152

and LO Peg are most consistent to the BY Dra type. However, for HD 81032 these properties suggest that it being an evolved RS CVn binary of the long-period type. Clearly, high-resolution optical spectroscopy of HD 81032 in order to confirm the presence of radial velocity variability and determine a spectroscopic binary orbit would be definitive evidence for its proposed binary nature. This study has recon- firmed that the selecting stars by their high X-ray to optical flux ratios is an efficient way to identify the active stars in solar neighborhood.

Correlations between various physical quantities (L , L , P and B-V) of active stars • x rad have been re-examined using a sample containing 248 active stars (101 dwarfs, 65 subgiants and 82 giants). It is a largest sample investigated so far. We did not ﬁnd any appreciable changes in the correlations reported in previous studies.

An Imaging Polarimeter has been fabricated for use with liquid-N cooled CCD cam- • 2 era and is designed to suit 104-cm Sampurnanand telescope with an f/13 focus at ARIES, Naini Tal. The instrument measures the linear polarization in broad B, V

and R band, and has a ﬁeld of view 20 20. ∼ ×

7.2 Future work

i) Doppler imaging is the best way to trace the spots on the surface of a star. With Doppler imaging the presence of dark regions on the star’s surface is determined from small distortions the spot produces on the rotationally broadened line proﬁles. This method permits the reconstruction of the surface brightness distribution of the rotating star. The Doppler imaging method requires high signal-to-noise ratio and high resolution spectroscopy along with good phase coverage in order to extract the spot information. LO Peg and FR Cnc have rotational period 0.42d and 0.82d, respectively, so, are the best candidate of Doppler imaging. To further explore the spot information on these stars, we are planning accordingly.

i) The binary nature of the star HD 81032 is yet to be known. This can be done only by high resolution phase resolved spectroscopy. So, high resolution spectroscopy of HD 81032 is planned. 7.2. Future work 153

iii) Chandra’s high resolution X-ray spectroscopy provides emission measure distribu- tions, electron densities, coronal abundances, and tantalizing hints about the structure and evolution of stellar coronae. High resolution spectroscopy of active stars and a detailed study of X-ray light curves are planned.

iv) We will continue the search for new active stars on the basis of their high X-ray to optical luminosity ratio.

v) The polarization study of active stars are lacking. We are planning to do the multi- band polarization measurement and its correlation with various activity parameters and orbital period of the active binary stars.

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