Brigham Young University BYU ScholarsArchive Theses and Dissertations 2007-09-06 Development of a Method for Calculating Delta Scuti Rotational Velocities and Hydrogen Beta Color Indices Tabitha Christi Buehler Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Astrophysics and Astronomy Commons, and the Physics Commons BYU ScholarsArchive Citation Buehler, Tabitha Christi, "Development of a Method for Calculating Delta Scuti Rotational Velocities and Hydrogen Beta Color Indices" (2007). Theses and Dissertations. 1538. https://scholarsarchive.byu.edu/etd/1538 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. DEVELOPMENT OF A METHOD FOR CALCULATING DELTA SCUTI ROTATIONAL VELOCITIES AND HYDROGEN-BETA COLOR INDICES by Tabitha Christi Bush A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics and Astronomy Brigham Young University December 2007 Copyright c 2007 Tabitha Christi Bush All Rights Reserved BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by Tabitha Christi Bush This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. Date Eric G. Hintz, Chair Date Michael D. Joner Date Benjamin J. Taylor Date J. Ward Moody BRIGHAM YOUNG UNIVERSITY As chair of the candidate’s graduate committee, I have read the thesis of Tabitha Christi Bush in its final form and have found that (1) its format, citations, and bib- liographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Eric G. Hintz Chair, Graduate Committee Accepted for the Department J. Ward Moody, Graduate Coordinator Department of Physics and Astronomy Accepted for the College Thomas W. Sederberg, Associate Dean College of Physical and Mathematical Sciences ABSTRACT DEVELOPMENT OF A METHOD FOR CALCULATING DELTA SCUTI ROTATIONAL VELOCITIES AND HYDROGEN-BETA COLOR INDICES Tabitha Christi Bush Department of Physics and Astronomy Master of Science To add to the understanding of the structure and evolution of δ Scuti stars, 167 δ Scutis north of -01◦ declination and brighter than 13th magnitude have been observed spectroscopically. A method for calculating rotational velocity values and Hβ color indices for the stars in the data set with no previously published values is developed, using the stars in the data set brighter than 7th magnitude. Rotational velocity values for four stars with previously unknown values and Hβ index values for five stars with previously unknown values are calculated. ACKNOWLEDGMENTS I would first like to thank my advisor, Dr. Eric Hintz, for guiding me in my research and giving me many opportunities over the past seven years. I have learned so much, and my love for astronomy and for research have grown. I would like to thank the rest of my committee and all others who helped me through revisions: Prof. Mike Joner, Lisa Joner, Maureen Hintz, Dr. J. Ward Moody, Dr. Benjamin Taylor, Kathleen Moncrieff, and David Buehler. Thanks to Dr. Taylor also for help with statistical analysis. I would like to thank my friends who have been a great support throughout this project and otherwise, especially David and Kathleen. And thanks to my parents, Joe and Georgeanne, my sister Jessica, and my brother Joey for always believing in me and being on my team. Contents Acknowledgments vi Table of Contents vii List of Tables ix List of Figures xi 1 Introduction and Background 1 1.1 Project Motivation ............................ 1 1.2 Delta Scuti Stars ............................. 3 1.3 Telescope Systems ............................ 6 1.4 Spectroscopy ............................... 8 1.5 Projected Rotational Velocity ...................... 10 1.6 Hydrogen-Beta Color Index ....................... 16 1.7 Project Scope ............................... 19 2 Procedures and Methods 21 2.1 Spectroscopic Observations ........................ 21 2.2 Image Reductions ............................. 25 2.2.1 Updating Headers and Trimming Frames ............ 25 2.2.2 Processing Bias Frames ...................... 28 2.2.3 Processing Flat Frames ...................... 29 2.2.4 Removing Cosmic Rays ...................... 30 2.2.5 Wavelength Calibration ..................... 31 2.2.6 Continuum Calibration ...................... 33 2.3 Projected Rotational Velocity Methods ................. 37 2.3.1 Finding Initial Spectral Broadening ............... 37 vii 2.4 Finding Initial Hydrogen-Beta Values .................. 41 3 Analysis and Results 45 3.1 Analysis of Broadening Values ...................... 45 3.2 Calculating Rotational Velocity Values ................. 55 3.3 Analysis of Hydrogen-Beta Values .................... 57 3.4 Calculating Hydrogen-Beta Values .................... 61 4 Conclusions 63 References 65 List of Tables 1.1 Stellar Spectral Types .......................... 5 2.1 Spectroscopic Observations of δ Scutis Brighter Than 7th Magnitude 22 2.2 Spectroscopic Observations of δ Scutis from 7th to 8th Magnitude .. 23 2.3 Spectroscopic Observations of δ Scutis from 8th to 9th Magnitude .. 24 2.4 Spectroscopic Observations of δ Scutis from 9th to 13th Magnitude . 24 2.5 CCD-Spectrograph Specifics ....................... 25 2.6 Spectral Features Measured ....................... 39 2.7 Average Raw Hβ Color Index Values .................. 44 2.8 Standard Deviations of Calculated Raw Hβ Color Index Values ... 44 3.1 Stars Used for TiII/FeII Relation with at Least Three Measurements Each .................................... 48 3.2 Stars Used for MgII Relation with at Least Three Measurements ... 50 3.3 Stars Rejected Due to High Standard Deviations ............ 51 3.4 v sin i Values from Royer et al. (2002b) and Rodriguez et al. (2000) Catalogs .................................. 53 3.5 Calculated v sin i Values ......................... 57 3.6 Relations for Filter/Calibration Combinations for Each Observing Night 58 3.7 Combined Relations for Filter/Calibration Combinations ....... 61 3.8 Hβ Color Index Values for Stars with No Previously Published Values 62 ix List of Figures 1.1 v sin i vs. Pulsation Amplitude for δ Scutis in Rodriguez (2000) Catalog 2 1.2 (B-V) Color Index vs. v sin i for δ Scutis in Rodriguez (2000) Catalog 3 1.3 Hertzsprung-Russell Diagram. ...................... 5 1.4 δ Scuti Light Curve ............................ 6 1.5 Coud´eTelescope Focus .......................... 7 1.6 Basic Spectrograph ............................ 8 1.7 Two Spectrum Examples ......................... 9 1.8 Projected Rotational Velocity ...................... 10 1.9 Rotational Broadening .......................... 11 1.10 Theoretical Stellar Line Profiles ..................... 12 1.11 Planck Curves. .............................. 17 1.12 Transmission Curves for Hβ Filters ................... 18 2.1 Examples of Unprocessed Image Frames. ................ 26 2.2 Example of Image Header File ...................... 27 2.3 Example of .cmds File .......................... 28 2.4 Parameters in ccdproc .......................... 29 2.5 Slit Aperture View of Flat Field Frame ................. 30 2.6 Defining the Aperture for the Flat Field ................ 31 2.7 A Spectrum Before and After Using cosmicrays. ............ 32 2.8 FeAr Arc Map ............................... 34 2.9 A Spectrum Before and After Wavelength Calibration ......... 35 2.10 A Spectrum Before and After Continuum Calibration ......... 36 2.11 Gaussian Profile Fitting of a Stellar Spectral Line ........... 38 2.12 Spectral Features Measured for v sin(i) Analysis ............ 40 2.13 Gaussian Profile Fitting of an Arc Lamp Line ............. 40 2.14 Profiles of Theoretical Gaussian Hβ Filters ............... 42 xi 2.15 sbands Output File ............................ 43 3.1 Initial Broadening Relations ....................... 46 3.2 Calibration of each Spectral Feature ................... 47 3.3 Broadening Calibration Using TiII 4501 A˚ and FeII 4508 A˚ Features . 48 3.4 Consistency Check Between TiII 4501 A˚ and FeII 4508 A˚ FWHM Values 49 3.5 Plot of MgII Feature FWHM vs. v sin i for at Least Three Observations of Each Star ................................ 50 3.6 v sin i Relations After Rejecting High Standard Deviations ...... 52 3.7 v sin i Relations Using Royer et al. (2002b) v sin i Values ....... 53 3.8 v sin i Relations Using Rodriguez et al. (2000)& Royer et al. (2002b) v sin i Values ................................ 54 3.9 Final v sin i Calibration Relation ..................... 55 3.10 Hβ Square Filter Relations for Two Nights ............... 58 3.11 Hβ Gaussian Filter Relations for Two Nights .............. 59 3.12 Combined Hβ Relation .......................... 60 Chapter 1 Introduction and Background 1.1 Project Motivation Many aspects of stellar evolution remain a puzzle. In order to more completely understand stellar evolution, several pieces must be put together. It is not possible to observe one star go through its whole life process, so stars at different stages