Unambiguous Black Hole Mass from Polarimetry and Application to Hot Jupiters Dissertation by Sloane J. Wiktorowicz In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2009 (Defended July 28, 2008)
ii c 2009 Sloane J. Wiktorowicz All Rights Reserved
iii This dissertation is dedicated to my wife Sharon, who has stood by my side and supported me while writing. I also dedicate this work to my family, who have encouraged me to pursue my love of the stars and whose advice and support through the years have been essential.
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v Acknowledgements Many thanks go to Keith Matthews, whose help and advice have been essential in construction of my instrument. I would like to thank Michael Ireland and Ian McEwan for valuable discussions on instrumentation, polarimetry, and signal processing. I appreciate the help of the Palomar Observatory staff, especially Bruce Baker, Karl Dunscombe, John Henning, Greg van Idsinga, and Steve Kunsman. Without their help, this instrument would literally not have gotten off the ground. I thank Shri Kulkarni, who inspired me to pursue instrumentation. I acknowledge David Stevenson for a valuable debate regarding condensation in a water-hydrogen mixture and Conner Wiktorowicz for his help in determining uncertainty along the photospheric adiabat. I would like to acknowledge funding from the Moore Foundation. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.
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vii Abstract A novel technique for detecting light scattered by extrasolar planets is presented that has the potential to constrain orbital inclination and planet mass. To develop this technique, I have commissioned a high precision polarimeter on the Hale 5-m telescope at Palomar Observatory. The high mass X- ray binary Cygnus X-1 has been observed, which is a proxy for extrasolar planet studies. The single scattering model of Brown et al. (1978), widely used in the literature, predicts an orbital inclination for Cygnus X-1 that is inconsistent with the lack of observed X-ray eclipses to 4σ 5σ. Previous studies have hinted at this discrepancy, but data quality was such that the confidence in such a discrepancy was not statistically significant. My observations represent the highest precision study of this object, and they illustrate the overwhelming complexity of the supergiant/black hole system. They also call into question the validity of the Brown et al. (1978) formalism, widely used by the community, for inclination estimation in binary systems. Extrasolar planet host stars have also been observed, and precision of order one part per million has been achieved on bright targets. Precision attained on fainter host stars is of order one part in 10 5. While scattered light from extrasolar planets has not been conclusively detected, a planetary transit in the HD 189733 system may have been observed in polarized light. Such an event is observed to be 1,000 times weaker in polarized light than in photometry, and it indicates a planetary transit of the Southern Hemisphere of the host star. Such geometric information is difficult to determine by other methods. The integrated polarization of the debris disk surrounding γ Ophiuchi has been observed to high precision, and the position angle of net polarization is aligned with the disk major axis as seen by the Spitzer Space Telescope. This indicates the disk is primarily composed of forward scattering dust grains larger than the wavelengths of visible light. Finally, Neptune-mass extrasolar planets orbiting close to their host stars have been modeled to be far too warm for liquid water oceans to exist in their upper atmospheres.
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ix Contents Acknowledgements v Abstract vii 1 Promises and Pitfalls of Polarimetry 1 1.1 Introduction......................................... 1 1.2 Promises of Polarimetry.................................. 4 1.2.1 Extrasolar Planets................................. 4 1.2.2 Black Holes and Neutron Stars.......................... 10 1.2.3 Circumstellar Disks................................ 10 1.2.4 Evolved Stars.................................... 11 1.3 Pitfalls of Polarimetry................................... 13 1.3.1 Telescope Polarization............................... 13 1.3.2 Interstellar Polarization.............................. 13 1.3.3 Intrinsic Polarization Variability......................... 20 2 The POLISH Instrument 25 2.1 Introduction......................................... 25 2.2 Black Hole Mass from Polarimetry............................ 26 2.3 The Polarimeter...................................... 28 2.4 Observing Strategy..................................... 34 2.5 Data Reduction....................................... 37 2.5.1 Polarization and Noise Calculations....................... 37 2.5.2 PEM Calibration.................................. 39 2.5.3 Mean Polarization................................. 42 2.6 Standard Stars with APDs................................ 42 2.6.1 Unpolarized Standard Stars and Systematic Effects............... 42
x 2.6.2 Polarized Standard Stars............................. 47 2.7 Standard Stars with PMTs................................ 51 2.8 Comparison to Literature................................. 53 2.8.1 Unpolarized Standard Stars............................ 53 2.8.2 Weakly Polarized Standard Stars......................... 55 2.8.3 Strongly Polarized Standard Stars........................ 61 2.8.4 Absolute Polarization............................... 61 2.8.5 Interstellar Polarization.............................. 67 2.9 Discussion.......................................... 68 2.10 Appendix A: Mueller Matrix for Lab Tests........................ 70 2.11 Appendix B: Mueller Matrix for POLISH........................ 71 2.12 Appendix C: Detector Noise................................ 75 3 Nightly Variability of Polarimetric Standard Stars 81 3.1 Introduction......................................... 81 3.2 Observations........................................ 82 3.3 Variability.......................................... 84 3.3.1 Intra-Night Variability and Systematic Effects.................. 84 3.3.2 Night-to-Night Variability............................. 89 3.4 Discussion.......................................... 99 3.4.1 Standard Stars................................... 99 3.4.2 Extrasolar Planets................................. 104 3.4.3 Debris Disk..................................... 113 3.4.4 Cepheid Variables................................. 116 3.5 Conclusion......................................... 119 3.6 Appendix D: Single Scattering Geometry........................ 125 4 Cygnus X-1 Inclination from Polarimetry 129 4.1 Introduction......................................... 129 4.2 Overview of Cygnus X-1.................................. 130 4.2.1 Accretion...................................... 130 4.2.2 Periodicities..................................... 132 4.2.3 Polarization..................................... 134 4.3 Inclination from Polarimetry............................... 136
xi 4.3.1 BME Scattering Model.............................. 136 4.3.2 Inclination Bias................................... 138 4.4 Results............................................ 140 4.5 Literature Estimates.................................... 147 4.5.1 Eclipses....................................... 147 4.5.2 Radial Velocity Mass Function.......................... 147 4.5.3 Radial Velocity Tomography........................... 151 4.5.4 Ellipsoidal Modulation............................... 152 4.5.5 Polarimetry..................................... 153 4.5.6 Disk Precession................................... 158 4.5.7 Quasi-Periodic Oscillation Scaling........................ 159 4.6 Discussion.......................................... 160 4.7 Conclusion......................................... 168 5 Liquid Water Oceans in Ice Giants 181 5.1 Introduction......................................... 181 5.2 Photospheric Adiabat................................... 184 5.2.1 Construction.................................... 184 5.2.2 Application to Neptune.............................. 188 5.3 Phase Transition...................................... 190 5.3.1 Cloud Base..................................... 190 5.3.2 Supercritical Fluid................................. 192 5.4 Ocean Requirements.................................... 193 5.4.1 Deep Interior Mixing Ratio............................ 193 5.4.2 Gravitational Signature.............................. 196 5.4.3 Photospheric Temperature............................. 197 5.5 The Water-Hydrogen-Helium System........................... 200 5.6 Extrasolar Hot Neptunes.................................. 202 5.7 Future Work........................................ 204 5.8 Conclusion......................................... 204 5.9 Appendix E: Moist Adiabat................................ 208
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xiii List of Figures 1.1 Stokes parameters projected onto the sky......................... 3 1.2 Theoretical orbital modulation of system polarization for a hot Jupiter system.... 7 1.3 Imaging polarimetry of Uranus............................... 7 1.4 Modeled orbital modulation of polarization of a hot Jupiter............... 9 1.5 Modeled spectrum of a hot Jupiter in photometry and polarimetry........... 9 1.6 Modeled scattered flux and polarization of a hot Jupiter through orbit......... 10 1.7 Imaging polarimetry of R Scl................................ 12 1.8 Correlation of net polarization and mass loss rate for evolved stars........... 12 1.9 Telescope polarization of the 4.2-m William Herschel Telescope............. 14 1.10 Interstellar polarization aligned to the galactic magnetic field.............. 14 1.11 Empirical wavelength dependence of interstellar polarization.............. 16 1.12 Theoretical wavelength dependence of interstellar polarization............. 16 1.13 Observed circular polarization sign change near λ = λ max................ 17 1.14 Increase in degree of interstellar polarization up to d 2 kpc.............. 17 1.15 Scattering of quasar radio emission by an interstellar dust cloud............ 19 2.1 Orbital modulation of system polarization for HMXBs.................. 27 2.2 Plan view of the POLISH optical path........................... 28 2.3 Ray trace diagram of the POLISH optical path...................... 29 2.4 Photographs of the POLISH instrument.......................... 29 2.5 Typical raw AC and DC data for the unpolarized star HR 5854............. 36 2.6 Typical raw data for the strongly polarized star HD 204827............... 36 2.7 Calibration of the PEM rotation angle........................... 40 2.8 Polarization of HR 5854 after PEM and gain correction................. 44 2.9 Polarization of HR 8974 after PEM and gain correction.................. 44 2.10 Run-averaged precision as a function of stellar polarization............... 54
xiv 2.11 Nightly mean polarization of the unpolarized star HR 5854............... 56 2.12 Intra-night observations of HR 5854 with APD1, UT 2007 Aug 3 and 4........ 56 2.13 Intra-night observations of HR 5854 with APD1, UT 2007 Aug 5 and 6......... 57 2.14 Nightly mean polarization of the unpolarized star HR 8974............... 57 2.15 Intra-night observations of HR 8974 with APD1, UT 2007 Aug 3, 5, and 6....... 58 2.16 Nightly mean polarization of the weakly polarized star HD 9270............ 58 2.17 Intra-night observations of HD 9270 with APD1, UT 2007 Aug 4, 5, and 6....... 59 2.18 Nightly mean polarization of the weakly polarized star γ Oph.............. 59 2.19 Intra-night observations of γ Oph with APD1, UT 2007 Aug 4, 5, and 6........ 60 2.20 Nightly mean polarization of the weakly polarized star Algenib............. 60 2.21 Intra-night observations of Algenib with APD1, UT 2007 Aug 5 and 6......... 62 2.22 Nightly mean polarization of the strongly polarized star HD 157999.......... 62 2.23 Intra-night observations of HD 157999 with APD1, UT 2007 Aug 5 and 6........ 63 2.24 Nightly mean polarization of the strongly polarized star HD 187929.......... 63 2.25 Intra-night observations of HD 187929 with APD1, UT 2007 Aug 3, 5, and 6...... 64 2.26 Nightly mean polarization of the weakly polarized star HD 212311........... 64 2.27 Intra-night observations of HD 212311 with PMT1, UT 2007 Aug 3 and 4....... 65 2.28 Intra-night observations of HD 212311 with PMT1, UT 2007 Aug 5 and 6....... 65 2.29 Nightly mean polarization of the strongly polarized star HD 204827.......... 66 2.30 Intra-night observations of HD 204827 with PMT1, UT 2007 Aug 3, 5, and 6...... 66 2.31 Precision achieved on standard stars compared to the literature............. 67 3.1 Quantum efficiency curves for the red enhanced and blue enhanced APDs....... 82 3.2 Nightly confidence range of normal distribution for all stars............... 88 3.3 Nightly confidence range of normal distribution for individual stars........... 88 3.4 CDFs of HR 5854...................................... 90 3.5 CDFs of HD 187929..................................... 91 3.6 Polarization as a function of stellar distance........................ 97 3.7 Expected and observed ratios of polarization between APDs............... 101 3.8 Observed polarization of the HD 175541 exoplanet Jupiter system........... 106 3.9 Observed polarization of the HD 149026 transiting hot Jupiter system......... 106 3.10 Polarimetric modulation of the HD 189733 transiting hot Jupiter system....... 109 3.11 Observed polarization of the HD 189733 transiting hot Jupiter system......... 109
xv 3.12 HD 189733 transit geometry................................ 110 3.13 Modeled degree of polarization during a transit...................... 110 3.14 Polarimetric observations of a transit of the HD 189733 hot Jupiter.......... 112 3.15 Possible transit of an extrasolar planet seen in polarized light.............. 112 3.16 Debris disk geometry.................................... 114 3.17 Position angle of net polarization for γ Oph........................ 115 3.18 Polarization variations in HD 187929 versus Cepheid pulsation phase.......... 119 4.1 Binned observations of Cygnus X-1, August 2007 data.................. 143 4.2 Binned observations of Cygnus X-1, June 2008 data................... 143 4.3 Examples of synthesized Q and U data sets........................ 146 4.4 Histogram and CDF between BME fits and synthesized data.............. 146 4.5 Confidence intervals for inclination estimates from the BME model........... 148 4.6 Cygnus X-1 inclination estimates from various methods................. 148 4.7 Geometry for eclipses and for radial velocity tomography................ 152 4.8 Polarimetric modulation observed in Aug 2007 and Jun 2008.............. 161 4.9 Summary of Cygnus X-1 polarimetric modulation.................... 162 4.10 U versus Q for the data sets in Figure 4.9......................... 162 5.1 Temperature-entropy curve for pure water......................... 182 5.2 Photospheric adiabat uncertainty.............................. 187 5.3 Photospheric adiabat overlying SF phase boundaries................... 189 5.4 Pressure-temperature profile along the photospheric adiabat............... 191 5.5 Critical curve: temperature vs. X............................. 194 5.6 Critical curve: pressure vs. X................................ 194 5.7 Minimum water mixing ratio for an ocean......................... 195 5.8 Density along the photospheric adiabat overlying density models............ 196 5.9 Ocean probability...................................... 199 5.10 P -T profiles along photospheric adiabats with different condensables.......... 201 5.11 Minimum deep interior water mixing ratio necessary for ocean existence........ 203
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xvii List of Tables 2.1 Stokes Parameters Given by Positive AC Phase...................... 33 2.2 Observed Standard Stars.................................. 35 2.3 Detector Quantities..................................... 39 2.4 Correction Parameters for Θ PEM = ±45......................... 41 2.5 Raw Polarization of Unpolarized Standard Stars..................... 45 2.6 Telescope Polarization with APDs............................. 46 2.7 Systematic Effects: Unpolarized Standard Stars with APDs............... 47 2.8 Weakly Polarized Standard Stars with APDs....................... 48 2.9 Strongly Polarized Standard Stars with APDs...................... 50 2.10 Systematic Effects: Polarized Standard Stars with APDs................ 51 2.11 Weakly Polarized Standard Stars with PMTs....................... 52 2.12 Strongly Polarized Standard Stars with PMTs...................... 52 2.13 Systematic Effects: Standard Stars with PMTs...................... 53 2.14 Corrections for Absolute Polarization........................... 61 3.1 Observed Stars........................................ 83 3.2 Confidence of Random Distribution............................ 87 3.3 HR 5854 Variability..................................... 92 3.4 HR 8974 Variability..................................... 92 3.5 HD 9270 & γ Oph Variability................................ 93 3.6 HD 212311 Variability.................................... 93 3.7 Stellar Variability...................................... 94 3.8 HD 204827 Variability.................................... 95 3.9 Cygnus X-1 Variability................................... 95 3.10 Variability of Interstellar Polarization........................... 100 3.11 Wavelength-Dependent Polarization............................ 100
xviii 3.12 Corrections for Absolute Polarization........................... 100 3.13 Variability of Exoplanet Host Stars............................. 105 3.14 HD 187929 Variability.................................... 119 4.1 Journal of Observations................................... 141 4.2 BME Fit Parameters..................................... 142 4.3 Comparison of Inclination Estimates............................ 149 4.4 Photometric, Precessional Modulation........................... 163 5.1 Deep Interior Mixing Ratios................................. 192 5.2 Cloud Bases......................................... 201