The Size, Structure, and Variability of Late-Type Stars Measured ...

More documents

Recommendations

Info

Figure 3.11: Predicted Monochromatic Radii vs. Wavelength from Bessell Model. maximum phase - circles, minimum phase - dots, arrows on left axis correspond to the Rosseland diameter at maximum (solid) and minimum (hollow) phase. (reproduction of Figure 8 from Bessell et al. (1989) [9]) 55
56 extension is reflected at wavelengths containing significant molecular absorption in which the monochromatic radius can be more than twice as large as the continuum radius. The variable star models of Höfner et al. (1998) [47] predict atmospheric structure for a wide variety of luminosities, effective temperatures, piston velocity amplitudes, and carbon to oxygen ratios. The latter parameter mostly affects the velocity at large radii where molecular absorption from oxides is significant, and the dust which forms in greater quantities in carbon-rich environments. As in the previous models, shocks are formed as the density wave travels outward, and these shocks are characterized by a velocity discontinuity of around 20 km/s. A temperature increase is associated with each shock front. The stellar atmosphere is greatly extended in the Höfner model as well. Figure 3.12 illustrates the structure of a 7000L ⊙ , 1M ⊙ star with an effective temperature of 2880 K, and a carbon to oxygen ratio of 1.4, driven with a piston velocity of 4 km/s. Shown is the predicted gas velocity, density, temperature, and degree of dust condensation as a function of radius at different phases (reproduction of Figure 5 from Höfner et al. (1998) [47]). The density is greater than the hydrostatic case for densities lower than about 10 −10.75 g/cm 3 . The shock fronts are most pronounced as discontinuities in the velocity structure but are also evident as increases in the density by an order of magnitude or so and as increases in the temperature. These features can be seen expanding with increasing phase. Dust begins to form around 1.9R ∗ . The prototypical mira, o Cet, is thought to have an overabundance of oxygen relative to carbon. Höfner et al. (1998) [47] contains an oxygen-rich model which has a structure that appears identical to the above model for radii less than 2R ∗ , and differs at greater radii only in that dust does not form, and the velocity approaches about 10 km/s at large radii. The O-rich model was not plotted with as great an accuracy in the paper, however, and we will consider the carbon-rich model without dust further in Section 3.4.3. There is experimental evidence as well that Mira variable atmospheres are extended significantly. H 2 spectral lines were observed by Hinkle et al. (2000) [43] and H 2 column densities higher than 5 × 10 24 cm −2 were inferred. Assuming a reasonable scale height and radius, densities greater than ∼ 10 −11.5 gm/cm 3 are needed in the atmospheric layers cool enough to form H 2 . The radio continuum measurements of Reid and Menten (1997) [84] are consistent with H − ff and H 2 − ff opacity3 begin dominant in the atmospheres of Mira variables and imply densities around 10 −11.8 gm/cm 3 at a radius about twice the optical 3 Here and elsewhere the notation X ff is used to describe the transitions X + +e − ⇐⇒ X + +e − . X − ff refers to X + e − ⇐⇒ X + e − , and X bf refers to X ⇐⇒ X + + e − .
Page 1 and 2:
The Size, Structure, and Variabilit
Page 3 and 4:
1 Abstract The Size, Structure, and
Page 5 and 6:
iv 5 Spectroscopy and ISI Measureme
Page 7 and 8:
vi 3.15 Density, Temperature, and C
Page 9 and 10:
viii Acknowledgements Over the cour
Page 11 and 12:
2 to achieve resolution characteris
Page 13 and 14: 4 sources are not coaligned perfect
Page 15 and 16: 6 Intensity Profile Hankel Transfor
Page 17 and 18: 8 Figure 1.3: Possible Effective Ba
Page 19 and 20: 10 6LJQDO'HWHFWRU 6LJQDO'HWHFWRU /D
Page 21 and 22: 1995A&A...304...69P 12 Figure 1.5:
Page 23 and 24: Figure 1.6: Stellar Evolution of a
Page 25 and 26: 16 such as Mira variables, become u
Page 27 and 28: 18 wavelengths, however, its range
Page 29 and 30: 20 Figure 2.1: ISI Data for o Cet f
Page 31 and 32: 22 Figure 2.3: Uniform Disk, Limb D
Page 33 and 34: 24 2.2 Comparison of ISI Data with
Page 35 and 36: 26 Table 2.3: Diameter Measurements
Page 37 and 38: 28 measurements. χ Cyg and R Leo a
Page 39 and 40: 30 metric flux (from the reference
Page 41 and 42: 32 their surface. Very often, mater
Page 43 and 44: 34 Mira. Finally, variations in tim
Page 45 and 46: 36
Page 47 and 48: 38 Figure 3.2: Intensity Distributi
Page 49 and 50: 40 Figure 3.4: Ratio of the Best-Fi
Page 51 and 52: Figure 3.5: Synthetic Near-Infrared
Page 53 and 54: 44 Angular Diameter (mas) 60 50 40
Page 55 and 56: 46 wavelengths which would cause th
Page 57 and 58: 48 3.4.1 Static Radiative Transfer
Page 59 and 60: 50 Figure 3.8: Ratio of Photospheri
Page 61 and 62: 52 3.4.2 The Effect of Dynamic Phen
Page 63: 54 Figure 3.10: “Standard” Bowe
Page 67 and 68: 58 photosphere. These results suppo
Page 69 and 70: 60 Figure 3.13: Continuum Opacity o
Page 71 and 72: 62 assuming only continuum sources.
Page 73 and 74: 64 Figure 3.16: Normalized Syntheti
Page 75 and 76: Figure 3.17: Density and Temperatur
Page 77 and 78: 68 Figure 3.19: Apparent Size of H
Page 79 and 80: 70 of Fox and Wood (1985) [31] are
Page 81 and 82: 72 3.5 Explanation of Variations in
Page 83 and 84: 74 Figure 3.21: 2.1 µm Image of 25
Page 85 and 86: 76 at visible wavelengths either by
Page 87 and 88: 78 4.1 Implications of Diameter Mea
Page 89 and 90: 80 11 µm Diameter of o Cet vs. Dat
Page 91 and 92: 82 Figure 4.3: A uniform intensity
Page 93 and 94: 84 phase observed in the continuum
Page 95 and 96: 86 5.1 General Results of 11 µm Sp
Page 97 and 98: 88 depth are the contours plotted a
Page 99 and 100: 90 Figure 5.3: Best Fitting Calcula
Page 101 and 102: 92 of its three parameters. The con
Page 103 and 104: 94 H 2 O on their measured diameter
Page 105 and 106: 96 5.3 Modelling Spectral Features
Page 107 and 108: 98 Figure 5.7: Stellar Intensity Pr
Page 109 and 110: Figure 5.9: Observed H 2 O Spectral
Page 111 and 112: Figure 5.10: Höfner Model Predicte
Page 113 and 114: 104 30 km/s causes the spectrum to
Page 115 and 116:
Figure 5.13: o Cet Spectra in Obser
Page 117 and 118:
108 density prediction matches the
Page 119 and 120:
110 Dixon. The infrared angular dia
Page 121 and 122:
112 [29] M. U. Feuchtinger, E. A. D
Page 123 and 124:
114 [50] A. P. Jacob, T. R. Bedding
Page 125 and 126:
116 [70] A. A. Michelson and F. G.
Page 127 and 128:
118 [92] Martin Schwarzschild. Over
Page 129:
120 [114] P. Woitke, D. Krüger, an
show all

The Size, Structure, and Variability of Late-Type Stars Measured ...

Create successful ePaper yourself

Delete template?

Save as template?