Abstract
Results of calculations of the cross-sections of the basic processes forming continuous absorption in the photospheres of solar-type stars in the visible and infrared spectral ranges are reported. (These processes are photoionization of H– ions and excited hydrogen atoms, as well as absorption of photons by “free” electrons being in the partially ionized plasma of the photosphere.) The effective cross-section of hydrogen satisfying the observational data or the results of laboratory experiments was introduced, and its nonmonotonic behavior caused by photoionization of excited hydrogen atoms was ascertained in the spectral range of λ from 650 to 820 nm. For a plane-parallel model of the Sun, the continuous absorption coefficient κ c (λ|z) was calculated as a function of the wavelength and coordinate. Its spectral features caused by the effective cross-section structure in the above-mentioned spectral range were for the first time analyzed. The spectral dependence of the radiation intensity in the solar disk center in the continuous spectral range of λ from 600 to 900 nm was studied. The calculation results were compared to the currently available data of observations. It has been shown that the deviation of the observed radiation intensity from the Planck distribution (i.e., the depression) is caused by the processes of photoionization of the excited hydrogen atoms in the states with a principal quantum number n = 3. In the range of λ from 650 to 820 nm, the mean relative deviation is approximately 4%. It has been established that the magnitude of the depression effect significantly depends on the effective temperature of the photosphere of a solar-type star.
Similar content being viewed by others
References
L. H. Aller, Atoms, Stars and Nebulae (Blackiston, Philadelphia, 1943; Mir, Moscow, 1976).
I. N. Atroshchenko, A. S. Gadun, S. I. Gopasyuk, et al., Variations in the Global Characteristics of the Sun, Ed. by E. A. Gurtovenko (Nauk. Dumka, Kiev, 1991) [in Russian].
K. A. Burlov-Vasil’ev, I. E. Vasil’eva, and Yu. B. Matveev, “New measurements of the absolute spectral energy distribution of solar radiation in the range= 650–1070 nm,” Kinematika Fiz. Nebesnykh Tel 12 (3), 75–91 (1996).
M. V. Vavrukh and O. M. Stel’makh, “Photoionization cross-section of negative hydrogen ions,” Visn. L’viv. Univ., Ser. Fiz. 47, 3 (2012).
M. V. Vavrukh and O. M. Stel’makh, “The cross-sections of the main processes that forms the continuous absorption coefficient in the photosphere of Sun-like stars,” Zh. Fiz. Dosl. 17, 4902 (2013).
I. O. Vakarchuk, Theory of Stellar Spectra (L’viv Nats. Univ. Ivana Franka, L’viv, 2002) [in Ukrainian].
O. M. Stel’makh, “The ionization-recombination equilibrium computation in stellar photospheres,” Visn. L’viv. Univ., Ser. Fiz. 49, 137–150 (2014).
W. A. Harrison, Solid State Theory (McGraw-Hill, New York, 1970; Mir, Moscow, 1972).
M. P. Ajmera and K. T. Chung, “Photodetachment of negative hydrogen ions,” Phys. Rev. A: At., Mol., Opt. Phys. 12, 475–479 (1975).
D. Bolsee, N. Pereira, W. Decuyper, et al., “Accurate determination of the TOA solar spectral NIR irradiance using a primary standard source and the Bouguer-Langley technique,” Sol. Phys. 289, 24–33 (2014).
J. T. Broad and W. P. Reinhardt, “One-and two-electron photoejection from H–: A multichannel J-matrix calculation,” Phys. Rev. A: At., Mol., Opt. Phys. 14, 2159–2173 (1976).
K. A. Burlov-Vasiljev, E. A. Gurtovenko, and Yu. B. Matvejev, “New absolute measurements of the solar spectrum 310–685 nm,” Sol. Phys. 157, 51–73 (1995).
K. A. Burlov-Vasiljev, Yu. B. Matvejev, and I. E. Vasiljeva, “New measurements of the solar disk-center spectral intensity in the near IR range 645–1070 nm,” Sol. Phys. 177, 25–40 (1998).
S. Chandrasekhar and F. H. Breen, “On the continuous absorption coefficient of the negative hydrogen ion. III,” Astrophys. J. 104, 430–445 (1946).
Y. A. Eltbaakh, M. H. Ruslan, M. A. Alhgoul, et al., “Measurement of total and spectral solar irradiance: Overview of existing research,” Renewable Sustainable Energy Rev. 15, 1403–1426 (2011).
M. Fligge, S. K. Solanki, J. M. Pap, et al., “Variations of solar spectral irradiance from near UV to the infrared–Measurements and results,” J. Atmos. Sol.-Terr. Phys. 63, 1479–1487 (2001).
J. M. Fontenla, E. Avrett, G. Thuillier, and J. Harder, “Semiempirical models of the solar atmosphere. I. The quiet and-active Sun photosphere at moderate resolution,” Astrophys. J. 639, 441–458 (2006).
J. M. Fontenla and W. Livingston, “High-resolution solar spectral irradiance from extreme ultraviolet to far infrared,” J. Geophys. Res.: Atmos. 116, D20108 (2011).
J. M. Fontenla, J. W. Harder, G. Rottman, et al., “The signature of solar activity in the infrared spectral irradiance,” Astrophys. J., Lett. 605, L85–L88 (2004).
J. A. Gaunt, “Continuous absorption,” Philos. Trans. R. Soc. London, A 229, 163–204 (1930).
S. Geltman, “The bound-free absorption coefficient of the hydrogen negative ion,” Astrophys. J. 136, 935–945 (1962).
W. Gordon, “Die Radialintegrale sin dim folgenden stets in atomaren Einheiten a angegeben,” Ann. Phys. (Berlin, Ger.) 2, 1031–1056 (1929).
C. Gueymard, “The Sun’s total and spectral irradiance for solar energy applications and solar radiation models,” Sol. Energy 76, 423–453 (2004).
C. A. Guyemard, “Reference solar spectra: Their evolution, standardization issues, and comparison to recent measurements,” Adv. Space Res. 37, 323–340 (2006).
D. Labs and H. Neckel, “The radiation of the solar photosphere from 2000 Å to 100 µm,” Z. Astrophys. 69, 1–73 (1968).
D. Labs and H. Neckel, “Transformation of the absolute solar radiation data into the international practical temperature scale of 1968,” Sol. Phys. 15, 79–87 (1970).
D. Labs and H. Neckel, “Improved data of solar spectral irradiance from 0.33 to 1.25 microns,” Sol. Phys. 74, 213–249 (1981).
E. Milne, “Radiative equilibrium: The relation between the spectral energy curve of a star and the law of darkening of the disc towards the limb, with special reference to the effects of scattering and the solar spectrum,” Philos. Trans. R. Soc. London, A 223, 201–255 (1923).
H. Neckel and D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys. 90, 205–258 (1984).
A. Shapiro, W. Schmutz, M. Schoell, et al., “NLTE solar irradiance modeling with the COSI code,” Astron. Astrophys. 517, A48 (2010).
S. J. Smith and D. S. Burch, “Relative measurement of the photodetachment cross section for H–,” Phys. Rev. 116, 1125–1131 (1959).
A. L. Stewart, “A perturbation-variation study of photodetachment from H–,” J. Phys. B: At. Mol. Phys. 11, 3851–3860 (1978).
M. P. Thekaekara, “Proposed standard values of the solar constant and the solar spectrum,” J. Environ. Sci. (Mount Prospect, Ill.) 13, 6–9 (1970).
M. P. Thekaekara, “Extraterrestrial solar spectrum, 3000–6100 Å at 1 Å intervals,” Appl. Opt. 13, 518–522 (1974).
M. P. Thekaekara and A. J. Drummond, “Standard values for the solar constant and its spectral components,” Nat. Phys. Sci. 229, 6–9 (1971).
M. P. Thekaekara, R. Kruger, and C. H. Duncan, “Solar irradiance measurements from a research aircraft,” Appl. Opt. 8, 1713–1732 (1969).
G. Thuillier, D. Bolsee, G. Schmidtke, et al., “The solar irradiance spectrum at solar activity minimum between solar cycles 23 and 24,” Sol. Phys. 289, 1938–1958 (2014).
G. Thuillier, T. Foujols, D. Bolsee, et al., “SOLAR/SOLSPEC: Instrument performance and its absolute calibration using a blackbody as primary standard source,” Sol. Phys. 257, 185–213 (2009).
G. Thuillier, J. P. Goutail, P. C. Simon, et al., “Measurement of the solar spectral irradiance from 200 to 3000 nanometers,” Science 225, 182–184 (1984).
G. Thuillier, J. W. Harder, A. Shapiro, et al., “The infrared solar spectrum measured by the SOLSPEC spectrometer onboard the International Space Station,” Sol. Phys. 290, 1581–1600 (2015).
G. Thuillier, M. Herse, D. Labs, et al., “The solar spectral irradiance from 200 to 2400 nm as measured by the SOLSPEC spectrometer from the Atlas and Eureka missions,” Sol. Phys. 214, 1–22 (2003).
G. Thuillier, M. Herse, P. C. Simon, et al., “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the Atlas I mission,” Sol. Phys. 177, 41–61 (1998).
G. Thuillier, M. Herse, P. C. Simon, et al., “The absolute solar spectral irradiance from 200 to 2500 nm as measured by the SOLSPEC spectrometer with the ATLAS and EURECA missions,” Phys. Chem. Earth, Part C: Sol., Terr. Planet. Sci. 25 (5–6), 375–377 (2000).
J. E. Vernazza, E. H. Avrett, and R. Loeser, “Structure of the solar chromosphere. I. Basic computation and summary of the results,” Astrophys. J. 184, 605–632 (1973).
J. E. Vernazza, E. H. Avrett, and R. Loeser, “Structure of the solar chromosphere. II. The underlying photosphere and temperature-minimum region,” Astrophys. J., Suppl. Ser. 30, 1–60 (1976).
J. E. Vernazza, E. H. Avrett, and R. Loeser, “Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun,” Astrophys. J., Suppl. Ser. 45, 635–725 (1981).
M. Weber, “Comment on the article by Thuillier et al., The infrared solar spectrum measured by the SOLSPEC spectrometer onboard the International Space Station,” Invited review, Sol. Phys. 290, 1601–1605 (2015).
R. Wildt, “Negative ions of hydrogen and the opacity of stellar atmospheres,” Astrophys. J. 90, 611–620 (1939).
R. Wildt, “The continuous spectrum of stellar atmospheres consisting only of atoms and negative ions of hydrogen,” Astrophys. J. 93, 47–51 (1941).
A. W. Wishart, “The bound-free photodetachment cross section of H–,” J. Phys. B: At. Mol. Phys. 12, 3511–3519 (1979).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Original Russian Text © M.V. Vavrukh, I.E. Vasil’eva, O.M. Stelmakh, N.L. Tyshko, 2016, published in Kinematika i Fizika Nebesnykh Tel, 2016, Vol. 32, No. 3, pp. 40–62.
About this article
Cite this article
Vavrukh, M.V., Vasil’eva, I.E., Stelmakh, O.M. et al. Continuous absorption and depression in the solar spectrum at wavelengths from 650 to 820 nm. Kinemat. Phys. Celest. Bodies 32, 129–144 (2016). https://doi.org/10.3103/S0884591316030053
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0884591316030053