Abstract

Various methods for obtaining the solar ultraviolet limb-darkening profiles are investigated in terms of their accuracy and adaptability for use on electronic computers. The experimental data consist of a series of spectra in the wavelengths shorter than 3000 Å taken with a somewhat astigmatic spectrograph flown in an Aerobee rocket and a similar set of carbon-arc spectra obtained with the same spectrograph shortly before the flight. For our particular purpose, the densitometer tracings of these spectra are made at right angles to the direction of dispersion. Special attention is directed to the possibility of determining the instrumental astigmatism profiles from the carbon-arc spectra on the basis of assuming a rectangular form for the carbon-arc profile unbroadened by astigmatism. It is found that this method is quite satisfactory. In order to correct the observed limb-darkening profiles for instrumental broadening, the Fourier inversion method appears to be superior to the other methods considered, although the direct numerical evaluation can also be satisfactorily applied.

© 1966 Optical Society of America

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References

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  1. V. A. Ambartsumyan, Theoretical Astrophysics (Pergamon Press, New York, 1958), Chap. 7.
  2. R. Tousey, Space Sci. Rev. 2, 3 (1963).
    [Crossref]
  3. F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
    [Crossref]
  4. F. W. Jones, Proc. Roy. Soc. (London) 166, 16 (1938).
    [Crossref]
  5. This point has been noted by Fellgett and Schmeidler while obtaining the form of the atmospheric scattering function for the purpose of sharpening solar limb-darkening data taken during a partial eclipse of the sun. P. B. Fellgett and F. B. Schmeidler, Roy. Astron. Soc. M. N. 112, 445 (1952).
  6. H. C. van de Hulst and J. J. Reesinck, Astrophys. J. 106, 121 (1947).
    [Crossref]
  7. P. H. van Cittert, Z. Phys. 69, 298 (1931).
    [Crossref]
  8. A. R. Stokes, Proc. Phys. Soc. (London) 61, 382 (1948).
    [Crossref]
  9. M. S. Paterson, Proc. Phys. Soc. (London) 63, 477 (1950).
    [Crossref]
  10. R. N. Bracewell, Australian J. Phys. 8, 200 (1955).
    [Crossref]
  11. R. N. Bracewell, J. Opt. Soc. Am. 45, 873 (1955).
    [Crossref]

1963 (1)

R. Tousey, Space Sci. Rev. 2, 3 (1963).
[Crossref]

1958 (1)

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

1955 (2)

R. N. Bracewell, Australian J. Phys. 8, 200 (1955).
[Crossref]

R. N. Bracewell, J. Opt. Soc. Am. 45, 873 (1955).
[Crossref]

1952 (1)

This point has been noted by Fellgett and Schmeidler while obtaining the form of the atmospheric scattering function for the purpose of sharpening solar limb-darkening data taken during a partial eclipse of the sun. P. B. Fellgett and F. B. Schmeidler, Roy. Astron. Soc. M. N. 112, 445 (1952).

1950 (1)

M. S. Paterson, Proc. Phys. Soc. (London) 63, 477 (1950).
[Crossref]

1948 (1)

A. R. Stokes, Proc. Phys. Soc. (London) 61, 382 (1948).
[Crossref]

1947 (1)

H. C. van de Hulst and J. J. Reesinck, Astrophys. J. 106, 121 (1947).
[Crossref]

1938 (1)

F. W. Jones, Proc. Roy. Soc. (London) 166, 16 (1938).
[Crossref]

1931 (1)

P. H. van Cittert, Z. Phys. 69, 298 (1931).
[Crossref]

Ambartsumyan, V. A.

V. A. Ambartsumyan, Theoretical Astrophysics (Pergamon Press, New York, 1958), Chap. 7.

Bracewell, R. N.

R. N. Bracewell, Australian J. Phys. 8, 200 (1955).
[Crossref]

R. N. Bracewell, J. Opt. Soc. Am. 45, 873 (1955).
[Crossref]

Fellgett, P. B.

This point has been noted by Fellgett and Schmeidler while obtaining the form of the atmospheric scattering function for the purpose of sharpening solar limb-darkening data taken during a partial eclipse of the sun. P. B. Fellgett and F. B. Schmeidler, Roy. Astron. Soc. M. N. 112, 445 (1952).

Johnson, F. S.

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

Jones, F. W.

F. W. Jones, Proc. Roy. Soc. (London) 166, 16 (1938).
[Crossref]

Malitson, H. H.

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

Paterson, M. S.

M. S. Paterson, Proc. Phys. Soc. (London) 63, 477 (1950).
[Crossref]

Purcell, J. D.

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

Reesinck, J. J.

H. C. van de Hulst and J. J. Reesinck, Astrophys. J. 106, 121 (1947).
[Crossref]

Schmeidler, F. B.

This point has been noted by Fellgett and Schmeidler while obtaining the form of the atmospheric scattering function for the purpose of sharpening solar limb-darkening data taken during a partial eclipse of the sun. P. B. Fellgett and F. B. Schmeidler, Roy. Astron. Soc. M. N. 112, 445 (1952).

Stokes, A. R.

A. R. Stokes, Proc. Phys. Soc. (London) 61, 382 (1948).
[Crossref]

Tousey, R.

R. Tousey, Space Sci. Rev. 2, 3 (1963).
[Crossref]

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

van Cittert, P. H.

P. H. van Cittert, Z. Phys. 69, 298 (1931).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst and J. J. Reesinck, Astrophys. J. 106, 121 (1947).
[Crossref]

Astrophys. J. (2)

F. S. Johnson, H. H. Malitson, J. D. Purcell, and R. Tousey, Astrophys. J. 127, 80 (1958).
[Crossref]

H. C. van de Hulst and J. J. Reesinck, Astrophys. J. 106, 121 (1947).
[Crossref]

Australian J. Phys. (1)

R. N. Bracewell, Australian J. Phys. 8, 200 (1955).
[Crossref]

J. Opt. Soc. Am. (1)

Proc. Phys. Soc. (London) (2)

A. R. Stokes, Proc. Phys. Soc. (London) 61, 382 (1948).
[Crossref]

M. S. Paterson, Proc. Phys. Soc. (London) 63, 477 (1950).
[Crossref]

Proc. Roy. Soc. (London) (1)

F. W. Jones, Proc. Roy. Soc. (London) 166, 16 (1938).
[Crossref]

Roy. Astron. Soc. M. N. (1)

This point has been noted by Fellgett and Schmeidler while obtaining the form of the atmospheric scattering function for the purpose of sharpening solar limb-darkening data taken during a partial eclipse of the sun. P. B. Fellgett and F. B. Schmeidler, Roy. Astron. Soc. M. N. 112, 445 (1952).

Space Sci. Rev. (1)

R. Tousey, Space Sci. Rev. 2, 3 (1963).
[Crossref]

Z. Phys. (1)

P. H. van Cittert, Z. Phys. 69, 298 (1931).
[Crossref]

Other (1)

V. A. Ambartsumyan, Theoretical Astrophysics (Pergamon Press, New York, 1958), Chap. 7.

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Figures (6)

F. 1
F. 1

Experimental solar limb-darkening profile. The logarithmic densitometer tracing has been made at right angles to the direction of dispersion at a wavelength of 2300 Å.

F. 2
F. 2

Experimental carbon-arc profile in logarithmic scale. Also traced at right angles to the direction of dispersion, the carbon-arc profile provides the means of obtaining the instrumental profile.

F. 3
F. 3

Superposition, principle of instrumental broadening. The observed profile (solid line), g(x), is the sum of radiance contributions from the elements, h(y)dy, of the true profile (dashed line). The contribution at the point x from the radiance element at the point y is determined by the instrumental profile, f(xy) (dotted line).

F. 4
F. 4

Reconstruction of carbon-arc profile foot portions. The instrumental profile for 2300 Å is obtained from the gradient of the reconstructed profile.

F. 5
F. 5

Samples of instrumental profiles obtained from reconstructed carbon-arc profiles.

F. 6
F. 6

Corrected solar limb-darkening profile for 2500 Å plotted as a function of cos θ.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

g ( x ) = f ( x y ) h ( y ) d y ,
G ( t ) = F ( t ) H ( t ) ,
G ( t ) = g ( x ) e i x t d x ,
h ( x ) = G ( t ) F ( t ) e i x t d t .
g ( x i ) = j f ( x i y j ) h ( y j ) .