Wideband Photometry of Saturn in 2008-2009 Richard W

Georgia Journal of Science Volume 68 No. 2 Scholarly Contributions from the Article 3 Membership and Others

2010 Wideband Photometry of Saturn in 2008-2009 Richard W. Schmude Jr. Gordon State College, [email protected]

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Recommended Citation Schmude, Richard W. Jr. (2010) "Wideband Photometry of Saturn in 2008-2009," Georgia Journal of Science, Vol. 68, No. 2, Article 3. Available at: http://digitalcommons.gaacademy.org/gjs/vol68/iss2/3

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Wideband Photometry of Saturn in 2008-2009

Richard Schmude, Jr. [email protected]

Abstract A total of 52 brightness measurements of Saturn were made during its 2008-2009 apparition. (An apparition is the time interval between when the planet is in conjunction with the Sun to the next time that it is conjunction with the Sun.) The selected normalized magnitudes of Saturn for b = 3.0° are B(1,0) = -7.87 ± 0.02, V(1,0) = - 9.00 ± 0.01, R(1,0) = -9.62 ± 0.01 and I(1,0) = -9.63 ± 0.01. (I have defined b as the square root of the absolute value of the product of the Saturnicentric latitude of the Earth and of the Sun; b is a latitude that is always within about 27° of Saturn’s equator.) The selected solar phase angle coefficient, in units of magnitudes per degree are c = 0.029 ± 0.009, c = 0.025 ± 0.005, c = 0.024 ± 0.005 and B V R c = 0.018 ± 0.006. I

Introduction Morishima and co-workers (1) point out that there are two competing models for Saturn’s rings which are the monolayer model and the multilayer model. In the monolayer model the rings are assumed to be one particle thick. In the multilayer model, however, the rings are assumed to be several particles thick. Knowing the correct model will enable astronomers to better model changes in the thermal emission of the rings and whether ring particles rotate around their own axes slowly or quickly. Reliable brightness measurements carried out over several years should help astronomers determine which model is more suitable for the rings of Saturn. This paper is a continuation of a 14-year study of the brightness and color of Saturn and its rings. During this study, the value of B', the Saturnicentric latitude of the Sun referred to the plane of the rings, went from 0° in 1995 to 27° in 2002 and back down to 0° in 2009. Therefore, two Saturn seasons, southern spring and summer, are covered in this 14-year study. The purpose of this paper is to publish additional information on the topics below at very low ring-tilt angles:

1) The brightness and color of Saturn + rings as it passes through different seasons, 2) Saturn’s solar phase angle coefficients in different colors and in different seasons, 3) the opposition surge in different colors, and 4) the influence of the Sun’s position in egardsr to the brightness and color of Saturn + rings.

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Method and Materials The author used an SSP-3 solid-state photometer along with filters transformed to the Johnson B, V, R and I system to make all measurements. He also used a 0.09 meter Maksutov telescope for the measurements. More information about the photometer and method is found elsewhere (2-5). The brightness values of Sigma-Leonis (σ-Leo) used in this study are B = 3.985, V = 4.043, R = 4.05 and I = 4.12. The B and V magnitudes are from Westfall (6) and Mermilliod (7). The R and I magnitudes are from Iriarte et al. (8). The B, V, R and I brightness values for the comparison stars Upsilon- Leonis (υ-Leo) and Chi-Leonis (χ-Leo) are from (8). Beta-Virginis (β-Vir) was the check star. The average measured brightness for this star, in the V filter, was magnitude 3.59 which is the accepted brightness value (8). In all cases, the author corrected the brightness measurements for both atmospheric extinction and color transformation. He used the two-star method for color transformation corrections (9). When Saturn’s altitude was high, the extinction coefficients were assumed to equal 0.38, 0.23, 0.16 and 0.12 magnitudes/air mass for the B, V, R and I filters, respectively. These are averages for Central Georgia (5).

Results The brightness measurements made during the 2008-2009 apparition are listed in Table I. The first column in this table lists the decimal date of the measurement in Universal Time. If, for example, a measurement was recorded at 6:00 UT on February 17, then the decimal date would be February 17.25. The second column lists the filter used. The third column lists the solar phase angle of Saturn at the time of measurement. (The solar phase angle is the angle between the Sun and the observer measured from the target which is Saturn in this case.) The measured brightness of Saturn, in stellar magnitudes, is listed in the fourth column. The normalized magnitude, X(1,α) for b = 3.0°, in stellar magnitudes, is listed in the fifth column. The quantity b (“a type of geometric average of Saturnicentric latitude of Sun and Earth from Saturn’s ring plane”) is computed from equation (1): b = (|B x B'|)0.5. (1) In this equation B is the Saturnicentric latitude of the Earth referred to the plane of the rings and B' is the Saturnicentric latitude of the Sun referred to the plane of the rings. The absolute value signs in equation (1) are needed since B and B' can have a negative value. The value of the normalized magnitude, X(1,α), is computed from equation (2): X(1, ) = X – 5.0 log[r × d] + m(3.0°) – m(b) (2). α mag In this equation, X is the measured brightness of Saturn’s rings in mag stellar magnitudes for filter X, r and d are the Saturn-Earth and Saturn-Sun distances in astronomical units, X(1,α) is the brightness that Saturn would have if it is 1.0 astronomical unit from both the Earth and Sun with b = 3.0°

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and at a solar phase angle equal to α, Δm(3.0°) is the brightness contribution from the rings at b = 3.0° and Δm(b) is the brightness contribution from the rings at an angle of b. Both Δm(3°) and Δm(b) are in stellar magnitudes and are computed from equations 3 to 6 in (10). The sixth column of Table I lists the comparison star used for each measurement. The seventh, eighth and ninth columns list the B, B' and b values, respectively. Previously (11), it was shown that the value of b is a more reliable indica- tor of ring brightness than B. Figure 1 proves this point. The Saturnicentric latitude of the Earth, B, with respect to the ring plane is nearly the same in the two images. In spite of this, the rings are not of the same brightness and, hence, one must also consider the value of B' when considering the brightness of the rings as is done in equation 1. The difference is due to shadowing and other factors. The rings in the bottom image are much darker because the Saturnicentric longitude of the Sun, B', with respect to the ring plane is only -0.9° compared to -2.0° in the top image. The minus sign is due to the fact that the Sun is south of the ring plane.

Figure 1. Two images of Saturn. The top image was taken by Cristian Fat- tinnanzi on April 6, 2009 at 21:21 UT. The values of B, B' and b on that date were -3.6°, -2.0° and 2.7°, respectively. The bottom image was taken by Anthony Wesley on June 15, 2009 at 8:29 UT. The values of B, B' and b on that date were -3.7°, -0.9° and 1.8°, respectively. The rings were darker in the bottom image because of the lower value of B'. Courtesy of Cristian Fattinnanzi and Anthony Wesley.

Published by Digital Commons @ the Georgia Academy of Science, 2010 3 Georgia Journal of Science, Vol. 68 [2010], Art. 3 99 b 2.0 2.0 2.0 2.0 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.8 1.8 1.9 1.9 1.9 1.9 2.2 2.2 2.2 2.2 2.4 3.0 3.1 3.1 (degrees) B' 2.9 2.9 2.9 2.9 3.1 3.1 3.1 3.5 3.5 3.5 3.5 3.7 3.7 3.8 3.8 3.8 3.8 4.0 4.0 4.0 4.0 4.1 4.4 4.4 4.4 (degrees) B 1.4 1.4 1.3 1.3 1.0 1.0 1.0 0.8 0.8 0.8 0.8 0.9 0.9 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2 1.4 2.1 2.2 2.2 (degrees) star υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo σ -Leo σ -Leo σ -Leo Comparison -9.56 -9.53 -7.75 -8.94 -9.49 -7.75 -8.87 -9.51 -9.50 -7.70 -8.86 -7.67 -8.88 -7.72 -8.84 -9.55 -9.48 -9.55 -9.47 -7.70 -8.86 -8.82 -8.88 -7.76 -8.89 x(1, α ) b = 3.0° (Magnitudes) 0.02 0.03 1.82 0.63 0.12 1.87 0.75 0.20 0.20 2.00 0.83 2.08 0.87 2.05 0.92 0.23 0.29 0.26 0.33 2.10 0.94 0.99 0.96 2.08 0.95 Measured Brightness (Magnitudes) α (degrees) I 3.7 I 5.7 I 6.0 I 5.8 R 3.7 B 3.8 R 4.7 B 4.7 R 5.7 B 5.7 B 6.0 V 3.8 B 6.0 R 6.0 R 5.8 B 5.8 V 5.7 B 4.5 V 6.0 V 6.0 V 5.8 V 5.6 V 4.6 Filter Date Feb. 2.219 Feb. 2.204 Feb. 1.436 Feb. 1.417 Jan. 19.437 Jan. 19.417 Jan. 19.397, 2009 V 4.7 Dec. 30.460 Dec. 30.439 Dec. 30.420 Dec. 30.404 Dec. 13.444 Dec. 13.422 Dec. 7.460 Dec. 7.445 Dec. 7.432 Dec. 7.419 Nov. 26.465 Nov. 26.456 Nov. 26.442 Nov. 26.428 Nov. 20.457 Oct. 30.448 Oct. 29.451 Oct. 29.439, 2008 V 4.5 Brightness measurements of Saturn I. Brightness measurements made between October 29, 2008 and July 25, 2009. Table http://digitalcommons.gaacademy.org/gjs/vol68/iss2/3 4 100 Schmude: Wideband Photometry of Saturn in 2008-2009 b 2.6 2.3 2.6 2.6 2.6 2.7 2.7 2.7 2.7 2.6 2.6 2.6 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.3 2.3 2.1 2.1 2.1 2.1 (degrees) B' 1.3 1.7 1.7 1.7 1.7 2.1 2.1 2.1 2.1 2.2 2.2 2.2 2.2 2.2 2.4 2.4 2.4 2.5 2.5 2.6 2.6 2.8 2.8 2.8 2.8 0.26 0.76 0.30 0.85 (degrees) B 2.2 2.4 4.1 4.0 4.0 3.9 3.9 3.4 3.4 3.4 3.4 3.1 3.1 3.1 3.1 3.0 2.5 2.5 2.5 2.4 2.4 2.1 2.1 1.6 1.6 1.6 1.6 (degrees) star χ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo σ -Leo σ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo υ -Leo Comparison -8.91 -8.84 -8.95 -9.53 -9.47 -7.77 -8.86 -9.60 -9.55 -7.83 -8.93 -9.63 -9.58 -7.84 -8.96 -8.97 -8.99 -7.88 -8.97 -9.63 -9.65 -8.97 -7.85 -9.56 -9.57 -8.92 -7.68 x(1, α ) b = 3.0° (Magnitudes) 1.08 0.84 1.02 0.06 0.10 1.81 0.71 1.68 0.59 1.67 0.54 0.53 0.51 1.62 0.53 0.54 1.67 0.00 0.63 1.87 -0.08 -0.04 -0.12 -0.07 -0.11 -0.14 -0.02 Measured Brightness (Magnitudes) α (degrees) I 4.4 I 2.4 I 1.4 I 0.7 I 3.1 R 4.4 B 4.4 R 2.4 B 2.4 V 4.4 VV 5.9 4.6 R 1.4 B 1.4 V 4.4 B 0.5 V 2.4 R 0.7 B 1.5 V 1.4 R 3.1 V 1.2 V 0.4 V 0.5 V 1.5 V 3.1 Filter Date July 25.083 May 19.153 July 22.083 April 22.150 April 22.127 April 21.180 April 21.159 March 30.189 March March 30.169 March March 30.153 March March 30.135 March March 21.221 March March 21.205 March March 21.185 March March 21.165 March March 19.155 March March 6.183 March March 5.198 March March 5.180 March March 3.171 March March 3.158 March Feb. 24.209 Feb. 24.193 Feb. 8.435 Feb. 8.411 Feb. 8.389 Feb. 8.368, 2009 B 3.1 Table I. Continued. Table

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Discussion Graphs of X(1,α) versus the solar phase angle, α are shown in Figure 2 for each of the four filters. The slope of the best fit line in each graph is the solar phase angle coefficient, c . The normalized magnitude at a solar phase X angle of 0° is the y-intercept, and it has the symbol of X(1,0). The resulting values of c and X(1,0) for b = 3° are summarized in Table II. Uncertainties X for both quantities were computed in the same way as is described elsewhere (12).

Figure 2. Graphs of the X(1,α) value of Saturn at b = 3.0° for different values of the solar phase angle in the 2008-2009 apparition. The four graphs are for the B, V, R and I filters. The open circles were not included in the evaluation of the quantities in Table 2 because these points are influenced by the opposition effect.

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Table II. Photometric constants for Saturn with b = 3.0°.

Number of Filter X(1,0) cX data points B -7.87 ± 0.02 0.029 ± 0.009 12 V -9.00 ± 0.01 0.025 ± 0.005 18 R -9.62 ± 0.01 0.024 ± 0.005 9 I -9.63 ± 0.01 0.018 ± 0.006 8

The B – V color index at a solar phase angle of 0° was 1.13 in the current apparition. This is higher than in the previous apparition. This is evidence that Saturn was not as blue in the current apparition as in the previous one. The R – I color index in the current apparition was only 0.01; this is lower than in the previous apparition. The low R – I value may be due to the rings closing up and, hence, having a smaller influence on the color of Saturn + rings. The R – I value was also very low during 1995 when the rings were edge-on (13). The opposition surge, at a solar phase angle of 0° was essentially zero in the V filter in 2008-2009 apparition. This is similar to what it was in the previous apparition. This is probably due to the fact that the rings are the cause of the opposition surge. Furthermore, in the last two apparitions, the rings contributed a much smaller amount of light to the Saturn system than in 2000-2006. There was probably a small opposition surge for the R and I filters in the 2008-2009 apparition based on this work.

Acknowledgements The author would like to thank Truman Boyle for the use of his dark site. The author is also grateful to Cristian Fattinnanzi and Anthony Wesley for allowing me to publish their images in this report.

References 1. Morishima R, Salo H and Ohtsuki K: A multilayer model for thermal infrared emission of Saturn’s rings: Basic formation and implications for Earth-based observations. Icarus 201: 634-654, 2009. 2. Schmude RW Jr: “The 1991 Apparition of Uranus. J Assoc Lunar and Planet Obs 36: 20-22, 1992. 3. Optec Inc: Model SSP-3 Solid-State Stellar Photometer Technical Manual for Theory of Operation and Operating Procedures, Optec Inc. Lowell MI, 1987. 4. Schmude RW Jr: Photometric and Polarimetric Observations of Mars in 2000-2002. J Roy Astron Soc Canada 96: 105-110, 2002.

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5. Schmude RW Jr: Uranus, Neptune, and Pluto and How to Observe Them. New York: Springer Science + Business Media, LLC, p. 215, 2008. 6. Westfall JE: Photometric Catalog of Zodiacal Stars. ALPO Mono- graph Number 12, 2008. 7. Mermilliod JC: Photoelectric Photometric Catalogue of Homog- enous Measurements in the UBV system. NASA, Astronomical Data Center, Selected Astronomical Catalogues. Volume 1. (CD-ROM), 1991. 8. Iriarte B, Johnson HL, Mitchell RI and Wisniewski, WK: Five- Color Photometry of Bright Stars. Sky & Telesc 30: No. 1, 21-31, 1965. 9. Hall DS and Genet RM: Photoelectric Photometry of Variable Stars. Second Edition, Richmond, VA: Willmann-Bell, Inc. 1988. 10. Schmude RW Jr: Wideband Photometry of Saturn: 1995-2002. J Roy Astron Soc Canada 97: 78-81, 2003. 11. Schmude RW Jr: Wideband Photometry of Saturn in 2007-2008. Ga J Sci 66: 106-113, 2008. 12. Schmude RW Jr: Photoelectric Magnitudes of Saturn in 1996. Ga J Sci 56: 175-181, 1998. 13. Schmude RW Jr: Observations of Saturn in 1995. Ga J Sci 55, 175-179, 1997.

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