COMET P/2008 X4 IN EXTREME FORWARD-SCATTERING GEOMETRY JUST BEFORE CHRISTMAS
Joseph N. Marcus
19 Arbor Road
St. Louis, MO63132, USA
Summary: Newly recovered comet P/2008 X4 = P/2003 K2 (Christensen) enters extreme forward-scattering geometry just before Christmas. At and around the time of minimum scattering angle (min= 0.7, with the comet nearly transiting the sun as viewed from Earth) on Dec. 23.64 UT, forward-scattering by dust grains will enhance the comets brightness a factor of 500, or 6.8 magnitudes in a conservative application of my predictive model (Marcus 2007a, b). My analysis of CCD magnitudes taken during the 2003 apparition and presented here indicate that the comet is intrinsically very faint (or “small”), with an absolute magnitude (at 1 AU from the sun and earth) of onlyH10 13. Even so, with the dramatic “boost” from the forward-scattering, this tiny comet may reach magnitude m1 = 2 or brighter in the SOHO coronograph fields. I provide an ephemeris which includespredicted magnitude enhancements during the prolonged forward-scattering interval of 2008 Dec. 14 to 2009 Jan. 2, when 45.
Introduction
On Dec. 8, A. Watson serendipitously recovered comet P/2003 K2 (Christensen) on the STEREO-SECCHI HI1 imager aboard the STEREO-B spacecraft (Marsden 2008). The ephemeris generated from the linked orbit (Marsden 2008) shows that this comet, designated P/2008 X4 = P/2003 K2, will pass nearly between the earth and the sun on Dec. 23.64 Universal Time (UT) at a minimum elongation of min= 0.4, just off the solar disk. At that time the scattering angle, (sun-comet-earth angle = 180 phase angle), will also reach a minimum at min = 0.7. At such small scattering angles, the brightness of the comet’s dust should be vastly enhanced from the forward-scattering of sunlight. I recently devised a model to predict the amount of brightness enhancement in comets (Marcus 2007a, b) and applied it successfully to predict and analyze the forward-scattering-associated magnitude surge in comet C/2006 P1 (McNaught), whichcatapulted this great comet into daylight visibility (Marcus 2007b). Nothing of that sort will happen to P/2008 X4: it is far too small to be seen from Earth in daylight. Still, it should be detectable by virtue of its forward-scattering-enhanced brightness in the SOHO satellite coronograph fields, where it may reach 2nd magnitude or brighter. Here I apply the model to predict the forward-scattering brightness enhancement during the second half of December and beginning January.
The baseline brightness of P/2008 X4 = P/2003 K2
This comet is extremely faint intrinsically. During 2003 it was observed only by CCD imaging, from which photometry was derived by Christensen (Green 2003), Nakamura [ICQ 2003, 25(3)], and Sherrod ( accessed 2008 Dec. 15). I reduce these observations heliocentric to magnitude, H1 = m1 5 log and plot them in the Figure. Linear regression yields the photometric solution H1 = 14.6 + 10.4 log r. Because for faint comets, CCD magnitudes – for whatever reason – are generally 1-2 magnitudes fainter than m1 magnitudes obtained visually with the human eye and instruments (e.g., Sosa and Fernández 2008), I adjust this formula to H1 = 13 + 10 log r. This solution is very slightly brighter than the formula H1 = 13.5 + 10 log r implicit in the current IAU ephemeris (Green 2008), but considerably dimmer than the more “optimistic” H1 = 13 + 15 log r of Yoshida (2008). I also plot a solitary point to represent several magnitudes by the SWAN spacecraft instruments, said to be 9 to 10 over the period 2003 Apr. 5-19 (Shanklin 2003).
Predicted forward-scattering brightness enhancement
I model the scattering, or “phase” function, (), with a modified compound Henyey-Greenstein function for comets (Marcus 2007a, b):
.
is the scattering angle, 0 gf 1 and 1 gb 0 are the forward-scattering and back-scattering asymmetry factors, 0 k 1 is the portioning coefficient between forward and backward scattering, and 90 is the dust-to-gas light ratio in the coma as viewed at 90. As before (Marcus 2007a, b), I set gf = 0.9, gb = 0.6, and k = 0.95. The magnitude of the scattering function is
.
I had previously used 90= 1 as representative of an “average” comet. However, because P/2008 X4 is evidently a “Jupiter family” short-period comet (Marsden 2008), which as a class tends to be “gassier” (more C2 and other molecular emissions in relation to the dust continnum spectrum), I favor a more conservative value here of 90 = 0.3.
The Table gives the predicted forward-scattering magnitude enhancement for P/2008 X4 during the prolonged forward-scattering geometry on 2008-9 Dec. 14 – Jan. 4 UT, when 45. The columns give the date (UT), comet-earth () and comet sun (r) distances (in AU), the elongation (), the comet’s position angle offset () from the sun (measured counterclockwise from north on the sky), the scattering angle (), and m() for 90 = 0.1 (very gassy), 0.3 (gassy) (“best guess,” column bolded), and 1 (average). Note that at min there is a ~1 mag separation in m() values between the 90 conditions. At min on Dec. 23 my best guess estimate for the base-line magnitude is m1 = 8.6. The baslines at the beginning and end of the interval should be near 9.0 and 9.3, respectively. m() is added to the baseline to obtain the magnitude predicted with forward-scattering enhancement taken into account, which could total 2nd magnitude on Dec. 23.
Although unlikely to be visible from Earth during this interval (except perhaps at the be-ginning and end), P/2008 X4 will likely be visible from the SOHO satellite in space located about 0.01 AU from Earth when 8. Because of this displacement, the angles in the epheme-ris will be slightly, but not significantly, different from those seen at SOHO, but this should have negligible effect on them( forecasts. Its photometric behavior in SOHO (and in the STEREO A and B satellite images) at different will help delineate this comet’s dust-scattering function.
References
Green DWE (2003). Comet C/2003 K2. IAUC 8136, May 27.
Green DWE (2008). Comet P/2008 X4. MPEC 2008-X81, Dec. 12.
Marcus JN (2007a). Forward-scattering enhancement of comet brightness. I. Background and Model. ICQ 29:39-66.
Marcus JN (2007b). Forward-scattering enhancement of comet brightness. II. The light curve of C/2006 P1 (McNaught). ICQ 29:119-130.
Marsden BG (2008). Comet C/2008 X4. MPEC 2008-X81.
Shanklin J (2003). Review of observations. The Comet’s Tale 10:20.
Sosa A, Fernández JA (2008). Cometary masses derived from non-gravitational forces. Mon Not R Astron Soc, in press (arXiv:0811.0745v1 Preprint, Nov. 5).
Yoshida S (2008). Weekly information about bright comets. accessed Dec. 15.
Forward-Scattering Brightness Enhancement Forecast for Comet P/2008 X4 (Christensen)
2008-9 (UT) / (AU) / r (AU) / / / / m()90=0.1 / m()
90=0.3 / m()
90=1.0
Dec. 14.0 / 0.523 / 0.550 / 24.1 / 108.2 / 46.9 / -0.4 / -0.7 / -1.2
Dec. 15.0 / 0.505 / 0.543 / 22.0 / 108.0 / 42.6 / -0.5 / -0.9 / -1.5
Dec. 16.0 / 0.500 / 0.542 / 19.8 / 107.7 / 38.1 / -0.6 / -1.2 / -1.8
Dec. 17.0 / 0.489 / 0.539 / 17.6 / 107.5 / 33.5 / -0.8 / -1.5 / -2.2
Dec. 18.0 / 0.479 / 0.536 / 15.2 / 107.4 / 28.7 / -1.1 / -1.9 / -2.6
Dec. 19.0 / 0.470 / 0.535 / 12.7 / 107.2 / 23.8 / -1.5 / -2.4 / -3.1
Dec. 20.0 / 0.462 / 0.535 / 10.1 / 107.3 / 18.8 / -2.1 / -3.0 / -3.8
Dec. 20.5 / 0.459 / 0.535 / 8.8 / 107.5 / 16.3 / -2.5 / -3.4 / -4.2
Dec. 21.0 / 0.456 / 0.535 / 7.4 / 107.7 / 13.7 / -2.9 / -3.9 / -4.7
Dec. 21.5 / 0.452 / 0.536 / 6.0 / 108.3 / 10.1 / -3.7 / -4.7 / -5.5
Dec. 22.0 / 0.450 / 0.537 / 4.7 / 109.2 / 8.6 / -4.0 / -5.0 / -5.9
Dec. 22.5 / 0.447 / 0.538 / 3.3 / 111.1 / 6.0 / -4.7 / -5.7 / -6.5
Dec. 23.0 / 0.445 / 0.539 / 1.9 / 116.2 / 3.4 / -5.4 / -6.4 / -7.2
Dec. 23.2 / 0.445 / 0.539 / 1.3 / 121.4 / 2.4 / -5.6 / -6.6 / -7.4
Dec. 23.4 / 0.444 / 0.540 / 0.8 / 133.9 / 1.4 / -5.7 / -6.7 / -7.6
Dec. 23.6 / 0.443 / 0.540 / 0.4 / 177.7 / 0.8 / -5.8 / -6.8 / -7.6
Dec. 23.8 / 0.443 / 0.541 / 0.6 / 242.5 / 1.1 / -5.8 / -6.8 / -7.6
Dec. 24.0 / 0.442 / 0.542 / 1.1 / 262.3 / 2.0 / -5.6 / -6.7 / -7.5
m(
Dec. 24.5 / 0.441 / 0.544 / 2.5 / 274.1 / 4.5 / -5.1 / -6.1 / -6.9
Dec. 25.0 / 0.440 / 0.546 / 3.9 / 277.3 / 7.1 / -4.4 / -5.4 / -6.2
Dec. 25.5 / 0.439 / 0.548 / 5.4 / 278.6 / 9.6 / -3.8 / -4.8 / -5.6
Dec. 26.0 / 0.439 / 0.550 / 6.8 / 279.4 / 12.2 / -3.2 / -4.2 / -5.0
Dec. 26.5 / 0.439 / 0.553 / 8.2 / 279.7 / 14.7 / -2.7 / -3.7 / -4.5
Dec. 27.0 / 0.439 / 0.556 / 9.6 / 280.0 / 17.2 / -2.3 / -3.3 / -4.1
Dec. 27.5 / 0.439 / 0.559 / 11.1 / 280.0 / 19.7 / -2.0 / -2.9 / -3.7
Dec. 28.0 / 0.440 / 0.562 / 12.5 / 280.1 / 22.2 / -1.7 / -2.6 / -3.3
Dec. 29.0 / 0.442 / 0.568 / 15.2 / 280.0 / 27.0 / -1.2 / -2.0 / -2.8
Dec. 30.0 / 0.446 / 0.576 / 17.9 / 279.9 / 31.7 / -0.9 / -1.6 / -2.3
Dec. 31.0 / 0.450 / 0.584 / 20.5 / 279.6 / 36.2 / -0.7 / -1.3 / -1.9
Jan. 01.0 / 0.455 / 0.593 / 23.1 / 279.4 / 40.6 / -0.5 / -1.0 / -1.6
Jan. 02.0 / 0.460 / 0.602 / 25.5 / 279.1 / 44.8 / -0.4 / -0.8 / -1.4
Jan. 03.0 / 0.466 / 0.612 / 27.9 / 278.7 / 48.8 / -0.3 / -0.7 / -1.1
Jan. 04.0 / 0.473 / 0.622 / 30.2 / 278.4 / 52.6 / -0.2 / -0.5 / -1.0