COMET P/2008 X4 IN EXTREME FORWARD-SCATTERING GEOMETRY JUST
BEFORE CHRISTMAS
Joseph N. Marcus
19 Arbor Road
St. Louis, MO 63132, USA
jnmarcus@sbcglobal.net
Summary: Newly recovered comet P/2008 X4 = P/2003 K2 (Christensen) enters extreme forwardscattering 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 only H10  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 includes predicted 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), which catapulted 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 (http://arksky.org/php/cdata.php?object=C/2003xxxK2, 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).
Light Curve of 210P/2003 K2 (Christensen)
8
SWAN observations
9
Heliocentric magnitude
10
11
12
Christensen
13
Nakamura
14
15
CCD Observations
Christensen (1)
Nakamura (2)
Sherrod (12)
16
17
18
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Log r
Predicted forward-scattering brightness enhancement
I model the scattering, or “phase” function, (), with a modified compound HenyeyGreenstein function for comets (Marcus 2007a, b):
3/ 2
3/ 2



 90  
1  g 2b
1  g f2
1 



k 
.
() 

(
1

k
)

 1  g 2  2g cos  
1   90   1  g f2  2g f cos  
 90 
b
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
m  ( )  2.5 log  () .
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 baseline 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 beginning 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 ephemeris will be slightly, but not significantly, different from those seen at SOHO, but this should have
negligible effect on the m( 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.
http://www.aerith.net/comet/weekly/current.html, 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
Dec. 15.0
Dec. 16.0
Dec. 17.0
Dec. 18.0
Dec. 19.0
0.523
0.505
0.500
0.489
0.479
0.470
0.550
0.543
0.542
0.539
0.536
0.535
24.1
22.0
19.8
17.6
15.2
12.7
108.2
108.0
107.7
107.5
107.4
107.2
46.9
42.6
38.1
33.5
28.7
23.8
-0.4
-0.5
-0.6
-0.8
-1.1
-1.5
-0.7
-0.9
-1.2
-1.5
-1.9
-2.4
-1.2
-1.5
-1.8
-2.2
-2.6
-3.1
Dec. 20.0
Dec. 20.5
Dec. 21.0
Dec. 21.5
Dec. 22.0
Dec. 22.5
0.462
0.459
0.456
0.452
0.450
0.447
0.535
0.535
0.535
0.536
0.537
0.538
10.1
8.8
7.4
6.0
4.7
3.3
107.3
107.5
107.7
108.3
109.2
111.1
18.8
16.3
13.7
10.1
8.6
6.0
-2.1
-2.5
-2.9
-3.7
-4.0
-4.7
-3.0
-3.4
-3.9
-4.7
-5.0
-5.7
-3.8
-4.2
-4.7
-5.5
-5.9
-6.5
Dec. 23.0
Dec. 23.2
Dec. 23.4
Dec. 23.6
Dec. 23.8
Dec. 24.0
0.445
0.445
0.444
0.443
0.443
0.442
0.539
0.539
0.540
0.540
0.541
0.542
1.9
1.3
0.8
0.4
0.6
1.1
116.2
121.4
133.9
177.7
242.5
262.3
3.4
2.4
1.4
0.8
1.1
2.0
-6.4
-6.6
-6.7
-6.8
-6.8
-6.7
-7.2
-7.4
-7.6
-7.6
-7.6
-7.5
Dec. 24.5
Dec. 25.0
Dec. 25.5
Dec. 26.0
Dec. 26.5
Dec. 27.0
Dec. 27.5
0.441
0.440
0.439
0.439
0.439
0.439
0.439
0.544
0.546
0.548
0.550
0.553
0.556
0.559
2.5
3.9
5.4
6.8
8.2
9.6
11.1
274.1
277.3
278.6
279.4
279.7
280.0
280.0
4.5
7.1
9.6
12.2
14.7
17.2
19.7
-5.4
-5.6
-5.7
-5.8
-5.8
-5.6
m(
-5.1
-4.4
-3.8
-3.2
-2.7
-2.3
-2.0
-6.1
-5.4
-4.8
-4.2
-3.7
-3.3
-2.9
-6.9
-6.2
-5.6
-5.0
-4.5
-4.1
-3.7
Dec. 28.0
Dec. 29.0
Dec. 30.0
Dec. 31.0
Jan. 01.0
Jan. 02.0
Jan. 03.0
Jan. 04.0
0.440
0.442
0.446
0.450
0.455
0.460
0.466
0.473
0.562
0.568
0.576
0.584
0.593
0.602
0.612
0.622
12.5
15.2
17.9
20.5
23.1
25.5
27.9
30.2
280.1
280.0
279.9
279.6
279.4
279.1
278.7
278.4
22.2
27.0
31.7
36.2
40.6
44.8
48.8
52.6
-1.7
-1.2
-0.9
-0.7
-0.5
-0.4
-0.3
-0.2
-2.6
-2.0
-1.6
-1.3
-1.0
-0.8
-0.7
-0.5
-3.3
-2.8
-2.3
-1.9
-1.6
-1.4
-1.1
-1.0