3 OH production rates

The derivation of OH production rates from the observation of the OH 18-cm lines requires the knowledge of the excitation conditions of the OH radical and of its distribution within the coma; this has been debated for some time and some of the parameters necessary for the modelling of cometary OH are still poorly known. A brief discussion of the present situation and of the assumptions and parameters used in the present paper is now in order. The sets of parameters used in several previous studies and in the present work are summarized in Table 3.

The excitation through UV pumping and subsequent fluorescence leads to inversion (or anti-inversion) of the ground-state $\Lambda$-doublet of OH. Following pioneering works of Biraud et al. (1974) and Mies (1974), this process was modelled by Despois et al. (1981) and Schleicher & A'Hearn (1988), leading to an evaluation of the OH inversion as a function of heliocentric radial velocity similar - within details - in the two studies. The most notable divergence between the two model inversion curves is the small difference in the heliocentric velocity at which the crossovers occur from an inverted to an anti-inverted ground state population. Observations indicate that the Despois et al. model is better at some crossing points, and the Schleicher et al. model is better at others (see Fig. 9 in Schleicher & A'Hearn 1988). We have adopted here the inversion curve of Despois et al. We recall that the derived OH production rates are roughly inversely proportional to the assumed inversion value. The reader may wish to avoid using production rates measured at times when the absolute value of the inversion is too small.

The OH $\Lambda$-doublet acts as a weak maser, amplifying (or attenuating) according to its inversion (or anti-inversion) the continuum background at the wavelengths of the 18-cm lines. Most of the time, the background temperature $T_{\rm bg}$ is close to 3 K, but it may be significantly higher when a comet crosses the galactic plane or an occasional discrete radio source. We have evaluated  $T_{\rm bg}$ from the Stockert continuum survey at 1420 MHz (Reich & Reich 1986) performed with a $25\hbox{$^\prime$ }$ beam, available as computer files. The 1420 MHz intensities are converted to 1667 MHz assuming a 2.7 K cosmic contribution and a galactic contribution with a mean spectral index of -2.6. Unfortunately, similar data south of $-19\hbox{$^\circ$ }$ declination are not yet available as computer files; the default value $T_{\rm bg} = 3.0$ K is then assumed.

The inversion of the OH $\Lambda$-doublet may be quenched by collisions with ions and electrons. Neglecting this effect leads to an underestimation of the OH production rate, which explains the large discrepancies between UV and radio OH production rates obtained in the past. OH quenching was modelled by Despois et al. (1981), Schloerb (1988), Gérard (1990) and by Budzien (1992); see also recent studies by Gérard et al. (1998), Colom et al. (1999) and Schloerb et al. (1999). We have adopted the model of Gérard (1990) for which the radius $r_{\rm q}$ of the quenching region scales as:

$$r_{\rm q} \propto r ~ Q[{\rm OH}]^\frac{1}{2}.$$ (1)

$r_{\rm q} = 65~000$ km has been determined for r = 1.38 AU and $Q{\rm [OH]} = 9.4 \times 10^{28}$ s^-1 from the observations of comet Halley. It should be noted, however, that the theory of OH quenching is still poorly constrained by the observations. $r_{\rm q}$ and Q[OH] were derived through an iterative process. In some cases (especially when the quenching zone is larger than the telescope beam), this process did not correctly converge.

The space distribution of the OH radical is described by a Haser-equivalent model (Combi & Delsemme 1980). The water and OH-radical lifetimes are set to $8.5 \times 10^4$ and $1.1 \times 10^5$ s, respectively (Table 3). We have not tried to include the effects of solar variability: they are discussed by Cochran & Schleicher (1993) and Budzien et al. (1994). The water expansion velocity $v_{\rm exp}$ is known to depend upon the heliocentric distance and the gas production rate. As shown by Bockelée-Morvan et al. (1990a), it can be derived from the OH line shapes when they are observed with a good signal-to-noise ratio. For determining the production rates or their upper limits in weak comets, we assumed this velocity to be $v_{\rm exp} = 0.8$ km s^-1. The ejection velocity of the OH radical following water photodissociation was assumed to be 0.95 km s^-1 (Crovisier 1989; Bockelée-Morvan et al. 1990a).

   

Table 3: Haser model parameters used in former and present analyses to derive water production rates for OH observations.

	standard	1986A	Haser-equivalentb	Haser-equivalentb
		a	with quenching	with quenching
				and trapezium
parent velocity [km s-1]	-	-	0.8	from line shapesc
parent lifetime [s]	-	-	$8.5 \times 10^4$	$8.5 \times 10^4$
parent scale length [km]	80 000	60 000	-	-
daughter velocity [km s-1]	1.5	1.4	0.95	0.95
daughter lifetime [s]	$4 \times 10^5$	105	$1.1 \times 10^5$	$1.1 \times 10^5$
quenching	none	none	[2]	[2]
used by	[1]	[3] [4]	[5]	[5] [6]
		this work	this work

^a The OH observers agreed upon this set of parameters at the time of the International Halley Watch. Note that Schloerb et al. (1987) give, for 1986A, vectorial model parameters which, when converted into Haser-equivalent parameters, are similar to those listed here.
^b The parent and daughter Haser-equivalent scale lengths are computed from the lifetimes and velocities according to the formulas of Combi & Delsemme (1980).
^c Derived from the fit of a trapezium to the line shape, according to Bockelée-Morvan et al. (1990a).
References: [1]: Despois et al. (1981); [2]: Gérard (1990); [3]: Gérard et al. (1988, 1989); [4]: Schloerb et al. (1987); [5]: Bockelée-Morvan et al. (1994); [6]: Bockelée-Morvan et al. (1990a).

Choosing the best parameters for deriving Q[OH] is a difficult task. The user of XCOM can specify her/his preferred parameters. In order to derive automatically a uniform set of results, we have chosen in the present work to analyse and present the data with two sets of parameters: those described above (Col. 4 of Table 3), and 1986A (Col. 2 of Table 3), which were parameters used at the time of the International Halley Watch. The latter set is particularly useful when the iterative process to evaluate the quenching radius does not properly converge. Of course, the resulting Q[OH] may differ from those we published elsewhere from the same observations.

For comets with reasonably small Q[OH] (typically <10⁺²⁸ s^-1) not too close to the Earth or to the Sun (typically $\Delta, r > 1$ AU), the correction for quenching is not important. For such comets, $v_{\rm exp}$ is also close to 0.8 km s^-1. In this case, the three last models of Table 3 lead to similar production rates. For other comets, neglecting quenching could lead to significantly underestimated production rates.

The water expansion velocity, uniformly set to $v_{\rm exp} = 0.8$ km s^-1 in the present analysis, also leads to underestimated production rates for those comets which have higher velocities. Retrieving $v_{\rm exp}$ from line shapes (last model of Table 3), following Bockelée-Morvan et al. 1990a) requires spectra with high signal-to-noise ratios and is not appropriate to the automatic analysis we are presenting here. In extreme cases (1P/Halley and C/1995 O1 (Hale-Bopp) close to perihelion), $v_{\rm exp}$ could be as high as 2 km s^-1. In such cases, Q[OH] could be underestimated by about a factor of two, or even more taking into account the non-linearity of the correction for quenching.

   

Table 4: Maximum production rates determined for each comet in the Nançay data base, compared with production rates from ground-based visible OH and Lyman $\alpha$.

comet			Nançayd)		other observations
a)	b)	c)	max Q[OH]	r	max Q[OH]	r
			[1028 s-1]	[AU]	[1028 s-1]	[AU]
1982 I	1980b	C/1980 E1 Bowell	<8.0	4.93
1982 IV	1982a	26P/Grigg-Skjellerup	<1.5	1.10	0.04	1.12	e)
1982 VI	1982g	C/1982 M1 Austin	9.4	0.76
1982 VII	1982e	6P/d'Arrest	$\approx$0.3	1.40	0.36	1.41	e)
1982 VIII	1982f	67P/Churyumov-Gerasimenko	$\approx$0.9	1.35	0.35	1.41	e)
1984 IV	1983n	27P/Crommelin	$\approx$1.1	0.76	1.0	0.71	e)
1984 XIII	1984i	C/1984 N1 Austin	25.4	0.51
1985 XIII	1984e	21P/Giacobini-Zinner	6.0	1.04	3.2	1.12	e)
1985 XVII	1985l	C/1985 R1 Hartley-Good	2.5	0.76	2.0	0.89	e)
1985 XIX	1985m	C/1985 T1 Thiele	3.9	1.33	1.5	1.41	e)
1986 III	1982i	1P/1982 U1 Halley	108.6	0.71	35.	0.71	e)
1987 II	1986n	C/1986 V1 Sorrells	8.5	1.79	7.6	1.78	e)
1987 III	1987c	C/1987 B1 Nishikawa-Takamizawa-Tago	11.3	0.90	3.8	1.12	e)
1987 VII	1986l	C/1986 P1 Wilson	19.6	1.35
1987 XXIX	1987s	C/1987 P1 Bradfield	9.5	0.93	3.9	1.12	e)
1988 I	1987d1	C/1987 W1 Ichimura	12.9?	0.26
1988 V	1988a	C/1988 A1 Liller	10.7	0.86	4.2	1.12	e)
1988 XV	1988j	C/1988 P1 Machholz	<0.8	0.81
1989 X	1989o	23P/1989 N1 Brorsen-Metcalf	23.5	0.53
1989 XIX	1989r	C/1989 Q1 Okazaki-Levy-Rudenko	7.6	0.65
1989 XXII	1989a1	C/1989 W1 Aarseth-Brewington	20.7	0.58
1990 V	1989c1	C/1989 X1 Austin	44.4	0.38
1990 XX	1990c	C/1990 K1 Levy	20.6	1.06
1992 III	1991g1	C/1991 Y1 Zanotta-Brewington	1.3	0.75
1992 VII	1992b	C/1992 B1 Bradfield	<1.3	0.58
1992 VIII	1991h1	C/1991 X2 Mueller	<2.4	0.43
1992 XIX	1991a1	C/1991 T2 Shoemaker-Levy	2.9	1.11	1.5	0.89	e)
1992 XXVIII	1992t	109P/1992 S2 Swift-Tuttle	54.2	0.97	25.	0.89	e)
1993 III	1992x	24P/Schaumasse	1.0	1.28
1994 V		2P/Encke	$\approx$1.3	0.50
1994 IX	1993p	C/1993 Q1 Mueller	4.9	0.99
1994 XI	1993v	C/1993 Y1 McNaught-Russell	4.4	0.94
1994 XV	1992r	8P/Tuttle	$\approx$3.2	1.03
1994 XXVI	1994o	141P/1994 P1 Machholz 2	$\approx$1.3	0.76
1994 XXX	1994l	19P/Borrelly	2.8	1.43
		15P/Finlay (1995)	<2.5	1.08
		C/1995 Q1 Bradfield	17.5 ?	0.46
		73P/Schwassmann-Wachmann 3 (1995)	22.2	0.95
		122P/1995 S1 de Vico (1995)	61.0	0.68
		45P/Honda-Mrkos-Pajdusáková (1996)	$\approx$1.5	0.55	0.5	0.85	f)
		C/1996 B2 Hyakutake	20.3	0.70	56.	0.54	f)
		22P/Kopff (1996)	2.9	1.68
		C/1996 Q1 Tabur	4.2	0.99	4.2	0.92	f)
		C/1995 O1 Hale-Bopp	463.3	0.92	1020.	0.91	f)
		46P/Wirtanen (1997)	<1.5	1.12	1.5	1.08	f)
		81P/Wild 2 (1997)	$\approx$0.8	1.74
		2P/Encke (1997)	<4.6	0.39	0.9	0.81	f)
		C/1998 J1 SOHO	30.3	0.87	71.	0.32	f)
		C/1998 P1 Williams	$\approx$8.1	1.19
		21P/Giacobini-Zinner (1998)	5.1	1.05
		C/1998 U5 LINEAR	$\approx$1.4	1.26
		C/1999 H1 Lee	13.9	0.85
		C/1999 N2 Lynn	6.4	0.77

a) Old-style definitive designation; b) old-style provisional designation; c) new-style designation (with year of perihelion for recent short-period comets); d) using parameters of Col. 4 in Table 3, see text; e) from visible observations of OH (A'Hearn et al. 1995); f) from Lyman $\alpha$ observations (Mäkinen et al. 2001a).

In extreme cases where the comet is highly productive like C/1995 O1 (Hale-Bopp) or came very close to the Earth like C/1996 B2 (Hyakutake), retrieving Q[OH] from observations aimed at the comet centre position, which are dominated by the quenched region, may be very difficult or even impossible. Help could come, however, from the analysis of observations made at offset positions. Such analyses are not presented here, and the reader is referred to our specific studies of comets Hyakutake and Hale-Bopp (Gérard et al. 1998; Colom et al. 1999).

How do our radio OH production rates compare with those obtained by other means? Systematic observations of the water (or OH) production rates have been achieved for an important number of comets: from ground-based observations of the A-X band of OH (A'Hearn et al. 1995); from space observations of the same band by IUE (for which no homogeneous analysis has yet been published); from Lyman $\alpha$ observations with SOHO/SWAN (Mäkinen et al. 2001a).

Table 4 lists the highest OH production rates determined for each comet in our data base (using parameters of Col. 4 of Table 3). For comparison, the Table reports Q[OH] derived from the ground-based spectrophotometric observations of A'Hearn et al. (1995), and Q[H₂O] from the Lyman $\alpha$ observations of SOHO/SWAN (Mäkinen et al. 2001a), when such data has been published for a comparable heliocentric distance. The production rates from the ground-based visible observations of OH are systematically weaker, by a factor of 2 to 3, than those from Nançay. This can be attributed to the choice of the Haser-model parameters adopted by A'Hearn et al. (1995) (they assumed a parent scale length of 24 000 km, much shorter than our value). There is a more sound agreement with the production rates from the Lyman $\alpha$ data set. It is beyond the scope of the present paper to present a more detailed comparison of these various production rate determinations, which would involve a case-by-case study of the time evolution of each comet.