DETECTION OF WATER IN THE SHOCKED GAS ASSOCIATED WITH IC 443: CONSTRAINTS ON SHOCK MODELS. R. L. Snell,. 1. D. Hollenbach,. 2.
The Astrophysical Journal, 620:758–773, 2005 February 20 # 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
DETECTION OF WATER IN THE SHOCKED GAS ASSOCIATED WITH IC 443: CONSTRAINTS ON SHOCK MODELS R. L. Snell,1 D. Hollenbach,2 J. E. Howe,1 D. A. Neufeld,3 M. J. Kaufman,4 G. J. Melnick,5 E. A. Bergin,5 and Z. Wang5 Receivved 2004 May 14; accepted 2004 November 3
ABSTRACT We have used the Submillimeter Wave Astronomy Satellite (SWAS ) to observe the ground-state 110 ! 101 transition of ortho-H2O at 557 GHz in three of the shocked molecular clumps associated with the supernova remnant IC 443. We also observed simultaneously the 487 GHz line (3; 1 ! 3; 2) of O2, the 492 GHz line (3 P1 ! 3 P0 ) of C i, and the 550 GHz line (J ¼ 5 ! 4) of 13CO. We detected the H2O, C i, and 13CO lines toward the shocked clumps B, C, and G. In addition, ground-based observations of the J ¼ 1 ! 0 transitions of CO and HCOþ were obtained. Assuming that the shocked gas has a temperature of 100 K and a density of 5 ; 105 cm3, we derive SWAS beam-averaged ortho-H2O column densities of 3:2 ; 1013 , 1:8 ; 1013 , and 3:9 ; 1013 cm2 in clumps B, C, and G, respectively. Combining the SWAS results with our ground-based observations, we derive a relative abundance of ortho-H2O to CO in the postshock gas of between 2 ; 104 and 3 ; 103 . On the basis of our results for H2O, published results of numerous atomic and molecular shock tracers, and archival Infrared Space Observatory (ISO) observations, we conclude that no single shock type can explain these observations. However, a combination of fast J-type shocks (100 km s1) and slow C-type shocks (12 km s1) or, more likely, slow J-type shocks (12–25 km s1) can most naturally explain the postshock velocities and the emission seen in various atomic and molecular tracers. Such a superposition of shocks might be expected as the supernova remnant overtakes a clumpy interstellar medium. The fast J-type shocks provide a strong source of ultraviolet radiation, which photodissociates the H2O in the cooling (T 300 K) gas behind the slow shocks and strongly affects the slow C-type shock structure by enhancing the fractional ionization. At these high ionization fractions, C-type shocks break down at speeds 10–12 km s1, while faster flows will produce J-type shocks. Our model favors a preshock gas-phase abundance of oxygen not in CO that is depleted by a least a factor of 2, presumably as water ice on grain surfaces. Both freezeout of H2O and photodissociation of H2O in the postshock gas must be significant to explain the weak H2O emission seen by SWAS and ISO from the shocked and postshock gas. Subject headinggs: ISM: abundances — ISM: clouds — ISM: molecules — radio lines: ISM — shock waves — supernova remnants
1. INTRODUCTION
ular gas seen by DeNoyer. Dickman et al. (1992) mapped both CO and HCOþ in this region and found many more regions of broad molecular emission lines. The regions of strongest broad emission were labeled clumps A through H (following the nomenclature of DeNoyer, who first identified clumps A, B, and C), and these clumps form an elliptical ring that defines where the supernova shock encounters the molecular cloud. The shocked clumps show a systematic velocity variation around the ring, suggesting that the shocked gas is distributed along the periphery of a tilted, expanding ring or torus as a consequence of the interaction of the supernova blast wave with a preexisting molecular cloud (Dickman et al. 1992). This flattened ring is also delineated by 2 m H2 emission (Burton et al. 1988; Richter et al. 1995a; Rho et al. 2001). The distinct kinematic signature of the shocked molecular gas in this ring makes this an excellent region in which to explore the physics and chemistry of high-speed shocks propagating into preexisting molecular material. IC 443 has been extensively studied, and the shocked gas has been detected in many different atomic and molecular tracers, including the 21 cm line of H i (Braun & Strom 1986a), vibrationally excited H2 (Burton et al. 1988), the 63 m line of [O i] (Burton et al. 1990, hereafter BHHE90), the pure rotational lines of H2 (Richter et al. 1995a; Cesarsky et al. 1999), and a variety of molecular species (DeNoyer & Frerking 1981; Ziurys et al. 1989; Turner, et al. 1992; van Dishoeck et al. 1993). Despite the attention given to this region, no single shock
One of the most striking examples of the interaction between a supernova remnant (SNR) and a molecular cloud occurs in IC 443. IC 443 is a relatively nearby SNR estimated to be at a distance of 1.5 kpc (Georgelin 1975; Fesen & Kirshner 1980; Fesen 1984). Evidence for this interaction was discovered by DeNoyer (1978), who first detected high-velocity H i emission and later detected broad emission and absorption lines of CO and OH (DeNoyer 1979a, 1979b). Line widths of up to 100 km s1 have been observed. Observations of the X-ray, optical, infrared, and radio emission (Fesen & Kirshner 1980; Braun & Strom 1986a, 1986b; Mufson et al. 1986) show that the SNR consists of multiple shells interacting with the interstellar medium. One of these subshells is expanding into a molecular cloud that lies across the face of the SNR and partially obscures the optical emission (Cornett et al. 1977; Scoville et al. 1977). This interaction produces the shocked and accelerated molec1 Department of Astronomy, LGRT 619, University of Massachusetts, 710 North Pleasant Street, Amherst, MA 01003. 2 NASA Ames Research Center, Moffett Field, CA 94035. 3 Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218. 4 Department of Physics, San Jose State University, 1 Washington Square, San Jose, CA 95192. 5 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138.
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WATER IN IC 443 model has been entirely successful at explaining these diverse observations. BHHE90 have discussed many of the problems shock models have in producing both the strong H2 2 m and [O i] 63 m emission. A more complete discussion of shock modeling of the emission from these clumps is presented in x 4. A sensitive diagnostic of shock chemistry is water. In shocks with speeds in excess of 15 km s1 it has been theorized (Draine 1995) that water ice can be sputtered off grain surfaces, potentially producing a high water vapor abundance. Gas-phase processes also contribute significantly because in the high-temperature shocked gas the series of neutral-neutral reactions, O þ H2 ! OH þ H followed by OH þ H2 ! H2 O þ H (Elitzur & de Jong 1973; Elitzur & Watson 1978), rapidly form H2O in the gas phase. These reactions have a significant activation barrier, and Kaufman & Neufeld (1996) and Bergin et al. (1998) found that shocks with velocities between ~10 and 40 km s1 will convert nearly all the oxygen into water within a cooling timescale. However, for higher shock speeds (shock speeds >25–50 km s1, depending on the preshock density, magnetic field strength, and ionization fraction) molecules, including H2, will be dissociated in the shock (Hollenbach & McKee 1980). Although H2 will reform in the postshock gas, for preshock densities less than 3 ; 104 cm3, by the time the H2 abundance is sufficient to enable water formation the gas temperature will be too low to permit these neutral-neutral reactions to occur and the formation of water proceeds only by the less efficient ion-molecule gas-phase chemistry. In general, the H2O abundance behind these dissociative shocks (Hollenbach & McKee 1989) is orders of magnitude lower than that behind nondissociative shocks (Neufeld & Dalgarno 1989). Thus, one of the striking characteristics of most nondissociating or partially dissociating shocks is the high abundance of water. Bergin et al. (1998) found that the large H2O to CO abundance ratio produced in the shocked gas could persist in the cool postshock gas for 106 yr. Therefore, direct measurement of the water abundance in the postshock gas in IC 443 should be an extremely valuable probe of the nature of the shocks in this region. In this paper we present the detection of H2O emission from IC 443 using the Submillimeter Wave Astronomy Satellite (SWAS ). SWAS detected the lowest rotational transition of orthoH2O (o-H2O) toward clumps B, C, and G, as well as emission from the J ¼ 5 ! 4 rotational transition of 13CO and emission from C i. Only upper limits were obtained for emission from O2 in these clumps. The H2O transition observed by SWAS arises from only 27 K above the ground state and thus should be sensitive to the presence of water in even relatively cool gas far behind the shock front. We combine the SWAS results with maps of 12CO and HCOþ obtained at the Five College Radio Astronomy Observatory (FCRAO) 14 m telescope of clumps B and G to determine the water abundance in the postshock gas. Combining our results with published observations and archival Infrared Space Observatory (ISO) results, we address the nature of the shocks in IC 443. 2. OBSERVATIONS 2.1. SWAS The observations with SWAS were obtained over the period 1999 September through 2003 November. SWAS simultaneously observed the 110 ! 101 transition of H2O at a rest frequency of 556.936 GHz, the J ¼ 5 ! 4 transition of 13CO at a rest frequency of 550.926 GHz, the 3 P1 ! 3 P0 transition of C i at a rest frequency of 492.161 GHz, and the 3; 1 ! 3; 2 transition of O2 at a rest frequency of 487.249 GHz. Three
Fig. 1.—Spectra of the 110 ! 101 transition of o-H2O, the 3 P1 ! 3 P0 transition of C i, and the J ¼ 5 ! 4 transition of 13CO obtained with SWAS toward IC 443B. Also shown are the spectra of the J ¼ 1 ! 0 transition of 12CO and the J ¼ 1 ! 0 transition of HCOþ convolved to the SWAS angular resolution from maps obtained at FCRAO toward IC 443B. The coordinates of IC 443B are ¼ 6h 17m 16:s3 and ¼ 22 25 0 41 00 (J2000.0).
positions within IC 443 were observed, that of clump B at ¼ 06h 17m 16:s3, ¼ 22 25 0 41 00 (J2000.0), clump C at ¼ 06h 17m 44:s2, ¼ 22 21 0 49B1 (J2000.0), and clump G at ¼ 06h 16m 41:s8, ¼ 22 31 0 41 00 (J2000.0). The data were acquired by nodding the satellite alternatively between IC 443 and a reference position free of molecular emission. Details concerning data acquisition, calibration, and reduction with SWAS are presented in Melnick et al. (2000). Each position was observed over many orbits, and the total integration time on source was 38.8 hr for position B, 124.2 hr for position C, and 22.7 hr for position G. The SWAS spectrometer was a single acoustooptical spectrometer with 1400 1 MHz channels, yielding a velocity channel spacing of approximately 0.6 km s1. The SWAS beam is elliptical: at the frequency of the H2O and 13CO transitions it has angular dimensions of 3A3 ; 4A5, while at the frequency of the C i and O2 transitions it has angular dimensions of 3A5 ; 5A0. At the distance of IC 443, the SWAS beam has a linear dimension on the order of 1.4–2.2 pc. The data shown in this paper are not corrected for the measured SWAS main-beam efficiency of 0.90 (Melnick et al. 2000); however, in all analyses we include this correction. 2.2. FCRAO Maps were obtained of the 12CO emission at a rest frequency of 115.271 GHz and the HCOþ emission at a rest frequency of 89.189 GHz in clumps B, C, and G using the FCRAO 14 m telescope during 2000 May and June and 2003 November. The map centers were the same positions used for the SWAS
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Fig. 2.—Spectra of the 110 ! 101 transition of o-H2O, the 3 P1 ! 3 P0 transition of C i, and the J ¼ 5 ! 4 transition of 13CO obtained with SWAS toward IC 443C. Also shown are the spectra of the J ¼ 1 ! 0 transition of 12CO and the J ¼ 1 ! 0 transition of HCOþ convolved to the SWAS angular resolution from data obtained at FCRAO toward IC 443G. The coordinates of IC 443C are ¼ 6h 17m 44:s2 and ¼ 22 21 0 49B1 (J2000.0).
observations. For the observations in 2000, the SEQUOIA array receiver was used when it had only 16 pixels. Maps of approximately 6A0 ; 6A0 in extent with observations spaced by 2200 were obtained toward clumps B and G. The spectrometer for each pixel was a digital autocorrelator configured to have 80 MHz of bandwidth and 256 spectral channels per pixel, leading to channel spacings of 0.81 km s1 for CO and 1.05 km s1 for HCOþ . For the observations in 2003, the array receiver had its full 32 pixels available and an approximately 8A0 ; 8A0 map of clump C was obtained using an on-the-fly mapping technique. A new digital autocorrelator spectrometer was used with a bandwidth of 50 MHz and 1024 spectral channels per pixel, leading to channel spacings of 0.13 km s1 for CO and 0.16 km s1 for HCOþ . The FWHM beam size of the FCRAO telescope at the 12CO frequency is 4500 and at the HCOþ frequency is 5800 . The 12CO and HCOþ data shown have not been corrected for main-beam efficiency, estimated to be 0.45 and 0.50 at the frequencies of the 12CO and HCOþ lines, respectively. These corrections have been applied in all subsequent analysis. 3. RESULTS AND ANALYSIS 3.1. Observvational Results Spectra of H2O, C i, and 13CO J ¼ 5 ! 4 obtained with SWAS are shown in Figures 1–3 for clumps B, C, and G, respectively. O2 emission was not detected in any of the clumps. Accompanying the SWAS spectra in these figures are FCRAO spectra of HCOþ and 12CO convolved to the SWAS angular resolution. The spectral line shape for the molecular emission in these clumps is complex. The emission, in general, is made up of a very broad emission component that arises in the shocked
gas and a narrow component that can be seen in either emission or absorption that arises in the ambient molecular clouds. In clumps B and C there is good velocity separation between the narrow-line emission from the preshock cloud at a VLSR ¼ 3 km s1 and the broad-line emission from the shocked gas at VLSR 80 to 5 km s1. Toward clumps B and C it is believed that the shock has accelerated the molecular gas nearly along the observed line of sight, thus producing the good velocity delineation of the preshock and postshock gas. We detected both the preshock cloud emission and the broad shocked gas emission in the lines of 12CO and C i, but only the shocked gas emission in H2O, 13CO J ¼ 5 ! 4, and HCOþ . The absence of the ambient cloud emission in higher excitation lines and lines requiring higher densities (H2O, 13CO J ¼ 5 ! 4, and HCOþ ) is well established for clump B (Ziurys et al. 1989; van Dishoeck et al. 1993), and it is generally believed that this ambient component does not have sufficient density and/or temperature to produce emission in these molecular transitions. The H2O line profile in clump B is similar to the line profiles of the shocked gas seen in either 12CO or HCOþ , and presumably the emission arises in the same gas that produces the emission in these species. In clump G the line profiles are more complicated. The shock is presumably moving mostly transverse to our line of sight; thus, the velocity of the molecular gas in the ambient cloud, at VLSR ¼ 3 km s1, is nearly coincident with the centroid velocity of the shocked gas, at VLSR 30 to 20 km s1. The broad symmetrical emission from the shocked gas indicates that there is some dispersion in shock direction, with components of the shock both redshifted and blueshifted relative to the ambient gas. Toward the center of the clump, the ambient gas is often detected in absorption against the broad shocked gas emission
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Fig. 3.—Spectra of the 110 ! 101 transition of o-H2O, the 3 P1 ! 3 P0 transition of C i, and the J ¼ 5 ! 4 transition of 13CO obtained with SWAS toward IC 443G. Also shown are the spectra of the J ¼ 1 ! 0 transition of 12 CO and the J ¼ 1 ! 0 transition of HCOþ convolved to the SWAS angular resolution from data obtained at FCRAO toward IC 443G. The coordinates of IC 443G are ¼ 6h 16m 41:s8 and ¼ 22 31 0 41 00 (J2000.0).
(Ziurys et al. 1989; van Dishoeck et al. 1993); the emission in H2O is typical of the line profiles seen toward this clump (such as that seen in HCOþ ). The unconvolved 12CO spectra toward the center of this clump have the same line profile. However, when the FCRAO data is convolved to the resolution of the SWAS data, the convolved spectrum includes regions beyond the shocked region where the ambient gas is seen in emission.
Because the convolved data have a significant contribution from the extended ambient cloud emission, this emission overwhelms the absorption, creating the profile seen in Figure 3. The C i emission has a line profile very similar to the convolved 12 CO emission, although it is much weaker. In C i, even higher spatial resolution observations (Keene et al. 1996) have a similar line profile as seen by SWAS. The 13CO J ¼ 5 4 line profile is also broad; however, it shows no sign of absorption by the ambient molecular gas. Since absorption is seen in 12CO transitions as high as J ¼ 6 ! 5 (Keene et al. 1996), we believe the emission must be optically thin in 13CO. In all three clumps the H2O and HCOþ line profiles are nearly identical and appear to be broader than the emission seen in either C i or 13CO. We have measured the fluxes in the broad component of the lines observed by SWAS. For C i we have fitted multiple Gaussian components in the narrow and broad features to isolate the flux from the shocked gas from that of the ambient cloud. For H2O in clump G, we have fitted a single broad emission feature that includes the emission that has been absorbed by the foreground low-excitation ambient gas. The 3 upper limits on the O2 fluxes were established by fitting the data and assuming that the emission had the same velocity extent as water. A summary of the line fluxes measured for these species is given in Table 1. Maps of the integrated intensity of the 12CO J ¼ 1 ! 0 emission obtained at FCRAO for all three clumps are shown in Figure 4. The emission from clumps B and C was integrated only over the velocity range of the shocked gas. In clump G, the velocity of the ambient gas (which is seen in absorption toward the shocked clump and in emission away from it) is included in the velocity range for computing the integrated intensity; however, the integrated intensity in clump G shown in Figure 4 is dominated by the shocked gas. Globally, the shocked molecular gas in IC 443 is delineated by the broad-line regions, and they form an elliptical ring ~200 in diameter (Dickman et al. 1992). However, the broad-line regions are not continuous but instead are distributed in a number of relatively well defined clumps. The maps of both 12CO and HCOþ show that the emission in both clumps B and G have angular diameters of less than 20 , or 1 pc. In clump C, broad emission is seen extending beyond the extent of the map shown in Figure 4. Broad emission extends both northeast of clump C, toward the clump labeled D by Dickman et al. (1992), and to the northwest of clump C. A single pointing of SWAS encompasses the entire shocked gas emission from each of the three clumps, and there is clearly significant beam dilution in the large SWAS beam. 3.2. H2O Abundance The large spontaneous emission rate for the 110 ! 101 transition of o-H2O has several consequences for its emission. First,
TABLE 1 SWAS Line Fluxes in IC 443
Species
B ( K km s1)
B (1020 W cm2)
C ( K km s1)
C (1020 W cm2)
G (K km s1)
G (1020 W cm2)
o-H2O ................. C i....................... 13 CO ................... O2 .......................
3.84 0.13 2.47 0.10 0.33 0.04 0.16
10.1 5.7 0.9 0.4
2.13 0.07 4.06 0.07 0.27 0.04 0.20
5.6 9.4 0.7 0.5
4.63 0.11 2.99 0.12 0.97 0.04 0.30
12.2 6.9 2.5 0.7
Notes.—The fluxes presented in this table have been corrected for the main-beam efficiency of SWAS. The specific transitions include 110 101 557 GHz o-H2O, the fine-structure [C i] 609 m line, the 13CO J ¼ 5 4 transition, and the O2 487 GHz line. The flux limits for O2 are 3 limits.
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Fig. 4.—Maps of the integrated intensity of the J ¼ 1 ! 0 transition of 12CO of the shocked gas in clumps B, C, and G. The contours are at 10%, 30%, 50% (dotted line), 70%, and 90% of the peak integrated intensity, which is 59.9 K km s1 in clump B, 42.4 K km s1 in clump C, and 70.3 K km s1 in clump G. The offsets are relative to the coordinates given in the text.
even for modest o-H2O column densities, this transition could have a large line-center optical depth. Second, the critical density for this transition is on the order of 109 cm3 (Melnick et al. 2000), well above the density normally found in molecular clouds. Thus, in general, one might expect the transition to be optically thick and subthermally excited, making analysis of the emission difficult. However, because the critical density is so large, unless there is extreme trapping in the line the emission is likely to be in the low collisional excitation limit as first described by Linke et al. (1977). In this limit, collisional deexcitation can be ignored and every collisional excitation results in a photon that eventually escapes the cloud, even though it may be absorbed and reemitted many times. Because every photon escapes, there is a linear relation between the integrated intensity of the line and the product of the gas density times total H2O column density, which greatly simplifies the interpretation of the emission. This approximation has been applied in the analysis of H2O emission by Wannier et al. (1991), Snell et al. (2000a), and Neufeld et al. (2000). We analyze the H2O emission from IC 443 using an excitation model that solves the statistical equilibrium equation using the large velocity gradient approximation to account for radiation trapping. This model can also account for much of the beam dilution of the shocked gas in the large SWAS beam. However, before applying this model it is instructive to examine the analytical expression derived assuming the low-excitation approximation. 3.2.1. Analytical Expression
Snell et al. (2000a) presented an analytical expression for the relative abundance of o-H2O based on the observed integrated intensity of the line in the low-excitation approximation. The SWAS beam-averaged o-H2O column density is given by R 8k 2 Tmb dv NH2 O ¼ ; ð1Þ nClu hc 3 R where Tmb dv is the main beam–corrected integrated intensity of the line, n is the gas density, and Clu is the collisional excitation rate coefficient. Note that the water column density, for a fixed integrated intensity, is inversely proportional to the gas density and is also sensitive to temperature through the collisional
excitation rate coefficent. Therefore, accurate physical properties of the gas (especially the density if T 27 K) are extremely important in deriving the water abundance. There have been several studies of the physical properties of the shocked gas in IC 443 B and G (Ziurys et al. 1989; Turner, et al. 1992; van Dishoeck et al. 1993). However, the most complete study was that of van Dishoeck et al. (1993), who observed several transitions of a number of different molecular species and fitted the emission for the density and temperature of the shocked gas. They found that clump B could be adequately fitted by a single density and temperature component; however, the fit in clump G was poor. A better fit was found for clump G with two physical components. The best-fitting singlecomponent model for the postshock gas in these clumps has a temperature of 100 K, a density of 5 ; 105 cm3, and a CO column density of 1 ; 1018 cm2 averaged over a beam size of 1500 –3000 . If we assume that the primary collision partner of water in the shocked gas is H2, we can then use the collisional rate coefficients of Phillips et al. (1996). Phillips et al. (1996) computed the collisional rate coefficients for collisions between o-H2O and both o-H2 and para-H2 ( p-H2) and found that the o-H2 rates are about an order of magnitude larger than the p-H2 rates. Thus, we need to specify the ortho-to-para ratio for H2 to compute the effective collisional rate coefficient. If we assume that this ratio is in LTE, then at 100 K the ratio of o-H2 to p-H2 is 1.6 and the effective collisional excitation rate coefficent for the 557 GHz transition of water is 1:44 ; 1010 cm3 s1. Even if the ortho-to-para ratio of H2 is as large as 3, as suggested by Cesarsky et al. (1999), then the collisional rate coefficient would only be ~20% larger, and the number of H2O molecules would be correspondingly smaller. We have assumed an LTE ratio for H2 in the results presented in this paper. On the basis of the integrated line intensities presented in Table 1, we estimate SWAS beam average o-H2O column densities of 3:2 ; 1013 , 1:8 ; 1013 , and 3:9 ; 1013 cm2 for clumps B, C, and G, respectively. 3.2.2. Singg le-Component Excitation Model
Our excitation model (see Snell et al. 2000a) permits us to solve for the water emission using a statistical equilibrium code to solve for the populations of the five lowest rotational levels of o-H2O. We include the effects of radiation trapping using the
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WATER IN IC 443 TABLE 2 Abundances Derived from the Single-Component Model
Fig. 5.—Curve of growth for the integrated intensity of the o-H2O emission based on the single-component models for clumps B and G and the twocomponent model for clump G. At low relative abundance of o-H2O, the integrated intensity rises linearly with increased relative abundance; in this region the emission is ‘‘effectively’’ thin, although the line center optical depth may be much larger than unity. At larger relative abundances, the curve of growth becomes nonlinear as collisional de-excitation becomes important. The light horizontal lines indicate the observed integrated intensities for clumps B and G.
large velocity gradient approximation to compute the radiation field. The model also allows us to account for spatial variation of the shocked gas within the large SWAS beam. We used both the p- and o-H2 collision rate coefficients with o-H2O (Phillips et al. 1996) and assumed, as before, that the ratio of o- to p-H2 is in LTE. We need a physical model for the clumps that includes column density, density, temperature, and line width of the gas. Ideally, we would like to compare the o-H2O column density to the total hydrogen gas column in these shocked clumps. However, the published observations of the postshock H i and H2 do not provide either adequate spatial coverage or details to permit such a determination for these clumps. Some of the most extensive mapping of the pure rotational transitions of H2 were obtained toward clump G by Cesarsky et al. (1999) using ISO. The distribution of H2 emission they found for clump G was very similar to that of 12CO seen in Figure 4, and the emissions in both H2 and 12CO peak in the same direction. In this direction, the H2 column density of shocked gas is ~2500 times larger than that found for 12CO, a ratio similar to that found in most molecular clouds. Unfortunately, a map of the H2 column density was not presented in their paper. The atomic hydrogen content of clump G is impossible to determine because of the confusion with Galactic emission at these velocities. However, the large negative velocities of the shocked gas in clump B are readily distinguishable from Galactic emission, and DeNoyer (1978) has estimated that the H i column density between VLSR ¼ 10 and 60 km s1 is 6:9 ; 1020 cm2. The column density of H i is ~1000 times larger than the peak CO column density of 6:5 ; 1017 cm2 in this clump, indicating that there is substantial atomic hydrogen in the postshock gas, possibly produced by the dissociation of H2. If the shocks in clumps B and G are similar, then the column density of H i and H2 may be similar in the postshocked gas. Because of the lack of complete H i and H2 data, we compare our results for H2O with observations of 12CO. The 12CO observations were obtained on a 2200 grid and used to define the gas column density distribution in the shocked clumps. We have assumed that the 12CO emission is in LTE and is optically thin. The LTE assumption is accurate for the high densities inferred
Parameter
Clump B
Clump C
Clump G
Density (cm3)................... Temperature ( K) ................ o-H2O/ 12CO ....................... C i / 12CO ............................ 13 CO/ 12CO ......................... O2 / 12CO.............................
5 ; 105 100 4.6 ; 104 0.66 1.6 ; 103 1.8
5 ; 105 100 4.1 ; 104 1.4 2.0 ; 103 3.0
5 ; 105 100 3.7 ; 104 0.51 3.0 ; 103 2.3
from the observations of Ziurys et al. (1989) and van Dishoeck et al. (1993). Observations of 13CO emission in clumps B and G (Dickman et al. 1992; van Dishoeck et al. 1993) suggest that the assumption of optically thin emission is also valid. We also use the observed 12CO line widths of the shocked gas to define the velocity dispersion for each position in the shocked clump. For a single-component model, we assume that the density and temperature are constant throughout the clump and use the same values discussed earlier. We start by assuming an abundance of o-H2O relative to 12CO and then compute the H2O emission for each of the grid positions. We convolve the distribution of H2O emission with the SWAS beam to produce the expected SWAS integrated intensity. Finally, we iterate the relative abundance of o-H2O until the modeled integrated intensity matches the observed integrated intensity. This model, unlike the analytical expression, does not ignore collisional de-excitations and also accounts for variations in the H2O optical depth based on the structures resolved by the FCRAO observations. We note that structures not resolved by our FCRAO observations are not correctly accounted for in our modeling. We can compute the curve of growth of the integrated intensity of the H2O emission with increasing relative abundance of H2O on the basis of the single-component models for these clumps, and this is illustrated for clumps B and G in Figure 5. For small relative o-H2O abundances, the integrated intensity of the line increases linearly with relative abundance. For both clumps B and G, the curve of growth becomes substantially nonlinear once the abundance of H2O relative to 12CO exceeds 102. The observed integrated intensities for clumps B and G fall on the linear part of the curve of growth, indicating that the emission is ‘‘effectively’’ optically thin. The relative abundances of o-H2O for each of the three clumps are presented in Table 2, assuming that the H2O emission is distributed the same as the shocked 12CO emission. Since these clumps are modeled at the FCRAO resolution, we can compute the peak o-H2O column density in these clumps, assuming that the CO and H2O have the same distribution, and we find that the peak column density ranges from 1:5 ; 1014 to 3:0 ; 1014 cm2. Finally, we note that if the ratio of CO to H2 is the canonical value of 1 ; 104 , then the abundance ratio of o-H2O/H2 is on the order of 4 ; 108 . It is likely that clumps B, C, and G have structure not fully resolved by our FCRAO observations. This substructure could cause an underestimation of the amount of collisional deexcitation in our modeling, and consequently will result in an underestimate of the H2O column density. We can use the curve of growth to determine when this effect might be important. We note from Figure 5 that the relative abundance of H2O or the column density of H2O would have to be 100 times larger than modeled before the curve of growth would become significantly nonlinear because of collisional de-excitation. Consequently, the filling factor of the shocked gas in the FCRAO
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4500 beam would have to be less than 1% before our relative abundance of H2O would be in error because of unresolved substructure. The interferometer maps of the CO and HCOþ emission in these clumps (Wang & Scoville 1992; Tauber et al. 1994) and the high spatial resolution ISO images of the pure rotational lines of H2 (Cesarsky et al. 1999) show that substructure is present in the shocked gas that is not fully resolved by the FCRAO observations. However, on the basis of these data, the dilution in the FCRAO is not very large, and nowhere close to the factor of 100 it would have to be to be a concern. Even if the o-H2O emission arose from only the filamentary structures observed by Richter (1995) in the rovibrational 2 m lines of H2 (filling factor k0.03), the o-H2O abundance derived is still unlikely to be appreciably in error. However, depending on the filling factor of shocked gas in the FCRAO beam, the peak column density of H2O could be significantly larger than quoted above. We have also used the line fluxes in Table 1 and our excitation model to determine the relative abundances of C i and 13CO in the three shocked clumps and an upper limit to the abundance of O2. We used the identical procedure described for H2O to determine the C i and 13CO abundances and O2 upper limits. The results of our analysis are presented in Table 2. The 3 upper limits obtained for O2 provide little constraint on its abundance because of the intrinsic weakness of the rotational transitions of O2. The ratio of C i to 12CO is somewhat larger than that measured in typical molecular clouds (Plume et al. 2000; Howe et al. 2000) but is consistent with what Keene et al. (1996) found in clump G. The abundance ratio of 13CO to 12CO is somewhat smaller than that derived for these clumps by van Dishoeck et al. (1993). The emission in the J ¼ 5 ! 4 transition of 13CO is very sensitive to temperature and may suggest that the gas is somewhat warmer than assumed. 3.2.3. Two-Component Excitation Model
Van Dishoeck et al. (1993) found that a single-component model did not adequately fit the molecular line data toward clump G, and they fitted a two-component model. The two components consist of a low-density component with n ¼ 1 ; 105 cm3 and T ¼ 80 K and a high-density component with n ¼ 3 ; 106 cm3 and T ¼ 200 K. They stressed in their paper that the two-component model is not unique and that different combinations of density and temperature provide equally good fits. Although the data of van Dishoeck et al. (1993) were adequately fitted by the two-component model, it is likely that there is a continuous range of densities and temperatures in the postshock gas. Van Dishoeck et al. (1993) find that 70% of total 12 CO column density is in the low-density component and 30% is in the high-density component. The two physical components do not have distinct kinematic signatures but instead must have approximately the same mixture of the two components at all velocities. We have assumed that this division between the two components is the same throughout clump G. Using our detailed model, we have considered three cases: first, that all of the H2O emission arises from the low-density component; second, that all of the H2O emission arises from the high-density component; and finally, that the water abundance is the same in both components. We fitted the data in the same manner as described in the previous section and derive the abundance of H2O relative to 12CO. The results of this modeling are presented in Table 3. In the first case, we derive an abundance of H2O relative to CO of 2:8 ; 103 , which is about a factor of 6 times larger than our one-component result. In this extreme case, the water emis-
Vol. 620 TABLE 3 Water Abundances Derived from the Two-Component Model for Clump G Parameter
Low Density
High Density
Density (cm3)................................... Temperature ( K) ................................ o-H2O/ 12COa ...................................... o-H2O/ 12COb......................................
1 ; 105 80 2.8 ; 103 1.8 ; 104
3 ; 106 200 2.0 ; 104 1.8 ; 104
a b
Assuming that the H2O emission arises only from one of the components. Assuming that the abundance of H2O is the same in both components.
sion arises solely from a component that has a lower density, temperature, and column density than the single-component model. Thus, the relative abundance of H2O must be much larger to reproduce the emission. However, in the second case, in which the emission all arises in the high-density component, the higher density and temperature offset the lower column density and the required relative abundance of H2O is about a factor of 2 lower than in the single-component case. Finally, if we assume that the water emission arises from both components with equal relative abundance, we derive a relative H2O abundance of 1:8 ; 104 , roughly a factor of 2 lower than that derived for the single-component model. We show the curve of growth for this third case in Figure 5, and the behavior is very similar to the single-component model discussed earlier. Thus, the relative H2O abundance we derive is approximately the same as in the single-component model, except in the extreme case in which the H2O emission only arises from the lowdensity component of the two-component model. Nevertheless, the abundance of H2O in clump G is much less than that of CO. Van Dishoeck et al. (1993) also fitted a two-component model for clump B for emission at two different velocities. The physical conditions in these two components are identical to clump G, so we expect the effect of two components to be approximately the same as we found for clump G. 4. SHOCK MODELS OF IC 443 IC 443 is thought to be a good astrophysical laboratory for studying molecular shocks, since there are no massive young stars present to create a superposition of photodissociation regions (PDRs) and shock regions. However, numerous observational studies of shocked molecular gas performed at millimeter, submillimeter, and infrared wavelengths compared with theoretical calculations of shock emission have resulted in rather unsatisfactory and even contradictory conclusions. BHHE90 performed over 50 C- and J-type shock calculations (see Draine 1980 for definitions of C- and J-type shocks) with the main constraint that the shock ram pressure be 106 – 107 cm3 (km s1)2, which is on the order of the thermal pressure in the SNR driving the shock. They found that ram pressures of at least 107 cm3 (km s1)2 are needed to produce the absolute intensities in the [O i] 63 m and H2 2 m lines, assuming that the shock filled the beam. They compared shock models with a long list of observations and made predictions from shock models on then-unobserved lines such as H2 0–0 S(2) 12 m and [C ii] 158 m. Their conclusions are summarized in Table 4; for clarity, we have not reproduced all the numbers from Table 6 in BHHE90 but have marked with a Y the model results that roughly (within a factor of 3) agree with the observations and marked with an N (Nu for underestimates and No for overestimates) those that greatly disagree.
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WATER IN IC 443 TABLE 4 Comparison of Shock Models and Observations
Observational Constraints (1)
Fast J-Type Shock (no 103104 cm3, Vs 50–100 km s1) (2)
Slow J-Type Shock (Ne 105, no 105 cm3, Vs 10–20 km s1) (3)
Fast C-Type Shock (Xe 107, no 104 cm3, Vs 40 km s1) (4)
Slow C-Type Shock (Xe 107, no 105 cm3, Vs 10 km s1) (5)
Slow C-Type Shock (Xe 105, no 105 cm3, Vs 10 km s1) (6)
H2 2 m .................................. H2 12 m ................................ Br ......................................... CO 22–21 ............................... [O i] 63 m............................. [C ii] 158 m .......................... IRAS 60, 100 m.................... Velocity ................................... N( H i)...................................... N, T, n ..................................... N( H2O)....................................
Nu Nu Y Y Y Y No? Y Y Nu? Y
Y Y Y Y Nu Nu Y Nu Y Nu No?
Y Y Y Y Nu Nu Y Y Nu Y No
Nu Nu Y Y Y Nu Y Nu Nu Y Y
Y Y Y Y Nu Nu Y Nu Nu Y No?
Notes.—The model and observed line intensities can be found in BHHE90 ( Table 6 ), with the exception of [C ii]; velocity; N( H i); the N, T, n combination suggested by van Dishoeck et al. (1993); and the N( H2O) measurement reported in this paper. For these parameters, see text. Y corresponds to an agreement between model and observation at the factor of 3 level. Nu denotes model underproduction by at least a factor of 10. No denotes model overproduction by a factor of at least 10. The question mark denotes possible matches with observations if additional assumptions are made (see text). We conclude that a best fit is a mix of fast J-type shocks with either slow J-type shocks or slow, high-ionization C-type shocks.
Since the BHHE90 paper, two key additional observations have been made that severely constrain the shock parameters. One is the observation of H2O reported in this paper: a SWAS beam-averaged column density of o-H2O of (2 3) ; 1013 cm2 and an inferred o-H2O column density averaged over the FCRAO beam of 3 ; 1014 cm2 within the shocked clumps. The other is unpublished ISO data on the [C ii] 158 m emission that have been kindly provided to us by M. Haas (2004, private communication). These data show the clear detection of widespread [C ii], at a level 0.2 of that of [O i] 63 m. We add these constraints to Table 4, in addition to the observation that the observed gas is moving at velocities of 10–100 km s1 with respect to the ambient gas. 4.1. Summary of Shock Models The five shock models displayed in Table 4 are summarized below. Fast J-type shock.—The fast J-type shock produces 2 orders of magnitude too little H2 emission. It can produce the observed [C ii] and [O i] emission, but in doing so it tends to produce too large a flux of optical and ultraviolet photons, which are absorbed by grains and emerge as 60 and 100 m continuum at levels 3–10 times IRAS observations according to current shock models (see BHHE90). BHHE90 ruled out the fast J-type shock for this reason, but the new [C ii] observation, the observations of high velocities, and our SWAS H2O observation give added motivation to consider a fast J-type shock. It must be noted that the shock models do not accurately calculate the grain temperatures and the resultant IR continuum spectra so that improvements in the models may bring the model continuum more in line with the observations. The fast J-type shock does not produce much water column, in accord with the SWAS observation; dissociates enough hydrogen to account for the large H i columns observed; and naturally explains the observed 50–100 km s1 speed of some of the gas. The fast J-type shock achieves the postshock n 105 cm3 suggested by van Dishoeck et al. (1993), but in the current models produces a lower temperature (T 30 K) than the 100 K advocated by the millimeter observations for the bulk of the N 1022 cm2 column.
Hollenbach & McKee (1989) noted the presence of a hydrogen molecule formation temperature plateau in denser fast J-type shocks. Here the N 1022 cm2 postshock column is heated by the collisional de-excitation of newly reformed H2 molecules. The collisional de-excitation rates at 100 K are not well known; if they are higher than the values adopted in the model, the n, T, N combination suggested by van Dishoeck et al. (1993) may be achieved behind fast J-type shocks. Slow J-type shock.—Slow (15–20 km s1), partially dissociating J-type shocks simply cannot produce the H2 emission and, at the same time, produce the observed [O i] emission. The problem is quite general to any postshock gas with high abundances of warm (T 300 2000 K) H2. At these temperatures the gas-phase atomic oxygen is quickly converted into OH and H2O, and the resultant [O i] emission is far too weak. In addition, if there is initially atomic oxygen in the gas phase, the resultant H2O column density is much larger than the SWAS observational limits quoted here. BHHE90 made two very ad hoc and unsatisfactory assumptions in their paper: (1) The shock must be a J-type shock even though the physical parameters of the flow seem to be more appropriate to C-type shocks. (2) The oxygen chemistry is suppressed so that H2O and OH are not quickly formed by reaction of H2 with OH and O, leaving [O i] 63 m very strong. The reactions of H2 with O to form OH and with OH to form H2O are well measured, so it is extremely unsatisfactory to ignore them. We note here that Richter et al. (1995a, 1995b) advocated lower ram pressure shocks, with n0 ¼ 4 ; 103 cm3 and vs 20 km s1, which they argued more closely matched the thermal pressure of the SNR. By invoking partial dissociation of H2, they were able to produce the observed high columns of H i, as well as maintain the observed LTE in the H2 rovibrational levels via H atom collisions. However, such low ram pressure shocks do not produce the observed absolute intensities in the H2 and [O i] 63 m lines, unless each line of sight passes through at least 10 shocks. The slow J-type shock also produces far too little [C ii], the postshock column N 1022 cm2 is too cold (T 20 K), and the gas is only accelerated by 10–20 km s1 in the shock. In
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order to match the observed 50 km s1 motions, the preshock gas is required to already be in supersonic motion. From a theoretical standpoint, the preshock conditions are such that partially dissociating J-type shocks would likely not exist if the ionization fraction is low but would be C-type shocks instead. However, slow J-type shocks would exist in molecular gas with high ionization fractions. Such J-type shocks may produce the hot H2 emission and explain the constancy of the observed H2 line ratios noted above. They will not, however, produce the [O i] and [C ii] emission. Fast C-type shock.—The fast C-type shock has the same key problem as the slow J-type shock: if it produces the H2 emission, it underproduces the observed [O i] by at least an order of magnitude. A fast C-type shock produces [C ii] emission that is orders of magnitude weaker than observed, and it requires a delicate fine tuning of shock velocities to produce the observed H i. A fast C-type shock is only possible in low-ionization regions. One would likely need to appeal to a high preexisting abundance of atomic H, which may be implausible. A fast C-type shock overproduces the H2O column density by at least an order of magnitude. Slow C-type shock (xe 107 ).—A slow C-type shock with low fractional ionization can produce the [O i] 63 m emission even with H2 present because the peak postshock temperature never exceeds 200 K, so the chemistry that transforms O to OH and H2O never is fully activated. However, by the same token the low temperatures mean that such slow shocks greatly underproduce the H2 2 m emission. Slow C-type shocks do not dissociate H2; the large H i columns would have to be preexisting. Like slow J-type shocks, the slow C-type shocks do not readily explain the high observed velocities. They underproduce the [C ii] emission by orders of magnitude; however, they do meet the SWAS requirement on a low H2O column. Slow C-type shock (xe 105 ).—In C-type shocks, the neutral gas is heated by the drift (ambipolar diffusion) of the ions and charged grains with respect to the neutrals, where the maximum drift speeds are on the order of the shock speed. The heating rate of the neutrals is then proportional to the ionization fraction, so that C-type shocks incident on ambient gas with higher ionization fraction will produce hotter postshock neutral gas. With an increased ionization fraction, the postshock gas attains temperatures 2000 K, thereby enabling the production of the H2 2 and 12 m emission. However, its quick conversion of any atomic oxygen to H2O reduces its [O i] 63 m intensity to levels far below that observed. It underproduces [C ii] and its low speed means, like the slow J-type shock, that the ambient preshock gas must already be in supersonic motion. Like the slow J-type shock, this slow C-type shock will overproduce H2O. Time-dependent shock.—Cesarsky et al. (1999) compared ISO observations of H2 0–0 S(2) through S(8) with the new, time-dependent shock models of Chie`ze et al. (1998). They point out that the shocks in IC 443 may not have had time to reach a steady state. In such a case, the shocked gas may show both C- and J-type characteristics: within the C-type shock, a J-type shock is established, heating a small fraction of the gas to high temperatures (Flower & Pineau des Foreˆts 1999). Cesarsky et al. (1999) fit these H2 observations with a n0 ¼ 104 cm3, vs ¼ 30 km s1 shock and a timescale of 1000–2000 yr. The Chie`ze et al. (1998) model that reproduces the pure H2 emission seen by ISO should be examined to see whether it can meet the other constraints. However, since it produces warm H2, it seems unlikely that it can produce the [O i] emission. It also seems likely to overproduce the H2O column and to underproduce the [C ii].
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No single-shock model can match the observations. However, before considering multiple-shock models we need to address a fundamental problem. The combination of H2 2 m and high-J rotational emission and the low H2O columns or abundances found here are a major problem for any shock model. The H2 emission necessitates molecular gas at temperatures greater than 1000 K. In such gas, all oxygen not in CO will be essentially instantly transformed to H2O. Therefore, shocks capable of producing the observed H2 emission will overproduce H2O. What then can prevent large columns of H2O from forming? 4.2. Processes That Suppress the Postshock H2O Column We have considered four processes that may prevent large columns of H2O from forming. We find two to be promising. Mechanism 1.—The H i/H2 ratio is high in the preshock gas. Note that in x 3.2.1 we discussed observations of high H i columns. Whereas high-temperature chemistry in molecular gas leads to the conversion of O to OH to H2O, in atomic gas the H atoms attack the molecules and drive this sequence in reverse order. Therefore, if the H atom to H2 molecule ratio is sufficiently high, little H2O would be produced. However, we ran shock codes with preshock ratios of H i/H2 as high as 10 and found that all oxygen not in CO was converted to H2O even in these quite ‘‘atomic’’ shocks. The reason is that the activation barrier for the H2 O þ H ! OH þ H2 reaction is very high (E=k 104 K), so even small fractions of H2 drive the reaction in the reverse direction and produce H2O. Therefore, a reasonably high H i/H2 ratio cannot provide the explanation for the low observed H2O columns. Mechanism 2.—H2O is produced copiously in the warm postshock gas but freezes out rapidly on grains in the cooling postshock gas. The column N of hydrogen downstream of the warm shocked gas can be written N ¼ no vs t;
ð2Þ
where t is the flow time for the warm gas to the point in question downstream. The time for an H2O molecule to collide with a grain, or the ‘‘freezing time,’’ since most collisions lead to sticking and incorporation into an ice mantle, is given by tf ¼ (ngr gr v H2 O )1 , where ngr is the number density of grains, gr is the grain cross section, and v H2 O is the thermal speed of an H2O molecule. This can be rewritten tf ¼ 2 ; 1011 (105 cm3 n1) s, where n is the postshock density in the gas. The hydrogen column to the freezing point is therefore given by Nf ¼ 2 ; 1022
vs no cm2 : 10 km s1 n
ð3Þ
The compression factors n/no behind both J- and C-type shocks are limited by the magnetic field and for the C- and slow J-type shocks we are considering are on the order of 10 (Hollenbach & McKee 1979). Assuming that the abundance of H2O produced in the warm gas is greater than or equal to 104, we obtain N (H2 O) 2 ; 1017 cm2. The maps of Richter (1995) of H2 2 m emission suggest filling factors of hot shocked gas in the SWAS beam of greater than or equal to 0.03. The predicted emission from H2O in the hot shocked gas would greatly exceed that observed by SWAS, even with a filling factor as low as 0.03. We therefore rule out postshock freezeout of H2O as an explanation. Mechanism 3.—All oxygen not in CO is frozen out as water ice mantles in the preshock gas. SWAS observations of H2O in
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numerous molecular cloud cores suggest that this is, in fact, very likely (Bergin et al. 2000). Here the hot H2 has no free oxygen to react with, so that no hot H2O is produced in the hot postshock gas and extremely low columns of H2O are produced behind such shocks. The only question for this process is whether the ice mantles are preserved in this shock environment. Draine (1995) shows that C-type shocks with speeds in excess of 15 km s1 will sputter ice mantles off the grains, owing to the large energies of the ions impacting their surfaces. Therefore, we cannot invoke this mechanism for the fast C-type shocks models with shock velocities in excess of 15 km s1. However, it presumably can apply for slow (shock velocities 10 km s1) C- and J-type shocks. We discuss below the possibility of elevated far-ultraviolet (FUV ) fields in the shock environment, such that shocks producing the hot H2 may experience postshock FUV fluxes of 108 –109 photons cm2 s1. This same FUV field might photodesorb H2O ice mantles. However, using photodesorbtion yields less than or equal to 103 (Bergin et al. 1995), we find that mantles should survive in such environments. We conclude that the preshock freezeout of H2O is a promising way to limit H2O emission from the shocked gas. We note that this mechanism produces little warm H2O emission, a prediction that may be confirmed with ISO observations of higher lying H2O transitions. Mechanism 4.—The gas-phase H2O is photodissociated by elevated FUV fields in the cooling postshock gas. Although there is negligible FUV radiation from nearby OB stars or the interstellar radiation field (ISRF), fast J-type shocks produce copious amounts of FUV, mainly as line radiation (Shull & McKee 1979; Hollenbach & McKee 1989). This radiation is quite ineffective at photodissociating H2 or CO, which selfshield and whose dissociating FUV transitions do not overlap appreciably with the shock lines. However, the shock FUV photons are effective at dissociating H2O, a process that involves FUV radiation from 6 to 13.6 eV. We envision a case in which the fast J-type shocks characterized in column (2) of Table 4 propagate through an interclump medium and their resultant FUV radiation impinges on the denser clumps in which the slower (H2 producing) shocks propagate. Because the total hydrogen column through the molecular gas observed in IC 443 is on the order of 1022 cm2 (see x 3.2.1), we estimate that the extinction between the fast J-type shock point of origin and the H2O-rich postshock gas is on the order of AV 2 3. We have then utilized our fast J-type shock code to estimate the local FUV flux in the H2O-rich gas to be 108 –109 photons cm2 s1 (in the units often used by photodissociation region PDR modelers, this corresponds to G0 ¼ 1 10, where G0 is the FUV flux in units of the local interstellar radiation field). We have rerun our slow J-type shock, fast C-type shock, and slow C-type shock cases with such an FUV field present (detailed results of the models are discussed in x4.4). For the slow J-type shock case, the H2 emission was essentially unchanged, as was the high H2O abundance in the T 300 K postshock gas. Here the rapid production of H2O completely overwhelmed the FUV photodissociation. However, once the postshock gas cooled below 300 K the production rate fell dramatically owing to the activation barriers involved and the H2O was rapidly photodissociated. The column of H2O in the slow J-type shock 2 numerical model is N (H2 O) ¼ 3 ; 1016 G1 0 cm , so that for G0 3 and a beam filling factor of 0.03 the SWAS beam average column is predicted to be 3 ; 1014 cm2, significantly larger than observed. Thus, the FUV flux produced by the J-type
shock must be significantly larger for this mechanism alone to reduce the abundance of H2O in the postshock gas to the levels observed by SWAS. In the C-type shock case, dramatic changes occur. The FUV field raises the ionization fraction to xe 105 , primarily from the presence of volatile heavy elements other than C with ionization potentials below 13.6 eV. This has no effect on the slow J-type shock but, for reasons explained above, creates orders of magnitude more heating in the C-type shock. Under these high ionization conditions, C-type shocks only occur for shock velocities below 15 km s1, as opposed to the cutoff of 40 km s1 under normal molecular cloud conditions. At the same time, the slow 10 km s1 C-type shock now heats H2 to 2000 K so that the 2 and 12 m emission is produced. High abundances of H2O are produced in the hot H2, but downstream as the gas cools below 300 K the H2O is photodissociated. 2 Again, our numerical results find N ( H2 O) ¼ 5 ; 1016 G1 0 cm , very similar to the slow J-type shock. Like the slow J-type shock, this model is only viable if the FUV flux is large. The columns of postshock H2O produced in the numerical code can be easily understood analytically. The timescale to photodissociate a water molecule is tH2 O ¼ 2 ; 109 (G0 )1 s. As in the freezeout calculations presented above, substitution of this into equation (2) and multiplication by the peak H2O abundance produced in the hot molecular gas gives N (H2 O) 4 ; 1016 G1 0
105
no vs cm2 ; 3 cm 10 km s1
ð4Þ
independent of whether the shock is a J- or C-type shock. This is the column of H2O in the cooling gas at the point where the flow time equals the photodissociation time. Beyond this, the cooling gas has little H2O. One of the objections to slow (shock velocities 10–20 km s1) J-type shocks in molecular gas was that they should be C-type shocks. With typical ionization fractions, shock speeds 40 km s1 are needed to produce J-type shocks. However, in this scenario slow J-type shocks are possible. Because of the high ionization fraction, shocks below 10–15 km s1 are C-type shocks and higher speed shocks are J-type shocks. Thus, 10 km s1 C-type shocks or 15–20 km s1 J-type shocks may provide the H2 emission, although they seem to overproduce H2O for reasonable FUV fields produced by fast J-type shocks. In contrast to the preshock freezeout model, this mechanism does produce significant warm H2O and therefore may produce observable IR emission from higher H2O levels. 4.3. Multiple-Shock Models Given that no single-shock model can match the observations, we consider models of multiple shocks, as might be expected in this clumpy medium, including the possibility of the preshock freezeout of H2O and the postshock FUV photodissociation of H2O. Can a simple superposition of two shocks (the simplest multishock case) provide a solution? BHHE90 suggested a combination of fast C-type shock and slow C-type shock, with the fast C-type shock producing the H2 emission and the slow C-type shock producing the [O i] emission. However, we now have two additional constraints that work against this scenario. These two shocks greatly underproduce [C ii], and the fast C-type shock produces too much H2O column compared to SWAS observations. In addition, they do not naturally explain the large H i columns. Including a fast J-type shock in a two-shock scenario has many advantages. It is the only shock that can produce the
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[C ii] emission. At the same time, it produces the [O i] emission. It naturally explains the postshock velocities, the high H i column, and the low H2O column. However, shock modelers will need to update their models to make an accurate test of whether such a fast J-type shock overproduces the observed IRAS 60 and 100 m fluxes. If fast J-type shocks are viable, then a combination with either a slow J- or slow C-type shock (with high xe) will match all the constraints in Table 4. The slow, nondissociating shocks are needed to provide the H2 emission. We emphasize again the consistency of such a superposition. The fast J-type shock naturally produces a level of ionization that will permit C-type shocks at velocities 10–15 km s1 and J-type shocks at velocities 10–15 km s1, and this level of ionization heats the slow C-type shock to temperatures that enable the observed H2 emission. In addition, both the fast J-type shock and the slower C- or J-type shock are driven by roughly the same ram pressure, as might be expected as a supernova overtakes a clumpy medium. We note that roughly the same ram pressure does not necessarily imply the same thermal pressure in the cooling postshock gas because magnetic pressure in the compressed postshock gas predominates (Hollenbach & McKee 1979; Brogan et al. 2000). This may explain why van Dishoeck et al. (1993) found a good fit with two components of very different thermal pressures. Two separate investigations support the idea of suppressed H2O columns in shocks, possibly because of FUV photodissociation of H2O in supernova shocks (Reach & Rho 1998; Lockett et al. 1999). The Reach & Rho investigation used ISO to detect IR emission of H2O, OH, and CO from warm postshock gas in the SNR 3C 391. The postshock emitting gas has a density of 2 ; 105 cm3 and a temperature of 100–1000 K. The presence of significant levels of OH (0.06 of H2O) suggests the photodissociation of H2O. Similarly, Lockett et al. (1999) model the OH maser emission from SNRs and find that FUV photodissociation of H2O is required to produce the OH. In another investigation, Reach & Rho (2000) used ISO to detect a number of atomic and ionic finestructure lines toward W28, W44, and 3C 391 along with the 0–0 S(3) and S(9) lines of H2. They too appealed to a combination of fast (100 km s1) J-type shocks (no 102 103 cm3) for the fine-structure emission and slow (20 km s1) C-type shocks for the H2 emission. To our knowledge, however, no previous work has self-consistently used the FUV radiation from the J-type shocks to affect the molecular emission from the slower molecular shocks. We conclude this section with a discussion of observational discriminants between the two processes we have invoked to suppress the H2O column in the slow shocks that produce the observed H2 emission. As noted above, if the oxygen not in CO is incorporated in ice mantles throughout the shock, then little hot gas-phase H2O is produced and therefore little IR emission is produced in higher excitation H2O lines. However, if gasphase oxygen other than CO is present, then strong IR lines of H2O will be produced, even if the H2O column is suppressed by FUV photodissociation in the cooling downstream gas. 4.4. Additional Constraints Provvided by ISO Observvations Searching the data archive of ISO, we have found a Long Wavelength Spectrometer (LWS) observation of clump C that yields valuable line flux measurements for several far-infrared CO, OH, and H2O transitions.6 The ISO LWS data were obtained 6
No LWS observations were carried out directly toward clumps B or G.
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as part of the program ISM _ IAS ( PI: P. Cox) and, as far as we are aware, have not previously been reduced and published. The observations were performed over the spectral range 45– 189 m in the LWS’s grating mode (known as LWS04) with the 7500 diameter ISO LWS beam centered on IC 443 clump C. The spectral resolution ranges from 0.60 m (FWHM ) or 952 km s1 at 189 to 0.29 m (FWHM) or 1933 km s1 at 45 m. We used the ISO Spectral Analysis Package (ISAP)7 to remove bad data points and to average the data from multiple scans. We then fitted linear baselines and Gaussian line profiles to sections of the spectrum where spectral lines were apparent. For each of the molecules CO, OH, and H2O we have identified three emission lines for which the signal-to-noise ratio exceeds 2.5. The spectra of these emission lines are shown in Figures 6 and 7 and the measured line fluxes are presented in Table 5. The probable errors on the line fluxes given there are (1 ) statistical errors; in addition, a systematic uncertainty of 30% applies. For comparison, we have also shown the line fluxes measured by Reach & Rho (1998) toward 3C 391:BML,8 the only other SNR from which far-infrared H2O emissions have been reported. Table 5 indicates that the far-infrared CO, OH, and H2O line fluxes measured toward IC 443 clump C are broadly similar to those measured by Reach & Rho toward 3C 391:BML. On average, the OH and H2O emissions are both about a factor of 2 stronger in IC 443 clump C than in 3C 391:BML, while the CO lines are typically slightly weaker. For 3C 391:BML, Rho & Reach inferred from the relative OH and H2O line fluxes an OH / H2O abundance ratio 0.1; they reasoned that its relatively large value argued for the importance of H2O photodissociation (mechanism 4 cited above among the possible explanations of the low H2O abundance inferred from SWAS observations). While agreeing with that inference for the case of IC 443 clump C as well, we find that the weakness of the far-infrared H2O lines relative to the H2 vibrational emission also requires the depletion of oxygen as water ice within the preshock gas, and this ice remains on the grain surface throughout the shock in IC 443 clump C (mechanism 3). From the H2 v ¼ 1 0 S(1) emission maps of Burton et al. (1988) and Richter (1995), we estimate that the H2 v ¼ 1 0 S(1) flux within the ISO LWS beam is 1:7 ; 1018 W cm2 , uncorrected for extinction. Of all the shock-excited water lines accessible to ISO LWS, the 414 –303 transition near 114 m is expected to be the strongest (Kaufman & Neufeld 1996). In C-type shocks, the flux ratio F[ H2O 414 –303]/F[H2 v ¼ 1 0 S(1)] is a strongly decreasing function of shock velocity: the water flux is insensitive to velocity once water forms, while H2 v ¼ 1 0 S(1) increases rapidly with increasing shock velocity. For a preshock H2 density of 105 cm3 and with all the oxygen not in CO converted to H2O, the models predict a minimum value of 0.34 for the fastest, hottest possible nondissociative shocks. Thus, the observed flux ratio of only 0.04 (even without any extinction correction) argues that the water abundance is suppressed even within the hot gas responsible for the H2 vibrational emission. Because most of the shock-excited H2O emission originates in warm (T > 600 K) gas and because the rate of H2O production within such hot gas is so rapid, unreasonably large FUV radiation fields would be required to suppress the water abundance
7 ISAP is a joint development by the LWS and SWS Instrument Teams and Data Centers. Contributing institutes are CESR, IAS, IPAC, MPE, RAL, and SRON. 8 The designation BML stands for ‘‘broad molecular line’’ region.
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WATER IN IC 443
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Fig. 6.—ISO LWS spectra of IC 443, clump C, showing the 79, 84, and 119 m OH lines and the 114 m H2O line.
significantly by photodissociation. Thus, the freezeout of oxygen onto icy grain mantles within the preshock gas must apparently be invoked to explain the weakness of the 414303 line flux measured by ISO. The above conclusion would only be strengthened if the H2 vibrational line were subject to significant extinction. It would also be strengthened if, as in many sources, there is an admixture of shock velocities, leading the hot (T 2000 K) H2-emitting gas behind the fastest shocks to be accompanied by larger column densities of cooler (600–1000 K) gas; the cooler component would excite the H2O 414 –303 transition much more effectively than the H2 v ¼ 1 0 band, further increasing the F[H2O 414 –303]/F[H2 v ¼ 1 0 S(1)] ratio expected in the absence of oxygen freezeout. We have explored in detail the conditions necessary to match the observed H2, H2O, CO, and OH line intensities toward clump C, using existing C- and J-type shock models, modified as appropriate for the conditions in IC 443. The modifications are those discussed in x4.2, including increases in the ionization fraction and photodissociation due to an enhanced FUV radiation field and depletions of oxygen and other species. Both models are able to reproduce the observed line emission, although J-type shock models are more robust in that the resulting emission is less sensitive to shock velocity. We therefore favor the slow J-type shock scenario but cannot rule out a slow C-type
shock to explain the molecular emission. Details of the models are given below. J-type shock model.—We have used the model of Hollenbach & McKee (1979, 1989) to compute the molecular emission produced by a slow J-type shock. Our best-fit models have preshock densities of 3 ; 104 cm3, a shock velocity of 20 km s1, and G0 10. The value of G0 is plausibly produced by the extinct fast J-type shocks in this region and gives approximately the correct OH/H2O line ratios9 and high fractional ionization levels. A shock velocity of 20 km s1 is well above the speed at which C-type shocks break down for the assumed high fractional ionization. The infrared line spectrum predicted by the model is relatively insensitive to the shock velocity in the range 9 Our J-type shock code breaks the FUV into three bins: 6 eV < h < 11:2 eV, Ly (separately), and 11:2 eV < h < 13:6 eV. Although the fast J-type shock produces mostly FUV line radiation (with some two-photon continuum), we believe our treatment of this radiation is nevertheless adequate because the cross sections for OH and H2O photodissociation do not vary significantly over a wide range of wavelength from threshold to 13.6 eV and the extinction of the J-type shock radiation is not well determined. Even though we effectively treat the FUV flux as continuum flux, in no model is CO appreciably photodissociated. This is the expected result with a more realistic FUV spectrum, since, unlike OH and H2O, CO photodissociation is initiated by CO line absorption that does not overlap appreciably with the emission-line spectrum of the fast J-type shock.
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Fig. 7.—ISO LWS spectra of IC 443, clump C, showing the J ¼ 17 ! 16, J ¼ 16 ! 15, and J ¼ 15 ! 14 CO lines and the 175 and 180 m H2O lines.
12 km s1 < vS < 25 km s1 , since collisional dissociation of H2 produces a 4000 K plateau beyond which cooling proceeds through collisionally excited infrared lines. This insensitivity of the infrared lines to the shock velocity in partially dissociating J-type shocks was noted by Brand et al. (1988). As in the C-type shock, H2O is photodissociated by FUV radiation
once the gas temperature drops below 400 K. Thus, in the bulk of the downstream column, which lies at T T400 K, the H2O abundance relative to CO is very low, in accord with the SWAS observations presented here. The results of this model give H2 and CO intensities that are in the correct ratio (i.e., I½1 0 S(1) 10 ; I½CO J ¼ 17 16).
TABLE 5 Far-Infrared Line Fluxes Measured by ISO LWS Toward Clump C
Transition
Wavelength (m)
Line Flux from IC 443C (1020 W cm2)
Line Flux from 3C 391:BMLa (1020 W cm2)
OH 21/ 2 – 23/ 2 J = 1/2–3/2............ OH 23/ 2 J = 7/2–5/ 2....................... OH 23/ 2 J = 5/2–3/ 2....................... OH 21 / 2 J = 3/21/2...................... CO J = 17–16.................................... CO J = 1615 ................................... CO J = 15–14.................................... H2O 414 –303...................................................... H2O 303 –212 ....................................... H2O 212 –101......................................................
79.12, 79.18 84.42, 84.60 119.23, 119.44 163.12, 163.40 153.267 162.812 173.631 113.527 174.626 179.527
30.3 3.8 32.9 4.9 8.2 0.8
