Mapping warm molecular hydrogen with Spitzer's Infrared Array Camera (IRAC)
aa r X i v : . [ a s t r o - ph ] J a n Mapping warm molecular hydrogen with
Spitzer’s
Infrared Array Camera (IRAC)
David A. Neufeld and Yuan Yuan
Department of Physics and Astronomy, Johns Hopkins University, 3400 North CharlesStreet, Baltimore, Maryland
ABSTRACT
Photometric maps, obtained with
Spitzer ’s Infrared Array Camera (IRAC),can provide a valuable probe of warm molecular hydrogen within the interstellarmedium. IRAC maps of the supernova remnant IC443, extracted from the
Spitzer archive, are strikingly similar to spectral line maps of the H pure rotationaltransitions that we obtained with the Infrared Spectrograph (IRS) instrumenton Spitzer . IRS spectroscopy indicates that IRAC Bands 3 and 4 are indeeddominated by the H v = 0–0 S(5) and S(7) transitions, respectively. Modelingof the H excitation suggests that Bands 1 and 2 are dominated by H v = 1 − v = 0–0 S(9). Large maps of the H emission in IC433, obtained withIRAC, show band ratios that are inconsistent with the presence of gas at a singletemperature. The relative strengths of IRAC Bands 2, 3, and 4 are consistentwith pure H emission from shocked material with a power-law distribution ofgas temperatures. CO vibrational emissions do not contribute significantly tothe observed Band 2 intensity. Assuming that the column density of H attemperatures T to T + dT is proportional to T − b for temperatures up to 4000 K,we obtained a typical estimate of 4.5 for b . The power-law index, b , showsvariations over the range ∼ − b in the range 4 −
5. Theobserved power-law index is consistent with the predictions of simple models forparaboloidal bow shocks.
Subject headings:
ISM: Molecules – ISM: Clouds – molecular processes – shockwaves
1. Introduction
Warm molecular hydrogen, at temperatures of several hundred to several thousand K,has been observed widely in molecular clouds that have been heated by interstellar shock 2 –waves (e.g. Gautier et al. 1976, Treffers et al. 1976, Combes & Pineau des Forets 2000.)Such clouds are frequently associated with protostellar outflows and supernova remnants(SNR), and emit a rich spectrum of rovibrational and pure rotational H emissions. Whilethe near-infrared rovibrational transitions have been observed extensively with ground-basedobservatories, observations of the mid-infrared pure rotational transitions are significantlyhampered by atmospheric absorption; thus ground-based observations can provide only afragmentary picture of the pure rotational spectrum of warm H , and space-based observa-tions from the Infrared Space Observatory (ISO) or the
Spitzer Space Telescope have beenneeded to provide a complete spectrum. In particular, recent observations with the InfraredSpectrograph (IRS) on
Spitzer have provided sensitive spectral line maps for the S(0) throughS(7) pure rotational transitions of H , allowing the gas temperature and ortho-to-para ratioof the emitting H to be determined. Such observations have revealed the presence of anadmixture of multiple gas temperatures along every sight-line that has been observed, withnon-equilibrium ortho-to-para ratios readily apparent in the cooler gas components, and haveprovided important constraints upon theoretical models for interstellar shock waves (Neufeldet al. 2006a, 2007).While warm molecular hydrogen has been studied primarily through spectroscopic obser-vations with the IRS on Spitzer , photometric observations with the Infrared Array Camera(IRAC) are also possible. As noted recently by Reach et al. (2006; see their Fig. 1), the v = 1 − v = 0 − fall within the IRAC bandpassand can contribute significantly to the intensities observed with IRAC; in some sources, theIRAC intensities are potentially dominated by H line emissions. In this paper, we investi-gate further the utility of IRAC observations in mapping the distribution of warm molecularhydrogen. In §
2, we discuss IRAC and IRS observations carried out toward the supernovaremnant IC443. In §
3, we compare the spatial distribution of the H line emissions, observedwith IRS, with the photometric maps obtained with IRAC. In §
4, we discuss how the rela-tive intensities within the four IRAC bands can be used to constrain the physical conditionswithin the warm molecular gas.
2. Observations
In a previous paper (Neufeld et al. 2007), we have discussed spectroscopic mappingobservations of warm molecular hydrogen, carried by
Spitzer /IRS toward small (1 ′ × ′ )regions in the SNR W44, W28, 3C391 and IC433. Full details of the observations and datareduction procedure have been described by Neufeld et al. (2006a; 2007) and will not berepeated here. In the case of IC443, our IRS observations targeted a region containing clump 3 –C (in the nomenclature of Denoyer 1979), and – of the four SNR sources observed – revealedthe spectrum most strongly dominated by line emissions (Neufeld et al. 2007, see their Fig.8). In Figure 1, we reproduce the observed IRS spectrum for a 25 ′′ diameter circular regioncentered on clump C (black curve), superposed on the spectral response functions for thefour IRAC bands (Fazio et al. 2004; blue). The red curve represents a model H spectrumfor spectral regions shortward of the IRS wavelength range; it will be discussed in § µ m) bandpass could be dominated by H S(4) andS(5) emissions, and the Band 3 (5.6 µ m) bandpass by H S(6) and S(7). Emissions frompolycyclic aromatic hydrocarbons (PAHs) do not appear to contribute significantly to theBand 3 and Band 4 intensities in IC433 (in contrast to some of the other supernova remnantsobserved by Neufeld et al. 2007.)To evaluate IRAC observations as a potential probe of warm molecular hydrogen, weextracted IRAC maps of IC443 from the
Spitzer archive. Two IRAC fields within IC433are available in the archive, both observed in Program 68 and one of them encompassingthe region mapped with IRS. The location of the regions observed with
Spitzer
IRAC andIRS are shown in Figure 2, superposed on a 2MASS map of the the entire remnant (Rhoet al. 2001). The southernmost field observed with IRAC has an angular area that is ∼ − respectively for Bands 1, 2, 3, and 4. As discussed in § θ , greater than ∼ ′′ , an extended source aperturecorrection is found to be necessary: the measured fluxes must be multiplied by a correctionfactor that decreases monotonically from 1.0 at θ = 9 ′′ to values at θ > ′′ of 0.91, 0.94,0.71, and 0.74 respectively for Bands 1, 2, 3, and 4. This correction factor is needed becausethe point spread functions for Bands 3 and 4 show more extended wings than expected andbecause there is a extremely diffuse scattering that distributes a portion of the incident fluxover the entire detector array (Reach et al. 2005.) In the context of the present observations,the appropriate correction factor is ill-defined because the maps show structure on a rangeof size scales. However, since our primary interest is in the brightest emission knots thatare generally less than 10 ′′ in extent, we will adopt the point source calibration withoutcorrection. The implications of the flux calibration uncertainties will be discussed further in 4 – §
3. Comparison of the IRS and IRAC maps
Given the spectral response functions (Fazio et al. 2004) plotted in Figure 1, H emissionalone is expected to yield the following IRAC intensities: I Band 3 (H )MJy sr − = 0 . I [H S (6)] + 0 . I [H S (7)]10 − erg cm − s − sr − (1) I Band 4 (H )MJy sr − = 0 . I [H S (4)] + 0 . I [H S (5)]10 − erg cm − s − sr − (2)We have rebinned the IRS and IRAC data on a common grid and compared, pixel-by-pixel, the IRAC-measured intensities, I Band 3 (IRAC) and I Band 4 (IRAC), with the quantities I Band 3 (H ) and I Band 4 (H ) given by equations (1) and (2) above. Figure 4 uses scatter plotsto present the results, with the best linear fit superposed. Most points lie very close to thebest linear fit. Small positive intercepts (2.0 and 2.5 MJy sr − respectively for Bands 3 and4) on the vertical axis for the best-fit line may suggest that the diffuse background in theIRS-mapped region is somewhat larger than that for the IRAC-mapped region as a whole.Alternatively, or in addition, they may result from instrumental scattering of radiation fromthe swath of bright emission within the IRS-mapped region (see discussion at the end of § ∼ . The slopes on the best-fit linear relationships are 1.10 and 1.03 respectively for Bands 3 and 4. Given the likelyuncertainties in the flux calibration for the IRS line maps – estimated by Neufeld et al.(2007) as < ∼
30% – these values are remarkably close to unity.In Figure 5, we compare maps of IC433 obtained from IRS observations using equations(1) and (2) with those obtained using IRAC. If we correct the former by multiplicative factors This comparison has revealed modest astrometry errors in the output of our IRS mapping software(Neufeld et al. 2006a; the errors are smaller than 1 ′′ at the center of the IRS-mapped field, rising to up 4 ′′ at the edges). A small shift ( ≤ ′′ ) of the central position in the IRS maps, combined with a 12% stretchalong the slit direction, bring the IRS and IRAC maps into excellent agreement. maps derived using the two different instruments. The only significant difference is apparentat offset ( − ′′ , − ′′ ), where a point continuum source shows up in the IRAC maps but notthe H spectral line maps. This is the K = 10 . line emission. While mapping a ∼ ∼
70 square arcminutes required only 13 minutesto observe. In the next section, we will consider how the IRAC colors (i.e. ratios of intensitiesfor different bands) can be used to constrain the physical conditions in the warm moleculargas.
4. Physical conditions in the gas traced by IRAC
In Figures 6 – 8 (lower panels), we present maps of the ratio of three independent pairs ofIRAC band intensities. In these figures, we suppressed regions in which the IRAC intensitiesare small, with a median-subtracted Band 3 intensity less than 5 MJy sr − , because here thenoise becomes significant and the contribution of diffuse emission may be important. Thisthreshold value is a factor 2.5 as large as the positive intercept obtained in Figure 4 (see § − has little effectupon the distribution of observed band ratios.The upper panels show histograms (arbitrary scale) that indicate the relative number ofpixels for which the logarithm of the band ratio lies in a given range. The colors appearingunderneath the histogram curve are matched to those appearing in the lower panel, so thehistogram serves as a color bar for the band ratio maps. Vertical dashed lines indicate thevalues of log(band ratio) corresponding to the lower sextile, median, and upper sextile ofthe distribution. Figures 6 – 8 show that different IRAC bands exhibit different degrees ofcorrelation. Bands 1 and 2 are most closely correlated (narrowest histogram for the bandratio), while Bands 1 and 4 are the least so. All 3 histograms indicate a skew distribution forthe band ratios, with an excess of pixels for which the shorter-wavelength of the two bandsis abnormally large. A cursory inspection of the ratio maps indicates that the right-handtail of the distribution (colored yellow) is mainly accounted for by discrete point sources, i.e.stars.In interpreting these band ratios, we have determined which H lines fall in each IRACband. In Table 1, we list the contribution of various H lines to each IRAC band, to-gether with the upper state energies. The former, computed using the spectral response 6 –functions plotted in Figure 1, are in units of 10 MJy sr − / (erg cm − s − sr − ). For exam-ple, the entry 0.909 appearing opposite H S(6) indicates that an H S(6) line intensity of10 − erg cm − s − sr − will add a contribution of 0 .
909 MJy sr − to the intensity measured inIRAC Band 3 (in accord with eqn. 1). Assuming that the H level populations are controlledby collisional excitation by H and He, we then used a statistical equilibrium calculation todetermine the expected IRAC band ratios as a function of the gas temperature and pres-sure. Here we adopted the collisional excitation rates of Flower & Roueff (1998a, 1998b,1999) and Flower, Roueff & Zeippen (1998). We also assumed the H ortho-to-para ratio tohave attained its equilibrium value of 3, consistent with the results of IRS spectroscopy forthe S(4) – S(7) transitions (Neufeld et al. 2007), and adopted a n (He) /n (H ) ratio of 0.2In Figure 9, we show the results of our statistical equilibrium calculation as a functionof temperature and density (blue curves). Here, the expected IRAC band ratios are shownin a two-color diagram, with the logarithm of the Band-2-to-Band-4 ratio plotted on thehorizontal axis and that of the Band-3-to-Band-4 ratio on the vertical axis. Both ratiosare strongly increasing functions of temperature, as expected because the Band 4, Band 3,and Band 2 wavelength ranges contain H lines of successively higher excitation (see Table1). The open triangle represents the median band ratios observed in the IRAC maps, withthe error bars designating the upper and lower sextiles. While the open triangle with thesolid error bars is obtained with the standard point source flux calibration that we considerappropriate for this application (see discussion in § mixture of gas temperatures is present alongevery sight-line; and/or (2) that Band 2 is dominated by emission from some source otherthan H . The first of these is known to be true, based upon IRS observations of the H S(0) – S(7) rotational emissions. For IC443 and every other source observed by Neufeldet al. (2006a) and (2007), the H rotational diagrams exhibit a distinct positive curvaturethat indicates multiple temperature components to be present. In evaluating the secondpossibility, we have considered possible contributions from the Br α recombination line ofatomic hydrogen (at 4.05 µ m) and the v = 1 − µ m).The first of these can be ruled out from observed upper limits on the Br γ line (Burton et al.1988), and the latter by ground-based observations of the 4.687 – 4.718 µ m region (Richteret al. 1995; this region is inaccessible to Spitzer /IRS). Although the possible contributionof CO vibrational emissions to the IRAC Band 2 intensity has been discussed previouslyfor shocked molecular gas (e.g. Reach et al. 2006), we find that the negligible contribution 7 –observed in IC443C is entirely unsurprising; this conclusion is discussed further at the endof §
4, following our discussion of the gas temperature distribution.In an attempt to model an admixture of gas temperatures, we have adopted a simplepower-law distribution of the form dN = aT − b dT, (3)where dN is column density of gas at temperature between T and T + dT ; and a and b areparameters that we will adjust to fit the band intensities. Here, we adopt a lower limit, T min on the gas temperature of 300 K and an upper limit, T max , of 4000 K. The exact lower limitis unimportant, since gas cooler than a few hundred K is too cold to emit significant H emission in the IRAC wavelength range; the upper limit represents the temperature abovewhich H is rapidly dissociated (Le Bourlot et al. 2002). The coefficient a in equation (3)can then be written a = N ( >
300 K)( b − T − b min − T − b max ) , where N ( >
300 K) is total column density of molecular hydrogen warmer than 300 K. Incomparing the predictions of our excitation model with the observations, we adopt an as-sumed extinction A V = 13 . µ m extinction, together with the interstellar extinction curves of Weingartner & Draine(2001; “Milky Way, R V = 3 . admixture of gas temperatures, with the effects of extinction included. For a suitablechoice of the assumed power-law index, b , and gas density, n (H ), the observed band ratiosare now consistent with the H excitation model. The median Band 3 / Band 4 and Band2 / Band 4 intensity ratios are best fit by b ∼ . n (H ) ∼ cm − . Unfortunately,because the observed band ratios lie close to the locus obtained in the high-density limit(i.e. in local thermodynamic equilibrium), the inferred density is strongly dependent uponthe measured band ratios and is therefore quite uncertain.The results of our excitation calculations are also plotted in Figures 6 – 8 (upper panel),for the second case where an admixture of temperatures is assumed. In each figure, theexpected band ratio – with the effects of extinction included – is plotted on the horizontalaxis as a function of the power-law index, b (plotted on the vertical axis), and for H densitiesof 10 , 10 , 10 and 10 cm − . One consistent behavior is particularly noteworthy: thoseratios with the strongest dependence on b show the largest variations within the map. Thusthe Band-1-to-Band-2 ratio, which shows the smallest spatial variation, has the weakestdependence upon b . This strongly suggests that the spatial variations in the measured bandratios reflect real variations in the temperature distribution of the emitting gas. 8 –In Figure 10, we present additional color-color diagrams for a selection of three differentpairs of band ratios. Instead of simply showing the median and upper and lower sextilefor the distribution of observed band ratios as we did in Figure 9, we now show the two-dimensional distribution function. Thus, the false color image (coded from black [smallestvalue] to blue to white [largest value]) represents the number of pixels for which the bandratios show a given pair of values. The white regions in these maps (representing the mostprobable combination of line ratios) are clearly elongated parallel to the lines of constantdensity. Again, this behavior suggests that the variations in the measured band ratios reflectreal variations in the temperature distribution of the emitting gas.Figure 10 reveals a significant discrepancy between the H excitation model and theobservations. While all the plotted band ratios suggest a power-law index b varying over therange 3 – 6, the best-fit density is not consistently determined. In particular, the relativestrengths of Bands 2 – 4 suggest a typical density n (H ) ∼ cm − (with large error barson the exact value), whereas the relative strength of Band 1 argues for a higher density ∼ cm − . Both values are considerably larger than the density ∼ few × cm − inferredpreviously from an analysis of the HD R(4)/R(3) line ratio (Neufeld et al. 2006b).These discrepancies may result from the presence of a mixture of gas densities withinthe source. They may also reflect a shortcoming in our treatment of the H excitation, inthat we only include the effects of collisions with H and He. For the v = 1 − – unlike pure rotational transitions in which excitation by H is less efficient –the cross-section for excitation by H can exceed that by H by several orders of magnitude(see Le Bourlot et al. 1999, their Table 3, for a tabulation of the relevant critical densitiesfor which collisional excitation by H or H dominates spontaneous radiative decay.) At thetypical temperatures indicated by our observations of IC443, we find that the excitationof vibrational emissions by collisions with H dominates for n (H) /n (H ) ratios greater than ∼ . , and by reaction of H with O and OH. Theoretical models forshock waves (e.g. Wilgenbus et al. 2000) suggest that significant atomic hydrogen abundancescan be achieved behind shocks that are fast enough to produce H at temperatures of a fewthousand K. For H abundances of this magnitude, the excitation of H vibrational transitionscan be dominated by collisions with H.To assess the typical contribution of various spectral lines to the IRAC band intensities,we have considered a “typical excitation model” for the excitation of H in IC443. Here 9 –we adopt b ∼ . n (H ) = 10 cm − to obtain the pure rotational line ratios. Forrovibrational transitions, we adopt a larger H density, n (H(Richteretal . ) ∼ cm − ,as an approximate method of treating of the effects of excitation by atomic hydrogen and/orthe presence of multiple density components. For this typical excitation model, we havecomputed the H line spectrum expected in the 3 − µ m region covered by IRAC Bands 1and 2. This spectrum is shown in Figure 1 (red curve, for an assumed spectral resolution λ/ ∆ λ = 60 FWHM) , and the fractional contribution of each line to each IRAC band isgiven in Table 1 (rightmost column). For this excitation model, Bands 1, 2, 3, and 4 arerespectively dominated by H v = 1 − v = 0 − v = 0 − v = 0 − , we adopted the expression given Thompson(1973, his equations [7] and [8], with his parameter A taken as 68, in accord with thelaboratory measurements of Millikan & White 1963.) In Figure 11, we plot the fractionalcontribution of CO emissions to IRAC Band 2, as a function of the H density and for anassumed CO/H abundance ratio of 10 − . As with the vibrational excitation of H , the crosssections for excitation by H greatly exceed those for excitation by He or H , so the resultsdepend upon the H/H abundance ratio. Results are given for H/H abundance ratios of 0,0.01, 0.1, and 1 (from bottom to top), and for temperature power-law indices, b , of 4 (bluecurves) and 5 (red curves). As before, an He/H ratio of 0.2 is assumed. For H/H ratios ≤ − , CO vibrational emissions contribute significantly (i.e. above the 10% level) only atdensities ≥ × cm − . At a density of 10 cm − , the contribution from CO is only < ∼ ratio ≤ − . Even for an H/H ratio of unity, the CO contribution is < ∼ n (H ) = 10 cm − ; while shock models do allow for the possibility of large H/H ratiosnear the threshold for dissociation, we consider it implausible that the effective H/H ratiofor the excitation of CO vibrational emissions could be as large as unity, because most ofthe CO emission originates in relatively cool gas that has been subject to shocks of velocitymuch less than the dissociation threshold. 10 –
5. Discussion
The excitation of molecular hydrogen behind interstellar shock waves has been thesubject of considerable discussion over the past two decades. In the late 1980’s, with theadvent of spectral line mapping at near-IR wavelengths, two key features of the H emissionwere noted: (1) the relative line strengths observed toward shocked regions are typicallyinconsistent with a single excitation temperature (Burton et al. 1989); and (2) even line ratiosthat are strongly dependent upon the gas temperature often show a remarkable constancythroughout a given source (Brand et al. 1989). These behaviors have subsequently beenobserved in a wide variety of sources, and are particularly evident in Spitzer observationswhere the S(1) – S(7) pure rotational lines are mapped over a common region (e.g. in boththe Herbig Haro objects – HH54 and HH7 – observed by Neufeld et al. 2006a; and in all thesupernova remnants – IC443, W28, W44, 3C391 – observed by Neufeld et al. 2007).It was recognized (Smith & Brand 1990) that these behaviors are unexpected for singleplanar shocks that are of “C-type” in the designation of Draine (1980). In such shocks,ion-neutral drift is a critical feature of the physics (Mullan 1971), allowing the velocitiesof the ionized and neutral species to change continuously (hence the designation “C-type”for “continuous”) in a warm region of roughly uniform temperature: as a result (a) therotational diagrams for the H level populations behind such shocks show little curvature(e.g. Neufeld et al. 2006a, Appendix B); and (b) temperature behind the shock front is astrong function of the shock velocity . The former is inconsistent with observational feature(1) above, and the latter is inconsistent with (2) unless the shock velocity is remarkablyconstant throughout the mapped region.Two separate explanations were offered to account for the observations, i.e. the keyfeatures (1) and (2) described above. First, Burton et al. (1989) noted that the coolingregion behind a “J-type” shock might successfully explain the H line ratios. In a “J-type”shock, where the ion and neutral species are well-coupled and show velocities that jumpdiscontinuously at the shock front (hence the designation “J-type” for “jump”), the gas isinitially heated to a high temperature and then cools radiatively, resulting in an admixtureof gas temperatures. Provided the shock is not fast enough to destroy molecular hydrogen, J-type shocks yield a rotational diagram with significant curvature but which shows a relativelyweak dependence upon the shock velocity.As a second and alternative explanation, Smith, Brand & Moorhouse (1991; hereafter While planar C-type shocks were subsequently shown to be unstable (Wardle 1991), numerical sim-ulations of the non-linear development of the instability (Neufeld & Stone 1997; MacLow & Smith 1997)suggested that both results (a) and (b) still apply.
11 –SBM) suggested bow shocks as the source of the observed H emissions. Such shocks resultwhen a supersonic flow encounters a clump of material or when a supersonic clump travelsthrough an ambient medium. In SBM’s model, multiple unresolved bow shocks are assumedto be present in each telescope beam. At the head of each bow shock, where the gas movesperpendicular to the shock front, the effective shock velocity is greatest; here the shockmay become dissociative and of J-type. On the sides of the bow shock, where the materialenters the shock front at an oblique angle, the shock velocity is smaller and the shock isnon-dissociative and of C-type. Assuming a parabolic shape for the shock surface, and de-composing a bow shock into a set of planar shocks of varying shock velocity, SBM consideredthe resultant H emission. The H rotational diagram is indeed expected to show significantcurvature, consistent with the observations. Furthermore, provided that the shock velocityat the head of the bow shock is sufficient to dissociate molecules, SBM showed that the H line ratios are independent of the flow velocity.Bow shocks offer several advantages over J-type shocks in explaining the observations.First, given the typical ionization level and magnetic field strengths in molecular clouds, non-dissociative shock waves are expected to be of C-type, not J-type. Second, high-resolutionobservations of shocked H (e.g. Schultz et al. 1999), carried out after the explanations ofBurton et al. (1989) and SBM were offered, have indeed revealed the presence of bow shocksthat were unresolved in previous observations. Finally, recent observations of the S(0) – S(7)rotational transitions of H (Neufeld et al. 2006a), carried out with Spitzer /IRS toward sixseparate sources, have shown that the H ortho-to-para ratio is smaller than its equilibriumvalue, with the cooler components along every sight-line showing the greatest departures fromequilibrium. This behavior is simply inconsistent with the J-type shock model, in which thewarmer gas components evolve to become the cooler components. To the contrary, the coolercomponents must arise in separate shocked regions.We can compare the power-law index, b , derived in § v to v + dv is associated with a shock surface area dA ∝ v − dv (Smith & Brand 1990); this proportionality applies for all velocities less than themaximum shock velocity, v max , attained at the head of the bow shock. Based upon a fit to theplanar C-type shock models of Kaufman & Neufeld (1996), Neufeld et al. (2006a, AppendixB) found that the warm shocked material could be adequately approximated by a slab ofconstant temperature ∝ v . and column density N (H ) ∝ v − . . These proportionalitiesyield a power-law temperature distribution, with the mass at temperature between T and T + dT obeying dM ∝ N (H ) dA ∝ v − . dv ∝ T − (3 . . / . dT ∝ T − . dT (3) .
12 –For bow shocks with a maximum shock velocity sufficient to dissociate H at the headof the bow, this leads to a power-law index b ∼ . temperature, T max . For slower bow shocks, the temperature distribution extends to sometemperature lower than T max . Thus an admixture of bow shocks, with a range of velocitiessome of which insufficient to achieve temperature T max at the head of the bow shock, couldlead to an overall temperature distribution which is steeper than dN ∝ T − . dT (i.e. tovalues of b greater than 3.8).These simple predictions are broadly consistent with the observations, which indicatevalues of b < . b couldresult from variations in the distribution of velocities at the heads of a set of unresolved bowshocks. We note, however, that our assumption of parabolic bow shocks in steady-state isa highly idealized one, and that numerical simulations would be needed to provide a morerealistic prediction for the shock structure and resultant temperature distribution in thepresence of possible instabilities (including the Wardle instability).
6. Summary
1. IRAC maps of IC443C, extracted from the
Spitzer archive, are strikingly similar to spectralline maps of the H pure rotational transitions, obtained with the IRS instrument.2. IRS spectroscopy indicates that IRAC Bands 3 and 4 are dominated in this source by theH v = 0–0 S(5) and S(7) transitions, respectively. Modeling of the H excitation suggeststhat Bands 1 and 2 are dominated by H v = 1 − v = 0–0 S(9).3. Mapping H with IRAC presents several advantages and disadvantages relative to mappingwith IRS. IRAC mapping:(a) is a factor ∼
500 faster in area mapped per unit observing time;(b) provides access to additional H transitions: v = 1 − v = 0 − are accessible to IRS;(d) fails to probe the H ortho-to-para ratio, since each band is sensitive to both ortho-and para-H transitions;(e) is only possible in sources with H -dominated mid-IR spectra. 13 –4. Large maps of the H emission in IC433, obtained with IRAC, show band ratios that areinconsistent with a single temperature component. The relative strengths of IRAC Bands2, 3, and 4 are consistent with pure H emission from shocked material with a power-lawdistribution of gas temperatures. CO vibrational emissions do not contribute significantlyto the observed Band 2 intensity.5. The relative strength of Band 1 is larger than that predicted in models for the collisionalexcitation of H by H and He. The observations can be reconciled with a model in which alarge atomic hydrogen abundance enhances the H vibrational emissions believed to dominateIRAC Band 1.6. Assuming that the column density of H at temperatures T to T + dT is proportional to T − b for temperatures up to 4000 K, we obtained a typical estimate of 4.5 for b . The power-law index, b , shows variations over the range ∼ − b in the range 4 − Spitzer Space Telescope , which is operated by the Jet Propulsion Lab-oratory, California Institute of Technology, under a NASA contract. We gratefully acknowl-edge the additional support of grant NAG5-13114 from NASA’s Long Term Space Astro-physics (LTSA) Research Program. This research has made use of the BASECOL database(http://amdpo.obspm.fr/basecol) – devoted to the rovibrational excitation of molecules –and of NASA’s Astrophysics Data System.
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This preprint was prepared with the AAS L A TEX macros v5.2.
16 –Table 1. Contribution of H line emission to the IRAC bandsTransition Wavelength Upper state energy IRAC Contribution a Fractional( µ m) E U /k in Kelvin contribution b H v = 1 − v = 1 − v = 1 − v = 0 − v = 0 − v = 0 − v = 0 − v = 1 − § v = 0 − v = 0 − v = 0 − v = 0 − v = 0 − v = 0 − a in units of 10 MJy sr − / (erg cm − s − sr − ) b Fractional contribution to the band, in percent, for our typical excitation model (see § ′′ (HPBW) diameter circularaperture centered at α = 06 h m s δ = +22 o ′ ′′ (J2000) in IC443C (correspondingto offset ( − ′′ , − ′′ ) in Figure 3 below). The spectra shown here are not background-subtracted, since no off-source measurements were made, and thus the continuum flux levelmust be regarded as somewhat uncertain. Blue curves: relative response function for the fourIRAC photometric bands (Fazio et al. 2004; shown here in arbitrary units). Red spectrum:predicted H spectrum for our typical excitation model (described in § µ m), H (1.65 µ m), and K S (2.17 µ m) intensities, the latter being dominated in thesouthern ridge by v = 1 − (Rho et al. 2001). 19 –Fig. 3 – Intensities observed in the four IRAC bands toward IC443C. The horizontal andvertical axes show the R.A. (∆ α cos δ ) and declination (∆ δ ) offsets in arcsec relative to α = 06 h m s δ = +22 o ′ ′′ (J2000). The white lines demark the edges of theregions mapped in each band. The black circles centered at offset (–24 ′′ , –20 ′′ ) indicate theregions for which the average spectra shown in Figure 1 were obtained. 20 –Fig. 4 – Scatter plots comparing the IRAC-measured intensities , I Band 3 (IRAC) and I Band 4 (IRAC) on the vertical axis, with the intensities I Band 3 (H ) and I Band 4 (H ) expectedgiven the IRS-measured spectral line maps for H S(4) – S(7). Each point corresponds toa single 1 . ′′ × . ′′ pixel. Solid lines show the result of a linear regression. The slopes onthe best-fit linear relationships are 1.10 and 1.03 respectively for Bands 3 and 4, and they-intercepts are 2.0 and 2.5 MJy sr − . 21 –Fig. 5 – Maps comparing the IRAC-measured intensities , I Band 3 (IRAC) and I Band 4 (IRAC),with the intensities I Band 3 (H ) and I Band 4 (H ) expected given the IRS-measured spectrallines maps for H S(4) – S(7). The horizontal and vertical axes show the R.A. (∆ α cos δ )and declination (∆ δ ) offsets in arcsec relative to α = 06 h m s δ = +22 o ′ ′′ (J2000). 22 –Fig. 6 – Lower panel: map of the median-subtracted IRAC Band 3 / Band 4 ratio in IC443.The horizontal and vertical axes show the R.A. (∆ α cos δ ) and declination (∆ δ ) offsets inarcsec relative to α = 06 h m s δ = +22 o ′ ′′ (J2000). Regions in which the IRACintensities are small (with a median-subtracted Band 3 intensity less than 3 MJy sr − ) aresuppressed and appear in black. The white lines demark the edges of the regions mapped ineach band. Upper panel: a histogram indicates the relative number of pixels for which thelogarithm of the band ratio lies in a given range (arbitrary scaling). The colors appearingunderneath the histogram curve are matched to those appearing in the lower panel, so thehistogram serves as a color bar for the band ratio maps. Vertical dashed lines indicate thevalues of log(band ratio) corresponding to the lower sextile, median, and upper sextile of thedistribution. Black curves indicate how the expected band ratio (plotted logarithmically onthe horizontal axis ) depends upon the power-law index, b (appearing on the vertical axis anddefined in § densities of 10 (dotted curve), 10 (dot-dashedcurve), 10 (dashed curve) and 10 cm − (solid curve). 23 –Fig. 7 – Same as Fig. 6, except for the Band 1 / Band 2 ratio 24 –Fig. 8 – Same as Fig. 6, except for the Band 1 / Band 4 ratio 25 –Fig. 9 – Two-color diagram showing the Band 2 (4.5 µ m) / Band 4 (8.0 µ m) and Band 3(5.6 µ m) / Band 4 (8.0 µ m) ratios expected for pure H emission with an assumed visualextinction A V = 13 . densities of 10 (dotted curve), 10 (dot-dashed curve), 10 (dashed curve) and 10 cm − (solid curve). Re-sults are shown for a range of temperatures up to 2000 K (top right of each curve), withsquares every 100 K and crosses every 500 K. The open triangle represents the median bandratios observed in the IRAC maps, with the error bars designating the upper and lowersextiles, all obtained with the standard point source flux calibration that we consider appro-priate for this application (see discussion in § dN = aT − b dT (see eqn. 3) and b in the range 3 (top right of each curve) to 6. Results areshown for H densities of 10 (dotted curve), 10 (dot-dashed curve), 10 (dashed curve) and10 cm − (solid curve). Squares appear when b is an integral multiple of one-half, and crosseswhere b is an integer. 26 –Fig. 10 – Color-color diagrams for a selection of two pairs of band ratios, showing the two-dimensional distribution function for the logarithm of the observed band ratios. The falsecolor image (coded from black [smallest value] to blue to white [largest value]) representsthe number of pixels for which the band ratios show a given pair of values. Heavy whitecurves show the ratios expected for H emission from gas with a power-law distribution oftemperatures. Results are shown for H densities of 10 (dotted curve), 10 (dot-dashedcurve), 10 (dashed curve) and 10 cm − (solid curve). Light white curves show the loci forpower-law indices, b , of 3 (rightmost curve in top panel; uppermost curve in bottom panel),4, 5, and 6. The right panels are zoomed versions of the left panels. 27 –Fig. 11 – Fractional contribution of CO emissions to IRAC Band 2, as a function of H density and for an assumed CO/H abundance ratio of 10 − . Results are given for H/H abundance ratios of 0, 0.01, 0.1, and 1 (from bottom to top), and for temperature power-lawindices, bb