Ultraviolet Observations of Comet 96/P Machholz at Perihelion

Photoionization rates were computed based on extreme-ultraviolet fluxes from the SEE instrument on the TIMED satellite (Woods et al. 2000). Fluxes were not available for the day of our observations, so we used the spectrum from one solar rotation later. The photoionization cross sections were taken from Reilman & Manson (1979). Table 3 gives the rates at perihelion, 0.1241 au, and they can be scaled to the other heliocentric distances. They are compatible with the photoionization rates used in comet studies over many decades, the major uncertainty being the level of solar activity at the time of the observation.

Two other processes can affect the ionization state: collisional ionization by electrons and charge transfer. The electron density and temperature are not known within the ion tail, but we can consider neutral H atoms in the solar wind, taking reference values of T = 4.0 × 10⁵ K based on the cooling of the solar wind as it expands away from the corona and n_e = 400 cm⁻³ based on the typical mass flux at 1 au and an intermediate solar wind velocity. The inner parts of the expanding hydrogen cloud are likely to be shielded from the solar wind, but since the neutrals cross magnetic field lines, the outer regions are exposed to the wind. The other elements expand slowly away from the nucleus, and their ions are confined to the ion tail. The temperature in the ion tail must be at least 30,000 K as a result of the energy deposited by photoionization, and we use that value. The density is poorly known, but considering the carbon outgassing rate derived in Section 3.6, the velocity range discussed in Section 3.5, and the apparent tail diameter of about 5 × 10⁵ cm, the electron density due to carbon ions alone is more than 100 cm⁻³. Considering the electrons produced by ionization of other species, the total density must be around 1000 cm⁻³, and we use that value for Table 3.

The rate of charge transfer of H i with solar wind protons is typically higher than the photoionization rate. The solar wind mass flux is fairly constant, near 3 × 10⁸ cm⁻² s⁻¹ at 1 au (Wang 2010), so scaling to 0.124 au and multiplying by the cross section of 1.1 × 10⁻¹⁵ cm² (Schultz et al. 2008) gives 2.2 × 10⁻⁵ s⁻¹. The charge-transfer process produces neutral H atoms with the solar wind speed and velocity distribution. While such neutrals produce the Lyα tails of sungrazing comets in the static corona near the Sun, in the case of Comet Machholz at 0.124 au, they are severely Doppler dimmed and do not contribute significantly to the observed Lyman line intensities. If they did contribute, they would be distinguished by a blueshift and line width determined by the solar Lyα profile and the velocity distribution of the solar wind protons, or around 100 km s⁻¹. One other charge-transfer process may be important. Because the ionization potentials of H and O are nearly equal, the charge transfer between neutral H and O⁺, along with its inverse, is relatively fast. The table gives the rate based on the Kingdon & Ferland (1996) cross section, a temperature of 30,000 K, and a neutral hydrogen density of 1000 cm⁻³, as would be typical for a distance of 0.1 R_⊙ from the nucleus and an outgassing rate of 5 × 10²⁹ s^–1. It is slow enough compared to the photoionization rate that it can be neglected.

We note, however, that compression and heating of electrons by the bow shock or plasma waves could increase the collisional ionization and excitation rates. Feldman et al. (2018) discussed signatures of collisional excitation and dissociation in the ALICE spectra of Comet 67P/Churyumov–Gerasimenko, and Cravens et al. (1987) used a three-temperature approximation to the electron distribution measured near Comet Halley by Gringauz et al. (1986) to compute ionization rates. In the case of Comet Machholz, the bow shock standoff distance is of order 10⁸ cm, which is small compared to the UVCS resolution elements. Nevertheless, the high density in that small region might make collisional processes significant.

Table 4 gives the photoexcitation rates of the lines we observe. The line intensities at 0.124 au are given in 10⁹ ph (cm² s)⁻¹ in a wavelength interval corresponding to 30 km s⁻¹ for H and 3 km s⁻¹ for the other ions. The scattering cross sections are inversely proportional to this assumed line width, so the width cancels out provided that the absorption profiles are narrow. The spectral fluxes at the line center for Lyα and Lyβ are based on TIMED/SEE fluxes, scaled from total flux to line center spectral flux with the formulae of Lemaire et al. (2015). The profile of Lyγ was not included in Lemaire et al. (2015), so we estimate the line shape from the figure in Curdt et al. (2001). The O i and C ii values are peak fluxes from the Curdt et al. (2001) SUMER atlas for the quiet Sun, scaled from solar minimum to the time of observation based on the assumption that they scale with Lyβ. The C iii and N iii lines are formed at higher temperatures. We assume that the increase in Lyβ compared to solar minimum results from the presence of active regions, and we use the quiet Sun–to–active region contrast given by Vernazza & Reeves (1978) to estimate the fraction of the Sun covered by active regions. We then use the contrast between the quiet Sun and active regions in the C iii and N iii lines to scale by a factor of 1.6 from the peak SUMER fluxes of Curdt et al. (2001).

Table 4 also gives the populations of the lower states that can absorb photons if statistical equilibrium within the ground levels holds, for instance, for the ²P_1/2 and ²P_3/2 states of N iii and the ³P₂, ³P₁, and ³P₀ states of O i. The oscillator strengths, f, for H i are from the NIST database (DOI:10.18434/T4W30F), those for O i are from Morton (1991), and those for C ii, C iii, and N iii are from Tachiev & Froese Fischer (1999) and Liang et al. (2012) from the CHIANTI (Del Zanna et al. 2021) database. The scattering cross sections, q_exc, are proportional to the oscillator strength, f, and branching ratios of 0.88 and 0.84 are included for Lyβ and Lyγ, respectively.

Because Comet Machholz was at perihelion, its velocity component toward the Sun was essentially zero, so Doppler dimming (reduction of the scattering rate when an atom is Doppler shifted away from the solar Lyα emission profile, somewhat analogous to the Swings effect) should not be significant. The plasma velocity within the ion tail is not independently known, however. Since the solar disk lines that illuminate the ions are fairly narrow, plasma speeds as low as 40 km s⁻¹ could lead to significant Doppler dimming. We will return to this point in discussing the elemental abundances.

Finally, we must consider the opacity in the Lyα line. For an outgassing rate of a few times 10²⁹ s⁻¹, the optical depths between the nucleus and the Sun and between the nucleus and SOHO are each expected to be on the order of 1. We can assess the optical depth from the crossings that measured both Lyα and Lyβ intensities, since their ratio is constant for optically thin scattering. Crossings 2, 4, and 5 all showed an increase in the Lyβ/Lyα ratio by a factor of 2.2 close to the nucleus, meaning that Lyα was attenuated by a total optical depth (comet–Sun and comet–SOHO) of τ ≈ 0.8. The observations of these three crossings were highly binned in the spatial direction in order to give the broadest possible wavelength coverage, so that 0.8 is the weighted average of τ over a 14'' × 70'' spatial bin, or about 8600 × 43,000 km.

The H i Lyα radiance profiles of the comet obtained during the first and last crossings (1 and 7 in Table 1) through the UVCS slit were least-squares fitted to a Haser model with H atom velocities of 20 and 8 km s⁻¹ (from photodissociation of H₂O and OH, respectively). In the model, described by Mancuso (2015), the value for the lifetime τ_H of the H atoms was left as a free parameter, together with the unknown outgassing rate, ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$, to be solved by comparing the coma model with the Lyα radiance measured along the UVCS slit from the exposures containing the nucleus. The model was applied to the data by imposing the same value of τ_H for the two crossings. More details on the other assumed parameters can be found in Mancuso (2015). The best-fit ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ values estimated near perihelion for the two UVCS crossings are, respectively, 5.09 × 10²⁹ and 4.58 × 10²⁹ molecules s⁻¹, with a best-fitting τ_H = 1.5 × 10⁶ s. However, that value of τ_H corresponds to a length scale above 10¹² cm, which is much larger than the extent of the measured radiance profiles, and it is therefore uncertain. In Figure 4, we compare our results for ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ with the ones obtained by Combi et al. (2011, 2019) with SOHO/SWAN at larger heliocentric distances as part of the full-sky imaging program during the apparitions near perihelion of 1996, 2002, 2007, and 2012. An average power-law fit (4.71 × 10²⁷ r(au)^−2.14 molecules s⁻¹) to the SWAN estimates with respect to heliocentric distance is also superposed to the data. Despite the small perihelion distance and resulting activity, no apparent long-term decrease in ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ was evident over a decade. As is evident from visual inspection of Figure 4, the results obtained near perihelion with the two UVCS measurements are fully consistent with the ones estimated by SWAN at larger distances. The peak Lyα intensities were higher by 20%–30% in crossings 4 and 5, indicating a slight increase in the outgassing rate. Other complications, including optical depth in Lyα and the effects of radiation pressure on the H i atoms, are discussed below, and they might alter the inferred water production rate at the 20%–30% level.

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To aid in interpreting the observations, we constructed models of the Lyα intensity and average velocity as seen from SOHO. Hydrogen atoms produced by photodissociation of H₂O and OH receive some kinetic energy, and most have initial speeds of 8–24 km s⁻¹. In the frame of the comet, they form a slowly expanding cloud, which we assume to be spherical. The atoms are destroyed by photoionization or collisional ionization at the rates given in Table 3. They also undergo charge transfer with solar wind protons, in which case they have the solar wind velocity and effectively cease to scatter Lyα photons due to Doppler dimming (the Swings effect). Thus, there is an exponential cutoff at a timescale of about t_cut = 2.7 × 10⁴ s, which corresponds to a spatial scale somewhat below 1 R_⊙. That is similar to the extent of the measured Lyα cloud.

Radiation pressure accelerates the H atoms, and the scattering rate in Table 4 implies an acceleration of 73 cm s⁻². In fact, the radiation pressure acceleration is comparable to the gravitational acceleration, just as for the micron-sized dust grains that are seen as the optical tail. Of course, the dust grains last much longer, and the range of sizes produces a range of ratios of radiative to gravitational forces. The main difference is that the H atoms are ejected at speeds an order of magnitude faster than the dust grains, so radiation pressure has a correspondingly smaller effect.

Given the initial speed and the acceleration, each atom follows an analytically described path relative to the nucleus. For a given initial speed, we eject particles at 1° intervals in altitude and azimuth about the axis pointing toward the Sun. Each particle scatters Lyα photons at the rate given in Table 4 multiplied by exp(−t/t_cut) to account for the destruction of the H atoms. The optical depth in Lyα can be significant, so we use the computed density of H atoms to calculate the optical depth between each point and the Sun and multiply the emissivity by exp(−τ). For the optical depth calculation, we approximate the velocity profile as a top hat with a width of twice the initial speed. This is somewhat crude, but the optical depth is only significant close to the nucleus for the outgassing rate of Comet Machholz.

The emission is computed in a 501 × 501 × 501 grid of cells of 7'' as seen from SOHO, which was 0.86 au from the comet during the first crossing. The 3D model was then rotated to match the SOHO point of view. Because the phase angle was in the range 162°–167° during these observations, the line of sight is not far from the vector between the comet and the Sun. Therefore, the radiation pressure accelerates atoms toward SOHO.

We then sum the emission along each line of sight to produce a 2D model of the Lyα intensity, and we average the velocity to predict the velocity centroids as a function of distance from the nucleus. Figure 5 shows the predicted intensity image for an initial speed of 16 km s⁻¹. While the contours are approximately circular, the outer contours are displaced somewhat away from the Sun relative to the nucleus.

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Though the hydrogen atoms follow different trajectories depending upon their initial velocities, the basic expectation is that they will be accelerated to speeds of order 20–30 km s⁻¹ away from the Sun as they travel a distance of order 1 R_⊙ from the nucleus. Because our line of sight is not far from the comet–Sun line, most of that velocity will appear as a blueshift that gets stronger with distance from the comet. Figure 6 shows the velocity centroid as a function of distance from the nucleus measured during the first slit crossing. It is compared with the prediction of the model for a cut through the nucleus at an angle of 30°, approximately the angle between the comet's trajectory and the slit. This model assumed that H atoms leave the coma at 16 km s⁻¹.

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The predicted velocity profile clearly leaves something to be desired. The motion of the comet during the three exposures that were averaged can account for some, but not all, of the discrepancy near the peak. Some of the discrepancy results from smoothing of the observations near the nucleus by the UVCS instrument profile at the fairly extreme grating position used here. We do not have exact figures, but we believe that the profile is smoothed by as much as 70'' in the spatial direction. In addition to the sharper peak of the predicted profile, the velocity centroid falls off too slowly as a function of distance ahead of the nucleus. A smaller initial speed would help somewhat, but that would cause the intensity to drop too quickly behind the nucleus.

There are serious limitations to the simple model. In particular, we assume that all of the hydrogen atoms are isotropically ejected at velocities of 16 km s⁻¹, while the speeds range from about 8 to 24 km s⁻¹. In addition, our treatment of optical depth effects is crude, and that will affect the line profile near the nucleus. Nevertheless, Figure 6 does show a zeroth-level agreement in that there is a blueshift of about 30 km s⁻¹ at distances of about 150 pixels or about 1 R_⊙ from the nucleus. With the help of more sophisticated models, it might be possible to constrain the initial velocity distribution of the H atoms. In particular, if the H atoms lose very much momentum to heavier atoms such as O by collisions during the initial expansion, that would imply longer times to reach 1 R_⊙ from the nucleus and blueshifts larger than those observed. At the high outgassing rates inferred above, the H atoms are expected to lose a considerable amount of momentum on collisions with oxygen (Combi & Smyth 1988). Perhaps low-velocity H atoms contribute to the region of small Doppler shifts near the nucleus seen in Figure 6.

We reconstruct intensity images with the method used for past UVCS observations of comets (Povich et al. 2003; Bemporad et al. 2005; Giordano et al. 2015), in effect using the motion of the comet across the slit as though we were making a raster scan of the slit across the comet. For each exposure, we measure the intensity of a line in each spatial bin along the slit and place it in a 2D array. The velocities of the comet perpendicular and parallel to the slit are known from the comet's orbit and the position angle of the slit. We multiply those velocities by the time between exposures (exposure time plus readout time, or about 130 s) and offset the intensities from subsequent exposures accordingly.

Figure 7 shows the composite LASCO images and reconstructed Lyα images from UVCS spectra at crossings 1, 2, 5, and 7, when Lyα was detected. Those images allow the comparison of the shape and orientation of the comet. The Lyα cloud is approximately, but not exactly, spherical, as predicted by the model in the previous section. A similar departure from spherical expansion was seen in reconstructed Lyα images of Comet Encke (Raymond et al. 2002). Figure 8 shows a larger version of the Lyα image from the first crossing, with contours indicating the intensity.

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A notable feature of the reconstructed images is the ion tail in C iii λ977 emission seen in Figure 9. A similar C iii tail was found in images reconstructed from UVCS spectra in Comet Kudo–Fujikawa (Povich et al. 2003). In that case, the ion tail was interrupted, apparently as a result of a disconnection event caused by interaction with a reversal in the direction of the interplanetary field (Brandt & Snow 2000). The image of the ion tail of Comet Machholz as seen from SOHO is foreshortened by about a factor of 2.4 because our line of sight is not far from the comet–Sun line. The angle between the C iii tail and the comet trajectory is roughly 70°. Assuming that material in the tail moves radially away from the Sun, and correcting for the projection due to the viewing angle, the angle between the tail and the comet's path implies a velocity of the material in the tail of about 100 km s⁻¹. That is in line with Scherb et al. (1990) and Rauer & Jockers (1993), who measured Doppler shifts increasing to 70 km s⁻¹ for H₂O⁺ ions along the tails of comets Halley and Levy 1990c, respectively. It is also in line with Jockers et al. (1972), who found that the motions of features along the plasma tail of Comet Tago–Sato–Kosaka 1969 IX increased from 40 km s⁻¹ close to the comet to 300 km s⁻¹ farther away. Unfortunately, we cannot directly measure the velocity by means of the Doppler shift because of the 150μ slit width used for this observation and the uneven filling of the slit, which can shift the line centroid to the red or blue during different exposures.

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An important consequence of the acceleration of C iii ions to speeds above 50 km s⁻¹ is severe Doppler dimming. The C iii line from the disk is only about 50 km s⁻¹ wide FWHM (Feldman et al. 2011). The width of the C iii velocity distribution in the tail is difficult to measure because of the large slit width, but FWHM < 120 km s⁻¹ is an upper limit. Acceleration of the plasma along the ion tail could strengthen the Doppler dimming and cause the observed fading with distance from the nucleus. However, the fraction of carbon in the form of C iii is very small near the nucleus (see Table 5 below) and apparently much larger in the tail, judging by the C iii/C ii ratio (Table 2). That offsets some of the effect of Doppler dimming. Some kinetic heating of the C iii ions by the process that accelerates the plasma tail could also reduce the Doppler dimming effect.

Table 5. Coma Column Densities and Outgassing Rates

Ion	λ	N	n	$\dot{N}$
	(Å)	(1012 cm−2)	(cm−3)	(1028 s−1)
H i Lyβ	1025.73	29.0	10,400	38.0
H i Lyγ	972.54	35.0	12,300	45.0
C ii	1036, 1037	2.8	992	0.73
C iii	977.03	0.31	110	0.008
N iii	989, 990	<1.4	<510	<0.37
O i	988.75	38.0	13,600	10.0
O i	990, 991	47.0	16,800	12.4
O i	1027, 1028	58.0	21,000	15.7

Download table as:  ASCIITypeset image

The elemental abundances are of special interest because of the unusually low C₂ and C₃ abundances relative to NH₂ in Comet Machholz (Langland-Shula & Smith 2007; Schleicher 2008).

Abundance analyses of sungrazing comets observed by UVCS yield total abundances because dust grains rapidly sublimate close to the Sun (Kimura et al. 2002). At 0.124 au, however, the sublimation times are longer, so the spectra of Comet 96/P Machholz reveal the composition of the volatile component. The intensities observed in the coma in Table 2 can be multiplied by 4π and divided by the photon scattering rates in Table 4 to obtain the column densities of the atoms and ions observed. The line-of-sight depth can be estimated from the size of the spatial element. Dividing that into the column density gives the density. We take the line-of-sight depth to be the average of the long and short dimensions of the 21'' × 70'' spatial element at a distance of 0.86 au, or 2.8 × 10⁹ cm. Finally, multiplying by the outflow speed and 4π gives the outgassing rate. We present those rates in Table 5 separately for each line to provide a consistency check. We assume outflow speeds of 15 km s⁻¹ for H and 3 km s⁻¹ for the other elements.

The C/O ratio is probably the most reliable because C and O atoms should have similar velocities as they leave the coma. The O/H ratio is more questionable because the O and H velocities are different (Combi & Smyth 1988), and both are uncertain. In addition, the H abundance determined from Lyα is subject to optical depth uncertainty, and it may be affected by radiation pressure on the H atoms. The factor of 1.5 discrepancy in the rate of production of O determined from different O i lines may be due to uncertainty in the measured intensity of the lines at 1027 and 1028 Å, which are on the wing of the much brighter Lyβ line. However, one expects a hydrogen-to-oxygen ratio of 2:1, and the derived ratio is twice that. If CO or CO₂ contributes a significant amount of O, the discrepancy is made worse. The easiest explanation would be that the oxygen outflow rate is larger than we assumed.

Close to the nucleus, the carbon is mostly C ii because C i is rapidly photoionized, and it takes so long to ionize C ii to C iii that only about 1% of the carbon in the central region is C iii. Overall, we estimate the ratio of the outgassing rates of carbon and nitrogen as $\dot{N}$(C)/$\dot{N}$(H) ∼ 0.02. For comparison, the sungrazer C/2003 K7 showed $\dot{N}$(C)/$\dot{N}$(H) = 0.0006–0.018, even with substantial dust sublimation at 3.37 R_⊙ (Ciaravella et al. 2010). We find that $\dot{N}$(C)/$\dot{N}$(O) < 1/10 in Comet Machholz, suggesting that much of the carbon could be locked up in dust.

Unfortunately, $\dot{N}$(N) is poorly constrained because we have no N ii lines and only an upper limit on N iii. There is no obvious enhancement of nitrogen ions, which may be surprising in view of optical indications of strong NH₂ emission compared to C₂ and C₃. That might again indicate that much of the carbon remains locked in grains or is in the form of CO or CO₂.

We do not detect any Si lines, unlike in comets C/2011 W (Lovejoy) and C/2003 K7 (Ciaravella et al. 2010; Raymond et al. 2018). That is probably due to the fact that Comet Machholz was beyond the heliocentric distance where silicate grains can rapidly sublimate, and it is likely that nearly all of the silicon is in grains.

As noted in Section 3.1, collisional excitation and ionization could contribute to a degree not included in our estimates. However, the scale of the bow shock region where such processes will be strong is roughly 1''², compared with a spatial resolution element of 1400''² for crossing 3.