deVico 1995 S1

Icarus 186 (2007) 178–191 www.elsevier.com/locate/icarus

CN, C2 radicals and dust in Comets Shoemaker–Levy 1991 T2 and P/deVico 1995 S1 Wacław Waniak ∗ , Maciej Winiarski, Paweł Magdziarz, Tomasz Kundera Astronomical Observatory of the Jagiellonian University, 30-244 Cracow, Orla 171, Poland Received 30 June 2004; revised 2 August 2006 Available online 24 October 2006

Abstract The results of the multiaperture photometry of Comet Shoemaker–Levy 1991 T2 in the pre-perihelion and P/deVico in the post-perihelion period with the narrowband CN, C2 and Blue Continuum (BC) IHW filters are presented. A Haser model of the molecular coma was used for the determination of the parent and daughter scale-lengths and production rates of the radicals. The comets showed some substantial differences between their parent scale-lengths. The CN parent scale-length (at 1.0 AU) was 16 × 103 km for Comet Shoemaker–Levy and 39 × 103 for P/deVico, the C2 parent scale-lengths were respectively 29 × 103 and 54 × 103 km. Such divergences could be interpreted in the frame of different scenarios of emission of cometary parents, either from a nucleus or from a volume source. The daughter scale-lengths for these comets were quite similar, namely: 306 × 103 and 318 × 103 km for CN and 69 × 103 and 66 × 103 km for C2 . We determined the Afρ parameter for apertures of different radii. A Monte Carlo model of the dust coma was used to obtain the dust ejection velocity. It was of the order of 0.1 km s−1 for both comets. The power index of the distribution of the β-parameter of dust particles (ratio of light pressure to the solar gravitation) was of the order of 3 for C/Shoemaker–Levy and close to 2 for P/deVico. The dependence on heliocentric distance (rh ) of the radical and dust production rates for P/deVico in the range of 0.7–1.0 AU was described by the power law function rh−α with a power index equal to: 5.55 ± 0.14 for CN, 5.70 ± 0.24 for C2 and 5.22 ± 0.19 for dust. Relative abundances of the dynamically new Comet Shoemaker–Levy and short-period P/deVico were quite similar with an enhancement of C2 comparing with standard values taken from A’Hearn et al. (1995). © 2006 Elsevier Inc. All rights reserved. Keywords: Comets, composition

1. Observations A narrowband multiaperture photometry of dynamically new Comet Shoemaker–Levy 1991 T2 was carried during the pre-perihelion period in June and July 1992. Post-perihelion observations of Comet P/deVico (1995 S1) were made in October and November 1995. Both comets were observed at the Cracow Observatory (Cassegrain reflector referred to henceforth as C500, equipped with a EMI 9789QB photomultiplier + photon counter) and at the Observational Station in the Bieszczady Mountains (refractor referred to henceforth as R203, equipped with a Sb-Cs FEU-92 photomultiplier + current to voltage converter). Table 1 contains information about the telescopes and photometric systems used. The central wavelength λ0 and * Corresponding author. Fax: +48 12 4251318.

E-mail address: [email protected] (W. Waniak). 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.08.010

FWHM of the filters refer to the transmission curves obtained for the convergent light beam given by the telescope. The brightness of the coma was recorded with a set of circular diaphragms of different radii pointed at the central condensation. The sky background was measured at least 1◦ from the nucleus, thereby avoiding the comet’s tail. In some cases multiple measurements for a given diaphragm and a given filter were carried out during a single run. Thus, we could examine the dependency of the internal photometric error on the diaphragm radius. We expected the main source of the error for the smallest apertures to be a pointing effect (the precision of our centering was better than a couple of arcsec). The results for the largest diaphragms could have been influenced by the sky background. However, no significant correlation between the photometric error and the diaphragm radius was found. Due to this circumstance we estimated the mean internal photometric error for a given filter during the entire period of our observa-

Narrowband photometry of C/Shoemaker–Levy and P/deVico

Table 2 Narrowband magnitudes of the standards

Table 1 Telescopes and interference filters used during observations Telescope

Filter

λ0 [nm]

FWHM [nm]

R203

CN BC C2 CN BC C2

387.1 493.2 514.4 387.2 493.2 516.2

4.1 7.0 8.4 4.2 7.5 8.2

C500

179

Note. R203, refractor placed at the Roztoki Observational Station in the Bieszczady Mountains; D = 203 mm, F = 3000 mm. C500, Cassegrain telescope placed at the Cracow Observatory, D = 500 mm, F = 6670 mm.

tions, averaging the results for different diaphragms. For Comet Shoemaker–Levy we obtained 0.05, 0.12 and 0.06 mag for CN, BC and C2 pass-bands. For P/deVico we determined 0.07, 0.06 and 0.04 mag for CN, BC and C2 . Flux calibration was achieved through observations of standard stars. Their synthetic narrowband magnitudes were obtained using spectra constructed by least-square fitting of the theoretical spectrophotometry given by Kurucz (1979) to the monochromatic magnitudes contained in Breger’s catalogue (Breger 1976a, 1976b). Different sets of standards were used on different nights. Thus, our approach could produce systematic errors in the absolute calibration of a comet’s brightness due to uncertainties and biases affecting our synthetic magnitudes. To avoid this, a set of internally consistent magnitudes was prepared for each comet. We measured the differences of narrowband magnitudes between almost all the standards. Next, the least-square approach was used to correct the theoretical values, assuming that the mean magnitude of all the standards before and after the correction should be the same. We supposed that all the discrepancies were in the synthetic magnitudes because we obtained them from theoretical spectra. Moreover, the mean errors of the observational differences (0.02 mag for CN, and 0.01 mag for BC and C2 ) were markedly smaller than the expected corrections. Table 2 presents the spectral types of the standards and their magnitudes both, synthetic—msyn and observationally corrected—mcorr . In the case of the Shoemaker–Levy comet the residual internal inconsistencies of the magnitudes are close to 0.03 for CN, BC and 0.02 for C2 . For P/deVico they are 0.03 for CN, C2 and 0.02 for BC, respectively. One pair of stars, i.e. BS 4883 and BS 4983, belongs to both ensembles of standards. Thus, we can get a rough idea of the errors of the zero points of these two sets by taking the mean discrepancies between their magnitudes in relation to both groups. They are of the order of 0.04 mag for CN and C2 and 0.06 for BC. It is important to bear in mind that such an error of the zero point has a very slight impact on the molecular scale-lengths given by the Haser model and the form of the temporal behavior of production rates of radicals and dust. The second order effect appearing when continuum measurements are subtracted from the molecular fluxes should not exceed a few milimagnitudes. The flux contribution produced by stars incidentally observed together with a comet through a given diaphragm were subtracted. Stars fainter than about 9.5 V mag have been disregarded, bearing in mind the precision of our observations.

BS

Sp.

CN Syn.

BC Corr.

Syn.

0542 3624 4033 4694 4883 4983 5062 5404 5982

B3 III Am A2 IV F0 IV G0 III G0 V A5 V F7 V B9 III

Comet Shoemaker–Levy 3.083 3.008 3.320 5.254 5.280 4.827 3.567 3.518 3.592 6.606 6.627 6.295 6.128 6.105 5.166 5.175 5.276 4.452 4.355 4.324 4.214 4.818 4.848 4.223 4.501 4.501 4.692

4300 4883 4983 5447 5971

A1m G0 III G0 V F2 V A0 II-III

4.734 6.128 5.175 5.010 4.718

Comet P/deVico 4.598 4.363 6.055 5.166 5.239 4.452 4.994 4.639 4.879 4.882

C2 Corr.

Syn.

Corr.

3.359 4.836 3.444 6.359 5.243 4.478 4.099 4.252 4.711

3.285 4.716 3.402 6.153 5.070 4.360 4.001 4.124 4.669

3.317 4.719 3.352 6.194 5.087 4.351 3.981 4.122 4.657

4.390 5.173 4.434 4.583 4.922

4.359 5.070 4.360 4.498 4.856

4.361 5.039 4.320 4.489 4.934

Note. msyn , narrowband magnitudes synthesized basing on the Breger spectrophotometry + Kurucz model spectra, and mcorr , narrowband magnitudes observationally corrected.

The extinction coefficients were determined almost every night. In other cases we used mean seasonal values. The mean errors of the extinction reduction for Shoemaker–Levy were 0.02 mag for CN and 0.01 mag for BC, C2 filters. In the case of P/deVico the corresponding errors were 0.02 for CN, BC and 0.01 for C2 . Tables 3 and 4 give the narrowband flux for both comets. To obtain the level of error in this case, one should put together all the uncertainties described above. We examined the changes of the total photometry error from night to night and from aperture to aperture and came to the conclusion that we can characterize the precision of our photometry for a given filter as the mean value averaged over the whole period of observations and the whole set of diaphragms. The mean errors of the flux for Shoemaker–Levy were close to 5% for CN, 11% for BC and 6% for C2 . For P/deVico the errors were 7, 6 and 5% for CN, BC and C2 , respectively. The values cited here do not take into account the uncertainty of the zero points of our photometric system, which are around a few percent. 2. Numbers of the molecules In order to determine the molecular emission, the cometary continuum was subtracted. Since the BC flux is contaminated by the short-wavelength wing of the C2 0–0 band we should jointly reduce the BC and C2 observations made with the same diaphragm. Unfortunately, in the case of P/deVico during the first two nights (Oct. 13.1 and 14.1) the C2 filter was not used. Thus, we determined the mean contribution of the C2 emission to the BC pass-band for the second group of nights when both filters were used. We assumed a 13% reflectivity gradient of the cometary dust at wavelengths where the two filters are centered (Jewitt and Meech, 1986). This result seems to be corroborated by Thomas and Keller (1989). Although, in general, the reflectivity gradient decreases with the wavelength and can

180

W. Waniak et al. / Icarus 186 (2007) 178–191

Table 3 Narrowband flux F , number of the molecules Nm and the Afρ dust parameter for the diaphragms used during the observations of Comet Shoemaker–Levy UT date (1992)

z [deg]

rh [AU]

 [AU]

log F [erg cm−2 s−1 ], log Nm or log Afρ [cm]

Rdia [arc sec] = 18

C500 June 25.90÷25.98

53÷50

0.990

1.109

June 27.94÷27.98

52÷49

0.971

1.068

June 28.88÷28.97

52÷50

0.962

1.049

June 29.87÷29.98

52÷50

0.953

1.031

June 30.92÷30.99

52÷51

0.944

1.013

July 01.90÷01.96

50÷52

0.936

0.997

July 06.95÷07.02

55÷58

0.898

0.930

July 08.97÷09.02

58÷62

0.885

0.912

July 09.92÷09.97

53÷62

0.880

0.906

July 17.90÷17.92

64÷69

0.845

0.906

July 20.90÷20.93

70÷77

0.839

0.931

−10.216 29.67 −10.215 29.62 −10.310 29.50 −10.139 29.65 −10.213 29.55 −10.092 29.66 −10.110 29.55 −9.935 29.69 −9.964 29.63 −9.824 29.81 −9.862 29.83

Rdia [arc sec] = 46

R203 June 26.00÷26.03

50÷48

0.989

1.107

June 28.86÷28.88

52÷53

0.962

1.050

June 30.88÷30.90

51÷52

0.945

1.014

June 01.92÷01.93

51÷52

0.936

0.997

June 01.98÷02.00

52÷53

0.936

0.996

July 08.90÷08.96

54÷56

0.886

0.913

July 09.91÷09.93

54÷60

0.880

0.906

July 16.86÷16.89

57÷64

0.848

0.901

July 20.87÷20.89

66÷72

0.839

0.931

July 21.87÷21.90

69÷75

0.838

0.941

July 22.85÷22.87

66÷71

0.837

0.953

– – – – – – – – – – −9.568∗ 30.06∗ −9.505 30.10 −9.412 30.21 −9.525 30.17 −9.793∗ 29.91∗ −9.691∗ 30.05∗

26 −10.029 29.86 −10.032 29.81 −10.128 29.69 −9.928 29.87 −9.975 29.80 −9.974 29.78 −9.833 29.84 −9.755 29.87 −9.765 29.84 −9.600 30.04 −9.654 30.05

35 CN filter −9.921∗ 29.97 ∗ −9.850 29.99 −9.872 29.95 −9.778 30.02 −9.778 30.00 −9.767 29.99 −9.656 30.01 −9.601 30.03 −9.572 30.03 −9.445 30.20 −9.587 30.11

48

71

99

140

198

277

−9.707 30.18 −9.658 30.19 −9.687 30.13 −9.626 30.17 −9.622 30.15 −9.788∗ 29.96∗ −9.566 30.10 −9.430 30.20 −9.419 30.19 −9.310 30.34 −9.502 30.20

−9.502 30.39 −9.454 30.39 −9.508 30.31 −9.420 30.38 −9.432 30.35 −9.334 30.43 – – −9.249 30.38 −9.231 30.38 – – −9.048 30.67

−9.348 30.55 −9.314 30.53 −9.376 30.45 −9.293 30.51 −9.313 30.47 −9.282 30.48 – – −9.123 30.51 −9.116 30.49 – – – –

−9.215 30.68 −9.206 30.64 −9.213 30.61 −9.198 30.60 −9.160 30.62 – – – – – – −9.007 30.60 – – – –

– – −9.114 30.73 −9.099 30.73 −9.066 30.74 – – – – – – – – −8.956 30.65 – – – –

– – – – −9.006 30.82 – – – – – – – – – – – – – – – –

59

62

87

112

163

216

317

−9.701 30.19 −9.566 30.25 −9.479 30.30 −9.539∗ 30.21∗ −9.592∗ 30.16∗ −9.395 30.24 −9.335 30.27 −9.276 30.35 −9.341 30.36 −9.576∗ 30.14∗ −9.545 30.20

– – – – – – – – – – −9.416∗ 30.21∗ −9.314 30.30 −9.247 30.38 −9.424 30.27 – – −9.435 30.32

−9.507 30.38 −9.386 30.43 −9.357 30.42 −9.314 30.44 −9.402∗ 30.35∗ −9.194 30.44 −9.163 30.45 −9.052 30.57 −9.214 30.49 −9.422 30.30 −9.287 30.47

−9.358 30.54 −9.288 30.53 −9.246 30.53 −9.130 30.63 −9.225 30.53 −9.100 30.54 −9.071 30.54 −9.007 30.62 −9.084 30.62 −9.182 30.55 −9.186 30.57

−9.220 30.67 −9.194 30.63 −9.058 30.72 −9.018 30.74 −9.031 30.73 −8.965 30.67 −8.922 30.69 −8.868 30.76 −8.982 30.73 −9.137 30.59 −9.032 30.73

−9.073 30.82 −9.068 30.76 −9.005 30.78 −8.924 30.84 −8.983 30.78 −8.870 30.77 −8.842 30.77 −8.814 30.81 −8.912 30.80 −9.012 30.72 −9.024 30.74

−9.106 30.79 −9.014 30.81 −8.930 30.85 −8.828 30.93 −8.914 30.84 −8.770 30.87 −8.758 30.86 −8.744 30.88 −8.798 30.91 −8.992 30.74 −8.881 30.88

BC filter Rdia [arc sec] = 18

C500 June 25.89÷25.98

53÷50

0.990

1.109

June 27.90÷27.99

52÷49

0.971

1.068

June 28.89÷28.97

52÷50

0.962

1.049

June 29.88÷29.98

52÷50

0.953

1.031

June 30.94÷30.99

52÷51

0.944

1.013

−11.036 2.607 −10.980 2.637 −11.167∗ 2.421∗ −10.920 2.660 −11.148∗ 2.384∗

26

35

48

71

99

140

198

277

−10.924 2.562 −10.870 2.597 −11.109∗ 2.317 ∗ −10.810 2.625 −10.883 2.524

−10.781 2.569 −10.774 2.540 −10.872 2.419 −10.785 2.491 −10.687 2.587

−10.692 2.521 −10.642 2.538 −10.703 2.453 −10.613 2.539 −10.600 2.537

−10.573 2.458 −10.522 2.480 −10.610 2.361 −10.475 2.500 −10.499 2.456

−10.453 2.447 −10.468 2.382 −10.543 2.285 −10.396 2.435 −10.436 2.373

−10.373 2.364 −10.429 2.261 −10.400 2.285 −10.384 2.284 −10.150∗ 2.535∗

– – −10.384 2.150 −10.319 2.222 −10.288 2.237 – –

– – – – −10.359 2.031 – – – –

(continued on next page)

Narrowband photometry of C/Shoemaker–Levy and P/deVico

181

Table 3 (continued) UT date (1992)

z [deg]

rh [AU]

 [AU]

log F [erg cm−2 s−1 ], log Nm or log Afρ [cm]

July 01.93÷01.97

50÷52

0.936

0.997

July 06.96÷07.03

55÷58

0.898

0.930

July 08.98÷09.02

58÷62

0.885

0.912

July 09.92÷09.97

53÷62

0.880

0.906

July 17.91÷17.92

64÷69

0.845

0.906

July 20.91÷20.93

70÷77

0.839

0.931

−11.320∗ 2.195∗ −10.982∗ 2.503∗ −10.724 2.741 −10.745∗ 2.712∗ −10.594∗ 2.830∗ −10.651∗ 2.778∗

June 28.98÷29.00

52÷50

0.961

1.048

June 30.93÷30.94

52÷53

0.944

1.013

July 01.93÷01.95

52÷53

0.936

0.997

July 09.01÷09.03

63÷64

0.885

0.912

July 10.02÷10.03

64÷66

0.879

0.906

Rdia [arc sec] = 46

R203

– – – – – – – – −10.414 2.672

−10.818 2.591 −10.677 2.665 −10.570 2.751 −10.571 2.746 −10.377 2.905 −10.443 2.850

−10.670 2.592 −10.562 2.661 −10.454 2.729 −10.454 2.718 −10.290 2.845 −10.334 2.811

−10.684 2.424 −10.577 2.455 −10.371 2.673 −10.348 2.690 −10.155 2.853 −10.122 2.907

−10.414 2.539 – – −10.214 2.663 −10.199 2.670 – – −10.193 2.633

−10.520 2.292 – – −10.175 2.555 −10.176 2.545 – – – –

– – – – – – −10.070 2.503 – – – –

– – – – – – −9.930 2.508 – – – –

59

62

87

112

163

216

317

−10.581 2.529 −10.515 2.563 −10.566∗ 2.486∗ −10.388 2.590 −10.293 2.692

– – – – – – – – −10.347 2.587

−10.494 2.433 −10.433 2.469 −10.302 2.603 −10.257 2.559 −10.191 2.622

−10.405 2.427 −10.353 2.444 −10.292 2.498 −10.157 2.552 −10.154 2.544

−10.262 2.410 −10.267 2.360 −10.186 2.439 −10.107 2.433 −10.052 2.487

−10.132 2.429 −10.135 1.386 −10.102 2.403 −10.100 2.315 −10.110 2.286

−10.050 2.348 −9.913∗ 2.463∗ −10.156 2.151 −10.017 2.240 −10.011 2.232

– – – – – – – – – – – –

C2 filter Rdia [arc sec] = 18

C500 June 25.89÷25.98

53÷50

0.990

1.109

June 27.94÷27.99

52÷49

0.971

1.068

June 28.89÷28.97

52÷50

0.962

1.049

June 29.88÷29.98

52÷50

0.953

1.030

June 30.91÷30.99

52÷51

0.944

1.013

July 01.90÷01.97

50÷52

0.936

0.997

July 06.95÷07.03

55÷58

0.898

0.930

July 08.98÷09.02

58÷62

0.885

0.912

July 09.92÷09.97

53÷62

0.880

0.906

July 17.90÷17.92

64÷69

0.845

0.906

July 20.90÷20.93

70÷77

0.839

0.931

June 28.92÷28.94

53÷52

0.962

1.049

June 29.90÷29.93

52÷53

0.953

1.031

June 30.91÷30.92

51÷52

0.945

1.013

July 01.89÷01.91

51÷52

0.936

0.997

July 08.98÷09.00

60÷62

0.885

0.912

July 09.96÷09.99

61÷63

0.879

0.906

−10.560 29.88 −10.547 29.85 −10.648∗ 29.70∗ −10.452∗ 29.92∗ −10.503 29.82 −10.666∗ 29.51∗ −10.524 29.58 −10.272 29.88 −10.298 29.81 −10.158 29.90 −10.213 29.85

Rdia [arc sec] = 46

R203

– – – – – – – – −9.840 30.29 −9.854 30.24

26

35

48

71

99

140

198

277

−10.363 30.11 −10.381 30.04 −10.487∗ 29.89∗ −10.320 30.06 −10.328 30.02 −10.362 29.95 −10.214 30.01 −10.106 30.08 −10.137 30.00 −9.944 30.17 −10.059 30.04

−10.221 30.27 −10.198 30.25 −10.262 30.16 −10.179 30.21 −10.150 30.23 −10.154 30.20 −10.242 29.91 −9.980 30.21 −9.966 30.21 −9.787 30.36 −9.864 30.28

−10.096 30.41 −10.049 30.42 −10.068 30.38 −10.033 30.37 −10.018 30.37 −10.036 30.32 −9.897 30.37 −9.840 30.37 −9.832 30.36 −9.671 30.48 −9.750 30.41

−9.924 30.60 −9.890 30.59 −9.919 30.54 −9.863 30.56 −9.871 30.53 −9.848 30.53 – – −9.707 30.51 −9.693 30.51 – – −9.612 30.56

−9.840 30.68 −9.780 30.70 −9.835 30.62 −9.766 30.66 −9.773 30.63 −9.936∗ 30.39∗ – – −9.619 30.60 −9.611 30.59 – – – –

−9.718 30.81 −9.719 30.76 −9.732 30.73 −9.708 30.71 −9.636 30.78 – – – – – – −9.537 30.66 – – – –

– – −9.649 30.83 −9.662 30.80 −9.635 30.79 – – – – – – – – −9.478 30.71 – – – –

– – – – −9.666 30.79 – – – – – – – – – – – – – – – –

59

62

87

112

163

216

317

−9.890 30.43 −9.882 30.44 −9.813 30.48 −9.811∗ 30.45∗ −9.703 30.44 −9.703 30.42

– – – – – – – – −9.680 30.47 −9.680 30.44

−9.722 30.62 −9.746 30.59 −9.682 30.62 −9.651 30.62 −9.589 30.56 −9.559 30.57

−9.686 30.65 −9.639 30.70 −9.612 30.69 −9.588 30.69 −9.492 30.66 −9.474 30.66

−9.557 30.79 −9.518 30.83 −9.491 30.82 −9.468 30.82 −9.405 30.75 −9.394 30.74

−9.504 30.84 −9.572 30.76 −9.454 30.86 −9.413 30.87 −9.393 30.75 −9.357 30.77

−9.480 30.86 −9.476 30.86 −9.405 30.90 −9.341 30.94 −9.379 30.75 −9.344 30.77 (continued on next page)

182

W. Waniak et al. / Icarus 186 (2007) 178–191

Table 3 (continued) UT date (1992)

z [deg]

rh [AU]

 [AU]

log F [erg cm−2 s−1 ], log Nm or log Afρ [cm]

July 16.92÷16.93

68÷70

0.848

0.901

July 20.92÷20.94

75÷80

0.839

0.931

July 22.89÷22.91

74÷79

0.837

0.954

– – −9.779 30.27 −9.954∗ 30.02∗

−9.611 30.44 −9.596 30.49 −9.760∗ 30.29∗

−9.596 30.46 −9.635 30.43 −9.700 30.37

– – −9.486 30.60 −9.542 30.56

– – −9.428 30.66 −9.491 30.60

– – −9.385 30.69 −9.417 30.67

– – −9.334 30.74 −9.472 30.57

– – −9.344 30.69 – –

Note. z, zenith distance; rh , heliocentric and geocentric distances; Rdia , diaphragm radius. Values not used for determination of the mean Afρ profile and the scale-lenghts are marked by asterisks. Numbers of the molecules contained in the cylinders formed by the diaphragms and the Afρ values are typed in italic.

Table 4 Narrowband flux F , number of the molecules Nm and the Afρ dust parameter for the diaphragms used during the observations of Comet P/deVico UT date (1995)

z [deg]

R203

rh [AU]  [AU] log F [erg cm−2 s−1 ], log Nm or log Afρ [cm] Rdia [arc sec] = 52

Oct. 13.12÷13.14 70÷64

0.675

0.963

Oct. 14.13÷14.16 68÷62

0.680

0.965

Oct. 23.14÷23.15 71÷66

0.477

1.029

Oct. 23.70÷23.72 76÷81

0.752

1.035

Oct. 24.16÷24.17 66÷64

0.757

1.041

Oct. 24.70÷24.74 77÷84

0.762

1.047

Oct. 25.15÷25.17 68÷65

0.767

1.053

Oct. 25.70÷25.72 74÷80

0.772

1.060

Oct. 27.15÷27.17 69÷66

0.788

1.080

Oct. 27.70÷27.72 72÷78

0.794

1.088

Oct. 28.16÷28.17 68÷66

0.799

1.095

C500

−8.206 31.15 −8.165 31.21 −8.650 30.98 −8.695 30.95 −8.702 30.97 −8.752 30.94 −8.746 30.97 −8.811 30.93 −8.911 30.87 −8.893 30.90 −8.883 30.92

Rdia [arc sec] = 35

Nov. 11.70÷11.71 68÷69

0.983

1.359

Nov. 13.71÷13.74 69÷78

1.011

1.401

61

76

−8.133 31.22 −8.124 31.25 −8.506 31.12 −8.613 31.03 – – −8.616 31.08 −8.644 31.07 −8.706 31.03 −8.718 31.07 −8.809 30.99 – – 48

102

121

175

223

301

389

495

633

CN filter −8.019 −7.911 31.34 31.45 −8.042 −7.880 31.33 31.50 −8.434 −8.254 31.19 31.38 −8.494 −8.344 31.15 31.31 −8.486 – 31.18 – −8.486 – 31.21 – – −8.400 – 31.32 −8.587 −8.461 31.15 31.28 −8.610 −8.482 31.18 31.31 −8.690 −8.556 31.11 31.24 – – – –

−7.788 31.57 −7.813 31.56 −8.214 31.42 −8.300 31.35 −8.241 31.43 −8.277 31.42 – – −8.399 31.34 −8.409 31.38 −8.495 31.30 −8.468 31.34

−7.656 31.70 −7.672 31.70 −8.070 31.56 −8.097 31.56 – – – – −8.228 31.49 −8.264 31.48 −8.280 31.51 −8.364 31.44 – –

−7.576 31.78 −7.609 31.77 −8.028 31.60 −8.018 31.64 −8.076 31.60 −8.113 31.59 – – −8.192 31.55 −8.208 31.58 −8.291 31.51 −8.293 31.51

– – −7.539 31.84 −7.968 31.66 −7.964 31.69 – – −8.037 31.66 −8.090 31.63 −8.120 31.62 −8.122 31.67 −8.210 31.59 – –

– – – – −7.908 31.72 −7.901 31.75 −7.944 31.73 −7.998 31.70 −8.058 31.66 −8.096 31.65 −8.076 31.72 −8.139 31.66 −8.169 31.64

– – −7.541 31.84 −7.868 31.76 −7.855 31.80 – – −7.953 31.75 −8.023 31.70 −8.037 31.71 −8.044 31.75 −8.115 31.69 – –

– – −7.488 31.89 −7.864 31.77 −7.837 31.82 −7.902 31.77 −7.942 31.76 −8.018 31.70 −8.027 31.72 −8.022 31.77 −8.071 31.73 −8.091 31.72

71

140

495

633

99

−9.844 – −9.437 – – 30.25 – 33.66 – – −9.902 −9.741 −9.458 −9.425 −9.205 38.67 38.70 38.68 38.72 38.69 BC filter

R203

Rdia [arc sec] = 52

Oct. 13.09÷13.11 77÷73

0.675

0.963

Oct. 14.10÷14.12 78÷70

0.680

0.965

Oct. 23.09÷23.11 81÷77

0.746

1.028

Oct. 24.09÷24.11 81÷76

0.756

1.040

Oct. 25.09÷25.11 82÷77

0.766

1.052

Oct. 25.93÷26.12 82÷83, 79÷73 0.776

1.064

Oct. 27.09÷27.14 82÷80, 72÷71 0.787

1.080

Oct. 27.73÷27.94 79÷82, 82÷78 0.795

1.090

−9.288 3.448 −9.339 3.404 −9.706 3.142 −9.748 3.131 −9.782 3.099 −9.794 3.114 −9.905 3.000 −9.899 3.029

61

76

102

121

175

223

301

389

−9.226 3.434 −9.242 3.424 −9.625 3.152 −9.660 3.132 −9.687 3.121 −9.762 3.070 −9.810 3.030 −9.820 3.038

−9.163 3.413 −9.177 3.406 −9.539 3.154 −9.563 3.150 −9.655 3.060 −9.622 3.127 −9.734 3.020 −9.734 3.044

−9.072 3.366 −9.091 3.353 −9.478 3.071 −9.509 3.059 −9.563 3.016 −9.568 3.048 −9.653 2.961 −9.653 2.984

−9.053 3.312 −9.059 3.314 −9.442 3.035 −9.481 3.015 −9.526 2.981 −9.505 3.031 −9.586 2.960 −9.620 2.942

– – −9.013 3.194 −9.389 2.919 −9.427 2.901 −9.467 2.875 −9.450 2.931 −9.541 2.838 −9.509 2.901

−9.015 3.092 −9.020 3.094 −9.354 2.858 −9.434 2.795 −9.415 2.843 −9.453 2.828 −9.501 2.788 −9.540 2.763

– – −9.025 2.963 −9.340 2.743 −9.382 2.728 −9.453 2.666 −9.467 2.683 −9.505 2.656 – –

– – – – – – – – – – – – – – – – – – −9.367 – – 2.637 – – – −9.403 – – 2.522 – – – – – – – −9.532 – – 2.512 – – −9.442 −9.422 −9.464 2.648 2.577 2.442 (continued on next page)

Narrowband photometry of C/Shoemaker–Levy and P/deVico

183

Table 4 (continued) UT date (1995) C500

z [deg] rh [AU]  [AU] log F [erg cm−2 s−1 ], log Nm or log Afρ [cm] Rdia [arc sec] = 35

Nov. 11.70÷11.71 68÷69 0.983

1.359

Nov. 13.71÷13.75 70÷78 1.011

1.401

48

71

99

140

−10.932 – −10.574 – – 2.485 – 2.539 – – −10.896 −10.854 −10.510 −10.519 −10.262 2.558 2.461 2.645 2.494 2.613 C2 filter

R203

Rdia [arc sec] = 52

Oct. 22.71÷22.72

78÷82 0.743

1.024

Oct. 23.12÷23.13

75÷73 0.747

1.028

Oct. 24.13÷24.15

73÷68 0.756

1.040

Oct. 25.12÷25.14

75÷70 0.766

1.053

Oct. 26.14÷26.17

71÷65 0.777

1.066

Oct. 27.11÷27.13

79÷74 0.787

1.080

Oct. 28.13÷28.15

76÷70 0.799

1.095

C500

−8.918 31.21 −8.877 31.27 −9.029 31.11 −8.993 31.18 −9.064 31.13 −9.073 31.16 −9.115 31.13

Rdia [arc sec] = 35

Nov. 11.70÷11.71 68÷70 0.983

1.359

Nov. 13.72÷13.75 70÷79 1.011

1.401

61

76

102

121

175

223

301

389

495

633

−8.862 31.26 −8.796 31.35 −8.888 31.27 −8.911 31.27 −9.020 31.17 −9.022 31.21 −9.049 31.20

−8.770 31.36 −8.744 31.40 −8.820 31.33 −8.844 31.33 −8.901 31.29 −8.938 31.29 −8.982 31.26

−8.686 31.45 −8.641 31.51 −8.728 31.44 −8.762 31.42 −8.855 31.33 −8.848 31.38 −8.889 31.36

−8.649 31.48 −8.688 31.45 −8.704 31.46 −8.722 31.46 −8.774 31.42 −8.805 31.42 −8.844 31.40

−8.581 31.55 −8.604 31.53 −8.638 31.52 −8.670 31.51 −8.757 31.43 −8.750 31.48 −8.800 31.44

−8.536 31.60 – – −8.618 31.54 −8.652 31.53 −8.732 31.46 −8.723 31.51 −8.773 31.47

−8.515 31.62 – – −8.600 31.56 −8.640 31.55 −8.715 31.48 −8.722 31.51 −8.767 31.48

– – – – −8.588 31.57 −8.630 31.55 −8.698 31.48 −8.705 31.52 −8.784 31.45

– – – – −8.592 31.56 −8.638 31.53 – – −8.706 31.51 −8.774 31.45

– – – – −8.573 31.58 −8.633 31.53 −8.648 31.53 −8.681 31.54 −8.791 31.43

48

71

99

140

−9.916 30.79 −9.875 30.89

– – −9.862 30.88

– – −9.678 31.07

−10.293 – 30.39 – −10.250 −10.170 30.50 30.58

Note. z, zenith distance of the comet; rh , heliocentric and geocentric distances; Rdia , diaphragm radius. Numbers of the molecules contained in the cylinders formed by the diaphragms and the Afρ values are typed in italic.

vary from a few to about 20% from comet to comet (see e.g. Storrs et al., 1992; Womack et al., 1994), the contribution is only slightly dependent on this gradient due to the fact that there is little difference between the central wavelengths of the BC and C2 filters (see Table 1). The solar spectrum was taken from Labs and Neckel (1968, 1970). The mean ratio of the parasitic contribution of the C2 band to the BC filter appeared almost independent on the aperture radius and equal to 0.072 of the BC flux. Taking this value into account we determined the unbiased level of the BC flux for the first two nights. This approach is correct when the parasitic contamination of the BC pass-band by the C2 emission is the same for both groups of nights. This means that dust and molecular production rates for P/deVico should vary with time in the same manner. As will be shown in the next section this indeed was the case. We have no BC results at all for some nights, or only have them for an insufficient number of apertures. In such cases we adopted a special approach. We began by obtaining the Afρ parameter (for definition see A’Hearn et al., 1984) characterizing the dust production rate for both comets (see Tables 3 and 4). In general the value of the Afρ parameter decreased with increasing diaphragm radius, which is fully consistent with the dynamics of cometary dust. We could determine the missing BC fluxes interpolating or extrapolating the dependency of the Afρ parameter upon the aperture radius. Unfortunately, substantial noise in the individual radial profiles would influence the results.

To overcome this difficulty in the case of C/Shoemaker– Levy we assumed that Afρ profiles had the same shape for all the nights in question, but were normalized according to changes in the dust production rate from night to night. Thus, we introduced a mean radial profile of the Afρ parameter valid for the entire period of observations. This approach assumes that the temporal change of the profile was markedly smaller than the noise in it. Such temporal variation is controlled mainly by changes in the heliocentric distance of the comet, seasonal effects and geometry of sight. As our observations were carried out for a limited range of distances (see Table 3) and phase angles (58÷71◦ ) this assumption seems to be correct. The second order polynomial properly describes the logarithmic radial Afρ profile. We derived two coefficients controlling the shape of the dependency and a number of shifts (one per each individual profile) by the least-square approach. Fig. 1 presents Afρ parameters obtained for all nights and diaphragms together with the mean radial Afρ profile. With this mean profile we were able to reconstruct Afρ values for all the diaphragms used. For those nights on which there were no BC observations we retrieved actual Afρ profiles using the dependency of the dust production rate and heliocentric distance of the comet. The dust emission rate was characterized by the Afρ0 parameter, a value of Afρ for the hypothetical aperture of the radius of 5 × 104 km (4.7 in logarithmic scale). This distance was chosen ad hoc. However, the bulk of the aperture photometry presented in literature was made through diaphragms of radii measuring a few

184

W. Waniak et al. / Icarus 186 (2007) 178–191

Fig. 1. Logarithmic dependency of the observationally obtained Afρ parameter for Comet Shoemaker–Levy versus diaphragm radius. The Afρ profiles for individual nights were shifted along the Afρ axis to be closest to the mean profile shown by a solid line.

tens of thousands of kilometers at 1.0 AU (see e.g. Schleicher et al., 1998). The correlation between Afρ0 parameter and heliocentric distance could well be described by an inverse power law. In the case of P/deVico the Afρ profile changed over time. Thus, we treated three separate groups of nights individually introducing three mean Afρ profiles by averaging all the results for a given aperture. The individual and mean radial profiles are presented in Fig. 2. For the last two nights any dependence of Afρ versus the diaphragm radius is visible. Thus, we took the mean values of the Afρ for apertures instead of using a radial profile. In the end, the individual Afρ values for appropriate diaphragms were obtained and converted to the BC flux. Even if our approach to the problem of obtaining “good” radial profiles of the Afρ is not very precise, it should not bias our results for CN and C2 by more than a couple of percentage points because the total contribution of the dust spectrum to these pass-bands is of the order of 10%. The dust continuum was subtracted from the molecular flux assuming, as previously, that the reflectivity gradient of the cometary dust was equal to 13%. Such an assumption could influence our results as the central wavelengths of the CN and BC filters are separated by 1000 Å. In order to show how much this effect could change the results of further analysis, we used two sets of the pure molecular fluxes. One was obtained by subtraction of the dust continuum with a reflectivity gradient of 13% and the other was obtained with a zero gradient. In the second case, for Comet Shoemaker–Levy the CN flux was on average 0.6% smaller and C2 flux was 1.2% greater than for the reddening equal to 13%. For P/deVico the CN flux was on average 0.3% smaller and the C2 flux 0.6% greater than for the assumed 13% reddening.

Fig. 2. Observationally obtained Afρ parameters versus the diaphragm radius for P/deVico. For the first group of two nights and the second group of six nights the Afρ profiles were shifted along the Afρ axis to be closest one another. The mean Afρ profiles for these two groups are depicted by small dots connected for clarity by thick segments. The original Afρ profiles are marked by open symbols.

Conversion of the flux observed in the profiles of the narrowband filters into the flux emitted in the molecular bands was achieved by adopting their spectral profiles based on the observations of Comet Kohoutek (A’Hearn, 1975) and Comet Encke (Newburn and Spinrad, 1984). The resultant C2 data were converted to the number of molecules using formulas and g-factors from Millis et al. (1982). In the case of CN we used Tatum’s tables (Tatum, 1984), which take into account the Swings effect. The numbers of CN and C2 molecules contained in cylinders formed by our diaphragms are presented in Table 3 for C/Shoemaker–Levy and Table 4 for P/deVico. They were derived using 13% reflectivity gradient. The mean errors of the number of molecules for Comet Shoemaker–Levy are expected to be: 5% for CN and 8% for C2 radicals. For P/deVico they are close to 7% and 5% for CN and C2 , respectively. The errors include the overall uncertainty of the molecular flux and the effect produced by subtracting the dust continuum. 3. Parent and daughter scale-lengths We used the Haser model (Haser, 1957) to determine parent and daughter scale-lengths as well as molecular production rates. This simplest approach, which incorporates the fewest number of model parameters, is consistent with our sampling of a few points of the coma radial profile. As was shown by Waniak et al. (1994), attempts to analyze such profiles using the Monte Carlo model introduced by Combi and Delsemme (1980) gave rather unsatisfactory results. The Haser paradigm is the one most frequently utilized in cometary investigations, thus we can easily compare our results with the results of other authors. Certainly, the vectorial model (Festou, 1981) or

Narrowband photometry of C/Shoemaker–Levy and P/deVico

the Monte Carlo approach should describe a molecular coma much better. The photochemical lifetimes of parents and daughters can be obtained when their ejection velocities are known. The Haser paradigm could only produce physical scale-lengths within the collision zone (a radius of the order of a thousand kilometers) where molecules move radially outward due to collisions. We modified the Haser model to take into account that temporal change in molecular production rate can influence the shape of the radial coma profile (see e.g. Combi and Fink, 1993; Magdziarz et al., 1995). As our starting point we accepted that this variation resulted from changes in the heliocentric distance of a comet. Thus, we assumed that the molecular production rate varies as rh−α (where rh —heliocentric distance). Through preliminary computations using the Haser model with constant production we found production rates Q for the individual observing nights. Than, we constructed dependencies between Q and heliocentric distance and fitted power law functions. We determined that, in the case of C/Shoemaker–Levy, the power index was close to 2.4 for CN and 0.5 for C2 . For P/deVico we found 5.2 for both CN and C2 . We adopted the canonical value of the molecular outflow velocity of 1.0 km s−1 . The parent and daughter scale-lengths lp and ld at 1.0 AU heliocentric distance were taken as the model parameters. The actual values were obtained as proportional to the square of heliocentric distance. As our interval of distances is close to 1.0 AU the resultant scale-lengths are only slightly influenced by the assumed relationship. To seek the optimal solution in the phase space of the parent and daughter scale-lengths we synthesized the radial coma profiles computing the number of molecules for a given diaphragm using its observationally obtained photometric scan. This takes into account the geometric projection of the aperture and nonuniform filter transparency. For computational purposes we selected the observational profiles obtained in fully photometric weather conditions, unbiased by the pointing effect or uncertain sky subtraction. No weighting of the data was used. Figs. 3 and 4 show examples of the best fit and the worst fit cases of the logarithmic radial profiles for both comets. The profiles present the numbers of molecules contained in the appropriate cylinders divided by their radii expressed in kilometers. These values are proportional to the column density. In our case, however using the last parameter would be confusing as it relates to a column with an infinitesimal cross-section. In the case of the constant velocity outflow, without any parentdaughter transitions or decay, the numbers of molecules divided by the diaphragm radii should not depend on the diaphragm radius (like Afρ parameter). Thus, our approach can visualize the actual behavior of the molecular coma showing the production and decay of the daughters. Figs. 5 and 6 show 2D plots of the mean square logarithmic discrepancy between the observed and reconstructed radial profiles for the CN and C2 radicals. By way of comparison we superimposed the results for the two comets in one figure. The best solutions were found using the simplex optimization method (Kallrath and Linnell, 1987) assuming that for both radicals parent scale-lengths were not larger than daughter ones.

185

Fig. 3. Exemplary logarithmic radial profiles (the best fit case and the worst fit case) for CN, and C2 radicals for C/Shoemaker–Levy presented as the numbers of molecules observed within the diaphragms and divided by the diaphragm radii in kilometers. Open squares joined by thin segments—observationally obtained profiles, dots connected by thick segments—computed from the Haser model for the mode I (see Table 5). Right Y axis regards C2 molecule. The UT dates of observation were typed in bold. Profiles obtained with C500 telescope were indicated at the left side, and obtained with R203 refractor were indicated at the right side of the plot.

Fig. 4. Logarithmic radial profiles for CN and C2 radicals for P/deVico. The best fit case and the worst fit case per each radical are presented as the numbers of molecules observed within the diaphragms and divided by the diaphragm radii in kilometers. Theoretical profiles were computed from the Haser model for the mode I (see Table 5). For detailed description of this plot see Fig. 3.

This presumption is of crucial importance because the Haser model cannot distinguish between parent and daughter scalelength values. We presented in both figures regions of acceptable values of the scale-lengths taking into account the discrepancy be-

186

W. Waniak et al. / Icarus 186 (2007) 178–191

Table 5 The parent and daughter scale-lengths for the radicals Mode

CN lp

C2 ld

lp

ld

I II III

15.6 15.8 15.3

Comet Shoemaker–Levy 306.4 306.0 294.6

29.4 28.2 29.2

68.7 70.8 69.3

I II III

39.2 39.4 37.7

Comet P/deVico 317.9 318.0 384.5

54.4 53.6 61.7

65.9 66.8 62.4

Note. The scale-lengths given in 103 km at 1 AU heliocentric distance. Mode I, input data obtained for the spectrophotometric gradient of 13% and the nonstationary Haser model; II, input data for the zero spectrophotometric gradient and nonstationary model; III, input data for the 13% gradient and stationary Haser model.

Fig. 5. Result of searching for the optimal Haser scale-lengths for CN. Solid contour lines are for C/Shoemaker–Levy and dashed ones are for P/deVico. The interval between contour lines is 0.02 of logarithm of the mean square discrepancy between observed and modeled profiles. The best solution is shown by + sign for C/Shoemaker–Levy and by × sign for P/deVico. Thick lines shows the borders of the regions of the acceptable scale-lengths (for details see text).

Fig. 6. Result of searching for the optimal solution for C2 radical in the phase space of the parent and daughter scale-lengths. Solid contour lines refer to C/Shoemaker–Levy whereas dashed ones are for P/deVico. The best solution is pointed out by + sign for C/Shoemaker–Levy and by × sign for P/deVico. For more details see Fig. 5.

tween computed and observed radial profiles. These areas were established as fully consistent with classical error bars of scalelengths, but seem to be much more informative. Outside these regions discrepancies between synthesized and observed profiles become distinctly systematic. Table 5 presents the scale-

lengths determined using a dust continuum subtraction assuming a 13% reflectivity gradient (mode I) and using a zero reflectivity gradient (mode II). To get a feeling of how the results depend on whether the stationary or time dependent Haser model was used, we also obtained the scale-lengths within the framework of the stationary approach (mode III). Worth noting is the fact that for both radicals parent scalelengths for the comets were quite different. What is more, the regions of acceptable solutions did not agree. We performed additional model computations with cross-changed scale-lengths. We synthesized the coma profiles for P/deVico using parameters for C/Shoemaker–Levy and vice versa. We received mean square discrepancies between observed and computed profiles that were twice as large as for the optimal solution and quite systematic. As one can see from Table 5 this clear discrepancy between the scale-lengths does not depend on which mode of computation is taken into account. We have carefully treated a number of effects which can bias the results, so we can assert that the discrepancy is real. As Comet de Vico was observed at close to minimum solar activity whereas Comet Shoemaker– Levy lay very close to solar maximum we have checked weather such differences in scale-lengths could be produced by the alteration of UV solar flux between both epochs. We proceeded in the same way as Fray et al. (2005) and came to the conclusion that if C/Shoemaker–Levy was observed at the same level of the solar activity as P/de Vico is, the scale-lenghts should be enlarged by about 25%. It is clearly not enough to overcome the obtained effect. This point will be discussed in the next section, together with the issue of the production rates of the comets. Our resultant CN scale-lengths are consistent with or at least of the same order as the other determined values (e.g. Cochran, 1986; Combi and Delsemme, 1986). Fink et al. (1991) obtained for P/Halley a CN parent scale-length of 28 × 103 km and a daughter scale-length of 320 × 103 km. Randall et al. (1993) determined scale-lengths of 13 × 103 and 210 × 103 km. The morphology of CN in the Hale–Bopp comet revealed (Woodney et al., 2002) scale-lengths equal to 35 × 103 for the parent and 450 × 103 km for the daughter. Lara et al. (2003) received values of 16 × 103 and 300 × 103 km, respectively. Rauer et al. (2003) present the largest CN parent scale-lenght, i.e.

Narrowband photometry of C/Shoemaker–Levy and P/deVico

54 × 103 km. The prominent compilation of CN parent and daughter scale-lengths together with an in-depth analysis of their heliocentric distance dependency as well as solar activity reduced values can be found in Fray et al. (2005). In the case of the C2 molecule the situation is more complicated. Many works have resulted in the parent scale-length being much shorter than the daughter one. Combi and Delsemme (1986) obtained lengths of 16 × 103 and 110 × 103 km, Winiarski et al. (1992) for the same parent scale-length, obtained a daughter scale-length of 85 × 103 km. Cochran (1986) determined scale-lengths of 25 × 103 and 120 × 103 km, Wyckoff et al. (1988) computed values of 32 × 103 and 100 × 103 km, Womack et al. (1994) present parent and daughter scale-lengths of 25 × 103 and 100 × 103 km, Waniak et al. (1994) found 23 × 103 and 110 × 103 km, respectively. Based on the long-term monitoring of Comet Hale–Bopp Rauer et al. (2003) calculated a parent scale-lenght of 16 × 103 km. Results also exist which show the daughter scale-length to be close to the parent ones. Fink et al. (1991) obtained 58×103 km for both scale-lengths and Randall et al. (1993) found 22 × 103 and 66 × 103 km. As one can see all the cited scale-lengths are in general agreement with the character of the phase space plot in Fig. 6. 4. Dust and radical production rates In the case of the P/deVico comet our observations were carried out at heliocentric distances ranging from 0.7 to 1.0 AU. We were thus able to compute the dependencies of the production rates of the molecular species and dust according to the heliocentric distance. We chose the Afρ0 parameter derived from the radial Afρ profiles at a distance of 5 × 104 km from the nucleus as a good measure of dust production (for our motivation see Section 2). The Afρ0 values are presented in Table 6 and in Fig. 7 as the logarithmic plot versus heliocentric distance. The errors do not include the discrepancy of the zero point of our photometry. In the case of C/Shoemaker–Levy for the nights when more than one profile was obtained we averaged the Afρ0 parameters. For P/deVico a power law function with the power index equal to 5.22 ± 0.19 describes the relationship very well. The first two nights (Oct. 13.1 and 14.1) were not used to determine the slope owing to a lack of C2 observations. Nevertheless, these points fit the overall dependency excellently. Taking the best values of the parent and daughter scalelengths obtained for the mode I we computed CN and C2 production rates. The results are presented in Table 6 and as logarithmic plots versus heliocentric distance in Fig. 7. The error bars include the overall errors of the number of molecules described in Section 2 and mean-square discrepancies between the observed and model coma profiles divided by the square root of the number of points in each profile. We have looked at how the uncertainty in determining the Haser scale-lengths influenced our results. The extreme values of the scale-lengths for radicals were put at both ends of the banana-like, thick lined areas in Figs. 5, 6. In the case of C/Shoemaker–Levy the logarithm of production rates varies around the values cited in Table 6 be-

187

Table 6 Production rates of the radicals and the Afρ0 parameters UT date

log Q [Nm s−1 ]

log Afρ0 [cm]

rh [AU]

CN

1992 June 26.0 June 28.0 June 28.9 June 29.9 June 30.9 July 01.9 July 07.0 July 09.0 July 09.9 July 16.9 July 17.9 July 20.9 July 21.9 July 22.9

0.989 0.971 0.962 0.953 0.944 0.936 0.898 0.885 0.879 0.848 0.845 0.839 0.838 0.837

Comet Shoemaker–Levy 25.59 ± 0.04 26.07 ± 0.03 25.60 ± 0.03 26.07 ± 0.03 25.57 ± 0.03 26.04 ± 0.03 25.62 ± 0.02 26.05 ± 0.02 25.61 ± 0.03 26.08 ± 0.03 25.66 ± 0.03 26.07 ± 0.05 25.63 ± 0.03 25.95 ± 0.10 25.68 ± 0.02 26.09 ± 0.03 25.66 ± 0.02 26.07 ± 0.02 25.75 ± 0.03 26.09 ± 0.04 25.84 ± 0.03 26.21 ± 0.04 25.76 ± 0.06 26.09 ± 0.04 25.59 ± 0.04 – 25.67 ± 0.03 26.01 ± 0.06

2.49 ± 0.06 2.46 ± 0.06 2.49 ± 0.13 2.47 ± 0.06 2.51 ± 0.09 2.52 ± 0.10 2.50 ± 0.10 2.59 ± 0.05 2.61 ± 0.05 – 2.77 ± 0.05 2.73 ± 0.10 – –

1995 Oct. 13.1 Oct. 14.1 Oct. 22.7 Oct. 23.1 Oct. 23.7 Oct. 24.1 Oct. 24.7 Oct. 25.1 Oct. 25.7 Oct. 26.1 Oct. 27.1 Oct. 27.8 Oct. 28.1 Nov. 11.7 Nov. 13.7

0.675 0.680 0.743 0.747 0.752 0.756 0.762 0.767 0.772 0.777 0.787 0.795 0.799 0.983 1.011

Comet P/deVico 26.71 ± 0.03 – 26.72 ± 0.03 – – 27.15 ± 0.03 26.51 ± 0.03 27.17 ± 0.03 26.50 ± 0.03 – 26.49 ± 0.03 27.12 ± 0.02 26.48 ± 0.03 – 26.45 ± 0.03 27.10 ± 0.02 26.43 ± 0.03 – – 27.03 ± 0.02 26.44 ± 0.03 27.04 ± 0.02 26.38 ± 0.03 – 26.38 ± 0.03 26.99 ± 0.02 25.85 ± 0.03 26.41 ± 0.03 25.80 ± 0.04 26.46 ± 0.03

3.42 ± 0.03 3.41 ± 0.03 – 3.15 ± 0.03 – 3.14 ± 0.04 – 3.13 ± 0.04 – 3.10 ± 0.03 3.02 ± 0.04 3.04 ± 0.04 – 2.51 ± 0.05 2.51 ± 0.07

C2

Note. Nm , number of molecules. Production rates of the radicals were determined using the scale-lengths obtained from the mode I of model computations (see Table 5).

tween −0.06 and 0.08 for CN and between −0.14 and 0.61 for C2 . For P/deVico such variations are from −0.09 to 0.08 for CN and from −0.41 to 0.37 for C2 . The dependencies between production rates and the Sun– comet distance were fitted by inverse power law functions. For C/Shoemaker–Levy we did not take into further consideration the results for nights when doubts concerning weather conditions existed (July 6.97 and 21.89). The power indices were 2.43 ± 0.51 for CN and 0.54 ± 0.52 for C2 . For P/deVico the values of the power index were: 5.55±0.14 for CN and 5.70 ± 0.24 for C2 . In the case of CN the first two points (Oct. 13.1 and 14.1) were not taken into account as the dust component subtracted from the molecular emission could be biased by the lack of C2 observations. The production rates of molecular species and dust for P/deVico changed rapidly with the heliocentric distance. This is rather characteristic of physically young comets. P/deVico has a semi-major axis and an eccentricity of orbit (Buckley et al., 1995) very close to the orbital parameters of P/Halley. The mean periods of the revolution round the Sun are close to 74 and 76 years, respectively. For P/Halley, however, molecular production rates changed less with the heliocentric distance. The slopes for CN and C2 post-

188

W. Waniak et al. / Icarus 186 (2007) 178–191

Table 7 The relative logarithmic abundances in comparison with typical values

Mean Range C/Shoemaker–Levy P/deVico

C2 /CN

Afρ0 /CN

0.06 −0.09÷0.29 0.41(0.35) ± 0.06 0.60(0.34) ± 0.04

−23.32 −24.01÷ −22.48 −23.11(−23.14)±0.07 −23.39(−23.42)±0.05

Note. The mean typical abundances and ranges are taken from A’Hearn et al. (1995). Relative production rates presented in parentheses were determined using the molecular scale-lengths by Randall et al. (1993).

Fig. 7. Heliocentric distance dependencies of production rates of CN, C2 and dust (characterized by the Afρ0 parameter) for Comet Shoemaker–Levy (open circles) and deVico (filled circles). The best fitted lines are presented. Their slopes for C/Shoemaker–Levy are as follows: −2.43 ± 0.51 for CN, −0.54 ± 0.52 for C2 and −4.05 ± 0.44 for dust. Correlation factors are equal to −0.82 for CN, −0.31 for C2 and −0.96 for Afρ0 , respectively. The result for July 7.0 was not taken into account as being influenced by poor weather conditions. The appropriate slopes for P/deVico are: −5.55 ± 0.14 for CN, −5.70 ± 0.24 for C2 and −5.22 ± 0.19 for dust with correlation factors of the order of −0.99.

perihelion were 2.21 and 2.41, respectively (Schleicher et al., 1998). It is not unlikely that the temporal variation of molecular reduction rates of P/deVico and especially C/Shoemaker–Levy had more to do with intrinsic cometary activity or certain seasonal effects introduced by active regions on the nucleus surface than with changes in the heliocentric distance. However, an indepth analysis of this point could be highly erroneous due to the insufficient frequent temporal sampling for both comets and additionally by the substantial error bars of production rates for Comet Shoemaker–Levy. If we want to compare our production rates and abundances with the results for other comets presented by different authors we should take same the scale-lengths used by them. The effect of scale-lenghts on production rates was discussed in great detail by Fink and Combi (2004). Thus, we accept the assumption that variations in the scale-lengths obtained for individual objects are not real and that unique universal parameters characterizing any comet exist. We recalculated our production rates, taking scale-lengths determined by Randall et al. (1993) and used by A’Hearn et al. (1995) in the prominent paper concerning the narrowband photometry of 85 comets. In general, we had far worse fits to the observed coma profiles than for our optimal solutions, especially for P/deVico. The recalculated production rates for C/Shoemaker–Levy expressed on a logarithmic scale increased on average by 0.03 for CN and decreased by 0.03 for C2 , respectively. In the case of P/deVico the corresponding rates rose on average by 0.03 for CN and dropped 0.23 for C2 .

In the light of our scale-lengths results (see the previous paragraph) we are not convinced that universal parameter values for the Haser model exist. Thus, we should rather determine their individual values for different comets if we want to obtain correct production rates. Table 7 presents the logarithmic relative productions with respect to CN averaged over the whole period of observations. We used the scale-lengths obtained by us as well as those taken from Randall et al. (1993). The errors cited there do not include uncertainty of zero points of our narrowband magnitudes, which can increase the margin of error by a few hundreds of a logarithm. By way of comparison we present in this table the mean values of relative abundances together with their ranges determined by A’Hearn et al. (1995). As one can discern both C/Shoemaker–Levy and P/deVico were C2 overabundant in comparison with the typical comet. In terms of dust production, both comets can be considered as quite typical with some depletion for P/deVico compared with C/Shoemaker–Levy. The relative abundances for these comets depend on heliocentric distance in quite different ways. In the case of P/deVico the production rates of CN and C2 were highly correlated. By way of contrast, for Comet Shoemaker–Levy the relative abundances varied within a relatively short range of heliocentric distances. It was shown in the previous section that the parent scale-lengths for CN and C2 for Comet Shoemaker–Levy were roughly twice as short as for P/deVico. One could explain this fact by supposing that the parent photolytic lifetimes for both comets were the same, but the ejection velocity for P/deVico was twice the value for C/Shoemaker–Levy. However this approach should be rejected as the daughter scale-lengths for both comets were of similar values. We propose a simple explanation of the phenomenon presented in this paper. It could be assumed that for P/deVico a prominent fraction of parent molecules of CN and C2 comes from a volume source surrounding the nucleus (see e.g. Shulz, 1993; Rousselot et al., 1994; Combi and Fink, 1997; Dello Russo et al., 1998). The HCON dust particles could be such a source. In this case radical production rates are fully controlled by the dust production rate. Molecular species should be produced with rates changing according to the heliocentric distance in the same manner. Also, the parent scale-lengths of radicals should be increased in comparison with the nominal values (arising from photolytic lifetimes) as parent molecules are ejected from dust particles at some distance from a nucleus. The radius of such volume source should be less than approximately 4 × 104 km to be consistent with our molecular

Narrowband photometry of C/Shoemaker–Levy and P/deVico

189

radial profiles (see Fig. 4). This value remains in general agreement with the results obtained by Combi and Fink (1997) from an analysis of the C2 spatial profiles of P/Halley. One question remains open, namely was dust emission rate for P/deVico enough to warrant the observed abundance of radicals produced from dust grains. Cochran et al. (2000) point out that the comet had very low continuum emission level. As their data were not absolutely calibrated it is hard to compare the results with our Afρ0 values. The competitive mechanism which could explain the effect of constant relative abundances of radicals and dust, valid for any dust content, would be the emission of the species from a highly homogeneous mixture residing on the surface of the nucleus of P/deVico. It such case, however, the reason of the different parent scale-lengths for both comets remains unclear. In contrast, if a prominent fraction of the parents is evaporated directly from the nucleus (being rather inhomogeneous), the production rates of different species can change with heliocentric distance in quite a different way. This could be a case with C/Shoemaker–Levy. 5. Dust coma modeling The radial profiles of the Afρ parameter for both comets decrease as the aperture radius increases. This is the result of the acceleration exerted on dust grains by solar radiation pressure. We tried to obtain certain parameters describing the cometary dust using the Monte Carlo model by Waniak et al. (1998). We parametrized the dynamic properties of dust particles according to parameter β, which is the ratio of the solar radiation pressure to the solar gravitational force: β = Frad /Fgrav = 5.59 × 10−5 Qpr /ρa,

(1)

where a is the grain radius in cm, ρ is the grain material density in g cm−3 , Qpr is the radiation pressure efficiency, which is dependent on the size, shape, structure and composition of a grain. We assumed that the β parameter of the dust particles is distributed according to the power law function (this means that for constant Qpr , radii of grains have an inverse distribution): f (β) = f0 β n

(2)

and that the dust ejection velocity νd is correlated to β parameter by the function (see e.g. Fulle, 1987): νd = νd0 β k

(3)

where νd0 is the ejection velocity for dust particles with a β parameter equal to 1.0 (grain size of the order of 1 µm). Taking into account a number of previous results (Fulle, 1987; Fulle and Sedmak, 1988; Cremonese and Fulle, 1989; Waniak, 1992; Waniak et al., 1998) we put index k equal to 0.2. The results of modeling are only slightly dependent on this parameter so it would be difficult to determine its precise value. The model parameters to be obtained were dust ejection velocity νd0 (Eq. (3)) and the index n describing the distribution of β parameter (Eq. (2)). The radial profile of the coma depends on the temporal variation of the production rate, which can be due to a change in the cometary heliocentric distance.

Fig. 8. Exemplary logarithmic radial Afρ profiles for Comets Shoemaker–Levy and deVico. The best fit case and the worst fit case for each comet are presented. Open squares connected for clarity by thin segments—observationally obtained, dots connected by thick segments—computed from the dust coma model with isotropic dust emission. The dates of observations are typed in bold.

This effect is of greater importance for the dust coma than for the molecules, as the outflow velocity of dust particles is an order of magnitude smaller than the ejection velocity of radicals. We took this into account when assuming that such a change was characterized by the inverse power law dependence of the Afρ0 parameter upon heliocentric distance (see Fig. 7). We synthesized the radial profiles of Afρ using both isotropic and anisotropic (increasing toward the sub-solar point) dust emission. As could be expected the resultant Afρ profiles for both approaches were very close. In the case of P/deVico we reconstructed the Afρ profiles for the second group of nights only (from Oct. 23.1 to 27.9). Fig. 8 presents the best fit and the worst fit cases for radial profiles. For C/Shoemaker–Levy we obtained a dust ejection velocity of 0.16 ± 0.04 km s−1 . The power index n should not exceed 3.3. The results of the actual model are fully consistent with the parameter values (0.1 km s−1 for dust ejection velocity and a power index n equal to 2.9) obtained from CCD photometry of the same comet (Waniak et al., 1998). For P/deVico we computed an ejection velocity of 0.13 ± 0.02 km s−1 and a power index n equal to 2.1 ± 0.6. Both values are in general agreement with the results for other comets (see e.g. Owens et al., 1998; Waniak, 1992, and references therein). 6. Conclusions The narrowband multiaperture photometry of C/Shoemaker– Levy 1991 T2 and P/deVico 1995 S1 allowed us to study the parent and daughter scale-lengths and production rates for CN and C2 . We analyzed the radial cumulative profiles of a number of molecules using the Haser model. As we only had measurements for only one dust continuum filter (BC) we did not deter-

190

W. Waniak et al. / Icarus 186 (2007) 178–191

mine the reflectivity gradient of cometary dust. Fortunately, the results appeared to very slightly depend on the assumed value. The parent scale-lengths for CN (at 1.0 AU) were 16 × 103 and 39 × 103 km and the daughter scale-lengths were equal to 306 × 103 and 318 × 103 km for C/Shoemaker–Levy and P/deVico, respectively. For C2 molecule the scale-lengths were 29 × 103 and 54 × 103 km for the parents and 69 × 103 and 66 × 103 km for the daughters. The results are in general agreement with previous determinations of the scale-lengths, although the parent scale-lengths for P/deVico were twice as long as for C/Shoemaker–Levy. This effect could be explained by the emission of parent molecules from the dust volume source surrounding the nucleus. For both comets the Afρ parameter markedly decreases as the diaphragm radius increases. Thus, the dust production rate was characterized by parameter Afρ at a distance of 5×104 km from the nucleus. We analyzed the heliocentric distance dependencies of the emission rates of the radicals and dust for each comet, but only in the case of P/deVico were the results certain. The inverse power law function rh−α with indices equal to 5.55 ± 0.14 for CN, 5.70 ± 0.24 for C2 and 5.22 ± 0.19 for dust can describe these dependencies very well. The correlation between the emission rates of all three species was prominent. The relative abundance of C2 compared with CN for both comets was enhanced by taking into account the ensemble photometry results for comets achieved by A’Hearn et al. (1995). The relative dust emission compared with CN was quite normal although P/deVico was somewhat dust depleted in comparison with C/Shoemaker–Levy. A Monte Carlo model of the dust coma was used to reconstruct the radial profiles of parameter Afρ. We obtained a dust ejection velocity of 0.16 and 0.13 km s−1 for comet Shoemaker–Levy and P/deVico, respectively. A power index of the distribution of β parameter (roughly inversely proportional to the size of dust grain) had an upper limit of 3.3 for C/Shoemaker–Levy and was close to 2.1 for P/deVico. These values correspond very well with the results of more sophisticated approaches to the problem of dust coma modeling based on CCD photometry. Acknowledgments The authors gratefully acknowledge two anonymous referees of this paper for many helpful comments and suggestions. References A’Hearn, M.F., 1975. Spectrophotometry of Comet Kohoutek (1973f = 1973XII). Astron. J. 80, 861–875. A’Hearn, M.F., Schleicher, D.G., Feldman, P.D., Millis, R.L., Thompson, D.T., 1984. Comet Bowell 1980b. Astron. J. 89, 579–591. A’Hearn, M.F., Millis, R.L., Schleicher, D.G., Osip, D.J., Birch, P.V., 1995. The ensamble properties of comets: Results from narrowband photometry of 85 comets, 1976–1992. Icarus 118, 223–270. Breger, M., 1976a. Evaluation of stellar spectrophotometry. Astrophys. J. Suppl. Ser. 32, 1–6. Breger, M., 1976b. Catalog of spectrophotometric scans of stars. Astrophys. J. Suppl. Ser. 32, 7–87.

Buckley, R.J., Marsden, B.G., Williams, G.V., Green, D.W.E., 1995. Comet P/1995 S1 = P/1846 D1 (deVico). IAU Circ., 6232. Cochran, A.L., 1986. A reevaluation of the Haser model scale lengths in comets. Astron. J. 90, 2609–2614. + Cochran, A.L., Cochran, W.D., Barker, E.S., 2000. N+ 2 and CO in Comets 122P/1995 S1 (deVico) and C/1995 O1 (Hale–Bopp). Icarus 146, 583–593. Combi, M.R., Delsemme, A.H., 1980. Neutral cometary atmospheres. I. An average random walk model for photodissociation in comets. Astrophys. J. 237, 633–640. Combi, M.R., Delsemme, A.H., 1986. Neutral cometary atmospheres. V. C2 and CN in comets. Astrophys. J. 308, 472–484. Combi, M.R., Fink, U., 1993. P/Halley: Effects of time-dependent production rates on spatial emission profiles. Astrophys. J. 409, 790–797. Combi, M.R., Fink, U., 1997. A critical study of molecular photodissociation and CHON grain sources for cometary C2 . Astrophys. J. 484, 879–890. Cremonese, G., Fulle, M., 1989. Photometrical analysis of the neck-line structure of Comet Halley. Icarus 80, 267–279. Dello Russo, N., DiSanti, M.A., Mumma, M.J., Magee-Sauer, K., Rettig, T.W., 1998. Carbonyl sulfide in Comets C/1996 B2 (Hyakutake) and C/1995 O1 (Hale–Bopp): Evidence for an extended source in Hale–Bopp. Icarus 135, 377–388. Festou, M.C., 1981. The density distribution of neutral compounds in cometary atmospheres. I. Model and equations. Astron. Astrophys. 95, 69–79. Fink, U., Combi, M.R., 2004. The effect of using different scale lengths on the production rates of Comet 46P/Wirtanen. Planet. Space Sci. 52, 573–580. Fink, U., Combi, M.R., DiSanti, M.A., 1991. Comet P/Halley: Spatial distribution and scale lengths for C2 , CN, NH2 , and H2 O. Astrophys. J. 383, 356–371. Fray, N., Bénilan, Y., Cottin, H., Gazeau, M.-C., Crovisier, J., 2005. The origin of the CN radical in comets: A review from observations and models. Planet. Space Sci. 53, 1243–1262. Fulle, M., 1987. A new approach to the Finson–Probstein method of interpreting cometary dust tails. Astron. Astrophys. 171, 327–335. Fulle, M., Sedmak, G., 1988. Photometrical analysis of the neck-line structure of Comet Bennett 1970 II. Icarus 74, 383–398. Haser, L., 1957. Distribution d’intensité dans la tête d’une comète. Bull. Acad. R. Sci. Liege 43, 740–750. Jewitt, D., Meech, K., 1986. Cometary grain scattering versus wavelength, or, “what color is comet dust?” Astrophys. J. 310, 937–952. Kallrath, J., Linnell, A.P., 1987. A new method to optimize parameters in solutions of eclipsing binary light curves. Astrophys. J. 313, 346–357. Kurucz, R.L., 1979. Model atmospheres for G, F, A, B, and O stars. Astrophys. J. Suppl. Ser. 40, 1–340. Labs, D., Neckel, H., 1968. The radiation of the solar photosphere from 2000 Å to 100 µm. Z. Astrophys. 69, 1–73. Labs, D., Neckel, H., 1970. Transformation of the absolute solar radiation data into the “International practical temperature scale of 1968”. Solar Phys. 15, 79–87. Lara, L.-M., Licandro, J., Oscoz, A., Motta, V., 2003. Behavior of Comet 21P/Giacobini–Zinner during the 1998 perihelion. Astron. Astrophys. 399, 763–772. Magdziarz, P., Winiarski, M., Waniak, W., 1995. CN photometry of Comet Levy 1990XX. Icarus 116, 40–45. Millis, R.L., A’Hearn, M.F., Thompson, D.T., 1982. Narrowband photometry of Comet P/Stephan–Oterma and the backscattering properties of cometary grains. Astron. J. 87, 1310–1317. Newburn Jr., R.L., Spinrad, H., 1984. Spectrophotometry of 17 comets. I. The emission features. Astron. J. 89, 289–309. Owens, A., Parmar, A.N., Oosterbroek, T., Orr, A., Antonelli, L.A., Fiore, F., Schulz, R., Tozzi, G.P., Maccarone, M.C., Piro, L., 1998. Evidence for dustrelated X-ray emission from Comet C/1995 O1 (Hale–Bopp). Astrophys. J. 493, L47–L51. Randall, C.E., Schleicher, D.G., Ballou, R.G., Osip, D.J., 1993. Observational constraints on molecular scalelength and lifetimes in comets. Bull. Am. Astron. Soc. 24. Abstract 1002. Rauer, H., Helbert, J., Arpigny, C., Benkhoff, J., Bockelée-Morvan, D., Boehnhardt, H., Colas, F., Crovisier, J., Hainaut, O., Jorda, L., Kueppers, M., Manfroid, J., Thomas, N., 2003. Long-term spectrophotometric monitoring of Comet C/1995 O1 (Hale–Bopp). Astron. Astrophys. 397, 1109–1122.

Narrowband photometry of C/Shoemaker–Levy and P/deVico

Rousselot, P., Clairemidi, J., Moreels, G., 1994. Evolution of the C2 spectrum in Halley’s inner coma: Evidence for a diffuse source. Astron. Astrophys. 286, 645–653. Schleicher, D.G., Millis, R.L., Birch, P.V., 1998. Narrowband photometry of Comet P/Halley: Variation with heliocentric distance, season, and solar phase angle. Icarus 132, 397–417. Storrs, A.D., Cochran, A.L., Barker, E.S., 1992. Spectrophotometry of the continuum in 18 comets. Icarus 98, 163–178. Shulz, R., 1993. CN column density distribution in Comet P/Halley. Astron. Astrophys. 268, 319–325. Tatum, J.B., 1984. Cyanogen radiance/column density ratio for comets calculated from the Swings effect. Astron. Astrophys. 135, 183–187. Thomas, N., Keller, H.U., 1989. The color of Comet P/Halley nucleus and dust. Astron. Astrophys. 213, 487–494. Waniak, W., 1992. A Monte Carlo approach to the analysis of the dust tail of Comet P/Halley. Icarus 100, 154–161.

191

Waniak, W., Magdziarz, P., Winiarski, M., 1994. Narrowband photometry of Comet Austin 1990V. Icarus 108, 92–102. Waniak, W., Zola, S., Krzesinski, J., 1998. Dust emission for Comets Shoemaker–Levy 1991a1 and McNaught–Russell 1993v. Icarus 136, 280– 301. Winiarski, M., Waniak, W., Magdziarz, P., 1992. Narrowband photometry of Comet Okazaki–Levy–Rudenko 1989r. Earth Moon Planets 59, 229–237. Womack, M., Lutz, B.L., Wagner, R.M., 1994. Pre- and postperihelion abundances of gas and dust in Comet Halley. Astrophys. J. 433, 886–894. Woodney, L.M., A’Hearn, M.F., Schleicher, D.G., Farnham, T.L., McMullin, J.P., Wright, M.C.H., Veal, J.M., Snyder, L.E., Pater, I., Forster, J.R., Palmer, P., Kuan, Y.-J., Williams, W.R., Cheung, C.C., Smith, B.R., 2002. Morphology of HCN and CN in Comet Hale–Bopp (1995 O1). Icarus 157, 193–204. Wyckoff, S., Tegler, S., Wehinger, P.A., Spinrad, H., Belton, M., 1988. Abundances in Comet Halley at the time of the spacecraft encounters. Astrophys. J. 325, 927–938.