Analysis of past comet apparitions

C/1995 O1 (Hale-Bopp)


The Great Comet of 1997 appeared very impressive during the first two moonless weeks of April: The bright and curved dust tail could be traced from the -0.5m head until Cassiopeia. The length of the tail finally increased to 20°. The ion tail could be observed easily. Beginning of April the ion tail was still an naked eye object, but later on it became difficult to observe as the moon the evening sky again. However, the ion tail showed a lot of impressive structures in a telescope and even with binoculars. The coma showed a conspicuous central condensation of 0.5-1.0m. The near-nucleus region still displayed spiral jets and bright envelopes.

At the end of April 1997 Hale-Bopp had moved closer to the horizon. The comet had faded to about 0.0 - 0.5m and was no longer that impressive object, which it was for weeks. It was nearly impossible to see the ion tail with binoculars, but the dust tail was still quite bright. In a telescope the near-nucleus region altered its appearance: the envelopes faded and only the spiral jets could be seen well.

Beginning of May 1997 Hale-Bopp became an object of the twilight. The comet of magnitude 0.5 - 1.0m still showed a dust tail that was visible with the naked eye. The structures within near the nucleus had moved to the eastern side and became more and more difficult, partly because of the bad seeing. The reports so far received indicate that the envelopes had disappeared with only one bright jet visible. Second week of May was the final opportunity for observers of the german comet section to see Hale-Bopp. It was a fuzzy star in the dusk. With binoculars it was still possible to trace the bright part of the dust tail. This last opportunity was used intensively and many observers felt sorry after their final observation of Hale-Bopp.

Starting in mid-April 1997 Hale-Bopp could be seen from the southern hemisphere too, although it was a rather difficult evening object, hovering around an altitude of 10°. In the second half of June and the first half of July the comet could only be seen in twilight from earth, so the crossing of the comet's orbit by the earth was not well documented. Since mid-July, however, the comet was rapidly climbing the morning sky, getting visible again in a dark sky. The incoming reports indicated a rather strange appearance: the dust tail, still of great surface brightness, stretched about 2° in the antisolar direction, then curved back and ran up to 3° in the direction of the sun! On July 25 Terry Lovejoy reported: In the 16x16cm reflector a short dense dust tail folds back on itself to eventually form a faint broad sunward feature of perhaps 2-3° length. The dust tail curves both ways like a fountain but more material curves around towards the east - a very strange perspective to see a comet. There is still a bright almost stellar pseudo-nucleus and the comet remains easily visible to the naked eye despite moonlight.

During August and September 1997 comet Hale-Bopp continued its decline and reached a brightness of 6.5m, a coma diameter of 8' and a tail length of 0.5-1° at the end of October. Werner Hasubick succeeded in observing this comet for the last time from Sicilia and Stromboli (Italy). On October 6 and 10 he could glimpse it in the dawn, only a few degrees above the horizon. In his 8x32 binoculars, however, he had to look carefully. The last sighting with unaided eyes took place in mid-November at 6.5m. Thus comet Hale-Bopp could be glimpsed with the unaided eye for 18 months, twice as long as comet Flaugergues (1811 I), the former record holder!

End of December 1997 and beginning of January 1998 it was possible to observe an anti-tail (the earth crossed the orbit of the comet on Jan. 4). On Jan. 6 G. Garradd estimated the length of the feature as 1.5° in his 25cm Newton. In addition he estimated the length of the dust tail to be about 4.5° in his 10x50 binoculars, significantly longer than weeks before. ESO-Observations (H. Böhnhardt, R. West) showed a needle-like, 10" wide feature, running 25' in direction of the sun and 4° in the opposite direction. This feature partially overlapped with the normal diffuse dust tail. It is interpreted as due to the presence of large and old dust grains in the cometary dust tail, released at least 100 days before the observations (IAUC 6812).

In spring 1998 comet C/1995 O1 (Hale-Bopp) was further receding from the inner solar system and getting fainter and smaller. At the beginning of May the distance between the sun and the comet has reached 5.1 AU with the comet being of magnitude 9.5m. The comet showed a diameter of the condensed coma (DC 5) of about 3' (750.000 km) and a tail length in the order of 0.1°.

At the end of 1998 the total brightness of the comet had declined to 11.0m. As a big surprise the inner coma of comet Hale-Bopp displayed a major brightness increase in December (at a distance of 7 AU from the sun!). Between Dec. 11. and 21. The brightness of the central condensation increased up to 3m, according to CCD-observations of G.J. Garradd. A. Pearce reported a 1.0' coma on Dec. 18 in his 20cm-reflector, noting that the starlike false nucleus accounted for 90-95% to the total brightness. The next night the very conspicuous central condensation caused to coma to be very difficult to see. Until Dec. 25 the conspicuous central condensation increased slowly in size, thereby growing fainter. Such an evolution reminds of comet 29P/Schwassmann-Wachmann 1 (IAUC 7073).

Around the middle of 1999 the brightness of the comet had decreased to 12.5m and the coma diameter to 1.5'. Then on Oct. 20/21 and 21/22 A. Pearce observed a 14m bright condensation at the center of the comet, which he had not noticed on Oct. 18. Auckland-Observatory confirmed a much more condensed coma on Oct. 22, compared to observations made on Oct. 15 (IAUC 7288). This increase in activity occured at a solar distance of 9.6 AU! On these days comet Hale-Bopp was 12.7m bright and presented a coma of nearly 1' (which got larger in the following days). On Dec. 13 it will reach a solar distance of 10.0 AU; by the end of the year the brightness should have decreased to 13.0m.

Until the beginning of July 1998 we have received 1076 observations of 22 members of the comet section (estimates including both tails are counted twice). The following analysis includes about 2500 international observations.

Heliocentric Magnitude development, pre-perihelion

Heliocentric Magnitude development, post-perihelion

Summarizing the whole apparition the light curve shows a complex behaviour: In summer/fall 1996 it showed a distinct transition, which resulted in a decrease of the absolute magnitude by 0.5 mag. Before perihelion in a detailed analysis it is necessary to divide the light curve into five phases according to the available observations. Phase 2 (-250d to -190d) represents the transition period, which cannot be described by a formula. At the moment it is open, if the distinction between phase 3 (-190d to -125d) and phase 4 (-125d to -60d) will stay. Significant is phase 5 (-60d to 0d): Two months before perihelion the brightness increased more rapidly than during all other phases. After perihelion the heliocentric brightness shows a discontinuity too, but this time considerably nearer the sun (+130d to +210d). The parameters published below are preliminary.

The comet's brightness evolution can be represented best by the following formulas:

               t < -250d :	m = -1.3m + 5×log D +  8.7×log r
        -250 < t < -190d :	m ~  2.2m + 5×log D +  2.5×log r
        -190 < t < -125d :	m = -0.9m + 5×log D +  9.0×log r
        -125 < t <  -60d :	m =  0.0m + 5×log D +  6.6×log r
         -60 < t <    0d :	m = -0.8m + 5×log D + 12.5×log r
           0 < t < +210d :	m = -1.0m + 5×log D +  8.0×log r
               t > +210d :	m = -1.4m + 5×log D + 10.0×log r

Neglecting the temporary alterations the overall evolution before and after perihelion can be described by the following formulae:

Pre-perihelion :  m = -0.5m + 5×log D + 7.7×log r
Post-perihelion:  m = -1.1m + 5×log D + 9.0×log r

The peak brightness is now very certain, being -0.7 mag ± 0.1 mag. Observations of magnitudes above -1.0 mag can be excluded. Such high estimates could have physiological reasons or parts of the bright dust tail were included.

Total Brightness and Coma diameter

The last observations with the unaided eye were reported in mid-November 1997, rating the comet at6.5m. This means that comet Hale-Bopp was visible with the naked eye for 18 months, twice aslong as comet Flaugergues (1811 I), which hold the record before.

According to AstroFAX-Circular 540 the comet will reach its next perihelion in August 4412 (±7 months). If it is possible to track Hale-Hopp right into the next century, the uncertainty will diminish to ± 1 month.

The differentiation between coma and inner dust tail was a difficult task, visible in the estimates range between 10' and 30'. The smaller value corresponds well with the inner coma oriented to the ion tail. The larger value seems to include parts of the dust tail. I would suggest a coma diameter between 20' and 25' in spring 1997. As a result the coma diameter during perihelion was as large as in summer 1997. Not surprisingly, however, the maximum absolute coma diameter of about 2.5 Mill. km was achieved in summer 1996. Until perihelion the diameter decreased constantly to still astonishing 1.5 million km! Since February the inner coma was forming an "U". It was interesting to follow the near-nucleus phenomena shifting from the western to the eastern side from March to May, 1997.

Development of the Degree of condensation

The degree of condensation (DC) increased constantly until it peaked to DC 8 in spring 1997. According to observations the DC then increased further to nearly 9, but I think that these estimates could have been the result of the observating circumstances getting worse, which enhanced the entral condensation. It would be much more convincing to see a slow decrease of the DC since the second half of April.

Development of the ion tail

Variations of the position angle of the ion tail

The ion tail could be seen visually since the beginning of this year. The first structures within the ion tail could be detected on photographs taken in mid-Frebruary. Two weeks later it was possible to observe them with a telescope. Meanwhile the length increased to about 15°. The best appearance of the ion tail for the naked eye was in mid of March. Around perihelion it reached its maximum length of about 20° (about 150 Mill. km). At the beginning of April the length had not decreased much, but the tail became broader and consequently the surface brightness dropped. For that reason the ion tail became more and more difficult in the course of the following weeks. However, it now showed a variety of structures, for example many bright streamers. It is interesting to note that observers reported the ion tail to be bright until 3-4° to within its end, where the surface brightness dropped sharply. End of April, beginning of May the ion tail had faded and only a few bright streamers were visible which were detected by only a few observers.

Development of the dust tail

Variations of the position angle of the dust tail

The dust tail which was an easy object since last summer, showed a much slower increase in length than the ion tail during the first weeks of 1997. Not until mid-March reached it 10°, displaying a great surface brightness. Photographically "striae" were detectable throughout March. Beginning of April the length further increased until it peaked at about 20-22° (some 150 Mill. km) around April 7. Later on the length decreased only slowly (it is most probable that the steep decrease visible in the diagram is caused by increasing extinction and twilight). During several weeks it was possible to observe bright streamers on the eastern edge of the dust tail. Overall, the brightness gradient on the leading (eastern) edge increased over the weeks, whereas the western part became more diffuse. It has to be stressed, that the four diagrams presenting the development of the tails are to be considered as preliminary. I tried to decide, whether a report belonged to the ion or dust tail, but in many cases this decision had to be based only on the reported position angle. For the final analyis this separation has to be made more detailed.

Two members of the german comet section worked on the project, proposed by me, to determine the tail length visually and photographically. Both could observe from the Alps and experienced excellent weather conditions. In the next issue of the bimonthly section journal "Schweifstern" I will publish the results.

Daniel Fischer reports on his expedition to the solar eclipse in Mongolia. Their small team was lucky to observe the totality under good conditions, but they were not successful to get Hale-Bopp during totality. One problem could have been the absolute brightness of 0 mag, another problem was the large elongation, which has made it difficult to determine the exact position. As a consequence, there are still only two documented comets visible during a solar eclipse.


Comet Hale-Bopp: the comet of the century

Mark Kidger has investigated the appearances of bright comets. Comparing observations of ancient comets with current ones is a difficult task, however, because the methods have changed over the centuries. Important to note is, that comet reports have to regarded as nearly complete only for the last five centuries.

According to his results, comet Hale-Bopp was the comet which displayed a magnitude greater than 0 mag for the longest continuous period, 7 weeks (analysis Kammerer: 46 days= 6.5 weeks). Comets De Cheseaux 1744 and Tycho 1577 were 6 weeks brighter than 0 mag and the Great Comet of 1882 5 weeks. All other bright comets since 1500 did display a magnitude greater than 0 mag for less than 2 weeks. Comet Hale-Bopp is expected to be visible with the unaided eye for 18 months (first detection was on May 17, 1996). Comet Flaugergues 1811 was visible with the naked eye for 9 months; all other comets fall dramatically short of both comets. As a result, comet Hale-Bopp was the one which could be seen with the unaided eye for the longest period and which was brighter than 0 mag for the longest continuous time (sci.astro, Astro-FAX-Zirkular 494)!

Jacques Sauval (Department of Astrophysics Observatoire Royal de Belgique) published tables which also demonstrate that Hale-Bopp was an exceptionally comet (WWW-pages of the ESO). However, his published values differ from those of Kidger and it seems that they are generally too great. They are based upon the publication "Helle Kometen von -86 bis +1950" from Hermann Mucke (Astronomisches Büro, Wien). Regarding this publication it has to be pointed out, that Mucke used a simple approach for deriving the published magnitudes, applying the formula m = m(0) + 5 log D + 10 log r. As a result, the published magnitudes differ from reported or otherwise published values in quite some cases. I therefore plan to double-check the tables. As a first step, however, I will just publish the tables, but add some remarks.

Table 1: Longest visibility of ancient comets

  Dt    Year    Comet              Theor. Visibility (m<0)  H10       Observations     Remarks
(weeks)                             (derived from Mucke)  (Mucke) (Marsden Catalogue) Kammerer
 10     1577    Brahe (1577 I)        25.09. - 07.12.     -0.5     01.11. - 26.01.        1)
 10      374    P/Halley              28.01. - 01.04.      1.0     03.03. - Mai           2)
 9.5      66    P/Halley              04.02. - 12.04.      0.0     31.01. - 11.04.        2)
 9.1     -11    P/Halley              22.08. - 25.10.      0.0     26.08. - 20.10.        2)
  8      607    P/Halley              03.03. - 28.04.      1.0     Feb.   - Juli          2)
  8      530    P/Halley              18.08. - 13.10.      1.0     28.08. - 27.09.        2)
 7.9    1997    Hale-Bopp (Sauval)    06.03. - 30.04.     -1.0     23.7.95-   ?
 7.3     -86    P/Halley              09.06. - 30.07.      0.0     Aug.   - Sept.         2)
 6.9     141    P/Halley              26.03. - 13.05.      0.0     26.03. - Mai           2)
 6.9     218    P/Halley              12.05. - 29.06.      0.0     18.04. - 18.05.        2)
 6.9     295    P/Halley              07.04. - 25.05.      1.0           Mai              2)
 6.9     837    P/Halley              28.02. - 17.04.      2.0     22.03. - 28.04.
 6.7    1744    Klinkenberg           30.01. - 18.03.      0.5     29.11. - 29.4.43
 6.6    1997    Hale-Bopp (Kammerer)  07.03. - 24.04.     -0.8     23.7.95-   ?           3)
 6.1    1472    Regiomontan           17.01. - 01.03.      2.0     25.12. - 21.2.72
 5.7    1066    P/Halley              20.03. - 29.04.      2.0     01.04. - 07.06.
 5.7    1433    1433                  15.10. - 24.11.      1.2     15.09. - 04.11.
 5.7    1532    Fracastor             17.09. - 27.10.      1.8     02.09. - 30.12.
 5.1    1769    Messier               10.09. - 16.10.      3.2     08.08. - 03.12.
 4.6    1882    Sept.Comet (1882 II)  02.09. - 04.10.      0.8     01.09. - 01.06.

Remarks: 1) -0.5 is the mean of results derived by Mucke (0.8) and by Vsekhsvyatskii (-1.8)!
         2) assumption of a seculiar decline of the absolute magnitude, degree is speculative
         3) Hale-Bopp: analysis by Kammerer

Table 2 lists the comets with the greatest absolute magnitudes. It is derived from the article 'A propos des cometes: orbites, luminosite, cometes remarquables' (pp.189-198) in the belgium astronomical journal 'Ciel et Terre' in 1985. Again, H10 was applied.

 
Table 2: The intrinsically brightest comets

Year            Name                             H10       Remarks Kammerer
1729            Sarabat                         -3.0?           3)
1997            Hale-Bopp                       -0.8            4)
1747            de Cheseaux                     -0.5
1577            Brahe                           -0.5            1)
1811            Flaugergues                      0.0
 -86            P/Halley                         0.0            2)
 -11            P/Halley                         0.0            2)
  66            P/Halley                         0.0            2)
 141            P/Halley                         0.0            2)
 218            P/Halley                         0.0            2)
1744            Klinkenberg                     +0.5
1882            Great Sept. Comet               +0.8
 295            P/Halley                        +1.0            2)
 374            P/Halley                        +1.0            2)
 530            P/Halley                        +1.0            2)
 607            P/Halley                        +1.0            2)
1914            Delavan                         +1.1
1433            Great Comet                     +1.2
1962            Humason                         +1.4
1500            1500                            +1.6
1807            Parisi                          +1.6

Remarks: 1) -0.5 is the mean of results derived by Mucke (0.8) and by Vsekhsvyatskii (-1.8)!
         2) assumption of a seculiar decline of the absolute magnitude, degree is speculative
         3) the perihelion distance of comet Sarabat was 4.1 AU: the deduction of the brightness parameters is very 
difficult, the reported magnitudes are equally good represented by m0=-3.0 mag / n=4 and m0=0.0 mag / n=2.
Therefore it is only certain, that comets Sarabat, Hale-Bopp, Brahe and de Cheseaux were all intrinsically very bright. 4) Hale-Bopp: analysis by Kammerer (J. Sauval gave -1.0 mag)

Table 3 lists the brightest comets as seen from earth, derived from the same article as table 2. Listed are the maximum magnitudes which could be observed by observers on earth, observations from space are excluded (with the exception of comet Kohoutek, it seems). For comet P/Halley, only the theoretically brightest return in 66 is listed.

Table 3: The brightest comets (m1<0)

 m1      q(AU)   H10     Year    Name                          Remarks Kammerer
Mucke   Marsden Mucke
-18?    0.006   +4.0    1680    (Kirch)
-10     0.008   +0.8    1882    Great September Comet
-10     0.008   +6.0    1965    Ikeya-Seki
-8      0.177   -0.5    1577    (Brahe)                            1)
-8      0.026   +3.8    1865    Great Southern Comet (Abbott)
-7      0.585   +0.0      66    P/Halley
-7      0.091   +3.4    1821    Nicollet-Pons
-7      0.006   +4.9    1843    Great March Comet
-6      0.222   +0.5    1744    (Klinkenberg)
-6      0.123   +3.2    1769    Messier
-6      0.005   +7.1    1880    Great Southern Comet (Gould)
-5?     0.38    +0.5    1402
-5      0.067   +6.0    1668    (Gottignies)
-5      0.042   +6.0    1695    (Jacob)
-5      0.043   +6.8    1847    Hind
-5      0.061   +7.0    1882    Wells
-4      0.486   +2.0    1472    (Regiomontanus)
-4      0.089   +6.0    1593    (Ripensis)
-4      0.106   +4.9    1665    (Hevelius)
-4      0.005   +6.3    1887    Great Southern Comet (Thome)
-4      0.129   +5.0    1910    Great January Comet
-3      0.169   +4.8    1582    (Brahe)
-3      0.215   +4.0    1758    (De la Nux)
-3      0.126   +6.2    1830    (Herapath)
-3      0.176   +5.2    1927    Skjellerup-Maritsany
-3      0.110   +6.0    1947    Southern Comet
-3      0.135   +5.5    1948    Eclipse Comet
-3      0.142   +5.2    1973    Kohoutek                           2)
-3      0.197   +4.6    1976    West                               3)
-2      0.77    +3.5    1092
-2      0.255   +3.0    1533    (Apian)
-2      0.223   +4.0    1737    (Bradley)
-2      0.342   +4.0    1819    (Tralles)
-2      0.227   +4.2    1823    (De Breaute-Pons)
-2      0.192   +5.2    1895    Perrine
-2      0.031   +6.6    1962    Seki-Lines
-1      0.825   +3.5    1264
-1      0.493   +1.2    1433
-1      0.519   +1.8    1532    (Fracastor)
-1      0.281   +4.5    1558    (Hesse-Gemma)
-1      1.026   +2.4    1664    (Hevelius)
-1      0.281   +4.4    1677    (Hevelius)
-1      0.674   +7.7    1770    P/Lexell (Messier)
-1      0.250   +4.9    1844    (Wilmot)
-1      0.909   +6.0    1853    Schweizer
-1      0.307   +4.8    1853    Klinkerfues
-1      0.822   +3.9    1861    Tebbutt
-0.7    0.914   -0.8    1997    Hale-Bopp                          4)
-0.5    0.316   +5.1    1957    Arend-Roland
 0.0    0.230   +5.5    1996    Hyakutake                          5)

Remarks: 1) -0.5 is the mean of results derived by Mucke (0.8) and by Vsekhsvyatskii (-1.8)!
         2) Kohoutek could not be seen brighter than 1.5 mag from earth.
         3) the maximum brightness of comet West most probably was -2 mag.
         4) Hale-Bopp: analysis by Kammerer
         5) the maximum brightness of comet Hyakutake was 0.0 mag (Sauval gave -0.5 mag)

Michael Jäger has participated in the project of determining the length of the tails of comet Hale-Bopp via the naked eye and photographs. He observed from the Alps, experiencing excellent conditions several times. He used TP 2415 hyp. in February and Kodak Pro Gold 400 thereafter, the lengths were estimated to within 1°. By considering the uncertainty of 1°, only in three cases (for the ion, dust and dust tail) did he notice longer visual tail lengths than the photographs of the same day show. However, two of these cases can be explained by the known experience that our eye-brain-system artificially lengthens faint, linear features if there are conspicuous stars or star groups in line. This was the case on March 15, when the ion tail pointed on the star group around delta Cep (a few days before I dropped a note to Daniel Green, proposing a significant increase within the estimates of those days, which then took place!) and on April 8 when the dust tail pointed to epsilon Cas. Only the case of April 12 so far cannot be settled, for I have no wide-angle photograph which definitely shows the dust tail in its whole extent and orientation. Conclusion: this project has shown, that photographs are more reliable than naked eye estimates (as was considered a fact before the extreme estimates of the tail of Hyakutake cast doubt on it). Naked eye estimates are prone to illusion effects, caused by our eye-brain-system. However, the project showed also, that the naked eye can compete with at least color emulsions.

Andreas Kammerer


Observations


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