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Churyumov-Gerasimenko
Advances in Space Research 38 (2006) 1958–1960 www.elsevier.com/locate/asr
Physical parameters of the plasma tail of Rosetta target comet 67P/Churyumov-Gerasimenko K.I. Churyumov
*
Kyiv Shevchenko National University, 3 Observatorna, Kyiv 04053, Ukraine Received 1 November 2004; received in revised form 12 October 2005; accepted 13 October 2005
Abstract On the basis of photometric processing of the two large scale photographic images of comet 67P obtained in Nizhny Arkhyz with the help of the 6-BTA reflector of SAO of RAS and using the diffusion model of L. Shulman and H. Nazarchuk some physical parameters of magnetic field of the comet plasma tail (coefficients of diffusion and induction of magnetic field) were determined. 2006 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Comet 67P/Churyumov-Gerasimenko; Plasma tail; Magnetic field; Diffusion model; Coefficient of diffusion; Induction
Parameters of the magnetic field in the comet 67P/ Churyumov-Gerasimenko plasma tail Comet 67P was discovered by K.I. Churyumov and S.I. Gerasimenko on 22 October, 1969 (Churyumov and Gerasimenko, 1972). The original plates with the large scale image of comet 67P/Churyumov-Gerasimenko were obtained by I.D. Karachentsev and K.I. Churyumov January 12.105 UT and 13.124 UT, 1983 with a 6-m telescope BTA of the Special Astrophysical Observatory of RussiaÕs Academy of Sciences at Mount Pastukhov (Fig. 1). These plates are first observations of a comet with one of the biggest ground based telescope. The BTA is located at the gorge of Seven Brooks at the height of 2070 m. The main mirror diameter is 6.05 m, the focal distance 24 m. The Ritchy cassette with a corrector and a field lens was used. The pictures of the comet 67P/Churyumov-Gerasimenko are obtained on emulsion Kodak IIaO with hypersensitivity in H2. For quantitative estimation of some physical parameters of the plasma tail of comet 67P/Churyumov-Cerasimenko the diffusion model (Nazarchuk and ShulÕman, 1968; Nazarchuk, 1969) was used. *
Tel.: +380 55 2161994; fax: +380 44 2272781. E-mail address: [email protected]
0273-1177/$30 2006 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2005.10.038
The diffusion model is based on the following assumptions. The cometary nucleus with its surroundings is considered a point source of matter; this assumption is acceptable because of the small size of a cometary nucleus as compared with its tail. The Green function for an instantaneous source is used. It is assumed that the center of mass of any instantaneously emitted package of particles moves with a uniform acceleration along the axis of the cometÕs tail, the outflow of matter has begun infinitely long ago, and the source power C is constant. A cometary ion is also considered to acquire random momenta from inhomogeneities of self-consistent fields which move through the tail; i.e., the process of the interaction between cometary ions and the solar wind is assumed to be macrostochastic. Then the motion of a cometary ion is a superposition of diffusion and transport to the tail. In this case, the Green function has the form of an anisotropic function for exponentially disappearing particles G¼
4pt
1 qffiffiffiffiffiffiffiffiffiffiffiffi Dk D?
! 2 2 ðx aðt Þ =2Þ y2 t exp ; 4Dk t 4D? t s
ð1Þ
where t* is the age of the particle package; Dk ¼ Dk cos2 b þ D? sin2 b is the coefficient of diffusion along
K.I. Churyumov / Advances in Space Research 38 (2006) 1958–1960
1959
cometary forms, 1 + l P 10 (where l is the effective acceleration of a particle), we have: ms ð7Þ a P c 2 ð1 þ lÞ; r where c is the gravitational constant and ms is the solar mass. From the obtained lower bounds for the acceleration (7), upper bounds for the lifetime of glowing particles were estimated: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CLk s6 . ð8Þ 2a cos b The surface brightness can be represented as Fig. 1. Comet 67P/Churyumov-Gerasimenko 13 Jan. 1983 (North is above).
IðX ; Y Þ ¼ k
C qffiffiffiffiffiffiffiffiffiffiffiffi 4p Dk D?
the cometÕs tail in the plane of the sky; Di and D^ are the coefficients of longitudinal and transversal diffusion, respectively; s is the average lifetime of glowing particles; and b is the angle between the tail axis and its projection onto the plane of the sky. Here, the x-axis is directed along the cometÕs tail (anti sun-ward), and the y-axis is perpendicular to it. The chemical composition of the glowing matter is assumed to be uniform in the tail. Then the surface brightness is proportional to the surface density of the glowing particles I = kn (x, y). Here nðx; y Þ ¼
C qffiffiffiffiffiffiffiffiffiffiffiffi 4p Dk D?
Z
1 0
0
B exp @
2
x at2
1
2
4Dk t
y2 t dtC A. 4D? t s t
ð2Þ
we
introduce
and the dimensionless quantity t h¼ . 2s
the
1 0
! ðX Ch2 Þ2 þ Y 2 dh . h exp h h
ð9Þ
As seen from (9), the surface brightness depends on one significant parameter C and three scale factors Li, L^, and ffi. The problem is in the determination of these valk 4ppCffiffiffiffiffiffiffiffi D D ?
k
ues from the surface-brightness distribution known from observations. The longitudinal and transverse photometric cross sections of the cometary plasma tail are fitted with ones calculated theoretically through the selection of the above parameters. With the use of the logarithmic, the theoretical law of the brightness decrease can be represented as the sum of a constant and a family of curves 2:5 log I ¼ const 2:5 log UðX ; Y ; CÞ;
ð10Þ
where Z U¼
ð11Þ
1
0
For convenience, coordinates x y X ¼ ; Y ¼ Lk L?
Z
! 2 ðX Ch2 Þ þ Y 2 dh . h exp h h
dimensionless ð3Þ
ð4Þ
Here, the longitudinal Li and the transverse L^ scale are chosen as follows: qffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ð5Þ Lk ¼ 2 Dk s; L? ¼ 2 D? s. We also introduce a dimensionless parameter C that determines the acceleration a sffiffiffiffiffiffi s3 C¼a cos b. ð6Þ Dk Lower estimates were obtained for the acceleration. Since for plasma tails, according to the mechanical theory of
The acceleration values from (7) were also used to determine the coefficients of the longitudinal and transversal diffusion: 2 ! 3=2 rffiffiffiffiffiffi Lk a L? Dk ¼ sin b 1 ; ð12Þ 8C cos b Lk sffiffiffiffiffiffiffiffiffiffiffiffiffiffi a cos b 2 . ð13Þ D? ¼ L? 8CLk These are lower estimates for the diffusion coefficients. The magnetic induction was estimated by the formula of Shabas (1999)
Table 1 Parameters of the diffusion model Date, UT
C
Li (km)
L^ (km)
Jan. 12.105, 1983 Jan. 13.124, 1983
14 15
2.2 · 105 2.1 · 105
2.21 · 104 1.476 · 104
1960
K.I. Churyumov / Advances in Space Research 38 (2006) 1958–1960
Table 2 Physical parameters in the plasma tail of comet 67P/Churyumov-Gerasimenko Date, UT
r (A.U.)
D (A.U.)
12 Jan. 1983
1.491
0.531
13 Jan. 1983
1.497
0.538
B ¼ 2 1011
T Lk =ðL? cos bÞ½nT. Dk
a (cm/s2)
s (s) 5
2.7 15 2.7 16
10 2.4 · 105 105 2.5 · 105
ð14Þ
The temperature of the cometary plasma was assumed to be 5 · 105 and 2 · 106 K for the minimum and the maximum estimate of the magnetic induction, respectively (Galeev, 1989; Wegmann et al., 1987). Comparison of the theoretical and observed photometric profiles made it possible to determine parameters of the diffusion model for plasma tails of 67P/ChuryumovGerasimenko comet. values are given pffiffiffiffiffiffiffiTheir ffi pffiffiffiffiffiffiffiffi ffi in the Table 1. Notes. Lk ¼ 2 Dk s and L? ¼ 2 D? s are longitudinal and cross characteristic scales, Di and D^ are longitudinal and cross diffusion coefficients. Values of the physical parameters of the plasma tail of comet 67P/Churyumov-Gerasimenko are given in Table 2. In order to evaluate induction of the magnetic field temperatures in the tail of the comet 67P/Churyumov-Gerasimenko were taken equal to 104 and 105 K. Conclusion Some physical parameters of the comet plasma tail, coefficients of diffusion Di, D^ and induction of magnetic field B are fitted with the ones: (Jan. 12.105, 1983 UT: Di = 5.07 · 1014 ‚ 1.21 · 1015 cm2/s, D^ = 5.73 · 1013 ‚ 1.37 · 1014 cm2/s, B = 46 ‚ 111 nT; Jan. 13.124, 1983 UT: Di = 4.67 · 1014 ‚ 1.14 · 1015 cm2/ s, D^ = 4.30 · 1013 ‚ 1.05 · 1014 cm2/s, B = 55 ‚ 134 nT). The obtained upper estimates of induction of the magnetic field B @ 111 nT for 12 Jan., 1983 and B @ 134 nT for 13 Jan., 1983 probably surpass real values of B in the come-
Di (cm/s) 14
5.07 · 10 1.21 · 1015 4.67 · 1014 1.14 · 1015
D^ (cm/s) 13
5.73 · 10 1.37 · 1014 4.30 · 1013 1.05 · 1014
B (nTl) 46 ‚ 111 55 ‚ 134
tary plasma tail. However good coincidence of the theoretical and observed data seems to be proof of the plasma nature of the comet tail in question. Moreover, the comet tail looks rather narrow and straight without a noticeable expansion that may be a proof in favor of the high magnetic field that keeps the cometary plasma in a narrow cylinder. The tail shape that practically did not change during the day makes it more probable to consider this tail to be a strongly magnetized plasma jet. This peculiarity of magnetic fields in the plasma tail of comet 67P/ChuryumovGerasimenko may be connected with magnetic properties of the surface layers of the cometary nucleus. Whether or not a comet nucleus possesses a magnetic field will however only be known after the ROMAP instrument on board the ROSETTA Lander will have conducted its magnetic field measurements in 2014. References Churyumov, K.I., Gerasimenko, S.I. Physical observations of the shortperiod comet 1969 IV. The motion, Evolution of orbits, and origin of comets, In: Chebotarev et al. (Eds.), Proceedings of Symposium 45 of the IAU, pp. 27–34, 1972. Galeev, A.A. Plasma processes in the outer coma. Astrophysics and Space Science Library 167, 1145–1170, 1989. Nazarchuk, G.K., ShulÕman, L.M. Diffusion model of cometary tails, Problemy kosmicheskoy fiziki, 3 (in Russian) 1968. Nazarchuk, G.K. Analysis of surface-brightness distribution in the tail of comet 1956h. Astrometriya and Astrophysica, 9, Kiev, Naukova Dumka, pp.77–99, 1969 (in Russian). Shabas, N.L. Physical parameters of the plasma tail of comet 67P/ Churyumov-Gerasimenko, Visnyk of Kyiv Univ., Astronomy, 35, pp. 80–83, 1999 (in Ukrainian). Wegmann, R., Schmidt, H.U., Hubner, W.F, Boice, D.C. Cometary MHD and Chemistry, Astron. Astrophysics 187, 339–350, 1987.
Physical parameters of the plasma tail of Rosetta target comet 67P/Churyumov-Gerasimenko K.I. Churyumov
*
Kyiv Shevchenko National University, 3 Observatorna, Kyiv 04053, Ukraine Received 1 November 2004; received in revised form 12 October 2005; accepted 13 October 2005
Abstract On the basis of photometric processing of the two large scale photographic images of comet 67P obtained in Nizhny Arkhyz with the help of the 6-BTA reflector of SAO of RAS and using the diffusion model of L. Shulman and H. Nazarchuk some physical parameters of magnetic field of the comet plasma tail (coefficients of diffusion and induction of magnetic field) were determined. 2006 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Comet 67P/Churyumov-Gerasimenko; Plasma tail; Magnetic field; Diffusion model; Coefficient of diffusion; Induction
Parameters of the magnetic field in the comet 67P/ Churyumov-Gerasimenko plasma tail Comet 67P was discovered by K.I. Churyumov and S.I. Gerasimenko on 22 October, 1969 (Churyumov and Gerasimenko, 1972). The original plates with the large scale image of comet 67P/Churyumov-Gerasimenko were obtained by I.D. Karachentsev and K.I. Churyumov January 12.105 UT and 13.124 UT, 1983 with a 6-m telescope BTA of the Special Astrophysical Observatory of RussiaÕs Academy of Sciences at Mount Pastukhov (Fig. 1). These plates are first observations of a comet with one of the biggest ground based telescope. The BTA is located at the gorge of Seven Brooks at the height of 2070 m. The main mirror diameter is 6.05 m, the focal distance 24 m. The Ritchy cassette with a corrector and a field lens was used. The pictures of the comet 67P/Churyumov-Gerasimenko are obtained on emulsion Kodak IIaO with hypersensitivity in H2. For quantitative estimation of some physical parameters of the plasma tail of comet 67P/Churyumov-Cerasimenko the diffusion model (Nazarchuk and ShulÕman, 1968; Nazarchuk, 1969) was used. *
Tel.: +380 55 2161994; fax: +380 44 2272781. E-mail address: [email protected]
0273-1177/$30 2006 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2005.10.038
The diffusion model is based on the following assumptions. The cometary nucleus with its surroundings is considered a point source of matter; this assumption is acceptable because of the small size of a cometary nucleus as compared with its tail. The Green function for an instantaneous source is used. It is assumed that the center of mass of any instantaneously emitted package of particles moves with a uniform acceleration along the axis of the cometÕs tail, the outflow of matter has begun infinitely long ago, and the source power C is constant. A cometary ion is also considered to acquire random momenta from inhomogeneities of self-consistent fields which move through the tail; i.e., the process of the interaction between cometary ions and the solar wind is assumed to be macrostochastic. Then the motion of a cometary ion is a superposition of diffusion and transport to the tail. In this case, the Green function has the form of an anisotropic function for exponentially disappearing particles G¼
4pt
1 qffiffiffiffiffiffiffiffiffiffiffiffi Dk D?
! 2 2 ðx aðt Þ =2Þ y2 t exp ; 4Dk t 4D? t s
ð1Þ
where t* is the age of the particle package; Dk ¼ Dk cos2 b þ D? sin2 b is the coefficient of diffusion along
K.I. Churyumov / Advances in Space Research 38 (2006) 1958–1960
1959
cometary forms, 1 + l P 10 (where l is the effective acceleration of a particle), we have: ms ð7Þ a P c 2 ð1 þ lÞ; r where c is the gravitational constant and ms is the solar mass. From the obtained lower bounds for the acceleration (7), upper bounds for the lifetime of glowing particles were estimated: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CLk s6 . ð8Þ 2a cos b The surface brightness can be represented as Fig. 1. Comet 67P/Churyumov-Gerasimenko 13 Jan. 1983 (North is above).
IðX ; Y Þ ¼ k
C qffiffiffiffiffiffiffiffiffiffiffiffi 4p Dk D?
the cometÕs tail in the plane of the sky; Di and D^ are the coefficients of longitudinal and transversal diffusion, respectively; s is the average lifetime of glowing particles; and b is the angle between the tail axis and its projection onto the plane of the sky. Here, the x-axis is directed along the cometÕs tail (anti sun-ward), and the y-axis is perpendicular to it. The chemical composition of the glowing matter is assumed to be uniform in the tail. Then the surface brightness is proportional to the surface density of the glowing particles I = kn (x, y). Here nðx; y Þ ¼
C qffiffiffiffiffiffiffiffiffiffiffiffi 4p Dk D?
Z
1 0
0
B exp @
2
x at2
1
2
4Dk t
y2 t dtC A. 4D? t s t
ð2Þ
we
introduce
and the dimensionless quantity t h¼ . 2s
the
1 0
! ðX Ch2 Þ2 þ Y 2 dh . h exp h h
ð9Þ
As seen from (9), the surface brightness depends on one significant parameter C and three scale factors Li, L^, and ffi. The problem is in the determination of these valk 4ppCffiffiffiffiffiffiffiffi D D ?
k
ues from the surface-brightness distribution known from observations. The longitudinal and transverse photometric cross sections of the cometary plasma tail are fitted with ones calculated theoretically through the selection of the above parameters. With the use of the logarithmic, the theoretical law of the brightness decrease can be represented as the sum of a constant and a family of curves 2:5 log I ¼ const 2:5 log UðX ; Y ; CÞ;
ð10Þ
where Z U¼
ð11Þ
1
0
For convenience, coordinates x y X ¼ ; Y ¼ Lk L?
Z
! 2 ðX Ch2 Þ þ Y 2 dh . h exp h h
dimensionless ð3Þ
ð4Þ
Here, the longitudinal Li and the transverse L^ scale are chosen as follows: qffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ð5Þ Lk ¼ 2 Dk s; L? ¼ 2 D? s. We also introduce a dimensionless parameter C that determines the acceleration a sffiffiffiffiffiffi s3 C¼a cos b. ð6Þ Dk Lower estimates were obtained for the acceleration. Since for plasma tails, according to the mechanical theory of
The acceleration values from (7) were also used to determine the coefficients of the longitudinal and transversal diffusion: 2 ! 3=2 rffiffiffiffiffiffi Lk a L? Dk ¼ sin b 1 ; ð12Þ 8C cos b Lk sffiffiffiffiffiffiffiffiffiffiffiffiffiffi a cos b 2 . ð13Þ D? ¼ L? 8CLk These are lower estimates for the diffusion coefficients. The magnetic induction was estimated by the formula of Shabas (1999)
Table 1 Parameters of the diffusion model Date, UT
C
Li (km)
L^ (km)
Jan. 12.105, 1983 Jan. 13.124, 1983
14 15
2.2 · 105 2.1 · 105
2.21 · 104 1.476 · 104
1960
K.I. Churyumov / Advances in Space Research 38 (2006) 1958–1960
Table 2 Physical parameters in the plasma tail of comet 67P/Churyumov-Gerasimenko Date, UT
r (A.U.)
D (A.U.)
12 Jan. 1983
1.491
0.531
13 Jan. 1983
1.497
0.538
B ¼ 2 1011
T Lk =ðL? cos bÞ½nT. Dk
a (cm/s2)
s (s) 5
2.7 15 2.7 16
10 2.4 · 105 105 2.5 · 105
ð14Þ
The temperature of the cometary plasma was assumed to be 5 · 105 and 2 · 106 K for the minimum and the maximum estimate of the magnetic induction, respectively (Galeev, 1989; Wegmann et al., 1987). Comparison of the theoretical and observed photometric profiles made it possible to determine parameters of the diffusion model for plasma tails of 67P/ChuryumovGerasimenko comet. values are given pffiffiffiffiffiffiffiTheir ffi pffiffiffiffiffiffiffiffi ffi in the Table 1. Notes. Lk ¼ 2 Dk s and L? ¼ 2 D? s are longitudinal and cross characteristic scales, Di and D^ are longitudinal and cross diffusion coefficients. Values of the physical parameters of the plasma tail of comet 67P/Churyumov-Gerasimenko are given in Table 2. In order to evaluate induction of the magnetic field temperatures in the tail of the comet 67P/Churyumov-Gerasimenko were taken equal to 104 and 105 K. Conclusion Some physical parameters of the comet plasma tail, coefficients of diffusion Di, D^ and induction of magnetic field B are fitted with the ones: (Jan. 12.105, 1983 UT: Di = 5.07 · 1014 ‚ 1.21 · 1015 cm2/s, D^ = 5.73 · 1013 ‚ 1.37 · 1014 cm2/s, B = 46 ‚ 111 nT; Jan. 13.124, 1983 UT: Di = 4.67 · 1014 ‚ 1.14 · 1015 cm2/ s, D^ = 4.30 · 1013 ‚ 1.05 · 1014 cm2/s, B = 55 ‚ 134 nT). The obtained upper estimates of induction of the magnetic field B @ 111 nT for 12 Jan., 1983 and B @ 134 nT for 13 Jan., 1983 probably surpass real values of B in the come-
Di (cm/s) 14
5.07 · 10 1.21 · 1015 4.67 · 1014 1.14 · 1015
D^ (cm/s) 13
5.73 · 10 1.37 · 1014 4.30 · 1013 1.05 · 1014
B (nTl) 46 ‚ 111 55 ‚ 134
tary plasma tail. However good coincidence of the theoretical and observed data seems to be proof of the plasma nature of the comet tail in question. Moreover, the comet tail looks rather narrow and straight without a noticeable expansion that may be a proof in favor of the high magnetic field that keeps the cometary plasma in a narrow cylinder. The tail shape that practically did not change during the day makes it more probable to consider this tail to be a strongly magnetized plasma jet. This peculiarity of magnetic fields in the plasma tail of comet 67P/ChuryumovGerasimenko may be connected with magnetic properties of the surface layers of the cometary nucleus. Whether or not a comet nucleus possesses a magnetic field will however only be known after the ROMAP instrument on board the ROSETTA Lander will have conducted its magnetic field measurements in 2014. References Churyumov, K.I., Gerasimenko, S.I. Physical observations of the shortperiod comet 1969 IV. The motion, Evolution of orbits, and origin of comets, In: Chebotarev et al. (Eds.), Proceedings of Symposium 45 of the IAU, pp. 27–34, 1972. Galeev, A.A. Plasma processes in the outer coma. Astrophysics and Space Science Library 167, 1145–1170, 1989. Nazarchuk, G.K., ShulÕman, L.M. Diffusion model of cometary tails, Problemy kosmicheskoy fiziki, 3 (in Russian) 1968. Nazarchuk, G.K. Analysis of surface-brightness distribution in the tail of comet 1956h. Astrometriya and Astrophysica, 9, Kiev, Naukova Dumka, pp.77–99, 1969 (in Russian). Shabas, N.L. Physical parameters of the plasma tail of comet 67P/ Churyumov-Gerasimenko, Visnyk of Kyiv Univ., Astronomy, 35, pp. 80–83, 1999 (in Ukrainian). Wegmann, R., Schmidt, H.U., Hubner, W.F, Boice, D.C. Cometary MHD and Chemistry, Astron. Astrophysics 187, 339–350, 1987.