A synthetical index of the potential threats about intense activities of meteors

New Astronomy 12 (2006) 52–59 www.elsevier.com/locate/newast

A synthetical index of the potential threats about intense activities of meteors Guang-jie Wu

*

National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, P.O.Box 110, Kunming, Yunnan Province 650011, China Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China Received 19 February 2006; received in revised form 30 May 2006; accepted 9 June 2006 Available online 28 June 2006 Communicated by G.F. Gilmore

Abstract In the present age, several techniques for the application to the observation of meteors and meteor showers have been developed in modern meteor astronomy. The initial definition for a meteor storm based on the visual observation with a Zenithal Hourly Rate of above 1000 seems insufficient now, since it only means a storm or burst of meteors in numbers and means that an eyewitness could have a chance to see a spectacular meteor show. Up to now, peoples have also recorded the meteoric flashes on the Moon during the Leonid meteor showers. Especially, the increasing activities of mankind in space for scientific, commercial and military purposes, have led to an increase in the problems concerning the safety of the satellites, space stations and astronauts. How the intense activity of a meteor storm is defined and forecast, some new points of view are needed. In this paper, several aspects about the intensity of the meteor storm are analyzed, including the number, mass, impulse, energy, electric charge, different purposes and different physical meanings. Finally, a synthetical index denoting the activity and potential threat of an intense meteor shower is suggested.  2006 Elsevier B.V. All rights reserved. PACS: 96.30.Za; 94.05.Hk; 95.75.z Keywords: Meteors; Meteorites and tektites; Spacecraft/atmosphere interactions; Observation and data reduction techniques

1. Introduction The shooting star, or meteoric phenomenon, is a complex physical and chemical phenomenon in the Earth’s atmosphere, which means that cosmic particles rush into the atmosphere and blaze. It is known that most of the meteoric streams come from comets. Though several new techniques for the application to the observation of meteor showers have been developed in modern meteor astronomy, the visual observation is still the most popular and fundamental. Based on the rather simple records of the number and magnitudes of the meteors, the population

*

Tel.: +86 871 3920153; fax: +86 871 3911845. E-mail addresses: [email protected].

1384-1076/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2006.06.002

index r and Zenithal Hourly Rate (ZHR) can be obtained and compared worldwide, indicating the magnitude distribution and intensity of the meteors, respectively. The initial definition for a meteor storm comes from a ZHR of above 1000. It is obvious that it only means a storm or burst of the meteors in numbers and means that an eyewitness could have a chance to see a spectacular meteor show. Today, human beings no longer regard the shooting stars as the theandric bodies. Moreover, the optical flashes produced by the Leonid meteoroids impacting the Lunar surface were successfully discovered (Dunham, 1999; Ortiz et al., 2000; Bellot Rubio et al., 2000). Peoples know more about the meteors and meteor showers than before. However, in resent years, the increasing activities of mankind in space for scientific, commercial and military purposes, have led to an increase in safety-related problems. The

G.-j. Wu / New Astronomy 12 (2006) 52–59

potential threats to space flight instruments and astronauts, stemming from some intense meteor storms and the space debris, have been noticed (McBride and McDonnell, 1999; Cerroni and Martelli, 1982; Foschini, 1998; Foschini, 2002). As early as 1977, the International Sun Earth Explorer (ISEE-1) was hit by a meteoroid, which results in the lose of 25% of the data. The Hubble Space Telescope also suffered the impact of about 6000 times during its first 4-year flying (Bedingfield et al., 1996; Foschini, 2002). On August 12, 1993, MIR-1 Space Station experienced about 2000 hits during 24 h and its solar panels were severely damaged. The astronauts aboard this station also reported some audible meteoroid hits (Beech et al., 1995; Foschini, 2002). In addition, in the same night, the Olympus Telecommunication Satellite of ESA lost its control and culminated in an early end of this mission, and it was presumed that there were electrical failures caused by the impact of the Perseids meteoroid (Caswell et al., 1995; Foschini, 2002). The widespread destruction can be caused by meteoroids. In despite of a meteoroid, which in general has the small mass, it possesses a great kinetic momentum and energy, since its geocentric velocity can be high up to 11–72 km s1. In addition, a tremendous amount of meteoroids might be encountered in a short time. In Leonids 1966, a ZHR of about 150,000 meteors was ever recorded (Yeomans, 1981; Jenniskens, 1995; McNaught and Asher, 1999; Wu, 2002). In despite of considering the new results after the Leonids 2001, Jenniskens (2002) concluded that the level should have been closer to 15,000 than 150,000, people often think that Leonids is one of the most dangerous meteor streams, even under the normal conditions (Jenniskens et al., 1998; McBride and McDonnell, 1999; Foschini, 2002). Moreover, in an impact, the shock waves can be generated and propagate along the colliding bodies, compressing and heating both the target and meteoroid. A plasma cloud may enclose the target and expands into the surrounding vacuum, releasing electromagnetic radiation in a wide spectral range. It is obvious that the most intense meteor streams are not only worth to be viewed and admired, but also are hazardous some times. How to define and forecast the intense activity of a meteor storm and how to reduce the underlying damage to the great extent, some new points of view and definitions for meteor storms are needed. In this paper, the author tries to think about several aspects of a meteor storm, including its number, mass, impulse, energy and electric state. Finally, a synthetical index of the potential threat about an intense activity of meteors is suggested. In addition, according to different special purposes, one can emphasize some aspect or others. 2. The Zenithal Hourly Rate and the true number flux density

ZHRo ¼

N Obs  r6:5Lm  sinðhr Þc  c1 p ; T eff

ð1Þ

where NObs is the total number of meteors recorded by the observer, Teff the effective observing time in hours, Lm the limiting stellar magnitude and hr the elevation of the shower’s radiant at the observing time. The perception correction cp varies between 0.4 and 2.5, having a median value close to 1.0 (Jenniskens, 1994). Usually, we can adopt c = 1.0 (Bellot Rubio, 1995; Wu and Zhang, 1998), but in some cases its value may be up to 1.4, even 1.8 (Watanabe et al., 1999; Jenniskens, 1994). These measurements may be obtained by different observers at different places in variable environments, however, through the above formula they are reduced under a standard condition and can be compared worldwide (Koschack and Rendtel, 1990a,b; Jenniskens, 1994; Wu and Zhang, 1998; Wu and Zhang, 2002; Zhang and Wu, 2002). Obviously, this definition of ZHR for the activity of a meteor shower is the most intuitional and simple one. In Eq. (1), the population index r represents the ratio of the true numbers of meteors in two neighboring magnitude classes of (m) and (m  1) Nm r¼ : ð2Þ N m1 In general, it is assumed that r is a constant at least in the whole magnitude range covered by the visual observation. Then, one may have N m ¼ N 0  rm :

ð3Þ

However, it is normal for a meteor to move fast and stay in the sky for less than one second. Therefore, the visual observation of meteors should depend upon the sensitivity to light and the perceptive speed of the naked eye. Only a fraction of meteors can be seen. The observed number of the meteors at a certain magnitude m is N m;Obs ¼ N m  P ðDmÞ;

ð4Þ

where Dm is the magnitude difference Dm ¼ Lm  m;

ð5Þ

and Dm P 0. P(Dm) is called the ‘‘probability of perception’’ or ‘‘perception function’’. P For the whole visual observation N Obs ¼ N m;Obs and the ratio of the total true number to the observed one is P Pþ1 Dm Nm 0 r cðrÞ ¼ P ¼ Pþ1 Dm : ð6Þ N m;Obs r  P ðDmÞ 0 This factor can be used to get the true number of meteors with the corrections of NObs, ZHRo, etc. From the data (as ‘‘KRO’’ and ‘‘±’’, the error, listed in Table 1) of five advanced observers, Koschack and Rendtel (1990b) took the correction as cðrÞ ¼ 13:10r  16:45;

For measuring the relative strength of the meteor showers, as far as the visual observation is concerned, the observed Zenithal Hourly Rate is defined as

53

ð7Þ

and Arlt (1998) gave a new expression cðrÞ ¼ 0:987  5:918r þ 6:637r2  0:754r3 :

ð8Þ

54

G.-j. Wu / New Astronomy 12 (2006) 52–59

Table 1 Comparison of c(r) calculated in this paper with the calculations of c(r) obtained by different authors r

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

Cal Arlt KRC KRO ±

3.43 3.64 1.89

5.22 5.42 4.51

7.33 7.44 7.13 7.34 0.36

9.69 9.67 9.75 9.66 0.56

12.2 12.1 12.4 12.2 0.8

14.9 14.6 15.0 14.8 1.1

17.7 17.2 17.6 17.5 1.5

20.5 19.9 20.2 20.2 1.8

23.3 22.6 22.9 23.0 2.2

26.0 25.3 25.5 25.6 2.6

28.8 28.0 28.1 28.2 3.0

31.5 30.5 30.7 30.8 3.4

34.1 33.0 33.3 33.3 3.8

36.7 35.3 36.0 35.7 4.1

ZHRo  cðrÞ Nm ¼ ; Ared ðrÞ  Ared ðrÞ

ð11Þ

These calculations obtained from the above formula are, respectively, expressed as ‘‘KRC’’ and ‘‘Arlt’’, listed in Table 1. One can understand from the above description that the probability of perception is a very important parameter in the visual observation. From each class of magnitude and the average over the entire field of view, Koschack and Rendtel found an average probability P(Dm) and expressed it as a table. In addition, they proved that an individual deviation from the ‘‘standard’’ perception function can be expressed by an error of the limiting magnitude, DLm, and may be regarded as a correction for the limiting magnitude instead of the probability of perception (Koschack and Rendtel, 1990a,b). Their suggestions have become the standard methods in the meteor community. On the other hand, for convenience sake and accurate calculation, an analytic perception function has been found out by the author and is finally expressed as P ðDmÞ ¼ 0:5 þ 0:505  tanhð0:66  Dm  0:013  Dm2  2:43Þ; ð9Þ while Dm < 9.4633, otherwise P(Dm) ” 1 (Wu, 2005; Wu and Li, 2003). In virtue of Eqs. (6) and (9), it is easy to calculate the values of the factor c(r) directly, which are listed in the first row of Table 1, i.e. ‘‘Cal’’. It is obvious that when r 6 2.6, the values of ‘‘Cal’’ are better than those of ‘‘KRC’’ and ‘‘Arlt’’. If not, the larger the r is, the larger the deviation is, since the analytic function P(Dm) is not fit for the c(r) values, ‘‘KRO’’, but for the probability of perception. However, all of the deviations are still much smaller than the deviations ‘‘±’’ of ‘‘KRO’’, so that the formulae of calculation (6) and (9) can be completely used anywhere, as they can be in this paper. In order to calculate the spatial number flux and density of a meteor stream the area surveyed by an observer at the meteor level (height H = 100 km) should be known. This area of the field depends upon the meteor’s magnitude distribution and there is no great systematic and significant difference for the observers. In general, the reduced area Ared can be expressed as 0:748

Ared ðrÞ ¼ 37; 200ðr  1:3Þ

km2 :

ð10Þ

Then, the true number flux density of the meteoroids producing meteors with a magnitude of at least 6.5 can be reduced as

P QN 6 ¼ QN ðm 6 6:5Þ ¼

T eff

and compared worldwide (Koschack and Rendtel, 1990a,b), which is in units of meteors h1 km2. Since X X rmup  rmlow þ1 Nm ¼ N0  ; ð12Þ rm ¼ N 0 1r for two different values of mlow X rmup  rm1low þ1 X N m1 ¼ mup N m2 ; ð13Þ r  rm2low þ1 and for any setting of the magnitude of mlow, the true number flux density is rmlow mup þ1  1 : ð14Þ r7:5mup  1 Then, the true spatial number density of the meteoroids is QN qN ¼ ; ð15Þ 3600V 0 QN ðmup 6 m 6 mlow Þ ¼ QN 6 

where the geocentric velocity V0 of the meteoroid is in units of km s1 and can be got from its spatial velocity V1: V 20 ¼ V 21 þ ð11:19Þ2 :

ð16Þ

In general, it is thought that a meteor storm at least has a ZHRo > 1000. If r is assumed to be 2.4, then, Ared(r) should be about 34,640 km2 and the flux density QN6 = 0.43 h1 km2. In view of r from 1.4 to 3.6, the flux density QN6 is about 0.02–1.58 h1 km2, it might be suitable to set QN P 0.4 h1 km2 as the standard of a meteor storm. 3. The effect of a meteor storm reflecting on the mass According to the concept of the true number flux density QN, the true mass flux density P N mM m QM ¼ ; ð17Þ T eff  Ared ðrÞ and the true spatial mass density qM ¼

QM 3600V 0

ð18Þ

can be defined, where Mm represents the mass of a meteoroid with a magnitude of m. Various empirical mass-magnitude formulae have been used in the literature (Hughes, 1987; Koschack and Rendtel, 1990a,b; Jenniskens et al., 1998; Wu and Zhang, 2002). In this paper, we would like to use

G.-j. Wu / New Astronomy 12 (2006) 52–59

55

Table 2 Variation in the integral mass NmMm along the magnitude class for the total of 1000 Leonids meteors, in units of g r

m = 6.0

4.0

2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

qw

1.8 2.4 2.6

0.033 0.043 0.046

0.064 0.047 0.043

0.125 0.052 0.040

0.244 0.057 0.037

0.475 0.062 0.035

0.924 0.068 0.032

1.800 0.075 0.030

3.505 0.082 0.028

6.825 0.090 0.026

13.292 0.098 0.025

25.884 0.108 0.023

0.71659 0.95546 1.03508

Table 3 Average mass M ðgÞ in the magnitude range (15.5, 6.5) and setting V1 = 10 km s1 r

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

M

2676

342.3

58.25

13.42

4.306

1.926

1.132

0.8011

0.6348

0.5385

0.4766

Table 4 Some examples of QM6 = QM (15.5 6 m 6 6.5) when ZHR0 = 1000, in units of g h1 km2 V1 1

20 km s 40 km s1 70 km s1

r = 1.4

1.6

1.8

2.0

2.2

2.4

2.8

3.2

28.50 1.781 0.1899

9.540 0.5962 0.0636

2.509 0.1568 0.0167

0.7260 0.0454 0.0048

0.2549 0.0159 0.0017

0.1159 0.0072 0.0008

0.0527 0.0033 0.0004

0.0449 0.0028 0.0003

m ¼ 14:247  2:5 log M m  10:0 log V 1 mag;

ð19Þ

where the mass Mm is in units of g (Hughes and Williams, 2000). From this equation, it is easy to get Mm ¼

10

V

:

ð20Þ

Therefore, for the variation of the integral mass Wm = NmMm in Eq. (17) along the magnitude class the ratio has a relationship W mþDm N mþDm M mþDm ¼  ¼ qDm w ; Wm Nm Mm

ð21Þ

where qw ¼ r  100:4 :

m

¼ N 0M 0

5:70:4m 4 1

In virtue of Eq. (21) one may have the summation X   N m M m ¼ N 0 M 0  qmw low þ qmw low1 þ    þ qmw up

ð22Þ

Obviously, when r < 2.512, qw will be smaller than an unit. It means that the integral mass will become larger and larger and finally will be not convergent while the meteor becomes brighter and brighter. On the other hand, for r > 2.512 the integral mass Wm will also become larger and might be not convergent while the meteor becomes fainter and fainter. So, the value of 2.512 is a critical number of the population index r. Some examples are listed in Table 2. Fortunately, up to now, no single event of a meteor with a brightness of above about 15 magnitude has been reported by the visual observation (Bellot Rubio et al., 2000), which is basically consistent with the biggest particle capable of escaping from Comet Temple-Tuttle, on the order of 5 kg, suggested by the Whipple’s comet model (Whipple, 1951). Therefore, the upper-limit of mup = 15.5 mag might be used in this paper. For the same reason, a lower limit of mass should be also set, for example, it could be the least micrometeor having a mass of Mmicro = 5.2 · 1014 g, which is allowed by the solar ray pressure round the Earth’s orbit (Ma et al., 2005).

qw up  qmw low þ1 : 1  qw

ð23Þ

So, from Eqs. (12) and (23), the average mass in the whole relevant magnitude range may be obtained P m m þ1 N m M m 105:70:4mup 1  r 1  qw low up M¼ P ¼   ; ð24Þ 1  qw 1  rmlow mup þ1 Nm V 41 which is a function of r, V1 and the magnitude range. The calculated values of M in the range of (15.5 6 m 6 6.5) are listed in Table 3, where V1 is provisionally set at 10 km s1. For other velocities, it is easy to get the average mass. In the above equations, the application range of Eqs. (3) and (19) has actually been extended to the whole range between mlow and mup. In general, the true mass flux density can be rewritten as P M  Nm QM ðmup 6 m 6 mlow Þ ¼ T eff  Ared ðrÞ ¼ M  QN ðmup 6 m 6 mlow Þ:

ð25Þ

From the examples of Table 4 it is obvious that corresponding to a burst number of ZHRo = 1000 the value of QM6 is 0.016 g h1 km2 for r = 2.2 and V1 = 40 km s1, so the Mass-Burst should have a value of QM P 0.01 g h1 km2. The use of the true mass flux density QM and true spatial mass density qM may make it easy to connect a meteor stream to its mother comet. It is known that, the number of the meteoroids in a stream may change due to the disintegration of some meteoroids. However, the total mass of these meteoroids and spatial mass density may be more easy to keep their initial values after breaking out from

56

G.-j. Wu / New Astronomy 12 (2006) 52–59

its mother comet and might be a more useful quantity for prediction. 4. The effect of a meteor storm indicating the impulse From the concept of the true mass flux density QM, the true impulse flux density P N mM mV 0 ; ð26Þ QI ¼ T eff  Ared ðrÞ and the true spatial impulse density QI qI ¼ 3600V 0

ð27Þ

can be defined. In addition, in their calculation one may have QI ðmup 6 m 6 mlow Þ ¼ V 0  QM ðmup 6 m 6 mlow Þ:

ð28Þ

Therefore, for the whole integral impulse effect of the meteor stream, QI = 0.4 g km1 h1 s1 might be used as a kind of standard of a meteoric impulse storm. Because the main danger comes from the catastrophic high-kinetic-energy impact and the impact-generated plasma, which can produce several kinds of electromagnetic interferences or trigger the electrostatic discharge of the charged surfaces that can disturb or even destroy the electronics on-board, the least impulse Ilow which introduces the possible destruction should be considered. From Eq. (19) the mlow can be obtained I low mlow ¼ 14:247  2:5 log  10:0 log V 1 mag: ð29Þ V0 5. The effect of a meteor storm indicating the energy By means of the same way, the true energy flux density of the stream  P N m  12 M m V 20 QE ¼ ; ð30Þ T eff  Ared ðrÞ and the true spatial energy density qE ¼

QE 3600V 0

ð31Þ

can be defined. In addition, from the calculation one may have QE ðmup

1 6 m 6 mlow Þ ¼ V 20 QM ðmup 6 m 6 mlow Þ: 2

ð32Þ

For the whole integral energy effect of the meteor stream, QE = 104 J h1 km2 might be used as a kind of standard of a meteoric energy burst. As is shown in the above discussions, in general, the least energy Elow, from which the meteor may introduce the destruction, should be considered. So, the mlow can be obtained mlow

2  Elow ¼ 14:247  2:5 log  10:0 log V 1 mag: V 20

ð33Þ

6. The effect of a meteor storm indicating the electric charge According to the same way as that for the calculation of the numbers, the true charge flux density of the meteoroids P N m qm ð34Þ QC ¼ T eff  Ared ðrÞ and the true spatial charge density qC ¼

QC ; 3600V 0

ð35Þ

can be defined, where qm is the electric charge of the meteor with a magnitude of m. However, we need discuss this matter under two different instances. 6.1. Meteoroids in the atmosphere While a meteoroid entering the atmosphere, we see a meteor phenomenon, the ionization of the air molecules takes place along the meteoric path, at last, forming an ion train which can reflect radio waves. Verniani (1973) found that the maximum electron line density along the meteor trail can be expressed as ax ¼ 7:7  1010 M 0:92 v3:91 m1 ; 0

ð36Þ

where the mass M of the incoming meteoroid in units of g, but the incoming geocentric velocity v0 in units of cm s1. In addition, the electron line density is found having a relationship to the visual magnitude (Kaiser, 1953) ð37Þ

m ¼ 40:0  2:5 log10 ax mag:

These two formula have been used by other people (Hughes, 1987; Babadzhanov et al., 1991). However, a little different expression ax ¼ 2:0  1010 M m V 4i m1

ð38Þ

also appeared in the literature. Where the mass Mm in units of g and the impact velocity of the meteoroid with the atmosphere of the Earth Vi is in units of km s1 (Hughes, 1978; Hughes and Williams, 2000; Zhang and Wu, 2002). In fact, Eq. (19) comes from Eqs. (37) and (38) and has been used widely. For the total charge of a meteor an empirical formula is found as q ¼ 3:04d1:02 R3:06 v3:48 C;

ð39Þ 3

where d is the meteoric density (kg m ), R the meteoroid radius (m) and v the speed (km s1). For example, a Leonid meteor with a radius of about 1 cm may produce the plasma with a charge of Q = 3.7 · 103 C and an electron density of ne = 6.6 · 1023 m3 (McBride and McDonnell, 1999; Foschini, 2002). It is easy to rewrite it as q ¼ 0:70525M 1:02 v3:48 C;

ð40Þ

where the mass M is in units of kg. It is easy to see that Eqs. (36), (38) and (40) have the very similar relationship of the electric charge (or electric

G.-j. Wu / New Astronomy 12 (2006) 52–59

line density) with the mass and velocity. If the exponents in Eq. (40) can be adopted as simple (an integer) as in Eq. (38), we may have 4

4 0

q ¼ 7  10 M m V C;

ð41Þ

where the mass Mm is in units of g. In addition, it will make the question become much more simple P N m qm ¼ 7  104 V 40 QC ðmup 6 m 6 mlow Þ ¼ T eff  Ared ðrÞ  QM ðmup 6 m 6 mlow Þ: ð42Þ 6.2. For a spacecraft in space

q ¼ 7  104 b  M m V 41 C; and

ðb < 1:0Þ

ð43Þ

P

QC ðmup 6 m 6 mlow Þ ¼

The values discussed in above sections can be adopted as the standard values of QN0, QM0, QI0 and QE0 QN 0 ¼ 0:4 h1 km2 ; QM0 ¼ 0:01 g h1 km2 ; QI0 ¼ 0:4 g km1 h1 s1 ; QE0 ¼ 104 J h1 km2 :

N m qm ¼ 7  104 b  V 41 T eff  Ared ðrÞ  QM ðmup 6 m 6 mlow Þ: ð44Þ

7. A synthetical index about the intensity of a meteor burst By synthesizing all effects of a meteor burst, a nondimensional index can be introduced   Q Q Q Q Q B¼ a N þb M þc I þd E þe C ða þ b þ c þ d þ eÞ: QN 0 QM 0 QI0 QE0 QC0 ð45Þ

ð46Þ

In addition, QC0 ¼ 40 C h1 km2 ;

ð47Þ 1

while which corresponds about V0 = 49 km s QM0 = 0.01 g h1 km2. However, the coefficients from a to e are not easy to be confirmed. We can firstly set a ¼ 0:20;

We really do not know the electric state of the meteoroid in space, it is possible the electrostatic is weak. However, the highest threat for a spacecraft might still be the hot plasma cloud generated during a direct violent impact with a meteoroid. This situation likes the impact of Leonids with the Moon and it can alter the electronic state of the meteoroid. It is worth to notice that the whole impact physical process is not the same as in the atmosphere. Unhappily, we do not know how much fraction of the initial kinetic energy can be converted into the radiation of the cloud and how much electric charges can be produced. However, a simple and reasonable presupposition is that the relationship of q, Mm and V1 can be still as the format of Eq. (41), but the coefficient should be smaller, so we have

57

b ¼ 0:15;

c ¼ 0:15;

d ¼ 0:25;

e ¼ 0:25: ð48Þ

In addition, B P 1.0 means a meteor storm. Evidently, we think they have nearly the equality, but have emphasized the dangerous of the energy and electric charge a little. On the other hand, we depressed the effects of the mass and impulse. It is because that the analysis of the satellite’s data makes it clear that even though the mechanical damage is not serious, the plasma cloud generated during the impact can be a serious threat. As an example, we can analyze and discuss the 10 active meteor showers used by Ma et al. (2005). For studying the potential hazard of a strong meteor shower, Ma et al. (2005) suggested a special ZHR*, which denotes a number flux, defined as the number of meteoroids passing across the zenith area for 1000 km2 h1 and each meteoroid can form a crater no less than 1 cm in diameter on an aluminum surface. In fact, this condition corresponds to a meteor with a kinetic energy of Ev ¼ 12 M v V 20 ¼ 70:7 J. Adopting Ev as Elow, then Mlow and mlow can be obtained. The calculations according to our equations in this paper are listed in Table 5. It is true that 1998 Giacobinids looks extremely stronger than others. However, see the possible appearance of the 10 meteor showers on the Moon. People have observed several times of the impact of Leonids with the Moon. The flashes are mainly the result of thermal emission from the hot plasma plumes created by the impact. The whole process takes place in a very short time interval on the order of 103 s (Artemieva et al., 2000; Bellot Rubio et al.,

Table 5 Calculations of 10 meteor showers setting Elow = 70.7 J Meteor shower

V1

r

ZHRo

mlow

QN

10QM

10QI

QE/103

QC

B

1991 1992 1993 1994 1995 1998 1998 1999 2001 2002

59 59 59 59 65 18 20 71 71 71

1.9 2.1 1.8 1.8 2.51 2.22 3.0 2.3 2.25 2.92

350 250 300 250 350 102 720 3700 3430 2940

7.55 7.55 7.55 7.55 7.34 10.45 10.16 7.16 7.16 7.16

0.107 0.136 0.065 0.055 0.385 0.751 37.40 2.331 1.949 5.077

0.051 0.010 0.088 0.073 0.002 0.267 0.410 0.028 0.032 0.006

3.067 0.629 5.257 4.381 0.120 5.651 9.397 2.001 2.315 0.461

9.210 1.889 15.78 13.15 0.3951 5.988 10.77 7.141 8.262 1.645

46.50 9.538 79.69 66.41 2.406 3.766 7.918 50.94 58.94 11.74

0.77 0.21 1.25 1.04 0.22 1.16 19.99 1.78 1.68 2.68

Perseids Perseids Perseids Perseids a Mon June Bootids Giacobinids Leonids Leonids Leonids

58

G.-j. Wu / New Astronomy 12 (2006) 52–59

Table 6 The possible appearance of the 10 meteor showers on the Moon, setting Mlow = 0.12 kg for Leonids to get Elow = 3.0246 · 108 J Meteor shower

ZHRo

mlow

QM

QI

QE/103

QC

B

B0

1991 1992 1993 1994 1995 1998 1998 1999 2001 2002

350 250 300 250 350 102 720 3700 3430 2940

9.06 9.06 9.06 9.06 9.27 6.46 6.69 9.45 9.45 9.45

0.0045 0.0008 0.0080 0.0067 6 · 105 0.0196 0.0017 0.0015 0.0019 4 · 105

0.2641 0.0462 0.4737 0.3948 0.0036 0.3567 0.0344 0.1045 0.1334 0.0025

7.799 1.363 13.99 11.66 0.1173 3.238 0.3467 3.686 4.705 0.0888

38.07 6.653 68.27 56.90 0.6946 1.495 0.1969 25.68 32.78 0.6187

0.60 0.10 1.07 0.90 0.01 0.52 0.05 0.31 0.40 0.01

0.39 0.06 0.69 0.58 0.01 0.51 0.05 0.17 0.22 0.01

Perseids Perseids Perseids Perseids a Mon June Bootids Giacobinids Leonids Leonids Leonids

2000). The internal energy of the plasma cloud is partially lost through the radiation of light. An important parameter in the impact of the meteoroid with the Moon is the fraction of the initial kinetic energy converted into the radiation or luminous efficiency g. From the observations of 1999 Leonids impacting the Moon, a value of g = 2 · 103 in the wavelength range of 400–900 nm was obtained with an uncertainty being roughly one order of magnitude. This efficiency is significantly greater than the previous estimates, since very high-velocity collisions like Leonids are much more difficult to reproduce in the laboratory. In addition, the masses of the meteoroids that produced the brightest and faintest Leonid flashes on the Moon turn out to be 4.9 and 0.12 kg, respectively (Bellot Rubio et al., 2000). If a Leonid meteoroid is set at 0.12 kg as Mlow, then Elow can be obtained and the representation of the 10 meteor showers can be calculated. In Table 6 the item QN has been omitted, since all of QN less than 4 · 106 h1 km2. At the last column, the parameter B is listed as B 0 and setting b = 0.1 in Eq. (44). The result is obvious that Perseids is the strongest shower, Bootids and Leonids are also stronger, but not Giacobinids. 8. Discussions According to the definition of ZHR* by Ma et al. (2005), 1998 Giacobinids should be the most intense meteor shower. However, we think that this definition excessively emphasizes the effect of the faint meteors. Especially, their Ev is set too low, so that all the values of mlow become too faint. In Table 5, all the values of mlow are fainter than the general visual limiting magnitudes. Even their equation of mass to magnitude is used, since the number of meteoroids in per unit mass interval is proportional to Ms, where s is called the mass distribution index (Hughes, 1987; Koschack and Rendtel, 1990a), the ratio of the cumulative number of meteoroids can be written as  s1  2:3 logðrÞ /ðM 6 Þ Mv Mv ¼ ¼ ¼ r6:5mlow : ð49Þ /ðM v Þ M6 M6 In their Table 3, Mv, M6 and r are given, so it is easy to get mlow. For the showers of 1998 June Bootids and 1998

Giacobinids, mlow can be still as faint as about 9.0 mag. The question is whether the critical Elow is correctly set or not. Table 6 reveals the fact that when Elow increases the results might be quite different. The question about the conversion efficiency g of the kinetic energy into the crater should also exist in the paper of Ma et al. (2005). It is impossible that all of the initial kinetic energy becomes the energy to create the crater. Well then, how much is the conversion efficiency? From the relevant literature, we have not found any reports on the description that the shower Giacobinids would be very hurtful. On the other hand, the most intense burst of 1993 Peiseids in Table 6 can be approved and the reason why the space instruments were severely damaged during 1993 Peiseids (see Section 1) can be found here. In Table 6, the behaves of the strong meteor showers on the Moon may give you some impressions, which is much different from the situation in Earth’s atmosphere. American will send their astronauts to the Moon again, China and other countries are establishing their plans of the exploration to the Moon, these behaves of the showers might give you some new ideal. All of the parameters in the calculation of the synthetical index about the intensity of a meteor burst are given in this paper. Certainly, the rationality of the values of these parameters should be verified in practice. In addition, in some cases, it is needed to adjust the values of some parameters properly based on different requirements. For example, the meteor phenomenon is observed at an altitude of about 100 km, in general. Any way, the altitude cannot exceed 200 km. The potential threat does not only exist for the running lower-altitude crafts, but also for the launch/landing processes of all kinds of spacecraft. However, if the potential risk was considered above 200 km for a spacecraft, the parameter b in Eq. (44) might be set properly. On the other hand, below 200 km the meteoroid is turning into plasma, which cannot keep as a rigid body, the parameter c might decrease since the impact character changed. As regards the number flux, the number of meteors should be directly proportional to the impact probability, the coefficient a should always have the unchanged value. For determining these parameters correctly, a lot of work may be needed.

G.-j. Wu / New Astronomy 12 (2006) 52–59

Acknowledgments The author deeply thanks the anonymous referees for the insightful and perceptive comments and suggestions, which have improved the presentation of the paper. The author is also grateful to Prof. Zongxu Ling for the English improvement on this manuscript. References Arlt, R., 1998. WGN, the Journal of the IMO 26 (6), 256. Artemieva, N.A., Shuvalov, V.V., Trubetskaya, I.A., 2000. Lunar and Planetary Science XXXI. Lunar Planetary Institute, Houston, No. 1402. Babadzhanov, P.B., Wu, Z.D., Williams, I.P., et al., 1991. MNRAS 253, 69. Bedingfield, K.L., Leach, R.D., Alexander, M.B., 1996. Spacecraft system failures and anomalies attributed to the natural space environment. NASA RP-1390. Beech, M., Brown, P., Jones, J., 1995. QJRAS 36, 127. Bellot Rubio, R.L., 1995. A&A 301, 602. Bellot Rubio, L.R., Ortiz, J.L., Sada, P.V., 2000. ApJ 542, L65. Caswell, R.D., McBride, N., Taylor, A., 1995. Int. J. Impact Eng. 17, 139. Cerroni, P., Martelli, G., 1982. P&SS 30, 395. Dunham, D.W., 1999. IAUC, 7320. Foschini, L., 1998. EL 43, 226. Foschini, L., 2002. In: Murad, E., Williams, I.P. (Eds.), Meteors in the Earth’s Atmosphere. Cambridge University Press, Cambridge, p. 249.

59

Hughes, D.W., 1978. In: McDonnell, J.A.M. (Ed.), Cosmic Dust. Wiley, Chichester, p. 123. Hughes, D.W., 1987. A&A 187, 879. Hughes, D.W., Williams, I.P., 2000. MNRAS 315, 629. Jenniskens, P., 1994. A&A 287, 990. Jenniskens, P., 1995. A&A 295, 206. Jenniskens, P., 2002. Proc. ACM Conf., 117. Jenniskens, P., de Lignie, M., Betlem, H., et al., 1998. EM&P 80, 311. Kaiser, T.R., 1953. Phil. Mag. Suppl. 2, 495. Koschack, R., Rendtel, J., 1990a. WGN, the Journal of the IMO 18 (2), 44. Koschack, R., Rendtel, J., 1990b. WGN, the Journal of the IMO 18 (4), 119. Ma, Y.H., Xu, P.X., Li, G.Y., et al., 2005. AcApS 46, 158. McBride, N., McDonnell, J.A.M., 1999. P&SS 47, 1005. McNaught, R.H., Asher, D.J., 1999. WGN, the Journal of the IMO 27 (2), 85. Ortiz, J.L., Sada, P.V., Bellot Rubio, L.R., et al., 2000. Natur 405, 921. Verniani, F., 1973. J. Geophys. Res. 78, 8429. Watanabe, J.I., Abe, S., Fukushima, H., et al., 1999. PASJ 51, L11. Whipple, F.L., 1951. ApJ 113, 464. Wu, G.J., 2002. ChA&A 26, 40. Wu, G.J., 2005. NewA 11, 68. Wu, G.J., Li, G.Y., 2003. EM&P 93 (1), 1. Wu, G.J., Zhang, Z.S., 1998. EM&P 81, 193. Wu, G.J., Zhang, Z.S., 2002. P&SS 50 (4), 379. Yeomans, D.K., 1981. Icar 47, 492. Zhang, Z.S., Wu, G.J., 2002. ChA&A 26, 208.