- Email: [email protected]
On the Crab Nebula VHE gamma-ray flux
UCLEARPHYSICS
PROCEEDINGS SUPPLEMENTS EI,SEVIHR
Nuclear Physics B (Proc. Suppl.) 39A (1995) 207-212
ON THE CRAB NEBULA VHE GAMMA-RAY FLUX A.A.Stepanian Crimean Astrophysical Observatory, P.O. Nauchny, Crimea, 334413, Ukraine The VHE gamma-ray flux of the Crab Nebula has been observed for many times by different groups in various energy ranges. The comparison of these data shows that values of fluxes obtained by various groups and various methods are not in agreement. It seems to us that this disagreement is mostly connected with differences in concepts of the effective area and in the energy threshold evaluation used by different groups. We propose a method of a flux derivation which do not use these concepts and permits us to obtain the correct value of the flux. Applied to data obtained in the Crimean Astrophysical Observatory, (1.3 -4-0.4) • 10 -11 quanta cm-2s -a is obtained for the flux above 1 TeV. The Crab Nebula VHE gamma-ray flux was derived on the basis of theoretical models. The calculation of De Jager and Harding agrees with the observations in the case of a relatively low magnetic field strength. The calculation derived by the present author gives, in contrast, a low gamma-ray flux. It is concluded that further investigations of the Crab Nebula are to be carried out.
1. I N T R O D U C T I O N The Crab Nebula has been one of the most attracive objects for astrophysicists and physicists since the time when the high degree of polarization of the optical radiation was discovered in 1953. Before that it was known as the strongest radiosource in the Taurus constellation. T h a t is why the first List of objects observed by Jelley and Galbraith [1] included the Taurus-A as a possible source of the VHE gamnlaradiation. Their equipment was very simple: it contained 60 crn diameter parabolic mirror with a photomultiplier in the focus, and the registering electronics. No gamma-radiation was found. Later, in 1959, Cocconi [2] pointed out that the flux of gamma-rays must be high if electrons, which are responsible for the optical radiation of the Nebula are secondary, and arrive due to collisions of hadrons with matter in the Nebula. Long-term observations were made in the Crimea by Lebedev Physical Institute group [3]. The threshold energy of their system of Cerenkov detectors was 5 - 1012 eV. The upper limit of the gamma-ray flux obtained in these observations showed that the VHE electrons in the Nebula are not secondary, but are injected directly. During the time of these long-term observations, a new branch of astronomy was born. Giacconi and 0920-5632/95/$09.50© 1995 Elsevier Science B.V. All rights reserved. SSDI 0920-5632(95)00023-2
colleagues [4] have discovered the X-radiation from the stellar source Sco X-1 Somewhat later the Naval Research Laboratory group have discovered the X-ray radiation from the central part of the Crab Nebula [5]. The existence of X-ray radiation means that the electron energy extends up to 1014 eV. This conclusion was based on the value of the magnetic field strength in the Nebula, estimated by various methods, and on the confident belief that the X-ray radiation is of synchrotron Origin. Remember that at that time nothing was known about the existence of pulsars. A new activity in VHE gammaray observations began in connection with the discovery of pulsars in 1968. It was the same year that a new Cerenkov detector, the largest up-to-date, started to operate in the USA at Mount Hopkins [6]. Three years of observations at Mount Hopkins showed that the Crab Nebula was the source of gamma-rays. The flux was estimated as (4.4 + 1.4)- 10 -11 quanta c m - 2 s -1 [7]. No periodic component was revealed. The threshold energy for those observations was 2 - 1 0 u eV. It was mentioned that the flux changes significantly, which was possibly connected with the so-called "spin-up" of the Crab pulsar NP0531+22. Somewhat later the periodic analysis of the observational d~.ta was
208
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207--212
made by Grindlay et al [8]. They found several cases when a periodic signal was observed in gamma-rays. T h e Crab Nebula was observed by many groups in the 70-th. Here we cannot mention all of them. Sometimes these results were in conflict with each other. Long-term observations of the periodic component were carried out with positive results by a group in India [9]. 2. T H E RECENT RESULTS
OBSERVATIONS
Using a second generation Cerenkov detector with an imaging camera permitted the Whipple Collaboration to obtain highly significant result for the Crab Nebula. They found [10] that the flux is equal to 1 . 8 . 1 0 -11 quanta .em-2s -1 for energies higher than 0.7 TeV, with a confidence level corresponding to 25 s.d.. The energy spectrum of g a m m a - q u a n t a was also measured. For E :>1 TeV, the flux corresponds to 0.88- 10 -11 quanta -cm-2s -1. It is very i m p o r t a n t that the VHE g a m m a - r a y flux from the Crab Nebula is stable according to the Whipple group data. T h e y observed it continuously for m a n y years. Only two more installations with imaging camera are in operation in the northern hemisphere. These are the H E G R A Cerenkov detector at the Canary Islands, and the Crimean Astrophysical Observatory installation GT-48. According to the H E G R A collaboration [11], the Crab Nebula g a m m a - r a y flux is equal to 4.3- 10-11cm-2s -1 for E > 1 Tev, i.e. approximately 4 times higher than the Whipple collaboration result. The recent analysis of Crimean GT-48 data for the year 1993 gives the flux value ( 1 . 3 + 0 . 4 ) . 1 0 - n c m - 2 s -a for E >1 TeV (details are described below). The steady flux from the Crab Nebula was observed by two groups which used the timing technique. The A S G A T group [12] gives the flux 2 . 7 . 1 0 - n c m - 2 s -1 for E > 0.6 TeV. This value corresponds to a flux 1 . 3 - 1 0 - n c m - 2 s - 1 above 1TeV. Another French group using the same method gives a much higher value [13]. Their energy threshold is a little higher, but if
we extrapolate the integral flux to 1 TeV, it is equal to 4.1 - 10-11cm-2s -1. Here it is assumed that the integral spectral index of the power law is equal to -1.5 . The same assumption was made for other cases, too. Thus, we see that there are differences in the values of the Crab Nebula TeV g a m m a - r a y flux given by various groups. We are not going to claim what value is correct. Rather we would like to stress that these discrepances are possibly connected with uncorrect estimations of the flux or energy. T i m e variations cannot be excluded, either. Only the detailed analysis and comparison of the methods of the energy and flux estimations made by various groups may resolve this problem. To set an example, we present the brief description of how we made our flux and energy estimations. 3.
DESCRIPTION OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY EQUIPMENT AND DATA PROCESSING
The installation consists of two identical altazimuthal mountings (sections) which are 20 m apart in the direction North-South (see Fig1). Six telescopes, which we call the elements, are placed in each mounting. The optics of every element consists of four 1.2-m mirrors that have a common focus. The mirrors of 3 elements are of 3.2-m focus length, and they serve for the detection of ultraviolet radiation in the range of 200+300 rim. The solar-blind PMs are in their focuses. The imaging cameras are in the focal plane of 5-metre focus elements. The signals of all 3 elements are summed linearly. After that, signals from both sections are sent to a coneidence circuit with 100 ns resolving time. The distinctive features of the telescope (the detecting of ultraviolet radiation and the possibility of getting stereo images) allows us to get new, independent parameters of the detected events. The optical axes of the sections were directed not on the source, but on the sky point which is higher by 0.5 degree, in order to avoid the star ( Tau to be in the field of view of the light receiver. The observational data on the g a m m a -
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207-212
quanta source in the Crab Nebula were obtained by using the described method during the period 18 to 23 October 1993.
Light detectors
Mirrors
B aJ~e8
209
the efficiency of the g a m m a - q u a n t a selection approximately by a factor of three. In Fig. 2, histograms of~the distribution of the parameter DRO for source and background are presented after using all of the enumerated filters (except DRO itself) and the p a r a m e t e r MISS. The DRO distribution for the source is shifted to lower values. It means t h a t the data set of the source is enriched by g a m m a - q u a n t a . It is necessary to mention that the analogous distribution, but for all events, was presented by Durham group at the Calgary Workshop [14].
ame 40
- ~ i v
Platform Bed "~ Jacks
30
I
I
E
I
source
-
--
background
Fig.l: The sketch of the mounting of tlie Crimean Astrophysical Observatory Gamma-telescope GT-48. The d a t a processing was carried out using the following filters: V > 100 ( V -total amplitude of flash) 0.075 ° < W I D T H < 0.175 ° E L L I P T I C I T Y > 0.5 Besides that the following new filters were used: UV - ratio of the ultraviolet signal to the visible one (UV < 0.03) DRO - angular distance between the centroids of images obtained in different sections for one and the same flash (DRO < 0.225°). Apparently, the value of the parameter DRO depends on the altitude of the detected shower. The higher the shower, the less is the value of DRO . After filtering the coordinate-dependent criteria were used: MISS < 0.150 A Z W I D T H < 0.2250 A L P H A < 27 °. The confidence level of g a m m a - r a y flux for all criteria is equal to 4.8 s.d. When the parameters UV and DRO are used separately, the efficiency of the selection (ratio excess/error) is increased by approximately a factor two. The joint use of ultraviolet and stereo effects improves
20
-
z
0
~"] 0.0
0.2
0.4
0.6
DRO ( d e g r e e s
i t 0.8
1.0
)
Fig.2:The parameter DRO frequency distribution after rejection with the selection criteria.
4. T H E F L U X E S T I M A T I O N
For the approximate estimation of the flux we used the method of simulations described at the Calgary Workshop [15]. Taking into account the probability of g a m m a - r a y initiated Cerenkov flashes to be detected by the imaging camera, one can find the g a m m a - r a y flux falling on the Earth atmosphere. According to our data and simulations the g a m m a - r a y flux is (1.3 + 0.4) • 10-11em-2s -1 . Usually all the researchers publish the value of g a m m a - r a y integral flux . Sometimes they use the value of the effective area. We would like to mention that the energy threshold and the
210
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 20~212
effective area are not independent of each other. T h e y are meaningful only if both are presented. Moreover, these values depend on the energy spectrum which is difficult to define accurately in one experiment. Here we present the method of the flux determination, for which it is not necessary to use the value of effective area or threshold energy. First of all, for simplicity, we assume t h a t the g a m m a - r a y flux may be presented as follows: d N / d E = A- E - v where A is constant. Then we accept the maximal core distance Rrnax and the g a m m a - r a y energy interval which the simulations should be made for. Strictly speaking, these values must be found empirically through simulations. All criteria used for hadron background rejection are taken into account. It is i m p o r t a n t to mention that the final result, i.e. the g a m m a - r a y flux, does not depend on the values of the maximal core distance and the energy interval, as far as they are in the range where the probability of detection is negligible for the Cerenkov flashes. C o m p a r i n g the number of detected gammalike events derived from observational data with the total number of the detected flashes in the simulation, one can easely find the total number of g a m m a - q u a n t a that fell on the area r R 2 during the observation period. Now it is easy to find the value of the constant A in the g a m m a - r a y spectrum. As a consequence, one can find the integral spectrum for any energy in the range of detector sensitivity.
Nebula structure proposed by Rees and Gunn [21]. The calculations of De Jager and Harding are based on the results of the paper of Kennel and Coroniti [23] who also exploited the concept of Rees and Gunn [21]. According to Stepanian [22] the magnetic field strength in the centre of the Crab Nebula is equal to 3.5.10 -4 G while De Jager and Harding take the value 0.8.10 -4 G in agrement with the paper of Kennel and Coroniti [23] who used the MHD model. It seems to me that the difference in the magnetic field strength is the main reason for the difference in the VHE g a m m a - r a y flux. The flux value is equal to 2 . 1 0 -1~ quanta cm -2 s -1 according to the paper [22] while the value of the flux in the paper [20] is tuned with the Whipple Observatory data. The m a t t e r is the following. The synchrotron losses of the VHE electrons are dominant and their life time is inversely proportional to magnetic field strength. The number of g a m m a quanta generated through the inverse C o m p t o n mechanism is proportional to their life-time in this case. Thus the VHE g a m m a - r a y flux from the Crab Nebula should be inverse proportional to the magnetic field strength. We also cannot exclude the possibility that the pulsed gamma-radiation in the vicinity of pulsar may be smoothed. This idea is considered in a paper of Bogovalov and Kotov [24]. It seems to us that only further observations and model improvements could give a more accurate i: icture of the Crab Nebula.
5. D I S C U S S I O N
Several theoretical calculations of the VHE g a m m a - r a y flux were made earlier [16], [17], [18], [19]. All those calculations were briefly discussed by De Jager and Harding [20]. Of course, all of t h e m contain some simplifications. The paper of Stepanian [19] is based on the calculations of the Crab Nebula magnetic field structure that have been obtained due to the comparison with the experimental data of the space distribution of the Crab Nebula radiation in the wide range of the electromagnetic radiation [22]. This model exploits the concept of the
6. C O N C L U S I O N S The consideration of published results of the VHE g a m m a - r a y flux leads us to the conclusion that they are not in good agreement (see Fig.3). Of course, time variations of the flux can not be completely excluded, but most of the disagreements are probably connected with differences in the concepts of flux estimation. The above proposed method of flux estimation - if it is applied to all measurements - will show whether the disagreements are real. Theoretical calculations compared with the
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207~212
reliable value of the gamma-ray flux may be very useful for understanding the structure of the Crab Nebula, the mechanism and place of particle acceleration etc. -10 10
I
I
I Fazio[7] ~ ASGAT[12]
I
7 ~9 t¢
Whipple -11
EI01 +
.EoRA CI11
CrAO | ~ Them.[13]
Them.[13] -12 1o
0.1
J 1 Energy
q 10
( TeV )
Fig.3: The positive results of the Crab Nebula observation. Thus the problem of the VHE gamma radiation should be open for the further analysis.
REFERENCES
1. Galbraith W. & Jelley J.V., Journ. Atmosph. Terr. Phys., 6, 250, (1955). 2. Cocconi G., Proc. of the 2nd Internat. Conf. on Cosmic Rays, Moscow, 2, 327, 1959. 3. Chudakov A.E., Dadikin V.L., Zatsepin V.I. & Nesterova N.M., Proe. of the Lebedev Phys. Institute, 26, 118, (1964). 4. Giacconi R., Gursky H., Paolini F. & Rossi B., Phys.Rev. Letts 9,439, 1962. 5. Bowyer S., Byram E., Chubb T. & Friedman H., Science, 146, 912, 1964. 6. Fazio G.G., Helmken H.F., Rieke G.H. & Weekes T.C., Proc. l l t h ICRC, Budapest, Hungary, 1, 115, 1969. 7. Fazio G.G., Helmken H.F., O'Mongain E. & Weekes T.C, Astrophys.J. 175, Ll17, 1972. 8. Grindlay J.E., Helmken H.F. & Weekes T.C, Astrophys.J., 209,592, 1976.
211
9. Gupta S.K. et al., Astrophys.J., 221, 268, 1978. 10. Lewis D.A. et al., Proc of 23rd ICRC, Calgary, Canada, 1,279, 1993. 11. Kreunrich F. et al., Proc. of 23rd ICRC, Calgary, Canada 1,251, 1993. 12. Goret Ph., Palfrey T., Tabary A., Vacanti G. & Bazer-Bachi R., Astron. & Astrophys., 270, 401, 1993. 13. Baillon P. et al., Proc. of 23rd ICRC, Calgary, Canada, 1,271, 1993. 14. FCG Bowden et al., Proc. of the Intern. Workshop, Calgary,Canada, 219, July 17-18, 1993. 15. Zyskin Yu.L., Stepanian A.A.& Kornienko A.P., Proc. of the Intern. Workshop, Calgary, Canada, 219, July 17-18, 1993. 16. Gould R.J., Phys. Rev. Lett. 15,577, 1965. 17. Rieke G.H. & Weekes T.C. , Astrophys.J., 155,429, 1969. 18. Grindlay J.E. & Hoffman J.A., Astrophys. Lett., 8,209, 1971. 19. Stepanian A.A. , Proc. of Vulcano Workshop, Vulcano, Italy, 337, May 1990. 20. De Jager O.C. & Harding A.K., Astrophys.J., 396, 161, 1992. 21. Rees M.J. & Gunn J.E., Mon. Not. R. Soc., 1, 167, 1974. 22. Stepanian A.A., Bulletin of Crimean Astrophys. Obs., 62, 80, 1982. 23. Kennel C.F. & Coroniti F. V., Astrophys. J., 283, 694, 1984. 24. Bogovalov S.V. & Kotov Yu.D., Mon. Not. R. Astron. Soc. 262, 75, 1993.
PROCEEDINGS SUPPLEMENTS EI,SEVIHR
Nuclear Physics B (Proc. Suppl.) 39A (1995) 207-212
ON THE CRAB NEBULA VHE GAMMA-RAY FLUX A.A.Stepanian Crimean Astrophysical Observatory, P.O. Nauchny, Crimea, 334413, Ukraine The VHE gamma-ray flux of the Crab Nebula has been observed for many times by different groups in various energy ranges. The comparison of these data shows that values of fluxes obtained by various groups and various methods are not in agreement. It seems to us that this disagreement is mostly connected with differences in concepts of the effective area and in the energy threshold evaluation used by different groups. We propose a method of a flux derivation which do not use these concepts and permits us to obtain the correct value of the flux. Applied to data obtained in the Crimean Astrophysical Observatory, (1.3 -4-0.4) • 10 -11 quanta cm-2s -a is obtained for the flux above 1 TeV. The Crab Nebula VHE gamma-ray flux was derived on the basis of theoretical models. The calculation of De Jager and Harding agrees with the observations in the case of a relatively low magnetic field strength. The calculation derived by the present author gives, in contrast, a low gamma-ray flux. It is concluded that further investigations of the Crab Nebula are to be carried out.
1. I N T R O D U C T I O N The Crab Nebula has been one of the most attracive objects for astrophysicists and physicists since the time when the high degree of polarization of the optical radiation was discovered in 1953. Before that it was known as the strongest radiosource in the Taurus constellation. T h a t is why the first List of objects observed by Jelley and Galbraith [1] included the Taurus-A as a possible source of the VHE gamnlaradiation. Their equipment was very simple: it contained 60 crn diameter parabolic mirror with a photomultiplier in the focus, and the registering electronics. No gamma-radiation was found. Later, in 1959, Cocconi [2] pointed out that the flux of gamma-rays must be high if electrons, which are responsible for the optical radiation of the Nebula are secondary, and arrive due to collisions of hadrons with matter in the Nebula. Long-term observations were made in the Crimea by Lebedev Physical Institute group [3]. The threshold energy of their system of Cerenkov detectors was 5 - 1012 eV. The upper limit of the gamma-ray flux obtained in these observations showed that the VHE electrons in the Nebula are not secondary, but are injected directly. During the time of these long-term observations, a new branch of astronomy was born. Giacconi and 0920-5632/95/$09.50© 1995 Elsevier Science B.V. All rights reserved. SSDI 0920-5632(95)00023-2
colleagues [4] have discovered the X-radiation from the stellar source Sco X-1 Somewhat later the Naval Research Laboratory group have discovered the X-ray radiation from the central part of the Crab Nebula [5]. The existence of X-ray radiation means that the electron energy extends up to 1014 eV. This conclusion was based on the value of the magnetic field strength in the Nebula, estimated by various methods, and on the confident belief that the X-ray radiation is of synchrotron Origin. Remember that at that time nothing was known about the existence of pulsars. A new activity in VHE gammaray observations began in connection with the discovery of pulsars in 1968. It was the same year that a new Cerenkov detector, the largest up-to-date, started to operate in the USA at Mount Hopkins [6]. Three years of observations at Mount Hopkins showed that the Crab Nebula was the source of gamma-rays. The flux was estimated as (4.4 + 1.4)- 10 -11 quanta c m - 2 s -1 [7]. No periodic component was revealed. The threshold energy for those observations was 2 - 1 0 u eV. It was mentioned that the flux changes significantly, which was possibly connected with the so-called "spin-up" of the Crab pulsar NP0531+22. Somewhat later the periodic analysis of the observational d~.ta was
208
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207--212
made by Grindlay et al [8]. They found several cases when a periodic signal was observed in gamma-rays. T h e Crab Nebula was observed by many groups in the 70-th. Here we cannot mention all of them. Sometimes these results were in conflict with each other. Long-term observations of the periodic component were carried out with positive results by a group in India [9]. 2. T H E RECENT RESULTS
OBSERVATIONS
Using a second generation Cerenkov detector with an imaging camera permitted the Whipple Collaboration to obtain highly significant result for the Crab Nebula. They found [10] that the flux is equal to 1 . 8 . 1 0 -11 quanta .em-2s -1 for energies higher than 0.7 TeV, with a confidence level corresponding to 25 s.d.. The energy spectrum of g a m m a - q u a n t a was also measured. For E :>1 TeV, the flux corresponds to 0.88- 10 -11 quanta -cm-2s -1. It is very i m p o r t a n t that the VHE g a m m a - r a y flux from the Crab Nebula is stable according to the Whipple group data. T h e y observed it continuously for m a n y years. Only two more installations with imaging camera are in operation in the northern hemisphere. These are the H E G R A Cerenkov detector at the Canary Islands, and the Crimean Astrophysical Observatory installation GT-48. According to the H E G R A collaboration [11], the Crab Nebula g a m m a - r a y flux is equal to 4.3- 10-11cm-2s -1 for E > 1 Tev, i.e. approximately 4 times higher than the Whipple collaboration result. The recent analysis of Crimean GT-48 data for the year 1993 gives the flux value ( 1 . 3 + 0 . 4 ) . 1 0 - n c m - 2 s -a for E >1 TeV (details are described below). The steady flux from the Crab Nebula was observed by two groups which used the timing technique. The A S G A T group [12] gives the flux 2 . 7 . 1 0 - n c m - 2 s -1 for E > 0.6 TeV. This value corresponds to a flux 1 . 3 - 1 0 - n c m - 2 s - 1 above 1TeV. Another French group using the same method gives a much higher value [13]. Their energy threshold is a little higher, but if
we extrapolate the integral flux to 1 TeV, it is equal to 4.1 - 10-11cm-2s -1. Here it is assumed that the integral spectral index of the power law is equal to -1.5 . The same assumption was made for other cases, too. Thus, we see that there are differences in the values of the Crab Nebula TeV g a m m a - r a y flux given by various groups. We are not going to claim what value is correct. Rather we would like to stress that these discrepances are possibly connected with uncorrect estimations of the flux or energy. T i m e variations cannot be excluded, either. Only the detailed analysis and comparison of the methods of the energy and flux estimations made by various groups may resolve this problem. To set an example, we present the brief description of how we made our flux and energy estimations. 3.
DESCRIPTION OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY EQUIPMENT AND DATA PROCESSING
The installation consists of two identical altazimuthal mountings (sections) which are 20 m apart in the direction North-South (see Fig1). Six telescopes, which we call the elements, are placed in each mounting. The optics of every element consists of four 1.2-m mirrors that have a common focus. The mirrors of 3 elements are of 3.2-m focus length, and they serve for the detection of ultraviolet radiation in the range of 200+300 rim. The solar-blind PMs are in their focuses. The imaging cameras are in the focal plane of 5-metre focus elements. The signals of all 3 elements are summed linearly. After that, signals from both sections are sent to a coneidence circuit with 100 ns resolving time. The distinctive features of the telescope (the detecting of ultraviolet radiation and the possibility of getting stereo images) allows us to get new, independent parameters of the detected events. The optical axes of the sections were directed not on the source, but on the sky point which is higher by 0.5 degree, in order to avoid the star ( Tau to be in the field of view of the light receiver. The observational data on the g a m m a -
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207-212
quanta source in the Crab Nebula were obtained by using the described method during the period 18 to 23 October 1993.
Light detectors
Mirrors
B aJ~e8
209
the efficiency of the g a m m a - q u a n t a selection approximately by a factor of three. In Fig. 2, histograms of~the distribution of the parameter DRO for source and background are presented after using all of the enumerated filters (except DRO itself) and the p a r a m e t e r MISS. The DRO distribution for the source is shifted to lower values. It means t h a t the data set of the source is enriched by g a m m a - q u a n t a . It is necessary to mention that the analogous distribution, but for all events, was presented by Durham group at the Calgary Workshop [14].
ame 40
- ~ i v
Platform Bed "~ Jacks
30
I
I
E
I
source
-
--
background
Fig.l: The sketch of the mounting of tlie Crimean Astrophysical Observatory Gamma-telescope GT-48. The d a t a processing was carried out using the following filters: V > 100 ( V -total amplitude of flash) 0.075 ° < W I D T H < 0.175 ° E L L I P T I C I T Y > 0.5 Besides that the following new filters were used: UV - ratio of the ultraviolet signal to the visible one (UV < 0.03) DRO - angular distance between the centroids of images obtained in different sections for one and the same flash (DRO < 0.225°). Apparently, the value of the parameter DRO depends on the altitude of the detected shower. The higher the shower, the less is the value of DRO . After filtering the coordinate-dependent criteria were used: MISS < 0.150 A Z W I D T H < 0.2250 A L P H A < 27 °. The confidence level of g a m m a - r a y flux for all criteria is equal to 4.8 s.d. When the parameters UV and DRO are used separately, the efficiency of the selection (ratio excess/error) is increased by approximately a factor two. The joint use of ultraviolet and stereo effects improves
20
-
z
0
~"] 0.0
0.2
0.4
0.6
DRO ( d e g r e e s
i t 0.8
1.0
)
Fig.2:The parameter DRO frequency distribution after rejection with the selection criteria.
4. T H E F L U X E S T I M A T I O N
For the approximate estimation of the flux we used the method of simulations described at the Calgary Workshop [15]. Taking into account the probability of g a m m a - r a y initiated Cerenkov flashes to be detected by the imaging camera, one can find the g a m m a - r a y flux falling on the Earth atmosphere. According to our data and simulations the g a m m a - r a y flux is (1.3 + 0.4) • 10-11em-2s -1 . Usually all the researchers publish the value of g a m m a - r a y integral flux . Sometimes they use the value of the effective area. We would like to mention that the energy threshold and the
210
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 20~212
effective area are not independent of each other. T h e y are meaningful only if both are presented. Moreover, these values depend on the energy spectrum which is difficult to define accurately in one experiment. Here we present the method of the flux determination, for which it is not necessary to use the value of effective area or threshold energy. First of all, for simplicity, we assume t h a t the g a m m a - r a y flux may be presented as follows: d N / d E = A- E - v where A is constant. Then we accept the maximal core distance Rrnax and the g a m m a - r a y energy interval which the simulations should be made for. Strictly speaking, these values must be found empirically through simulations. All criteria used for hadron background rejection are taken into account. It is i m p o r t a n t to mention that the final result, i.e. the g a m m a - r a y flux, does not depend on the values of the maximal core distance and the energy interval, as far as they are in the range where the probability of detection is negligible for the Cerenkov flashes. C o m p a r i n g the number of detected gammalike events derived from observational data with the total number of the detected flashes in the simulation, one can easely find the total number of g a m m a - q u a n t a that fell on the area r R 2 during the observation period. Now it is easy to find the value of the constant A in the g a m m a - r a y spectrum. As a consequence, one can find the integral spectrum for any energy in the range of detector sensitivity.
Nebula structure proposed by Rees and Gunn [21]. The calculations of De Jager and Harding are based on the results of the paper of Kennel and Coroniti [23] who also exploited the concept of Rees and Gunn [21]. According to Stepanian [22] the magnetic field strength in the centre of the Crab Nebula is equal to 3.5.10 -4 G while De Jager and Harding take the value 0.8.10 -4 G in agrement with the paper of Kennel and Coroniti [23] who used the MHD model. It seems to me that the difference in the magnetic field strength is the main reason for the difference in the VHE g a m m a - r a y flux. The flux value is equal to 2 . 1 0 -1~ quanta cm -2 s -1 according to the paper [22] while the value of the flux in the paper [20] is tuned with the Whipple Observatory data. The m a t t e r is the following. The synchrotron losses of the VHE electrons are dominant and their life time is inversely proportional to magnetic field strength. The number of g a m m a quanta generated through the inverse C o m p t o n mechanism is proportional to their life-time in this case. Thus the VHE g a m m a - r a y flux from the Crab Nebula should be inverse proportional to the magnetic field strength. We also cannot exclude the possibility that the pulsed gamma-radiation in the vicinity of pulsar may be smoothed. This idea is considered in a paper of Bogovalov and Kotov [24]. It seems to us that only further observations and model improvements could give a more accurate i: icture of the Crab Nebula.
5. D I S C U S S I O N
Several theoretical calculations of the VHE g a m m a - r a y flux were made earlier [16], [17], [18], [19]. All those calculations were briefly discussed by De Jager and Harding [20]. Of course, all of t h e m contain some simplifications. The paper of Stepanian [19] is based on the calculations of the Crab Nebula magnetic field structure that have been obtained due to the comparison with the experimental data of the space distribution of the Crab Nebula radiation in the wide range of the electromagnetic radiation [22]. This model exploits the concept of the
6. C O N C L U S I O N S The consideration of published results of the VHE g a m m a - r a y flux leads us to the conclusion that they are not in good agreement (see Fig.3). Of course, time variations of the flux can not be completely excluded, but most of the disagreements are probably connected with differences in the concepts of flux estimation. The above proposed method of flux estimation - if it is applied to all measurements - will show whether the disagreements are real. Theoretical calculations compared with the
A.A. Stepanian/Nuclear Physics B (Proc. Suppl.) 39A (1995) 207~212
reliable value of the gamma-ray flux may be very useful for understanding the structure of the Crab Nebula, the mechanism and place of particle acceleration etc. -10 10
I
I
I Fazio[7] ~ ASGAT[12]
I
7 ~9 t¢
Whipple -11
EI01 +
.EoRA CI11
CrAO | ~ Them.[13]
Them.[13] -12 1o
0.1
J 1 Energy
q 10
( TeV )
Fig.3: The positive results of the Crab Nebula observation. Thus the problem of the VHE gamma radiation should be open for the further analysis.
REFERENCES
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