The anisotropy of cosmic rays observed by the Utah Fly's Eye detector has been studied. Emphasis has been placed on examining distributions of events in galactic coordinates. No statistically significant departure from isotropy has been observed for energies greater than 0.4 EeV (1 EeV = 10 to the 18th power eV). Results of the standard harmonic analysis in right ascension are also presented

Baltrusaitis, R. M.

Cady, R.

Cassiday, G. I.

Cooper, R.

Elbert, J. W.

Gerhardy, P. R.

Ko, S.

Loh, E. C.

Mizumoto, Y.

Salamon, M. H.

English

NASA Technical Reports Server

2 4 6 OG5.3-4
ARRIVAL DIRECTIONS OF COSMIC RAYS OF E > .4 EeV
Baltrusaitis, R.M., Cady, R., Cassiday, G.L., Cooper, R., Elbert, J.W.,
Gerhardy, P.R., Ko, S., Loh, E.C., Mizumoto, Y., Salamon, M.,
Sokolsky, P., Steck, D.
Department of Physics, University of Utah, Salt Lake City, UT 84112
ABSTRACT
The anisotropy of cosmic rays observed by the Utah Fly's
Eye detector has been studied. Emphasis has been placed on
examining distributions of events in galactic coordinates.
No statistically significant departure from isotropy has been
observed for energies greater than 0.4 EeV (1EeV = 10IB eV).
Results of the standard harmonic analysis in right ascension
are also presented.
1. Introduction. At the highest energies, the arrival directions
of cosmic rays are expected to begin to reveal their origins. In
this analysis the observed number of events is compared to the number
predicted for an isotropic distribution as a function of both galactic
longitude and sin (galactic latitude) for each energy interval, so
searches can be (Badefor clustering in two dimensions. The event
distributions have also been fit to two different models for galactic
latitude dependence: 1. An excess of events from the general direction
of the galactic plane of the form I(b) = Io[(1 _.f) + f exp(-b2)] whereb is the g lactic latitude in radians (1), and A gradient with
respect to galactic latitude of the form I(h) = Io(1 + s'b), where b is
the galactic latitude in degrees. A simil_ analysis of the data is
performed in the two-dimensionalcelestial coordinates, and fits have
been made to the amplitude A and phase _o of the first harmonic of the
form I(_) = Io(1 + A cos(_ - _o)), where _ is the right ascension.
2. Description of Analysis. We report here the arrival directions
of extensive air showers observed by the Utah Fly's Eye detector,
situated at 41°N latitude, between the dates of Nov. 1981 and April
1985. A detailed description of the detector is reported in ref. 2.
Only data recorded on clear nights with no clouds higher than 10° above
the horizon were accepted. The total live time corresponding to these
"weather cuts" is 58.2 days. Further cuts on the data were made to
ensure well-measured tracks with good control over the error in
direction: the average error in zenith angle after cuts is _ = 3.8°.
Events passing all cuts were then binned in both galactic and celestial
coordinates for four energy intervals: 0.4 - 1.0 EeV, 1.0 - 3.0 EeV,
3.0 - 10.0 EeV, and > 10 EeV. All distributionswere made in equal-
area bins of 5° in galactic longitude (or right ascension) versus 0.4
in sin latitude (or sin declination).
Since the Fly's Eye can only operate on clear moonless
nights, the irregular pattern of observation times precludes the
assumption of uniform acceptance in right ascension made by experiments
running continously. The procedure used to calculate the number of
 5.3-4 
I  I ONS  I        
altr saitis, . ., ady, ., assiday, . ., ooper, ., lbert, J. ., 
erhardy, . ., o, ., oh, . ., r~izumoto, ., ala on, ., 
l , ., t , . 
epart e t f hysics, niversity f ta , alt ake it , UT 84112 
T 
he anisotropy of cos ic rays observed by the tah ly's 
ye etect r as ee  st ie . phasis as ee  laced on 
exa ining distributions of events in galactic coordinates. 
o st tistica11y i ifica t rt re from isotropy s  
observed for energies greater than 0.4 EeV (1 EeV = 10 18 e ). 
esults f t e stan ard ar ic a al sis i  ri t asce sion 
are also presented. 
. I trod tion. t t  i t r i , t  rrival ir tion  
of cos ic rays are expected to begin to reveal their origins. In 
t is a al sis t e served nu ber f e e ts is c ared t  t e nu ber 
predicted for an isotropic distribution as a function of both galactic 
l itude and sin ( alactic latitude) f r eac  e ergy i ter al, so 
s rch s   made f r l stering i  t  i e si s. e t 
i stri ti ons a e al s  een fit t  t\'/o iff re t odel s f r al acti c 
latitude dependence: 1. An excess of events from the general direction 
of the galactic plane of the form I(b) = 10[(1 - f) + f exp(-b 2)] where  is t  l tic l titude in r ians ( ), a  2   r i t it  
respect to galactic latitude of the form l(b) = 10 (1 + s·b), where b is the galactic latitude in degrees.  si ilar analysis of the data is 
erformed in the t - ime sional celestial c r i ates, and fits a e 
been ade to the a plitude  and phase ao of the first har onic of the 
form I(a) = 10 (1 + A COS(a - ao», where a is the right ascension. 
2. Description of Analysis. We report here the arrival directions 
of extensive air sho ers observed by the tah l 's ye etect r, 
situated at 41°N latitude, between the dates of ov. 1981 and pril 
.  etailed escri tion f t e etector is re rted i  ref. . 
nly data recorded on clear nights ith no clouds higher than 10° above 
the rizon ere acce te . he t tal live time c rresponding to t ese 
eat r t " i  .  . rt r t   th  ta er  a  to 
ensure ell-measured tracks ith good control over the error in 
direction: the average error in zenith angle after cuts is a = 3.8°. 
vents passing all cuts ere then binned in both galactic and celestial 
c r i ates f r f r e ergy i tervals: .  - .  e , .  - .  e , 
3.0 - 10.0 EeV, and> 10 EeV. ll distributions ere ade in equal-
area bins of 5° in galactic longitude (or right ascension) versus 0.4 
 n titude  n l ion). 
Since the Fly's Eye can only operate on clear oonless 
nights, the irregular pattern of observation times precludes the 
assu ption of uniform acceptance in right ascension made by experiments 
running continously. The procedure used to calculate the nu ber of 
https://ntrs.nasa.gov/search.jsp?R=19850025758 2020-03-20T18:01:03+00:00Z
2 4 7 OG5.3-4
events expected as a function of galactic longitude and sin(latitude)
from an isotropic distribution is outlined in this section. The distri-
bution in celestial coordinates follows exactly the same prescription.
The absolute start and stop times for each data run have
been recorded. For each 15 minute interval of detector on-time, the
zenith angle for each bin of galactic coordinates is computed. Since
the distribution in azimuth is uniform, the detector acceptance in
zenith angle is the only quantity necessary to compute the acceptance
times live-time product at each time interval and each pair of coordi-
nates. Two different techniques have been used to find the acceptance
as a function of zenith angle. The first is to use the Monte Carlo
simulation of the detector. In principle, this allows an absolute rate
determination in galactic coordinates, although only the relative rate
was used for this analysis. The second technique uses the measured
zenith angle distribution of the data itself to get the relative
acceptance. An acceptance of I gives a flat distribution in cos(oz),
so measuring the deviation from a fixed number gives the ez dependence.
The relative acceptance in zenith angle calculated directly from the
data agrees very Well with that predicted by the Monte Carlo simulation:
the results reported here were shown to be insensitive to the distri-
bution used.
The acceptance-weighted live times thus generated give the
relative rates expected in each bin of galactic coordinates. The
absolute normalization is then fixed by demanding that the total number
of events predicted be equal to the total number of events observed in
each energy interval. Deviations in the data from isotropy should then
appear as local excesses (or deficits) of events compared with the
number predicted.
Given the number of events observed and predicted in each bin,
fits to various models for a possible anisotropy can be made. The number
. of events expected is weighted by the appropriate model-dependent factor
(for example, (I + s.b) to fit for a galactic latitude gradient s), the
"expected" array is renormalized to preserve the same total number of
events, and the joint probability for the observed to predicted distri-
- bution is calculated. Maximizing the probability with respect to
variation in the parameters of the model (for example, s) gives the best
fit to the data as well as the associated errors on the best-fit values
of the parameters.
"_ 3. Results and Discussion. Figure I
shows our acceptance in galactic
coordinates from Monte Carlo events
between 3-10 EeV. Note that the
. ,_ - region between galactic longitude
240 ° to 0 ° and galactic latitude +30
to -90 ° are not visibie to the Fly's
Eye. Observed rates projected onto
- a single axis must, of course,
be evaluated with this fact in mind.
Fig. I. The Fly's Eye Acceptance.
 OGS.3-4 
e e ts e ected as a f ction f lactic l gitude and si (latitude) 
  otropic stribution  tlined  is tion.  istri-
bution in celestial coordinates follows exactly the same prescription. 
he a s lute start and st  ti es f r eac  ata run have 
 r rded. r   i ute i terval f tector -time, t  
zenith angle for each bin of galactic coordinates is co puted. ince 
the distribution in azi uth is uniform, the detector acceptance in 
zenith angle is the only quantity necessary to co pute the acceptance 
ti es live-time r duct t eac  ti e i terval a  eac  air f c rdi-
nates. Two different techniques have been used to find the acceptance 
as a function of zenith angle. he first is to use the onte arlo 
i ulation f t  tector. I  rinciple, t is llo s  s lute r te 
termination i  lactic ordinates, lt ough ly t  r lative r te 
as used f r t is a alysis. he sec  tec nique ses t e eas re  
ze ith a le istribution f t e ata itself t  et t e relative 
acceptance. An acceptance of 1 gives a flat distribution in COS(9z), 
so easuring the deviation fro  a fixed nu ber gives the 9z dependence. 
The relative acceptance in zenith angle calculated directly fro  the 
ta rees r  w' " ith t at redicted  t  te rlo si ulation: 
t e r sults r orted r  r  s  t   i sensitive t  t e istri-
tion . 
The acceptance-weighted live ti es thus generated give the 
relative rates expected in each bin of galactic coordinates. The 
absolute normalization is then fixed by de anding that the total nu ber 
f ts redicted  l t  t e t tal r f ts rved i  
each energy interval. Devi ati ons in the data from isotropy shoul d then 
appear as local excesses (or deficits) of events co pared ith the 
nu ber redicted. 
iven the nu ber of events observed and predicted in each bin, 
fits to various odels for a possible anisotropy can be ade. he nu ber 
of events expected is eighted by the appropriate odel-dependent factor 
(for exa ple, (1 + s'b) to fit for a galactic latitude gradient s), the 
"expected" array is renormalized to preserve the sa e total nu ber of 
events, and the joint probability for the observed to predicted distri-
bution is calculated. aximizing the probability with respect to 
variation in the para eters of the model (for exa ple, s) gives the best 
it t  the ta  ell  the ssociated rrors  the est-fit alues 
f the rameters. 
Fig. 1. The Fly's Eye cceptance. 
3. Results and Discussion. Figure 1 
shows our acceptance in galactic 
ordinates ro  o t  arlo ents 
between 3-10 EeV. Note that the 
region between galactic longitude 
240 0 to 00 and galactic latitude +30 
to _90 0 are not visible to the Fly's 
Eye. Observed rates projected onto 
a single axis ust, of course, 
 aluated ith this act n ind. 
0G5.3-4
248
The ratio of events observed to events expected as a
function of galactic latitude are shown in Fig. 2. Table 1 gives the
results for the two galactic models considered. Column a) shows fits
to a latitude gradient s of the form (1 + s.b); column b) shows the
2
fits to a galactic plane excess (1 - f + fe-b ) with b in radians. No
statistically significant deviations from isotropy are observed,
although the trend in the latitude gradient agrees with that observed
by other experiments (3). The data disagrees mildly with the analysis
presented in ref. (1) for the galactic plane excess model, at about
1 _ level. However, our inability to see a rather large region of the
galactic disk, in particular the galactic center, should be kept in
mind when interpreting these results.
latitude(degrees) l_]|itude(de3rees)
-_0 -40 -20 0 20 40 60 -60 -40 "20 0 20 40 60
J J i v
20 0.4< E<I.OEeV 2.0L I< E< 3EeV
1,5 _ 1.5
¢ 8
0,5 0.5 ,-
8 l i i (_ i f I i i i I i i i i i i
-I.0 -. -.6 -,4 -.2 .2 .4 .6 ,8 1.0 "1.0 -.8 -,6 -.4 ",2 0 .2 ,4 .6 .8 1.0
sin(galactic latitude) sin {galactic latitude)
/
lalitude (degrees) latitude (degrees)
-60 -40 -20 0 20 " 40 60 -60 -40 -20 0 20 40 60 "
, i = i ., i ,
2.0 3< E< IOEeV 2.0 - E>IOEeV
i,s _ Ls T
0.5 0.5. I
J.
i i i t i i i i I i i i i i i i i i
-I.0 -.8 -.6 -.4 -,2 0 .2 ,4 .6 ,8 1.0 -I.0 -.8 -,6 -,4 -.2 0 .2 .4 .6 ,8 1,0
S;n(goloclic latitude) sin (galactic latitude) "=
Fig. 2. Observed rates as a function of galactic latitude.
O S. 4 
8 
e r tio f e e ts served to e e ts e ected s  
f ction of galactic latitude are shown in ig. 2. a le 1 gives the 
s lts f  t  two l tic odels si ed. olumn ) shows fits 
  l itude i     form (1  ·b ; lumn )  h  
 
its t   l tic l  s (1 - f  - ) it   in i . o 
stically ig ificant i ions from isotropy  , 
lthough t  trend in th  latitude i t s it  t t ved 
by ot er ex erime ts (3). he ata isagrees il ly it  t e a alysis 
s nted i  f. ( ) f  t  l tic l  ss odel, t t 
 cr l l. o eve ,  i ility    h r l  ion   
l tic i , in ticular th  l tic t , ld e t in 
ind hen interpreting these res lts. 
latitude degre s) tolltude (de1'ees) 
~~O ·  ·      ·60 ·40 ·2      
.0 0.4< E<1.0EeV .0 1< E < 3 EeV 
" ~ 1.5 " 1.5 <> 
:;; I u I " . .;; a. f I ~ I I I ..... 1 I Q. I I '0 I I ..... I I ~I.O I I -g 1.0 T I ! • 5: ;: I 1 .D ~ 0 
.D 
.5 
0 
 
-1.0 -.  -.6 -,4 -.2 0 .2 .4 .6 .8 1.0 -1.0 -.8 -.6 -.4 -.    .    .0 
sin (90lactic latitude) i  ( l ti  l tit ) 
lotitude (degrees) l tit  ( r s) 
-60 -40 -20 0 20 . 40 60 -60 - 0 - 0     
2.0 
1 
:3 < E< 10EeV I E> 10 EeV ! .  ~ 1.5 I I 11 1.5 to r :ii I :;; I '0 K ~ • 1 Q. 1 :;; 1.0 1 I 1 I I ~ 1.0 I " I ~ I :: '" 5: 1l .D ! I I 0 0 0.5 0.5 
-1.0 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 t.O -1.0 -.8 -.  -.  -.    .   .  .0 
sin (galoclic latitude) sin (galactic latitude) 
ig. 2. bserved rates as a function of galactic latit~de. 
2 4 9 OG5.3-4
Table I. Galactic latitude fits
a) b)
Energy <E> Number of Slope Galactic P1ane
(EeV) (Eev) Events s(lO-3/deg) Excess f
0.4-1.0 .64 760 -0.1±1.6 0.06±0.20
1.0-3.0 1.7 575 -1.5±1.7 0.15±0.21
0.3
3.0-10,0 5.0 170 -1.5 ± 3.0 0.0 t_._
>10.0 18.8 45 0.6±6.0 0_1,o
In celestial coordinates, the fits were made to the amplitude
and phase of the first harmonic in right ascension, and are shown in
Table 2. Here, there is some evidence for non-zero anisotropy, again
in agreement with other experiments.
Table 2. First harmonic in right ascension
Energy Amplitude Phase _o
(EeV) A (degrees)
0.4-1.0 .15 ± .08 300 ± 30
1.0-3.0 .07 ± .08 25 ± 80
3.0-10.0 .25 ± .16 350 ± 40
>10.0 .34 ± .34 290 ± 60
4. Conclusions. If we believe that the cosmic rays above 1EeV
. are predominantly protons from our own galaxy, then it is perhaps sur-
prising that there is no evidence in our data for an enhancement from
the general direction of the galactic disk. Certainly, more evidence
on the composition of cosmic rays at this energy will be crucial to a
real understanding of production sources and mechanisms. If a sig-
nificant fraction of the observed cosmic rays are in fact galactic
iron, or are "universal" extra-galactic protons, then the observed
smoothness of the data would be reasonable.
Acknowledgment
This work was supported by the U.S. National Science
Foundation under grant PHY-8201089.
References
I. Wdowczyk, J. and Wolfendale, A.W., J. Phys. G: Nucl. Phys. 10
(1984) 1453.
2. Baltrusaitis, R.M. et al., The Utah Fly's Eye Detector, submitted
. to Nucl. Inst. Meth.
3. Astley, S.M. et al., Proc. Int. Conf. on Cosmic Rays (Paris) 2,
156, 1981.
249 
abl e 1. alactic 
gy > b   EeV) Eev) s 
. -1.0 .64 0 
.0-3.0 .7 5 
3.0-10.0 5.0 170 
>10.0 18.8 45 
1 atitude fits 
) 
ope 
(1O /deg) 
- .1 ± 1.6 
-1.5 ± 1.7 
-1.5 ± 3.0 
0.6 ± 6.0 
5.3-4 
 
al ic l  
  
.06 ± 0.20 
.15 ± 0.21 
0.0 * 0.3 
.5 
.0 
n ial r es, he ts e  e o he pl tude 
nd e  he r  m c n g  ion, d e hown n 
l   er  h re  ome dence or ro sotropy, in 
n eem t i h h  im s. 
  i  rm c n ig  cension 
gy pli ude e a  EeV)  ees) 
.4-1.0 .15 ± .08 300   
1.0-3.0 .07 ± .08 25 ± 80 
.0-10.0 .25  .16 0   
.0 .34 ± .34 290  60 
 oncl .   eve h  he c ays e  Ee  
e i ly ons rom   ax  hen   haps 
sing h  here   dence n  a   ncem t rom 
he al ection  h  ic sk. ert y, or  dence 
n h  posi ion  c ays  h s gy i l  al o  
l tanding  ion ces  ec sm .   g-
ica  raction  he rved c ays  n  ic 
ro    sal" t a ic on , hen he rved 
t ss f th  ta ld  r o le. 
l dgm t 
i  or   ted  he .  at onal ence 
ion   - . 
ef rences 
1. do cz   d olf , . .     ucl   lQ 
1984)  
 alt i s,   l   t h l '   et t , it ed 
to ucl. I st. et . 
 st  M     .   c  is) ~, 
  


Arrival directions of cosmic rays of E  .4 EeV

Arrival directions of cosmic rays of E .4 EeV

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