Full text of DOI:10.1134/1.163823

Astronomy Reports, Vol. 44, No. 1, 2000, pp. 45–55. Translated from Astronomicheskiœ Zhurnal, Vol. 77, No. 1, 2000, pp. 52–63.
Original Russian Text Copyright © 2000 by Malofeev, Malov.
The Unusual Profile of the Radio Pulsar Geminga
V. M. Malofeev and O. I. Malov
Pushchino Radio Astronomy Observatory, Astro Space Center of the Lebedev Institute of Physics,
Russian Academy of Sciences, Pushchino, Moscow oblast, 142292 Russia
Received December 9, 1998
Abstract—The results of observations of the radio emission profiles of the Geminga pulsar at 102.5, 87, 58,
and 39 MHz are reported. Individual pulses are presented for the first time, and rare occasions of strong emis-
sion over the entire pulsar rotation period have been detected. A detailed analysis of the shapes, durations, and
arrival phases of the pulses at 102.5 MHz is presented. These data reflect the unique character of the radio emis-
sion of Geminga. © 2000 MAIK “Nauka/Interperiodica”.
1
. INTRODUCTION
one group from India [9]. At the same time, attempts to
detect the pulsar at the higher frequencies 317–410 MHz
The nature of the first gamma-ray source Geminga
1] was revealed after the detection of a pulsar, first in
X-rays [2] and then in gamma rays [3]. A preliminary
identification of Geminga with a weak 25 . 5 optical
object [4] was recently confirmed via measurement of
its parallax, from which it was possible to determine the
[10–12] and 1400 MHz [12], and at the lower fre-
[
quency 35 MHz [11] have thus far been unsuccessful.
In 1997–1998, we undertook intensive studies (par-
tially reported in [6]) at 102.5 MHz and other meter-
wave frequencies using the DKR-1000, the other large
radio telescope of the Lebedev Institute of Physics at
Pushchino. These observations yielded positive results at
the lower frequencies of 61 and 41 MHz [13]. In the cur-
rent paper, we present integrated (group and individual)
pulses of Geminga at four frequencies: 102.5, 58, 41,
and, for the first time, 87 MHz. In addition, we present
a detailed analysis of the profile shapes and their arrival
phases at 102.5 MHz.
m
5
9
distance to the object, equal to 157± pc [5]. Geminga
3
4
is, thus, a nearby, young neutron star with all attributes
typical of the rare group of “multiwavelength” objects,
which includes the famous young Crab and Vela pul-
sars, which reside in supernova remnants. These
objects radiate over the entire electromagnetic spec-
trum, from gamma to radio wavelengths. This made the
lack of detectable radio emission in Geminga, which
turned out to be the nearest object of this group, all the
more surprising. Moreover, until recently, all pulsars
had first been discovered at radio frequencies, includ-
ing those that are more than ten times more distant than
Geminga. Most “multiwavelength” pulsars are strong
radio objects. Until recently, only Geminga remained
the only “radio quiet” pulsar, in spite of numerous
attempts to find either stationary or pulsed emission
2
. OBSERVATIONS
Detailed information about the antenna, receiving
equipment, observation procedure, data processing, and
probable flux-measurement errors is given in [14] and, in
part, in [6]. Here, we will briefly present parameters rel-
evant to our observations of the Geminga pulsar.
(
see References in [6]), including observations using
the largest radio telescopes in the world.
The observations were carried out regularly from
December 1990 until July 1998 in 16 series with dura-
tions of 4 to 14 days. We used the LPA (Large Phased
Antenna) meridian radio telescope and the East–West
antenna DKR-1000 (Broadband Cross Radio Telescope).
On the LPA operating at a frequency of 102.5 ± 2 MHz,
Finally, at the end of 1996, the uniquenesses of this
object was put in doubt. Three research groups at the
Pushchino Radio Astronomy Observatory indepen-
dently detected pulsed radio emission from Geminga
m
the observation time is ~3.5 /cosδ at the half-maxi-
[
6–8]. All three groups used the same radio telescope
mum level of the beam, where δ is the source declina-
tion. Thus, we could observe 954 individual pulses of
Geminga each day. Due to its large geometrical area,
the LPA is one of the most sensitive radio telescopes in
the world. The antenna consists of 16 384 dipoles occu-
pying an area of 384 × 187 square meters; i.e., it has an
effective area
and receiving equipment but applied different observ-
ing and data-processing methods. They obtained differ-
ent flux densities, shapes, and widths for the integrated
pulse but similar values for the dispersion measure. We
perform a more detailed comparison of the profiles and
consider probable reasons for these discrepancies
below.
The presence of pulsed radio emission at the nearby
frequency of 103 MHz has already been confirmed by
4
2
A ≈ 3 × 10 m cos(δ – 55°) ,
(1)
eff
1
063-7729/00/4401-0045$20.00 © 2000 MAIK “Nauka/Interperiodica”

4
6
MALOFEEV, MALOV
enabling us to achieve high sensitivity. A detailed cal-
culation of this quantity is given in [14]. As an exam-
ple, the flux density measured for PSR 0353+52 at
3. DATA PROCESSING AND RESULTS
The observations yielded files containing the pulsar
signal, either accumulated with the observed period (2P
1
02.5 MHz is S = 3.5 mJy. The East–West DKR-1000
or 3P) or in groups of pulses with P = 10P in all chan-
H
antenna operates at 30–110 MHz and has a geometrical
nels. The data processing included a search for the
4
2
area of 2 × 10 m . Due to the scanning system used, the
“
zero” level in each channel, gain equalization using a
m
observation time on this telescope is 15 /cosδ. The
calibration signal, rejection of channels affected by
interference according to two criteria (the gain factor
and ratio of the noise σ in the current and reference
channels, see [14] for details), elimination of the seg-
ment with the calibration signal, and summation of the
signal in all channels taking into account the time shift
due to the dispersion delay of the signal in the analyzer
passband. We then determined the new “zero” level,
calculated a moving average of either five or three
points with a resolution of 2.56 and 7.68 ms, respec-
tively, and calculated or estimated the pulse energy.
effective area depends on frequency and has a maxi-
mum at 80–90 MHz. The effective area is estimated to
3
2
be (8–10) × 10 m , enabling us to measure the fluxes
and study the profiles of dozens of pulsars at low fre-
quencies (see, for example, [15]). The possibility of
using another large meter-wave radio telescope for
studies of Geminga cannot be overestimated, since the
observations at other frequencies not only allowed us to
confirm the existence of pulsed emission from this
object, but led to new and very important results.
The observations of Geminga were carried out in
two regimes. In the first, we usually used 32, and some-
times 64, 96, or 128, channels of an AS-128 spectrum
analyzer with a channel passband of 20 kHz. We
employed a uniform procedure for the synchronous
accumulation of the signal in selected channels during
the transit of the pulsar through the radio-telescope
beam. The daily time for the start of the signal record-
ing was calculated beforehand in order to preserve the
arrival phase of the pulse. For this calculation, we used
We now give some more details about the criteria
used to remove channels with interference. We applied
both a traditional procedure, comparing the σ in all
channels with those in reference channels, and com-
pared calibration signals. Both criteria frequently
worked together, but in many cases, the latter was more
sensitive to interference that raised the overall level but
left σ nearly unchanged. Note that the removal of chan-
nels affected by interference is a very efficient way to
battle stationary radio stations, but this procedure does
not completely eliminate weak random pulsed indus-
˙
the period and its derivative (P, P ), the coordinates
given in the catalog of Taylor et al. [16], and the soft- trial interference; therefore, a very important aspect of
ware of Shabanova [17]. During the observations, we the processing was separating the pulsar signal from the
used the time-service signals of our observatory [18]. remaining interference. For most of the pulsars in our
Virtually all the observations in this regime were car- survey [14], this procedure has been completed and
ried out with a receiver time constant of 3 ms and sam- yielded very good results. It was also applied to the
pling interval of 2.56 ms. In order to precisely measure Geminga observation, but here, we encountered some
the pulsar flux, we fed in a noise-generator signal dur- difficulties. Geminga’s signal has an unusual character.
ing the first 15 readings, which was calibrated against Nothing similar has been observed for any other radio
discrete radio sources with known flux densities (see pulsar. First, its flux, pulse duration (over wide limits),
details in [14]). The observations were carried out with profile shape [6], and pulse arrival phase (see details
a measuring complex based on an AT-486 personal below) vary from day to day. Thus, in the case of Gem-
computer [19]. To ensure certain identification of the inga, the standard procedure for detection of the phase
pulsar pulse, all integrations were carried out with dou- of the pulsed signal via summation of several days of
ble or triple the observation period (i.e., P = 0.237 s × 2 observations sometimes failed. Second, checking the
H
or P = 0.237 s × 3). This procedure was thoroughly dispersion delay of a pulse was possible only for strong
H
mastered during our survey of faint pulsars [14].
signals. Third, the magnitude of the dispersion is very
3
small (2.9 pc/cm [6]), and the expected delay was only
In the second regime, the individual pulses were
recorded over a time window corresponding to 10 pul-
4
–5 sampling points (readings), even for the edge frequen-
cies, when observing with 32 channels at 102.5 MHz
though it was measurable at 58 and 41 MHz). How-
sar periods (i.e., P = 0.237 s × 10). In a single observ-
H
(
ing session, we collected 90 such groups of pulses on
the LPA and 410 on the DKR-1000 antenna. To
improve the signal-to-noise ratio, we used a time con-
stant of 10 ms and sampling interval of 7.68 ms. In
approximately half the sessions, the recording regime
was such that each of the ten periods in the time win-
dow itself represented the sum of two (or five) pulsar
periods. In addition, to reduce the data volume, in the
ever, this procedure successfully selected interference
whose amplitude was maximum and duration was min-
imum when the dispersion measure was set to zero.
3
.1. The Integrated Profile
First we will spend some time on the 102.5-MHz
individual pulse mode, we used only 16 20-kHz chan- observations, since they are the most numerous. Anal-
nels at each frequency. This enabled us to study emis- ysis of profiles integrated over several hundred periods
sion intensity variations within an observing session.
per day and then summed over several days (i.e., thou-
ASTRONOMY REPORTS Vol. 44 No. 1 2000

THE UNUSUAL PROFILE OF THE RADIO PULSAR GEMINGA
47
sands of periods) showed that the profile shape is not
Intensity, rel. units
.0
stable [6]. There remained the hope that the summed
profile obtained by integrating some 27507 periods
1
(a)
(from the data of the first half-year of observations)
0
.5
0
would prove stable and provide an identity card for
Geminga, as is the case for profiles obtained for other
pulsars after accumulation over several hundred peri-
ods. To check this hypothesis, we continued observa-
tions of Geminga at 102.5 MHz.
–
0.5
.0
Figure 1 presents the mean profiles obtained over
four observing sessions, carried out during the seven
subsequent months. As earlier, the summed profiles for
individual sessions demonstrate a wide variety of
shapes and durations. Furthermore, in two sessions
1
(b)
(c)
(d)
0
.5
0
(
August and December), we observed an interpulse at
the end of the period, which was not clearly visible in
the summed profiles in any of the sessions in the first
half-year of observations. Note that, in all four ses-
sions, the mean profile has two or more components,
and the summed profile width at half-maximum is
larger.
–
–
0.5
.0
1
0.5
0
In the August session, the dashed curve shows a
comparison signal accumulated over eight days of
observations in a direction close to Geminga with the
same parameters as for Geminga. This noise signal was
reduced to the same gain as the observation of Gem-
inga and clearly demonstrates the noise level and the
level of probable weak interference. We can see that, in
this session, the amplitude of the signal from Geminga
is from 3σ (left-hand components) to 5σ for the inter-
pulse (right components). The most surprising thing,
however, is that the sum of all the sessions in the second
half of the year (28560 periods) yielded a profile that
was again different from that obtained from approxi-
mately the same number of periods accumulated in the
first six months [6]. Thus, 30000 periods appear to be
insufficient to obtain a stable profile. This amazing fact
obviously separates out Geminga from other radio pul-
sars. At first, it seemed that our receiving passband was
insufficiently wide to smooth signal frequency varia-
tions due to scintillations on inhomogeneities of the
interstellar medium. But two facts show that this is not
the case.
0.5
1
.0
0
.5
0
–0.5
.0
1
(e)
0
.5
0
–
0.5
0
0.2
0.4
0.6
0.8 1.0
First, broadband observations (with 64, 96, and 128
channels; i.e., 1.28, 1.92, and 2.56 MHz, respectively)
also do not yield a stable profile shape and pulse width.
Second, for strong pulses, we observed a signal even
in individual groups of channels separated by hun-
dreds of kHz. An estimate of the characteristic scale of
scintillations on the three days with strong pulses yields
Phase, fraction of the period
Fig. 1. Integrated profiles of Geminga at 102.5 MHz obtained
in four observational sessions: (a) July 6–7, 1997 (7 days, 6700
periods); (b) August 1997 (14 days, 8904 periods), the dotted
curve shows the summed signal for 8 days of test observations;
c) November 1997 (4 days, 2864 periods); (d) December 1997
6 days, 10092 periods); (e) the total of the four sessions
31 days, 28 560 periods), the dashed curve describes the enve-
(
(
(
4
00–800 kHz; recalculating it to the radius of fre-
quency correlation gives a value close to 80–160 kHz.
This is fairly typical for nearby pulsars in our wave-
length range [20], and, consequently, the behavior of
the profile of Geminga should be similar to that of other
pulsars—for example, PSR 0950+08, in which, from
time to time, a minor change of the profile shape is
lope of the main pulse (the downward arrow shows the mean
phase) and interpulse (the upward arrow shows the mean
phase). The width of the envelope corresponds to 2σ of the dis-
tribution of the durations of the main pulse and interpulse,
which are presented in Figs. 4a, 4b; the distributions of the
arrival phases of the centers of the main pulse and interpulse
are given in Figs. 4c, 4d.
ASTRONOMY REPORTS Vol. 44 No. 1 2000

4
8
MALOFEEV, MALOV
Number of days
both duration and shape. New observational sessions
1
0
8
6
4
2
confirm this. In 23% of 83 days without strong interfer-
ence (there were 105 days of observation in all), we saw
only a noiselike signal, when the pulsed component did
not exceed (2–3)σ. In 19% of cases, there was a narrow
pulse with approximately the same phase as in the
summed profile in Fig. 1. Broad profiles with two or
more components were observed in 44% of cases. Very
broad profiles, which, as a rule, had large fluxes, were
visible on 14% of days. Finally, an interpulse with a
phase near 0.75P–1.0P was recorded on 39 of 83 days,
when the signal exceeded 3σ, and, on some days, the
intensity of the interpulse exceeded that of the main
pulse.
(
a)
0
0
20 40 60 80 100 120 140 160
b)
1
(
8
6
4
2
In order to identify the signal of Geminga with cer-
tainty, we always used observations with double or triple
the accumulation period. As controls, we observed strong
and weak pulsars in a similar mode. For normal pulsars,
two or three independent accumulated profiles very sel-
dom differed in the details of their shape or by more than
20% in amplitude, but Geminga again presented a sur-
prise. In only 39% of cases did we observe two of two or
three of three pulses. Moreover, quite frequently, the
pulse shape and duration differed appreciably.
0
20 40 60 80 100 120 140 160
2
1
1
0
5
0
5
(
c)
Duration, ms
The histograms in Figs. 2a and 2b can be used to obtain
a more complete picture of the distributions of the main
pulse and interpulse durations at 102.5 MHz. These distri-
butions are unusually broad, occupying about half the
period and only vaguely resembling a normal distribu-
tion. Figures 2c and 2d present histograms of the arrival
phases for the centers of the main pulse and interpulse,
measured at the half-maximum pulse amplitudes. These
are already closer to normal distributions, especially that
for the main pulse, but they are also unusually broad and
occupy up to one-third of the period. The statistical aver-
ages of the arrival phases of the main pulse and interpulse
are 80 ms and 208 ms, respectively, so that the separation
between the main pulse and interpulse is 0.51 ± 0.07 pul-
sar periods; this is quite similar to the situation at gamma-
ray energies [21]. For comparison, the scatter of the
period durations and arrival phases for PSR 0950+08,
observed as a reference pulsar over 30 days at the same
frequency and using the same method as for Geminga are
0
20 40 60 80 100 120 140 160
1
1
2
(
d)
0
8
6
4
2
0
8
0
100 120 140 160 180 200 220 240
Phase, ms
Fig. 2. Histograms of the durations of the (a) main pulse and
b) interpulse at 102.5 MHz and the arrival phases of the
centers of the (c) main pulse and (d) interpulse. The arrows
on the axis show the (a) and (b) mean durations and (c and d)
mean arrival phases of the main pulse and interpulse.
(
∆W
= 12 ms = 0.05P, ∆Φ ~ 30 ms ≈ 0.12P. Note that
0.5
this pulsar is not typical, since it has a composite pulse
shape with a high degree of linear polarization and
complicated behavior of the polarization position angle
observed, but the duration varies only by about ten mil-
liseconds.
[
22]. At our frequency, since the antenna receiver is
sensitive to linearly polarized radiation, the pulsar
shape changes strongly from day to day, so that the
pulse centroid also shifts. In most pulsars, these quan-
tities vary within one percent of the period.
Shitov and Pugachev [8] estimated the probable
radius of frequency correlation at 102.5 MHz using the
statistical correlation of pulse broadening due to scat-
tering in the interstellar medium with the dispersion
Figure 3 presents examples of the mean profiles at
measure; it proved to be 100 kHz. They also estimated 87 MHz (Figs. 3a, 3b), 58 MHz (Fig. 3c), and 39 MHz
this quantity to be 180 kHz for one day (November 15, (Fig. 3d). The profile in Fig. 3a is presented with the
1
996). Both values are close to our measurements. We double period for one day of observations. This exam-
already noted in [6] that the profiles accumulated over ple of very strong emission demonstrates the rare recur-
3
00 to 900 periods over one day substantially differ in rence, in detail, of the two shapes of the mean pulses
ASTRONOMY REPORTS Vol. 44 No. 1 2000

THE UNUSUAL PROFILE OF THE RADIO PULSAR GEMINGA
49
near 240° and 600°, independently accumulated over
372 periods. Figure 3b presents a convolution of the
upper profile. This is a broad, composite profile, occu-
pying more than half the period and probably contain-
ing three to four components.
Examples of summed mean profiles for several days
of observations at 58 and 39 MHz are presented in Figs. 3c
and 3d. In spite of the poor statistics (13–18 days of
observations at each frequency), the duration of the
profile remains, on average, constant as the frequency
changes, though a tendency for increasing duration
with decreasing frequency was observed earlier. In the
table, we list these quantities at the 0.5 amplitude level,
with the number of periods accumulated indicated.
Intensity, rel. units
1
(a)
1
.0
0
.5
0
0
120 240
360 480 600
(b)
1
0
.0
.5
0
The emission of pulsars differs from that of other
radio sources in two ways: The periodicity and fre-
quency dispersion of the signal. Figures 1 and 3 present
examples of summed periodic signals; however, to be
fully convinced of the presence of pulsar-type emis-
sion, we present in Fig. 4 a magnificent example of
strong emission from Geminga at 40.9 MHz on August
2
1, 1997, demonstrating the frequency dispersion of
the signal. The observations were carried out with the
double accumulation period, and each profile is a signal
compensated and summed over eight frequency chan-
nels (in each case 318 double periods were combined).
0
50 100 150 200 250 300 350
c)
1
0
.0
(
3
.2. Individual Pulses
.5
0
The very unusual behavior of the shape and phase of
the Geminga mean profile could most likely be
explained in two ways. The first is the presence of rare
but very strong pulses, and the second is a permanent
random wandering of the arrival phase of the pulses in
two windows, each covering one-third of the period
(Figs. 2c, 2d). To test these possibilities, we carried out at
least two observing sessions at each of the four frequen-
cies (102.5, 87, 60, and 41 MHz) in the group (sometimes
individual) integration regime. These observations
yielded very valuable additional information about the
radio emission of Geminga.
0
50 100 150 200 250 300 350
1
.0 (d)
However, before proceeding to the results for Gem-
inga, we show the profile of the test pulsar PSR 0950+08
for May 12, 1998, obtained in the same recording regime.
Figure 5a presents a group of pulses accumulated using
0.5
0
1
0 pulsar periods, i.e., Pobs = 10P. Each pulse in the
window represents the sum of six periods. Figure 5b
shows a convolution of the upper profile with a period
of 2P. Note the surprising stability of the phase and dura-
tion of the pulses in the upper panel. At the same time,
we can see wide scatter of the pulse amplitudes for an
integration over six pulsar periods. However, the profiles
accumulated over 24 periods (Fig. 5b) are already virtu-
ally indistinguishable. At phases of 200° and 560°, we
can see a weak interpulse with an amplitude of about
0
50 100 150 200 250 300 350
Phase, deg
Fig. 3. Examples of integrated pulses at three frequencies:
a) double period, 87 MHz, January 27, 1998, total 1372
periods; (b) period of profile (a) convolved with the total
over 2744 periods; (c) total of five days, or 9472 periods,
8.746 MHz; (d) total of four days, or 9920 periods,
9.046 MHz. The downward and upward arrows indicate
arrival phases of the centers of the main pulse and inter-
pulse, respectively.
(
5
3
4
% of the main pulse.
Surprisingly, in the observations of Geminga,
among the huge number of pulse groups considered, we
ASTRONOMY REPORTS Vol. 44 No. 1 2000

5
0
MALOFEEV, MALOV
Intensity, rel. units
.0
Intensity, rel. units
(a)
1
1
(a)
0
.5
0
–
0.5
0
1
0
.0
.5
0
(b)
0
1
2
3
4
5
6
7
8
9
Phase, pulsar periods
(b)
1
–
–
–
0.5
1
0
.0
.5
0
(
c)
0
0
100
200
300
Phase, deg
400
500
600 700
0.5
Fig. 5. Observation of PSR 0950+08 at 102.5 MHz for May
1
5, 1998: (a) Group 31 contains a time interval P equal to
H
1
0 pulsar periods, and the integration carried out over 6P ;
H
(
b) integrated profile of the same group obtained by con-
1
0
.0
.5
0
(d)
volving the data with PH equal to two pulsar periods. The
downward and upward arrows on theX axis show the arrival
phases of the centers of the main pulse and interpulse,
respectively.
found several obviously strong groups with an appre-
ciable periodic signal at all four frequencies. The pulse
appeared not only in short integrations (5 periods), but,
in some cases, even in the individual pulse recording
regime.
0.5
Figure 6 shows pulses of a group with period P = 10P
H
0
100 200 300 400 500 600 700
(at 102.5 MHz) accumulated on May 11, 1998. We can
see five to six pulses with the period of Geminga (Fig. 6a).
Figure 6b shows the convolution of the upper profiles over
nine Geminga periods. The downward arrows show the
phase of the main pulse (aligned with the phases of the
integrated pulses in Fig. 1) and the upward arrow the
phase of the interpulse in Fig. 6. Though we talk about
summing five periods in Fig. 6a and 45 in Fig. 6b, in
fact, we do not know how many actual pulses participated
in the sum. There could be from one to five for the top
Phase, deg
Fig. 4. Example of pulse dispersion at frequencies of about
0.7 MHz for August 21, 1997. From top to bottom, pulses
integrated with the double period obtained by integrating
18 pulses and summing over channels are shown: (a)
channels 1–8 (40.977–40.817 MHz); (b) 9–16 (40.817–
0.657 MHz); (c) 17–24 (40.657–40.497 MHz); (d) 25–
2 (40.497–40.337 MHz). The dotted curve shows the
4
3
4
3
expected position of the pulses for a dispersion measure of
.9 pc/cm .
3
2
ASTRONOMY REPORTS Vol. 44 No. 1 2000

THE UNUSUAL PROFILE OF THE RADIO PULSAR GEMINGA
51
Durations of integrated pulses at the half-maximum (N is the number of integration periods, M is the number of days of ob-
servation)
Main pulse
N, 104
Interpulse
N, 104
Frequency, MHz
02.5
duration, ms
M
duration, ms
M
1
73 ± 31
71 ± 24
63 ± 23
69 ± 33
4.4
3.5
3.5
2.2
64
13
18
14
44 ± 27
70 ± 37
63 ± 28
62 ± 27
2.3
3.8
3.2
3.3
39
15
16
16
87.5
58.7
40
panel and from five to 45 for the bottom panel. We can ally, the double-period profile (Fig. 7b) for this group is
speak more definitely about individual pulses at 58 MHz, one of the best examples of two strong main pulses and
where it was possible to find a group (number 162) of two slightly weaker interpulses (in a sum of only nine
six individual pulses on July 23, 1998. Even at 41 MHz pulsar periods). All the above examples (Figs. 6, 7)
on July 22, 1998 (Fig. 7), we could find a group of four convincingly demonstrate the existence of nonrandom
strong individual interpulses and main pulses. Gener- radio emission with the period of Geminga.
Intensity, rel. units
Intensity, rel. units
(
a)
1
1.0
(a)
0
.5
0
0
0
1
2
3
4
5
6
7
8
9
0
2
4
6
8
10
Phase, pulsar periods
Phase, pulsar periods
(
b)
1
0
.0
1
(b)
.5
0
0
0
100
200
300
Phase, deg
0
100 200
300 400
Phase, deg
500 600 700
Fig. 7. Observation of individual pulses of Geminga at
Fig. 6. Observation of Geminga at 102.5 MHz for May 11,
40.976 MHz for July 22, 1998: (a) group 211 contains a seg-
1
998: (a) group 50 contains a segment PH = 10P, and the
ment P = 10P, and the integration is carried out over 5P ;
H
H
integration is carried out over 5P ; (b) integrated profile of
(b) integrated profile of the same group obtained by con-
volving the data with PH = 2P. The arrows on the X-axis
mark the centers of the arrival phases of the main pulse and
interpulse, in accordance with Fig. 5d. The pulse arrival
phases at 40.976 MHz were recalculated from 39.046 MHz
H
the same group obtained by convolving the data with the
pulsar period. The downward and upward arrows on the
X-axis show the centers of the arrival phases of the main
pulse and interpulse, in accordance with the notation and
alignment with the phases presented in Figs. 1 and 4.
3
using a dispersion measure of 2.9 pc/cm .
ASTRONOMY REPORTS Vol. 44 No. 1 2000

5
2
MALOFEEV, MALOV
Intensity, rel. units
1
ing among many thousands of groups testifies to a
strong burst of emission from Geminga lasting from 4
to 20 periods. We observed two giant pulses, repeated
after one pulsar period. The first pulse (or the sum of
five pulses) had both the main pulse and interpulse,
while the second provided a completely unique exam-
ple of very strong emission during the entire period of
revolution of the pulsar. It is natural that, in this case,
the summed profile (Fig. 8b) contains the main pulse
and interpulse with almost identical amplitudes and a
raised zero level. The presence of emission throughout
the period can also be traced at 41 MHz (Fig. 7a),
though with decreased intensity at the phase of the
main pulse (pulse number 3). These examples demon-
strate the first case of a pulsar having such strong emis-
sion throughout its period. It is known that PSR
(
a)
0
0
1
2
3
4
5
6
7
8
9
10
Phase, pulsar periods
0
950+08, PSR 0826-34 [23, 24], and some other pul-
sars [25] display interpulse emission, but this emission
has at most about 35% of the main pulse amplitude (in
PSR 0826-34), and even then, is present only during
about half the period; in the remaining objects, it is
smaller than 1% at 400 MHz [25] and smaller than 2%
at 102.5 MHz [26]. Below, we summarize the data
obtained for groups and individual pulses.
1
(b)
(1) The strong emission of Geminga occurs in por-
tions from one to 50–100 pulses long, since prominent
pulse groups (when the signal-to-noise ratio exceeds
four) appear in several percent of the (several thousand)
recordings. In addition, there are long-term fluctuations
with a timescale of several days and, probably, months
(
details will be given in a forthcoming paper).
0
100
200
300
(2) Both the main pulse and interpulse are observed
Phase, deg
in different combinations, either separately or together,
with approximately identical signal amplitudes. There-
fore, our division into the main pulse and interpulse is
purely conventional.
(3) The durations of individual pulses (and inte-
grated pulses as well) vary over a wide range from ~0.1
to 1.0 period (Figs. 7a, 8a).
Fig. 8. An example of a group of very strong and broad
pulses at 87 MHz for May 12, 1998: (a) group 23 includes a
segment containing PH = 10P (the integration was carried
out over 5P ); (b) integrated profile of the same group (the
H
main pulse and interpulse were obtained by summing over
4
5 Geminga periods). The arrows in the upper panel corre-
spond to the centers of the arrival phases of the main pulse
and interpulse indicated in the lower panel, which, in turn,
are aligned with the mean arrival phases at this frequency
for all the days.
(4) The arrival phase of both the main pulse and
interpulse varies continually and over a wide range,
covering up to one-third of the period. At times, this
happens in an interval of only several dozen periods.
Returning to the unusual behavior of the phase and
shape of the integrated profile of Geminga, we have
established the existence of changes of the arrival phase
of pulses and of rare, but very strong, pulses. Several
times, we observed a shift of the integrated pulses by
4
. DISCUSSION
One effective criterion for the presence of a periodic
signal from Geminga, rather than a random periodic
noise signal, is that there be extreme in the dependences
of the amplitude and pulse width on a period specified
by hand when the pulses within groups are summed.
The largest amplitude and shortest duration for a
summed pulse should occur at the period of Gem-
inga—i.e., 237 ms—or every 31 readings (one read-
ing = 7.68 ms). We have analyzed the dependences of
the amplitude and pulse duration on the specified
0
.1–0.3 of the period in short integrations of 45 periods,
separated by an interval of 50–100 Geminga periods;
i.e., 12 or 24 s later. The examples in Figs. 6 and 7 show
a small shift of the pulse or interpulse arrival phase
compared to the expected phase of the integrated pulse
(
Figs. 1 and 3). While the estimated flux for the previ-
ous examples of groups or individual pulses is several
Janskys, the estimated flux for the giant pulses and period, which varied from 28 to 35 readings (from 215
interpulses for May 12, 1998 (group 23) presented in to 269 ms). On almost all these curves, the maximum
Fig. 8 is tens of Janskys at 87 MHz. This unique record- of the amplitude and minimum of the pulse duration
ASTRONOMY REPORTS Vol. 44 No. 1 2000

THE UNUSUAL PROFILE OF THE RADIO PULSAR GEMINGA
53
occur at a period close to 237 ms. The same procedure
µ
Ω
was used for double and triple periods, when two or
three pulses were visible, and, in most cases, the maxi-
mum (minimum) was at the period of Geminga.
Because of the large ratio of the pulse width to its
period, the amplitude maximum and duration minimum
are not as sharp as, for example, those of PSR 0950+08.
We should say a few words about the differences in
the mean pulse shape at 102.5 MHz obtained by the
three Pushchino teams [6–8] (the data on fluxes and
dispersions will be discussed in a subsequent paper).
From the data of 35 observational sessions considered
in [7], the duration of the main pulse was found to be
4
6 ms—i.e., a factor of 1.6 smaller than our value—and
the duration of the main pulse derived from the data for
the eight best sessions in [8] is 120 ms, which is also a
factor of 1.6 larger than our value. How can this dis-
crepancy be explained? First, if we look at the distribu-
tion of durations presented in Fig. 2a, the presence of a
significant number of cases with a duration of about
Fig. 9. Schematic representation of a coaxial rotator. The
dashed curve shows the trajectory of the observer’s line of
sight.
4
6 ms is obvious, and there are also 16 cases with dura-
tions from 100 to 140 ms; this even exceeds the number
of similar cases in [8]. Second, as indicated in [7], the
mean profile is obtained by summing the profiles for period, and the appearance of a spectral feature in the
the best cross-correlation for separate days, that is, with Fourier analysis of a group of ten pulses. For their data
a shift of the arrival phase, and this naturally results in set 3, all three criteria yielded a positive result. Never-
an artificial narrowing of the mean profile. Further- theless, they concluded that the signal had a noiselike
more, some of these data (it is difficult to tell how many, nature, only because they did not see a certain feature
but it is probable that it is rather large fraction, given the in the second pulse that is present in the first pulse when
recent situation with interference on the LPA) certainly integrated with the double period over 10 min. We
contain pulsed interference, because no information about believe that this pulse, as well as the pulse in their data
any cleaning of the data is given in [7]. The presence of set 7, are pulses from Geminga. This suggestion is
strong interference should also appreciably distort the true based on our above analysis of the emission of Gem-
pattern. Third, Shitov and Pugachev [8] gave examples of inga. In almost 60% of successful observations, the
integrated pulses with a composite profile, for example, strong variability of this object results in an absence of
for July 12, 1992, and November 13, 1996, which were features, and of the second pulse, when integrating with
obtained using a small time constant (about 2 ms) and con- the double period. If we measure the duration of the
sist, in our view, of several components with durations two profiles presented in [11], it turns out to be ~50 ms
that are considerably shorter than 120 ms. Some pro- at the half-maximum level. This is close to, but slightly
files for 1998 (for which the duration of 120 ms was smaller than the duration measured by us at the nearby
measured) were obtained with a large time constant of frequency of 40 MHz, where W = 69 and 62 ms for the
0.5
1
9.3 ms, which, naturally, smoothed all the narrow fea- main pulse and interpulse, respectively (table), though
tures and broadened the profile of Geminga. Thus, we we had a larger number (14–16) of 15-min integrations
conclude that there are no real inconsistencies between (data sets in the terminology of the Indian group).
the different results obtained, and our more varied and
The extremely unusual behavior of the radio emis-
rich data set contains all cases presented in [7, 8]. Given sion of Geminga, which can appear at different phases
the extensive set of pulse shapes and widths shown by of the period (Fig. 2c, 2d) or even occupy the entire
Geminga, we suggest that we are dealing with different period (Fig. 8), forces us to speak more cautiously
pulse shapes observed at different epochs.
about stability of the period. There is the impression
that the main pulse and interpulse are only the most
probable phases of emission, in contrast to the behavior
of the overwhelming majority of radio pulsars, in
which these phases are strictly fixed. In this sense, the
behavior of the radio and gamma-ray emission [21] is
very similar; i.e., the emission comes from almost any
phase of the period, but the most probable arrival
phases lie inside the envelope shown in Fig. 1 by the
dot-and-dash curve.
We should also add a few words about the pulse shapes
obtained by other groups at other observatories. One
group in India [9] reported only a confirmation of emis-
sion from Geminga at the nearby frequency of 103 MHz.
Another Indian group [11] concluded that they had not
detected radio emission from Geminga, but presented
two integrated profiles at 35 MHz. The three criteria
they used to test seven 10-minute data sets (their term),
in fact, were the same as for our groups: the presence of
a pulse when integrated with the Geminga period, the
One possible model for the radiating region could be
presence of two pulses when integrated with the double an almost coaxial rotator. Figure 9 shows an approximate
ASTRONOMY REPORTS Vol. 44 No. 1 2000

5
4
MALOFEEV, MALOV
model, in which the observer’s line of sight is close to
(3) The arrival phases of the main pulse and inter-
the edge of the emission cone throughout most of the pulse also vary over unusually wide limits (up to one-
period, where it can cross several regions (spots) of third of the period). At 102.5 MHz, the interpulse is
emission. In this model, one necessary condition is that separated from the main pulse by 0.51 ± 0.09 of the
the cone of emission not be circular, but instead be period.
extended along the meridian; this is consistent with, for
example, the polarization measurements described in
(
4) In the emission of Geminga, strong flares with
durations from one to several dozen periods are
observed, when the flux increases by factors of tens and
possibly hundreds. The intensities of the interpulse and
main pulse are similar; they can be present either alter-
nately or simultaneously.
[27] and the model of Malov [28], which can explain
some peculiarities of the radio emission of PSR 1822-09.
This simple scheme can account for (1) the presence and
long duration of the envelopes of both the main pulse and
interpulse, (2) the wide variation of the duration and
shapes of integrated and individual pulses, and (3) the
presence of large changes in the arrival phases of the
main pulse and interpulse. However, in this scheme, we
attribute the last two effects to selected regions of emis-
sion (spots) with varying sizes and separations between
them. This is an old idea. There have long been
attempts to explain the subpulses and individual pulses
of some pulsars using such regions (see, for example,
(
5) We have estimated the radius of frequency cor-
relation of the interstellar scintillations toward Gem-
inga to be 120 ± 60 kHz at 102.5 MHz.
(
6) The unusual behavior of the durations, shapes,
and arrival phases of the main pulse and interpulse can
be explained by a model in which Geminga is a nearly
coaxial rotator, so that the observer’s line of sight
almost never leaves the emission cone of the pulsar. In
this case, the shape of an individual pulse is determined
by the width and intensity of the emission of individual
regions inside the cone, whereas the shape of the inte-
grated profile is determined, in addition, by the number
of regions, their possible motions, and their evolution.
[29, 30]).
The major difficulty is to explain the very rare,
strong emission of Geminga over nearly the entire
period using this model. In this case, we must invoke
either precession of the spin axis or an unexpected,
transient rise of the emission region in height, with an
associated growth in the size of the hollow cone. Then,
the line of sight could for a short time completely sink
inside the hollow cone, and, in combination with high
activity of the pulsar emission, we could observe emis-
sion over the entire period. We understand that this is a
very approximate model that requires confirmation and
refinement (in particular, taking into account the fre-
quency dependences of the durations, shapes, and
arrival phases of the main pulse and interpulse).
Recently, at least two theoretical papers [31, 32] have
attempted to explain such peculiarities of the radio
emission of Geminga as its low radio luminosity and
the shape of the radio spectrum. Both papers propose
coaxial-rotator models, but, naturally, they do not
include explanations for the new peculiarities in the
behavior of the durations, shapes, and phases of the
pulses of Geminga brought to light by the present study.
We hope that such theoretical studies will soon appear.
(
7) Though the detection of pulsed radio emission
from Geminga changed this object’s classification as a
unique multiwavelength radio quiet pulsar, the charac-
ter of its radio emission gives every indication that
Geminga is, nevertheless, a unique radio pulsar.
ACKNOWLEDGMENTS
The authors express their gratitude to the staff of the
Meter-Wave Laboratory of the Pushchino Radio
Astronomy Observatory, headed by S.M. Kutuzov, in
particular, to K. Lapaev for enormous help with the
observations under difficult conditions and L. Potapova
for invaluable help with the preparation of this work for
publication. We also thank the Russian Foundation for
Basic Research (project no. 97-02-17372), INTAS Pro-
gram (grant no. 96-0154), and Russian Program in
Astronomy for partial financial support. The work was
carried out on facilities of the State Committee for Sci-
ence and Technology of the Russian Federation, radio
telescopes LPA and DKR-1000 (registration nos. 01-11
and 01-09).
5
. CONCLUSION
(
1) From data obtained at four meter-wave frequen-
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Translated by G. Rudnitskiœ
ASTRONOMY REPORTS Vol. 44 No. 1 2000