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A possible turn­over in pulsar spectra at
mm­wavelengths?
By M i c h a e l K r a me ry, R i c h a r d W i e l e b i n s k iy,
Axe l J e s s ne ry, K i r i a k i M. X i l o u r i sz--y
AND M i c h a i l T i mo f eevxy
e­mail: p671mik@mpifr­bonn.mpg.de
y Max­Planck­Institut f¨ur Radioastronomie, Auf dem H¨ugel 69,D­53121 Bonn, GERMANY
z University of Crete, Physics Department, Heraklion, 714 09 Crete, GREECE
-- Foundation for Research and Technology HELLAS, Heraklion 711 09 Crete, GREECE
x Astro Space Center, Physical Lebedev Institute, Moscow 117810, RUSSIA
We present the results of recent pulsar observations at frequencies between 27.9 GHz and 34.8
GHz, i.e. in a wavelength range of 10.75 mm to 8.61 mm, made with the Effelsberg radiotele­
scope. The measured flux densities of two out of nine detected pulsars suggest that the spectrum
flattens at high frequencies or even shows a turn­over.
1. Introduction
Pulsars are in general weak radio sources, in particular at high frequencies. Their
spectrum is typically quite steep (mean spectral index ú \Gamma1:66, Taylor et al. (1993))
and shows a maximum intensity around a few hundred MHz below which a low frequency
cut off is often observed (Figure 1). Above this cut off frequency either a single or
broken power law is fitted to the data. A break occurring sometimes at about a few
GHz introduces a further steepening (Malofeev et al. (1994)). Observations by Sieber &
Wielebinski (1987) show a continuation of the steep radio spectrum even at 24 GHz.
A few pulsars are also visible outside the radio regime, i.e. at infrared, optical or even
shorter wavelengths. Observations of the Crab pulsar at infrared wavelengths yield a
remarkable high flux density, which is much larger than the flux density at high radio
frequencies (e.g. Smith (1977)). A simple extrapolation between the radio and infrared
wavelengths thus suggests the existence of a turnover frequency marking the beginning
of new increasing part of the spectrum between the radio and infrared.
However, the question of the exact pulsar emission mechanism remains still to be
answered. Numerous radiation processes proposed for the observed radio emission can
explain the form of the spectra fairly well. Nevertheless, they fail to explain for the
various other known phenomena in radio pulsar emission.
The tremendous brightness temperatures inferred from low frequency measurements
(¸ 10 29 K) constrain the radio emission to be coherent -- a requirement which cannot
be easily fulfilled per se. A widely discussed emission process is the radiation emitted
by bunched particles moving along the curved magnetic field lines (e.g. Komesaroff
(1970)). In this model the radiation results by the acceleration of the particles due to
the curvature of the field lines. As long as the bunch size is small compared to the
emitted wavelengths, coherent emission is possible. At higher frequencies where the
bunch size becomes comparable to the wavelength, the coherence condition would break
down and the incoherent part of the spectrum would be revealed (Figure 1). This break
frequency should not be expected in the radio regime but at infrared wavelengths (cf.
Michel (1982)), i.e. the emission is expected to be coherent throughout the whole radio
1

2 M. Kramer et al.: A possible turn­over in pulsar spectra at mm­wavelengths?
10 2
10 3
10 4
[MHz]
n
I n
10 10 2
10 3
10 4
[MHz]
n
I n
10
a 1
a 2
a
low frequency
turn over
high frequency
break
a)
10 0
10 5
10 10
10 15
10 20
log frequency [Hz]
10
10
10 10
10 15
10 20
10 25
log
flux
density
[arbit.
units]
+1/3
coherent
incoherent
+1/3
b)
Figure 1. a) schematic pulsar spectra typically observed and b) spectrum as it would be
expected for bunched particles emitting curvature radiation (adapted from Michel (1982)).
window. However, our observations presented in the following, point towards another
surprising conclusion.
The characteristics of pulsar emission observed at very high radio frequencies is also
of particular interest, since the model of a radius­to­frequency mapping based on obser­
vational results suggests that emission detected at higher frequencies is emitted closer to
the neutron star's surface than that seen at lower frequencies (Cordes (1978)). Observing
the polarization properties could thus provide a tool to investigate such detailed ques­
tions as if the dipole approximation of the magnetic field holds also close to the pulsar
surface. In this work we will only focus on pulsar spectra.
2. Observations
All observations presented here were performed with the Effelsberg 100m­radiotelescope
of the MPIfR. We obtained our measurements by using two different receivers. One was
installed in the primary focus and could be tuned between 26 and 36 GHz. It contained a
HEMT amplifier which yielded a system temperature of about 80 to 100 K, depending on
bandwidth and selected centre frequency. We used a bandwidth of 2 GHz and received
one linear polarization.
The second receiver was in the secondary focus, equipped with two HEMT amplifier
channels. The system temperature of 120 K was higher than in the first case, mainly due
to the fact that this was the prototype of a future (better) 9­horn system. We received
two left and right circular polarizations while this time the centre frequency was fixed at
32 GHz. The bandwidth was again 2 GHz.
At 32 GHz the gain of the telescope is 0:37 K Jy \Gamma1 and the half power beam width
25 arcsec. The observations took place between 1992 October and 1994 July, covering a
frequency range between 27.9 and 34.8 GHz (Table 1). In total we tried to observe 13
sources and finally detected 9 of them.
3. Results
One of the most interesting sources observed is PSR B0329+54, which is known to
exhibit a variation in the pulse shape. Figure 2a shows time aligned profiles of this pulsar
between 10.6 GHz and 33.9 GHz. The mode change becomes visible by the occurrence
of two distinct average pulse profiles easily perceptible by the profiles presented for the
normal and abnormal mode at 10.6 GHz. In the abnormal mode the trailing component
gets stronger than the central one, which is also observed at 27.9 GHz. At the very high
frequencies the leading component vanishes completely, and in the normal mode also the
trailing component is hardly or even not detectable. The resulting spectrum is shown in

M. Kramer et al.: A possible turn­over in pulsar spectra at mm­wavelengths? 3
Date š=GHz –=mm B=MHz
October 1992 33.9 8.8 2000
34.8 8.6 500
December 1993 29.3 10.2 2000
February 1994 27.9 10.8 2000
32.1 9.3 2000
July 1994 32.0 9.4 2000
Table 1. List of performed observation giving the epoch, the centre frequency, the
corresponding wavelength and the used bandwidth.
1000 10000
Frequency [MHz]
0.1
1.0
10.0
100.0
1000.0
Energy
[mJy
sec]
Figure 2. a) time aligned profiles of PSR B0329+54 and b) resulting spectrum for this pulsar.
Figure 2b. The low frequency points (open circles) are mainly taken from Malofeev et al.
(1994) and Lorimer et al. (1994) while the dashed line corresponds to the broken power
law fitted by Malofeev et al. (1994). Apparently, all the new measurements (represented
by diamonds) are well above the extrapolation of the fitted spectrum. However, if we
compare the new values with the corresponding profiles, we note that the 27.9 GHz point
belongs to a profile in the abnormal mode. During this measurement we clearly detected
two distinct components, resulting in the largest value among our new flux densities. At
29.3 GHz we observed only one component and thus the point is much lower. On the other
hand, the 32 GHz flux measurement represents an average value of many independent
observations detecting the pulsar during different modes. As a result, in the spectrum
the corresponding data point falls just in between the high 27.9 GHz and the low 29.3
GHz point. We note that Sieber & Wielebinski (1987) also detected only one component
at 24.6 GHz. If we try to estimate the flux density which they would have measured

4 M. Kramer et al.: A possible turn­over in pulsar spectra at mm­wavelengths?
1000 10000
Frequency [MHz]
0.1
1.0
10.0
100.0
Energy
[mJy
sec]
PSR B2020+28
Figure 3. Derived spectra of B2020+28. The new data (diamond) are consistent with lower
frequency data (circles).
for two components, we get a value which is well consistent with our new results. Since
the fitted spectrum seems to depend heavily on the 24.6 GHz point, we believe that the
mode changing has biased their result. In fact, if we assume a higher flux density at 24.6
GHz, all flux measurements can be fitted by a single power law. Summarizing, besides
the fact that mode changing is still active at such high frequencies, there seems to be
nothing special about the spectrum of this pulsar.
Figure 3 shows another example for a derived spectrum including low frequency meas­
urements of Lorimer et al. (1994). PSR B2020+28 exhibits a continuation of the known
spectrum down to 32 GHz indicated by the dotted line.
While seven out of nine sources detected reveal high frequency flux densities which are
well consistent with low frequency data. Figure 4 finally presents PSR 2021+51, i.e. one
of two sources which led to the title of this work. This pulsar was already successfully
observed during the first detection of pulsars in 1992 October (Wielebinski et al. (1993))
and is the second strongest source observed. As a surprising result of our observations,
PSRs B1929+10 and B2021+51 show a turnover in their spectra.
4. Discussion
The flux densities were measured by using two different receiving systems while the
observations themselves were performed at different epochs often separated by at least
a few weeks. The calibration was done by comparing the pulse energy to the output of
an internal noise diode switched on for the first fifty phase bins of each integration. The
noise diode was itself calibrated during our regular pointing observations using known
continuum flux calibrators such as 3C286 or NGC7027, which have been well studied
even up to 43 GHz (Ott et al. (1994)). Furthermore, most of any other effects one could
think of (e.g. pointing errors), would have produced less flux rather than more.
In the example of PSR B0329+54, the broken power law fitted to lower frequency data
was biased by one single measurement. This is not the case for all other pulsars in our
sample including PSRs B1929+10 and B2021+51.
An effect which is severe for low frequency flux measurements is interstellar scintilla­
tion. Inhomogeneities in the interstellar medium and resulting interferences between the

M. Kramer et al.: A possible turn­over in pulsar spectra at mm­wavelengths? 5
1000 10000
Frequency [MHz]
0.1
1.0
10.0
100.0
Energy
[mJy
sec]
PSR B2021+51
Figure 4. Derived spectra of the second strongest pulsar observed at mm­wavelengths.
propagating electromagnetic waves cause sometimes dramatic variations in the observed
intensities. The amplitude of the intensity modulation introduced by this effect should
decrease with frequency and it is not necessarily expected at very high radio frequencies.
However, for the strong pulsars we do observe intensity variations. The time scale of
these variations which could also be caused by intrinsic reasons, seems to be of the order
of 30 min or less. Our observations of a certain source lasted often longer than one or
two hours. Given the present data, we cannot exclude the possibility of variations on
longer time scales like several hours. However, it seems to be unlikely that we should
have observed the pulsars always at a particular intensity maximum, since all mean flux
densities of independent observations agree within their uncertainties.
An explanation of an apparent turnover like in the case of PSR B0329+54 is not
possible for B1929+10 or B2021+51. These pulsars do not exhibit a mode changing and
their profiles show the same number of components already at 10.6 GHz.
In summary, a turnover in the spectrum remains as the most reasonable explanation
for the observed flux densities of PSRs B1929+10 and B2021+51.
5. Conclusions
A straightforward calculation of the involved brightness temperatures is given by
TB = c 2 S š
2úk b š 2
`
D
l
' 2
(5.1)
whereas S š is the observed flux density, D the distance to pulsar and l the size of the
emitting region. We assume that the emitting region is given by l = c \Delta \Deltat while \Deltat
corresponds to the observed pulse width.
Table 2 gives the list of derived brightness temperatures for the detected sources.
Surprisingly, all our values fall in a range between 10 12 K and 10 16 K. We note that
the temperatures presented represent lower limits, since the emitting region might be
smaller than the light traveling time used for the calculations. In fact, an emitting
region constrained in this way corresponds to a place close to the light cylinder. The

6 M. Kramer et al.: A possible turn­over in pulsar spectra at mm­wavelengths?
Period [sec] TB [K]
PSR B 0329+54 0.715 5:8 \Delta 10 14
0355+54 0.156 6:3 \Delta 10 16
0540+23 0.246 6:2 \Delta 10 15
1133+16 1.188 7:5 \Delta 10 12
1706\Gamma16 0.654 4:0 \Delta 10 14
1929+10 0.227 5:2 \Delta 10 13
2020+28 0.343 3:6 \Delta 10 14
2021+51 0.529 6:6 \Delta 10 14
Table 2. Brightness temperatures determined for the flux densities observed at 32 GHz.
thermodynamical limit of an incoherent emitting source is given by (Lesch et al. (1994))
T max
b
!
¸
flm e c 2
3kB ' 5 \Delta 10 12 K
h fl
10 3
i
(5.2)
whereas fl means the Lorentz factor of the source and m e the electron mass. Since this
upper limit is very close to our derived brightness temperatures, the values given in Table
2 can be easily obtained if we take the relativistic boosting of the emission into account.
Even if we assume an emission height very close to the neutron star, the brightness
temperatures become only a few orders of magnitude larger and can be still explained
by incoherent emission.
In Conclusion, the usual assumption of coherent emission processes for radio pulsar
emission is not necessarily valid at high frequencies (for a more detailed study see Lesch
et al. (1994)).
We thank the staff of the electronic and receiver division of the MPIfR for the great
enthusiasm in the realization of this work. We thank J. Gil, V.M. Malofeev and in partic­
ular J.H. Seiradakis for stimulating discussions leading to the first observing proposals.
REFERENCES
Cordes J.M., 1978, ApJ, 222, 1006.
Komesaroff M.M., 1970, Nature, 225, 612.
Lesch H., Jessner A., Kramer M. & Xilouris K.M., 1994, in preparation.
Lorimer D.R., Yates J.A., Lyne A.G., Gould D.M., 1994, preprint.
Malofeev V.M., Gil J.A., Graham D.A., et al., 1994, A&A, 285, 201.
Michel F.C., 1982, Rev.Mod.Phys., 54, 1.
Ott M., Witzel A., Quirrenbach A., et al., 1994, A&A, 284, 331.
Sieber W. & Wielebinski R., 1987, A&A, 177, 345.
Smith F.G., 1977, Pulsars, (Cambridge University Press).
Taylor J.H., Manchester R.N. & Lyne A.G., 1993, ApJS, 88, 88.
Wielebinski R., Jessner A., Kramer M., Gil J.A., 1993, A&A, 272, L13.