Please Note: the e-mail address(es) and any external links in this paper were correct when it was written in 1995, but may no longer be valid.
Radioastronomie, Auf dem Hügel 69,D-53121
University of Crete, Physics Department, Heraklion, 714 09 Crete, GREECE
Foundation for Research and Technology HELLAS, Heraklion 711 09 Crete, GREECE
Astro Space Center, Physical Lebedev Institute, Moscow 117810, RUSSIA
Pulsars are in general weak radio sources, in particular at high frequencies. Their spectrum is typically quite steep (mean spectral index , 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.
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)).
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 ( 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 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 radius-to-frequency mapping based on observational 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 questions 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.
All observations presented here were performed with the Effelsberg 100m-radiotelescope 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) 9-horn 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 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.
Table 1: List of performed observation giving the epoch, the centre frequency, the corresponding wavelength and the used bandwidth.
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 Figure 2b.
Figure 2: a) time aligned profiles of PSR B0329+54 and b) resulting spectrum for this pulsar.
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 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 measurements of Lorimer et al. (1994). PSR B2020+28 exhibits a continuation of the known spectrum down to 32 GHz indicated by the dotted line.
Figure 3: Derived spectra of B2020+28. The new data (diamond) are consistent with lower frequency data (circles).
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.
Figure 4: Derived spectra of the second strongest pulsar observed at mm-wavelengths.
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 scintillation. Inhomogeneities in the interstellar medium and resulting interferences between the 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.
A straightforward calculation of the involved brightness temperatures is given by
whereas is the observed flux density, the distance to pulsar and the size of the emitting region. We assume that the emitting region is given by while corresponds to the observed pulse width.
Table 2: Brightness temperatures determined for the flux densities observed at 32 GHz.
Table 2 gives the list of derived brightness temperatures for the detected sources. Surprisingly, all our values fall in a range between and . 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 thermodynamical limit of an incoherent emitting source is given by (Lesch et al. (1994))
whereas means the Lorentz factor of the source and 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)).