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Astron. Astrophys. 325, 57-73 (1997)

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3. The synchrotron spectra of individual sources

In this section we will discuss our new infrared data in connection with the existing multi-wavelength data, as well as with new data we have collected as part of our ongoing multi-wavelength hot spot project. The optical data in Table 3 are those not contained in Paper I and include some unpublished measurements of Cygnus A. Table 4 contains radio data for those hot spots which are not contained in Paper I. The radio flux for Cygnus A, hot spots A and D is taken directly from Table 3 in Carilli et al. (1991) and therefore not repeated in Table 4.


Table 4. Radio data for the hotspots not contained in Paper I.

In all cases where we detected an NIR counterpart of the radio hot spot (all of which also have optical detections) we fit synchrotron model spectra to the overall flux distribution. As in Paper I, the synchrotron spectra are modelled by assuming a magnetic field which is randomly distributed in a plane ("Mach disk") inclined by [FORMULA] with respect to the plane of sky (cf. Table 6). Two different models of the energy distribution of relativistic electrons are taken:

  • (i) uses the energy spectrum predicted by diffusive shock acceleration including the effect of synchrotron losses as derived by Heavens & Meisenheimer (1987).
  • (ii) refers to a broken power-law spectrum with instantaneous maximum energy cutoff. This is an idealized form of model (i) which results in the steepest possible cutoff at high frequencies.

Both models are characterized by 4 free parameters: the low frequency spectral index [FORMULA], the cutoff frequency [FORMULA], the ratio [FORMULA] between the cutoff and break energies in the electron spectrum, and a flux normalization [FORMULA] (5 GHz).

These model fits are displayed in Figs. 2. The fit parameters for each source are summarized in Table 5 and histograms in Fig. 4 show their distribution Although no infrared counterparts have been identified useful model fits could also be obtained for 3C 123 and Cygnus A where the millimetre data and K-band upper limits confine the spectra. The following notes on each individual source discuss the spectra and contains further explanatory details where appropriate.


Table 5. Parameters from the synchrotron model fits.


Table 6. Physical conditions in the hot spot emission regions.

3C 20 West.

The hot spots in the two lobes of 3C 20 are discussed in detail by Hiltner et al. (1994) and we will take much of the data directly from that work. The western is the stronger of the two hot spots associated with 3C 20. It was already discussed in Paper I. It consists of two components, a southern compact feature (B in the 15 GHz map of Paper I) which has a tail which leads northwards and ends in a secondary intensity peak (component A). Data obtained with a 0:0014 beam resolve B into an elliptical object with dimensions [FORMULA]. B has an optical counterpart (photometry is taken from Paper I) and its optical emission is highly polarized ([FORMULA] 7%, Hiltner et al. 1994). The source has also been detected at 1.3 mm with the IRAM telescope (Paper I). The source is clearly detected in our K-band image (Fig. 1a), providing an important new constraint on the overall spectrum. The new spectral fits confirm the parameter values given in Paper I (see Fig. 2a and Table 5). The optical photometry of this faint hot spot is not accurate enough to decide between the model fits (i) and (ii).

[FIGURE] Fig. 2a. Synchroton spectrum of hot spot component B 3C 20 West. The thick line shows the spectral fit assuming model (i). The thin line represents model (ii).

3C 20 East.

The hot spot complex in the eastern lobe of this radio galaxy is the weaker of the radio lobes, and also consists of two components. Component A is the more compact of the two components ([FORMULA] as measured from data obtained using a 0:0014 beam) and so is best regarded as the primary hot spot. Component B is brighter than A but is more extended, and is edge-brightened. No optical identification was found on a 1500s R -band image obtained at Calar Alto in October 1985 (Hiltner et al. 1994), and the resulting 5 [FORMULA] upper-limit is shown in Table 3. Similarly, no infrared identification has been obtained here (Fig. 1b), providing only the upper limit shown in Table 2. We have no millimetre data for this source as yet. Thus the synchrotron spectrum beyond the radio regime remains undetermined. Nevertheless it can be seen on Fig. 2b that a minor shift in the cutoff spectrum of 3C 20 west would be sufficient to account for the non-detection of 3C 20 east. An alternative possibility would be a steeper radio-to-optical spectrum with the same cutoff frequency as found in 3C 20 W.

[FIGURE] Fig. 2b. Possible spectra of 3C 20 East. The thick line corresponds to the spectrum of 3C 20 W, which was shifted by -0.2 in [FORMULA]. The thin line shows that also a steeper radio-to-optical power-law (with an unchanged cutoff frequency: "3C 20W tilted") could explain the non-detection in the near infrared and optical bands.

3C 33 South.

The optical counterpart to this hot spot was the first example observed to be highly polarized ([FORMULA] %, Meisenheimer & Röser 1986) and was detected in the infrared with the aperture photometer at UKIRT (Paper I). Our infrared image of the hot spot (Fig. 1c) clearly shows an extension to the northeast which is also seen in the optical image. We measure a (corrected) K -band flux for the hot spot of [FORMULA] Jy. Crane & Stockton (1989) present a K -band image of 3C 33 S obtained with exactly the same instrumentation (IRCAM in the 0.62 arcsec per pixel mode) as our own data, and obtain a flux of [FORMULA] Jy which agrees with our value to within the errors. Although their image involved a total integration time of 6480s (as opposed to our integration time of only 1800s) the sky appears to be noisier than on our own data, probably due to flat-fielding difficulties.

Our earlier flux measurement based on aperture photometry (Paper I, [FORMULA] Jy) is slightly larger than these two measurements on images. Since it was necessary to subtract the contribution from the bright star which lies less than 5 arcsec away in order to derive the flux for the hot spot from that data (by image reconstruction) we consider this small difference as rather reassuring. 1 Nevertheless, having available two independent measurements based on imaging data we ignore our old value in the spectral fits (Fig. 2c). As expected this leads to a slightly higher cutoff frequency (Table 5) than given in Paper I. As discussed in Paper I the radio flux from the source might be decomposed into a "pure" hot spot and the contribution from a parabola shaped ridge of the lobe. Since the extended parabola might well radiate synchrotron light (see Meisenheimer 1989, Crane & Stiavelli 1992) we will discuss in this Paper the spectrum of the entire source. Its power-law slope [FORMULA] is much steeper than in most other hot spots (see Fig. 3a) and resembles that found in the jets of M 87 and 3C 273.

[FIGURE] Fig. 2c. Spectrum of 3C 33 South (model fits as in Fig. 2a).

3C 65.

This radio source is identified with a galaxy at [FORMULA] and is the most distant member of our sample. The source has two bright hot spots (see the 5 GHz map of Longair 1977 and Table 4) The two hot spots are separated by 17 arcsecs and so could be imaged simultaneously. The galaxy itself is easily detected in our infrared image (Fig. 1d), but there is no obvious infrared emission from either of the hot spots. The only deep optical image of this source which encompasses the hot spots is that obtained by Gunn et al. (1981) at the Palomar 5m. The hot spots were undetected in their i -band image and we have used this non-detection to derive a rough estimate for the upper limit to the optical flux quoted in Table 3.

3C 111 East.

This hot spot was detected in the infrared with the aperture photometer at UKIRT (Paper I) and is easily detected in our infrared image (Fig. 1e). A 1500s R -band image obtained at Calar Alto in October 1985 with the 3.5 m provided the optical measurement quoted in Paper I. The source has also been detected at 1.3mm by IRAM (Paper I). The reddening corrected K -band flux ([FORMULA] Jy) obtained from our earlier aperture photometry (via image reconstruction and subtraction of the bright star to the north-east) agrees well with the value that we obtain from our infrared imaging ([FORMULA] Jy). Accordingly, the spectral fits presented in Paper I are completely unchanged - albeit with a smaller error (Fig. 2d and Tab 5). The slightly smaller [FORMULA] value of the fit with a steep cutoff model (ii) is less significant than it appeared in paper I.

[FIGURE] Fig. 2d. Spectrum of 3C 111 East (model fits as in Fig. 2a).

3C 123 East.

The eastern hot spot of this source (component G on our 15 GHz VLA map shown in Paper I) is extremely bright in the radio and is characterised by its very high contrast with the surrounding radio emission. A deep R-band image obtained with the 3.5m at Calar Alto failed to provide an optical identification. A single scan was made with the infrared aperture photometer at UKIRT (Paper I) providing a limiting K-band flux of 39 µJy ([FORMULA]). Our new infrared imaging (Fig. 1f) does not constrain the upper limit to better than 72 µJy ([FORMULA]) due to the poor flat-field that was derived for this object since most of the field is covered by the radio galaxy. Although we have no detection in the infrared, the hot spot has been detected at 1.3mm (Paper I), and is by far the brightest that we have observed at this wavelength. A recent measurement at 3 mm (98 GHz, see Table 4) strongly favors the "minimum cutoff" spectrum already proposed in Paper I without an obvious break at radio frequencies. It is much better described by a straight power law [FORMULA] which cuts off at an unusually low frequency [FORMULA] Hz. If there is a spectral break it has to lie somewhere beyond 15 GHz. (see Fig. 2e and Table 5). This spectrum predicts a K-band flux which lies orders of magnitude below the best sensitivities we reached in this work.

[FIGURE] Fig. 2e. Spectrum of 3C 123 East (model fits as in Fig. 2a).

The large extent of the hot spot along the radio axis and a complicated field structure indicate that the simple one-dimensional model assumed in Paper I is not appropriate.

3C 303 West.

The radio source associated with the `N' galaxy 3 C303 is quite complex. The western lobe consists of two components, a high surface brightness hot spot (A in the nomenclature of Laing 1981) and a more diffuse component (B). The hot spot A is actually double (components A1 and A2 in the 408 MHz map of Lonsdale et al. 1983), A2 being the brightest in the radio. Most of the polarized flux of the lobe comes from the fainter component A2. A jet is emanating from the radio nucleus (very clearly shown in the 1.4 GHz map of Perley 1989), enters A2 and ends in a low-surface brightness feature beyond the hot spot.

Early photographic imaging of the western lobe (Lelièvre & Wlérick 1975, Kronberg 1976) revealed the presence of three objects in the region of A, all with UV-excesses (denoted G, C and H in the nomenclature of the latter author). Object G coincides with A2 to better than [FORMULA] and provided the first optical candidate for any radio hot spot. A spectrum of object G showed a faint, blue continuum and no emission or absorption features (Kronberg et al. 1977). Lonsdale et al. (1983) noted that a power-law connection between radio and optical emission of the the hot spot would have almost the same slope as the spectrum between 408 MHz and 5 GHz, thus leading to the suggestion that the optical emission is a direct extension of the synchrotron emission seen in the radio. We obtained R -band polarization observations of this hot spot (using the same instrumentation and observing procedures as for 3C 20, Hiltner et al. 1994). But the poor S/N-ratio of these data, together with the low polarization values expected for A2 prohibited definite conclusion about the synchrotron nature of the light from object G.

The candidate optical counterpart G is easily detected in our infrared image (Fig. 1g). It shows exactly the double structure of A2 orientated along PA [FORMULA] which is known from the radio maps. In addition we detected a clear signal of the radio jet which connects the core (just outside the left boundary of Fig. 1g) with the hot spot. The object just to the south-west of the hot spot is a quasar at [FORMULA] (Kronberg et al. 1977). Table 3 shows the optical flux values of G obtained by Keel (1988) and Lelièvre & Wlérick (1975). We have flux calibrated the latter authors' data using the calibration of Hayes (1985). Although the large scatter of the optical data prohibit definite conclusions about the high frequency spectrum (see Fig. 2(f)) we think that both the steep radio-to-optical spectral index [FORMULA] and the high value of the cutoff frequency [FORMULA] Hz, as well as the detection of the radio jet qualify this hot spot candidate as bright knot in the jet, rather than a genuine radio hot spot. We therefore do not consider 3C 303 west in the general discussion of hot spot spectra (Section 4).

[FIGURE] Fig. 2f. Spectrum od component A2 in 3C 303 West (model fits as in Fig. 2a).

3C 405 - Cygnus A.

The hot spots in the lobes of the classical double radio source Cygnus A are by far the brightest known, and indeed Swarup et al. (1963) first identified the hot spot phenomenon in a discussion of this source. Hargrave & Ryle (1974) were prompted in a study of this source to suggest for the first time the need for a continuing particle acceleration in the hot spots themselves, although they did not discuss any mechanisms. We will use the nomenclature of their 5 GHz map in this present discussion. Both of the hot spots are double (Miley & Wade 1971) and there is some evidence that each consists of a primary hot spot connected by a tail of flat-spectrum, highly polarized emission to a secondary hot spot (Lonsdale & Barthel 1986, Carilli et al. 1989). The hot spots in the western lobe (components A and B) are together the brightest: B is the more compact of the pair ([FORMULA] arcsec, Dreher 1981), but A is brighter in the radio. Both A and B have sharp leading edges (Linfield 1981).

Kronberg et al. (1977) obtained deep IIIa-J plates with the Palomar 5m and found that component B coincides with a stellar object ([FORMULA]) but there was no candidate for A (to [FORMULA]). Similarly no candidate for the brightest component of the eastern lobe (component D) was found. Given the low galactic latitude of Cygnus A ([FORMULA]), these authors prophetically commented on the possible chance coincidence of galactic objects with the hot spots, and furthermore, the sole optical candidate for B was offset by [FORMULA] arcsec in both RA and DEC from the radio emission. The original astrometry was subsequently improved (Kronberg et al. 1977: Erratum), leading to a good coincidence between hot spot B and its possible optical counterpart and a candidate near hot spot A. We confirmed the new astrometry on deep CCD images in three bands, B, R, I (Röser et al. 1995). However, no optical polarization could be detected for the candidate identification of hot spot B whereas the radio emission is highly polarized. The optical candidates for B and A are clearly detected on our K-band image (Fig. 1h). But the combination of our optical photometry (Table 3) with the K-band flux reveals that the spectra of both objects peak around [FORMULA] m and cannot be regarded as the high-frequency continuation of the radio to millimetre synchrotron spectrum (Fig. 2g,h). On the other hand, blackbody spectra with T = 4000 K (candidate for B) and T = 4600 K (A), respectively, describe the near-IR/optical photometry quite well. So we conclude that both are foreground K stars. This also explains the lack of detectable optical polarization.

[FIGURE] Fig. 2g. Spectra of the hot spots A and B in the western lobe of Cygnus A (3C 405). The optical counterpart of hot spot A is an K-star (flux values symbolized by stars). The millimetre spectrum together with the K-band upper limit confines the high frequency spectrum to the range between the thin lines. The best-fit spectrum is represented by a thick line. The optical counterpart of hot spot B is also an K-star. The steep power-law spectrum is not confined by the high frequency data.
[FIGURE] Fig. 2h. Spectrum of hot spot D in the eastern lobe of Cygnus A (3C 405). The millimetre spectrum together with the K-band upper limit confines the high frequency spectrum to the range between the thin lines. The best-fit spectrum is represented by a thick line.

The coincidence of both hot spots with galactic foreground stars will prohibit the detection of their near-IR emission until the resolution is improved to the 0:001 level which should allow to separate the light from the stars. Nevertheless, from the fit of the blackbody spectra we reckon that in both cases the underlying hot spot cannot contribute more than half of the measured K-band flux. It is obvious from Fig 2g that the corresponding upper limit (corrected for galactic extinction) does not constrain the high frequency tail of hot spot B's synchrotron spectrum as a straight power-law extrapolation of the radio-millimetre spectrum passes below this limit. In the case of hot spot A, however, the K-band upper limit requires that the spectrum bends down somewhere between [FORMULA] and [FORMULA] Hz (Fig. 2h). Assuming a similar high frequency cutoff as observed in other radio hot spots (model (i)) the combination of a straight radio to millimetre spectrum and the upper limit at K constrains the position of the cutoff at [FORMULA] Hz.

In the case of the dominant eastern hot spot D the situation is more clear-cut since neither our deep optical nor our K-band image show any object near the hot spot position (Fig. 1h). Again the upper limit at K provides the most stringent constraint on the high frequency spectrum (Fig. 2h). Assuming the standard cutoff spectrum (model (i)) places the cutoff at [FORMULA] Hz.

Thus, due to their very high millimetre flux, the upper limits from our K-band images are already sufficient to constrain the cutoff frequency in the spectra of the brightest hot spots A and D to better than a factor of 2. While presumably hot spot A will remain hidden behind the foreground K-star, it should be possible to detect the near-IR counterpart of hot spot D (best-fit expectation: K = 21:m3) on a very deep image with state of the art NIR arrays.

Both hot spots show spectra which are nicely fitted by a [FORMULA] break. This was already demonstrated by Carilli et al. (1991). Knowing the overall synchrotron spectrum, however, enables a more complete description of the physical parameters than was possible from the break in the radio spectrum alone (see Roland et al. 1988).

It is curious to note that both hot spots of Cygnus A, which in many respects has served as the example for radio galaxies in general, show low frequency power-law slopes [FORMULA], that is exactly the value which is predicted by first order Fermi acceleration at a strong non-relativistic shock front (Bell 1978).

Recent ROSAT observations of Cygnus A (Harris et al. 1994) detected both dominant hot spots (A,D) at frequencies beyond [FORMULA] Hz. The authors favour a synchrotron-self-Compton origin of the X-rays from which they derive hot spot magnetic field of 16 and 25 nT for hot spots A and D, respectively.

Pictor A West

Although the western hot spot of Pictor A could not be observed in the present work due to its southern declination we have to mention that recent K-band imaging has proven our original near-IR photometry to be erroneous. Thus the unexplained discrepancy between the optical and near-IR spectrum (see e.g. Fig. 6 in Paper I) has disappeared and the spectrum can be well described by a power-law spectrum with a high frequency cutoff at [FORMULA] Hz (see Fig. 2(i), more details will be given in Röser et al. 1997). Based on better radio maps of Pictor A (Perley et al. 1997) we rule out any break in the GHz regime but find that a rather steep power-law ([FORMULA]) extends from 1 GHz to the high frequency cutoff. The much improved radio-to-optical spectrum definitely rules out the speculation by Röser & Meisenheimer (1987) that the synchrotron spectrum extends straight into the X-ray regime. Thus the extraordinary bright optical hot spot in Pictor A west (the only one which has been so far detected above the limit of the POSS plates on the ESO quick blue survey) is not caused by an extraordinary spectrum but by a cutoff frequency which is slightly higher than that typical of optically detected hot spots (see Table 5 and Fig. 4b). As in Cygnus A the X-rays are presumably caused by the Synchroton-Self-Compton effect or thermal Bremsstrahlung of the hot plasma near the working surface of the jet.

[FIGURE] Fig. 2i. Spectrum of the hot spot in the western lobe of Pictor A (we thank Richard Perley for the permission to use the radio data before publication).

The best resolved radio maps of Pictor A west (Perley et al. 1997) show that the hot spot displays a sandwich structure orientated perpendicular to the jet axis. The subcomponents cannot be resolved with 0:0015 resolution. The axial width of the entire structure is 0:004, which gives a morphological orientation angle [FORMULA] which is so close to the polarimetric angle [FORMULA] that only an upper limit [FORMULA] kpc can be given for the axial extent of the brightest emission region. But it should be kept in mind that both the full radio and the optical emission region is distributed over [FORMULA] kpc along the jet axis (Perley et al. 1997, Thomson et al. 1995).

[FIGURE] Fig. 3. Distribution of fit parameters for the hot spot spectra: a Low frequency spectral index [FORMULA], b cutoff frequency [FORMULA], c break frequency [FORMULA]. The grey shading indicates low loss hot spots, the black shading high loss hot spots, the diagonal hatching the brightest knots in the jets of M 87 and 3C 273, and the open box the eastern lobe in M 87, respectively. The optical counterpart in 3C 303 west is labelled "303".
[FIGURE] Fig. 4. Distribution of derived hot spot parameters: a Best-guess magnetic field [FORMULA], b jet speed upstream of the hot spot [FORMULA], c geometric parameter [FORMULA]. Shading as in Fig. 3.
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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998