B. The Radio-to-X-Ray Spectrum of the Jet
In this section I will discuss spectra of the jet, as well as the optical and X-ray morphologies and their comparison to the radio. Figure 9 shows the spectra of the knots between various wavebands (Biretta, Stern, and Harris 1991, hereinafter BSH91). Care must be taken to use similar resolutions and integration regions at the different wavebands; here a resolution of ~ 1.2" is used and the brightness is integrated in contiguous boxes along the jet, with each box containing one knot. Unfortunately a different procedure must be used with the X-ray data, which involves PSF fitting and subtraction, but hopefully this is not a serious problem.
Figure 9. Spectral index of knots in M87 jet between various wavebands vs. distance from nucleus. Spectral index defined as S -. Approximate positions of knots are labeled near bottom of plot. From BSH91.
All of the knots are roughly consistent with a radio spectral index rr of about 0.5 measured between 1.4 and 15 GHz, where the spectral index is defined in the sense S -. Large uncertainties near the end of the jet result from increasing difficulty in separating the "jet" from the background emission of the western "lobe" where the two begin to merge. There are no published results yet at higher resolution, but some preliminary work suggests the spectral index is probably slightly steeper ( ~ 0.6) between the knots than in the knot centers. Forster (1980) finds the spectral index of the western lobe (jetted lobe) is about 0.65, while the eastern lobe is steeper at about 0.85.
The radio-to-optical spectral indices are well determined, due largely to the huge frequency baseline between the radio and optical bands. For the inner jet (knots D, E, F, and I) and A the indices are all between ro = 0.62 and 0.65. After knot A there is a systematic steepening with increasing distance from the nucleus, so that between knots B and H ro steepens from 0.65 to 0.80. It is clear that the radio-to-optical spectrum is steeper than the radio spectrum, but whether this is caused by a gradual change above 15 GHz, or a sudden break near the optical band, is not known. Comparison of radio and ground-based optical polarization images show that both the fractional polarizations, and polarization position angles, are very similar between these two bands (Schlötelburg, Meisenheimer, and Röser 1988; Fraix-Burnet, Le Borgne, and Nieto 1989). This strongly confirms that the optical emission is synchrotron emission and suggests much of it originates in the same physical volume as the radio emission.
The above indices are from ground-based optical images, and involve averaging over a large region encompassing each knot. It is possible to study the radio-to-optical spectral index, and the optical morphology, at ~ 0.1" resolution using the Hubble Space Telescope. Figure 10 compares two different deconvolutions of an HST Faint Object Camera image against a 15 GHz VLA image. This FOC image is a signal-to-noise optimized sum of 29 images made through various filters, with the overall intensity scaled to that at 372 nm wavelength. At first glance the HST and VLA images are remarkably similar (Boksenberg et al. 1992), though closer examination reveals a number of differences. The most pervasive difference is that the optical emission tends to be concentrated near the center of the jet and in the centers of the knots (Sparks, Biretta, and Macchetto 1993). This is most apparent for the inner jet (region encompassing knots D, E, F, and I). One manifestation is that the radio images show a low surface brightness component of emission which appears to fill the width of the jet, hence defining the jet edges, and also fills much of the regions between knots. This emission component appears to be very weak or absent at optical frequencies. Another manifestation is that the jet is narrower at optical frequencies than at radio frequencies. Figure 11 compares the intensity profiles across knot A and illustrates the narrower profile for the FOC data; similar differences are seen everywhere in the jet. Other differences in details of the structure are also apparent: The optical emission from knot E is mostly from a small region near the jet center, whereas the radio emission is from a more extended region. There are also striking differences in the structure between the nucleus and knot D, though this region is perhaps suspect at both wavebands due to deconvolution of the bright nucleus. Figure 12 shows the spectral index between the radio and FOC images, and illustrates many of the effects just noted. The flattest spectrum is seen in the brightest region of knot D with ro 0.5. In general the knot centers have indices ~ 0.6 and the inter-knot regions are steeper at ~ 0.7. We note that the 0.2" long jet in the nucleus (Fig. 3) has been detected in HST Planetary Camera images, and it appears to have a similar spectral index, ro ~ 0.74 (Lauer et al. 1992).
Figure 10. Comparison of optical and radio images of M87 jet at ~ 0.15" resolution. The optical images are composites of 29 HST FOC images scaled to an effective wavelength of 372 nm (806 THz). Both Fourier Quotient (top) and Lucy (middle) deconvolutions are shown. The radio image (bottom) is from 15 GHz VLA data. The images are rotated so that up is toward P.A. 21°. (a.) Low contrast image showing bright structures. Nucleus and knots are labeled along bottom of figure. (b.) High contrast image showing faint features. Original data from Sparks, Biretta, and Macchetto 1993. (Two small circular dark spots in radio image at knot F are photographic artifacts.)
Figure 11. Comparison of radio (VLA 15 GHz) and optical (HST FOC 372 nm) intensity profiles across jet at the position of knot A. The jet appears appreciably narrower in the optical band. The intensities are arbitrarily scaled to give similar profile heights; resolution is ~ 0.10". The horizontal scale is in FOC pixels, with 1 pixel = 0.022".
Spectral indices within the optical band are more difficult to determine, and there is some controversy in this area. The short frequency baseline will exacerbate any small systematic errors, and differences in seeing and integration areas may also affect the results. For example, values of the optical spectral index of knot A, the brightest knot, range from oo ~ 0.57±0.05 (Keel 1988) to 1.21±0.09 (BSH91). Recently there appears to be some consensus developing for a value roughly between 0.9 and 1.0 (Perez-Fournon et al. 1988; Meisenheimer 1991; Zeilinger, Möller, and Stiavelli 1993). In any case, it appears fairly clear that the spectrum is appreciably steeper within the optical band than between the radio and optical. There is also agreement among different authors that knots of the inner jet have similar spectra, but that there is a systematic steepening after knot A which reaches ~ 0.5 around knot G. Meisenheimer (1991) reports evidence for steeper optical spectral indices between the knots by about ~ 0.1 as compared to the knot centers. Infrared and ultraviolet data (Stocke et al. 1981; Smith et al. 1983; Killeen et al. 1984; Perola and Tarenghi 1980; Sparks, Biretta, and Macchetto 1993) seem consistent with simple power-law interpolations between the radio, optical, and X-ray bands, provided corrections are made for differing aperture sizes (BSH91).
Figure 12. Radio to optical spectral index map at ~ 0.15" resolution using data from Fig. 10. The top image uses a Lucy deconvolution of the HST data, while the bottom image uses a Fourier Quotient deconvolution Spectral index runs from = 0.75 (white) to = 0.55 (black) and is defined as S -. The inset shows knot D with a range from = 0.65 to 0.45. North is up.
Einstein X-ray images with 3" resolution show two emission components (Schreier, Gorenstein, and Fiegelson 1982), and if the eastern one is aligned with the nucleus, we find that the western component aligns precisely with knot A (Figure 13). Subtracting these two dominant components reveals fainter emission at the positions of knots D and B (BSH91). Knot D has the flattest optical-to-X-ray spectral index of 1.08 ± 0.03. Knot A is steeper at ox = 1.30 ± 0.01, and B and C are steeper yet (Figure 9). The overall radio-to-X-ray spectrum is shown by Figure 14. The emission process for the X-rays is not entirely clear. Some support for synchrotron emission is provided by the consistency between the extrapolated optical spectrum and the observed X-ray flux, and by the trend for ox to steepen systematically between knots A, B, and C as seen for ro and oo, but these are circumstantial evidences at best.
Figure 13. Comparison of radio (grey scale) and X-ray (contour plot) images of jet. The images have been aligned at the bright eastern component, which is assumed to be the nucleus in the X-ray image. (a.) X-ray image showing dominant emission components at nucleus and knot A. (b.) X-ray image with point sources subtracted at the positions of the nucleus and knot A (crosses). Weak emission is evident from knots D and B. From BSH91.
Figure 14. Radio to X-ray spectra of core and brightest knots in jet. While the spectra are generally similar, there is a trend for them to steepen with distance from the nucleus - knot D has the flattest spectrum, and knot C has the steepest. From BSH91.
We noted in Section B that there were systematic differences between the morphologies of the inner jet and the rest of the jet. Differences are also apparent in the spectra, and can be highlighted by constructing a Hertzsprung-Russell diagram for knots in the jet (Figure 15). Apparently knots of the inner jet all have similar ro and brightness, while the transition region and outer jet define a sequence of decreasing brightness and steepening spectra.
Figure 15. Hertsprung-Russell style diagram for knots in jet. The vertical axis shows radio (5 GHz) to optical (i band) spectral index, while the horizontal axis is radio peak brightness (Jy beam-1 at 5 GHz). The dashed line connects the knots in order of distance from the nucleus. Knots D, E, F, and I ("inner jet") occupy a small region, while knots A, B, C, G, and H define a sequence of steepening spectra and decreasing brightness. Knots of the inner jet (D, F, and I) have spectra similar to knot A, but are much fainter.
To summarize this section, we have seen that the optical and X-ray morphologies of the jet are remarkably similar to the radio. Throughout the jet the radio spectral index is ~ 0.5. The inner jet has ro ~ 0.65 and oo ~ 1.2, and the optical emission tends to concentrate in the knot centers. Knots A, B, and C ("transition" region) show steepening ro, oo, and ox with increasing distance from the nucleus, and edges of the jet are optically weak. Beyond knot C ("outer jet") there is very little optical or X-ray emission.