2.3. What Causes the Turnover in GPS Sources?

The interpretation of the turnover and its possible evolution depends on the assumed mechanism for the turnover. In the GPS sources, the two major possibilities that have been discussed so far in the literature are synchrotron self-absorption (Kellermann 1966a; Hodges, Mutel, & Phillips 1984; Mutel, Hodges, & Phillips 1985; O'Dea et al. 1991; Readhead et al. 1996b) and free-free absorption (Kellermann 1966a; O'Dea et al. 1991; Bicknell, Dopita, & O'Dea 1996). Absorption by induced Compton scattering has also been suggested as a possibility by Kuncic, Bicknell, & Dopita (1998). Table 3 gives some parameters of GPS radio sources. If we assume that the sources are near minimum pressure (which is close to equipartition; see, e.g., Burns, Owen, & Rudnick 1979), then we can compare the values of the magnetic field estimated via minimum pressure and synchrotron self-absorption. This is subject to several caveats, since (1) we do not know whether the sources are in minimum pressure, ⁽⁶⁾ (2) the parameters derived from synchrotron self-absorption are dependent on high powers of the input parameters, thus magnifying the effect of any errors in the source observables, and (3) there are no other independent measures of the magnetic field strength. Given these uncertainties, we note that the estimates of the magnetic field are in rough agreement. Thus, the data are consistent with the hypothesis that the turnover is due to synchrotron self-absorption.

Table 3. Derived GPS Source Parameters

			Pmin	BminP	BSSA
Source	Component	B	(dyn cm-2)	(G)	(G)	References
1518+047	N1	7.7×1011	1.3×10-5	1.2×10-2	8.1×10-5	2
	N2	3.2×1011	8.7×10-6	9.7×10-3	4.7×10-4	2
	S1	2.6×1011	4.7×10-5	2.2×10-2	1.4×10-3	2
	S2	3.1×1011	6.8×10-5	2.7×10-2	9.6×10-4	2
1607+268	N1	1.0×1012	2.2×10-5	1.5×10-2	8.0×10-5	2
	N2	1.2×1011	4.8×10-5	7.2×10-3	6.0×10-3	2
	S1	2.2×1011	7.7×10-6	9.1×10-3	1.7×10-3	2
	S2	2.6×1010	2.5×10-6	5.1×10-3	1.2×10-1	2
	S3	7.2×1011	2.9×10-5	1.8×10-2	1.6×10-4	2
2050+364	W1	4.2×1011	5.6×10-5	2.4×10-2	9.2×10-4	2
	E1	3.7×1011	1.4×10-5	1.2×10-2	5.4×10-4	2
	E2	8.4×1011	2.9×10-5	1.8×10-2	1.0×10-4	2
	E3	4.0×1011	1.7×10-5	1.3×10-2	4.4×10-4	2
2352+495	N HS	9.3×1010	2.7×10-5	1.7×10-2	3.7×10-2	1
	S HS	4.0×1010	5.7×10-6	7.8×10-3	5.3×10-2	1
	N Lobe	3.5×1010	1.2×10-6	3.7×10-3	3.7×10-2	1
	S Lobe	8.3×1010	8.0×10-7	2.9×10-3	3.7×10-3	1
	Cocoon	1.3×1010	7.8×10-8	9.2×10-4	9.0×10-2	1
NOTES. The BSSA in the 2352+495 cocoon is an upper limit since the turnover frequency is also an upper limit. REFERENCES 1. Readhead et al. 1996. 2. Mutel et al. 1985.

If the turnover in the spectrum is due to synchrotron self-absorption, then the turnover frequency in a homogeneous, self-absorbed, incoherent synchrotron radio source with a power-law electron energy distribution is given by

(2)

where the magnetic field B is in G, the flux density at the peak S_m is in Jy, z is the redshift, and the angular size is in milliarcseconds (see, e.g., Kellermann & Pauliny-Toth 1981).

Given the evidence for (1) high densities in the optical emission-line clouds (section 8), (2) strong depolarization of the radio source (section 4), and (3) strong confinement of the radio sources, it seems plausible that the densities may be high enough that free-free absorption may play a role in these sources (van Breugel, Heckman, & Miley 1984a; O'Dea et al. 1991). The emission measure for free-free absorption is as follows (see, e.g., Osterbrock 1977):

(3)

where is the optical depth at frequency in GHz, and T is the temperature in K. For a free-free absorption optical depth of unity at 1 GHz, the emission measure is then n_e²L 3.05 × 10⁶ cm^-6 pc, giving an electron density of n_e 2 × 10³ cm^-3 for a path length of 1 pc.

Readhead et al. (1996b) argue against free-free absorption by a simple uniform screen causing the turnover in 2352+495. However, as discussed by Bicknell et al. (1997), the optical depth in a free-free absorption screen will vary with radius if produced in a shock around the radio source in a medium whose density declines with radius. If free-free absorption is important in determining the spectral turnovers in GPS sources, then the turnovers due to synchrotron self-absorption must occur at lower frequencies _m and with higher flux density at the turnover S_m than observed. Since the magnetic field depends on these observables as B _m⁵ S_m^-2, the true magnetic field would be less than estimated using the observed turnover and attributing it to synchrotron self-absorption.

At this point both synchrotron self-absorption and free-free absorption are consistent with the observations. I believe that Occam's razor currently favors synchrotron self-absorption; however, additional observations are needed to establish which is the dominant effect.

⁶ Güijosa & Daly (1996) suggest that the agreement between the Doppler factors estimated assuming an inverse Compton origin for the X-rays and that obtained by assuming that the sources are in equipartition (i.e., the "equipartition Doppler factor"; Readhead 1994, Singal & Gopal-Krishna 1985) indicates that the sources are close to equipartition. Back.