text stringlengths 128 2.05k |
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Comments are as follow: N - No optical counterpart identified above the SSS limit. V - One of the 52 sources with uncertain morphology from the 1.4 GHz FIRST contours. Contours were obtained from our VLA A [MATH] configuration observations. |
A - One of the 52 sources with uncertain morphology from the 1.4 GHz FIRST contours. Contours were obtained from NRAO archives. S - Steep-spectrum QSO, since the source has a stellar-type optical counterpart and is classified as FRII. |
Because of the very low quality of the data for this source, its morphology remains uncertain. At first, this source looked like a steep-spectrum source with an FRI morphology. However, it is actually a well known radio loud QSO used as a VLBA calibrator. |
This source’s contours probably show a QSO with a suggestion of a jet. photometric redshifts derived from the R-z relation; see § |
References: (1) Liu & Zhang ( 2002 ; (2) Cappi, Benoist & da Costa ( 2003 ; (3) Enya et al. ( 2002 ; (4) Saripalli, Gopal-Krishna & Reich ( 1986 ; (5) Marzke & Huchra ( 1996 ; (6) Strom et al. ( 1990 ; (7) |
Machalski ( 1998 ; (8) Nilsson ( 1998 ; (9) Stickel, Fried & Kuehr ( 1993 ; (10) Snellen et al. ( 2002 ; (11) Abazajian et al. ( 2004 ; (12) Falco et al. ( 1999 ; (13) |
Hewitt & Burbidge ( 1989 ; (14) Spinrad et al. ( 1985 ; (15) Barkhouse & Hall ( 2001 ; (16) Hewitt & Burbidge ( 1991 ; (17) Ellingson & Yee ( 1994 ; (18) Abazajian et al. ( 2005 ; (19) |
Daly & Djorgovski ( 2004 ; (20) Gandhi, Fabian & Crawford ( 2006 ; (21) Polatidis & Conway ( 2003 ; (22) Best, Röttgering & Lehnert ( 1999 ; (23) Croom et al. ( 2004 ; (24) Mathez ( 1969 ; (25) |
Tinti & de Zotti ( 2006 ; (26) Madore et al. ( 1992 ; (27) Wegner et al. ( 2001 ; (28) Singal ( 1993 ; (29) Roche, Eales & Hippelein ( 1998 ; (30) Maxfield et al. ( 1995 ; (31) |
Lara et al. ( 2001 ; (32) Hewett, Foltz & Chaffee ( 2001 ; (33) Stickel & Kuehr (1) ( 1994 ; (34) Ryabinkov, Kaminker & Varshalovich ( 2003 ; (35) Vermeulen & Taylor ( 1995 ; (36) Trager et al. ( 2000 ; (37) |
Adelman-McCarthy et al. ( 2006 ; (39) Beckmann et al. ( 2006 ; (40) Smith et al. ( 2000 ; (41) Owen, Ledlow & Keel ( 1995 ; (42) Rines et al. ( 2001 ; (43) Pinkney et al. ( 2000 ; (44) |
van Breugel & Dey ( 1993 ; (45) Herbig & Readhead ( 1992 ; (46) Colless et al. ( 2001 ; (47) Thompson, Djorgovski & de Carvalho ( 1990 ; (48) Holt, Tadhunter & Morganti ( 2003 ; (49) Thimm et al. ( 1994 ; (50) |
Miller, Ledlow & Owen ( 2002 ; (51) Woo et al. ( 2005 ; (52) Gregory & Burns ( 1982 ; (53) Schneider et al. ( 2001 ; (54) Willott, Rawlings & Jarvis ( 2000 ; (55) Heckman et al. ( 1994 ; (56) |
de Grijp et al. ( 1992 ; (57) Grimes, Rawlings & Willott ( 2005 ; (58) Hill, Goodrich & Depoy ( 1996 ; (59) Stickel & Kuehr (2) ( 1994 ; (60) Polatidis et al. ( 1995 ; (61) Jones & Preston ( 2001 ; (62) |
Smith, Smith & Spinrad ( 1976 ; (63) Wills & Wills ( 1976 ; (64) Abazajian et al. ( 2003 ; (65) Bon05 ( 2005 (66) Cannon et al. ( 2006 |
# Source: arxiv 0808.0637 # Title: On the origin of radio emission in radio quiet quasars # Sections: all # Downloaded: 2026-03-02T07:59:11.628640+00:00 |
On the origin of radio emission in radio quiet quasars Abstract The radio emission in radio loud quasars originates in a jet carrying relativistic electrons. In radio quiet quasars (RQQs) the relative radio emission is [MATH] times weaker, and its origin is not established yet. We show here that there is a strong corre... |
[MATH] , holds for coronally active stars. The Güdel-Benz relation, together with correlated stellar X-ray and radio variability, implies that the coronae are magnetically heated. We therefore raise the possibility that AGN coronae are also magnetically heated, and that the radio emission in RQQ also originates in coro... |
keywords: quasars: general. Introduction AGN emit continuum radiation from the radio to the hard X-rays, and in some objects beyond. The overall spectral energy distribution (SED) of AGN has a characterstic shape, with a relatively small dispersion (e.g. Sanders et al. 1989, Elvis et al. 1994), except in the radio band... |
[MATH] , from the most radio loud AGN to the most radio quiet AGN, where the radio emission is undetectable. Furthermore, there is evidence that the distributions of absolute radio power (Miller et al. 1990) and relative radio power, commonly measured using [MATH] are bimodal (Kellerman et al. 1989), with radio loud (R... |
[MATH] and radio quiet (RQ) AGN having [MATH] , though the strength of the bi-modality may be weaker than initially estimated (White et al. 2007). The radio emission of RL AGN originates in a fast jet carrying relativistic electrons, as clearly established through high resolution radio imaging (e.g. Begelman et al. 198... |
Early radio imaging of RQ AGN confined the radio emission to arcsec scale, which allowed the option of supernovae related radio emission from compact starburst activity (Wilson & Willis 1980; Ulvestad & Wilson 1984; Sopp & Alexander 1991; Condon et al. 1991; Terlevich et al. 1992). However, sub arcsecond imaging of RQ ... |
Further hints on the origin of the radio emission in RQ AGN can be provided by correlating it with other emission properties. In this paper we focus on the correlation of the radio emission with the X-ray emission (herafter the R-X relation). Earlier studies of this relation (Brinkmann et al. 2000; Salvato et al. 2004;... |
To avoid a correlation induced by selection effects, one needs a well defined and complete sample of AGN, which is selected independently of the radio and X-ray emission properties, and yet includes complete radio and X-ray detections. The best sample for this purpose is PG Bright Quasar Survey sample (Schmidt & Green ... |
The Radio - X-ray relation 2.1 The PG Quasar Sample As noted above, we study the R-X relation in AGN using the optically selected PG quasar sample. We use the Boroson & Green (1992, hereafter BG92) subsample of 87 PG quasars with [MATH] , which was studied extensively over a wide range of energies. The radio fluxes are... |
[MATH] % (78/87) of the objects in the sample. The X-ray fluxes are taken from Brandt, Laor & Wills (2000) and Laor & Brandt (2002), who provide detections for [MATH] % (84/87) of the objects based on Rosat observations. Table 1 presents all the data used for the current analysis. Specifically, column (2) lists the red... |
We integrate over 0.2-20 keV in order to get an estimate of the bolometric accretion disk coronal emission. The typical AGN emission rises steeply below 0.2 keV, most likely due to photospheric accretion disk emission, while above |
[MATH] keV the spectrum becomes steeper, as indicated by the shape of the X-ray background (e.g. Gilli et al. 2007). Thus, the 0.2-20 keV should represent the bulk of the coronal emission. However, rather than perform a direct integration for each object, we use the following surprisingly accurate approximation, [MATH]... |
[MATH] (1 keV) to L , which is negligible for our purpose here. Figure 1 presents the distribution of the 87 BG92 objects in the L vs. plane. There are 71 radio quiet and 16 radio loud AGN in this sample, where we use the Kellerman et al. (1989) definition for radio loud AGN as having observed frame [MATH] . As seen in... |
higher L compared to radio quiet AGN, at a given L (see also Terashima & Wilson 2003; Capetti & Balmaverde 2007). The origin of the radio emission in radio loud AGN is well established, and we therefore do not consider these objects further here. There is strong evidence that X-ray and UV absorption occur simultaneousl... |
Figure 2a presents L vs. L for the 59 unabsorbed RQQ together with the best fit linear correlations. Minimizing the scatter in L [MATH] being the independent variable) gives a best fit linear relation |
[EQUATION] with a dispersion of [MATH] in log [MATH] , where [MATH] erg s -1 and [MATH] erg s -1 . Minimizing the scatter in L [MATH] independent) gives |
[EQUATION] with a dispersion of [MATH] in log [MATH] . The Spearman rank order correlation coefficient is [MATH] , which has a chance probability of [MATH] . The X-ray flux is correlated with the radio flux with [MATH] and [MATH] , which indicates that the correlation of [MATH] and [MATH] is not induced by [MATH] , as ... |
The tight relation between the radio and X-ray emission, despite the disparity by a factor of [MATH] in energy, may provide a hint for the origin of the radio emission in RQQ, as further discussed below. |
2.2 The Palomar-Ho et al. sample of low-luminosity AGN How far down in luminosity does the R-X relation extend? Unfortunately, there is no comparable optically selected sample of low luminosity type 1 AGN with nearly complete X-ray, UV, and radio detections, as the PG sample used above. However, the Palomar optical spe... |
Figure 2b shows a “zoom-out” of the R-X relation to include the 12 lower luminosity PH AGN. The values of [MATH] from Ho & Ulvestad (2001) were corrected for the revised distances in Panessa et al. (2006), excluding NGC 4395, where the more recent Thim et al. (2004) value of 4.3 Mpc is used. We also corrected [MATH] in... |
[MATH] keV, and the resulting bolometric correction error is not a significant source of scatter. Since NGC 4395 shows very large and rapid X-ray variability, we have used the time-averaged absorption-corrected L [MATH] erg s -1 , measured by Moran et al. (2005, corrected for a distance of 4.3 Mpc). Clearly, it would b... |
The 12 PH AGN extend the R-X relation from the range of log L [MATH] probed by the PG sample, to the range of log L [MATH] . The solid line in Fig.2b is not a fit, but just a line marking L /L [MATH] a typical value for the PG quasars. The PH AGN sample together with the PG sample, suggest a tight linear R-X relation f... |
2.3 The Most Luminous RQ AGN There is yet no study of the X-ray and radio emission properties of a complete sample of the most luminous RQ AGN. However, some indications can be obtained by combining the results of independent studies of the X-ray emission and of the radio emission in the most luminous AGN (Steffen et a... |
[MATH] (with no error quoted for the slope) for AGN with a luminosity extending to [MATH] (2500Å)= [MATH] erg s -1 (corresponding to [MATH] ). Thus, both the radio and X-ray emissions become relatively weaker with increasing UV luminosity. Combining the two correlations above gives [MATH] i.e. marginally consistent wit... |
2.4 Ultraluminous X-ray Sources At yet lower luminosities, possible counterparts to accreting massive black holes are the Ultraluminous X-Ray Sources (ULXs). These are point like, off-nuclear sources, detected in nearby galaxies, with isotropic luminosities of up to log [MATH] The high luminosity can be interpreted eit... |
In Fig.2b we plot four ULXs that have candidate radio counterparts. Little information is available about the radio emission properties of ULXs. Following a literature search we found four objects with relatively secure radio identifications. For simplicity, in all cases we extrapolated the unabsorbed X-ray luminositie... |
For the ULX in NGC 5408 (Kaaret et al. 2003) we infer [MATH] erg s -1 and [MATH] erg s -1 For [MATH] of the ULX in Holmberg II we take the average of the low and high states to obtain [MATH] erg s -1 (Dewangan et al. 2004) and |
[MATH] erg s -1 (Miller et al. 2005). The third and most luminous ULX, X-1 in M 82 (Kaaret et al. 2006), was observed simultaneously with Chandra and the VLA. The luminosities obtained are |
[MATH] erg s -1 (extrapolated from 0.3–7.0 keV) and [MATH] erg s -1 (on 2005 Feb. 5). We note that the radio identification of this ULX was questioned by Körding et al. (2005). Another likely association was found for ULX 2 in NGC 7424 (Soria et al. 2006), where |
[MATH] erg s -1 (using the power-law model), and [MATH] erg s -1 . The radio source is offset by [MATH] arcsec, or 80 pc, from the X-ray position, but given the lack of other nearby point sources, the probability of a chance coincidence is low (Soria et al. 2006). |
Interestingly, the four ULXs are located close to the [MATH] [MATH] line (Fig.2b). Since the radio and X-ray emission of the PG and PH AGN are most likely unbeamed, this may imply that the ULX radio and X-ray emission is unbeamed as well, as indicated by various other arguments (Mushotzky 2006). Furthermore, this may i... |
2.5 Coronally Active Stars A strong correlation is known to exist between the quiescent radio and X-ray emission in coronally active cool stars (Güdel & Benz 1993), where L /L [MATH] , also known as the Güdel-Benz relation. In Figure 2c we further increase the luminosity range of the R-X plot to include coronally activ... |
[MATH] orders of magnitude in luminosity between these two types of active objects. The X-ray emission in coronally active stars is due to free-free and line emission from hot thermal plasma (T [MATH] K), while the radio is synchrotron emission from non-thermal electrons embedded in a magnetic field. The stellar R-X re... |
[EQUATION] (Güdel 2002, and references therein). Such a relation is expected when the X-ray cooling time is significantly longer than the radio cooling time, so the X-ray emitting gas serves as a bolometer for the time integrated heating, while the radio emission provides a measure for the instantenous heating rate. |
The fact that RQ AGN and coronally active stars follow a similar R-X relation may indicate similar physical processes in both objects, as further discussed in section 3. |
2.6 Galactic Black Holes The R-X relation was also extensively explored in massive Galactic X-ray binary systems (GBHs, e.g. Merloni et al. 2003; Falcke et al. 2004). Do GBHs also follow the Güdel-Benz relation? In Figure 3 we show the R-X relation for eight GBHs, in the low hard state, from the compilation of Merloni ... |
[MATH] dependence of the radio/X-ray emission ratio of jets (e.g. Merloni et al. 2003; Falcke et al. 2004). Another possible model invokes advection-dominated accretion with a truncated inner disk (recently reviewed by Narayan & McClintock 2008). Alternatively, if the X-ray and radio emission of GBHs in the low hard st... |
We note in passing, that the least luminous GBH observed, A [MATH] , detected at the quiescent state by Gallo et al. (2006), with Log L =31.31 and Log L =26.80, overlaps in Fig.3 with the coronally active stars. Gallo et al. argued that the radio and X-rays cannot be coronal emission from the companion star, based on i... |
Some Implications 3.1 The Radio Emission Isotropy The small scatter in the R-X relation for RQ AGN, described above, implies that the angular distribution of the emission in both bands is not significantly different. The strength of the X-ray emission in AGN is correlated with the broad line emission strength (e.g. Kri... |
Blundell et al. (2003) suggested a detection of superluminal motion in a RQQ based on high brightness temperature. However, extended structures in VLBA observations of other RQQs were not confirmed by Ulvestad et al. (2005), indicating that there is yet no direct evidence for superluminal motion in RQQs. |
3.2 The analogy between AGN and coronally active stars The power-law X-ray emission of AGN is distinctly non-thermal, i.e. it does not originate from free-free emission of photoionized or collisionally ionized plasma. The energetically least demanding non-thermal mechanism is Comptonization of the optical-UV disk conti... |
Observational implications of the X-ray emitting corona model have been worked out in relation to the expected X-ray continuum (e.g. Haardt & Maraschi 1993; Dove et al. 1997; Niedźwiecki 2005), X-ray spectral features (e.g. Ross & Fabian 1993; Matt et al. 1997; Nayakshin et al. 2000; Ballantyne et al. 2001) and X-ray v... |
The fact that AGN follow the Güdel-Benz relation, seen in objects where both the radio and X-ray emission are of coronal origin, together with the fact that the X-ray emission in AGN is likely of coronal origin, leads naturally to the suggestion that the radio emission in RQ AGN is also coronal in origin. |
Typical luminous AGN are approximately [MATH] orders of magnitude more luminous than stellar coronae (Fig. 2), why should similar physics apply to stellar and AGN coronae? |
Although luminous AGN are vastly more luminous than stars, their peak emission generally occurs in the near UV (e.g. Zheng et al. 1997), indicating maximal surface disk temperatures of [MATH] K, within an order of magnitude of the photospheric temperatures of coronally active stars. The dimensions of the X-ray emitting... |
[MATH] cm, corresponding to a volume of [MATH] cm Stellar coronal volumes, on the other hand, are of the order of [MATH] cm , based on loop half-length measurements [MATH] ) and cross-section radius estimates ( [MATH] ). Thus, the coronal volume in AGN is likely to be |
[MATH] orders of magnitude larger than in stars. If the coronal luminosity is proportional to the coronal volume [MATH] then the value of [MATH] may be comparable in stellar and in AGN coronae. The potential similarity of [MATH] and [MATH] in stellar and AGN coronae may then imply similar local physical processes, desp... |
3.3 Is the X-ray and radio emission of GBHs also of coronal origin? 3.3.1 The dependence of L /L on [MATH] The radio emission of GBHs lies a factor of 10-100 below the Güdel-Benz relation. |
Can the radio and X-ray emission of GBHs also be explained as coronal emission? Merloni & Fabian (2002) suggested that the level of coronal activity in GBHs is related to [MATH] , such that the coronal activity diminishes with increasing [MATH] , as indicated by the disappearance of the X-ray power law component and th... |
[MATH] in GBHs is related to their overall high accretion disk [MATH] compared to AGN. Specifically, the effective accretion disk surface temperature at a given dimensionless |
[MATH] , where [MATH] is [EQUATION] where [MATH] and [MATH] (e.g. Shakura & Sunyaev 1973). In luminous GBHs [MATH] , while in luminous AGN [MATH] , implying that [MATH] in GBHs is [MATH] times higher than in AGN (assuming [MATH] ), as indeed observed (peak emission at keV in GBHs versus tens of eV in AGN). Thus, one ma... |
[MATH] in the corona scale roughly as [MATH] leading to [MATH] times lower [MATH] in GBHs compared to AGN. A potentially key object in that respect is A [MATH] the least luminous GBH detected (section 2.6), which is [MATH] times less luminous than typical luminous GBHs. In this object [MATH] , and thus if it harbors an... |
[MATH] is set by [MATH] We note in this context that if ULXs are powered by intermediate mass BHs [MATH] ) they may also be expected to be intermediate in their |
[MATH] between luminous AGN and GBHs. The scant available data (Fig.2) indicates they may lie somewhat below the Güdel-Benz relation, but the scatter is too large to reach any solid conclusion. |
Interestingly, Merloni et al. (2003) found a ”fundamental plane” relation connecting GBHs and AGN through [MATH] (see also Falcke et al. 2004). Their sample includes 5 RL AGN, and 23 Seyfert 2 galaxies. Objects of this type are not present in our sample. When these objects are excluded one gets a slightly modified rela... |
[EQUATION] (A. Merloni, private communication). This relation can be recast in the form [EQUATION] Using the Just et al. (2007) relation [MATH] or roughly [MATH] and assuming [MATH] , which appears to apply in both high and low luminosity AGN (Maoz 2007), we get |
[EQUATION] or [EQUATION] where we use [MATH] For a Shakura & Sunyaev accretion disk, this can be recast in the form [EQUATION] i.e. consistent with the suggestion that the radio and X-ray emissions are both coronal in origin and that |
[MATH] . Thus, [MATH] may be the physical parameter which drives the ”fundamental plane” relation noted by Merloni et al. (2003) and Falcke et al. (2004). |
We do not see a significant correlation between [MATH] and [MATH] , or equivalently we do not see the Merloni et al. relation for the PG sample only. This may be due to the small range in values of [MATH] in this sample (a factor of [MATH] ) compared to the large scatter in [MATH] values (a factor of [MATH] , Fig.3), w... |
[MATH] in a given object (e.g. Corbel et al. 2000; Gallo et al. 2003, 2006), consistent with the “fundamental plane” relation at a fixed [MATH] (eq.5). It would thus be interesting to explore if this non-linear relation is seen in individual AGN as well. |
3.3.2 Correlated variability Malzac et al.(2003) found an intriguing pattern of variability in the GBH XTE J1118+480, where [EQUATION] |
The optical luminosity is interpreted as synchrotron emission from a jet, and the X-ray as coronal emission. This unusual variability pattern is reminiscent of the Neupert effect (section 2.5), seen in coronally active stars, where [MATH] is replaced by [MATH] , and the sign in eq. (3) is positive, rather than negative... |
3.4 The jet interpretation The currently favored interpretation for the R-X relation in GBHs and in AGN is that it results from a disk/jet coupling (e.g. Merloni et al. 2003; Falcke et al. 2004) or more specifically from a corona/jet coupling, as the corona feeds the base of the jet (e.g. Merloni & Fabian 2002; Markoff... |
3.5 The size of the radio emitting region 3.5.1 The synchrotron emission mechanism Below we derive a lower limit on the size of the radio emitting region in RQ AGN, based on the maximum flux per unit area emitted by a synchrotron source. The observed flux density from an isotropically emitting source is |
[EQUATION] where [MATH] is the intensity (independent of angles), and [MATH] is the angular size of the source. For a source with a projected shape of a circle with a radius [MATH] [MATH] , where [MATH] is the angular size distance. In a homogeneous source |
[EQUATION] where [MATH] is the source function, [MATH] the power emitted per unit volume per unit frequency and [MATH] is the absorption coefficient. The minimum emitting area required to produce an observed [MATH] is obtained when [MATH] is maximal, i.e. [MATH] which is obtained when the source is optically thick. Bel... |
based on the theory of synchrotron emission formulated by Ginzburg & Syrovatskii (1969) and later presented by Rybicki & Lightman (1979, hereafter RL). |
We assume a homogeneous synchrotron source, with a uniform magnetic field [MATH] and a uniform distribution of relativistic electrons, having a power-law energy distribution of the form |
[EQUATION] The electrons radiate synchrotron emission with a power per unit volume per unit frequency of (equation 6.36 in RL), [EQUATION] |
where [MATH] is the component of [MATH] perpendicular to the direction of motion of the electrons, and [EQUATION] The absorption coefficient is given by |
[EQUATION] as derived from equation 6.53 in RL, by replacing [MATH] from equation 6.20a there (G. Rybicki, private communication), with [MATH] . Here |
[EQUATION] The synchrotron source function is therefore [EQUATION] or [EQUATION] where the ratio of the [MATH] functions [MATH] , for [MATH] , and 1.197 for [MATH] . The luminosity density of the source is |
[MATH] , which together with equation 11 gives the radius of the synchrotron radio-sphere [EQUATION] where we assume that the luminosity and angular size distances, [MATH] , are the same (a good approximation for the low- [MATH] objects studied here). Thus the minimum size of the area emitting [MATH] in synchrotron emi... |
[EQUATION] where [MATH] is the radius of the radio-sphere in pc, [MATH] erg s -1 Hz -1 , and [MATH] is the observed frequency in GHz. For |
[MATH] the prefactor is 0.63, instead of 0.54. In the special case where the magnetic energy density is in equipartition with the photon energy density, |
[EQUATION] where [MATH] is the bolometric luminosity, the magnetic field can be estimated by: [EQUATION] where [MATH] . Assuming [MATH] in equation 19 then gives |
[EQUATION] Note that [MATH] as in eq.21 is also expected if there is a large scale current flow along the disk axis (the field of a wire). A steeper dependence, [MATH] is expected for flux freezing in an expanding magnetized outflow. |
3.5.2 The implied range of sizes for the emitting region Does the observed radio spectral slope indicates that the emitting source is optically thick? A homogeneous synchrotron source, with a semi-infinite slab geometry, produces in the optically thick limit a spectrum with |
[MATH] (eq.17), and in the optically thin limit [MATH] (eq.14), or [MATH] for a likely power-law slope [MATH] of the radiating electrons. The observed spectral slopes in RQQ at [MATH] GHz are in the range [MATH] (e.g. Barvainis et al. 1996, 2005; Ulvestad et al. 2005), indicating that the radio source is either optical... |
[MATH] , or about 100 light days, in luminous ( [MATH] [MATH] ) AGN, with a steep spectral slope at [MATH] (using eq.22). This radius is [MATH] times larger than the likely size of the smallest X-ray emitting region in such objects ( [MATH] light day based on variability). Similarly, in the lowest luminosity type 1 AGN... |
[MATH] , or a light crossing time of [MATH] ks, which is also [MATH] times larger than the smallest X-ray emitting region, as indicated by the most rapid variability seen in e.g. NGC 4395 (Iwasawa et al. 2000; Moran et al. 2005). The similar ratio of [MATH] for the 5 GHz to X-ray emitting sizes in high and low luminosi... |
The fact that the radio spectra never show a clear optically thick signature, i.e. a spectral slope [MATH] , despite the fact that this is a relatively robust prediction, independent of the details of the electrons energy distribution, indicates that the simple homogeneous source scenario is not valid. A plausible simp... |
[EQUATION] or for [MATH] [EQUATION] Thus we can relate each emission radius with a corresponding frequency [MATH] . Since the synchrotron self-absorption coefficient |
[MATH] , higher frequencies originate at smaller radii, and the emissivity integrated over the emitting volume can produce a flat spectrum, as invoked in RL AGN (e.g. Blandford & Konigl 1979 and citations thereafter). To probe synchrotron emission coming from the X-ray emitting volume, say from a region which is [MATH]... |
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