The non-linear dependence of flux on black hole mass and accretion rate in core-dominated jets

By S. Heinz, R. Sunyaev. 2003

314 citations recorded by the source corpus.

We derive the non-linear relation between the core flux F v of accretion-powered jets at a given frequency and the mass M of the central compact object. For scale-invariant jet models, the mathematical structure of the equations describing the synchrotron emission from jets enables us to cancel out the model-dependent complications of jet dynamics, retaining only a simple, model-independent algebraic relation between F v and M. This approach allows us to derive the F v -M relation for any accretion disc scenario that provides a set of input boundary conditions for the magnetic field and the relativistic particle pressure in the jet, such as standard and advection-dominated accretion flow (ADAF) disc solutions. Surprisingly, the mass dependence of F v is very similar in different accretion scenarios For typical flat-spectrum core-dominated radio jets and standard accretion scenarios, we find F v ∼ M 1 7 / 1 2 . The 7-9 orders of magnitude difference in black hole mass between microquasars and active galactic nuclei (AGN) jets imply that AGN jets must be about 3-4 orders of magnitude more radio-loud than microquasars, i.e. the ratio of radio to bolometric luminosity is much smaller in microquasars than in AGN jets. Because of the generality of these results, measurements of this F v -M dependence are a powerful probe of jet and accretion physics. We show how sour analysis can be extended to derive a similar scaling relation between the accretion rate m and F v for different accretion disc models. For radiatively inefficient accretion modes, we find that the flat-spectrum emission follows F v α (Mm) 1 7 / 1 2 .

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4440af1393904d79656bc6990240d00c0ba7e243

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Citations in the corpus

Radiative efficiency, variability and Bondi accretion on to massive black holes: the transition from radio AGN to quasars in brightest cluster galaxies (2012, background): “Falcke & Biermann 1995; Heinz & Sunyaev 2003).”
The anti‐hierarchical growth of supermassive black holes (2004, background): “Thus, we obtain the expected result that for RIAF flows (q 2.3) the total jet kinetic power is proportional to only the physical accretion rate Wjet ∝ ṁM ∝ Ṁ (see Falcke & Biermann 1996; Heinz & Sunyaev 2003; Fender et al. 2003).”
Properties of flat-spectrum radio-loud Narrow-Line Seyfert 1 Galaxies (2014, methodology): “4, according to the theory developed by Heinz & Sunyaev (2003) and confirmed by Foschini (2011b, 2012b,c, 2014).”
Hot Accretion Flows Around Black Holes (2014, background): “…in which thermal gas in a hot accretion flow is responsible for the X-ray emission and relativistic electrons in a jet produce the radio emission, Heinz & Sunyaev (2003) showed that the fundamental plane can be naturally explained (see also Merloni et al. 2003, Heinz 2004, Yuan et al. 2005, Yuan…”
Modelling the behaviour of accretion flows in X-ray binaries (2007, background): “This can be quantitatively matched by an ADAF-like hot inner flow producing the X-ray emission, and acting as the base of the jet which produces the correlated radio flux (Heinz & Sunyaev 2003).”
Nuclear Activity in Nearby Galaxies (2008, methodology): “This empirical correlation agrees well with the theoretical relations between radio flux, BH mass, and accretion rate derived from the scale-invariant disk-jet model of Heinz & Sunyaev (2003).”
Going with the Flow: Can the Base of Jets Subsume the Role of Compact Accretion Disk Coronae? (2005, methodology): “…0.7 slope of the log LR–log LX correlation follows directly from analytic predictions of scaling synchrotron jet models (Falcke & Biermann 1995; Markoff et al. 2003) and can be generalized for other X-ray emission processes in terms of their dependence on the accretion rate (Heinz & Sunyaev 2003).”
GX 339—4: the distance, state transitions, hysteresis and spectral correlations (2004, background): “In particular, Heinz & Sunyaev (2003) derived power law dependences between the jet radio flux and Ṁ .”
Grand unification of AGN activity in the ΛCDM cosmology (2009, methodology): “The mechanical BZ jet luminosities presented in the previous section are converted into radio luminosities according to thet oretical calculations of Heinz & Sunyaev (2003) (see also Falcke et al. 1995).”
Jets from black hole X-ray binaries: testing, refining and extending empirical models for the coupling to X-rays (2009, background): “A +1.4 index is in fact as expected for jets from a radiatively efficient accretion flow (e.g. Heinz & Sunyaev 2003; see Migliari & Fender 2006 for the possible case of such an index for neutron stars) and so this is not quite ruled out.”
A RELATIONSHIP BETWEEN AGN JET POWER AND RADIO POWER (2010, background): “For flat-spectrum, compact radio cores (i.e. small scale jets and not radio lobes), several jet models predict Γ = 12/17 (≈ 0.71) (Blandford & Konigl 1979; Falcke & Biermann 1995; Heinz & Sunyaev 2003).”
A radio-emitting outflow in the quiescent state of A0620−00: implications for modelling low-luminosity black hole binaries (2006, background): “…by optically thin synchrotron radiation from the innermost region of the jet (cf. Falcke & Bierman 1995), MHdM03 apply the theoretical relations by Heinz & Sunyaev (2003), and conclude that the FP is inconsistent with the X-ray emission coming from a radiatively efficient inflow andis only…”
Measuring the kinetic power of active galactic nuclei in the radio mode (2007, background): “Finally, we note that the slope of the correlation between LR,FP and Lkin is consistent with the predictions of synchrotron models for the flat spectrum jet cores according to which (Heinz & Sunyaev 2003)LR ∝ L (17+8αν )/12 kin M −αν , whereαν is the radio spectral index.”
Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets (2013, methodology): “It is possible to do this, however, by using the disk X-ray luminosity as a proxy for ˙ M (e.g., Heinz & Sunyaev 2003; Merloni et al. 2003; Falcke et al. 2004; Fender et al. 2004; Fender & Belloni 2004), but one must have knowledge of the radiative eﬃciency of the disk, which is generally both low…”
A Fundamental plane of black hole activity (2003, methodology): “From general arguments, we expect any mechanically coo ed flow to obeyφ2B ∝ M −1ṁ (Heinz & Sunyaev 2003).”
A synthesis model for AGN evolution: supermassive black holes growth and feedback modes (2008, background): “…other hand, the physical model forthe radiative emission in the core of a relativistic jet is relatively well established (Blandford & Koenigl 1979; Heinz & Sunyaev 2003),as opposed to the complicated physics of radio emission and particle acceleration in the large scale lobes of a radio jet,…”
Using the Fundamental Plane of black hole activity to distinguish X-ray processes from weakly accreting black holes (2011, background): “Briefly, the amount of synchrotron radiation emitted from a scale invariant jet depends on the black hole mass and accretion rate (Falcke & Biermann 1995; Heinz & Sunyaev 2003).”
THE FUNDAMENTAL PLANE OF ACCRETION ONTO BLACK HOLES WITH DYNAMICAL MASSES (2009, background): “In the context of models that assume jet properties do scale simply with mass (e.g.,Falcke & Biermann 1995; Heinz & Sunyaev 2003), the fundamental plane can even be used to constrain the nature of the accretion inflow.”
Radiatively efficient accreting black holes in the hard state: the case study of H1743-322 (2011, background): “From the standard equations for synchrotron emission (e.g., Rybicki & Lightman 1979), one can obtain the following scaling between the jet luminosity Lν at a given frequency and the jet power (see e.g., Heinz & Sunyaev 2003): c© 2011 RAS, MNRAS 000, 1–16”