GA-NIFS: A massive black hole in a low-metallicity AGN at z ∼ 5.55 revealed by JWST/NIRSpec IFS

We present rest-frame optical data of the compact z = 5 . 55 galaxy GS_3073 obtained using the integral ﬁeld spectroscopy mode of the Near-InfraRed Spectrograph on board the James Webb Space Telescope. The galaxy’s prominent broad components in several hydrogen and helium lines (though absent in the forbidden lines) and v detection of a large equivalent width of He ii λ 4686, EW(He ii ) ∼ 20Å, unambiguously identify it as an active galactic nucleus (AGN). We measured a gas phase metallicity of Z gas / Z (cid:12) ∼ 0 . 21 + 0 . 08 − 0 . 04 , which is lower than what has been inferred for both more luminous AGN at a similar redshift and lower redshift AGN. We empirically show that classical emission line ratio diagnostic diagrams cannot be used to distinguish between the primary ionisation source (AGN or star formation) for systems with such low metallicity, though di ﬀ erent diagnostic diagrams involving He ii λ 4686 prove very useful, independent of metallicity. We measured the central black hole mass to be log( M BH / M (cid:12) ) ∼ 8 . 2 ± 0 . 4 based on the luminosity and width of the broad line region of the H α emission. While this places GS_3073 at the lower end of known high-redshift black hole masses, it still appears to be overly massive when compared to its host galaxy’s mass properties. We detected an outﬂow with a projected velocity (cid:38) 700kms − 1 and inferred an ionised gas mass outﬂow rate of about 100 M (cid:12) yr − 1 , suggesting that one billion years after the Big Bang, GS_3073 is able to enrich the intergalactic medium with metals.


Introduction
In the nucleated instability (also called core instability) hypothesis of giant planet formation, a critical mass for static core envelope protoplanets has been found.Mizuno (1980) determined the critical mass of the core to be about 12 M ⊕ (M ⊕ = 5.975 × 10 27 g is the Earth mass), which is independent of the outer boundary conditions and therefore independent of the location in the solar nebula.This critical value for the core mass corresponds closely to the cores of today's giant planets.
Although no hydrodynamical study has been available many workers conjectured that a collapse or rapid contraction will ensue after accumulating the critical mass.The main motivation for this article is to investigate the stability of the static envelope at the critical mass.With this aim the local, linear stability of static radiative gas spheres is investigated on the basis of Baker's (1966) standard one-zone model.
Phenomena similar to the ones described above for giant planet formation have been found in hydrodynamical models concerning star formation where protostellar cores explode (Tscharnuter 1987, Balluch 1988), whereas earlier studies found quasi-steady collapse flows.The similarities in the (micro)physics, i.e., constitutive relations of protostellar cores and protogiant planets serve as a further motivation for this study.
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Baker's standard one-zone model
In this section the one-zone model of Baker (1966), originally used to study the Cepheïd pulsation mechanism, will be briefly reviewed.The resulting stability criteria will be rewritten in terms of local state variables, local timescales and constitutive relations.Baker (1966) investigates the stability of thin layers in selfgravitating, spherical gas clouds with the following properties: hydrostatic equilibrium, -thermal equilibrium, -energy transport by grey radiation diffusion.
For the one-zone-model Baker obtains necessary conditions for dynamical, secular and vibrational (or pulsational) stability (Eqs.(34a, b, c) in Baker 1966).Using Baker's notation: M r mass internal to the radius r m mass of the zone r 0 unperturbed zone radius ρ 0 unperturbed density in the zone T 0 unperturbed temperature in the zone L r0 unperturbed luminosity E th thermal energy of the zone and with the definitions of the local cooling time (see Fig. 1) A&A proofs: manuscript no.aanda and the local free-fall time Baker's K and σ 0 have the following form: where E th ≈ m(P 0 /ρ 0 ) has been used and is a thermodynamical quantity which is of order 1 and equal to 1 for nonreacting mixtures of classical perfect gases.The physical meaning of σ 0 and K is clearly visible in the equations above.σ 0 represents a frequency of the order one per free-fall time.
K is proportional to the ratio of the free-fall time and the cooling time.Substituting into Baker's criteria, using thermodynamic identities and definitions of thermodynamic quantities, one obtains, after some pages of algebra, the conditions for stability given below: For a physical discussion of the stability criteria see Baker (1966) or Cox (1980).We observe that these criteria for dynamical, secular and vibrational stability, respectively, can be factorized into 1. a factor containing local timescales only, 2. a factor containing only constitutive relations and their derivatives.
The first factors, depending on only timescales, are positive by definition.The signs of the left hand sides of the inequalities (6), ( 7) and ( 8) therefore depend exclusively on the second factors containing the constitutive relations.Since they depend only on state variables, the stability criteria themselves are functions of the thermodynamic state in the local zone.The one-zone stability can therefore be determined from a simple equation of state, given for example, as a function of density and temperature.
Once the microphysics, i.e. the thermodynamics and opacities (see Table 1), are specified (in practice by specifying a chemical composition) the one-zone stability can be inferred if the thermodynamic state is specified.The zone -or in other words the layer -will be stable or unstable in whatever object it is imbedded as long as it satisfies the one-zone-model assumptions.Only the specific growth rates (depending upon the time scales) will be different for layers in different objects.
We will now write down the sign (and therefore stability) determining parts of the left-hand sides of the inequalities ( 6), ( 7) and ( 8) and thereby obtain stability equations of state.
The sign determining part of inequality ( 6) is 3Γ 1 − 4 and it reduces to the criterion for dynamical stability Stability of the thermodynamical equilibrium demands and holds for a wide range of physical situations.With we find the sign determining terms in inequalities ( 7) and ( 8) respectively and obtain the following form of the criteria for dynamical, secular and vibrational stability, respectively: The constitutive relations are to be evaluated for the unperturbed thermodynamic state (say (ρ 0 , T 0 )) of the zone.We see that the one-zone stability of the layer depends only on the constitutive relations Γ 1 , ∇ ad , χ T , χ ρ , κ P , κ T .These depend only on the unperturbed thermodynamical state of the layer.Therefore the above relations define the one-zone-stability equations of state S dyn , S sec and S vib .See Fig. 2

Conclusions
1.The conditions for the stability of static, radiative layers in gas spheres, as described by Baker's (1966) standard onezone model, can be expressed as stability equations of state.These stability equations of state depend only on the local thermodynamic state of the layer.2. If the constitutive relations -equations of state and Rosseland mean opacities -are specified, the stability equations of state can be evaluated without specifying properties of the layer.3.For solar composition gas the κ-mechanism is working in the regions of the ice and dust features in the opacities, the H 2 dissociation and the combined H, first He ionization zone, as indicated by vibrational instability.These regions of instability are much larger in extent and degree of instability than the second He ionization zone that drives the Cepheïd pulsations.
for a picture of S vib .Regions of secular instability are listed in Table1.G